0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n175.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:59:54 CST 2018
147.10/147.32	% done 16346 iterations in 147.110s
147.10/147.32	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
147.10/147.32	% SZS output start Refutation
147.10/147.33	tff(cS_LEM2_pme, conjecture,
147.10/147.33	  (((![X:(iS > $o)]:
147.10/147.33	       (((![Xx:iS,Xy:iS]: ((X(Xy) & X(Xx)) => X(cP(Xx,Xy)))) & X(c0)) =>
147.10/147.33	        (![Xx:iS]: X(Xx)))) & 
147.10/147.33	    (![Xx:iS,Xy:iS,Xu:iS,Xv:iS]:
147.10/147.33	       ((cP(Xx,Xu) = cP(Xy,Xv)) => ((Xu = Xv) & (Xx = Xy)))) & 
147.10/147.33	    (![Xx:iS,Xy:iS]: (cP(Xx,Xy) != c0))) =>
147.10/147.33	   (![Xx:iS,Xy:iS,Xu:iS,Xv:iS]:
147.10/147.33	      (((![R:((iS * iS * iS) > $o)]:
147.10/147.33	           ((![Xa:iS,Xb:iS,Xc:iS]:
147.10/147.33	               (((?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
147.10/147.33	                    (R(Xx2,Xy2,Xz2) & R(Xx1,Xy1,Xz1) & (Xc = cP(Xz1,Xz2)) & 
147.10/147.33	                     (Xb = cP(Xy1,Xy2)) & (Xa = cP(Xx1,Xx2)))) | 
147.10/147.33	                 ((Xa = Xc) & (Xb = c0)) | ((Xb = Xc) & (Xa = c0))) =>
147.10/147.33	                R(Xa,Xb,Xc))) =>
147.10/147.33	            R(Xu,Xv,Xv))) & 
147.10/147.33	        (![R:((iS * iS * iS) > $o)]:
147.10/147.33	           ((![Xa:iS,Xb:iS,Xc:iS]:
147.10/147.33	               (((?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
147.10/147.33	                    (R(Xx2,Xy2,Xz2) & R(Xx1,Xy1,Xz1) & (Xc = cP(Xz1,Xz2)) & 
147.10/147.33	                     (Xb = cP(Xy1,Xy2)) & (Xa = cP(Xx1,Xx2)))) | 
147.10/147.33	                 ((Xa = Xc) & (Xb = c0)) | ((Xb = Xc) & (Xa = c0))) =>
147.10/147.33	                R(Xa,Xb,Xc))) =>
147.10/147.33	            R(Xx,Xy,Xy)))) =>
147.10/147.33	       (![R:((iS * iS * iS) > $o)]:
147.10/147.33	          ((![Xa:iS,Xb:iS,Xc:iS]:
147.10/147.33	              (((?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
147.10/147.33	                   (R(Xx2,Xy2,Xz2) & R(Xx1,Xy1,Xz1) & (Xc = cP(Xz1,Xz2)) & 
147.10/147.33	                    (Xb = cP(Xy1,Xy2)) & (Xa = cP(Xx1,Xx2)))) | 
147.10/147.33	                ((Xa = Xc) & (Xb = c0)) | ((Xb = Xc) & (Xa = c0))) =>
147.10/147.33	               R(Xa,Xb,Xc))) =>
147.10/147.33	           R(cP(Xx,Xu),cP(Xy,Xv),cP(Xy,Xv)))))))).
147.10/147.33	tff(zf_stmt_0, negated_conjecture,
147.10/147.33	  (~
147.10/147.33	    (((![X:(iS > $o)]:
147.10/147.33	         (((![Xx:iS,Xy:iS]: ((X(Xy) & X(Xx)) => X(cP(Xx,Xy)))) & X(c0)) =>
147.10/147.33	          (![Xx:iS]: X(Xx)))) & 
147.10/147.33	      (![Xx:iS,Xy:iS,Xu:iS,Xv:iS]:
147.10/147.33	         ((cP(Xx,Xu) = cP(Xy,Xv)) => ((Xu = Xv) & (Xx = Xy)))) & 
147.10/147.33	      (![Xx:iS,Xy:iS]: (cP(Xx,Xy) != c0))) =>
147.10/147.33	     (![Xx:iS,Xy:iS,Xu:iS,Xv:iS]:
147.10/147.33	        (((![R:((iS * iS * iS) > $o)]:
147.10/147.33	             ((![Xa:iS,Xb:iS,Xc:iS]:
147.10/147.33	                 (((?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
147.10/147.33	                      (R(Xx2,Xy2,Xz2) & R(Xx1,Xy1,Xz1) & 
147.10/147.33	                       (Xc = cP(Xz1,Xz2)) & (Xb = cP(Xy1,Xy2)) & 
147.10/147.33	                       (Xa = cP(Xx1,Xx2)))) | 
147.10/147.33	                   ((Xa = Xc) & (Xb = c0)) | ((Xb = Xc) & (Xa = c0))) =>
147.10/147.33	                  R(Xa,Xb,Xc))) =>
147.10/147.33	              R(Xu,Xv,Xv))) & 
147.10/147.33	          (![R:((iS * iS * iS) > $o)]:
147.10/147.33	             ((![Xa:iS,Xb:iS,Xc:iS]:
147.10/147.33	                 (((?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
147.10/147.33	                      (R(Xx2,Xy2,Xz2) & R(Xx1,Xy1,Xz1) & 
147.10/147.33	                       (Xc = cP(Xz1,Xz2)) & (Xb = cP(Xy1,Xy2)) & 
147.10/147.33	                       (Xa = cP(Xx1,Xx2)))) | 
147.10/147.33	                   ((Xa = Xc) & (Xb = c0)) | ((Xb = Xc) & (Xa = c0))) =>
147.10/147.33	                  R(Xa,Xb,Xc))) =>
147.10/147.33	              R(Xx,Xy,Xy)))) =>
147.10/147.33	         (![R:((iS * iS * iS) > $o)]:
147.10/147.33	            ((![Xa:iS,Xb:iS,Xc:iS]:
147.10/147.33	                (((?[Xx1:iS,Xx2:iS,Xy1:iS,Xy2:iS,Xz1:iS,Xz2:iS]:
147.10/147.33	                     (R(Xx2,Xy2,Xz2) & R(Xx1,Xy1,Xz1) & (Xc = cP(Xz1,Xz2)) & 
147.10/147.33	                      (Xb = cP(Xy1,Xy2)) & (Xa = cP(Xx1,Xx2)))) | 
147.10/147.33	                  ((Xa = Xc) & (Xb = c0)) | ((Xb = Xc) & (Xa = c0))) =>
147.10/147.33	                 R(Xa,Xb,Xc))) =>
147.10/147.33	             R(cP(Xx,Xu),cP(Xy,Xv),cP(Xy,Xv))))))))).
147.10/147.33	tff('0', plain,
147.10/147.33	    ![X9 : (iS * iS * iS) > $o]:
147.10/147.33	      (X9(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xb1(X9) = cP(sk_Xy11(X9), sk_Xy21(X9))
147.10/147.33	       | sk_Xb1(X9) = c0
147.10/147.33	       | sk_Xa1(X9) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('1', plain,
147.10/147.33	    ![X9 : (iS * iS * iS) > $o]:
147.10/147.33	      (X9(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xc1(X9) = cP(sk_Xz11(X9), sk_Xz21(X9))
147.10/147.33	       | sk_Xb1(X9) = c0
147.10/147.33	       | sk_Xa1(X9) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('2', plain,
147.10/147.33	    ![X8 : (iS * iS * iS) > $o]:
147.10/147.33	      (X8(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xc(X8) = cP(sk_Xz1(X8), sk_Xz2(X8))
147.10/147.33	       | sk_Xb(X8) = c0
147.10/147.33	       | sk_Xa(X8) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('3', plain,
147.10/147.33	    ![X10 : iS, X11 : iS, X12 : iS, X13 : iS, X14 : iS, X15 : iS, X16 : iS, 
147.10/147.33	      X17 : iS, X18 : iS]:
147.10/147.33	      (sk_R(X10, X11, X12)
147.10/147.33	       | ~ sk_R(X13, X14, X15)
147.10/147.33	       | X11 != cP(X14, X16)
147.10/147.33	       | X10 != cP(X13, X17)
147.10/147.33	       | X12 != cP(X15, X18)
147.10/147.33	       | ~ sk_R(X17, X16, X18)),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('4', plain,
147.10/147.33	    ![X13 : iS, X14 : iS, X15 : iS, X16 : iS, X17 : iS, X18 : iS]:
147.10/147.33	      (~ sk_R(X17, X16, X18)
147.10/147.33	       | ~ sk_R(X13, X14, X15)
147.10/147.33	       | sk_R(cP(X13, X17), cP(X14, X16), cP(X15, X18))),
147.10/147.33	    inference('simplify', [status(thm)], ['3'])).
147.10/147.33	tff('5', plain, ~ sk_R(cP(sk_Xx, sk_Xu), cP(sk_Xy, sk_Xv), cP(sk_Xy, sk_Xv)),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('6', plain,
147.10/147.33	    (~ $true | ~ sk_R(sk_Xx, sk_Xy, sk_Xy) | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['4', '5'])).
147.10/147.33	tff('7', plain, (~ sk_R(sk_Xu, sk_Xv, sk_Xv) | ~ sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('simplify', [status(thm)], ['6'])).
147.10/147.33	tff('8', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['2', '7'])).
147.10/147.33	tff('9', plain,
147.10/147.33	    (~ sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['8'])).
147.10/147.33	tff('10', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['1', '9'])).
147.10/147.33	tff('11', plain,
147.10/147.33	    (sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['10'])).
147.10/147.33	tff('12', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['0', '9'])).
147.10/147.33	tff('13', plain,
147.10/147.33	    (sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['12'])).
147.10/147.33	tff('14', plain,
147.10/147.33	    ![X8 : (iS * iS * iS) > $o]:
147.10/147.33	      (X8(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xb(X8) = cP(sk_Xy1(X8), sk_Xy2(X8))
147.10/147.33	       | sk_Xb(X8) = c0
147.10/147.33	       | sk_Xa(X8) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('15', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['14', '7'])).
147.10/147.33	tff('16', plain,
147.10/147.33	    (~ sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['15'])).
147.10/147.33	tff('17', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['1', '16'])).
147.10/147.33	tff('18', plain,
147.10/147.33	    (sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['17'])).
147.10/147.33	tff('19', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['0', '16'])).
147.10/147.33	tff('20', plain,
147.10/147.33	    (sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['19'])).
147.10/147.33	tff('21', plain,
147.10/147.33	    ![X9 : (iS * iS * iS) > $o]:
147.10/147.33	      (X9(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | X9(sk_Xx21(X9), sk_Xy21(X9), sk_Xz21(X9))
147.10/147.33	       | sk_Xb1(X9) = c0
147.10/147.33	       | sk_Xa1(X9) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('22', plain,
147.10/147.33	    ![X9 : (iS * iS * iS) > $o]:
147.10/147.33	      (X9(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | X9(sk_Xx11(X9), sk_Xy11(X9), sk_Xz11(X9))
147.10/147.33	       | sk_Xb1(X9) = c0
147.10/147.33	       | sk_Xa1(X9) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('23', plain,
147.10/147.33	    ![X9 : (iS * iS * iS) > $o]:
147.10/147.33	      (X9(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xa1(X9) = cP(sk_Xx11(X9), sk_Xx21(X9))
147.10/147.33	       | sk_Xb1(X9) = c0
147.10/147.33	       | sk_Xa1(X9) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('24', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o, X1 : iS, X2 : iS, X3 : iS, X4 : iS]:
147.10/147.33	      (sk_R(sk_Xa1(X0), cP(X4, X3), cP(X2, X1))
147.10/147.33	       | sk_Xa1(X0) = c0
147.10/147.33	       | sk_Xb1(X0) = c0
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | ~ sk_R(sk_Xx11(X0), X4, X2)
147.10/147.33	       | ~ sk_R(sk_Xx21(X0), X3, X1)),
147.10/147.33	    inference('sup+', [status(thm)], ['23', '4'])).
147.10/147.33	tff('25', plain,
147.10/147.33	    ![X0 : iS, X1 : iS]:
147.10/147.33	      (~ $true
147.10/147.33	       | sk_Xa1(sk_R) = c0
147.10/147.33	       | sk_Xb1(sk_R) = c0
147.10/147.33	       | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | ~ sk_R(sk_Xx21(sk_R), X1, X0)
147.10/147.33	       | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xb1(sk_R) = c0
147.10/147.33	       | sk_Xa1(sk_R) = c0
147.10/147.33	       | sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), X1), cP(sk_Xz11(sk_R), X0))),
147.10/147.33	    inference('sup-', [status(thm)], ['22', '24'])).
147.10/147.33	tff('26', plain,
147.10/147.33	    ![X0 : iS, X1 : iS]:
147.10/147.33	      (sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), X1), cP(sk_Xz11(sk_R), X0))
147.10/147.33	       | ~ sk_R(sk_Xx21(sk_R), X1, X0)
147.10/147.33	       | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xb1(sk_R) = c0
147.10/147.33	       | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['25'])).
147.10/147.33	tff('27', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), 
147.10/147.33	         cP(sk_Xz11(sk_R), sk_Xz21(sk_R)))),
147.10/147.33	    inference('sup-', [status(thm)], ['21', '26'])).
147.10/147.33	tff('28', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), 
147.10/147.33	       cP(sk_Xz11(sk_R), sk_Xz21(sk_R)))
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['27'])).
147.10/147.33	tff('29', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), cP(sk_Xz11(sk_R), sk_Xz21(sk_R)))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup+', [status(thm)], ['20', '28'])).
147.10/147.33	tff('30', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), cP(sk_Xz11(sk_R), sk_Xz21(sk_R)))),
147.10/147.33	    inference('simplify', [status(thm)], ['29'])).
147.10/147.33	tff('31', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup+', [status(thm)], ['18', '30'])).
147.10/147.33	tff('32', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['31'])).
147.10/147.33	tff('33', plain,
147.10/147.33	    ![X9 : (iS * iS * iS) > $o]:
147.10/147.33	      (X9(sk_Xu, sk_Xv, sk_Xv) | ~ X9(sk_Xa1(X9), sk_Xb1(X9), sk_Xc1(X9))),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('34', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['32', '33'])).
147.10/147.33	tff('35', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['34'])).
147.10/147.33	tff('36', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['35', '16'])).
147.10/147.33	tff('37', plain,
147.10/147.33	    (sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['36'])).
147.10/147.33	tff('38', plain,
147.10/147.33	    ![X8 : (iS * iS * iS) > $o]:
147.10/147.33	      (X8(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | X8(sk_Xx2(X8), sk_Xy2(X8), sk_Xz2(X8))
147.10/147.33	       | sk_Xb(X8) = c0
147.10/147.33	       | sk_Xa(X8) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('39', plain,
147.10/147.33	    ![X8 : (iS * iS * iS) > $o]:
147.10/147.33	      (X8(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | X8(sk_Xx1(X8), sk_Xy1(X8), sk_Xz1(X8))
147.10/147.33	       | sk_Xb(X8) = c0
147.10/147.33	       | sk_Xa(X8) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('40', plain,
147.10/147.33	    ![X8 : (iS * iS * iS) > $o]:
147.10/147.33	      (X8(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xa(X8) = cP(sk_Xx1(X8), sk_Xx2(X8))
147.10/147.33	       | sk_Xb(X8) = c0
147.10/147.33	       | sk_Xa(X8) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('41', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o, X1 : iS, X2 : iS, X3 : iS, X4 : iS]:
147.10/147.33	      (sk_R(sk_Xa(X0), cP(X4, X3), cP(X2, X1))
147.10/147.33	       | sk_Xa(X0) = c0
147.10/147.33	       | sk_Xb(X0) = c0
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | ~ sk_R(sk_Xx1(X0), X4, X2)
147.10/147.33	       | ~ sk_R(sk_Xx2(X0), X3, X1)),
147.10/147.33	    inference('sup+', [status(thm)], ['40', '4'])).
147.10/147.33	tff('42', plain,
147.10/147.33	    ![X0 : iS, X1 : iS]:
147.10/147.33	      (~ $true
147.10/147.33	       | sk_Xa(sk_R) = c0
147.10/147.33	       | sk_Xb(sk_R) = c0
147.10/147.33	       | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | ~ sk_R(sk_Xx2(sk_R), X1, X0)
147.10/147.33	       | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xb(sk_R) = c0
147.10/147.33	       | sk_Xa(sk_R) = c0
147.10/147.33	       | sk_R(sk_Xa(sk_R), cP(sk_Xy1(sk_R), X1), cP(sk_Xz1(sk_R), X0))),
147.10/147.33	    inference('sup-', [status(thm)], ['39', '41'])).
147.10/147.33	tff('43', plain,
147.10/147.33	    ![X0 : iS, X1 : iS]:
147.10/147.33	      (sk_R(sk_Xa(sk_R), cP(sk_Xy1(sk_R), X1), cP(sk_Xz1(sk_R), X0))
147.10/147.33	       | ~ sk_R(sk_Xx2(sk_R), X1, X0)
147.10/147.33	       | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xb(sk_R) = c0
147.10/147.33	       | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['42'])).
147.10/147.33	tff('44', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_R(sk_Xa(sk_R), cP(sk_Xy1(sk_R), sk_Xy2(sk_R)), 
147.10/147.33	         cP(sk_Xz1(sk_R), sk_Xz2(sk_R)))),
147.10/147.33	    inference('sup-', [status(thm)], ['38', '43'])).
147.10/147.33	tff('45', plain,
147.10/147.33	    (sk_R(sk_Xa(sk_R), cP(sk_Xy1(sk_R), sk_Xy2(sk_R)), 
147.10/147.33	       cP(sk_Xz1(sk_R), sk_Xz2(sk_R)))
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['44'])).
147.10/147.33	tff('46', plain,
147.10/147.33	    (sk_R(sk_Xa(sk_R), sk_Xb(sk_R), cP(sk_Xz1(sk_R), sk_Xz2(sk_R)))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup+', [status(thm)], ['37', '45'])).
147.10/147.33	tff('47', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa(sk_R), sk_Xb(sk_R), cP(sk_Xz1(sk_R), sk_Xz2(sk_R)))),
147.10/147.33	    inference('simplify', [status(thm)], ['46'])).
147.10/147.33	tff('48', plain,
147.10/147.33	    (sk_R(sk_Xa(sk_R), sk_Xb(sk_R), sk_Xc(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup+', [status(thm)], ['13', '47'])).
147.10/147.33	tff('49', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa(sk_R), sk_Xb(sk_R), sk_Xc(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['48'])).
147.10/147.33	tff('50', plain,
147.10/147.33	    ![X8 : (iS * iS * iS) > $o]:
147.10/147.33	      (X8(sk_Xx, sk_Xy, sk_Xy) | ~ X8(sk_Xa(X8), sk_Xb(X8), sk_Xc(X8))),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('51', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup-', [status(thm)], ['49', '50'])).
147.10/147.33	tff('52', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['51'])).
147.10/147.33	tff('53', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['52', '7'])).
147.10/147.33	tff('54', plain,
147.10/147.33	    (~ sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['53'])).
147.10/147.33	tff('55', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['0', '54'])).
147.10/147.33	tff('56', plain,
147.10/147.33	    (sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['55'])).
147.10/147.33	tff('57', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), cP(sk_Xz11(sk_R), sk_Xz21(sk_R)))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup+', [status(thm)], ['56', '28'])).
147.10/147.33	tff('58', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), cP(sk_Xz11(sk_R), sk_Xz21(sk_R)))),
147.10/147.33	    inference('simplify', [status(thm)], ['57'])).
147.10/147.33	tff('59', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup+', [status(thm)], ['11', '58'])).
147.10/147.33	tff('60', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['59'])).
147.10/147.33	tff('61', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['60', '33'])).
147.10/147.33	tff('62', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['61'])).
147.10/147.33	tff('63', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['62', '9'])).
147.10/147.33	tff('64', plain,
147.10/147.33	    (sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['63'])).
147.10/147.33	tff('65', plain,
147.10/147.33	    (sk_R(sk_Xa(sk_R), sk_Xb(sk_R), sk_Xc(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup+', [status(thm)], ['64', '47'])).
147.10/147.33	tff('66', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa(sk_R), sk_Xb(sk_R), sk_Xc(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['65'])).
147.10/147.33	tff('67', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup-', [status(thm)], ['66', '50'])).
147.10/147.33	tff('68', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['67'])).
147.10/147.33	tff('69', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['68', '7'])).
147.10/147.33	tff('70', plain,
147.10/147.33	    (~ sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['69'])).
147.10/147.33	tff('71', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['1', '70'])).
147.10/147.33	tff('72', plain,
147.10/147.33	    (sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['71'])).
147.10/147.33	tff('73', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup+', [status(thm)], ['72', '58'])).
147.10/147.33	tff('74', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['73'])).
147.10/147.33	tff('75', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['74', '33'])).
147.10/147.33	tff('76', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['75'])).
147.10/147.33	tff('77', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['76', '70'])).
147.10/147.33	tff('78', plain,
147.10/147.33	    (sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['77'])).
147.10/147.33	tff('79', plain,
147.10/147.33	    ![X9 : (iS * iS * iS) > $o]:
147.10/147.33	      (X9(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xb1(X9) = cP(sk_Xy11(X9), sk_Xy21(X9))
147.10/147.33	       | sk_Xa1(X9) = sk_Xc1(X9)
147.10/147.33	       | sk_Xa1(X9) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('80', plain, ![X6 : iS, X7 : iS]: cP(X6, X7) != c0,
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('81', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xb1(X0) != c0
147.10/147.33	       | sk_Xa1(X0) = c0
147.10/147.33	       | sk_Xa1(X0) = sk_Xc1(X0)
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['79', '80'])).
147.10/147.33	tff('82', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (~ X0(sk_Xa1(X0), sk_Xb1(X0), sk_Xa1(X0))
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xa1(X0) = c0
147.10/147.33	       | sk_Xb1(X0) != c0
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['81', '33'])).
147.10/147.33	tff('83', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xb1(X0) != c0
147.10/147.33	       | sk_Xa1(X0) = c0
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | ~ X0(sk_Xa1(X0), sk_Xb1(X0), sk_Xa1(X0))),
147.10/147.33	    inference('simplify', [status(thm)], ['82'])).
147.10/147.33	tff('84', plain,
147.10/147.33	    (~ sk_R(sk_Xa1(sk_R), c0, sk_Xa1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0),
147.10/147.33	    inference('sup-', [status(thm)], ['78', '83'])).
147.10/147.33	tff('85', plain,
147.10/147.33	    ![X10 : iS, X11 : iS, X12 : iS]:
147.10/147.33	      (sk_R(X10, X11, X12) | X10 != X12 | X11 != c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('86', plain, ![X12 : iS]: sk_R(X12, c0, X12),
147.10/147.33	    inference('simplify', [status(thm)], ['85'])).
147.10/147.33	tff('87', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0),
147.10/147.33	    inference('demod', [status(thm)], ['84', '86'])).
147.10/147.33	tff('88', plain,
147.10/147.33	    (sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['87'])).
147.10/147.33	tff('89', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['88', '16'])).
147.10/147.33	tff('90', plain,
147.10/147.33	    (sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['89'])).
147.10/147.33	tff('91', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['88', '9'])).
147.10/147.33	tff('92', plain,
147.10/147.33	    (sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['91'])).
147.10/147.33	tff('93', plain,
147.10/147.33	    (sk_R(sk_Xa(sk_R), cP(sk_Xy1(sk_R), sk_Xy2(sk_R)), sk_Xc(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup+', [status(thm)], ['92', '45'])).
147.10/147.33	tff('94', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa(sk_R), cP(sk_Xy1(sk_R), sk_Xy2(sk_R)), sk_Xc(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['93'])).
147.10/147.33	tff('95', plain,
147.10/147.33	    (sk_R(sk_Xa(sk_R), sk_Xb(sk_R), sk_Xc(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup+', [status(thm)], ['90', '94'])).
147.10/147.33	tff('96', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa(sk_R), sk_Xb(sk_R), sk_Xc(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['95'])).
147.10/147.33	tff('97', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup-', [status(thm)], ['96', '50'])).
147.10/147.33	tff('98', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['97'])).
147.10/147.33	tff('99', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['98', '7'])).
147.10/147.33	tff('100', plain,
147.10/147.33	    (~ sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['99'])).
147.10/147.33	tff('101', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0),
147.10/147.33	    inference('sup-', [status(thm)], ['88', '100'])).
147.10/147.33	tff('102', plain,
147.10/147.33	    (sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['101'])).
147.10/147.33	tff('103', plain,
147.10/147.33	    (c0 != c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['78', '102'])).
147.10/147.33	tff('104', plain, (sk_Xb(sk_R) = c0 | sk_Xa(sk_R) = c0 | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['103'])).
147.10/147.33	tff('105', plain,
147.10/147.33	    ![X8 : (iS * iS * iS) > $o]:
147.10/147.33	      (X8(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xb(X8) = cP(sk_Xy1(X8), sk_Xy2(X8))
147.10/147.33	       | sk_Xa(X8) = sk_Xc(X8)
147.10/147.33	       | sk_Xa(X8) = c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('106', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xb(X0) != c0
147.10/147.33	       | sk_Xa(X0) = c0
147.10/147.33	       | sk_Xa(X0) = sk_Xc(X0)
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup-', [status(thm)], ['105', '80'])).
147.10/147.33	tff('107', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (~ X0(sk_Xa(X0), sk_Xb(X0), sk_Xa(X0))
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xa(X0) = c0
147.10/147.33	       | sk_Xb(X0) != c0
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup-', [status(thm)], ['106', '50'])).
147.10/147.33	tff('108', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xb(X0) != c0
147.10/147.33	       | sk_Xa(X0) = c0
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | ~ X0(sk_Xa(X0), sk_Xb(X0), sk_Xa(X0))),
147.10/147.33	    inference('simplify', [status(thm)], ['107'])).
147.10/147.33	tff('109', plain,
147.10/147.33	    (~ sk_R(sk_Xa(sk_R), c0, sk_Xa(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) != c0),
147.10/147.33	    inference('sup-', [status(thm)], ['104', '108'])).
147.10/147.33	tff('110', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) != c0),
147.10/147.33	    inference('demod', [status(thm)], ['109', '86'])).
147.10/147.33	tff('111', plain,
147.10/147.33	    (sk_Xb(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['110'])).
147.10/147.33	tff('112', plain,
147.10/147.33	    (sk_Xa1(sk_R) = c0 | sk_Xa(sk_R) = c0 | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('clc', [status(thm)], ['111', '104'])).
147.10/147.33	tff('113', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['112', '7'])).
147.10/147.33	tff('114', plain,
147.10/147.33	    (~ sk_R(sk_Xu, sk_Xv, sk_Xv) | sk_Xa1(sk_R) = c0 | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['113'])).
147.10/147.33	tff('115', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['0', '114'])).
147.10/147.33	tff('116', plain,
147.10/147.33	    (sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['115'])).
147.10/147.33	tff('117', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['1', '114'])).
147.10/147.33	tff('118', plain,
147.10/147.33	    (sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['117'])).
147.10/147.33	tff('119', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup+', [status(thm)], ['118', '28'])).
147.10/147.33	tff('120', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), sk_Xc1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['119'])).
147.10/147.33	tff('121', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['120', '114'])).
147.10/147.33	tff('122', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('sup+', [status(thm)], ['116', '121'])).
147.10/147.33	tff('123', plain,
147.10/147.33	    (sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['122'])).
147.10/147.33	tff('124', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['123', '33'])).
147.10/147.33	tff('125', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['124'])).
147.10/147.33	tff('126', plain, (sk_Xa1(sk_R) = c0 | sk_Xb1(sk_R) = c0 | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['125', '114'])).
147.10/147.33	tff('127', plain,
147.10/147.33	    (~ sk_R(sk_Xa1(sk_R), c0, sk_Xa1(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0),
147.10/147.33	    inference('sup-', [status(thm)], ['126', '83'])).
147.10/147.33	tff('128', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0),
147.10/147.33	    inference('demod', [status(thm)], ['127', '86'])).
147.10/147.33	tff('129', plain,
147.10/147.33	    (sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['128'])).
147.10/147.33	tff('130', plain,
147.10/147.33	    (sk_Xa(sk_R) = c0 | sk_Xa1(sk_R) = c0 | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('clc', [status(thm)], ['129', '126'])).
147.10/147.33	tff('131', plain, (sk_Xa1(sk_R) = c0 | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['130', '114'])).
147.10/147.33	tff('132', plain,
147.10/147.33	    ![X9 : (iS * iS * iS) > $o]:
147.10/147.33	      (X9(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xa1(X9) = cP(sk_Xx11(X9), sk_Xx21(X9))
147.10/147.33	       | sk_Xa1(X9) = sk_Xc1(X9)
147.10/147.33	       | sk_Xb1(X9) = sk_Xc1(X9)),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('133', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xa1(X0) != c0
147.10/147.33	       | sk_Xb1(X0) = sk_Xc1(X0)
147.10/147.33	       | sk_Xa1(X0) = sk_Xc1(X0)
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['132', '80'])).
147.10/147.33	tff('134', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (~ X0(sk_Xa1(X0), sk_Xb1(X0), sk_Xb1(X0))
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xa1(X0) = sk_Xc1(X0)
147.10/147.33	       | sk_Xa1(X0) != c0
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['133', '33'])).
147.10/147.33	tff('135', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xa1(X0) != c0
147.10/147.33	       | sk_Xa1(X0) = sk_Xc1(X0)
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | ~ X0(sk_Xa1(X0), sk_Xb1(X0), sk_Xb1(X0))),
147.10/147.33	    inference('simplify', [status(thm)], ['134'])).
147.10/147.33	tff('136', plain,
147.10/147.33	    (~ sk_R(c0, sk_Xb1(sk_R), sk_Xb1(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
147.10/147.33	     | sk_Xa1(sk_R) != c0),
147.10/147.33	    inference('sup-', [status(thm)], ['131', '135'])).
147.10/147.33	tff('137', plain,
147.10/147.33	    ![X10 : iS, X11 : iS, X12 : iS]:
147.10/147.33	      (sk_R(X10, X11, X12) | X11 != X12 | X10 != c0),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('138', plain, ![X12 : iS]: sk_R(c0, X12, X12),
147.10/147.33	    inference('simplify', [status(thm)], ['137'])).
147.10/147.33	tff('139', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
147.10/147.33	     | sk_Xa1(sk_R) != c0),
147.10/147.33	    inference('demod', [status(thm)], ['136', '138'])).
147.10/147.33	tff('140', plain,
147.10/147.33	    (sk_Xa1(sk_R) != c0
147.10/147.33	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['139'])).
147.10/147.33	tff('141', plain,
147.10/147.33	    (sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)),
147.10/147.33	    inference('clc', [status(thm)], ['140', '131'])).
147.10/147.33	tff('142', plain,
147.10/147.33	    ![X9 : (iS * iS * iS) > $o]:
147.10/147.33	      (X9(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xa1(X9) = cP(sk_Xx11(X9), sk_Xx21(X9))
147.10/147.33	       | sk_Xb1(X9) = c0
147.10/147.33	       | sk_Xb1(X9) = sk_Xc1(X9)),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('143', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xa1(X0) != c0
147.10/147.33	       | sk_Xb1(X0) = sk_Xc1(X0)
147.10/147.33	       | sk_Xb1(X0) = c0
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['142', '80'])).
147.10/147.33	tff('144', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (~ X0(sk_Xa1(X0), sk_Xb1(X0), sk_Xb1(X0))
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xb1(X0) = c0
147.10/147.33	       | sk_Xa1(X0) != c0
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['143', '33'])).
147.10/147.33	tff('145', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xa1(X0) != c0
147.10/147.33	       | sk_Xb1(X0) = c0
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | ~ X0(sk_Xa1(X0), sk_Xb1(X0), sk_Xb1(X0))),
147.10/147.33	    inference('simplify', [status(thm)], ['144'])).
147.10/147.33	tff('146', plain,
147.10/147.33	    (~ sk_R(c0, sk_Xb1(sk_R), sk_Xb1(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) != c0),
147.10/147.33	    inference('sup-', [status(thm)], ['131', '145'])).
147.10/147.33	tff('147', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) != c0),
147.10/147.33	    inference('demod', [status(thm)], ['146', '138'])).
147.10/147.33	tff('148', plain,
147.10/147.33	    (sk_Xa1(sk_R) != c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['147'])).
147.10/147.33	tff('149', plain,
147.10/147.33	    (sk_Xa(sk_R) = c0 | sk_R(sk_Xu, sk_Xv, sk_Xv) | sk_Xb1(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['148', '131'])).
147.10/147.33	tff('150', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['149', '16'])).
147.10/147.33	tff('151', plain,
147.10/147.33	    (sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['150'])).
147.10/147.33	tff('152', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['149', '9'])).
147.10/147.33	tff('153', plain,
147.10/147.33	    (sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['152'])).
147.10/147.33	tff('154', plain,
147.10/147.33	    (sk_R(sk_Xa(sk_R), cP(sk_Xy1(sk_R), sk_Xy2(sk_R)), sk_Xc(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup+', [status(thm)], ['153', '45'])).
147.10/147.33	tff('155', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa(sk_R), cP(sk_Xy1(sk_R), sk_Xy2(sk_R)), sk_Xc(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['154'])).
147.10/147.33	tff('156', plain,
147.10/147.33	    (sk_R(sk_Xa(sk_R), sk_Xb(sk_R), sk_Xc(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup+', [status(thm)], ['151', '155'])).
147.10/147.33	tff('157', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa(sk_R), sk_Xb(sk_R), sk_Xc(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['156'])).
147.10/147.33	tff('158', plain,
147.10/147.33	    (sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('clc', [status(thm)], ['157', '50'])).
147.10/147.33	tff('159', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['158', '7'])).
147.10/147.33	tff('160', plain,
147.10/147.33	    (~ sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['159'])).
147.10/147.33	tff('161', plain, (sk_Xb(sk_R) = c0 | sk_Xa(sk_R) = c0 | sk_Xb1(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['160', '149'])).
147.10/147.33	tff('162', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xb1(X0) != sk_Xa1(X0)
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xa1(X0) = sk_Xc1(X0)
147.10/147.33	       | sk_Xa1(X0) != c0),
147.10/147.33	    inference('eq_fact', [status(thm)], ['133'])).
147.10/147.33	tff('163', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (~ X0(sk_Xa1(X0), sk_Xb1(X0), sk_Xa1(X0))
147.10/147.33	       | sk_Xa1(X0) != c0
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xb1(X0) != sk_Xa1(X0)
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['162', '33'])).
147.10/147.33	tff('164', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xb1(X0) != sk_Xa1(X0)
147.10/147.33	       | X0(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	       | sk_Xa1(X0) != c0
147.10/147.33	       | ~ X0(sk_Xa1(X0), sk_Xb1(X0), sk_Xa1(X0))),
147.10/147.33	    inference('simplify', [status(thm)], ['163'])).
147.10/147.33	tff('165', plain,
147.10/147.33	    (~ sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), c0)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
147.10/147.33	    inference('sup-', [status(thm)], ['131', '164'])).
147.10/147.33	tff('166', plain,
147.10/147.33	    (sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | ~ sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), c0)),
147.10/147.33	    inference('clc', [status(thm)], ['165', '131'])).
147.10/147.33	tff('167', plain,
147.10/147.33	    (~ sk_R(c0, sk_Xb1(sk_R), c0)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
147.10/147.33	    inference('sup-', [status(thm)], ['131', '166'])).
147.10/147.33	tff('168', plain,
147.10/147.33	    (sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | ~ sk_R(c0, sk_Xb1(sk_R), c0)),
147.10/147.33	    inference('simplify', [status(thm)], ['167'])).
147.10/147.33	tff('169', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | ~ sk_R(c0, sk_Xb1(sk_R), c0)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['168', '16'])).
147.10/147.33	tff('170', plain,
147.10/147.33	    (sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | ~ sk_R(c0, sk_Xb1(sk_R), c0)),
147.10/147.33	    inference('simplify', [status(thm)], ['169'])).
147.10/147.33	tff('171', plain,
147.10/147.33	    (~ sk_R(c0, c0, c0)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['161', '170'])).
147.10/147.33	tff('172', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))),
147.10/147.33	    inference('demod', [status(thm)], ['171', '138'])).
147.10/147.33	tff('173', plain,
147.10/147.33	    (sk_Xb(sk_R) = cP(sk_Xy1(sk_R), sk_Xy2(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['172'])).
147.10/147.33	tff('174', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | ~ sk_R(c0, sk_Xb1(sk_R), c0)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['168', '9'])).
147.10/147.33	tff('175', plain,
147.10/147.33	    (sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | ~ sk_R(c0, sk_Xb1(sk_R), c0)),
147.10/147.33	    inference('simplify', [status(thm)], ['174'])).
147.10/147.33	tff('176', plain,
147.10/147.33	    (~ sk_R(c0, c0, c0)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['161', '175'])).
147.10/147.33	tff('177', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))),
147.10/147.33	    inference('demod', [status(thm)], ['176', '138'])).
147.10/147.33	tff('178', plain,
147.10/147.33	    (sk_Xc(sk_R) = cP(sk_Xz1(sk_R), sk_Xz2(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['177'])).
147.10/147.33	tff('179', plain,
147.10/147.33	    (sk_R(sk_Xa(sk_R), cP(sk_Xy1(sk_R), sk_Xy2(sk_R)), sk_Xc(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup+', [status(thm)], ['178', '45'])).
147.10/147.33	tff('180', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa(sk_R), cP(sk_Xy1(sk_R), sk_Xy2(sk_R)), sk_Xc(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['179'])).
147.10/147.33	tff('181', plain,
147.10/147.33	    (sk_R(sk_Xa(sk_R), sk_Xb(sk_R), sk_Xc(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup+', [status(thm)], ['173', '180'])).
147.10/147.33	tff('182', plain,
147.10/147.33	    (sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa(sk_R), sk_Xb(sk_R), sk_Xc(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['181'])).
147.10/147.33	tff('183', plain,
147.10/147.33	    (sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('clc', [status(thm)], ['182', '50'])).
147.10/147.33	tff('184', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['183', '7'])).
147.10/147.33	tff('185', plain,
147.10/147.33	    (~ sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
147.10/147.33	    inference('simplify', [status(thm)], ['184'])).
147.10/147.33	tff('186', plain,
147.10/147.33	    (~ sk_R(sk_Xa1(sk_R), c0, c0)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
147.10/147.33	    inference('sup-', [status(thm)], ['161', '166'])).
147.10/147.33	tff('187', plain,
147.10/147.33	    (sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | ~ sk_R(sk_Xa1(sk_R), c0, c0)),
147.10/147.33	    inference('simplify', [status(thm)], ['186'])).
147.10/147.33	tff('188', plain,
147.10/147.33	    (~ sk_R(c0, c0, c0)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
147.10/147.33	    inference('sup-', [status(thm)], ['131', '187'])).
147.10/147.33	tff('189', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
147.10/147.33	    inference('demod', [status(thm)], ['188', '138'])).
147.10/147.33	tff('190', plain,
147.10/147.33	    (sk_Xb1(sk_R) != sk_Xa1(sk_R)
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['189'])).
147.10/147.33	tff('191', plain,
147.10/147.33	    (sk_Xb1(sk_R) != sk_Xa1(sk_R) | sk_Xb(sk_R) = c0 | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['185', '190'])).
147.10/147.33	tff('192', plain,
147.10/147.33	    (c0 != sk_Xa1(sk_R)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['161', '191'])).
147.10/147.33	tff('193', plain, (sk_Xb(sk_R) = c0 | sk_Xa(sk_R) = c0 | c0 != sk_Xa1(sk_R)),
147.10/147.33	    inference('simplify', [status(thm)], ['192'])).
147.10/147.33	tff('194', plain, (sk_Xa(sk_R) = c0 | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['193', '131'])).
147.10/147.33	tff('195', plain,
147.10/147.33	    (~ sk_R(sk_Xa(sk_R), c0, sk_Xa(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) != c0),
147.10/147.33	    inference('sup-', [status(thm)], ['194', '108'])).
147.10/147.33	tff('196', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) != c0),
147.10/147.33	    inference('demod', [status(thm)], ['195', '86'])).
147.10/147.33	tff('197', plain,
147.10/147.33	    (sk_Xb(sk_R) != c0 | sk_R(sk_Xx, sk_Xy, sk_Xy) | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['196'])).
147.10/147.33	tff('198', plain, (sk_Xa(sk_R) = c0 | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('clc', [status(thm)], ['197', '194'])).
147.10/147.33	tff('199', plain, (~ $true | sk_Xa(sk_R) = c0 | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['198', '7'])).
147.10/147.33	tff('200', plain, (~ sk_R(sk_Xu, sk_Xv, sk_Xv) | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['199'])).
147.10/147.33	tff('201', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['141', '200'])).
147.10/147.33	tff('202', plain, (sk_Xa(sk_R) = c0 | sk_Xa1(sk_R) = sk_Xc1(sk_R)),
147.10/147.33	    inference('simplify', [status(thm)], ['201'])).
147.10/147.33	tff('203', plain,
147.10/147.33	    (~ $true | sk_Xb1(sk_R) = c0 | sk_Xa(sk_R) = c0 | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['149', '200'])).
147.10/147.33	tff('204', plain, (sk_Xa(sk_R) = c0 | sk_Xb1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['203'])).
147.10/147.33	tff('205', plain,
147.10/147.33	    (~ sk_R(c0, sk_Xb1(sk_R), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['131', '33'])).
147.10/147.33	tff('206', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa(sk_R) = c0
147.10/147.33	     | ~ sk_R(c0, sk_Xb1(sk_R), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['205', '200'])).
147.10/147.33	tff('207', plain,
147.10/147.33	    (~ sk_R(c0, sk_Xb1(sk_R), sk_Xc1(sk_R)) | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['206'])).
147.10/147.33	tff('208', plain,
147.10/147.33	    (~ sk_R(c0, c0, sk_Xc1(sk_R)) | sk_Xa(sk_R) = c0 | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['204', '207'])).
147.10/147.33	tff('209', plain, (sk_Xa(sk_R) = c0 | ~ sk_R(c0, c0, sk_Xc1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['208'])).
147.10/147.33	tff('210', plain,
147.10/147.33	    (~ sk_R(c0, c0, sk_Xa1(sk_R)) | sk_Xa(sk_R) = c0 | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['202', '209'])).
147.10/147.33	tff('211', plain, (sk_Xa(sk_R) = c0 | ~ sk_R(c0, c0, sk_Xa1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['210'])).
147.10/147.33	tff('212', plain, (~ sk_R(c0, c0, c0) | sk_Xa(sk_R) = c0 | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['131', '211'])).
147.10/147.33	tff('213', plain, (~ $true | sk_Xa(sk_R) = c0 | sk_Xa(sk_R) = c0),
147.10/147.33	    inference('demod', [status(thm)], ['212', '138'])).
147.10/147.33	tff('214', plain, sk_Xa(sk_R) = c0,
147.10/147.33	    inference('simplify', [status(thm)], ['213'])).
147.10/147.33	tff('215', plain,
147.10/147.33	    ![X8 : (iS * iS * iS) > $o]:
147.10/147.33	      (X8(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xa(X8) = cP(sk_Xx1(X8), sk_Xx2(X8))
147.10/147.33	       | sk_Xb(X8) = c0
147.10/147.33	       | sk_Xb(X8) = sk_Xc(X8)),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('216', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xa(X0) != c0
147.10/147.33	       | sk_Xb(X0) = sk_Xc(X0)
147.10/147.33	       | sk_Xb(X0) = c0
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup-', [status(thm)], ['215', '80'])).
147.10/147.33	tff('217', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (~ X0(sk_Xa(X0), sk_Xb(X0), sk_Xb(X0))
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xb(X0) = c0
147.10/147.33	       | sk_Xa(X0) != c0
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup-', [status(thm)], ['216', '50'])).
147.10/147.33	tff('218', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xa(X0) != c0
147.10/147.33	       | sk_Xb(X0) = c0
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | ~ X0(sk_Xa(X0), sk_Xb(X0), sk_Xb(X0))),
147.10/147.33	    inference('simplify', [status(thm)], ['217'])).
147.10/147.33	tff('219', plain,
147.10/147.33	    (~ sk_R(c0, sk_Xb(sk_R), sk_Xb(sk_R))
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) != c0),
147.10/147.33	    inference('sup-', [status(thm)], ['214', '218'])).
147.10/147.33	tff('220', plain,
147.10/147.33	    (~ $true | sk_R(sk_Xx, sk_Xy, sk_Xy) | sk_Xb(sk_R) = c0 | c0 != c0),
147.10/147.33	    inference('demod', [status(thm)], ['219', '138', '214'])).
147.10/147.33	tff('221', plain, (sk_Xb(sk_R) = c0 | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('simplify', [status(thm)], ['220'])).
147.10/147.33	tff('222', plain, (~ $true | sk_Xb(sk_R) = c0 | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['221', '7'])).
147.10/147.33	tff('223', plain, (~ sk_R(sk_Xu, sk_Xv, sk_Xv) | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['222'])).
147.10/147.33	tff('224', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['0', '223'])).
147.10/147.33	tff('225', plain,
147.10/147.33	    (sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['224'])).
147.10/147.33	tff('226', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('sup-', [status(thm)], ['1', '223'])).
147.10/147.33	tff('227', plain,
147.10/147.33	    (sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['226'])).
147.10/147.33	tff('228', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup+', [status(thm)], ['227', '28'])).
147.10/147.33	tff('229', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), sk_Xc1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['228'])).
147.10/147.33	tff('230', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['229', '223'])).
147.10/147.33	tff('231', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('sup+', [status(thm)], ['225', '230'])).
147.10/147.33	tff('232', plain,
147.10/147.33	    (sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['231'])).
147.10/147.33	tff('233', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['232', '33'])).
147.10/147.33	tff('234', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['233'])).
147.10/147.33	tff('235', plain, (sk_Xa1(sk_R) = c0 | sk_Xb1(sk_R) = c0 | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['234', '223'])).
147.10/147.33	tff('236', plain,
147.10/147.33	    (~ sk_R(sk_Xa1(sk_R), c0, sk_Xa1(sk_R))
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0),
147.10/147.33	    inference('sup-', [status(thm)], ['235', '83'])).
147.10/147.33	tff('237', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xb(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0),
147.10/147.33	    inference('demod', [status(thm)], ['236', '86'])).
147.10/147.33	tff('238', plain,
147.10/147.33	    (sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['237'])).
147.10/147.33	tff('239', plain,
147.10/147.33	    (sk_Xb(sk_R) = c0 | sk_Xa1(sk_R) = c0 | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('clc', [status(thm)], ['238', '235'])).
147.10/147.33	tff('240', plain, (sk_Xa1(sk_R) = c0 | sk_Xb(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['239', '223'])).
147.10/147.33	tff('241', plain,
147.10/147.33	    ![X8 : (iS * iS * iS) > $o]:
147.10/147.33	      (X8(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xa(X8) = cP(sk_Xx1(X8), sk_Xx2(X8))
147.10/147.33	       | sk_Xa(X8) = sk_Xc(X8)
147.10/147.33	       | sk_Xb(X8) = sk_Xc(X8)),
147.10/147.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
147.10/147.33	tff('242', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xa(X0) != c0
147.10/147.33	       | sk_Xb(X0) = sk_Xc(X0)
147.10/147.33	       | sk_Xa(X0) = sk_Xc(X0)
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup-', [status(thm)], ['241', '80'])).
147.10/147.33	tff('243', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xb(X0) != sk_Xa(X0)
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xa(X0) = sk_Xc(X0)
147.10/147.33	       | sk_Xa(X0) != c0),
147.10/147.33	    inference('eq_fact', [status(thm)], ['242'])).
147.10/147.33	tff('244', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (~ X0(sk_Xa(X0), sk_Xb(X0), sk_Xa(X0))
147.10/147.33	       | sk_Xa(X0) != c0
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xb(X0) != sk_Xa(X0)
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('sup-', [status(thm)], ['243', '50'])).
147.10/147.33	tff('245', plain,
147.10/147.33	    ![X0 : (iS * iS * iS) > $o]:
147.10/147.33	      (sk_Xb(X0) != sk_Xa(X0)
147.10/147.33	       | X0(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	       | sk_Xa(X0) != c0
147.10/147.33	       | ~ X0(sk_Xa(X0), sk_Xb(X0), sk_Xa(X0))),
147.10/147.33	    inference('simplify', [status(thm)], ['244'])).
147.10/147.33	tff('246', plain,
147.10/147.33	    (~ sk_R(sk_Xa(sk_R), sk_Xb(sk_R), c0)
147.10/147.33	     | sk_Xa(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) != sk_Xa(sk_R)),
147.10/147.33	    inference('sup-', [status(thm)], ['214', '245'])).
147.10/147.33	tff('247', plain,
147.10/147.33	    (~ sk_R(c0, sk_Xb(sk_R), c0)
147.10/147.33	     | c0 != c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) != c0),
147.10/147.33	    inference('demod', [status(thm)], ['246', '214', '214', '214'])).
147.10/147.33	tff('248', plain,
147.10/147.33	    (sk_Xb(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | ~ sk_R(c0, sk_Xb(sk_R), c0)),
147.10/147.33	    inference('simplify', [status(thm)], ['247'])).
147.10/147.33	tff('249', plain, (~ sk_R(c0, sk_Xb(sk_R), c0) | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('clc', [status(thm)], ['248', '221'])).
147.10/147.33	tff('250', plain,
147.10/147.33	    (~ $true | ~ sk_R(c0, sk_Xb(sk_R), c0) | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['249', '7'])).
147.10/147.33	tff('251', plain,
147.10/147.33	    (~ sk_R(sk_Xu, sk_Xv, sk_Xv) | ~ sk_R(c0, sk_Xb(sk_R), c0)),
147.10/147.33	    inference('simplify', [status(thm)], ['250'])).
147.10/147.33	tff('252', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | ~ sk_R(c0, sk_Xb(sk_R), c0)),
147.10/147.33	    inference('sup-', [status(thm)], ['0', '251'])).
147.10/147.33	tff('253', plain,
147.10/147.33	    (~ sk_R(c0, sk_Xb(sk_R), c0)
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['252'])).
147.10/147.33	tff('254', plain,
147.10/147.33	    (~ sk_R(c0, c0, c0)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['240', '253'])).
147.10/147.33	tff('255', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))),
147.10/147.33	    inference('demod', [status(thm)], ['254', '138'])).
147.10/147.33	tff('256', plain,
147.10/147.33	    (sk_Xb1(sk_R) = cP(sk_Xy11(sk_R), sk_Xy21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['255'])).
147.10/147.33	tff('257', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | ~ sk_R(c0, sk_Xb(sk_R), c0)),
147.10/147.33	    inference('sup-', [status(thm)], ['1', '251'])).
147.10/147.33	tff('258', plain,
147.10/147.33	    (~ sk_R(c0, sk_Xb(sk_R), c0)
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['257'])).
147.10/147.33	tff('259', plain,
147.10/147.33	    (~ sk_R(c0, c0, c0)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))),
147.10/147.33	    inference('sup-', [status(thm)], ['240', '258'])).
147.10/147.33	tff('260', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))),
147.10/147.33	    inference('demod', [status(thm)], ['259', '138'])).
147.10/147.33	tff('261', plain,
147.10/147.33	    (sk_Xc1(sk_R) = cP(sk_Xz11(sk_R), sk_Xz21(sk_R))
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['260'])).
147.10/147.33	tff('262', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup+', [status(thm)], ['261', '28'])).
147.10/147.33	tff('263', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), sk_Xc1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['262'])).
147.10/147.33	tff('264', plain,
147.10/147.33	    (~ sk_R(sk_Xa(sk_R), c0, sk_Xa(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) != sk_Xa(sk_R)),
147.10/147.33	    inference('sup-', [status(thm)], ['240', '245'])).
147.10/147.33	tff('265', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | c0 != c0
147.10/147.33	     | sk_R(sk_Xx, sk_Xy, sk_Xy)
147.10/147.33	     | sk_Xb(sk_R) != c0),
147.10/147.33	    inference('demod', [status(thm)],
147.10/147.33	              ['264', '214', '214', '138', '214', '214'])).
147.10/147.33	tff('266', plain,
147.10/147.33	    (sk_Xb(sk_R) != c0 | sk_R(sk_Xx, sk_Xy, sk_Xy) | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['265'])).
147.10/147.33	tff('267', plain, (sk_Xa1(sk_R) = c0 | sk_R(sk_Xx, sk_Xy, sk_Xy)),
147.10/147.33	    inference('clc', [status(thm)], ['266', '240'])).
147.10/147.33	tff('268', plain,
147.10/147.33	    (~ $true | sk_Xa1(sk_R) = c0 | ~ sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['267', '7'])).
147.10/147.33	tff('269', plain, (~ sk_R(sk_Xu, sk_Xv, sk_Xv) | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['268'])).
147.10/147.33	tff('270', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), cP(sk_Xy11(sk_R), sk_Xy21(sk_R)), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['263', '269'])).
147.10/147.33	tff('271', plain,
147.10/147.33	    (sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('sup+', [status(thm)], ['256', '270'])).
147.10/147.33	tff('272', plain,
147.10/147.33	    (sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xc1(sk_R))),
147.10/147.33	    inference('simplify', [status(thm)], ['271'])).
147.10/147.33	tff('273', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) = c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['272', '33'])).
147.10/147.33	tff('274', plain,
147.10/147.33	    (sk_R(sk_Xu, sk_Xv, sk_Xv) | sk_Xb1(sk_R) = c0 | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['273'])).
147.10/147.33	tff('275', plain, (sk_Xa1(sk_R) = c0 | sk_Xb1(sk_R) = c0),
147.10/147.33	    inference('clc', [status(thm)], ['274', '269'])).
147.10/147.33	tff('276', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | ~ sk_R(c0, sk_Xb(sk_R), c0)),
147.10/147.33	    inference('sup-', [status(thm)], ['81', '251'])).
147.10/147.33	tff('277', plain,
147.10/147.33	    (~ sk_R(c0, sk_Xb(sk_R), c0)
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)),
147.10/147.33	    inference('simplify', [status(thm)], ['276'])).
147.10/147.33	tff('278', plain,
147.10/147.33	    (~ sk_R(c0, c0, c0)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0),
147.10/147.33	    inference('sup-', [status(thm)], ['240', '277'])).
147.10/147.33	tff('279', plain,
147.10/147.33	    (~ $true
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0),
147.10/147.33	    inference('demod', [status(thm)], ['278', '138'])).
147.10/147.33	tff('280', plain,
147.10/147.33	    (sk_Xb1(sk_R) != c0 | sk_Xa1(sk_R) = sk_Xc1(sk_R) | sk_Xa1(sk_R) = c0),
147.10/147.33	    inference('simplify', [status(thm)], ['279'])).
147.10/147.33	tff('281', plain,
147.10/147.33	    (~ sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xa1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.33	    inference('sup-', [status(thm)], ['280', '33'])).
147.10/147.33	tff('282', plain,
147.10/147.33	    (sk_Xb1(sk_R) != c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | ~ sk_R(sk_Xa1(sk_R), sk_Xb1(sk_R), sk_Xa1(sk_R))),
147.10/147.33	    inference('clc', [status(thm)], ['281', '269'])).
147.10/147.33	tff('283', plain,
147.10/147.33	    (~ sk_R(sk_Xa1(sk_R), c0, sk_Xa1(sk_R))
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xa1(sk_R) = c0
147.10/147.33	     | sk_Xb1(sk_R) != c0),
147.10/147.34	    inference('sup-', [status(thm)], ['275', '282'])).
147.10/147.34	tff('284', plain,
147.10/147.34	    (~ $true | sk_Xa1(sk_R) = c0 | sk_Xa1(sk_R) = c0 | sk_Xb1(sk_R) != c0),
147.10/147.34	    inference('demod', [status(thm)], ['283', '86'])).
147.10/147.34	tff('285', plain, (sk_Xb1(sk_R) != c0 | sk_Xa1(sk_R) = c0),
147.10/147.34	    inference('simplify', [status(thm)], ['284'])).
147.10/147.34	tff('286', plain, sk_Xa1(sk_R) = c0,
147.10/147.34	    inference('clc', [status(thm)], ['285', '275'])).
147.10/147.34	tff('287', plain,
147.10/147.34	    (~ sk_R(c0, sk_Xb1(sk_R), sk_Xb1(sk_R))
147.10/147.34	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.34	     | sk_Xb1(sk_R) = c0
147.10/147.34	     | sk_Xa1(sk_R) != c0),
147.10/147.34	    inference('sup-', [status(thm)], ['286', '145'])).
147.10/147.34	tff('288', plain,
147.10/147.34	    (~ $true | sk_R(sk_Xu, sk_Xv, sk_Xv) | sk_Xb1(sk_R) = c0 | c0 != c0),
147.10/147.34	    inference('demod', [status(thm)], ['287', '138', '286'])).
147.10/147.34	tff('289', plain, (sk_Xb1(sk_R) = c0 | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.34	    inference('simplify', [status(thm)], ['288'])).
147.10/147.34	tff('290', plain,
147.10/147.34	    (~ $true | sk_Xb1(sk_R) = c0 | ~ sk_R(c0, sk_Xb(sk_R), c0)),
147.10/147.34	    inference('sup-', [status(thm)], ['289', '251'])).
147.10/147.34	tff('291', plain, (~ sk_R(c0, sk_Xb(sk_R), c0) | sk_Xb1(sk_R) = c0),
147.10/147.34	    inference('simplify', [status(thm)], ['290'])).
147.10/147.34	tff('292', plain,
147.10/147.34	    (~ sk_R(c0, sk_Xb1(sk_R), sk_Xb1(sk_R))
147.10/147.34	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.34	     | sk_Xa1(sk_R) = sk_Xc1(sk_R)
147.10/147.34	     | sk_Xa1(sk_R) != c0),
147.10/147.34	    inference('sup-', [status(thm)], ['286', '135'])).
147.10/147.34	tff('293', plain,
147.10/147.34	    (~ $true | sk_R(sk_Xu, sk_Xv, sk_Xv) | c0 = sk_Xc1(sk_R) | c0 != c0),
147.10/147.34	    inference('demod', [status(thm)], ['292', '138', '286', '286'])).
147.10/147.34	tff('294', plain, (c0 = sk_Xc1(sk_R) | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.34	    inference('simplify', [status(thm)], ['293'])).
147.10/147.34	tff('295', plain, (~ $true | c0 = sk_Xc1(sk_R) | sk_Xb(sk_R) = c0),
147.10/147.34	    inference('sup-', [status(thm)], ['294', '223'])).
147.10/147.34	tff('296', plain, (sk_Xb(sk_R) = c0 | c0 = sk_Xc1(sk_R)),
147.10/147.34	    inference('simplify', [status(thm)], ['295'])).
147.10/147.34	tff('297', plain, (~ $true | sk_Xb1(sk_R) = c0 | sk_Xb(sk_R) = c0),
147.10/147.34	    inference('sup-', [status(thm)], ['289', '223'])).
147.10/147.34	tff('298', plain, (sk_Xb(sk_R) = c0 | sk_Xb1(sk_R) = c0),
147.10/147.34	    inference('simplify', [status(thm)], ['297'])).
147.10/147.34	tff('299', plain,
147.10/147.34	    (~ sk_R(c0, sk_Xb1(sk_R), sk_Xc1(sk_R)) | sk_R(sk_Xu, sk_Xv, sk_Xv)),
147.10/147.34	    inference('sup-', [status(thm)], ['286', '33'])).
147.10/147.34	tff('300', plain,
147.10/147.34	    (~ $true | ~ sk_R(c0, sk_Xb1(sk_R), sk_Xc1(sk_R)) | sk_Xb(sk_R) = c0),
147.10/147.34	    inference('sup-', [status(thm)], ['299', '223'])).
147.10/147.34	tff('301', plain,
147.10/147.34	    (sk_Xb(sk_R) = c0 | ~ sk_R(c0, sk_Xb1(sk_R), sk_Xc1(sk_R))),
147.10/147.34	    inference('simplify', [status(thm)], ['300'])).
147.10/147.34	tff('302', plain,
147.10/147.34	    (~ sk_R(c0, c0, sk_Xc1(sk_R)) | sk_Xb(sk_R) = c0 | sk_Xb(sk_R) = c0),
147.10/147.34	    inference('sup-', [status(thm)], ['298', '301'])).
147.10/147.34	tff('303', plain, (sk_Xb(sk_R) = c0 | ~ sk_R(c0, c0, sk_Xc1(sk_R))),
147.10/147.34	    inference('simplify', [status(thm)], ['302'])).
147.10/147.34	tff('304', plain, (~ sk_R(c0, c0, c0) | sk_Xb(sk_R) = c0 | sk_Xb(sk_R) = c0),
147.10/147.34	    inference('sup-', [status(thm)], ['296', '303'])).
147.10/147.34	tff('305', plain, (~ $true | sk_Xb(sk_R) = c0 | sk_Xb(sk_R) = c0),
147.10/147.34	    inference('demod', [status(thm)], ['304', '138'])).
147.10/147.34	tff('306', plain, sk_Xb(sk_R) = c0,
147.10/147.34	    inference('simplify', [status(thm)], ['305'])).
147.10/147.34	tff('307', plain, (~ $true | sk_Xb1(sk_R) = c0),
147.10/147.34	    inference('demod', [status(thm)], ['291', '306', '138'])).
147.10/147.34	tff('308', plain, sk_Xb1(sk_R) = c0,
147.10/147.34	    inference('simplify', [status(thm)], ['307'])).
147.10/147.34	tff('309', plain,
147.10/147.34	    (~ sk_R(sk_Xa1(sk_R), c0, sk_Xa1(sk_R))
147.10/147.34	     | sk_Xa1(sk_R) != c0
147.10/147.34	     | sk_R(sk_Xu, sk_Xv, sk_Xv)
147.10/147.34	     | sk_Xb1(sk_R) != sk_Xa1(sk_R)),
147.10/147.34	    inference('sup-', [status(thm)], ['308', '164'])).
147.10/147.34	tff('310', plain,
147.10/147.34	    (~ $true | c0 != c0 | sk_R(sk_Xu, sk_Xv, sk_Xv) | c0 != c0),
147.10/147.34	    inference('demod', [status(thm)],
147.10/147.34	              ['309', '286', '286', '138', '286', '308', '286'])).
147.10/147.34	tff('311', plain, sk_R(sk_Xu, sk_Xv, sk_Xv),
147.10/147.34	    inference('simplify', [status(thm)], ['310'])).
147.10/147.34	tff('312', plain, (~ sk_R(sk_Xu, sk_Xv, sk_Xv) | ~ $true),
147.10/147.34	    inference('demod', [status(thm)], ['251', '306', '138'])).
147.10/147.34	tff('313', plain, ~ sk_R(sk_Xu, sk_Xv, sk_Xv),
147.10/147.34	    inference('simplify', [status(thm)], ['312'])).
147.10/147.34	tff('314', plain, ~ $true, inference('sup-', [status(thm)], ['311', '313'])).
147.10/147.34	tff('315', plain, $false, inference('simplify', [status(thm)], ['314'])).
147.10/147.34	
147.10/147.34	% SZS output end Refutation
147.10/147.34	EOF
