%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL239-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 11:49:27 AM UTC 2026
% Result : Unsatisfiable 1.76s 0.76s
% Output : CNFRefutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 10
% Syntax : Number of clauses : 132 ( 132 unt; 0 nHn; 3 RR)
% Number of literals : 132 ( 131 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-4 aty)
% Number of variables : 225 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
theorem(not(and(p,not(p)))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(c2,axiom,
implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
cnf(c3,plain,
implies(X3,not(X2)) = or(not(X3),not(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
not(implies(X3,not(X2))) = not(or(not(X3),not(X2))),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
and(P,Q) = not(or(not(P),not(Q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
cnf(c6,plain,
and(X3,X2) = not(or(not(X3),not(X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
not(or(not(X3),not(X2))) = and(X3,X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
not(implies(X3,not(X2))) = and(X3,X2),
inference(transitivity,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
not(implies(X2,not(not(X2)))) = and(X2,not(X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
and(X2,not(X2)) = not(implies(X2,not(not(X2)))),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
not(and(X2,not(X2))) = not(not(implies(X2,not(not(X2))))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
theorem(not(and(X2,not(X2)))) = theorem(not(not(implies(X2,not(not(X2)))))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c14,plain,
ifeq(true,true,theorem(not(not(implies(X2,not(not(X2)))))),true) = theorem(not(not(implies(X2,not(not(X2)))))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
theorem(not(not(implies(X2,not(not(X2)))))) = ifeq(true,true,theorem(not(not(implies(X2,not(not(X2)))))),true),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
implies(X2,not(not(X2))) = or(not(X2),not(not(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
theorem(implies(X2,not(not(X2)))) = theorem(or(not(X2),not(not(X2)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
ifeq(true,true,theorem(or(X2,not(X2))),true) = theorem(or(X2,not(X2))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c19,plain,
theorem(or(X2,not(X2))) = ifeq(true,true,theorem(or(X2,not(X2))),true),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
ifeq(true,true,theorem(implies(X2,X2)),true) = theorem(implies(X2,X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c21,plain,
theorem(implies(X2,X2)) = ifeq(true,true,theorem(implies(X2,X2)),true),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
ifeq(true,true,theorem(or(X3,implies(X2,X2))),true) = theorem(or(X3,implies(X2,X2))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c23,plain,
theorem(or(X3,implies(X2,X2))) = ifeq(true,true,theorem(or(X3,implies(X2,X2))),true),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
ifeq(true,true,theorem(implies(implies(X3,or(X2,X4)),or(X2,implies(X3,X4)))),true) = theorem(implies(implies(X3,or(X2,X4)),or(X2,implies(X3,X4)))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c25,plain,
theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))) = ifeq(true,true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
implies(X3,X2) = or(not(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
or(X3,implies(X4,X2)) = or(X3,or(not(X4),X2)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2))) = implies(implies(X4,or(X3,X2)),or(X3,or(not(X4),X2))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
axiom(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))) = axiom(implies(implies(X4,or(X3,X2)),or(X3,or(not(X4),X2)))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
implies(X4,or(X3,X2)) = or(not(X4),or(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
implies(implies(X4,or(X3,X2)),or(X3,or(not(X4),X2))) = implies(or(not(X4),or(X3,X2)),or(X3,or(not(X4),X2))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
axiom(implies(implies(X4,or(X3,X2)),or(X3,or(not(X4),X2)))) = axiom(implies(or(not(X4),or(X3,X2)),or(X3,or(not(X4),X2)))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,axiom,
axiom(implies(or(A2,or(B2,C2)),or(B2,or(A2,C2)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
cnf(c34,plain,
axiom(implies(or(not(X4),or(X3,X2)),or(X3,or(not(X4),X2)))) = true,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
axiom(implies(implies(X4,or(X3,X2)),or(X3,or(not(X4),X2)))) = true,
inference(transitivity,[status(thm)],[c32,c34]) ).
cnf(c36,plain,
axiom(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c29,c35]) ).
cnf(c37,plain,
true = axiom(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
ifeq(true,true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true) = ifeq(axiom(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
ifeq(axiom(X2),true,theorem(X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
cnf(c40,plain,
ifeq(axiom(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
ifeq(true,true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c38,c40]) ).
cnf(c42,plain,
theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c25,c41]) ).
cnf(c43,plain,
theorem(implies(implies(X2,or(X3,X2)),or(X3,implies(X2,X2)))) = true,
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
true = theorem(implies(implies(X2,or(X3,X2)),or(X3,implies(X2,X2)))),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
ifeq(true,true,theorem(or(X3,implies(X2,X2))),true) = ifeq(theorem(implies(implies(X2,or(X3,X2)),or(X3,implies(X2,X2)))),true,theorem(or(X3,implies(X2,X2))),true),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
ifeq(true,true,theorem(X2),true) = theorem(X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c47,plain,
theorem(X2) = ifeq(true,true,theorem(X2),true),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,theorem(X2),true) = ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,ifeq(true,true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
ifeq(true,true,theorem(implies(X3,or(X2,X3))),true) = theorem(implies(X3,or(X2,X3))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c50,plain,
theorem(implies(X3,or(X2,X3))) = ifeq(true,true,theorem(implies(X3,or(X2,X3))),true),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,axiom,
axiom(implies(A2,or(B2,A2))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
cnf(c52,plain,
axiom(implies(X3,or(X2,X3))) = true,
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
true = axiom(implies(X3,or(X2,X3))),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
ifeq(true,true,theorem(implies(X3,or(X2,X3))),true) = ifeq(axiom(implies(X3,or(X2,X3))),true,theorem(implies(X3,or(X2,X3))),true),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
ifeq(axiom(implies(X3,or(X2,X3))),true,theorem(implies(X3,or(X2,X3))),true) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c56,plain,
ifeq(true,true,theorem(implies(X3,or(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c54,c55]) ).
cnf(c57,plain,
theorem(implies(X3,or(X2,X3))) = true,
inference(transitivity,[status(thm)],[c50,c56]) ).
cnf(c58,plain,
true = theorem(implies(X3,or(X2,X3))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
ifeq(true,true,theorem(X2),true) = ifeq(theorem(implies(X4,or(X3,X4))),true,theorem(X2),true),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,ifeq(true,true,theorem(X2),true),true) = ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,ifeq(theorem(implies(X4,or(X3,X4))),true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,axiom,
ifeq(theorem(implies(Y2,X2)),true,ifeq(theorem(Y2),true,theorem(X2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
cnf(c62,plain,
ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,ifeq(theorem(implies(X4,or(X3,X4))),true,theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,ifeq(true,true,theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c60,c62]) ).
cnf(c64,plain,
ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c48,c63]) ).
cnf(c65,plain,
ifeq(theorem(implies(implies(X2,or(X3,X2)),or(X3,implies(X2,X2)))),true,theorem(or(X3,implies(X2,X2))),true) = true,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
ifeq(true,true,theorem(or(X3,implies(X2,X2))),true) = true,
inference(transitivity,[status(thm)],[c45,c65]) ).
cnf(c67,plain,
theorem(or(X3,implies(X2,X2))) = true,
inference(transitivity,[status(thm)],[c23,c66]) ).
cnf(c68,plain,
theorem(or(implies(X2,X2),implies(X2,X2))) = true,
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
true = theorem(or(implies(X2,X2),implies(X2,X2))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
ifeq(true,true,theorem(implies(X2,X2)),true) = ifeq(theorem(or(implies(X2,X2),implies(X2,X2))),true,theorem(implies(X2,X2)),true),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
ifeq(true,true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = ifeq(theorem(or(X2,X2)),true,theorem(X2),true),
inference(substitution,[status(thm)],[c13]) ).
cnf(c72,plain,
ifeq(theorem(or(X2,X2)),true,theorem(X2),true) = ifeq(true,true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
ifeq(true,true,theorem(implies(or(X2,X2),X2)),true) = theorem(implies(or(X2,X2),X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c74,plain,
theorem(implies(or(X2,X2),X2)) = ifeq(true,true,theorem(implies(or(X2,X2),X2)),true),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,axiom,
axiom(implies(or(A2,A2),A2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
cnf(c76,plain,
axiom(implies(or(X2,X2),X2)) = true,
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
true = axiom(implies(or(X2,X2),X2)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
ifeq(true,true,theorem(implies(or(X2,X2),X2)),true) = ifeq(axiom(implies(or(X2,X2),X2)),true,theorem(implies(or(X2,X2),X2)),true),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
ifeq(axiom(implies(or(X2,X2),X2)),true,theorem(implies(or(X2,X2),X2)),true) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c80,plain,
ifeq(true,true,theorem(implies(or(X2,X2),X2)),true) = true,
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
theorem(implies(or(X2,X2),X2)) = true,
inference(transitivity,[status(thm)],[c74,c80]) ).
cnf(c82,plain,
true = theorem(implies(or(X2,X2),X2)),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
ifeq(true,true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = ifeq(theorem(implies(or(X2,X2),X2)),true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
ifeq(theorem(implies(or(X2,X2),X2)),true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c61]) ).
cnf(c85,plain,
ifeq(true,true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
ifeq(theorem(or(X2,X2)),true,theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c72,c85]) ).
cnf(c87,plain,
ifeq(theorem(or(implies(X2,X2),implies(X2,X2))),true,theorem(implies(X2,X2)),true) = true,
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
ifeq(true,true,theorem(implies(X2,X2)),true) = true,
inference(transitivity,[status(thm)],[c70,c87]) ).
cnf(c89,plain,
theorem(implies(X2,X2)) = true,
inference(transitivity,[status(thm)],[c21,c88]) ).
cnf(c90,plain,
true = theorem(implies(X2,X2)),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
ifeq(true,true,theorem(or(X2,not(X2))),true) = ifeq(theorem(implies(X2,X2)),true,theorem(or(X2,not(X2))),true),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
ifeq(true,true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true) = ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),
inference(substitution,[status(thm)],[c13]) ).
cnf(c93,plain,
ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true) = ifeq(true,true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
implies(X3,X2) = or(not(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c95,plain,
implies(implies(X3,X2),or(X2,not(X3))) = implies(or(not(X3),X2),or(X2,not(X3))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
theorem(implies(implies(X3,X2),or(X2,not(X3)))) = theorem(implies(or(not(X3),X2),or(X2,not(X3)))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
ifeq(true,true,theorem(implies(or(X3,X2),or(X2,X3))),true) = theorem(implies(or(X3,X2),or(X2,X3))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c98,plain,
theorem(implies(or(X3,X2),or(X2,X3))) = ifeq(true,true,theorem(implies(or(X3,X2),or(X2,X3))),true),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,axiom,
axiom(implies(or(A2,B2),or(B2,A2))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
cnf(c100,plain,
axiom(implies(or(X3,X2),or(X2,X3))) = true,
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
true = axiom(implies(or(X3,X2),or(X2,X3))),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
ifeq(true,true,theorem(implies(or(X3,X2),or(X2,X3))),true) = ifeq(axiom(implies(or(X3,X2),or(X2,X3))),true,theorem(implies(or(X3,X2),or(X2,X3))),true),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
ifeq(axiom(implies(or(X3,X2),or(X2,X3))),true,theorem(implies(or(X3,X2),or(X2,X3))),true) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c104,plain,
ifeq(true,true,theorem(implies(or(X3,X2),or(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c102,c103]) ).
cnf(c105,plain,
theorem(implies(or(X3,X2),or(X2,X3))) = true,
inference(transitivity,[status(thm)],[c98,c104]) ).
cnf(c106,plain,
theorem(implies(or(not(X3),X2),or(X2,not(X3)))) = true,
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
theorem(implies(implies(X3,X2),or(X2,not(X3)))) = true,
inference(transitivity,[status(thm)],[c96,c106]) ).
cnf(c108,plain,
true = theorem(implies(implies(X3,X2),or(X2,not(X3)))),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
ifeq(true,true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true) = ifeq(theorem(implies(implies(X3,X2),or(X2,not(X3)))),true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
ifeq(theorem(implies(implies(X3,X2),or(X2,not(X3)))),true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true) = true,
inference(substitution,[status(thm)],[c61]) ).
cnf(c111,plain,
ifeq(true,true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true) = true,
inference(transitivity,[status(thm)],[c109,c110]) ).
cnf(c112,plain,
ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true) = true,
inference(transitivity,[status(thm)],[c93,c111]) ).
cnf(c113,plain,
ifeq(theorem(implies(X2,X2)),true,theorem(or(X2,not(X2))),true) = true,
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
ifeq(true,true,theorem(or(X2,not(X2))),true) = true,
inference(transitivity,[status(thm)],[c91,c113]) ).
cnf(c115,plain,
theorem(or(X2,not(X2))) = true,
inference(transitivity,[status(thm)],[c19,c114]) ).
cnf(c116,plain,
theorem(or(not(X2),not(not(X2)))) = true,
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
theorem(implies(X2,not(not(X2)))) = true,
inference(transitivity,[status(thm)],[c17,c116]) ).
cnf(c118,plain,
true = theorem(implies(X2,not(not(X2)))),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
ifeq(true,true,theorem(not(not(implies(X2,not(not(X2)))))),true) = ifeq(theorem(implies(X2,not(not(X2)))),true,theorem(not(not(implies(X2,not(not(X2)))))),true),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
ifeq(true,true,ifeq(theorem(X2),true,theorem(not(not(X2))),true),true) = ifeq(theorem(X2),true,theorem(not(not(X2))),true),
inference(substitution,[status(thm)],[c13]) ).
cnf(c121,plain,
ifeq(theorem(X2),true,theorem(not(not(X2))),true) = ifeq(true,true,ifeq(theorem(X2),true,theorem(not(not(X2))),true),true),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
true = theorem(implies(X2,not(not(X2)))),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c123,plain,
ifeq(true,true,ifeq(theorem(X2),true,theorem(not(not(X2))),true),true) = ifeq(theorem(implies(X2,not(not(X2)))),true,ifeq(theorem(X2),true,theorem(not(not(X2))),true),true),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
ifeq(theorem(implies(X2,not(not(X2)))),true,ifeq(theorem(X2),true,theorem(not(not(X2))),true),true) = true,
inference(substitution,[status(thm)],[c61]) ).
cnf(c125,plain,
ifeq(true,true,ifeq(theorem(X2),true,theorem(not(not(X2))),true),true) = true,
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
ifeq(theorem(X2),true,theorem(not(not(X2))),true) = true,
inference(transitivity,[status(thm)],[c121,c125]) ).
cnf(c127,plain,
ifeq(theorem(implies(X2,not(not(X2)))),true,theorem(not(not(implies(X2,not(not(X2)))))),true) = true,
inference(substitution,[status(thm)],[c126]) ).
cnf(c128,plain,
ifeq(true,true,theorem(not(not(implies(X2,not(not(X2)))))),true) = true,
inference(transitivity,[status(thm)],[c119,c127]) ).
cnf(c129,plain,
theorem(not(not(implies(X2,not(not(X2)))))) = true,
inference(transitivity,[status(thm)],[c15,c128]) ).
cnf(c130,plain,
theorem(not(and(X2,not(X2)))) = true,
inference(transitivity,[status(thm)],[c12,c129]) ).
cnf(c131,plain,
theorem(not(and(p,not(p)))) = true,
inference(substitution,[status(thm)],[c130]) ).
cnf(c132,plain,
$false,
inference(resolution,[status(thm)],[c1,c131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL239-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:30:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.76/0.76 Command-line arguments: --no-flatten-goal
% 1.76/0.76
% 1.76/0.76 % SZS status Unsatisfiable
% 1.76/0.76
% 1.76/0.77 % SZS output start CNFRefutation
% See solution above
% 2.55/0.89
% 2.55/0.89 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------