0.00/0.01	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n073.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 15:50:09 CST 2018
0.44/0.69	% done 526 iterations in 0.479s
0.44/0.69	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
0.44/0.69	% SZS output start Refutation
0.44/0.69	tff(cPROB757, conjecture,
0.44/0.69	  (((![Xx1,Xx2,Xy1,Xy2]:
0.44/0.69	       ((el1(Xx1,cHH_2) & el1(Xx2,cHH_2) & el1(Xy1,cHH_2) & el1(Xy2,cHH_2) & 
0.44/0.69	         (Xx1 = Xx2) & (Xy1 = Xy2)) =>
0.44/0.69	        (cTIMES(Xx1,Xy1) = cTIMES(Xx2,Xy2)))) & 
0.44/0.69	    (![Xx1,Xx2]:
0.44/0.69	       ((el1(Xx1,cSS_PRIME) & el1(Xx2,cSS_PRIME)) =>
0.44/0.69	        el1(cTIMES(Xx1,Xx2),cSS_PRIME))) & 
0.44/0.69	    (![Xx1,Xx2,Xy1,Xy2]:
0.44/0.69	       ((el1(Xx1,cHH_1) & el1(Xx2,cHH_1) & el1(Xy1,cHH_1) & el1(Xy2,cHH_1) & 
0.44/0.69	         (Xx1 = Xx2) & (Xy1 = Xy2)) =>
0.44/0.69	        (cTIMES(Xx1,Xy1) = cTIMES(Xx2,Xy2)))) & 
0.44/0.69	    (![Xphi:($i > $i)]:
0.44/0.69	       (cHOM_FROM_SS_PRIME(Xphi) <=>
0.44/0.69	        (![Xx,Xy]:
0.44/0.69	           ((el1(Xx,cSS_PRIME) & el1(Xy,cSS_PRIME)) =>
0.44/0.69	            (Xphi(cTIMES(Xx,Xy)) = cTIMES(Xphi(Xx),Xphi(Xy))))))) & 
0.44/0.69	    (cHOM_FROM_HH_1(cBIGPHI) <=>
0.44/0.69	     (![Xx,Xy]:
0.44/0.69	        ((el1(Xx,cHH_1) & el1(Xy,cHH_1)) =>
0.44/0.69	         (cBIGPHI(cTIMES(Xx,Xy)) = cTIMES(cBIGPHI(Xx),cBIGPHI(Xy)))))) & 
0.44/0.69	    (![Xx,Xy]: ((el1(Xx,cHH_1) & el1(Xy,cHH_1)) => el1(cTIMES(Xx,Xy),cHH_1))) & 
0.44/0.69	    (![Xx]: (el1(Xx,cSS_PRIME) => el1(cPHI_2(Xx),cHH_2))) & 
0.44/0.69	    (![Xx]: (el1(Xx,cHH_1) => el1(cBIGPHI(Xx),cHH_2))) & 
0.44/0.69	    (![Xx]: (el1(Xx,cSS_PRIME) => el1(cPHI_1(Xx),cHH_1))) & 
0.44/0.69	    (![Xx,Xy]:
0.44/0.69	       ((el1(Xx,cHH_1) & el1(Xy,cHH_1) & (Xx = Xy)) =>
0.44/0.69	        (cBIGHI(Xx) = cBIGPHI(Xy)))) & 
0.44/0.69	    (![Xx]: (el1(Xx,cSS_PRIME) => (cBIGPHI(cPHI_1(Xx)) = cPHI_2(Xx)))) & 
0.44/0.69	    (![Xy]:
0.44/0.69	       (el1(Xy,cHH_1) => (?[Xx]: (el1(Xx,cSS_PRIME) & (cPHI_1(Xx) = Xy))))) & 
0.44/0.69	    cHOM_FROM_SS_PRIME(cPHI_1) & cHOM_FROM_SS_PRIME(cPHI_2)) =>
0.44/0.69	   cHOM_FROM_HH_1(cBIGPHI))).
0.44/0.69	tff(zf_stmt_0, type, zip_tseitin3 : ($i * $i) > $o).
0.44/0.69	tff(zf_stmt_1, axiom,
0.44/0.69	  (zip_tseitin3(Xy,Xx) <=>
0.44/0.69	   (zip_tseitin2(Xy,Xx) =>
0.44/0.69	    (cBIGPHI(cTIMES(Xx,Xy)) = cTIMES(cBIGPHI(Xx),cBIGPHI(Xy)))))).
0.44/0.69	tff(zf_stmt_2, type, zip_tseitin2 : ($i * $i) > $o).
0.44/0.69	tff(zf_stmt_3, axiom,
0.44/0.69	  (zip_tseitin2(Xy,Xx) <=> (el1(Xy,cHH_1) & el1(Xx,cHH_1)))).
0.44/0.69	tff(zf_stmt_4, type, zip_tseitin1 : ($i * $i * $i > $i) > $o).
0.44/0.69	tff(zf_stmt_5, axiom,
0.44/0.69	  (zip_tseitin1(Xy,Xx,Xphi) <=>
0.44/0.69	   (zip_tseitin0(Xy,Xx) => (Xphi(cTIMES(Xx,Xy)) = cTIMES(Xphi(Xx),Xphi(Xy)))))).
0.44/0.69	tff(zf_stmt_6, type, zip_tseitin0 : ($i * $i) > $o).
0.44/0.69	tff(zf_stmt_7, axiom,
0.44/0.69	  (zip_tseitin0(Xy,Xx) <=> (el1(Xy,cSS_PRIME) & el1(Xx,cSS_PRIME)))).
0.44/0.69	tff(zf_stmt_8, conjecture,
0.44/0.69	  ((cHOM_FROM_SS_PRIME(cPHI_2) & cHOM_FROM_SS_PRIME(cPHI_1) & 
0.44/0.69	    (![Xy]:
0.44/0.69	       (el1(Xy,cHH_1) => (?[Xx]: ((cPHI_1(Xx) = Xy) & el1(Xx,cSS_PRIME))))) & 
0.44/0.69	    (![Xx]: (el1(Xx,cSS_PRIME) => (cBIGPHI(cPHI_1(Xx)) = cPHI_2(Xx)))) & 
0.44/0.69	    (![Xx,Xy]:
0.44/0.69	       (((Xx = Xy) & el1(Xy,cHH_1) & el1(Xx,cHH_1)) =>
0.44/0.69	        (cBIGHI(Xx) = cBIGPHI(Xy)))) & 
0.44/0.69	    (![Xx]: (el1(Xx,cSS_PRIME) => el1(cPHI_1(Xx),cHH_1))) & 
0.44/0.69	    (![Xx]: (el1(Xx,cHH_1) => el1(cBIGPHI(Xx),cHH_2))) & 
0.44/0.69	    (![Xx]: (el1(Xx,cSS_PRIME) => el1(cPHI_2(Xx),cHH_2))) & 
0.44/0.69	    (![Xx,Xy]: ((el1(Xy,cHH_1) & el1(Xx,cHH_1)) => el1(cTIMES(Xx,Xy),cHH_1))) & 
0.44/0.69	    (cHOM_FROM_HH_1(cBIGPHI) <=> (![Xx,Xy]: zip_tseitin3(Xy,Xx))) & 
0.44/0.69	    (![Xphi:($i > $i)]:
0.44/0.69	       (cHOM_FROM_SS_PRIME(Xphi) <=> (![Xx,Xy]: zip_tseitin1(Xy,Xx,Xphi)))) & 
0.44/0.69	    (![Xx1,Xx2,Xy1,Xy2]:
0.44/0.69	       (((Xy1 = Xy2) & (Xx1 = Xx2) & el1(Xy2,cHH_1) & el1(Xy1,cHH_1) & 
0.44/0.69	         el1(Xx2,cHH_1) & el1(Xx1,cHH_1)) =>
0.44/0.69	        (cTIMES(Xx1,Xy1) = cTIMES(Xx2,Xy2)))) & 
0.44/0.69	    (![Xx1,Xx2]:
0.44/0.69	       ((el1(Xx2,cSS_PRIME) & el1(Xx1,cSS_PRIME)) =>
0.44/0.69	        el1(cTIMES(Xx1,Xx2),cSS_PRIME))) & 
0.44/0.69	    (![Xx1,Xx2,Xy1,Xy2]:
0.44/0.69	       (((Xy1 = Xy2) & (Xx1 = Xx2) & el1(Xy2,cHH_2) & el1(Xy1,cHH_2) & 
0.44/0.69	         el1(Xx2,cHH_2) & el1(Xx1,cHH_2)) =>
0.44/0.69	        (cTIMES(Xx1,Xy1) = cTIMES(Xx2,Xy2))))) =>
0.44/0.69	   cHOM_FROM_HH_1(cBIGPHI))).
0.44/0.69	tff(zf_stmt_9, negated_conjecture,
0.44/0.69	  (~
0.44/0.69	    ((cHOM_FROM_SS_PRIME(cPHI_2) & cHOM_FROM_SS_PRIME(cPHI_1) & 
0.44/0.69	      (![Xy]:
0.44/0.69	         (el1(Xy,cHH_1) => (?[Xx]: ((cPHI_1(Xx) = Xy) & el1(Xx,cSS_PRIME))))) & 
0.44/0.69	      (![Xx]: (el1(Xx,cSS_PRIME) => (cBIGPHI(cPHI_1(Xx)) = cPHI_2(Xx)))) & 
0.44/0.69	      (![Xx,Xy]:
0.44/0.69	         (((Xx = Xy) & el1(Xy,cHH_1) & el1(Xx,cHH_1)) =>
0.44/0.69	          (cBIGHI(Xx) = cBIGPHI(Xy)))) & 
0.44/0.69	      (![Xx]: (el1(Xx,cSS_PRIME) => el1(cPHI_1(Xx),cHH_1))) & 
0.44/0.69	      (![Xx]: (el1(Xx,cHH_1) => el1(cBIGPHI(Xx),cHH_2))) & 
0.44/0.69	      (![Xx]: (el1(Xx,cSS_PRIME) => el1(cPHI_2(Xx),cHH_2))) & 
0.44/0.69	      (![Xx,Xy]:
0.44/0.69	         ((el1(Xy,cHH_1) & el1(Xx,cHH_1)) => el1(cTIMES(Xx,Xy),cHH_1))) & 
0.44/0.69	      (cHOM_FROM_HH_1(cBIGPHI) <=> (![Xx,Xy]: zip_tseitin3(Xy,Xx))) & 
0.44/0.69	      (![Xphi:($i > $i)]:
0.44/0.69	         (cHOM_FROM_SS_PRIME(Xphi) <=> (![Xx,Xy]: zip_tseitin1(Xy,Xx,Xphi)))) & 
0.44/0.69	      (![Xx1,Xx2,Xy1,Xy2]:
0.44/0.69	         (((Xy1 = Xy2) & (Xx1 = Xx2) & el1(Xy2,cHH_1) & el1(Xy1,cHH_1) & 
0.44/0.69	           el1(Xx2,cHH_1) & el1(Xx1,cHH_1)) =>
0.44/0.69	          (cTIMES(Xx1,Xy1) = cTIMES(Xx2,Xy2)))) & 
0.44/0.69	      (![Xx1,Xx2]:
0.44/0.69	         ((el1(Xx2,cSS_PRIME) & el1(Xx1,cSS_PRIME)) =>
0.44/0.69	          el1(cTIMES(Xx1,Xx2),cSS_PRIME))) & 
0.44/0.69	      (![Xx1,Xx2,Xy1,Xy2]:
0.44/0.69	         (((Xy1 = Xy2) & (Xx1 = Xx2) & el1(Xy2,cHH_2) & el1(Xy1,cHH_2) & 
0.44/0.69	           el1(Xx2,cHH_2) & el1(Xx1,cHH_2)) =>
0.44/0.69	          (cTIMES(Xx1,Xy1) = cTIMES(Xx2,Xy2))))) =>
0.44/0.69	     cHOM_FROM_HH_1(cBIGPHI)))).
0.44/0.69	tff('0', plain, ![X5]: (cPHI_1(sk_Xx2(X5)) = X5 | ~ el1(X5, cHH_1)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.44/0.69	tff('1', plain,
0.44/0.69	    ![X6]: (cBIGPHI(cPHI_1(X6)) = cPHI_2(X6) | ~ el1(X6, cSS_PRIME)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.44/0.69	tff('2', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (zip_tseitin0(X0, X1) | ~ el1(X1, cSS_PRIME) | ~ el1(X0, cSS_PRIME)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.44/0.69	tff('3', plain, cHOM_FROM_SS_PRIME(cPHI_1),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.44/0.69	tff('4', plain,
0.44/0.69	    ![X17, X18, X19 : $i > $i]:
0.44/0.69	      (zip_tseitin1(X17, X18, X19) | ~ cHOM_FROM_SS_PRIME(X19)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.44/0.69	tff('5', plain, ![X0, X1]: (~ $true | zip_tseitin1(X1, X0, cPHI_1)),
0.44/0.69	    inference('sup-', [status(thm)], ['3', '4'])).
0.44/0.69	tff('6', plain, ![X0, X1]: zip_tseitin1(X1, X0, cPHI_1),
0.44/0.69	    inference('simplify', [status(thm)], ['5'])).
0.44/0.69	tff('7', plain,
0.44/0.69	    ![X0, X1, X2 : $i > $i]:
0.44/0.69	      (~ zip_tseitin0(X0, X1)
0.44/0.69	       | X2(cTIMES(X1, X0)) = cTIMES(X2(X1), X2(X0))
0.44/0.69	       | ~ zip_tseitin1(X0, X1, X2)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.44/0.69	tff('8', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ $true
0.44/0.69	       | cPHI_1(cTIMES(X0, X1)) = cTIMES(cPHI_1(X0), cPHI_1(X1))
0.44/0.69	       | ~ zip_tseitin0(X1, X0)),
0.44/0.69	    inference('sup-', [status(thm)], ['6', '7'])).
0.44/0.69	tff('9', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ zip_tseitin0(X1, X0)
0.44/0.69	       | cPHI_1(cTIMES(X0, X1)) = cTIMES(cPHI_1(X0), cPHI_1(X1))),
0.44/0.69	    inference('simplify', [status(thm)], ['8'])).
0.44/0.69	tff('10', plain, cHOM_FROM_SS_PRIME(cPHI_2),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.44/0.69	tff('11', plain, ![X0, X1]: (~ $true | zip_tseitin1(X1, X0, cPHI_2)),
0.44/0.69	    inference('sup-', [status(thm)], ['10', '4'])).
0.44/0.69	tff('12', plain, ![X0, X1]: zip_tseitin1(X1, X0, cPHI_2),
0.44/0.69	    inference('simplify', [status(thm)], ['11'])).
0.44/0.69	tff('13', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ $true
0.44/0.69	       | cPHI_2(cTIMES(X0, X1)) = cTIMES(cPHI_2(X0), cPHI_2(X1))
0.44/0.69	       | ~ zip_tseitin0(X1, X0)),
0.44/0.69	    inference('sup-', [status(thm)], ['12', '7'])).
0.44/0.69	tff('14', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ zip_tseitin0(X1, X0)
0.44/0.69	       | cPHI_2(cTIMES(X0, X1)) = cTIMES(cPHI_2(X0), cPHI_2(X1))),
0.44/0.69	    inference('simplify', [status(thm)], ['13'])).
0.44/0.69	tff('15', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (cBIGPHI(cPHI_1(cTIMES(X1, X0))) = cTIMES(cPHI_2(X1), cPHI_2(X0))
0.44/0.69	       | ~ zip_tseitin0(X0, X1)
0.44/0.69	       | ~ el1(cTIMES(X1, X0), cSS_PRIME)),
0.44/0.69	    inference('sup+', [status(thm)], ['14', '1'])).
0.44/0.69	tff('16', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (cBIGPHI(cTIMES(cPHI_1(X1), cPHI_1(X0)))
0.44/0.69	        = cTIMES(cPHI_2(X1), cPHI_2(X0))
0.44/0.69	       | ~ zip_tseitin0(X0, X1)
0.44/0.69	       | ~ el1(cTIMES(X1, X0), cSS_PRIME)
0.44/0.69	       | ~ zip_tseitin0(X0, X1)),
0.44/0.69	    inference('sup+', [status(thm)], ['9', '15'])).
0.44/0.69	tff('17', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ el1(cTIMES(X1, X0), cSS_PRIME)
0.44/0.69	       | ~ zip_tseitin0(X0, X1)
0.44/0.69	       | cBIGPHI(cTIMES(cPHI_1(X1), cPHI_1(X0)))
0.44/0.69	          = cTIMES(cPHI_2(X1), cPHI_2(X0))),
0.44/0.69	    inference('simplify', [status(thm)], ['16'])).
0.44/0.69	tff('18', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ $true
0.44/0.69	       | ~ el1(X1, cSS_PRIME)
0.44/0.69	       | ~ el1(X0, cSS_PRIME)
0.44/0.69	       | cBIGPHI(cTIMES(cPHI_1(X0), cPHI_1(X1)))
0.44/0.69	          = cTIMES(cPHI_2(X0), cPHI_2(X1))
0.44/0.69	       | ~ el1(cTIMES(X0, X1), cSS_PRIME)),
0.44/0.69	    inference('sup-', [status(thm)], ['2', '17'])).
0.44/0.69	tff('19', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ el1(cTIMES(X0, X1), cSS_PRIME)
0.44/0.69	       | cBIGPHI(cTIMES(cPHI_1(X0), cPHI_1(X1)))
0.44/0.69	          = cTIMES(cPHI_2(X0), cPHI_2(X1))
0.44/0.69	       | ~ el1(X0, cSS_PRIME)
0.44/0.69	       | ~ el1(X1, cSS_PRIME)),
0.44/0.69	    inference('simplify', [status(thm)], ['18'])).
0.44/0.69	tff('20', plain,
0.44/0.69	    ![X24, X25]:
0.44/0.69	      (~ el1(X24, cSS_PRIME)
0.44/0.69	       | ~ el1(X25, cSS_PRIME)
0.44/0.69	       | el1(cTIMES(X24, X25), cSS_PRIME)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.44/0.69	tff('21', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ el1(X1, cSS_PRIME)
0.44/0.69	       | ~ el1(X0, cSS_PRIME)
0.44/0.69	       | cBIGPHI(cTIMES(cPHI_1(X0), cPHI_1(X1)))
0.44/0.69	          = cTIMES(cPHI_2(X0), cPHI_2(X1))),
0.44/0.69	    inference('clc', [status(thm)], ['19', '20'])).
0.44/0.69	tff('22', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (cBIGPHI(cTIMES(cPHI_1(X0), cPHI_1(X1)))
0.44/0.69	        = cTIMES(cBIGPHI(cPHI_1(X0)), cPHI_2(X1))
0.44/0.69	       | ~ el1(X0, cSS_PRIME)
0.44/0.69	       | ~ el1(X0, cSS_PRIME)
0.44/0.69	       | ~ el1(X1, cSS_PRIME)),
0.44/0.69	    inference('sup+', [status(thm)], ['1', '21'])).
0.44/0.69	tff('23', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ el1(X1, cSS_PRIME)
0.44/0.69	       | ~ el1(X0, cSS_PRIME)
0.44/0.69	       | cBIGPHI(cTIMES(cPHI_1(X0), cPHI_1(X1)))
0.44/0.69	          = cTIMES(cBIGPHI(cPHI_1(X0)), cPHI_2(X1))),
0.44/0.69	    inference('simplify', [status(thm)], ['22'])).
0.44/0.69	tff('24', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (cBIGPHI(cTIMES(X0, cPHI_1(X1)))
0.44/0.69	        = cTIMES(cBIGPHI(cPHI_1(sk_Xx2(X0))), cPHI_2(X1))
0.44/0.69	       | ~ el1(X0, cHH_1)
0.44/0.69	       | ~ el1(sk_Xx2(X0), cSS_PRIME)
0.44/0.69	       | ~ el1(X1, cSS_PRIME)),
0.44/0.69	    inference('sup+', [status(thm)], ['0', '23'])).
0.44/0.69	tff('25', plain, ![X5]: (el1(sk_Xx2(X5), cSS_PRIME) | ~ el1(X5, cHH_1)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.44/0.69	tff('26', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ el1(X1, cSS_PRIME)
0.44/0.69	       | ~ el1(X0, cHH_1)
0.44/0.69	       | cBIGPHI(cTIMES(X0, cPHI_1(X1)))
0.44/0.69	          = cTIMES(cBIGPHI(cPHI_1(sk_Xx2(X0))), cPHI_2(X1))),
0.44/0.69	    inference('clc', [status(thm)], ['24', '25'])).
0.44/0.69	tff('27', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (cBIGPHI(cTIMES(X0, cPHI_1(X1))) = cTIMES(cBIGPHI(X0), cPHI_2(X1))
0.44/0.69	       | ~ el1(X0, cHH_1)
0.44/0.69	       | ~ el1(X0, cHH_1)
0.44/0.69	       | ~ el1(X1, cSS_PRIME)),
0.44/0.69	    inference('sup+', [status(thm)], ['0', '26'])).
0.44/0.69	tff('28', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ el1(X1, cSS_PRIME)
0.44/0.69	       | ~ el1(X0, cHH_1)
0.44/0.69	       | cBIGPHI(cTIMES(X0, cPHI_1(X1))) = cTIMES(cBIGPHI(X0), cPHI_2(X1))),
0.44/0.69	    inference('simplify', [status(thm)], ['27'])).
0.44/0.69	tff('29', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (cBIGPHI(cTIMES(X1, cPHI_1(X0)))
0.44/0.69	        = cTIMES(cBIGPHI(X1), cBIGPHI(cPHI_1(X0)))
0.44/0.69	       | ~ el1(X0, cSS_PRIME)
0.44/0.69	       | ~ el1(X1, cHH_1)
0.44/0.69	       | ~ el1(X0, cSS_PRIME)),
0.44/0.69	    inference('sup+', [status(thm)], ['1', '28'])).
0.44/0.69	tff('30', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ el1(X1, cHH_1)
0.44/0.69	       | ~ el1(X0, cSS_PRIME)
0.44/0.69	       | cBIGPHI(cTIMES(X1, cPHI_1(X0)))
0.44/0.69	          = cTIMES(cBIGPHI(X1), cBIGPHI(cPHI_1(X0)))),
0.44/0.69	    inference('simplify', [status(thm)], ['29'])).
0.44/0.69	tff('31', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (cBIGPHI(cTIMES(X1, X0))
0.44/0.69	        = cTIMES(cBIGPHI(X1), cBIGPHI(cPHI_1(sk_Xx2(X0))))
0.44/0.69	       | ~ el1(X0, cHH_1)
0.44/0.69	       | ~ el1(sk_Xx2(X0), cSS_PRIME)
0.44/0.69	       | ~ el1(X1, cHH_1)),
0.44/0.69	    inference('sup+', [status(thm)], ['0', '30'])).
0.44/0.69	tff('32', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ el1(X1, cHH_1)
0.44/0.69	       | ~ el1(X0, cHH_1)
0.44/0.69	       | cBIGPHI(cTIMES(X1, X0))
0.44/0.69	          = cTIMES(cBIGPHI(X1), cBIGPHI(cPHI_1(sk_Xx2(X0))))),
0.44/0.69	    inference('clc', [status(thm)], ['31', '25'])).
0.44/0.69	tff('33', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (cBIGPHI(cTIMES(X1, X0)) = cTIMES(cBIGPHI(X1), cBIGPHI(X0))
0.44/0.69	       | ~ el1(X0, cHH_1)
0.44/0.69	       | ~ el1(X0, cHH_1)
0.44/0.69	       | ~ el1(X1, cHH_1)),
0.44/0.69	    inference('sup+', [status(thm)], ['0', '32'])).
0.44/0.69	tff('34', plain,
0.44/0.69	    ![X0, X1]:
0.44/0.69	      (~ el1(X1, cHH_1)
0.44/0.69	       | ~ el1(X0, cHH_1)
0.44/0.69	       | cBIGPHI(cTIMES(X1, X0)) = cTIMES(cBIGPHI(X1), cBIGPHI(X0))),
0.44/0.69	    inference('simplify', [status(thm)], ['33'])).
0.44/0.69	tff('35', plain,
0.44/0.69	    ![X3, X4]:
0.44/0.69	      (zip_tseitin3(X3, X4)
0.44/0.69	       | cBIGPHI(cTIMES(X4, X3)) != cTIMES(cBIGPHI(X4), cBIGPHI(X3))),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.44/0.69	tff('36', plain, (cHOM_FROM_HH_1(cBIGPHI) | ~ zip_tseitin3(sk_Xy1, sk_Xx1)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.44/0.69	tff('37', plain, ~ cHOM_FROM_HH_1(cBIGPHI),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.44/0.69	tff('38', plain, ~ zip_tseitin3(sk_Xy1, sk_Xx1),
0.44/0.69	    inference('clc', [status(thm)], ['36', '37'])).
0.44/0.69	tff('39', plain,
0.44/0.69	    (~ $true
0.44/0.69	     | cBIGPHI(cTIMES(sk_Xx1, sk_Xy1))
0.44/0.69	        != cTIMES(cBIGPHI(sk_Xx1), cBIGPHI(sk_Xy1))),
0.44/0.69	    inference('sup-', [status(thm)], ['35', '38'])).
0.44/0.69	tff('40', plain,
0.44/0.69	    cBIGPHI(cTIMES(sk_Xx1, sk_Xy1))
0.44/0.69	     != cTIMES(cBIGPHI(sk_Xx1), cBIGPHI(sk_Xy1)),
0.44/0.69	    inference('simplify', [status(thm)], ['39'])).
0.44/0.69	tff('41', plain,
0.44/0.69	    (cTIMES(cBIGPHI(sk_Xx1), cBIGPHI(sk_Xy1))
0.44/0.69	      != cTIMES(cBIGPHI(sk_Xx1), cBIGPHI(sk_Xy1))
0.44/0.69	     | ~ el1(sk_Xy1, cHH_1)
0.44/0.69	     | ~ el1(sk_Xx1, cHH_1)),
0.44/0.69	    inference('sup-', [status(thm)], ['34', '40'])).
0.44/0.69	tff('42', plain, ![X3, X4]: (zip_tseitin3(X3, X4) | zip_tseitin2(X3, X4)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.44/0.69	tff('43', plain, (~ $true | zip_tseitin2(sk_Xy1, sk_Xx1)),
0.44/0.69	    inference('sup-', [status(thm)], ['42', '38'])).
0.44/0.69	tff('44', plain, zip_tseitin2(sk_Xy1, sk_Xx1),
0.44/0.69	    inference('simplify', [status(thm)], ['43'])).
0.44/0.69	tff('45', plain, ![X3, X4]: (el1(X3, cHH_1) | ~ zip_tseitin2(X3, X4)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.44/0.69	tff('46', plain, (~ $true | el1(sk_Xy1, cHH_1)),
0.44/0.69	    inference('sup-', [status(thm)], ['44', '45'])).
0.44/0.69	tff('47', plain, el1(sk_Xy1, cHH_1),
0.44/0.69	    inference('simplify', [status(thm)], ['46'])).
0.44/0.69	tff('48', plain, ![X3, X4]: (el1(X4, cHH_1) | ~ zip_tseitin2(X3, X4)),
0.44/0.69	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.44/0.69	tff('49', plain, (~ $true | el1(sk_Xx1, cHH_1)),
0.44/0.69	    inference('sup-', [status(thm)], ['44', '48'])).
0.44/0.69	tff('50', plain, el1(sk_Xx1, cHH_1),
0.44/0.69	    inference('simplify', [status(thm)], ['49'])).
0.44/0.69	tff('51', plain,
0.44/0.69	    (cTIMES(cBIGPHI(sk_Xx1), cBIGPHI(sk_Xy1))
0.44/0.69	      != cTIMES(cBIGPHI(sk_Xx1), cBIGPHI(sk_Xy1))
0.44/0.69	     | ~ $true
0.44/0.69	     | ~ $true),
0.44/0.69	    inference('demod', [status(thm)], ['41', '47', '50'])).
0.44/0.69	tff('52', plain, $false, inference('simplify', [status(thm)], ['51'])).
0.44/0.69	
0.44/0.69	% SZS output end Refutation
0.44/0.69	EOF
