%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL218-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 11:49:23 AM UTC 2026
% Result : Unsatisfiable 11.78s 1.94s
% Output : CNFRefutation 11.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 8
% Syntax : Number of clauses : 88 ( 88 unt; 0 nHn; 3 RR)
% Number of literals : 88 ( 87 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 228 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) != 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,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X4),X2))),true) = theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X4),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X4),X2))) = ifeq(true,true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X4),X2))),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,theorem(or(not(or(X4,not(or(X3,X2)))),or(not(X3),X4))),true) = theorem(or(not(or(X4,not(or(X3,X2)))),or(not(X3),X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
theorem(or(not(or(X4,not(or(X3,X2)))),or(not(X3),X4))) = ifeq(true,true,theorem(or(not(or(X4,not(or(X3,X2)))),or(not(X3),X4))),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(true,true,theorem(or(not(X4),or(not(or(X3,not(or(X4,X2)))),X3))),true) = theorem(or(not(X4),or(not(or(X3,not(or(X4,X2)))),X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
theorem(or(not(X4),or(not(or(X3,not(or(X4,X2)))),X3))) = ifeq(true,true,theorem(or(not(X4),or(not(or(X3,not(or(X4,X2)))),X3))),true),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq(true,true,theorem(or(not(or(X4,X3)),or(not(or(X2,not(or(X3,X4)))),X2))),true) = theorem(or(not(or(X4,X3)),or(not(or(X2,not(or(X3,X4)))),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
theorem(or(not(or(X4,X3)),or(not(or(X2,not(or(X3,X4)))),X2))) = ifeq(true,true,theorem(or(not(or(X4,X3)),or(not(or(X2,not(or(X3,X4)))),X2))),true),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq(true,true,theorem(or(X3,or(not(or(X2,X3)),X2))),true) = theorem(or(X3,or(not(or(X2,X3)),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
theorem(or(X3,or(not(or(X2,X3)),X2))) = ifeq(true,true,theorem(or(X3,or(not(or(X2,X3)),X2))),true),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
ifeq(true,true,theorem(or(not(or(X3,X2)),or(X2,X3))),true) = theorem(or(not(or(X3,X2)),or(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
theorem(or(not(or(X3,X2)),or(X2,X3))) = ifeq(true,true,theorem(or(not(or(X3,X2)),or(X2,X3))),true),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,axiom,
axiom(or(not(or(A2,B2)),or(B2,A2))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
cnf(c16,plain,
axiom(or(not(or(X3,X2)),or(X2,X3))) = true,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
true = axiom(or(not(or(X3,X2)),or(X2,X3))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
ifeq(true,true,theorem(or(not(or(X3,X2)),or(X2,X3))),true) = ifeq(axiom(or(not(or(X3,X2)),or(X2,X3))),true,theorem(or(not(or(X3,X2)),or(X2,X3))),true),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
ifeq(axiom(X),true,theorem(X),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
cnf(c20,plain,
ifeq(axiom(or(not(or(X3,X2)),or(X2,X3))),true,theorem(or(not(or(X3,X2)),or(X2,X3))),true) = true,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
ifeq(true,true,theorem(or(not(or(X3,X2)),or(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
theorem(or(not(or(X3,X2)),or(X2,X3))) = true,
inference(transitivity,[status(thm)],[c14,c21]) ).
cnf(c23,plain,
theorem(or(not(or(X2,X3)),or(X3,X2))) = true,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
true = theorem(or(not(or(X2,X3)),or(X3,X2))),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
ifeq(true,true,theorem(or(X3,or(not(or(X2,X3)),X2))),true) = ifeq(theorem(or(not(or(X2,X3)),or(X3,X2))),true,theorem(or(X3,or(not(or(X2,X3)),X2))),true),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
ifeq(true,true,theorem(or(X3,or(X4,X2))),true) = theorem(or(X3,or(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
theorem(or(X3,or(X4,X2))) = ifeq(true,true,theorem(or(X3,or(X4,X2))),true),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true) = ifeq(theorem(or(X4,or(X3,X2))),true,ifeq(true,true,theorem(or(X3,or(X4,X2))),true),true),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,axiom,
axiom(or(not(or(A2,or(B2,C2))),or(B2,or(A2,C2)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
cnf(c30,plain,
axiom(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))) = true,
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
true = axiom(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
ifeq(true,true,theorem(or(X3,or(X4,X2))),true) = ifeq(axiom(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true,theorem(or(X3,or(X4,X2))),true),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
ifeq(theorem(or(X4,or(X3,X2))),true,ifeq(true,true,theorem(or(X3,or(X4,X2))),true),true) = ifeq(theorem(or(X4,or(X3,X2))),true,ifeq(axiom(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true,theorem(or(X3,or(X4,X2))),true),true),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
ifeq(theorem(Y),true,ifeq(axiom(or(not(Y),X2)),true,theorem(X2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
cnf(c35,plain,
ifeq(theorem(or(X4,or(X3,X2))),true,ifeq(axiom(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true,theorem(or(X3,or(X4,X2))),true),true) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq(theorem(or(X4,or(X3,X2))),true,ifeq(true,true,theorem(or(X3,or(X4,X2))),true),true) = true,
inference(transitivity,[status(thm)],[c33,c35]) ).
cnf(c37,plain,
ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c28,c36]) ).
cnf(c38,plain,
ifeq(theorem(or(not(or(X2,X3)),or(X3,X2))),true,theorem(or(X3,or(not(or(X2,X3)),X2))),true) = true,
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
ifeq(true,true,theorem(or(X3,or(not(or(X2,X3)),X2))),true) = true,
inference(transitivity,[status(thm)],[c25,c38]) ).
cnf(c40,plain,
theorem(or(X3,or(not(or(X2,X3)),X2))) = true,
inference(transitivity,[status(thm)],[c12,c39]) ).
cnf(c41,plain,
theorem(or(not(or(X3,X4)),or(not(or(X2,not(or(X3,X4)))),X2))) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
true = theorem(or(not(or(X3,X4)),or(not(or(X2,not(or(X3,X4)))),X2))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
ifeq(true,true,theorem(or(not(or(X4,X3)),or(not(or(X2,not(or(X3,X4)))),X2))),true) = ifeq(theorem(or(not(or(X3,X4)),or(not(or(X2,not(or(X3,X4)))),X2))),true,theorem(or(not(or(X4,X3)),or(not(or(X2,not(or(X3,X4)))),X2))),true),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
ifeq(true,true,theorem(or(not(or(X3,X4)),X2)),true) = theorem(or(not(or(X3,X4)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
theorem(or(not(or(X3,X4)),X2)) = ifeq(true,true,theorem(or(not(or(X3,X4)),X2)),true),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(or(X3,X4)),X2)),true) = ifeq(theorem(or(not(or(X4,X3)),X2)),true,ifeq(true,true,theorem(or(not(or(X3,X4)),X2)),true),true),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
axiom(or(not(or(X2,X3)),or(X3,X2))) = true,
inference(substitution,[status(thm)],[c15]) ).
cnf(c48,plain,
true = axiom(or(not(or(X2,X3)),or(X3,X2))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
ifeq(true,true,theorem(or(not(or(X3,X4)),X2)),true) = ifeq(axiom(or(not(or(X3,X4)),or(X4,X3))),true,theorem(or(not(or(X3,X4)),X2)),true),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
ifeq(theorem(or(not(or(X4,X3)),X2)),true,ifeq(true,true,theorem(or(not(or(X3,X4)),X2)),true),true) = ifeq(theorem(or(not(or(X4,X3)),X2)),true,ifeq(axiom(or(not(or(X3,X4)),or(X4,X3))),true,theorem(or(not(or(X3,X4)),X2)),true),true),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,axiom,
ifeq(theorem(or(not(Y2),Z)),true,ifeq(axiom(or(not(X2),Y2)),true,theorem(or(not(X2),Z)),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_3) ).
cnf(c52,plain,
ifeq(theorem(or(not(or(X4,X3)),X2)),true,ifeq(axiom(or(not(or(X3,X4)),or(X4,X3))),true,theorem(or(not(or(X3,X4)),X2)),true),true) = true,
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
ifeq(theorem(or(not(or(X4,X3)),X2)),true,ifeq(true,true,theorem(or(not(or(X3,X4)),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(or(X3,X4)),X2)),true) = true,
inference(transitivity,[status(thm)],[c46,c53]) ).
cnf(c55,plain,
ifeq(theorem(or(not(or(X3,X4)),or(not(or(X2,not(or(X3,X4)))),X2))),true,theorem(or(not(or(X4,X3)),or(not(or(X2,not(or(X3,X4)))),X2))),true) = true,
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
ifeq(true,true,theorem(or(not(or(X4,X3)),or(not(or(X2,not(or(X3,X4)))),X2))),true) = true,
inference(transitivity,[status(thm)],[c43,c55]) ).
cnf(c57,plain,
theorem(or(not(or(X4,X3)),or(not(or(X2,not(or(X3,X4)))),X2))) = true,
inference(transitivity,[status(thm)],[c10,c56]) ).
cnf(c58,plain,
theorem(or(not(or(X2,X4)),or(not(or(X3,not(or(X4,X2)))),X3))) = true,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
true = theorem(or(not(or(X2,X4)),or(not(or(X3,not(or(X4,X2)))),X3))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
ifeq(true,true,theorem(or(not(X4),or(not(or(X3,not(or(X4,X2)))),X3))),true) = ifeq(theorem(or(not(or(X2,X4)),or(not(or(X3,not(or(X4,X2)))),X3))),true,theorem(or(not(X4),or(not(or(X3,not(or(X4,X2)))),X3))),true),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
ifeq(true,true,theorem(or(not(X3),X2)),true) = theorem(or(not(X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c62,plain,
theorem(or(not(X3),X2)) = ifeq(true,true,theorem(or(not(X3),X2)),true),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true) = ifeq(theorem(or(not(or(X4,X3)),X2)),true,ifeq(true,true,theorem(or(not(X3),X2)),true),true),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,axiom,
axiom(or(not(A2),or(B2,A2))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
cnf(c65,plain,
axiom(or(not(X2),or(X3,X2))) = true,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
true = axiom(or(not(X2),or(X3,X2))),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
ifeq(true,true,theorem(or(not(X3),X2)),true) = ifeq(axiom(or(not(X3),or(X4,X3))),true,theorem(or(not(X3),X2)),true),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
ifeq(theorem(or(not(or(X4,X3)),X2)),true,ifeq(true,true,theorem(or(not(X3),X2)),true),true) = ifeq(theorem(or(not(or(X4,X3)),X2)),true,ifeq(axiom(or(not(X3),or(X4,X3))),true,theorem(or(not(X3),X2)),true),true),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
ifeq(theorem(or(not(or(X4,X3)),X2)),true,ifeq(axiom(or(not(X3),or(X4,X3))),true,theorem(or(not(X3),X2)),true),true) = true,
inference(substitution,[status(thm)],[c51]) ).
cnf(c70,plain,
ifeq(theorem(or(not(or(X4,X3)),X2)),true,ifeq(true,true,theorem(or(not(X3),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true) = true,
inference(transitivity,[status(thm)],[c63,c70]) ).
cnf(c72,plain,
ifeq(theorem(or(not(or(X2,X4)),or(not(or(X3,not(or(X4,X2)))),X3))),true,theorem(or(not(X4),or(not(or(X3,not(or(X4,X2)))),X3))),true) = true,
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
ifeq(true,true,theorem(or(not(X4),or(not(or(X3,not(or(X4,X2)))),X3))),true) = true,
inference(transitivity,[status(thm)],[c60,c72]) ).
cnf(c74,plain,
theorem(or(not(X4),or(not(or(X3,not(or(X4,X2)))),X3))) = true,
inference(transitivity,[status(thm)],[c8,c73]) ).
cnf(c75,plain,
theorem(or(not(X3),or(not(or(X4,not(or(X3,X2)))),X4))) = true,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
true = theorem(or(not(X3),or(not(or(X4,not(or(X3,X2)))),X4))),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
ifeq(true,true,theorem(or(not(or(X4,not(or(X3,X2)))),or(not(X3),X4))),true) = ifeq(theorem(or(not(X3),or(not(or(X4,not(or(X3,X2)))),X4))),true,theorem(or(not(or(X4,not(or(X3,X2)))),or(not(X3),X4))),true),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
ifeq(theorem(or(not(X3),or(not(or(X4,not(or(X3,X2)))),X4))),true,theorem(or(not(or(X4,not(or(X3,X2)))),or(not(X3),X4))),true) = true,
inference(substitution,[status(thm)],[c37]) ).
cnf(c79,plain,
ifeq(true,true,theorem(or(not(or(X4,not(or(X3,X2)))),or(not(X3),X4))),true) = true,
inference(transitivity,[status(thm)],[c77,c78]) ).
cnf(c80,plain,
theorem(or(not(or(X4,not(or(X3,X2)))),or(not(X3),X4))) = true,
inference(transitivity,[status(thm)],[c6,c79]) ).
cnf(c81,plain,
theorem(or(not(or(X2,not(or(X4,X3)))),or(not(X4),X2))) = true,
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
true = theorem(or(not(or(X2,not(or(X4,X3)))),or(not(X4),X2))),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
ifeq(true,true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X4),X2))),true) = ifeq(theorem(or(not(or(X2,not(or(X4,X3)))),or(not(X4),X2))),true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X4),X2))),true),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
ifeq(theorem(or(not(or(X2,not(or(X4,X3)))),or(not(X4),X2))),true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X4),X2))),true) = true,
inference(substitution,[status(thm)],[c54]) ).
cnf(c85,plain,
ifeq(true,true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X4),X2))),true) = true,
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X4),X2))) = true,
inference(transitivity,[status(thm)],[c4,c85]) ).
cnf(c87,plain,
theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) = true,
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
$false,
inference(resolution,[status(thm)],[c1,c87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL218-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 15:26:36 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.78/1.94 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
% 11.78/1.94
% 11.78/1.94 % SZS status Unsatisfiable
% 11.78/1.94
% 11.78/1.94 % SZS output start CNFRefutation
% See solution above
% 11.78/2.00
% 11.78/2.00 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------