%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN563-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:48:06 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.37s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% Syntax : Number of clauses : 88 ( 88 unt; 0 nHn; 54 RR)
% Number of literals : 88 ( 87 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 65 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c3,plain,
ifeq(true,true,a,b) = a,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
a = ifeq(true,true,a,b),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
ifeq2(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c6,plain,
ifeq2(true,true,p6(f4(c7),f3(f4(c8))),true) = p6(f4(c7),f3(f4(c8))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
p6(f4(c7),f3(f4(c8))) = ifeq2(true,true,p6(f4(c7),f3(f4(c8))),true),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
ifeq2(true,true,p5(c7,f3(f4(c8))),true) = p5(c7,f3(f4(c8))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c9,plain,
p5(c7,f3(f4(c8))) = ifeq2(true,true,p5(c7,f3(f4(c8))),true),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
ifeq2(true,true,p5(f3(f3(c7)),f3(f4(c8))),true) = p5(f3(f3(c7)),f3(f4(c8))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c11,plain,
p5(f3(f3(c7)),f3(f4(c8))) = ifeq2(true,true,p5(f3(f3(c7)),f3(f4(c8))),true),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
ifeq2(true,true,p2(f3(f4(c7)),f3(f4(c8))),true) = p2(f3(f4(c7)),f3(f4(c8))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c13,plain,
p2(f3(f4(c7)),f3(f4(c8))) = ifeq2(true,true,p2(f3(f4(c7)),f3(f4(c8))),true),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
p2(f4(c7),f4(c8)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
true = p2(f4(c7),f4(c8)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
ifeq2(true,true,p2(f3(f4(c7)),f3(f4(c8))),true) = ifeq2(p2(f4(c7),f4(c8)),true,p2(f3(f4(c7)),f3(f4(c8))),true),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,negated_conjecture,
ifeq2(p2(X3,X4),true,p2(f3(X3),f3(X4)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_11) ).
cnf(c18,plain,
ifeq2(p2(f4(c7),f4(c8)),true,p2(f3(f4(c7)),f3(f4(c8))),true) = true,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
ifeq2(true,true,p2(f3(f4(c7)),f3(f4(c8))),true) = true,
inference(transitivity,[status(thm)],[c16,c18]) ).
cnf(c20,plain,
p2(f3(f4(c7)),f3(f4(c8))) = true,
inference(transitivity,[status(thm)],[c13,c19]) ).
cnf(c21,plain,
true = p2(f3(f4(c7)),f3(f4(c8))),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
ifeq2(true,true,p5(f3(f3(c7)),f3(f4(c8))),true) = ifeq2(p2(f3(f4(c7)),f3(f4(c8))),true,p5(f3(f3(c7)),f3(f4(c8))),true),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
ifeq2(true,true,p5(f3(f3(X2)),X),true) = p5(f3(f3(X2)),X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c24,plain,
p5(f3(f3(X2)),X) = ifeq2(true,true,p5(f3(f3(X2)),X),true),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
ifeq2(p2(f3(f4(X2)),X),true,p5(f3(f3(X2)),X),true) = ifeq2(p2(f3(f4(X2)),X),true,ifeq2(true,true,p5(f3(f3(X2)),X),true),true),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,negated_conjecture,
p5(f3(f3(X16)),f3(f4(X16))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_7) ).
cnf(c27,plain,
p5(f3(f3(X)),f3(f4(X))) = true,
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
true = p5(f3(f3(X)),f3(f4(X))),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
ifeq2(true,true,p5(f3(f3(X2)),X),true) = ifeq2(p5(f3(f3(X2)),f3(f4(X2))),true,p5(f3(f3(X2)),X),true),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
ifeq2(p2(f3(f4(X2)),X),true,ifeq2(true,true,p5(f3(f3(X2)),X),true),true) = ifeq2(p2(f3(f4(X2)),X),true,ifeq2(p5(f3(f3(X2)),f3(f4(X2))),true,p5(f3(f3(X2)),X),true),true),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
ifeq2(true,true,ifeq2(p2(X2,X),true,ifeq2(p5(X5,X2),true,p5(X5,X),true),true),true) = ifeq2(p2(X2,X),true,ifeq2(p5(X5,X2),true,p5(X5,X),true),true),
inference(substitution,[status(thm)],[c5]) ).
cnf(c32,plain,
ifeq2(p2(X5,X2),true,ifeq2(p5(X,X5),true,p5(X,X2),true),true) = ifeq2(true,true,ifeq2(p2(X5,X2),true,ifeq2(p5(X,X5),true,p5(X,X2),true),true),true),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,negated_conjecture,
p2(X0,X0) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).
cnf(c34,plain,
p2(X,X) = true,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
true = p2(X,X),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq2(true,true,ifeq2(p2(X5,X2),true,ifeq2(p5(X,X5),true,p5(X,X2),true),true),true) = ifeq2(p2(X,X),true,ifeq2(p2(X5,X2),true,ifeq2(p5(X,X5),true,p5(X,X2),true),true),true),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,negated_conjecture,
ifeq2(p2(X14,X12),true,ifeq2(p2(X15,X13),true,ifeq2(p5(X14,X15),true,p5(X12,X13),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_17) ).
cnf(c38,plain,
ifeq2(p2(X,X),true,ifeq2(p2(X5,X2),true,ifeq2(p5(X,X5),true,p5(X,X2),true),true),true) = true,
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
ifeq2(true,true,ifeq2(p2(X5,X2),true,ifeq2(p5(X,X5),true,p5(X,X2),true),true),true) = true,
inference(transitivity,[status(thm)],[c36,c38]) ).
cnf(c40,plain,
ifeq2(p2(X5,X2),true,ifeq2(p5(X,X5),true,p5(X,X2),true),true) = true,
inference(transitivity,[status(thm)],[c32,c39]) ).
cnf(c41,plain,
ifeq2(p2(f3(f4(X2)),X),true,ifeq2(p5(f3(f3(X2)),f3(f4(X2))),true,p5(f3(f3(X2)),X),true),true) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
ifeq2(p2(f3(f4(X2)),X),true,ifeq2(true,true,p5(f3(f3(X2)),X),true),true) = true,
inference(transitivity,[status(thm)],[c30,c41]) ).
cnf(c43,plain,
ifeq2(p2(f3(f4(X2)),X),true,p5(f3(f3(X2)),X),true) = true,
inference(transitivity,[status(thm)],[c25,c42]) ).
cnf(c44,plain,
ifeq2(p2(f3(f4(c7)),f3(f4(c8))),true,p5(f3(f3(c7)),f3(f4(c8))),true) = true,
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
ifeq2(true,true,p5(f3(f3(c7)),f3(f4(c8))),true) = true,
inference(transitivity,[status(thm)],[c22,c44]) ).
cnf(c46,plain,
p5(f3(f3(c7)),f3(f4(c8))) = true,
inference(transitivity,[status(thm)],[c11,c45]) ).
cnf(c47,plain,
true = p5(f3(f3(c7)),f3(f4(c8))),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
ifeq2(true,true,p5(c7,f3(f4(c8))),true) = ifeq2(p5(f3(f3(c7)),f3(f4(c8))),true,p5(c7,f3(f4(c8))),true),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
ifeq2(true,true,ifeq2(p5(f3(f3(c7)),X),true,p5(c7,X),true),true) = ifeq2(p5(f3(f3(c7)),X),true,p5(c7,X),true),
inference(substitution,[status(thm)],[c5]) ).
cnf(c50,plain,
ifeq2(p5(f3(f3(c7)),X),true,p5(c7,X),true) = ifeq2(true,true,ifeq2(p5(f3(f3(c7)),X),true,p5(c7,X),true),true),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
ifeq2(true,true,p6(c7,f3(f3(c7))),true) = p6(c7,f3(f3(c7))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c52,plain,
p6(c7,f3(f3(c7))) = ifeq2(true,true,p6(c7,f3(f3(c7))),true),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
ifeq2(true,true,p6(c7,f3(c7)),true) = p6(c7,f3(c7)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c54,plain,
p6(c7,f3(c7)) = ifeq2(true,true,p6(c7,f3(c7)),true),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,negated_conjecture,
p6(X22,X22) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_2) ).
cnf(c56,plain,
p6(c7,c7) = true,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
true = p6(c7,c7),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
ifeq2(true,true,p6(c7,f3(c7)),true) = ifeq2(p6(c7,c7),true,p6(c7,f3(c7)),true),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,negated_conjecture,
ifeq2(p6(c7,X27),true,p6(c7,f3(X27)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_9) ).
cnf(c60,plain,
ifeq2(p6(c7,c7),true,p6(c7,f3(c7)),true) = true,
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
ifeq2(true,true,p6(c7,f3(c7)),true) = true,
inference(transitivity,[status(thm)],[c58,c60]) ).
cnf(c62,plain,
p6(c7,f3(c7)) = true,
inference(transitivity,[status(thm)],[c54,c61]) ).
cnf(c63,plain,
true = p6(c7,f3(c7)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
ifeq2(true,true,p6(c7,f3(f3(c7))),true) = ifeq2(p6(c7,f3(c7)),true,p6(c7,f3(f3(c7))),true),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
ifeq2(p6(c7,f3(c7)),true,p6(c7,f3(f3(c7))),true) = true,
inference(substitution,[status(thm)],[c59]) ).
cnf(c66,plain,
ifeq2(true,true,p6(c7,f3(f3(c7))),true) = true,
inference(transitivity,[status(thm)],[c64,c65]) ).
cnf(c67,plain,
p6(c7,f3(f3(c7))) = true,
inference(transitivity,[status(thm)],[c52,c66]) ).
cnf(c68,plain,
true = p6(c7,f3(f3(c7))),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
ifeq2(true,true,ifeq2(p5(f3(f3(c7)),X),true,p5(c7,X),true),true) = ifeq2(p6(c7,f3(f3(c7))),true,ifeq2(p5(f3(f3(c7)),X),true,p5(c7,X),true),true),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,negated_conjecture,
ifeq2(p6(X7,X9),true,ifeq2(p5(X9,X8),true,p5(X7,X8),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_15) ).
cnf(c71,plain,
ifeq2(p6(c7,f3(f3(c7))),true,ifeq2(p5(f3(f3(c7)),X),true,p5(c7,X),true),true) = true,
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
ifeq2(true,true,ifeq2(p5(f3(f3(c7)),X),true,p5(c7,X),true),true) = true,
inference(transitivity,[status(thm)],[c69,c71]) ).
cnf(c73,plain,
ifeq2(p5(f3(f3(c7)),X),true,p5(c7,X),true) = true,
inference(transitivity,[status(thm)],[c50,c72]) ).
cnf(c74,plain,
ifeq2(p5(f3(f3(c7)),f3(f4(c8))),true,p5(c7,f3(f4(c8))),true) = true,
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
ifeq2(true,true,p5(c7,f3(f4(c8))),true) = true,
inference(transitivity,[status(thm)],[c48,c74]) ).
cnf(c76,plain,
p5(c7,f3(f4(c8))) = true,
inference(transitivity,[status(thm)],[c9,c75]) ).
cnf(c77,plain,
true = p5(c7,f3(f4(c8))),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
ifeq2(true,true,p6(f4(c7),f3(f4(c8))),true) = ifeq2(p5(c7,f3(f4(c8))),true,p6(f4(c7),f3(f4(c8))),true),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,negated_conjecture,
ifeq2(p5(X10,X11),true,p6(f4(X10),X11),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_10) ).
cnf(c80,plain,
ifeq2(p5(c7,f3(f4(c8))),true,p6(f4(c7),f3(f4(c8))),true) = true,
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
ifeq2(true,true,p6(f4(c7),f3(f4(c8))),true) = true,
inference(transitivity,[status(thm)],[c78,c80]) ).
cnf(c82,plain,
p6(f4(c7),f3(f4(c8))) = true,
inference(transitivity,[status(thm)],[c7,c81]) ).
cnf(c83,plain,
true = p6(f4(c7),f3(f4(c8))),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
ifeq(true,true,a,b) = ifeq(p6(f4(c7),f3(f4(c8))),true,a,b),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,axiom,
ifeq(p6(f4(c7),f3(f4(c8))),true,a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c86,plain,
ifeq(true,true,a,b) = b,
inference(transitivity,[status(thm)],[c84,c85]) ).
cnf(c87,plain,
a = b,
inference(transitivity,[status(thm)],[c4,c86]) ).
cnf(c88,plain,
$false,
inference(resolution,[status(thm)],[c1,c87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN563-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n019.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 16:29:18 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.37 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.21/0.37
% 0.21/0.37 % SZS status Unsatisfiable
% 0.21/0.37
% 0.21/0.38 % SZS output start CNFRefutation
% See solution above
% 1.28/0.42
% 1.28/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------