%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN116-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 01:47:07 PM UTC 2026
% Result : Unsatisfiable 4.46s 0.84s
% Output : CNFRefutation 4.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of clauses : 95 ( 95 unt; 0 nHn; 42 RR)
% Number of literals : 95 ( 94 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 73 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
k5(b) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(true,true,k5(X2),true) = k5(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
k5(X2) = ifeq(true,true,k5(X2),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,s4(a),true) = s4(a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
s4(a) = ifeq(true,true,s4(a),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(true,true,l1(a,a),true) = l1(a,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
l1(a,a) = ifeq(true,true,l1(a,a),true),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
n0(b,a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c10,plain,
true = n0(b,a),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq(true,true,l1(a,a),true) = ifeq(n0(b,a),true,l1(a,a),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
ifeq(n0(H,G),true,l1(G,G),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_002) ).
cnf(c13,plain,
ifeq(n0(b,a),true,l1(a,a),true) = true,
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
ifeq(true,true,l1(a,a),true) = true,
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
l1(a,a) = true,
inference(transitivity,[status(thm)],[c8,c14]) ).
cnf(c16,plain,
true = l1(a,a),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
ifeq(true,true,s4(a),true) = ifeq(l1(a,a),true,s4(a),true),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
ifeq(true,true,ifeq(l1(X2,a),true,s4(X2),true),true) = ifeq(l1(X2,a),true,s4(X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
ifeq(l1(X2,a),true,s4(X2),true) = ifeq(true,true,ifeq(l1(X2,a),true,s4(X2),true),true),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
ifeq(true,true,p3(a,a,a),true) = p3(a,a,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
p3(a,a,a) = ifeq(true,true,p3(a,a,a),true),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
ifeq(true,true,n2(a),true) = n2(a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
n2(a) = ifeq(true,true,n2(a),true),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
ifeq(true,true,p1(a,a,a),true) = p1(a,a,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
p1(a,a,a) = ifeq(true,true,p1(a,a,a),true),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,axiom,
l0(a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c27,plain,
true = l0(a),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
ifeq(true,true,p1(a,a,a),true) = ifeq(l0(a),true,p1(a,a,a),true),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,axiom,
ifeq(l0(a),true,p1(a,a,a),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c30,plain,
ifeq(true,true,p1(a,a,a),true) = true,
inference(transitivity,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
p1(a,a,a) = true,
inference(transitivity,[status(thm)],[c25,c30]) ).
cnf(c32,plain,
true = p1(a,a,a),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
ifeq(true,true,n2(a),true) = ifeq(p1(a,a,a),true,n2(a),true),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
ifeq(p1(B2,C2,A2),true,n2(A2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_137) ).
cnf(c35,plain,
ifeq(p1(a,a,a),true,n2(a),true) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq(true,true,n2(a),true) = true,
inference(transitivity,[status(thm)],[c33,c35]) ).
cnf(c37,plain,
n2(a) = true,
inference(transitivity,[status(thm)],[c23,c36]) ).
cnf(c38,plain,
true = n2(a),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
ifeq(true,true,p3(a,a,a),true) = ifeq(n2(a),true,p3(a,a,a),true),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,axiom,
ifeq(n2(H2),true,p3(H2,H2,H2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_244) ).
cnf(c41,plain,
ifeq(n2(a),true,p3(a,a,a),true) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
ifeq(true,true,p3(a,a,a),true) = true,
inference(transitivity,[status(thm)],[c39,c41]) ).
cnf(c43,plain,
p3(a,a,a) = true,
inference(transitivity,[status(thm)],[c21,c42]) ).
cnf(c44,plain,
true = p3(a,a,a),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
ifeq(true,true,ifeq(l1(X2,a),true,s4(X2),true),true) = ifeq(p3(a,a,a),true,ifeq(l1(X2,a),true,s4(X2),true),true),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
ifeq(p3(B2,C2,D),true,ifeq(l1(A2,C2),true,s4(A2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_299) ).
cnf(c47,plain,
ifeq(p3(a,a,a),true,ifeq(l1(X2,a),true,s4(X2),true),true) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
ifeq(true,true,ifeq(l1(X2,a),true,s4(X2),true),true) = true,
inference(transitivity,[status(thm)],[c45,c47]) ).
cnf(c49,plain,
ifeq(l1(X2,a),true,s4(X2),true) = true,
inference(transitivity,[status(thm)],[c19,c48]) ).
cnf(c50,plain,
ifeq(l1(a,a),true,s4(a),true) = true,
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
ifeq(true,true,s4(a),true) = true,
inference(transitivity,[status(thm)],[c17,c50]) ).
cnf(c52,plain,
s4(a) = true,
inference(transitivity,[status(thm)],[c6,c51]) ).
cnf(c53,plain,
true = s4(a),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
ifeq(true,true,k5(X2),true) = ifeq(s4(a),true,k5(X2),true),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
ifeq(true,true,k5(X2),true) = k5(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c56,plain,
k5(X2) = ifeq(true,true,k5(X2),true),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
ifeq(s4(X3),true,k5(X2),true) = ifeq(s4(X3),true,ifeq(true,true,k5(X2),true),true),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
ifeq(true,true,r3(X2,X2,X2),true) = r3(X2,X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
r3(X2,X2,X2) = ifeq(true,true,r3(X2,X2,X2),true),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
ifeq(true,true,p2(X2,X2,X2),true) = p2(X2,X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c61,plain,
p2(X2,X2,X2) = ifeq(true,true,p2(X2,X2,X2),true),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
ifeq(true,true,m1(X2,X2,X2),true) = m1(X2,X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c63,plain,
m1(X2,X2,X2) = ifeq(true,true,m1(X2,X2,X2),true),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,axiom,
m0(X,d,Y) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
cnf(c65,plain,
m0(d,d,X2) = true,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
true = m0(d,d,X2),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
ifeq(true,true,m1(X2,X2,X2),true) = ifeq(m0(d,d,X2),true,m1(X2,X2,X2),true),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,axiom,
ifeq(m0(A2,A2,J),true,m1(J,J,J),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_006) ).
cnf(c69,plain,
ifeq(m0(d,d,X2),true,m1(X2,X2,X2),true) = true,
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
ifeq(true,true,m1(X2,X2,X2),true) = true,
inference(transitivity,[status(thm)],[c67,c69]) ).
cnf(c71,plain,
m1(X2,X2,X2) = true,
inference(transitivity,[status(thm)],[c63,c70]) ).
cnf(c72,plain,
true = m1(X2,X2,X2),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
ifeq(true,true,p2(X2,X2,X2),true) = ifeq(m1(X2,X2,X2),true,p2(X2,X2,X2),true),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,axiom,
ifeq(m1(G2,G2,F),true,p2(F,F,F),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_150) ).
cnf(c75,plain,
ifeq(m1(X2,X2,X2),true,p2(X2,X2,X2),true) = true,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
ifeq(true,true,p2(X2,X2,X2),true) = true,
inference(transitivity,[status(thm)],[c73,c75]) ).
cnf(c77,plain,
p2(X2,X2,X2) = true,
inference(transitivity,[status(thm)],[c61,c76]) ).
cnf(c78,plain,
true = p2(X2,X2,X2),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
ifeq(true,true,r3(X2,X2,X2),true) = ifeq(p2(X2,X2,X2),true,r3(X2,X2,X2),true),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,axiom,
ifeq(p2(B2,D2,C2),true,r3(B2,C2,B2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_267) ).
cnf(c81,plain,
ifeq(p2(X2,X2,X2),true,r3(X2,X2,X2),true) = true,
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
ifeq(true,true,r3(X2,X2,X2),true) = true,
inference(transitivity,[status(thm)],[c79,c81]) ).
cnf(c83,plain,
r3(X2,X2,X2) = true,
inference(transitivity,[status(thm)],[c59,c82]) ).
cnf(c84,plain,
true = r3(X2,X2,X2),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
ifeq(true,true,k5(X2),true) = ifeq(r3(X2,X2,X2),true,k5(X2),true),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
ifeq(s4(X3),true,ifeq(true,true,k5(X2),true),true) = ifeq(s4(X3),true,ifeq(r3(X2,X2,X2),true,k5(X2),true),true),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,axiom,
ifeq(s4(F2),true,ifeq(r3(G2,E,E),true,k5(E),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_300) ).
cnf(c88,plain,
ifeq(s4(X3),true,ifeq(r3(X2,X2,X2),true,k5(X2),true),true) = true,
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
ifeq(s4(X3),true,ifeq(true,true,k5(X2),true),true) = true,
inference(transitivity,[status(thm)],[c86,c88]) ).
cnf(c90,plain,
ifeq(s4(X3),true,k5(X2),true) = true,
inference(transitivity,[status(thm)],[c57,c89]) ).
cnf(c91,plain,
ifeq(s4(a),true,k5(X2),true) = true,
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
ifeq(true,true,k5(X2),true) = true,
inference(transitivity,[status(thm)],[c54,c91]) ).
cnf(c93,plain,
k5(X2) = true,
inference(transitivity,[status(thm)],[c4,c92]) ).
cnf(c94,plain,
k5(b) = true,
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
$false,
inference(resolution,[status(thm)],[c1,c94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN116-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n015.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 15:38:01 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.46/0.84 Command-line arguments: --flatten-regeneralise
% 4.46/0.84
% 4.46/0.84 % SZS status Unsatisfiable
% 4.46/0.84
% 4.46/0.84 % SZS output start CNFRefutation
% See solution above
% 4.46/0.86
% 4.46/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------