0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_int
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-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
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	  --ho-purify int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n082.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:52:24 CST 2018
9.55/9.74	% done 6706 iterations in 9.538s
9.55/9.74	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
9.55/9.74	% SZS output start Refutation
9.55/9.75	tff(cTHM525_pme, conjecture,
9.55/9.75	  (![Xr:((a * a) > $o)]:
9.55/9.75	     ((![Xx:a,Xy:a,Xz:a]:
9.55/9.75	         (((![Xq:(a > $o)]:
9.55/9.75	              (((![Xv:a,Xw:a]: ((Xr(Xv,Xw) & Xq(Xv)) => Xq(Xw))) & 
9.55/9.75	                (![Xw:a]: (Xr(Xy,Xw) => Xq(Xw)))) =>
9.55/9.75	               Xq(Xz))) & 
9.55/9.75	           (![Xq:(a > $o)]:
9.55/9.75	              (((![Xv:a,Xw:a]: ((Xr(Xv,Xw) & Xq(Xv)) => Xq(Xw))) & 
9.55/9.75	                (![Xw:a]: (Xr(Xx,Xw) => Xq(Xw)))) =>
9.55/9.75	               Xq(Xy)))) =>
9.55/9.75	          (![Xq:(a > $o)]:
9.55/9.75	             (((![Xv:a,Xw:a]: ((Xr(Xv,Xw) & Xq(Xv)) => Xq(Xw))) & 
9.55/9.75	               (![Xw:a]: (Xr(Xx,Xw) => Xq(Xw)))) =>
9.55/9.75	              Xq(Xz))))) & 
9.55/9.75	      (![Xx:a,Xy:a]:
9.55/9.75	         (Xr(Xx,Xy) =>
9.55/9.75	          (![Xq:(a > $o)]:
9.55/9.75	             (((![Xv:a,Xw:a]: ((Xr(Xv,Xw) & Xq(Xv)) => Xq(Xw))) & 
9.55/9.75	               (![Xw:a]: (Xr(Xx,Xw) => Xq(Xw)))) =>
9.55/9.75	              Xq(Xy)))))))).
9.55/9.75	tff(zf_stmt_0, negated_conjecture,
9.55/9.75	  (~
9.55/9.75	    (![Xr:((a * a) > $o)]:
9.55/9.75	       ((![Xx:a,Xy:a,Xz:a]:
9.55/9.75	           (((![Xq:(a > $o)]:
9.55/9.75	                (((![Xv:a,Xw:a]: ((Xr(Xv,Xw) & Xq(Xv)) => Xq(Xw))) & 
9.55/9.75	                  (![Xw:a]: (Xr(Xy,Xw) => Xq(Xw)))) =>
9.55/9.75	                 Xq(Xz))) & 
9.55/9.75	             (![Xq:(a > $o)]:
9.55/9.75	                (((![Xv:a,Xw:a]: ((Xr(Xv,Xw) & Xq(Xv)) => Xq(Xw))) & 
9.55/9.75	                  (![Xw:a]: (Xr(Xx,Xw) => Xq(Xw)))) =>
9.55/9.75	                 Xq(Xy)))) =>
9.55/9.75	            (![Xq:(a > $o)]:
9.55/9.75	               (((![Xv:a,Xw:a]: ((Xr(Xv,Xw) & Xq(Xv)) => Xq(Xw))) & 
9.55/9.75	                 (![Xw:a]: (Xr(Xx,Xw) => Xq(Xw)))) =>
9.55/9.75	                Xq(Xz))))) & 
9.55/9.75	        (![Xx:a,Xy:a]:
9.55/9.75	           (Xr(Xx,Xy) =>
9.55/9.75	            (![Xq:(a > $o)]:
9.55/9.75	               (((![Xv:a,Xw:a]: ((Xr(Xv,Xw) & Xq(Xv)) => Xq(Xw))) & 
9.55/9.75	                 (![Xw:a]: (Xr(Xx,Xw) => Xq(Xw)))) =>
9.55/9.75	                Xq(Xy))))))))).
9.55/9.75	tff('0', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (X4(sk_Xv1(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('1', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | X4(sk_Xv1(X5))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['0'])).
9.55/9.75	tff('2', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('3', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X5(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['2'])).
9.55/9.75	tff('4', plain,
9.55/9.75	    ![X6 : a, X7 : a]:
9.55/9.75	      (sk_Xq(X6) | ~ sk_Xr(X7, X6) | ~ sk_Xq(X7) | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('5', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | sk_Xq(sk_Xw3(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['3', '4'])).
9.55/9.75	tff('6', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw3(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['5'])).
9.55/9.75	tff('7', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (~ X4(sk_Xw3(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('8', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | ~ X4(sk_Xw3(X5))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['7'])).
9.55/9.75	tff('9', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('sup-', [status(thm)], ['6', '8'])).
9.55/9.75	tff('10', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['9'])).
9.55/9.75	tff('11', plain, (~ sk_Xq(sk_Xz) | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('12', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('clc', [status(thm)], ['10', '11'])).
9.55/9.75	tff('13', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('sup-', [status(thm)], ['1', '12'])).
9.55/9.75	tff('14', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1(sk_Xz)
9.55/9.75	       | X1 != X0
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['13'])).
9.55/9.75	tff('15', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X1 != X0
9.55/9.75	       | X1(sk_Xz)),
9.55/9.75	    inference('clc', [status(thm)], ['14', '11'])).
9.55/9.75	tff('16', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq != X0
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('sup-', [status(thm)], ['15', '11'])).
9.55/9.75	tff('17', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xx1, sk_Xy1) | sk_Xr(sk_Xy, sk_Xw2(X0)) | sk_Xq != X0),
9.55/9.75	    inference('simplify', [status(thm)], ['16'])).
9.55/9.75	tff('18', plain, (sk_Xr(sk_Xy, sk_Xw2(sk_Xq)) | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('eq_res', [status(thm)], ['17'])).
9.55/9.75	tff('19', plain,
9.55/9.75	    (~ $true
9.55/9.75	     | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	     | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	     | ~ sk_Xq(sk_Xy)
9.55/9.75	     | sk_Xq(sk_Xw2(sk_Xq))),
9.55/9.75	    inference('sup-', [status(thm)], ['18', '4'])).
9.55/9.75	tff('20', plain,
9.55/9.75	    (sk_Xq(sk_Xw2(sk_Xq)) | ~ sk_Xq(sk_Xy) | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['19'])).
9.55/9.75	tff('21', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (X4(sk_Xv1(X4)) | ~ X4(sk_Xw2(X4)) | X4(sk_Xz) | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('22', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | X4(sk_Xv1(X5))
9.55/9.75	       | ~ X4(sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['21'])).
9.55/9.75	tff('23', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | ~ X4(sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('24', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o, X6 : a > $o]:
9.55/9.75	      (X6 != X4
9.55/9.75	       | X5 != X4
9.55/9.75	       | sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | ~ X5(sk_Xw2(X4))
9.55/9.75	       | X6(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['23'])).
9.55/9.75	tff('25', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | sk_Xr(sk_Xv1(X0), sk_Xw3(X0))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('eq_res', [status(thm)], ['24'])).
9.55/9.75	tff('26', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (X2 != X0
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X2))
9.55/9.75	       | sk_Xr(sk_Xv1(X2), sk_Xw3(X2))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['25'])).
9.55/9.75	tff('27', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv1(X0), sk_Xw3(X0))
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('eq_res', [status(thm)], ['26'])).
9.55/9.75	tff('28', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | sk_Xq(sk_Xw3(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['27', '4'])).
9.55/9.75	tff('29', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw3(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['28'])).
9.55/9.75	tff('30', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (~ X4(sk_Xw3(X4))
9.55/9.75	       | ~ X4(sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('31', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | ~ X4(sk_Xw3(X5))
9.55/9.75	       | ~ X4(sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['30'])).
9.55/9.75	tff('32', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('sup-', [status(thm)], ['29', '31'])).
9.55/9.75	tff('33', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['32'])).
9.55/9.75	tff('34', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('clc', [status(thm)], ['33', '11'])).
9.55/9.75	tff('35', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('sup-', [status(thm)], ['22', '34'])).
9.55/9.75	tff('36', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['35'])).
9.55/9.75	tff('37', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('clc', [status(thm)], ['36', '11'])).
9.55/9.75	tff('38', plain,
9.55/9.75	    (~ $true
9.55/9.75	     | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	     | ~ sk_Xq(sk_Xy)
9.55/9.75	     | sk_Xq != sk_Xq
9.55/9.75	     | sk_Xq(sk_Xz)
9.55/9.75	     | sk_Xq != sk_Xq
9.55/9.75	     | ~ sk_Xq(sk_Xw2(sk_Xq))
9.55/9.75	     | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('sup-', [status(thm)], ['20', '37'])).
9.55/9.75	tff('39', plain,
9.55/9.75	    (~ sk_Xq(sk_Xw2(sk_Xq))
9.55/9.75	     | sk_Xq(sk_Xz)
9.55/9.75	     | ~ sk_Xq(sk_Xy)
9.55/9.75	     | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['38'])).
9.55/9.75	tff('40', plain, (sk_Xr(sk_Xx1, sk_Xy1) | ~ sk_Xq(sk_Xy) | sk_Xq(sk_Xz)),
9.55/9.75	    inference('clc', [status(thm)], ['39', '20'])).
9.55/9.75	tff('41', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('42', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['41'])).
9.55/9.75	tff('43', plain,
9.55/9.75	    ![X5 : a]: (~ sk_Xr(sk_Xx, X5) | sk_Xq(X5) | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('44', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['42', '43'])).
9.55/9.75	tff('45', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['44'])).
9.55/9.75	tff('46', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw1(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['45', '4'])).
9.55/9.75	tff('47', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw1(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['46'])).
9.55/9.75	tff('48', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ X0(sk_Xw1(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('49', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | ~ X0(sk_Xw1(X1))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['48'])).
9.55/9.75	tff('50', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw1(X0))
9.55/9.75	       | X0 != X1
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['49', '43'])).
9.55/9.75	tff('51', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | X0 != X1
9.55/9.75	       | ~ X1(sk_Xw1(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['50'])).
9.55/9.75	tff('52', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['47', '51'])).
9.55/9.75	tff('53', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['52'])).
9.55/9.75	tff('54', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (X0(sk_Xv(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('55', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | X0(sk_Xv(X1))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['54'])).
9.55/9.75	tff('56', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1(sk_Xv(X0))
9.55/9.75	       | X0 != X1
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['55', '43'])).
9.55/9.75	tff('57', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | X0 != X1
9.55/9.75	       | X1(sk_Xv(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['56'])).
9.55/9.75	tff('58', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('clc', [status(thm)], ['53', '57'])).
9.55/9.75	tff('59', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (X0(sk_Xv(X0)) | ~ X0(sk_Xw(X0)) | X0(sk_Xy) | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('60', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | X0(sk_Xv(X1))
9.55/9.75	       | ~ X0(sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['59'])).
9.55/9.75	tff('61', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | ~ X0(sk_Xw(X0))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('62', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (X2 != X0
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X2(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['61'])).
9.55/9.75	tff('63', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('eq_res', [status(thm)], ['62'])).
9.55/9.75	tff('64', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (X2 != X0
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X2))
9.55/9.75	       | sk_Xr(sk_Xv(X2), sk_Xw1(X2))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['63'])).
9.55/9.75	tff('65', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('eq_res', [status(thm)], ['64'])).
9.55/9.75	tff('66', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw1(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['65', '4'])).
9.55/9.75	tff('67', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw1(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['66'])).
9.55/9.75	tff('68', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ X0(sk_Xw1(X0)) | ~ X0(sk_Xw(X0)) | X0(sk_Xy) | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('69', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | ~ X0(sk_Xw1(X1))
9.55/9.75	       | ~ X0(sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['68'])).
9.55/9.75	tff('70', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('sup-', [status(thm)], ['67', '69'])).
9.55/9.75	tff('71', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['70'])).
9.55/9.75	tff('72', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('clc', [status(thm)], ['71', '58'])).
9.55/9.75	tff('73', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('sup-', [status(thm)], ['60', '72'])).
9.55/9.75	tff('74', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['73'])).
9.55/9.75	tff('75', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('clc', [status(thm)], ['74', '58'])).
9.55/9.75	tff('76', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('sup-', [status(thm)], ['58', '75'])).
9.55/9.75	tff('77', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xx1, sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('simplify', [status(thm)], ['76'])).
9.55/9.75	tff('78', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | sk_Xq != X0
9.55/9.75	       | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('eq_fact', [status(thm)], ['77'])).
9.55/9.75	tff('79', plain,
9.55/9.75	    ![X0 : a > $o]: (sk_Xr(sk_Xx1, sk_Xy1) | sk_Xq(sk_Xy) | X0 != sk_Xq),
9.55/9.75	    inference('simplify', [status(thm)], ['78'])).
9.55/9.75	tff('80', plain, (sk_Xq(sk_Xy) | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('eq_res', [status(thm)], ['79'])).
9.55/9.75	tff('81', plain, (sk_Xq(sk_Xz) | sk_Xr(sk_Xx1, sk_Xy1)),
9.55/9.75	    inference('clc', [status(thm)], ['40', '80'])).
9.55/9.75	tff('82', plain, sk_Xr(sk_Xx1, sk_Xy1),
9.55/9.75	    inference('clc', [status(thm)], ['81', '11'])).
9.55/9.75	tff('83', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('84', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X5(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['83'])).
9.55/9.75	tff('85', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | sk_Xr(sk_Xv1(X1), sk_Xw3(X1))
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '84'])).
9.55/9.75	tff('86', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | sk_Xr(sk_Xv1(X1), sk_Xw3(X1))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['85'])).
9.55/9.75	tff('87', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (X4(sk_Xv1(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('88', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | X4(sk_Xv1(X5))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['87'])).
9.55/9.75	tff('89', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('90', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X5(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['89'])).
9.55/9.75	tff('91', plain,
9.55/9.75	    ![X6 : a, X7 : a]:
9.55/9.75	      (sk_Xq(X6) | ~ sk_Xr(X7, X6) | ~ sk_Xq(X7) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('92', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | sk_Xq(sk_Xw3(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['90', '91'])).
9.55/9.75	tff('93', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw3(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['92'])).
9.55/9.75	tff('94', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (~ X4(sk_Xw3(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('95', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | ~ X4(sk_Xw3(X5))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['94'])).
9.55/9.75	tff('96', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('sup-', [status(thm)], ['93', '95'])).
9.55/9.75	tff('97', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['96'])).
9.55/9.75	tff('98', plain, (~ sk_Xq(sk_Xz) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('99', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('clc', [status(thm)], ['97', '98'])).
9.55/9.75	tff('100', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('sup-', [status(thm)], ['88', '99'])).
9.55/9.75	tff('101', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1(sk_Xz)
9.55/9.75	       | X1 != X0
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['100'])).
9.55/9.75	tff('102', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X1 != X0
9.55/9.75	       | X1(sk_Xz)),
9.55/9.75	    inference('clc', [status(thm)], ['101', '98'])).
9.55/9.75	tff('103', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq != X0
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('sup-', [status(thm)], ['102', '98'])).
9.55/9.75	tff('104', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ sk_Xq1(sk_Xy1) | sk_Xr(sk_Xy, sk_Xw2(X0)) | sk_Xq != X0),
9.55/9.75	    inference('simplify', [status(thm)], ['103'])).
9.55/9.75	tff('105', plain, (sk_Xr(sk_Xy, sk_Xw2(sk_Xq)) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('eq_res', [status(thm)], ['104'])).
9.55/9.75	tff('106', plain,
9.55/9.75	    (~ $true
9.55/9.75	     | ~ sk_Xq1(sk_Xy1)
9.55/9.75	     | ~ sk_Xq1(sk_Xy1)
9.55/9.75	     | ~ sk_Xq(sk_Xy)
9.55/9.75	     | sk_Xq(sk_Xw2(sk_Xq))),
9.55/9.75	    inference('sup-', [status(thm)], ['105', '91'])).
9.55/9.75	tff('107', plain, (sk_Xq(sk_Xw2(sk_Xq)) | ~ sk_Xq(sk_Xy) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['106'])).
9.55/9.75	tff('108', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (X4(sk_Xv1(X4)) | ~ X4(sk_Xw2(X4)) | X4(sk_Xz) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('109', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | X4(sk_Xv1(X5))
9.55/9.75	       | ~ X4(sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['108'])).
9.55/9.75	tff('110', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | ~ X4(sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('111', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o, X6 : a > $o]:
9.55/9.75	      (X6 != X4
9.55/9.75	       | X5 != X4
9.55/9.75	       | sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | ~ X5(sk_Xw2(X4))
9.55/9.75	       | X6(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['110'])).
9.55/9.75	tff('112', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | sk_Xr(sk_Xv1(X0), sk_Xw3(X0))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('eq_res', [status(thm)], ['111'])).
9.55/9.75	tff('113', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (X2 != X0
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X2))
9.55/9.75	       | sk_Xr(sk_Xv1(X2), sk_Xw3(X2))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['112'])).
9.55/9.75	tff('114', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv1(X0), sk_Xw3(X0))
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('eq_res', [status(thm)], ['113'])).
9.55/9.75	tff('115', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | sk_Xq(sk_Xw3(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['114', '91'])).
9.55/9.75	tff('116', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw3(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['115'])).
9.55/9.75	tff('117', plain,
9.55/9.75	    ![X4 : a > $o]:
9.55/9.75	      (~ X4(sk_Xw3(X4)) | ~ X4(sk_Xw2(X4)) | X4(sk_Xz) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('118', plain,
9.55/9.75	    ![X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | ~ X4(sk_Xw3(X5))
9.55/9.75	       | ~ X4(sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['117'])).
9.55/9.75	tff('119', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('sup-', [status(thm)], ['116', '118'])).
9.55/9.75	tff('120', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['119'])).
9.55/9.75	tff('121', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('clc', [status(thm)], ['120', '98'])).
9.55/9.75	tff('122', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('sup-', [status(thm)], ['109', '121'])).
9.55/9.75	tff('123', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['122'])).
9.55/9.75	tff('124', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ sk_Xq1(sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ X1(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('clc', [status(thm)], ['123', '98'])).
9.55/9.75	tff('125', plain,
9.55/9.75	    (~ $true
9.55/9.75	     | ~ sk_Xq1(sk_Xy1)
9.55/9.75	     | ~ sk_Xq(sk_Xy)
9.55/9.75	     | sk_Xq != sk_Xq
9.55/9.75	     | sk_Xq(sk_Xz)
9.55/9.75	     | sk_Xq != sk_Xq
9.55/9.75	     | ~ sk_Xq(sk_Xw2(sk_Xq))
9.55/9.75	     | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('sup-', [status(thm)], ['107', '124'])).
9.55/9.75	tff('126', plain,
9.55/9.75	    (~ sk_Xq(sk_Xw2(sk_Xq))
9.55/9.75	     | sk_Xq(sk_Xz)
9.55/9.75	     | ~ sk_Xq(sk_Xy)
9.55/9.75	     | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['125'])).
9.55/9.75	tff('127', plain, (~ sk_Xq1(sk_Xy1) | ~ sk_Xq(sk_Xy) | sk_Xq(sk_Xz)),
9.55/9.75	    inference('clc', [status(thm)], ['126', '107'])).
9.55/9.75	tff('128', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('129', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['128'])).
9.55/9.75	tff('130', plain,
9.55/9.75	    ![X5 : a]: (~ sk_Xr(sk_Xx, X5) | sk_Xq(X5) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('131', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['129', '130'])).
9.55/9.75	tff('132', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['131'])).
9.55/9.75	tff('133', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw1(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['132', '91'])).
9.55/9.75	tff('134', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw1(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['133'])).
9.55/9.75	tff('135', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ X0(sk_Xw1(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('136', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | ~ X0(sk_Xw1(X1))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['135'])).
9.55/9.75	tff('137', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw1(X0))
9.55/9.75	       | X0 != X1
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['136', '130'])).
9.55/9.75	tff('138', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | X0 != X1
9.55/9.75	       | ~ X1(sk_Xw1(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['137'])).
9.55/9.75	tff('139', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['134', '138'])).
9.55/9.75	tff('140', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['139'])).
9.55/9.75	tff('141', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (X0(sk_Xv(X0)) | sk_Xr(sk_Xx, sk_Xw(X0)) | X0(sk_Xy) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('142', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | X0(sk_Xv(X1))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['141'])).
9.55/9.75	tff('143', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1(sk_Xv(X0))
9.55/9.75	       | X0 != X1
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['142', '130'])).
9.55/9.75	tff('144', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | X0 != X1
9.55/9.75	       | X1(sk_Xv(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['143'])).
9.55/9.75	tff('145', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('clc', [status(thm)], ['140', '144'])).
9.55/9.75	tff('146', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (X0(sk_Xv(X0)) | ~ X0(sk_Xw(X0)) | X0(sk_Xy) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('147', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | X0(sk_Xv(X1))
9.55/9.75	       | ~ X0(sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['146'])).
9.55/9.75	tff('148', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | ~ X0(sk_Xw(X0))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('149', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (X2 != X0
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X2(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['148'])).
9.55/9.75	tff('150', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('eq_res', [status(thm)], ['149'])).
9.55/9.75	tff('151', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (X2 != X0
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X2))
9.55/9.75	       | sk_Xr(sk_Xv(X2), sk_Xw1(X2))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['150'])).
9.55/9.75	tff('152', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('eq_res', [status(thm)], ['151'])).
9.55/9.75	tff('153', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw1(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['152', '91'])).
9.55/9.75	tff('154', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw1(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['153'])).
9.55/9.75	tff('155', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ X0(sk_Xw1(X0)) | ~ X0(sk_Xw(X0)) | X0(sk_Xy) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('156', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | ~ X0(sk_Xw1(X1))
9.55/9.75	       | ~ X0(sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['155'])).
9.55/9.75	tff('157', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('sup-', [status(thm)], ['154', '156'])).
9.55/9.75	tff('158', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['157'])).
9.55/9.75	tff('159', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('clc', [status(thm)], ['158', '145'])).
9.55/9.75	tff('160', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('sup-', [status(thm)], ['147', '159'])).
9.55/9.75	tff('161', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['160'])).
9.55/9.75	tff('162', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ X1(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('clc', [status(thm)], ['161', '145'])).
9.55/9.75	tff('163', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('sup-', [status(thm)], ['145', '162'])).
9.55/9.75	tff('164', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ sk_Xq1(sk_Xy1) | X1(sk_Xy) | X1 != X0 | sk_Xq(sk_Xy) | X0 != sk_Xq),
9.55/9.75	    inference('simplify', [status(thm)], ['163'])).
9.55/9.75	tff('165', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ $true | X0 != sk_Xq | sk_Xq(sk_Xy) | sk_Xq != X0 | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('eq_fact', [status(thm)], ['164'])).
9.55/9.75	tff('166', plain,
9.55/9.75	    ![X0 : a > $o]: (~ sk_Xq1(sk_Xy1) | sk_Xq(sk_Xy) | X0 != sk_Xq),
9.55/9.75	    inference('simplify', [status(thm)], ['165'])).
9.55/9.75	tff('167', plain, (sk_Xq(sk_Xy) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('eq_res', [status(thm)], ['166'])).
9.55/9.75	tff('168', plain, (sk_Xq(sk_Xz) | ~ sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('clc', [status(thm)], ['127', '167'])).
9.55/9.75	tff('169', plain, ~ sk_Xq1(sk_Xy1),
9.55/9.75	    inference('clc', [status(thm)], ['168', '98'])).
9.55/9.75	tff('170', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | sk_Xr(sk_Xv1(X1), sk_Xw3(X1))
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('clc', [status(thm)], ['86', '169'])).
9.55/9.75	tff('171', plain,
9.55/9.75	    ![X3 : a, X6 : a, X7 : a]:
9.55/9.75	      (sk_Xq(X6)
9.55/9.75	       | ~ sk_Xr(X7, X6)
9.55/9.75	       | ~ sk_Xq(X7)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('172', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X2 != X0
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X2(sk_Xz)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | sk_Xq(sk_Xw3(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['170', '171'])).
9.55/9.75	tff('173', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw3(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | X2(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X2 != X0),
9.55/9.75	    inference('simplify', [status(thm)], ['172'])).
9.55/9.75	tff('174', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X1))
9.55/9.75	       | sk_Xq(sk_Xw3(X1))),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '173'])).
9.55/9.75	tff('175', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw3(X1))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X1))
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['174'])).
9.55/9.75	tff('176', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X1))
9.55/9.75	       | sk_Xq(sk_Xw3(X1))),
9.55/9.75	    inference('clc', [status(thm)], ['175', '169'])).
9.55/9.75	tff('177', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o]:
9.55/9.75	      (~ X4(sk_Xw3(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('178', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | ~ X4(sk_Xw3(X5))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['177'])).
9.55/9.75	tff('179', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | ~ X0(sk_Xw3(X1))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '178'])).
9.55/9.75	tff('180', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | ~ X0(sk_Xw3(X1))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['179'])).
9.55/9.75	tff('181', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0(sk_Xz) | sk_Xr(sk_Xy, sk_Xw2(X1)) | ~ X0(sk_Xw3(X1)) | X1 != X0),
9.55/9.75	    inference('clc', [status(thm)], ['180', '169'])).
9.55/9.75	tff('182', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | sk_Xq(sk_Xz)),
9.55/9.75	    inference('sup-', [status(thm)], ['176', '181'])).
9.55/9.75	tff('183', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xz)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))),
9.55/9.75	    inference('simplify', [status(thm)], ['182'])).
9.55/9.75	tff('184', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o]:
9.55/9.75	      (X4(sk_Xv1(X4))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('185', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | X4(sk_Xv1(X5))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['184'])).
9.55/9.75	tff('186', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xv1(X1))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '185'])).
9.55/9.75	tff('187', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | X0(sk_Xv1(X1))
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['186'])).
9.55/9.75	tff('188', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0(sk_Xz) | sk_Xr(sk_Xy, sk_Xw2(X1)) | X0(sk_Xv1(X1)) | X1 != X0),
9.55/9.75	    inference('clc', [status(thm)], ['187', '169'])).
9.55/9.75	tff('189', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1(sk_Xz)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xz)),
9.55/9.75	    inference('clc', [status(thm)], ['183', '188'])).
9.55/9.75	tff('190', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq != X0
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X0))),
9.55/9.75	    inference('eq_fact', [status(thm)], ['189'])).
9.55/9.75	tff('191', plain,
9.55/9.75	    ![X0 : a > $o]: (sk_Xr(sk_Xy, sk_Xw2(X0)) | X0 != sk_Xq | sk_Xq(sk_Xz)),
9.55/9.75	    inference('simplify', [status(thm)], ['190'])).
9.55/9.75	tff('192', plain,
9.55/9.75	    ![X3 : a]: (~ sk_Xq(sk_Xz) | sk_Xq1(X3) | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('193', plain,
9.55/9.75	    ![X0 : a, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X1 != sk_Xq
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X0)
9.55/9.75	       | sk_Xq1(X0)),
9.55/9.75	    inference('sup-', [status(thm)], ['191', '192'])).
9.55/9.75	tff('194', plain,
9.55/9.75	    ![X0 : a, X1 : a > $o]:
9.55/9.75	      (sk_Xq1(X0)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X0)
9.55/9.75	       | sk_Xr(sk_Xy, sk_Xw2(X1))
9.55/9.75	       | X1 != sk_Xq),
9.55/9.75	    inference('simplify', [status(thm)], ['193'])).
9.55/9.75	tff('195', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ $true | X0 != sk_Xq | sk_Xr(sk_Xy, sk_Xw2(X0)) | sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '194'])).
9.55/9.75	tff('196', plain,
9.55/9.75	    ![X0 : a > $o]: (sk_Xq1(sk_Xy1) | sk_Xr(sk_Xy, sk_Xw2(X0)) | X0 != sk_Xq),
9.55/9.75	    inference('simplify', [status(thm)], ['195'])).
9.55/9.75	tff('197', plain, ![X0 : a > $o]: (X0 != sk_Xq | sk_Xr(sk_Xy, sk_Xw2(X0))),
9.55/9.75	    inference('clc', [status(thm)], ['196', '169'])).
9.55/9.75	tff('198', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xq(sk_Xy)
9.55/9.75	       | sk_Xq(sk_Xw2(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['197', '171'])).
9.55/9.75	tff('199', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a]:
9.55/9.75	      (sk_Xq(sk_Xw2(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xy)
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('simplify', [status(thm)], ['198'])).
9.55/9.75	tff('200', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xy)
9.55/9.75	       | sk_Xq(sk_Xw2(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '199'])).
9.55/9.75	tff('201', plain,
9.55/9.75	    ![X0 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw2(X0)) | ~ sk_Xq(sk_Xy) | sk_Xq1(sk_Xy1) | X0 != sk_Xq),
9.55/9.75	    inference('simplify', [status(thm)], ['200'])).
9.55/9.75	tff('202', plain,
9.55/9.75	    ![X0 : a > $o]: (X0 != sk_Xq | ~ sk_Xq(sk_Xy) | sk_Xq(sk_Xw2(X0))),
9.55/9.75	    inference('clc', [status(thm)], ['201', '169'])).
9.55/9.75	tff('203', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o]:
9.55/9.75	      (sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | ~ X4(sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('204', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o, X5 : a > $o, X6 : a > $o]:
9.55/9.75	      (X6 != X4
9.55/9.75	       | X5 != X4
9.55/9.75	       | sk_Xr(sk_Xv1(X4), sk_Xw3(X4))
9.55/9.75	       | ~ X5(sk_Xw2(X4))
9.55/9.75	       | X6(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['203'])).
9.55/9.75	tff('205', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X2))
9.55/9.75	       | sk_Xr(sk_Xv1(X2), sk_Xw3(X2))
9.55/9.75	       | X1 != X2
9.55/9.75	       | X0 != X2),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '204'])).
9.55/9.75	tff('206', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (X0 != X2
9.55/9.75	       | X1 != X2
9.55/9.75	       | sk_Xr(sk_Xv1(X2), sk_Xw3(X2))
9.55/9.75	       | ~ X1(sk_Xw2(X2))
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['205'])).
9.55/9.75	tff('207', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (X0(sk_Xz)
9.55/9.75	       | ~ X1(sk_Xw2(X2))
9.55/9.75	       | sk_Xr(sk_Xv1(X2), sk_Xw3(X2))
9.55/9.75	       | X1 != X2
9.55/9.75	       | X0 != X2),
9.55/9.75	    inference('clc', [status(thm)], ['206', '169'])).
9.55/9.75	tff('208', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o, X3 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X2 != X0
9.55/9.75	       | X3 != X0
9.55/9.75	       | ~ X3(sk_Xw2(X0))
9.55/9.75	       | X2(sk_Xz)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | sk_Xq(sk_Xw3(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['207', '171'])).
9.55/9.75	tff('209', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o, X3 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw3(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | X2(sk_Xz)
9.55/9.75	       | ~ X3(sk_Xw2(X0))
9.55/9.75	       | X3 != X0
9.55/9.75	       | X2 != X0),
9.55/9.75	    inference('simplify', [status(thm)], ['208'])).
9.55/9.75	tff('210', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | X2 != X1
9.55/9.75	       | ~ X2(sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X1))
9.55/9.75	       | sk_Xq(sk_Xw3(X1))),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '209'])).
9.55/9.75	tff('211', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw3(X1))
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X1))
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | ~ X2(sk_Xw2(X1))
9.55/9.75	       | X2 != X1
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['210'])).
9.55/9.75	tff('212', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | X2 != X1
9.55/9.75	       | ~ X2(sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X1))
9.55/9.75	       | sk_Xq(sk_Xw3(X1))),
9.55/9.75	    inference('clc', [status(thm)], ['211', '169'])).
9.55/9.75	tff('213', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o]:
9.55/9.75	      (~ X4(sk_Xw3(X4))
9.55/9.75	       | ~ X4(sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('214', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | ~ X4(sk_Xw3(X5))
9.55/9.75	       | ~ X4(sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['213'])).
9.55/9.75	tff('215', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | ~ X0(sk_Xw2(X1))
9.55/9.75	       | ~ X0(sk_Xw3(X1))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '214'])).
9.55/9.75	tff('216', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | ~ X0(sk_Xw3(X1))
9.55/9.75	       | ~ X0(sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['215'])).
9.55/9.75	tff('217', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0(sk_Xz) | ~ X0(sk_Xw2(X1)) | ~ X0(sk_Xw3(X1)) | X1 != X0),
9.55/9.75	    inference('clc', [status(thm)], ['216', '169'])).
9.55/9.75	tff('218', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ X2(sk_Xw2(X0))
9.55/9.75	       | X2 != X0
9.55/9.75	       | X1 != X0
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | sk_Xq(sk_Xz)),
9.55/9.75	    inference('sup-', [status(thm)], ['212', '217'])).
9.55/9.75	tff('219', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X1 != X0
9.55/9.75	       | X2 != X0
9.55/9.75	       | ~ X2(sk_Xw2(X0))
9.55/9.75	       | X1(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xv1(X0))),
9.55/9.75	    inference('simplify', [status(thm)], ['218'])).
9.55/9.75	tff('220', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o]:
9.55/9.75	      (X4(sk_Xv1(X4))
9.55/9.75	       | ~ X4(sk_Xw2(X4))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('221', plain,
9.55/9.75	    ![X3 : a, X4 : a > $o, X5 : a > $o]:
9.55/9.75	      (X5 != X4
9.55/9.75	       | X4(sk_Xv1(X5))
9.55/9.75	       | ~ X4(sk_Xw2(X5))
9.55/9.75	       | X4(sk_Xz)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['220'])).
9.55/9.75	tff('222', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | ~ X0(sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xv1(X1))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '221'])).
9.55/9.75	tff('223', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | X0(sk_Xv1(X1))
9.55/9.75	       | ~ X0(sk_Xw2(X1))
9.55/9.75	       | X0(sk_Xz)
9.55/9.75	       | sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['222'])).
9.55/9.75	tff('224', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0(sk_Xz) | ~ X0(sk_Xw2(X1)) | X0(sk_Xv1(X1)) | X1 != X0),
9.55/9.75	    inference('clc', [status(thm)], ['223', '169'])).
9.55/9.75	tff('225', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.75	      (X1(sk_Xz)
9.55/9.75	       | ~ X2(sk_Xw2(X0))
9.55/9.75	       | X2 != X0
9.55/9.75	       | X1 != X0
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | sk_Xq(sk_Xz)),
9.55/9.75	    inference('clc', [status(thm)], ['219', '224'])).
9.55/9.75	tff('226', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xz)
9.55/9.75	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.75	       | X0 != sk_Xq
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xq != X0
9.55/9.75	       | X1(sk_Xz)),
9.55/9.75	    inference('sup-', [status(thm)], ['202', '225'])).
9.55/9.75	tff('227', plain,
9.55/9.75	    ![X0 : a > $o, X3 : a]:
9.55/9.75	      (sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('228', plain,
9.55/9.75	    ![X0 : a > $o, X3 : a, X4 : a > $o]:
9.55/9.75	      (X4 != X0
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X4(sk_Xy)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['227'])).
9.55/9.75	tff('229', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | sk_Xr(sk_Xv(X1), sk_Xw1(X1))
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '228'])).
9.55/9.75	tff('230', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1
9.55/9.75	       | sk_Xr(sk_Xv(X1), sk_Xw1(X1))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['229'])).
9.55/9.75	tff('231', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | sk_Xr(sk_Xv(X1), sk_Xw1(X1))
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('clc', [status(thm)], ['230', '169'])).
9.55/9.75	tff('232', plain,
9.55/9.75	    ![X3 : a, X5 : a]:
9.55/9.75	      (~ sk_Xr(sk_Xx, X5) | sk_Xq(X5) | sk_Xq1(X3) | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('233', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X2 != X0
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | X2(sk_Xy)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['231', '232'])).
9.55/9.75	tff('234', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | X2(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.75	       | X2 != X0),
9.55/9.75	    inference('simplify', [status(thm)], ['233'])).
9.55/9.75	tff('235', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | sk_Xr(sk_Xv(X1), sk_Xw1(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xw(X1))),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '234'])).
9.55/9.75	tff('236', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X1))
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xv(X1), sk_Xw1(X1))
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['235'])).
9.55/9.75	tff('237', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1 | sk_Xr(sk_Xv(X1), sk_Xw1(X1)) | X0(sk_Xy) | sk_Xq(sk_Xw(X1))),
9.55/9.75	    inference('clc', [status(thm)], ['236', '169'])).
9.55/9.75	tff('238', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | X2(sk_Xy)
9.55/9.75	       | X2 != X0
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw1(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['237', '171'])).
9.55/9.75	tff('239', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw1(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | X2 != X0
9.55/9.75	       | X2(sk_Xy)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('simplify', [status(thm)], ['238'])).
9.55/9.75	tff('240', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw1(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '239'])).
9.55/9.75	tff('241', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw1(X0))
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X1 != X0
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('simplify', [status(thm)], ['240'])).
9.55/9.75	tff('242', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | sk_Xq(sk_Xw1(X0))),
9.55/9.75	    inference('clc', [status(thm)], ['241', '169'])).
9.55/9.75	tff('243', plain,
9.55/9.75	    ![X0 : a > $o, X3 : a]:
9.55/9.75	      (~ X0(sk_Xw1(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('244', plain,
9.55/9.75	    ![X0 : a > $o, X3 : a, X4 : a > $o]:
9.55/9.75	      (X4 != X0
9.55/9.75	       | ~ X0(sk_Xw1(X4))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X4))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['243'])).
9.55/9.75	tff('245', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | ~ X0(sk_Xw1(X1))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '244'])).
9.55/9.75	tff('246', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | ~ X0(sk_Xw1(X1))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['245'])).
9.55/9.75	tff('247', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0(sk_Xy) | sk_Xr(sk_Xx, sk_Xw(X1)) | ~ X0(sk_Xw1(X1)) | X1 != X0),
9.55/9.75	    inference('clc', [status(thm)], ['246', '169'])).
9.55/9.75	tff('248', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X2
9.55/9.75	       | ~ X2(sk_Xw1(X0))
9.55/9.75	       | X2(sk_Xy)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['247', '232'])).
9.55/9.75	tff('249', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | X2(sk_Xy)
9.55/9.75	       | ~ X2(sk_Xw1(X0))
9.55/9.75	       | X0 != X2),
9.55/9.75	    inference('simplify', [status(thm)], ['248'])).
9.55/9.75	tff('250', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | ~ X1(sk_Xw1(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '249'])).
9.55/9.75	tff('251', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | ~ X1(sk_Xw1(X0))
9.55/9.75	       | X0 != X1),
9.55/9.75	    inference('simplify', [status(thm)], ['250'])).
9.55/9.75	tff('252', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != X1 | ~ X1(sk_Xw1(X0)) | X1(sk_Xy) | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('clc', [status(thm)], ['251', '169'])).
9.55/9.75	tff('253', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.75	       | X1 != X0
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | X0 != sk_Xq),
9.55/9.75	    inference('sup-', [status(thm)], ['242', '252'])).
9.55/9.75	tff('254', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0 != sk_Xq
9.55/9.75	       | sk_Xq(sk_Xy)
9.55/9.75	       | sk_Xq(sk_Xw(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | X1 != X0
9.55/9.75	       | ~ sk_Xq(sk_Xv(X0))),
9.55/9.75	    inference('simplify', [status(thm)], ['253'])).
9.55/9.75	tff('255', plain,
9.55/9.75	    ![X0 : a > $o, X3 : a]:
9.55/9.75	      (X0(sk_Xv(X0))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X0))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.75	tff('256', plain,
9.55/9.75	    ![X0 : a > $o, X3 : a, X4 : a > $o]:
9.55/9.75	      (X4 != X0
9.55/9.75	       | X0(sk_Xv(X4))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X4))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xq1(X3)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.75	    inference('ho.purify_applied_variable', [status(thm)], ['255'])).
9.55/9.75	tff('257', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | X0(sk_Xv(X1))
9.55/9.75	       | X1 != X0),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '256'])).
9.55/9.75	tff('258', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X1 != X0
9.55/9.75	       | X0(sk_Xv(X1))
9.55/9.75	       | sk_Xr(sk_Xx, sk_Xw(X1))
9.55/9.75	       | X0(sk_Xy)
9.55/9.75	       | sk_Xq1(sk_Xy1)),
9.55/9.75	    inference('simplify', [status(thm)], ['257'])).
9.55/9.75	tff('259', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (X0(sk_Xy) | sk_Xr(sk_Xx, sk_Xw(X1)) | X0(sk_Xv(X1)) | X1 != X0),
9.55/9.75	    inference('clc', [status(thm)], ['258', '169'])).
9.55/9.75	tff('260', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X2
9.55/9.75	       | X2(sk_Xv(X0))
9.55/9.75	       | X2(sk_Xy)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['259', '232'])).
9.55/9.75	tff('261', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
9.55/9.75	      (sk_Xq(sk_Xw(X0))
9.55/9.75	       | sk_Xq1(X1)
9.55/9.75	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.75	       | X2(sk_Xy)
9.55/9.75	       | X2(sk_Xv(X0))
9.55/9.75	       | X0 != X2),
9.55/9.75	    inference('simplify', [status(thm)], ['260'])).
9.55/9.75	tff('262', plain,
9.55/9.75	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.75	      (~ $true
9.55/9.75	       | X0 != X1
9.55/9.75	       | X1(sk_Xv(X0))
9.55/9.75	       | X1(sk_Xy)
9.55/9.75	       | sk_Xq1(sk_Xy1)
9.55/9.75	       | sk_Xq(sk_Xw(X0))),
9.55/9.75	    inference('sup-', [status(thm)], ['82', '261'])).
9.55/9.75	tff('263', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (sk_Xq(sk_Xw(X0))
9.55/9.76	       | sk_Xq1(sk_Xy1)
9.55/9.76	       | X1(sk_Xy)
9.55/9.76	       | X1(sk_Xv(X0))
9.55/9.76	       | X0 != X1),
9.55/9.76	    inference('simplify', [status(thm)], ['262'])).
9.55/9.76	tff('264', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (X0 != X1 | X1(sk_Xv(X0)) | X1(sk_Xy) | sk_Xq(sk_Xw(X0))),
9.55/9.76	    inference('clc', [status(thm)], ['263', '169'])).
9.55/9.76	tff('265', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (X1 != X0 | X1(sk_Xy) | sk_Xq(sk_Xw(X0)) | sk_Xq(sk_Xy) | X0 != sk_Xq),
9.55/9.76	    inference('clc', [status(thm)], ['254', '264'])).
9.55/9.76	tff('266', plain,
9.55/9.76	    ![X0 : a > $o, X3 : a]:
9.55/9.76	      (X0(sk_Xv(X0))
9.55/9.76	       | ~ X0(sk_Xw(X0))
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | sk_Xq1(X3)
9.55/9.76	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.76	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.76	tff('267', plain,
9.55/9.76	    ![X0 : a > $o, X3 : a, X4 : a > $o]:
9.55/9.76	      (X4 != X0
9.55/9.76	       | X0(sk_Xv(X4))
9.55/9.76	       | ~ X0(sk_Xw(X4))
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | sk_Xq1(X3)
9.55/9.76	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.76	    inference('ho.purify_applied_variable', [status(thm)], ['266'])).
9.55/9.76	tff('268', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | sk_Xq1(sk_Xy1)
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | ~ X0(sk_Xw(X1))
9.55/9.76	       | X0(sk_Xv(X1))
9.55/9.76	       | X1 != X0),
9.55/9.76	    inference('sup-', [status(thm)], ['82', '267'])).
9.55/9.76	tff('269', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (X1 != X0
9.55/9.76	       | X0(sk_Xv(X1))
9.55/9.76	       | ~ X0(sk_Xw(X1))
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | sk_Xq1(sk_Xy1)),
9.55/9.76	    inference('simplify', [status(thm)], ['268'])).
9.55/9.76	tff('270', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (X0(sk_Xy) | ~ X0(sk_Xw(X1)) | X0(sk_Xv(X1)) | X1 != X0),
9.55/9.76	    inference('clc', [status(thm)], ['269', '169'])).
9.55/9.76	tff('271', plain,
9.55/9.76	    ![X0 : a > $o, X3 : a]:
9.55/9.76	      (sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.76	       | ~ X0(sk_Xw(X0))
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | sk_Xq1(X3)
9.55/9.76	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.76	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.76	tff('272', plain,
9.55/9.76	    ![X0 : a > $o, X3 : a, X4 : a > $o, X5 : a > $o]:
9.55/9.76	      (X5 != X0
9.55/9.76	       | X4 != X0
9.55/9.76	       | sk_Xr(sk_Xv(X0), sk_Xw1(X0))
9.55/9.76	       | ~ X4(sk_Xw(X0))
9.55/9.76	       | X5(sk_Xy)
9.55/9.76	       | sk_Xq1(X3)
9.55/9.76	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.76	    inference('ho.purify_applied_variable', [status(thm)], ['271'])).
9.55/9.76	tff('273', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | sk_Xq1(sk_Xy1)
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | ~ X1(sk_Xw(X2))
9.55/9.76	       | sk_Xr(sk_Xv(X2), sk_Xw1(X2))
9.55/9.76	       | X1 != X2
9.55/9.76	       | X0 != X2),
9.55/9.76	    inference('sup-', [status(thm)], ['82', '272'])).
9.55/9.76	tff('274', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (X0 != X2
9.55/9.76	       | X1 != X2
9.55/9.76	       | sk_Xr(sk_Xv(X2), sk_Xw1(X2))
9.55/9.76	       | ~ X1(sk_Xw(X2))
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | sk_Xq1(sk_Xy1)),
9.55/9.76	    inference('simplify', [status(thm)], ['273'])).
9.55/9.76	tff('275', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (X0(sk_Xy)
9.55/9.76	       | ~ X1(sk_Xw(X2))
9.55/9.76	       | sk_Xr(sk_Xv(X2), sk_Xw1(X2))
9.55/9.76	       | X1 != X2
9.55/9.76	       | X0 != X2),
9.55/9.76	    inference('clc', [status(thm)], ['274', '169'])).
9.55/9.76	tff('276', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a, X2 : a > $o, X3 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | X2 != X0
9.55/9.76	       | X3 != X0
9.55/9.76	       | ~ X3(sk_Xw(X0))
9.55/9.76	       | X2(sk_Xy)
9.55/9.76	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.76	       | sk_Xq1(X1)
9.55/9.76	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.76	       | sk_Xq(sk_Xw1(X0))),
9.55/9.76	    inference('sup-', [status(thm)], ['275', '171'])).
9.55/9.76	tff('277', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a, X2 : a > $o, X3 : a > $o]:
9.55/9.76	      (sk_Xq(sk_Xw1(X0))
9.55/9.76	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.76	       | sk_Xq1(X1)
9.55/9.76	       | ~ sk_Xr(sk_Xx1, X1)
9.55/9.76	       | X2(sk_Xy)
9.55/9.76	       | ~ X3(sk_Xw(X0))
9.55/9.76	       | X3 != X0
9.55/9.76	       | X2 != X0),
9.55/9.76	    inference('simplify', [status(thm)], ['276'])).
9.55/9.76	tff('278', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | X0 != X1
9.55/9.76	       | X2 != X1
9.55/9.76	       | ~ X2(sk_Xw(X1))
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | sk_Xq1(sk_Xy1)
9.55/9.76	       | ~ sk_Xq(sk_Xv(X1))
9.55/9.76	       | sk_Xq(sk_Xw1(X1))),
9.55/9.76	    inference('sup-', [status(thm)], ['82', '277'])).
9.55/9.76	tff('279', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (sk_Xq(sk_Xw1(X1))
9.55/9.76	       | ~ sk_Xq(sk_Xv(X1))
9.55/9.76	       | sk_Xq1(sk_Xy1)
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | ~ X2(sk_Xw(X1))
9.55/9.76	       | X2 != X1
9.55/9.76	       | X0 != X1),
9.55/9.76	    inference('simplify', [status(thm)], ['278'])).
9.55/9.76	tff('280', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (X0 != X1
9.55/9.76	       | X2 != X1
9.55/9.76	       | ~ X2(sk_Xw(X1))
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | ~ sk_Xq(sk_Xv(X1))
9.55/9.76	       | sk_Xq(sk_Xw1(X1))),
9.55/9.76	    inference('clc', [status(thm)], ['279', '169'])).
9.55/9.76	tff('281', plain,
9.55/9.76	    ![X0 : a > $o, X3 : a]:
9.55/9.76	      (~ X0(sk_Xw1(X0))
9.55/9.76	       | ~ X0(sk_Xw(X0))
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | sk_Xq1(X3)
9.55/9.76	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.76	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.55/9.76	tff('282', plain,
9.55/9.76	    ![X0 : a > $o, X3 : a, X4 : a > $o]:
9.55/9.76	      (X4 != X0
9.55/9.76	       | ~ X0(sk_Xw1(X4))
9.55/9.76	       | ~ X0(sk_Xw(X4))
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | sk_Xq1(X3)
9.55/9.76	       | ~ sk_Xr(sk_Xx1, X3)),
9.55/9.76	    inference('ho.purify_applied_variable', [status(thm)], ['281'])).
9.55/9.76	tff('283', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | sk_Xq1(sk_Xy1)
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | ~ X0(sk_Xw(X1))
9.55/9.76	       | ~ X0(sk_Xw1(X1))
9.55/9.76	       | X1 != X0),
9.55/9.76	    inference('sup-', [status(thm)], ['82', '282'])).
9.55/9.76	tff('284', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (X1 != X0
9.55/9.76	       | ~ X0(sk_Xw1(X1))
9.55/9.76	       | ~ X0(sk_Xw(X1))
9.55/9.76	       | X0(sk_Xy)
9.55/9.76	       | sk_Xq1(sk_Xy1)),
9.55/9.76	    inference('simplify', [status(thm)], ['283'])).
9.55/9.76	tff('285', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (X0(sk_Xy) | ~ X0(sk_Xw(X1)) | ~ X0(sk_Xw1(X1)) | X1 != X0),
9.55/9.76	    inference('clc', [status(thm)], ['284', '169'])).
9.55/9.76	tff('286', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | ~ sk_Xq(sk_Xv(X0))
9.55/9.76	       | X1(sk_Xy)
9.55/9.76	       | ~ X2(sk_Xw(X0))
9.55/9.76	       | X2 != X0
9.55/9.76	       | X1 != X0
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.76	       | sk_Xq(sk_Xy)),
9.55/9.76	    inference('sup-', [status(thm)], ['280', '285'])).
9.55/9.76	tff('287', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (sk_Xq(sk_Xy)
9.55/9.76	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | X1 != X0
9.55/9.76	       | X2 != X0
9.55/9.76	       | ~ X2(sk_Xw(X0))
9.55/9.76	       | X1(sk_Xy)
9.55/9.76	       | ~ sk_Xq(sk_Xv(X0))),
9.55/9.76	    inference('simplify', [status(thm)], ['286'])).
9.55/9.76	tff('288', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (~ sk_Xq(sk_Xv(X0))
9.55/9.76	       | X1(sk_Xy)
9.55/9.76	       | ~ X2(sk_Xw(X0))
9.55/9.76	       | X2 != X0
9.55/9.76	       | X1 != X0
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | sk_Xq(sk_Xy)),
9.55/9.76	    inference('clc', [status(thm)], ['287', '265'])).
9.55/9.76	tff('289', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.76	       | sk_Xq(sk_Xy)
9.55/9.76	       | sk_Xq(sk_Xy)
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | X1 != X0
9.55/9.76	       | X2 != X0
9.55/9.76	       | ~ X2(sk_Xw(X0))
9.55/9.76	       | X1(sk_Xy)),
9.55/9.76	    inference('sup-', [status(thm)], ['270', '288'])).
9.55/9.76	tff('290', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (X1(sk_Xy)
9.55/9.76	       | ~ X2(sk_Xw(X0))
9.55/9.76	       | X2 != X0
9.55/9.76	       | X1 != X0
9.55/9.76	       | sk_Xq(sk_Xy)
9.55/9.76	       | ~ sk_Xq(sk_Xw(X0))
9.55/9.76	       | X0 != sk_Xq),
9.55/9.76	    inference('simplify', [status(thm)], ['289'])).
9.55/9.76	tff('291', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
9.55/9.76	      (X0 != sk_Xq
9.55/9.76	       | sk_Xq(sk_Xy)
9.55/9.76	       | X1 != X0
9.55/9.76	       | X2 != X0
9.55/9.76	       | ~ X2(sk_Xw(X0))
9.55/9.76	       | X1(sk_Xy)),
9.55/9.76	    inference('clc', [status(thm)], ['290', '265'])).
9.55/9.76	tff('292', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | sk_Xq(sk_Xy)
9.55/9.76	       | ~ X0(sk_Xw(X1))
9.55/9.76	       | X0 != X1
9.55/9.76	       | sk_Xq != X1
9.55/9.76	       | X1 != sk_Xq),
9.55/9.76	    inference('eq_fact', [status(thm)], ['291'])).
9.55/9.76	tff('293', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (sk_Xq != X1 | X0 != X1 | ~ X0(sk_Xw(X1)) | sk_Xq(sk_Xy)),
9.55/9.76	    inference('simplify', [status(thm)], ['292'])).
9.55/9.76	tff('294', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | sk_Xq(sk_Xy)
9.55/9.76	       | X1(sk_Xy)
9.55/9.76	       | X1 != X0
9.55/9.76	       | sk_Xq(sk_Xy)
9.55/9.76	       | sk_Xq != X0
9.55/9.76	       | sk_Xq != X0),
9.55/9.76	    inference('sup-', [status(thm)], ['265', '293'])).
9.55/9.76	tff('295', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (X1 != X0 | X1(sk_Xy) | sk_Xq(sk_Xy) | X0 != sk_Xq),
9.55/9.76	    inference('simplify', [status(thm)], ['294'])).
9.55/9.76	tff('296', plain,
9.55/9.76	    ![X0 : a > $o]: (~ $true | X0 != sk_Xq | sk_Xq(sk_Xy) | sk_Xq != X0),
9.55/9.76	    inference('eq_fact', [status(thm)], ['295'])).
9.55/9.76	tff('297', plain, ![X0 : a > $o]: (sk_Xq(sk_Xy) | X0 != sk_Xq),
9.55/9.76	    inference('simplify', [status(thm)], ['296'])).
9.55/9.76	tff('298', plain, sk_Xq(sk_Xy), inference('eq_res', [status(thm)], ['297'])).
9.55/9.76	tff('299', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | ~ $true
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | sk_Xq(sk_Xz)
9.55/9.76	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | X1 != X0
9.55/9.76	       | sk_Xq != X0
9.55/9.76	       | X1(sk_Xz)),
9.55/9.76	    inference('demod', [status(thm)], ['226', '298'])).
9.55/9.76	tff('300', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (X1(sk_Xz)
9.55/9.76	       | X1 != X0
9.55/9.76	       | ~ sk_Xq(sk_Xw2(X0))
9.55/9.76	       | sk_Xq(sk_Xz)
9.55/9.76	       | X0 != sk_Xq),
9.55/9.76	    inference('simplify', [status(thm)], ['299'])).
9.55/9.76	tff('301', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | ~ sk_Xq(sk_Xy)
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | sk_Xq(sk_Xz)
9.55/9.76	       | X1 != X0
9.55/9.76	       | X1(sk_Xz)),
9.55/9.76	    inference('sup-', [status(thm)], ['202', '300'])).
9.55/9.76	tff('302', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (~ $true
9.55/9.76	       | ~ $true
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | X0 != sk_Xq
9.55/9.76	       | sk_Xq(sk_Xz)
9.55/9.76	       | X1 != X0
9.55/9.76	       | X1(sk_Xz)),
9.55/9.76	    inference('demod', [status(thm)], ['301', '298'])).
9.55/9.76	tff('303', plain,
9.55/9.76	    ![X0 : a > $o, X1 : a > $o]:
9.55/9.76	      (X1(sk_Xz) | X1 != X0 | sk_Xq(sk_Xz) | X0 != sk_Xq),
9.55/9.76	    inference('simplify', [status(thm)], ['302'])).
9.55/9.76	tff('304', plain,
9.55/9.76	    ![X0 : a > $o]: (~ $true | X0 != sk_Xq | sk_Xq(sk_Xz) | sk_Xq != X0),
9.55/9.76	    inference('eq_fact', [status(thm)], ['303'])).
9.55/9.76	tff('305', plain, ![X0 : a > $o]: (sk_Xq(sk_Xz) | X0 != sk_Xq),
9.55/9.76	    inference('simplify', [status(thm)], ['304'])).
9.55/9.76	tff('306', plain, sk_Xq(sk_Xz), inference('eq_res', [status(thm)], ['305'])).
9.55/9.76	tff('307', plain, ![X0 : a]: (~ $true | ~ sk_Xr(sk_Xx1, X0) | sk_Xq1(X0)),
9.55/9.76	    inference('sup-', [status(thm)], ['306', '192'])).
9.55/9.76	tff('308', plain, ![X0 : a]: (sk_Xq1(X0) | ~ sk_Xr(sk_Xx1, X0)),
9.55/9.76	    inference('simplify', [status(thm)], ['307'])).
9.55/9.76	tff('309', plain, (~ $true | sk_Xq1(sk_Xy1)),
9.55/9.76	    inference('sup-', [status(thm)], ['82', '308'])).
9.55/9.76	tff('310', plain, sk_Xq1(sk_Xy1),
9.55/9.76	    inference('simplify', [status(thm)], ['309'])).
9.55/9.76	tff('311', plain, ~ $true, inference('sup-', [status(thm)], ['310', '169'])).
9.55/9.76	tff('312', plain, $false, inference('simplify', [status(thm)], ['311'])).
9.55/9.76	
9.55/9.76	% SZS output end Refutation
9.55/9.76	EOF
