%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 11:49:02 AM UTC 2026
% Result : Unsatisfiable 3.74s 1.02s
% Output : CNFRefutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of clauses : 109 ( 109 unt; 0 nHn; 3 RR)
% Number of literals : 109 ( 108 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 233 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(c2,axiom,
implies(not(X),not(Y)) = implies(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_10) ).
cnf(c3,plain,
implies(not(X2),not(implies(X3,X2))) = implies(implies(X3,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
implies(implies(X3,X2),X2) = implies(not(X2),not(implies(X3,X2))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
implies(not(X2),not(implies(X3,X2))) = implies(implies(X3,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,axiom,
implies(implies(X2,Y2),Y2) = implies(implies(Y2,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
cnf(c7,plain,
implies(implies(X2,X3),X3) = implies(implies(X3,X2),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
implies(implies(X3,X2),X2) = implies(implies(X2,X3),X3),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
implies(not(X3),not(implies(X2,X3))) = implies(implies(X2,X3),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
implies(implies(X2,X3),X3) = implies(not(X3),not(implies(X2,X3))),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
implies(implies(X3,X2),X2) = implies(not(X3),not(implies(X2,X3))),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
implies(not(X2),not(implies(X3,X2))) = implies(not(X3),not(implies(X2,X3))),
inference(transitivity,[status(thm)],[c5,c11]) ).
cnf(c13,plain,
implies(not(X3),not(implies(X2,X3))) = implies(implies(X2,X3),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
implies(not(X2),not(implies(X3,X2))) = implies(implies(X2,X3),X3),
inference(transitivity,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
implies(implies(X3,X2),X2) = implies(implies(X2,X3),X3),
inference(transitivity,[status(thm)],[c4,c14]) ).
cnf(c16,plain,
implies(implies(X2,X3),X3) = implies(implies(X3,X2),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
implies(implies(X3,X2),X2) = implies(implies(X2,X3),X3),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
not(implies(implies(X3,X2),X2)) = not(implies(implies(X2,X3),X3)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
implies(not(X3),not(implies(implies(X3,X2),X2))) = implies(not(X3),not(implies(implies(X2,X3),X3))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
implies(not(X3),not(implies(implies(X2,X3),X3))) = implies(not(implies(X2,X3)),not(implies(X3,implies(X2,X3)))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c21,axiom,
implies(X2,implies(Y2,X2)) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_4) ).
cnf(c22,plain,
implies(X3,implies(X2,X3)) = truth,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
not(implies(X3,implies(X2,X3))) = not(truth),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
implies(not(implies(X2,X3)),not(implies(X3,implies(X2,X3)))) = implies(not(implies(X2,X3)),not(truth)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,axiom,
implies(X2,not(truth)) = not(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_8) ).
cnf(c26,plain,
implies(not(implies(X2,X3)),not(truth)) = not(not(implies(X2,X3))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,axiom,
not(not(X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_9) ).
cnf(c28,plain,
not(not(implies(X2,X3))) = implies(X2,X3),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
implies(not(implies(X2,X3)),not(truth)) = implies(X2,X3),
inference(transitivity,[status(thm)],[c26,c28]) ).
cnf(c30,plain,
implies(not(implies(X2,X3)),not(implies(X3,implies(X2,X3)))) = implies(X2,X3),
inference(transitivity,[status(thm)],[c24,c29]) ).
cnf(c31,plain,
implies(not(X3),not(implies(implies(X2,X3),X3))) = implies(X2,X3),
inference(transitivity,[status(thm)],[c20,c30]) ).
cnf(c32,plain,
implies(not(X3),not(implies(implies(X3,X2),X2))) = implies(X2,X3),
inference(transitivity,[status(thm)],[c19,c31]) ).
cnf(c33,plain,
implies(not(X2),not(implies(implies(X2,X3),X3))) = implies(X3,X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
implies(X3,X2) = implies(not(X2),not(implies(implies(X2,X3),X3))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
implies(implies(X2,X3),implies(X3,X2)) = implies(implies(X2,X3),implies(not(X2),not(implies(implies(X2,X3),X3)))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
not(not(implies(X3,X2))) = implies(X3,X2),
inference(substitution,[status(thm)],[c27]) ).
cnf(c37,plain,
implies(X2,X3) = not(not(implies(X2,X3))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
implies(implies(X2,X4),X3) = implies(not(not(implies(X2,X4))),X3),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
implies(X2,implies(implies(X2,X4),X3)) = implies(X2,implies(not(not(implies(X2,X4))),X3)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
implies(not(X2),not(not(X3))) = implies(not(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c41,plain,
implies(not(X3),X2) = implies(not(X2),not(not(X3))),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
implies(not(X2),not(not(X3))) = implies(not(X2),X3),
inference(congruence,[status(thm)],[c27]) ).
cnf(c43,plain,
implies(not(X3),X2) = implies(not(X2),X3),
inference(transitivity,[status(thm)],[c41,c42]) ).
cnf(c44,plain,
implies(not(X2),implies(X4,X3)) = implies(not(implies(X4,X3)),X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
implies(not(implies(X4,X3)),X2) = implies(not(X2),implies(X4,X3)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,axiom,
implies(X2,implies(Y2,Z)) = implies(Y2,implies(X2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_7) ).
cnf(c47,plain,
implies(X3,implies(not(X4),X2)) = implies(not(X4),implies(X3,X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
implies(not(X4),implies(X3,X2)) = implies(X3,implies(not(X4),X2)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
implies(X3,implies(not(X4),X2)) = implies(X3,implies(not(X2),X4)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c50,plain,
implies(not(X4),implies(X3,X2)) = implies(X3,implies(not(X2),X4)),
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
implies(not(X2),implies(X4,X3)) = implies(X4,implies(not(X3),X2)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
implies(not(implies(X4,X3)),X2) = implies(X4,implies(not(X3),X2)),
inference(transitivity,[status(thm)],[c45,c51]) ).
cnf(c53,plain,
implies(not(implies(X2,not(implies(X2,X4)))),X3) = implies(X2,implies(not(not(implies(X2,X4))),X3)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
implies(X2,implies(not(not(implies(X2,X4))),X3)) = implies(not(implies(X2,not(implies(X2,X4)))),X3),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
implies(not(X3),not(X2)) = implies(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c56,plain,
implies(X2,X3) = implies(not(X3),not(X2)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
not(implies(X2,X3)) = not(implies(not(X3),not(X2))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
implies(X2,not(implies(X2,X3))) = implies(X2,not(implies(not(X3),not(X2)))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
implies(not(X2),X3) = implies(not(X3),X2),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c60,plain,
not(implies(not(X2),X3)) = not(implies(not(X3),X2)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
implies(not(X2),not(implies(not(X2),X3))) = implies(not(X2),not(implies(not(X3),X2))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
implies(not(not(X3)),not(implies(X2,not(X3)))) = implies(not(X2),not(implies(not(X3),X2))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c63,plain,
implies(not(X2),not(implies(not(X3),X2))) = implies(not(not(X3)),not(implies(X2,not(X3)))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
implies(not(not(X3)),not(implies(X2,not(X3)))) = implies(X3,not(implies(X2,not(X3)))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c65,plain,
implies(not(X2),not(implies(not(X3),X2))) = implies(X3,not(implies(X2,not(X3)))),
inference(transitivity,[status(thm)],[c63,c64]) ).
cnf(c66,plain,
implies(not(X2),not(implies(not(X2),X3))) = implies(X3,not(implies(X2,not(X3)))),
inference(transitivity,[status(thm)],[c61,c65]) ).
cnf(c67,plain,
implies(not(not(X3)),not(implies(not(not(X3)),X2))) = implies(X2,not(implies(not(X3),not(X2)))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
implies(X2,not(implies(not(X3),not(X2)))) = implies(not(not(X3)),not(implies(not(not(X3)),X2))),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
implies(not(not(X3)),X2) = implies(X3,X2),
inference(congruence,[status(thm)],[c27]) ).
cnf(c70,plain,
not(implies(not(not(X3)),X2)) = not(implies(X3,X2)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
implies(not(not(X3)),not(implies(not(not(X3)),X2))) = implies(not(not(X3)),not(implies(X3,X2))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
implies(not(not(X3)),not(implies(X3,X2))) = implies(X3,not(implies(X3,X2))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c73,plain,
implies(not(not(X3)),not(implies(not(not(X3)),X2))) = implies(X3,not(implies(X3,X2))),
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
implies(X2,not(implies(not(X3),not(X2)))) = implies(X3,not(implies(X3,X2))),
inference(transitivity,[status(thm)],[c68,c73]) ).
cnf(c75,plain,
implies(X2,not(implies(X2,X3))) = implies(X3,not(implies(X3,X2))),
inference(transitivity,[status(thm)],[c58,c74]) ).
cnf(c76,plain,
not(implies(X2,not(implies(X2,X3)))) = not(implies(X3,not(implies(X3,X2)))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
implies(not(implies(X2,not(implies(X2,X4)))),X3) = implies(not(implies(X4,not(implies(X4,X2)))),X3),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
implies(not(implies(X4,not(implies(X4,X2)))),X3) = implies(X4,implies(not(not(implies(X4,X2))),X3)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c79,plain,
not(not(implies(X3,X2))) = implies(X3,X2),
inference(substitution,[status(thm)],[c27]) ).
cnf(c80,plain,
implies(not(not(implies(X4,X2))),X3) = implies(implies(X4,X2),X3),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
implies(X4,implies(not(not(implies(X4,X2))),X3)) = implies(X4,implies(implies(X4,X2),X3)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
implies(not(X3),not(implies(X4,X2))) = implies(implies(X4,X2),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c83,plain,
implies(implies(X4,X2),X3) = implies(not(X3),not(implies(X4,X2))),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
implies(X4,implies(implies(X4,X2),X3)) = implies(X4,implies(not(X3),not(implies(X4,X2)))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
implies(X4,implies(not(not(implies(X4,X2))),X3)) = implies(X4,implies(not(X3),not(implies(X4,X2)))),
inference(transitivity,[status(thm)],[c81,c84]) ).
cnf(c86,plain,
implies(not(implies(X4,not(implies(X4,X2)))),X3) = implies(X4,implies(not(X3),not(implies(X4,X2)))),
inference(transitivity,[status(thm)],[c78,c85]) ).
cnf(c87,plain,
implies(not(implies(X2,not(implies(X2,X4)))),X3) = implies(X4,implies(not(X3),not(implies(X4,X2)))),
inference(transitivity,[status(thm)],[c77,c86]) ).
cnf(c88,plain,
implies(X2,implies(not(not(implies(X2,X4))),X3)) = implies(X4,implies(not(X3),not(implies(X4,X2)))),
inference(transitivity,[status(thm)],[c54,c87]) ).
cnf(c89,plain,
implies(X2,implies(implies(X2,X4),X3)) = implies(X4,implies(not(X3),not(implies(X4,X2)))),
inference(transitivity,[status(thm)],[c39,c88]) ).
cnf(c90,plain,
implies(X3,implies(implies(X3,implies(X2,X3)),X2)) = implies(implies(X2,X3),implies(not(X2),not(implies(implies(X2,X3),X3)))),
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
implies(implies(X2,X3),implies(not(X2),not(implies(implies(X2,X3),X3)))) = implies(X3,implies(implies(X3,implies(X2,X3)),X2)),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
implies(implies(X3,implies(X2,X3)),implies(X3,X2)) = implies(X3,implies(implies(X3,implies(X2,X3)),X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c93,plain,
implies(X3,implies(implies(X3,implies(X2,X3)),X2)) = implies(implies(X3,implies(X2,X3)),implies(X3,X2)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
implies(X3,implies(X2,X3)) = truth,
inference(substitution,[status(thm)],[c21]) ).
cnf(c95,plain,
implies(implies(X3,implies(X2,X3)),implies(X3,X2)) = implies(truth,implies(X3,X2)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,axiom,
implies(truth,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
cnf(c97,plain,
implies(truth,implies(X3,X2)) = implies(X3,X2),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
implies(implies(X3,implies(X2,X3)),implies(X3,X2)) = implies(X3,X2),
inference(transitivity,[status(thm)],[c95,c97]) ).
cnf(c99,plain,
implies(X3,implies(implies(X3,implies(X2,X3)),X2)) = implies(X3,X2),
inference(transitivity,[status(thm)],[c93,c98]) ).
cnf(c100,plain,
implies(implies(X2,X3),implies(not(X2),not(implies(implies(X2,X3),X3)))) = implies(X3,X2),
inference(transitivity,[status(thm)],[c91,c99]) ).
cnf(c101,plain,
implies(implies(X2,X3),implies(X3,X2)) = implies(X3,X2),
inference(transitivity,[status(thm)],[c35,c100]) ).
cnf(c102,plain,
implies(implies(X3,X2),implies(X2,X3)) = implies(X2,X3),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
implies(X2,X3) = implies(implies(X3,X2),implies(X2,X3)),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
implies(implies(implies(X3,X2),implies(X2,X3)),implies(X2,X3)) = implies(implies(implies(X3,X2),implies(X2,X3)),implies(implies(X3,X2),implies(X2,X3))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,axiom,
implies(X2,X2) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1) ).
cnf(c106,plain,
implies(implies(implies(X3,X2),implies(X2,X3)),implies(implies(X3,X2),implies(X2,X3))) = truth,
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
implies(implies(implies(X3,X2),implies(X2,X3)),implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c104,c106]) ).
cnf(c108,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth,
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
$false,
inference(resolution,[status(thm)],[c1,c108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 15:24:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.74/1.02 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.74/1.02
% 3.74/1.02 % SZS status Unsatisfiable
% 3.74/1.02
% 3.74/1.02 % SZS output start CNFRefutation
% See solution above
% 4.86/1.07
% 4.86/1.07 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------