0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_int
0.00/0.00	% Ordering    : kbo
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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n060.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:42:23 CST 2018
23.35/23.60	% done 1280 iterations in 23.397s
23.35/23.60	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
23.35/23.60	% SZS output start Refutation
23.35/23.60	tff('thm/iterate/MONOIDAL_AC_', conjecture,
23.35/23.60	  (![A:$tType,A0:((A * A) > A)]:
23.35/23.60	     ('const/iterate/monoidal'(A,A0) =>
23.35/23.60	      ((![A1:A,A2:A,A3:A]: (A0(A1,A0(A2,A3)) = A0(A2,A0(A1,A3)))) & 
23.35/23.60	       (![A1:A,A2:A,A3:A]: (A0(A0(A1,A2),A3) = A0(A1,A0(A2,A3)))) & 
23.35/23.60	       (![A1:A,A2:A]: (A0(A1,A2) = A0(A2,A1))) & 
23.35/23.60	       (![A1:A]: (A0(A1,'const/iterate/neutral'(A,A0)) = A1)) & 
23.35/23.60	       (![A1:A]: (A0('const/iterate/neutral'(A,A0),A1) = A1)))))).
23.35/23.60	tff(zf_stmt_0, negated_conjecture,
23.35/23.60	  (~
23.35/23.60	    (![A:$tType,A0:((A * A) > A)]:
23.35/23.60	       ('const/iterate/monoidal'(A,A0) =>
23.35/23.60	        ((![A1:A,A2:A,A3:A]: (A0(A1,A0(A2,A3)) = A0(A2,A0(A1,A3)))) & 
23.35/23.60	         (![A1:A,A2:A,A3:A]: (A0(A0(A1,A2),A3) = A0(A1,A0(A2,A3)))) & 
23.35/23.60	         (![A1:A,A2:A]: (A0(A1,A2) = A0(A2,A1))) & 
23.35/23.60	         (![A1:A]: (A0(A1,'const/iterate/neutral'(A,A0)) = A1)) & 
23.35/23.60	         (![A1:A]: (A0('const/iterate/neutral'(A,A0),A1) = A1))))))).
23.35/23.60	tff('0', plain, 'const/iterate/monoidal'(sk_A, sk_A0),
23.35/23.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
23.35/23.60	tff('thm/iterate/monoidal_', axiom,
23.35/23.60	  (![A:$tType,A0:((A * A) > A)]:
23.35/23.60	     ('const/iterate/monoidal'(A,A0) <=>
23.35/23.60	      ((![A1:A]: (A0('const/iterate/neutral'(A,A0),A1) = A1)) & 
23.35/23.60	       (![A1:A,A2:A,A3:A]: (A0(A1,A0(A2,A3)) = A0(A0(A1,A2),A3))) & 
23.35/23.60	       (![A1:A,A2:A]: (A0(A1,A2) = A0(A2,A1))))))).
23.35/23.60	tff('1', plain,
23.35/23.60	    ![X2 : $tType, X4 : (X2 * X2) > X2, X8 : X2, X9 : X2]:
23.35/23.60	      (X4(X9, X8) = X4(X8, X9) | ~ 'const/iterate/monoidal'(X2, X4)),
23.35/23.60	    inference('cnf', [status(esa)], [thm/iterate/monoidal_])).
23.35/23.60	tff('2', plain,
23.35/23.60	    ![X2 : $tType, X4 : (X2 * X2) > X2, X8 : X2, X9 : X2, 
23.35/23.60	      X10 : (X2 * X2) > X2]:
23.35/23.60	      (X10 != X4
23.35/23.60	       | X4(X9, X8) = X4(X8, X9)
23.35/23.60	       | ~ 'const/iterate/monoidal'(X2, X10)),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['1'])).
23.35/23.60	tff('3', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : sk_A, X2 : sk_A]:
23.35/23.60	      (~ $true | X0(X2, X1) = X0(X1, X2) | sk_A0 != X0),
23.35/23.60	    inference('sup-', [status(thm)], ['0', '2'])).
23.35/23.60	tff('4', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : sk_A, X2 : sk_A]:
23.35/23.60	      (sk_A0 != X0 | X0(X2, X1) = X0(X1, X2)),
23.35/23.60	    inference('simplify', [status(thm)], ['3'])).
23.35/23.60	tff('5', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : sk_A, X2 : sk_A, 
23.35/23.60	      X3 : (sk_A * sk_A) > sk_A, X4 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X4 != X0 | X3 != X0 | sk_A0 != X0 | X3(X2, X1) = X4(X1, X2)),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['4'])).
23.35/23.60	tff('6', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : sk_A, X2 : sk_A, 
23.35/23.60	      X3 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X0(X2, X1) = X3(X1, X2) | sk_A0 != X3 | X0 != X3),
23.35/23.60	    inference('eq_res', [status(thm)], ['5'])).
23.35/23.60	tff('7', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : sk_A, X2 : sk_A, 
23.35/23.60	      X3 : (sk_A * sk_A) > sk_A, X4 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X4 != X3 | X0(X2, X1) = X3(X1, X2) | sk_A0 != X4 | X0 != X3),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['6'])).
23.35/23.60	tff('8', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, X2 : sk_A, 
23.35/23.60	      X3 : sk_A]: (sk_A0 != X0 | X1(X3, X2) = X1(X2, X3) | X0 != X1),
23.35/23.60	    inference('eq_res', [status(thm)], ['7'])).
23.35/23.60	tff('9', plain,
23.35/23.60	    ![X2 : $tType, X3 : X2, X4 : (X2 * X2) > X2]:
23.35/23.60	      (X4('const/iterate/neutral'(X2, X4), X3) = X3
23.35/23.60	       | ~ 'const/iterate/monoidal'(X2, X4)),
23.35/23.60	    inference('cnf', [status(esa)], [thm/iterate/monoidal_])).
23.35/23.60	tff('10', plain,
23.35/23.60	    ![X2 : $tType, X3 : X2, X4 : (X2 * X2) > X2, X5 : (X2 * X2) > X2]:
23.35/23.60	      (X5 != X4
23.35/23.60	       | X4('const/iterate/neutral'(X2, X5), X3) = X3
23.35/23.60	       | ~ 'const/iterate/monoidal'(X2, X5)),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['9'])).
23.35/23.60	tff('11', plain,
23.35/23.60	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : (X0 * X0) > X0, X3 : X0, 
23.35/23.60	      X4 : (X0 * X0) > X0]:
23.35/23.60	      (X1(X3, 'const/iterate/neutral'(X0, X2)) = X3
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X4)
23.35/23.60	       | X4 != X1
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X2)
23.35/23.60	       | X2 != X1),
23.35/23.60	    inference('sup+', [status(thm)], ['2', '10'])).
23.35/23.60	tff('12', plain,
23.35/23.60	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : (X0 * X0) > X0, X3 : X0]:
23.35/23.60	      (X1 != X2
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X1)
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X2)
23.35/23.60	       | X2(X3, 'const/iterate/neutral'(X0, X1)) = X3),
23.35/23.60	    inference('eq_res', [status(thm)], ['11'])).
23.35/23.60	tff('13', plain,
23.35/23.60	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : (X0 * X0) > X0, X3 : X0, 
23.35/23.60	      X4 : (X0 * X0) > X0]:
23.35/23.60	      (X4 != X2
23.35/23.60	       | X1 != X2
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X1)
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X2)
23.35/23.60	       | X4(X3, 'const/iterate/neutral'(X0, X1)) = X3),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['12'])).
23.35/23.60	tff('14', plain,
23.35/23.60	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : (X0 * X0) > X0, X3 : X0]:
23.35/23.60	      (X1(X3, 'const/iterate/neutral'(X0, X2)) = X3
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X2)
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X2)
23.35/23.60	       | X1 != X2),
23.35/23.60	    inference('eq_res', [status(thm)], ['13'])).
23.35/23.60	tff('15', plain,
23.35/23.60	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : (X0 * X0) > X0, X3 : X0]:
23.35/23.60	      (X1 != X2
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X2)
23.35/23.60	       | X1(X3, 'const/iterate/neutral'(X0, X2)) = X3),
23.35/23.60	    inference('simplify', [status(thm)], ['14'])).
23.35/23.60	tff('16', plain,
23.35/23.60	    ![X2 : $tType, X4 : (X2 * X2) > X2, X5 : X2, X6 : X2, X7 : X2]:
23.35/23.60	      (X4(X5, X4(X6, X7)) = X4(X4(X5, X6), X7)
23.35/23.60	       | ~ 'const/iterate/monoidal'(X2, X4)),
23.35/23.60	    inference('cnf', [status(esa)], [thm/iterate/monoidal_])).
23.35/23.60	tff('17', plain,
23.35/23.60	    ![X2 : $tType, X4 : (X2 * X2) > X2, X5 : X2, X6 : X2, X7 : X2, 
23.35/23.60	      X8 : (X2 * X2) > X2]:
23.35/23.60	      (X8 != X4
23.35/23.60	       | X4(X5, X4(X6, X7)) = X4(X4(X5, X6), X7)
23.35/23.60	       | ~ 'const/iterate/monoidal'(X2, X8)),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['16'])).
23.35/23.60	tff('18', plain,
23.35/23.60	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : X0, X3 : X0, X4 : X0, 
23.35/23.60	      X5 : (X0 * X0) > X0, X6 : (X0 * X0) > X0]:
23.35/23.60	      (X1(X3, X1(X2, X4)) = X1(X4, X1(X3, X2))
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X6)
23.35/23.60	       | X6 != X1
23.35/23.60	       | ~ 'const/iterate/monoidal'(X0, X5)
23.35/23.60	       | X5 != X1),
23.35/23.60	    inference('sup+', [status(thm)], ['2', '17'])).
23.35/23.60	tff('19', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, X2 : sk_A, 
23.35/23.60	      X3 : sk_A, X4 : sk_A]:
23.35/23.60	      (~ $true
23.35/23.60	       | X0 != X1
23.35/23.60	       | ~ 'const/iterate/monoidal'(sk_A, X0)
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | X1(X4, X1(X3, X2)) = X1(X2, X1(X4, X3))),
23.35/23.60	    inference('sup-', [status(thm)], ['0', '18'])).
23.35/23.60	tff('20', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, X2 : sk_A, 
23.35/23.60	      X3 : sk_A, X4 : sk_A]:
23.35/23.60	      (X1(X4, X1(X3, X2)) = X1(X2, X1(X4, X3))
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | ~ 'const/iterate/monoidal'(sk_A, X0)
23.35/23.60	       | X0 != X1),
23.35/23.60	    inference('simplify', [status(thm)], ['19'])).
23.35/23.60	tff('21', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, X2 : sk_A, 
23.35/23.60	      X3 : sk_A, X4 : sk_A, X5 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X5 != X1
23.35/23.60	       | X1(X4, X1(X3, X2)) = X1(X2, X1(X4, X3))
23.35/23.60	       | sk_A0 != X5
23.35/23.60	       | ~ 'const/iterate/monoidal'(sk_A, X0)
23.35/23.60	       | X0 != X1),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['20'])).
23.35/23.60	tff('22', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, X2 : sk_A, 
23.35/23.60	      X3 : sk_A, X4 : sk_A]:
23.35/23.60	      (~ $true
23.35/23.60	       | sk_A0 != X0
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | X0(X4, X0(X3, X2)) = X0(X2, X0(X4, X3))
23.35/23.60	       | X1 != X0),
23.35/23.60	    inference('sup-', [status(thm)], ['0', '21'])).
23.35/23.60	tff('23', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, X2 : sk_A, 
23.35/23.60	      X3 : sk_A, X4 : sk_A]:
23.35/23.60	      (X1 != X0
23.35/23.60	       | X0(X4, X0(X3, X2)) = X0(X2, X0(X4, X3))
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | sk_A0 != X0),
23.35/23.60	    inference('simplify', [status(thm)], ['22'])).
23.35/23.60	tff('24', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, X2 : sk_A, 
23.35/23.60	      X3 : sk_A, X4 : sk_A, X5 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X5 != X0
23.35/23.60	       | X1 != X0
23.35/23.60	       | X0(X4, X0(X3, X2)) = X0(X2, X0(X4, X3))
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | sk_A0 != X5),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['23'])).
23.35/23.60	tff('25', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : sk_A, X2 : sk_A, X3 : sk_A, 
23.35/23.60	      X4 : (sk_A * sk_A) > sk_A, X5 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X6 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X0(X3, X0(X2, X1)) = X0(X2, X0(X3, X1))
23.35/23.60	       | X6 != X0
23.35/23.60	       | sk_A0 != X6
23.35/23.60	       | sk_A0 != X4
23.35/23.60	       | sk_A0 != X5
23.35/23.60	       | X5 != X0
23.35/23.60	       | X4 != X0),
23.35/23.60	    inference('sup+', [status(thm)], ['8', '24'])).
23.35/23.60	tff('26', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : sk_A, X2 : sk_A, 
23.35/23.60	      X3 : (sk_A * sk_A) > sk_A, X4 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X5 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X0(X2, X1) = X3(X2, X1)
23.35/23.60	       | ~ 'const/iterate/monoidal'(sk_A, X5)
23.35/23.60	       | X5 != X0
23.35/23.60	       | sk_A0 != X4
23.35/23.60	       | X0 != X4
23.35/23.60	       | X3 != X4),
23.35/23.60	    inference('sup+', [status(thm)], ['2', '5'])).
23.35/23.60	tff('27', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : sk_A, X4 : sk_A]:
23.35/23.60	      (~ $true
23.35/23.60	       | X0 != X1
23.35/23.60	       | X2 != X1
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | X2(X4, X3) = X0(X4, X3)),
23.35/23.60	    inference('sup-', [status(thm)], ['0', '26'])).
23.35/23.60	tff('28', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : sk_A, X4 : sk_A]:
23.35/23.60	      (X2(X4, X3) = X0(X4, X3)
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | X2 != X1
23.35/23.60	       | X0 != X1),
23.35/23.60	    inference('simplify', [status(thm)], ['27'])).
23.35/23.60	tff('29', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : sk_A, X4 : sk_A, 
23.35/23.60	      X5 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X5 != X2
23.35/23.60	       | X2(X4, X3) = X0(X4, X3)
23.35/23.60	       | sk_A0 != X5
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | X2 != X1
23.35/23.60	       | X0 != X1),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['28'])).
23.35/23.60	tff('30', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : sk_A, X4 : sk_A]:
23.35/23.60	      (X0 != X1
23.35/23.60	       | X2 != X1
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | X2(X4, X3) = X0(X4, X3)),
23.35/23.60	    inference('eq_res', [status(thm)], ['29'])).
23.35/23.60	tff('31', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : sk_A, X4 : sk_A, 
23.35/23.60	      X5 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X5 != X2
23.35/23.60	       | X0 != X1
23.35/23.60	       | X2 != X1
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | X5(X4, X3) = X0(X4, X3)),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['30'])).
23.35/23.60	tff('32', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : sk_A, X2 : sk_A, 
23.35/23.60	      X3 : (sk_A * sk_A) > sk_A, X4 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X0(X2, X1) = X3(X2, X1)
23.35/23.60	       | sk_A0 != X4
23.35/23.60	       | sk_A0 != X4
23.35/23.60	       | X3 != X4
23.35/23.60	       | X0 != X4),
23.35/23.60	    inference('eq_res', [status(thm)], ['31'])).
23.35/23.60	tff('33', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : sk_A, X2 : sk_A, 
23.35/23.60	      X3 : (sk_A * sk_A) > sk_A, X4 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X0 != X4 | X3 != X4 | sk_A0 != X4 | X0(X2, X1) = X3(X2, X1)),
23.35/23.60	    inference('simplify', [status(thm)], ['32'])).
23.35/23.60	tff('34', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : sk_A, X2 : sk_A, 
23.35/23.60	      X3 : (sk_A * sk_A) > sk_A, X4 : sk_A, X5 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X6 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X3(X2, X3(X1, X4)) = X3(X0(X2, X1), X4)
23.35/23.60	       | sk_A0 != X6
23.35/23.60	       | X3 != X6
23.35/23.60	       | X0 != X6
23.35/23.60	       | ~ 'const/iterate/monoidal'(sk_A, X5)
23.35/23.60	       | X5 != X3),
23.35/23.60	    inference('sup+', [status(thm)], ['33', '17'])).
23.35/23.60	tff('35', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : sk_A, X4 : sk_A, X5 : sk_A]:
23.35/23.60	      (~ $true
23.35/23.60	       | sk_A0 != X0
23.35/23.60	       | X1 != X2
23.35/23.60	       | X0 != X2
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | X0(X5, X0(X4, X3)) = X0(X1(X5, X4), X3)),
23.35/23.60	    inference('sup-', [status(thm)], ['0', '34'])).
23.35/23.60	tff('36', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : sk_A, X4 : sk_A, X5 : sk_A]:
23.35/23.60	      (X0(X5, X0(X4, X3)) = X0(X1(X5, X4), X3)
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | X0 != X2
23.35/23.60	       | X1 != X2
23.35/23.60	       | sk_A0 != X0),
23.35/23.60	    inference('simplify', [status(thm)], ['35'])).
23.35/23.60	tff('37', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : sk_A, X4 : sk_A, X5 : sk_A, 
23.35/23.60	      X6 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X6 != X0
23.35/23.60	       | X0(X5, X0(X4, X3)) = X0(X1(X5, X4), X3)
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | X0 != X2
23.35/23.60	       | X1 != X2
23.35/23.60	       | sk_A0 != X6),
23.35/23.60	    inference('ho.purify_applied_variable', [status(thm)], ['36'])).
23.35/23.60	tff('38', plain,
23.35/23.60	    (sk_A0(sk_A13, sk_A0(sk_A22, sk_A31))
23.35/23.60	      != sk_A0(sk_A22, sk_A0(sk_A13, sk_A31))
23.35/23.60	     | sk_A0(sk_A0(sk_A14, sk_A23), sk_A32)
23.35/23.60	        != sk_A0(sk_A14, sk_A0(sk_A23, sk_A32))
23.35/23.60	     | sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)
23.35/23.60	     | sk_A0(sk_A16, 'const/iterate/neutral'(sk_A, sk_A0)) != sk_A16
23.35/23.60	     | sk_A0('const/iterate/neutral'(sk_A, sk_A0), sk_A17) != sk_A17),
23.35/23.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
23.35/23.60	tff('39', plain,
23.35/23.60	    (sk_A17 != sk_A17
23.35/23.60	     | ~ 'const/iterate/monoidal'(sk_A, sk_A0)
23.35/23.60	     | sk_A0 != sk_A0
23.35/23.60	     | sk_A0(sk_A16, 'const/iterate/neutral'(sk_A, sk_A0)) != sk_A16
23.35/23.60	     | sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)
23.35/23.60	     | sk_A0(sk_A0(sk_A14, sk_A23), sk_A32)
23.35/23.60	        != sk_A0(sk_A14, sk_A0(sk_A23, sk_A32))
23.35/23.60	     | sk_A0(sk_A13, sk_A0(sk_A22, sk_A31))
23.35/23.60	        != sk_A0(sk_A22, sk_A0(sk_A13, sk_A31))),
23.35/23.60	    inference('sup-', [status(thm)], ['10', '38'])).
23.35/23.60	tff('40', plain,
23.35/23.60	    (sk_A17 != sk_A17
23.35/23.60	     | ~ $true
23.35/23.60	     | sk_A0 != sk_A0
23.35/23.60	     | sk_A0(sk_A16, 'const/iterate/neutral'(sk_A, sk_A0)) != sk_A16
23.35/23.60	     | sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)
23.35/23.60	     | sk_A0(sk_A0(sk_A14, sk_A23), sk_A32)
23.35/23.60	        != sk_A0(sk_A14, sk_A0(sk_A23, sk_A32))
23.35/23.60	     | sk_A0(sk_A13, sk_A0(sk_A22, sk_A31))
23.35/23.60	        != sk_A0(sk_A22, sk_A0(sk_A13, sk_A31))),
23.35/23.60	    inference('demod', [status(thm)], ['39', '0'])).
23.35/23.60	tff('41', plain,
23.35/23.60	    (sk_A0(sk_A13, sk_A0(sk_A22, sk_A31))
23.35/23.60	      != sk_A0(sk_A22, sk_A0(sk_A13, sk_A31))
23.35/23.60	     | sk_A0(sk_A0(sk_A14, sk_A23), sk_A32)
23.35/23.60	        != sk_A0(sk_A14, sk_A0(sk_A23, sk_A32))
23.35/23.60	     | sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)
23.35/23.60	     | sk_A0(sk_A16, 'const/iterate/neutral'(sk_A, sk_A0)) != sk_A16),
23.35/23.60	    inference('simplify', [status(thm)], ['40'])).
23.35/23.60	tff('42', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A0(sk_A14, sk_A0(sk_A23, sk_A32))
23.35/23.60	        != sk_A0(sk_A14, sk_A0(sk_A23, sk_A32))
23.35/23.60	       | sk_A0 != X0
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | X0 != sk_A0
23.35/23.60	       | sk_A0(sk_A16, 'const/iterate/neutral'(sk_A, sk_A0)) != sk_A16
23.35/23.60	       | sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)
23.35/23.60	       | sk_A0(sk_A13, sk_A0(sk_A22, sk_A31))
23.35/23.60	          != sk_A0(sk_A22, sk_A0(sk_A13, sk_A31))),
23.35/23.60	    inference('sup-', [status(thm)], ['37', '41'])).
23.35/23.60	tff('43', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A0(sk_A13, sk_A0(sk_A22, sk_A31))
23.35/23.60	        != sk_A0(sk_A22, sk_A0(sk_A13, sk_A31))
23.35/23.60	       | sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)
23.35/23.60	       | sk_A0(sk_A16, 'const/iterate/neutral'(sk_A, sk_A0)) != sk_A16
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | sk_A0 != X0),
23.35/23.60	    inference('simplify', [status(thm)], ['42'])).
23.35/23.60	tff('44', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X4 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A0(sk_A13, sk_A0(sk_A22, sk_A31))
23.35/23.60	        != sk_A0(sk_A13, sk_A0(sk_A22, sk_A31))
23.35/23.60	       | X2 != sk_A0
23.35/23.60	       | X3 != sk_A0
23.35/23.60	       | sk_A0 != X3
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | sk_A0 != X4
23.35/23.60	       | X4 != sk_A0
23.35/23.60	       | sk_A0 != X0
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | sk_A0(sk_A16, 'const/iterate/neutral'(sk_A, sk_A0)) != sk_A16
23.35/23.60	       | sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)),
23.35/23.60	    inference('sup-', [status(thm)], ['25', '43'])).
23.35/23.60	tff('45', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X4 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)
23.35/23.60	       | sk_A0(sk_A16, 'const/iterate/neutral'(sk_A, sk_A0)) != sk_A16
23.35/23.60	       | sk_A0 != X1
23.35/23.60	       | sk_A0 != X0
23.35/23.60	       | sk_A0 != X4
23.35/23.60	       | X3 != sk_A0
23.35/23.60	       | X2 != sk_A0),
23.35/23.60	    inference('simplify', [status(thm)], ['44'])).
23.35/23.60	tff('46', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X4 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A16 != sk_A16
23.35/23.60	       | ~ 'const/iterate/monoidal'(sk_A, sk_A0)
23.35/23.60	       | sk_A0 != sk_A0
23.35/23.60	       | X0 != sk_A0
23.35/23.60	       | X1 != sk_A0
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | sk_A0 != X3
23.35/23.60	       | sk_A0 != X4
23.35/23.60	       | sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)),
23.35/23.60	    inference('sup-', [status(thm)], ['15', '45'])).
23.35/23.60	tff('47', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X4 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A16 != sk_A16
23.35/23.60	       | ~ $true
23.35/23.60	       | sk_A0 != sk_A0
23.35/23.60	       | X0 != sk_A0
23.35/23.60	       | X1 != sk_A0
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | sk_A0 != X3
23.35/23.60	       | sk_A0 != X4
23.35/23.60	       | sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)),
23.35/23.60	    inference('demod', [status(thm)], ['46', '0'])).
23.35/23.60	tff('48', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X4 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A0(sk_A15, sk_A24) != sk_A0(sk_A24, sk_A15)
23.35/23.60	       | sk_A0 != X4
23.35/23.60	       | sk_A0 != X3
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | X1 != sk_A0
23.35/23.60	       | X0 != sk_A0),
23.35/23.60	    inference('simplify', [status(thm)], ['47'])).
23.35/23.60	tff('49', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X4 : (sk_A * sk_A) > sk_A, X5 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A0(sk_A15, sk_A24) != sk_A0(sk_A15, sk_A24)
23.35/23.60	       | X5 != sk_A0
23.35/23.60	       | sk_A0 != X5
23.35/23.60	       | X0 != sk_A0
23.35/23.60	       | X1 != sk_A0
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | sk_A0 != X3
23.35/23.60	       | sk_A0 != X4),
23.35/23.60	    inference('sup-', [status(thm)], ['8', '48'])).
23.35/23.60	tff('50', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X4 : (sk_A * sk_A) > sk_A, X5 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A0 != X4
23.35/23.60	       | sk_A0 != X3
23.35/23.60	       | sk_A0 != X2
23.35/23.60	       | X1 != sk_A0
23.35/23.60	       | X0 != sk_A0
23.35/23.60	       | X5 != sk_A0),
23.35/23.60	    inference('simplify', [status(thm)], ['49'])).
23.35/23.60	tff('51', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X4 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (X0 != sk_A0 | X1 != sk_A0 | X2 != sk_A0 | sk_A0 != X3 | sk_A0 != X4),
23.35/23.60	    inference('eq_res', [status(thm)], ['50'])).
23.35/23.60	tff('52', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A, X3 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A0 != X0 | sk_A0 != X1 | X2 != sk_A0 | X3 != sk_A0),
23.35/23.60	    inference('eq_res', [status(thm)], ['51'])).
23.35/23.60	tff('53', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A, 
23.35/23.60	      X2 : (sk_A * sk_A) > sk_A]: (X0 != sk_A0 | X1 != sk_A0 | sk_A0 != X2),
23.35/23.60	    inference('eq_res', [status(thm)], ['52'])).
23.35/23.60	tff('54', plain,
23.35/23.60	    ![X0 : (sk_A * sk_A) > sk_A, X1 : (sk_A * sk_A) > sk_A]:
23.35/23.60	      (sk_A0 != X0 | X1 != sk_A0),
23.35/23.60	    inference('condensation', [status(thm)], ['53'])).
23.35/23.60	tff('55', plain, ![X0 : (sk_A * sk_A) > sk_A]: X0 != sk_A0,
23.35/23.60	    inference('condensation', [status(thm)], ['54'])).
23.35/23.60	tff('56', plain, $false, inference('eq_res', [status(thm)], ['55'])).
23.35/23.60	
23.35/23.60	% SZS output end Refutation
23.35/23.61	EOF
