%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL109-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 11:49:03 AM UTC 2026
% Result : Unsatisfiable 16.92s 2.62s
% Output : CNFRefutation 19.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 5
% Syntax : Number of clauses : 333 ( 333 unt; 0 nHn; 64 RR)
% Number of literals : 333 ( 332 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 468 ( 40 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(truth,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
cnf(c3,plain,
implies(truth,implies(not(X3),not(X2))) = implies(not(X3),not(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
implies(not(X3),not(X2)) = implies(truth,implies(not(X3),not(X2))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
implies(truth,implies(X2,not(truth))) = implies(X2,not(truth)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
implies(X2,not(truth)) = implies(truth,implies(X2,not(truth))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
implies(truth,implies(not(X3),implies(X3,X2))) = implies(not(X3),implies(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
implies(not(X3),implies(X3,X2)) = implies(truth,implies(not(X3),implies(X3,X2))),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
implies(implies(not(X2),not(Y)),implies(Y,X2)) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).
cnf(c10,plain,
implies(implies(not(X2),not(X3)),implies(X3,X2)) = truth,
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
truth = implies(implies(not(X2),not(X3)),implies(X3,X2)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
implies(truth,implies(not(X3),implies(X3,X2))) = implies(implies(implies(not(X2),not(X3)),implies(X3,X2)),implies(not(X3),implies(X3,X2))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
implies(truth,implies(implies(implies(X3,X2),X4),implies(X2,X4))) = implies(implies(implies(X3,X2),X4),implies(X2,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
implies(implies(implies(X4,X3),X2),implies(X3,X2)) = implies(truth,implies(implies(implies(X4,X3),X2),implies(X3,X2))),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c16,plain,
implies(X3,implies(X2,X3)) = implies(implies(truth,X3),implies(X2,X3)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
implies(truth,implies(implies(truth,X3),implies(X2,X3))) = implies(implies(truth,X3),implies(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
implies(implies(truth,X3),implies(X2,X3)) = implies(truth,implies(implies(truth,X3),implies(X2,X3))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c20,plain,
implies(X2,X2) = implies(implies(truth,X2),X2),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
implies(truth,implies(implies(truth,X2),X2)) = implies(implies(truth,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
implies(implies(truth,X2),X2) = implies(truth,implies(implies(truth,X2),X2)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c24,plain,
implies(implies(X3,X2),X2) = implies(implies(X3,X2),implies(truth,X2)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
implies(X3,implies(implies(X3,X2),X2)) = implies(X3,implies(implies(X3,X2),implies(truth,X2))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c27,plain,
implies(X3,implies(implies(X3,X2),implies(truth,X2))) = implies(implies(truth,X3),implies(implies(X3,X2),implies(truth,X2))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,axiom,
implies(implies(X2,Y2),implies(implies(Y2,Z),implies(X2,Z))) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_2) ).
cnf(c29,plain,
implies(implies(truth,X3),implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
implies(X3,implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(transitivity,[status(thm)],[c27,c29]) ).
cnf(c31,plain,
implies(X3,implies(implies(X3,X2),X2)) = truth,
inference(transitivity,[status(thm)],[c25,c30]) ).
cnf(c32,plain,
implies(truth,implies(implies(truth,X2),X2)) = truth,
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
implies(implies(truth,X2),X2) = truth,
inference(transitivity,[status(thm)],[c22,c32]) ).
cnf(c34,plain,
implies(X2,X2) = truth,
inference(transitivity,[status(thm)],[c20,c33]) ).
cnf(c35,plain,
truth = implies(X2,X2),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
implies(X2,truth) = implies(X2,implies(X2,X2)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,axiom,
implies(implies(X2,Y2),Y2) = implies(implies(Y2,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
cnf(c38,plain,
implies(implies(truth,X2),X2) = implies(implies(X2,truth),truth),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
implies(implies(X2,truth),truth) = implies(implies(truth,X2),X2),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
implies(implies(truth,X2),X2) = implies(X2,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c41,plain,
implies(implies(X2,truth),truth) = implies(X2,X2),
inference(transitivity,[status(thm)],[c39,c40]) ).
cnf(c42,plain,
implies(X2,X2) = implies(implies(X2,truth),truth),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
implies(X2,implies(X2,X2)) = implies(X2,implies(implies(X2,truth),truth)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
implies(X2,implies(implies(X2,truth),truth)) = truth,
inference(substitution,[status(thm)],[c31]) ).
cnf(c45,plain,
implies(X2,implies(X2,X2)) = truth,
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
implies(X2,truth) = truth,
inference(transitivity,[status(thm)],[c36,c45]) ).
cnf(c47,plain,
truth = implies(X2,truth),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
implies(truth,implies(implies(truth,X3),implies(X2,X3))) = implies(implies(X2,truth),implies(implies(truth,X3),implies(X2,X3))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
implies(implies(X2,truth),implies(implies(truth,X3),implies(X2,X3))) = truth,
inference(substitution,[status(thm)],[c28]) ).
cnf(c50,plain,
implies(truth,implies(implies(truth,X3),implies(X2,X3))) = truth,
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
implies(implies(truth,X3),implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c18,c50]) ).
cnf(c52,plain,
implies(X3,implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c16,c51]) ).
cnf(c53,plain,
implies(X2,implies(X3,X2)) = truth,
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
truth = implies(X2,implies(X3,X2)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
implies(truth,implies(implies(implies(X4,X3),X2),implies(X3,X2))) = implies(implies(X3,implies(X4,X3)),implies(implies(implies(X4,X3),X2),implies(X3,X2))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
implies(implies(X3,implies(X4,X3)),implies(implies(implies(X4,X3),X2),implies(X3,X2))) = truth,
inference(substitution,[status(thm)],[c28]) ).
cnf(c57,plain,
implies(truth,implies(implies(implies(X4,X3),X2),implies(X3,X2))) = truth,
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
implies(implies(implies(X4,X3),X2),implies(X3,X2)) = truth,
inference(transitivity,[status(thm)],[c14,c57]) ).
cnf(c59,plain,
implies(implies(implies(not(X2),not(X3)),implies(X3,X2)),implies(not(X3),implies(X3,X2))) = truth,
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
implies(truth,implies(not(X3),implies(X3,X2))) = truth,
inference(transitivity,[status(thm)],[c12,c59]) ).
cnf(c61,plain,
implies(not(X3),implies(X3,X2)) = truth,
inference(transitivity,[status(thm)],[c8,c60]) ).
cnf(c62,plain,
implies(not(X2),implies(X2,not(truth))) = truth,
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
truth = implies(not(X2),implies(X2,not(truth))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
implies(truth,implies(X2,not(truth))) = implies(implies(not(X2),implies(X2,not(truth))),implies(X2,not(truth))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
implies(implies(implies(X2,not(truth)),not(X2)),not(X2)) = implies(implies(not(X2),implies(X2,not(truth))),implies(X2,not(truth))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c66,plain,
implies(implies(not(X2),implies(X2,not(truth))),implies(X2,not(truth))) = implies(implies(implies(X2,not(truth)),not(X2)),not(X2)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
implies(truth,not(X2)) = not(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c68,plain,
not(X2) = implies(truth,not(X2)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
implies(implies(X2,not(truth)),not(X2)) = implies(implies(X2,not(truth)),implies(truth,not(X2))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
implies(truth,implies(not(truth),X2)) = implies(not(truth),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c71,plain,
implies(not(truth),X2) = implies(truth,implies(not(truth),X2)),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
implies(not(X2),truth) = truth,
inference(substitution,[status(thm)],[c46]) ).
cnf(c73,plain,
truth = implies(not(X2),truth),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
implies(truth,implies(not(truth),X2)) = implies(implies(not(X2),truth),implies(not(truth),X2)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c76,plain,
not(not(truth)) = implies(truth,not(not(truth))),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
implies(truth,implies(truth,not(not(truth)))) = implies(truth,not(not(truth))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c78,plain,
implies(truth,not(not(truth))) = implies(truth,implies(truth,not(not(truth)))),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
implies(implies(X2,X3),X3) = implies(implies(X3,X2),X2),
inference(substitution,[status(thm)],[c37]) ).
cnf(c80,plain,
implies(implies(X3,X2),X2) = implies(implies(X2,X3),X3),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
implies(implies(implies(X3,X2),X2),X3) = implies(implies(implies(X2,X3),X3),X3),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
implies(implies(implies(X2,X3),X3),X3) = implies(implies(X3,implies(X2,X3)),implies(X2,X3)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c83,plain,
implies(implies(X3,implies(X2,X3)),implies(X2,X3)) = implies(truth,implies(X2,X3)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c84,plain,
implies(truth,implies(X2,X3)) = implies(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c85,plain,
implies(implies(X3,implies(X2,X3)),implies(X2,X3)) = implies(X2,X3),
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
implies(implies(implies(X2,X3),X3),X3) = implies(X2,X3),
inference(transitivity,[status(thm)],[c82,c85]) ).
cnf(c87,plain,
implies(implies(implies(X3,X2),X2),X3) = implies(X2,X3),
inference(transitivity,[status(thm)],[c81,c86]) ).
cnf(c88,plain,
implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth)) = implies(not(not(truth)),not(truth)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
implies(not(not(truth)),not(truth)) = implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = implies(implies(not(truth),not(not(truth))),not(not(truth))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c91,plain,
implies(implies(not(truth),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),not(truth)),not(truth)),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c93,plain,
implies(implies(not(X2),not(truth)),X2) = implies(implies(not(X2),not(truth)),implies(truth,X2)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
implies(implies(not(X2),not(truth)),implies(truth,X2)) = truth,
inference(substitution,[status(thm)],[c9]) ).
cnf(c95,plain,
implies(implies(not(X2),not(truth)),X2) = truth,
inference(transitivity,[status(thm)],[c93,c94]) ).
cnf(c96,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
implies(implies(not(truth),not(not(truth))),not(not(truth))) = truth,
inference(transitivity,[status(thm)],[c91,c96]) ).
cnf(c98,plain,
implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth)) = implies(truth,not(truth)),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
implies(truth,not(truth)) = not(truth),
inference(substitution,[status(thm)],[c2]) ).
cnf(c100,plain,
implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth)) = not(truth),
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
implies(not(not(truth)),not(truth)) = not(truth),
inference(transitivity,[status(thm)],[c89,c100]) ).
cnf(c102,plain,
not(truth) = implies(not(not(truth)),not(truth)),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
implies(not(not(not(truth))),not(truth)) = implies(not(not(not(truth))),implies(not(not(truth)),not(truth))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
implies(truth,implies(not(not(truth)),not(not(not(truth))))) = implies(not(not(truth)),not(not(not(truth)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c105,plain,
implies(not(not(truth)),not(not(not(truth)))) = implies(truth,implies(not(not(truth)),not(not(not(truth))))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))) = truth,
inference(substitution,[status(thm)],[c52]) ).
cnf(c107,plain,
truth = implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
implies(truth,implies(not(not(truth)),not(not(not(truth))))) = implies(implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))),implies(not(not(truth)),not(not(not(truth))))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
implies(implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = implies(implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))),implies(not(not(truth)),not(not(not(truth))))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c110,plain,
implies(implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))),implies(not(not(truth)),not(not(not(truth))))) = implies(implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c112,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) = implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
implies(truth,implies(not(truth),not(not(truth)))) = implies(not(truth),not(not(truth))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c114,plain,
implies(not(truth),not(not(truth))) = implies(truth,implies(not(truth),not(not(truth)))),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
implies(not(not(truth)),implies(not(truth),not(not(truth)))) = truth,
inference(substitution,[status(thm)],[c52]) ).
cnf(c116,plain,
truth = implies(not(not(truth)),implies(not(truth),not(not(truth)))),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
implies(truth,implies(not(truth),not(not(truth)))) = implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c119,plain,
implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))) = implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(not(truth))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(not(truth))) = implies(truth,not(not(truth))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c121,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c122,plain,
implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(not(truth))) = not(not(truth)),
inference(transitivity,[status(thm)],[c120,c121]) ).
cnf(c123,plain,
implies(implies(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))) = not(not(truth)),
inference(transitivity,[status(thm)],[c119,c122]) ).
cnf(c124,plain,
implies(truth,implies(not(truth),not(not(truth)))) = not(not(truth)),
inference(transitivity,[status(thm)],[c117,c123]) ).
cnf(c125,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(transitivity,[status(thm)],[c114,c124]) ).
cnf(c126,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) = truth,
inference(substitution,[status(thm)],[c9]) ).
cnf(c129,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth,
inference(transitivity,[status(thm)],[c127,c128]) ).
cnf(c130,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) = truth,
inference(transitivity,[status(thm)],[c112,c129]) ).
cnf(c131,plain,
implies(implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = implies(truth,not(not(not(truth)))),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
implies(truth,not(not(not(truth)))) = not(not(not(truth))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c133,plain,
implies(implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = not(not(not(truth))),
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
implies(implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))),implies(not(not(truth)),not(not(not(truth))))) = not(not(not(truth))),
inference(transitivity,[status(thm)],[c110,c133]) ).
cnf(c135,plain,
implies(truth,implies(not(not(truth)),not(not(not(truth))))) = not(not(not(truth))),
inference(transitivity,[status(thm)],[c108,c134]) ).
cnf(c136,plain,
implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))),
inference(transitivity,[status(thm)],[c105,c135]) ).
cnf(c137,plain,
not(not(not(truth))) = implies(not(not(truth)),not(not(not(truth)))),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))) = truth,
inference(substitution,[status(thm)],[c9]) ).
cnf(c140,plain,
implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = truth,
inference(transitivity,[status(thm)],[c138,c139]) ).
cnf(c141,plain,
implies(not(not(not(truth))),not(truth)) = truth,
inference(transitivity,[status(thm)],[c103,c140]) ).
cnf(c142,plain,
truth = implies(not(not(not(truth))),not(truth)),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
implies(truth,implies(truth,not(not(truth)))) = implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) = truth,
inference(substitution,[status(thm)],[c9]) ).
cnf(c145,plain,
implies(truth,implies(truth,not(not(truth)))) = truth,
inference(transitivity,[status(thm)],[c143,c144]) ).
cnf(c146,plain,
implies(truth,not(not(truth))) = truth,
inference(transitivity,[status(thm)],[c78,c145]) ).
cnf(c147,plain,
not(not(truth)) = truth,
inference(transitivity,[status(thm)],[c76,c146]) ).
cnf(c148,plain,
truth = not(not(truth)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
implies(not(X2),truth) = implies(not(X2),not(not(truth))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
implies(implies(not(X2),truth),implies(not(truth),X2)) = implies(implies(not(X2),not(not(truth))),implies(not(truth),X2)),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
implies(implies(not(X2),not(not(truth))),implies(not(truth),X2)) = truth,
inference(substitution,[status(thm)],[c9]) ).
cnf(c152,plain,
implies(implies(not(X2),truth),implies(not(truth),X2)) = truth,
inference(transitivity,[status(thm)],[c150,c151]) ).
cnf(c153,plain,
implies(truth,implies(not(truth),X2)) = truth,
inference(transitivity,[status(thm)],[c74,c152]) ).
cnf(c154,plain,
implies(not(truth),X2) = truth,
inference(transitivity,[status(thm)],[c71,c153]) ).
cnf(c155,plain,
implies(not(truth),not(X2)) = truth,
inference(substitution,[status(thm)],[c154]) ).
cnf(c156,plain,
truth = implies(not(truth),not(X2)),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
implies(truth,not(X2)) = implies(implies(not(truth),not(X2)),not(X2)),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
implies(implies(X2,not(truth)),implies(truth,not(X2))) = implies(implies(X2,not(truth)),implies(implies(not(truth),not(X2)),not(X2))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
implies(implies(not(X2),not(truth)),not(truth)) = implies(implies(not(truth),not(X2)),not(X2)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c160,plain,
implies(implies(not(truth),not(X2)),not(X2)) = implies(implies(not(X2),not(truth)),not(truth)),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
implies(implies(X2,not(truth)),implies(implies(not(truth),not(X2)),not(X2))) = implies(implies(X2,not(truth)),implies(implies(not(X2),not(truth)),not(truth))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
implies(truth,implies(implies(X3,X2),implies(implies(not(X3),not(truth)),X2))) = implies(implies(X3,X2),implies(implies(not(X3),not(truth)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c163,plain,
implies(implies(X3,X2),implies(implies(not(X3),not(truth)),X2)) = implies(truth,implies(implies(X3,X2),implies(implies(not(X3),not(truth)),X2))),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
truth = implies(implies(not(X2),not(truth)),X2),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c165,plain,
implies(truth,implies(implies(X3,X2),implies(implies(not(X3),not(truth)),X2))) = implies(implies(implies(not(X3),not(truth)),X3),implies(implies(X3,X2),implies(implies(not(X3),not(truth)),X2))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
implies(implies(implies(not(X3),not(truth)),X3),implies(implies(X3,X2),implies(implies(not(X3),not(truth)),X2))) = truth,
inference(substitution,[status(thm)],[c28]) ).
cnf(c167,plain,
implies(truth,implies(implies(X3,X2),implies(implies(not(X3),not(truth)),X2))) = truth,
inference(transitivity,[status(thm)],[c165,c166]) ).
cnf(c168,plain,
implies(implies(X3,X2),implies(implies(not(X3),not(truth)),X2)) = truth,
inference(transitivity,[status(thm)],[c163,c167]) ).
cnf(c169,plain,
implies(implies(X2,not(truth)),implies(implies(not(X2),not(truth)),not(truth))) = truth,
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
implies(implies(X2,not(truth)),implies(implies(not(truth),not(X2)),not(X2))) = truth,
inference(transitivity,[status(thm)],[c161,c169]) ).
cnf(c171,plain,
implies(implies(X2,not(truth)),implies(truth,not(X2))) = truth,
inference(transitivity,[status(thm)],[c158,c170]) ).
cnf(c172,plain,
implies(implies(X2,not(truth)),not(X2)) = truth,
inference(transitivity,[status(thm)],[c69,c171]) ).
cnf(c173,plain,
implies(implies(implies(X2,not(truth)),not(X2)),not(X2)) = implies(truth,not(X2)),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
implies(truth,not(X2)) = not(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c175,plain,
implies(implies(implies(X2,not(truth)),not(X2)),not(X2)) = not(X2),
inference(transitivity,[status(thm)],[c173,c174]) ).
cnf(c176,plain,
implies(implies(not(X2),implies(X2,not(truth))),implies(X2,not(truth))) = not(X2),
inference(transitivity,[status(thm)],[c66,c175]) ).
cnf(c177,plain,
implies(truth,implies(X2,not(truth))) = not(X2),
inference(transitivity,[status(thm)],[c64,c176]) ).
cnf(c178,plain,
implies(X2,not(truth)) = not(X2),
inference(transitivity,[status(thm)],[c6,c177]) ).
cnf(c179,plain,
not(X2) = implies(X2,not(truth)),
inference(symmetry,[status(thm)],[c178]) ).
cnf(c180,plain,
implies(not(X2),not(X3)) = implies(not(X2),implies(X3,not(truth))),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
implies(implies(X3,X2),implies(not(X2),not(X3))) = implies(implies(X3,X2),implies(not(X2),implies(X3,not(truth)))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
not(X2) = implies(X2,not(truth)),
inference(symmetry,[status(thm)],[c178]) ).
cnf(c183,plain,
implies(not(X2),implies(X3,not(truth))) = implies(implies(X2,not(truth)),implies(X3,not(truth))),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
implies(implies(X3,X2),implies(not(X2),implies(X3,not(truth)))) = implies(implies(X3,X2),implies(implies(X2,not(truth)),implies(X3,not(truth)))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
implies(implies(X3,X2),implies(implies(X2,not(truth)),implies(X3,not(truth)))) = truth,
inference(substitution,[status(thm)],[c28]) ).
cnf(c186,plain,
implies(implies(X3,X2),implies(not(X2),implies(X3,not(truth)))) = truth,
inference(transitivity,[status(thm)],[c184,c185]) ).
cnf(c187,plain,
implies(implies(X3,X2),implies(not(X2),not(X3))) = truth,
inference(transitivity,[status(thm)],[c181,c186]) ).
cnf(c188,plain,
implies(implies(X2,X3),implies(not(X3),not(X2))) = truth,
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
truth = implies(implies(X2,X3),implies(not(X3),not(X2))),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
implies(truth,implies(not(X3),not(X2))) = implies(implies(implies(X2,X3),implies(not(X3),not(X2))),implies(not(X3),not(X2))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
implies(implies(implies(X2,X3),implies(not(X3),not(X2))),implies(not(X3),not(X2))) = implies(implies(implies(not(X3),not(X2)),implies(X2,X3)),implies(X2,X3)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c192,plain,
implies(implies(not(X3),not(X2)),implies(X2,X3)) = truth,
inference(substitution,[status(thm)],[c9]) ).
cnf(c193,plain,
implies(implies(implies(not(X3),not(X2)),implies(X2,X3)),implies(X2,X3)) = implies(truth,implies(X2,X3)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
implies(truth,implies(X2,X3)) = implies(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c195,plain,
implies(implies(implies(not(X3),not(X2)),implies(X2,X3)),implies(X2,X3)) = implies(X2,X3),
inference(transitivity,[status(thm)],[c193,c194]) ).
cnf(c196,plain,
implies(implies(implies(X2,X3),implies(not(X3),not(X2))),implies(not(X3),not(X2))) = implies(X2,X3),
inference(transitivity,[status(thm)],[c191,c195]) ).
cnf(c197,plain,
implies(truth,implies(not(X3),not(X2))) = implies(X2,X3),
inference(transitivity,[status(thm)],[c190,c196]) ).
cnf(c198,plain,
implies(not(X3),not(X2)) = implies(X2,X3),
inference(transitivity,[status(thm)],[c4,c197]) ).
cnf(c199,plain,
implies(not(not(X2)),not(X3)) = implies(X3,not(X2)),
inference(substitution,[status(thm)],[c198]) ).
cnf(c200,plain,
implies(X3,not(X2)) = implies(not(not(X2)),not(X3)),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
implies(truth,not(not(X2))) = not(not(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c202,plain,
not(not(X2)) = implies(truth,not(not(X2))),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
implies(truth,implies(X2,not(not(X2)))) = implies(X2,not(not(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c204,plain,
implies(X2,not(not(X2))) = implies(truth,implies(X2,not(not(X2)))),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c206,plain,
implies(not(not(X2)),X2) = implies(not(not(X2)),implies(truth,X2)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
implies(implies(implies(not(X2),not(X3)),implies(X3,X2)),implies(X3,X2)) = implies(implies(implies(X3,X2),implies(not(X2),not(X3))),implies(not(X2),not(X3))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c208,plain,
implies(implies(implies(X3,X2),implies(not(X2),not(X3))),implies(not(X2),not(X3))) = implies(implies(implies(not(X2),not(X3)),implies(X3,X2)),implies(X3,X2)),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
implies(implies(not(X2),not(X3)),implies(X3,X2)) = truth,
inference(substitution,[status(thm)],[c9]) ).
cnf(c210,plain,
implies(implies(implies(not(X2),not(X3)),implies(X3,X2)),implies(X3,X2)) = implies(truth,implies(X3,X2)),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
implies(truth,implies(X3,X2)) = implies(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c212,plain,
implies(implies(implies(not(X2),not(X3)),implies(X3,X2)),implies(X3,X2)) = implies(X3,X2),
inference(transitivity,[status(thm)],[c210,c211]) ).
cnf(c213,plain,
implies(implies(implies(X3,X2),implies(not(X2),not(X3))),implies(not(X2),not(X3))) = implies(X3,X2),
inference(transitivity,[status(thm)],[c208,c212]) ).
cnf(c214,plain,
implies(implies(implies(X2,X3),implies(not(X3),not(X2))),implies(not(X3),not(X2))) = implies(X2,X3),
inference(substitution,[status(thm)],[c213]) ).
cnf(c215,plain,
implies(X2,X3) = implies(implies(implies(X2,X3),implies(not(X3),not(X2))),implies(not(X3),not(X2))),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
implies(not(not(X3)),implies(X2,X3)) = implies(not(not(X3)),implies(implies(implies(X2,X3),implies(not(X3),not(X2))),implies(not(X3),not(X2)))),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
implies(truth,implies(not(X4),implies(X3,implies(X4,X2)))) = implies(not(X4),implies(X3,implies(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c218,plain,
implies(not(X4),implies(X3,implies(X4,X2))) = implies(truth,implies(not(X4),implies(X3,implies(X4,X2)))),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
truth = implies(not(X3),implies(X3,X2)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c220,plain,
implies(truth,implies(not(X4),implies(X3,implies(X4,X2)))) = implies(implies(not(X4),implies(X4,X2)),implies(not(X4),implies(X3,implies(X4,X2)))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
implies(truth,implies(X4,implies(X2,X3))) = implies(X4,implies(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c222,plain,
implies(X4,implies(X2,X3)) = implies(truth,implies(X4,implies(X2,X3))),
inference(symmetry,[status(thm)],[c221]) ).
cnf(c223,plain,
implies(implies(X4,X3),implies(X4,implies(X2,X3))) = implies(implies(X4,X3),implies(truth,implies(X4,implies(X2,X3)))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
truth = implies(X3,implies(X2,X3)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c225,plain,
implies(truth,implies(X4,implies(X2,X3))) = implies(implies(X3,implies(X2,X3)),implies(X4,implies(X2,X3))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
implies(implies(X4,X3),implies(truth,implies(X4,implies(X2,X3)))) = implies(implies(X4,X3),implies(implies(X3,implies(X2,X3)),implies(X4,implies(X2,X3)))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
implies(implies(X4,X3),implies(implies(X3,implies(X2,X3)),implies(X4,implies(X2,X3)))) = truth,
inference(substitution,[status(thm)],[c28]) ).
cnf(c228,plain,
implies(implies(X4,X3),implies(truth,implies(X4,implies(X2,X3)))) = truth,
inference(transitivity,[status(thm)],[c226,c227]) ).
cnf(c229,plain,
implies(implies(X4,X3),implies(X4,implies(X2,X3))) = truth,
inference(transitivity,[status(thm)],[c223,c228]) ).
cnf(c230,plain,
implies(implies(not(X4),implies(X4,X2)),implies(not(X4),implies(X3,implies(X4,X2)))) = truth,
inference(substitution,[status(thm)],[c229]) ).
cnf(c231,plain,
implies(truth,implies(not(X4),implies(X3,implies(X4,X2)))) = truth,
inference(transitivity,[status(thm)],[c220,c230]) ).
cnf(c232,plain,
implies(not(X4),implies(X3,implies(X4,X2))) = truth,
inference(transitivity,[status(thm)],[c218,c231]) ).
cnf(c233,plain,
implies(not(not(X3)),implies(implies(implies(X2,X3),implies(not(X3),not(X2))),implies(not(X3),not(X2)))) = truth,
inference(substitution,[status(thm)],[c232]) ).
cnf(c234,plain,
implies(not(not(X3)),implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c216,c233]) ).
cnf(c235,plain,
implies(not(not(X2)),implies(truth,X2)) = truth,
inference(substitution,[status(thm)],[c234]) ).
cnf(c236,plain,
implies(not(not(X2)),X2) = truth,
inference(transitivity,[status(thm)],[c206,c235]) ).
cnf(c237,plain,
implies(not(not(not(X2))),not(X2)) = truth,
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,plain,
truth = implies(not(not(not(X2))),not(X2)),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
implies(truth,implies(X2,not(not(X2)))) = implies(implies(not(not(not(X2))),not(X2)),implies(X2,not(not(X2)))),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
implies(implies(not(not(not(X2))),not(X2)),implies(X2,not(not(X2)))) = truth,
inference(substitution,[status(thm)],[c9]) ).
cnf(c241,plain,
implies(truth,implies(X2,not(not(X2)))) = truth,
inference(transitivity,[status(thm)],[c239,c240]) ).
cnf(c242,plain,
implies(X2,not(not(X2))) = truth,
inference(transitivity,[status(thm)],[c204,c241]) ).
cnf(c243,plain,
truth = implies(X2,not(not(X2))),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
implies(truth,not(not(X2))) = implies(implies(X2,not(not(X2))),not(not(X2))),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
implies(implies(X2,not(not(X2))),not(not(X2))) = implies(implies(not(not(X2)),X2),X2),
inference(substitution,[status(thm)],[c37]) ).
cnf(c246,plain,
implies(implies(not(not(X2)),X2),X2) = implies(truth,X2),
inference(congruence,[status(thm)],[c236]) ).
cnf(c247,plain,
implies(implies(not(not(X2)),X2),X2) = X2,
inference(transitivity,[status(thm)],[c246,c2]) ).
cnf(c248,plain,
implies(implies(X2,not(not(X2))),not(not(X2))) = X2,
inference(transitivity,[status(thm)],[c245,c247]) ).
cnf(c249,plain,
implies(truth,not(not(X2))) = X2,
inference(transitivity,[status(thm)],[c244,c248]) ).
cnf(c250,plain,
not(not(X2)) = X2,
inference(transitivity,[status(thm)],[c202,c249]) ).
cnf(c251,plain,
implies(not(not(X2)),not(X3)) = implies(X2,not(X3)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
implies(X3,not(X2)) = implies(X2,not(X3)),
inference(transitivity,[status(thm)],[c200,c251]) ).
cnf(c253,plain,
implies(X3,not(implies(X3,X2))) = implies(implies(X3,X2),not(X3)),
inference(substitution,[status(thm)],[c252]) ).
cnf(c254,plain,
implies(implies(X3,X2),not(X3)) = implies(X3,not(implies(X3,X2))),
inference(symmetry,[status(thm)],[c253]) ).
cnf(c255,plain,
not(implies(implies(X3,X2),not(X3))) = not(implies(X3,not(implies(X3,X2)))),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))) = implies(implies(X3,X2),not(implies(X3,not(implies(X3,X2))))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
not(not(implies(X3,X2))) = implies(X3,X2),
inference(substitution,[status(thm)],[c250]) ).
cnf(c258,plain,
implies(X3,X2) = not(not(implies(X3,X2))),
inference(symmetry,[status(thm)],[c257]) ).
cnf(c259,plain,
implies(implies(X3,X2),not(implies(X3,not(implies(X3,X2))))) = implies(not(not(implies(X3,X2))),not(implies(X3,not(implies(X3,X2))))),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
implies(not(X2),not(implies(X3,X2))) = implies(implies(X3,X2),X2),
inference(substitution,[status(thm)],[c198]) ).
cnf(c261,plain,
implies(implies(X2,X3),X3) = implies(implies(X3,X2),X2),
inference(substitution,[status(thm)],[c37]) ).
cnf(c262,plain,
implies(implies(X3,X2),X2) = implies(implies(X2,X3),X3),
inference(symmetry,[status(thm)],[c261]) ).
cnf(c263,plain,
implies(not(X3),not(implies(X2,X3))) = implies(implies(X2,X3),X3),
inference(substitution,[status(thm)],[c198]) ).
cnf(c264,plain,
implies(implies(X2,X3),X3) = implies(not(X3),not(implies(X2,X3))),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
implies(implies(X3,X2),X2) = implies(not(X3),not(implies(X2,X3))),
inference(transitivity,[status(thm)],[c262,c264]) ).
cnf(c266,plain,
implies(not(X2),not(implies(X3,X2))) = implies(not(X3),not(implies(X2,X3))),
inference(transitivity,[status(thm)],[c260,c265]) ).
cnf(c267,plain,
implies(not(not(implies(X3,X2))),not(implies(X3,not(implies(X3,X2))))) = implies(not(X3),not(implies(not(implies(X3,X2)),X3))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c268,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c269,plain,
implies(not(implies(X3,X2)),X3) = implies(not(implies(X3,X2)),not(not(X3))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
implies(not(X2),not(truth)) = not(not(X2)),
inference(substitution,[status(thm)],[c178]) ).
cnf(c271,plain,
not(not(X2)) = implies(not(X2),not(truth)),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
implies(not(implies(X3,X2)),not(not(X3))) = implies(not(implies(X3,X2)),implies(not(X3),not(truth))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
implies(implies(X3,X2),not(truth)) = not(implies(X3,X2)),
inference(substitution,[status(thm)],[c178]) ).
cnf(c274,plain,
not(implies(X3,X2)) = implies(implies(X3,X2),not(truth)),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
implies(not(implies(X3,X2)),implies(not(X3),not(truth))) = implies(implies(implies(X3,X2),not(truth)),implies(not(X3),not(truth))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
implies(truth,implies(implies(implies(X4,X3),X2),implies(not(X4),X2))) = implies(implies(implies(X4,X3),X2),implies(not(X4),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c277,plain,
implies(implies(implies(X4,X3),X2),implies(not(X4),X2)) = implies(truth,implies(implies(implies(X4,X3),X2),implies(not(X4),X2))),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
truth = implies(not(X3),implies(X3,X2)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c279,plain,
implies(truth,implies(implies(implies(X4,X3),X2),implies(not(X4),X2))) = implies(implies(not(X4),implies(X4,X3)),implies(implies(implies(X4,X3),X2),implies(not(X4),X2))),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
implies(implies(not(X4),implies(X4,X3)),implies(implies(implies(X4,X3),X2),implies(not(X4),X2))) = truth,
inference(substitution,[status(thm)],[c28]) ).
cnf(c281,plain,
implies(truth,implies(implies(implies(X4,X3),X2),implies(not(X4),X2))) = truth,
inference(transitivity,[status(thm)],[c279,c280]) ).
cnf(c282,plain,
implies(implies(implies(X4,X3),X2),implies(not(X4),X2)) = truth,
inference(transitivity,[status(thm)],[c277,c281]) ).
cnf(c283,plain,
implies(implies(implies(X3,X2),not(truth)),implies(not(X3),not(truth))) = truth,
inference(substitution,[status(thm)],[c282]) ).
cnf(c284,plain,
implies(not(implies(X3,X2)),implies(not(X3),not(truth))) = truth,
inference(transitivity,[status(thm)],[c275,c283]) ).
cnf(c285,plain,
implies(not(implies(X3,X2)),not(not(X3))) = truth,
inference(transitivity,[status(thm)],[c272,c284]) ).
cnf(c286,plain,
implies(not(implies(X3,X2)),X3) = truth,
inference(transitivity,[status(thm)],[c269,c285]) ).
cnf(c287,plain,
not(implies(not(implies(X3,X2)),X3)) = not(truth),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
implies(not(X3),not(implies(not(implies(X3,X2)),X3))) = implies(not(X3),not(truth)),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
implies(not(X2),not(truth)) = not(not(X2)),
inference(substitution,[status(thm)],[c178]) ).
cnf(c290,plain,
implies(not(X2),not(truth)) = X2,
inference(transitivity,[status(thm)],[c289,c250]) ).
cnf(c291,plain,
implies(not(X3),not(implies(not(implies(X3,X2)),X3))) = X3,
inference(transitivity,[status(thm)],[c288,c290]) ).
cnf(c292,plain,
implies(not(not(implies(X3,X2))),not(implies(X3,not(implies(X3,X2))))) = X3,
inference(transitivity,[status(thm)],[c267,c291]) ).
cnf(c293,plain,
implies(implies(X3,X2),not(implies(X3,not(implies(X3,X2))))) = X3,
inference(transitivity,[status(thm)],[c259,c292]) ).
cnf(c294,plain,
implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))) = X3,
inference(transitivity,[status(thm)],[c256,c293]) ).
cnf(c295,plain,
X3 = implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c296,plain,
implies(X2,X3) = implies(X2,implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3))))),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
implies(implies(implies(X3,X2),implies(X2,X3)),implies(X2,X3)) = implies(implies(implies(X3,X2),implies(X2,X3)),implies(X2,implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))))),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
implies(not(X2),not(X3)) = implies(X3,X2),
inference(substitution,[status(thm)],[c198]) ).
cnf(c299,plain,
implies(X3,X2) = implies(not(X2),not(X3)),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
implies(implies(X3,X2),not(X3)) = implies(implies(not(X2),not(X3)),not(X3)),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
implies(implies(not(X2),not(X3)),not(X3)) = implies(implies(not(X3),not(X2)),not(X2)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c302,plain,
implies(implies(not(X3),not(X2)),not(X2)) = implies(implies(X2,X3),not(X2)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c303,plain,
implies(implies(not(X2),not(X3)),not(X3)) = implies(implies(X2,X3),not(X2)),
inference(transitivity,[status(thm)],[c301,c302]) ).
cnf(c304,plain,
implies(implies(X3,X2),not(X3)) = implies(implies(X2,X3),not(X2)),
inference(transitivity,[status(thm)],[c300,c303]) ).
cnf(c305,plain,
implies(implies(X2,X3),not(X2)) = implies(implies(X3,X2),not(X3)),
inference(symmetry,[status(thm)],[c304]) ).
cnf(c306,plain,
not(implies(implies(X2,X3),not(X2))) = not(implies(implies(X3,X2),not(X3))),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
implies(implies(X3,X2),not(implies(implies(X2,X3),not(X2)))) = implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
implies(X3,not(implies(X3,X2))) = implies(implies(X3,X2),not(X3)),
inference(substitution,[status(thm)],[c252]) ).
cnf(c309,plain,
implies(implies(X3,X2),not(X3)) = implies(X3,not(implies(X3,X2))),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c310,plain,
not(implies(implies(X3,X2),not(X3))) = not(implies(X3,not(implies(X3,X2)))),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))) = implies(implies(X3,X2),not(implies(X3,not(implies(X3,X2))))),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
not(not(implies(X3,X2))) = implies(X3,X2),
inference(substitution,[status(thm)],[c250]) ).
cnf(c313,plain,
implies(X3,X2) = not(not(implies(X3,X2))),
inference(symmetry,[status(thm)],[c312]) ).
cnf(c314,plain,
implies(implies(X3,X2),not(implies(X3,not(implies(X3,X2))))) = implies(not(not(implies(X3,X2))),not(implies(X3,not(implies(X3,X2))))),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
implies(not(not(implies(X3,X2))),not(implies(X3,not(implies(X3,X2))))) = implies(not(X3),not(implies(not(implies(X3,X2)),X3))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c316,plain,
not(implies(not(implies(X3,X2)),X3)) = not(truth),
inference(congruence,[status(thm)],[c286]) ).
cnf(c317,plain,
implies(not(X3),not(implies(not(implies(X3,X2)),X3))) = implies(not(X3),not(truth)),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
implies(not(X2),not(truth)) = not(not(X2)),
inference(substitution,[status(thm)],[c178]) ).
cnf(c319,plain,
implies(not(X2),not(truth)) = X2,
inference(transitivity,[status(thm)],[c318,c250]) ).
cnf(c320,plain,
implies(not(X3),not(implies(not(implies(X3,X2)),X3))) = X3,
inference(transitivity,[status(thm)],[c317,c319]) ).
cnf(c321,plain,
implies(not(not(implies(X3,X2))),not(implies(X3,not(implies(X3,X2))))) = X3,
inference(transitivity,[status(thm)],[c315,c320]) ).
cnf(c322,plain,
implies(implies(X3,X2),not(implies(X3,not(implies(X3,X2))))) = X3,
inference(transitivity,[status(thm)],[c314,c321]) ).
cnf(c323,plain,
implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))) = X3,
inference(transitivity,[status(thm)],[c311,c322]) ).
cnf(c324,plain,
implies(implies(X3,X2),not(implies(implies(X2,X3),not(X2)))) = X3,
inference(transitivity,[status(thm)],[c307,c323]) ).
cnf(c325,plain,
implies(implies(X2,X3),not(implies(implies(X3,X2),not(X3)))) = X2,
inference(substitution,[status(thm)],[c324]) ).
cnf(c326,plain,
X2 = implies(implies(X2,X3),not(implies(implies(X3,X2),not(X3)))),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
implies(X2,implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3))))) = implies(implies(implies(X2,X3),not(implies(implies(X3,X2),not(X3)))),implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3))))),
inference(congruence,[status(thm)],[c326]) ).
cnf(c328,plain,
implies(implies(implies(X3,X2),implies(X2,X3)),implies(X2,implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))))) = implies(implies(implies(X3,X2),implies(X2,X3)),implies(implies(implies(X2,X3),not(implies(implies(X3,X2),not(X3)))),implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))))),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
implies(implies(implies(X3,X2),implies(X2,X3)),implies(implies(implies(X2,X3),not(implies(implies(X3,X2),not(X3)))),implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))))) = truth,
inference(substitution,[status(thm)],[c28]) ).
cnf(c330,plain,
implies(implies(implies(X3,X2),implies(X2,X3)),implies(X2,implies(implies(X3,X2),not(implies(implies(X3,X2),not(X3)))))) = truth,
inference(transitivity,[status(thm)],[c328,c329]) ).
cnf(c331,plain,
implies(implies(implies(X3,X2),implies(X2,X3)),implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c297,c330]) ).
cnf(c332,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth,
inference(substitution,[status(thm)],[c331]) ).
cnf(c333,plain,
$false,
inference(resolution,[status(thm)],[c1,c332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL109-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:22:16 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.92/2.62 Command-line arguments: --flatten --complete-subsets
% 16.92/2.62
% 16.92/2.62 % SZS status Unsatisfiable
% 16.92/2.63
% 16.92/2.67 % SZS output start CNFRefutation
% See solution above
% 19.07/2.92
% 19.07/2.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------