%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL153-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 11:49:09 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 11
% Syntax : Number of clauses : 177 ( 177 unt; 0 nHn; 18 RR)
% Number of literals : 177 ( 176 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 205 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
not(x) != xor(x,truth),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c2,axiom,
or(X,Y) = implies(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition) ).
cnf(c3,plain,
or(and(X3,not(X2)),and(not(X3),X2)) = implies(not(and(X3,not(X2))),and(not(X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
implies(not(and(X3,not(X2))),and(not(X3),X2)) = or(and(X3,not(X2)),and(not(X3),X2)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
xor(X2,Y2) = or(and(X2,not(Y2)),and(not(X2),Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition) ).
cnf(c6,plain,
xor(X3,X2) = or(and(X3,not(X2)),and(not(X3),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
or(and(X3,not(X2)),and(not(X3),X2)) = xor(X3,X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
implies(not(and(X3,not(X2))),and(not(X3),X2)) = xor(X3,X2),
inference(transitivity,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
implies(not(and(X2,not(truth))),and(not(X2),truth)) = xor(X2,truth),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
xor(X2,truth) = implies(not(and(X2,not(truth))),and(not(X2),truth)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
not(falsehood) = not(not(truth)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
implies(not(falsehood),not(X2)) = implies(not(not(truth)),not(X2)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
not(implies(not(falsehood),not(X2))) = not(implies(not(not(truth)),not(X2))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
or(not(X3),not(X2)) = implies(not(not(X3)),not(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
implies(not(not(X3)),not(X2)) = or(not(X3),not(X2)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
not(implies(not(not(X3)),not(X2))) = not(or(not(X3),not(X2))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
and(X2,Y2) = not(or(not(X2),not(Y2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition) ).
cnf(c20,plain,
and(X3,X2) = not(or(not(X3),not(X2))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
not(or(not(X3),not(X2))) = and(X3,X2),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
not(implies(not(not(X3)),not(X2))) = and(X3,X2),
inference(transitivity,[status(thm)],[c18,c21]) ).
cnf(c23,plain,
not(implies(not(not(truth)),not(X2))) = and(truth,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,axiom,
and(X2,Y2) = and(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutativity) ).
cnf(c25,plain,
and(truth,X2) = and(X2,truth),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
not(implies(not(not(truth)),not(X2))) = and(X2,truth),
inference(transitivity,[status(thm)],[c23,c25]) ).
cnf(c27,plain,
not(implies(not(falsehood),not(X2))) = and(X2,truth),
inference(transitivity,[status(thm)],[c15,c26]) ).
cnf(c28,plain,
and(X2,truth) = not(implies(not(falsehood),not(X2))),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
or(X2,X3) = implies(not(X2),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c30,plain,
implies(not(X2),X3) = or(X2,X3),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,axiom,
or(X2,Y2) = or(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_commutativity) ).
cnf(c32,plain,
or(X3,X2) = or(X2,X3),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
or(X2,X3) = or(X3,X2),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
or(X3,X2) = implies(not(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c35,plain,
or(X2,X3) = implies(not(X3),X2),
inference(transitivity,[status(thm)],[c33,c34]) ).
cnf(c36,plain,
implies(not(X2),X3) = implies(not(X3),X2),
inference(transitivity,[status(thm)],[c30,c35]) ).
cnf(c37,plain,
implies(not(not(X2)),falsehood) = implies(not(falsehood),not(X2)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
implies(not(falsehood),not(X2)) = implies(not(not(X2)),falsehood),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
not(implies(not(falsehood),not(X2))) = not(implies(not(not(X2)),falsehood)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,axiom,
implies(truth,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
cnf(c41,plain,
implies(truth,implies(not(X2),falsehood)) = implies(not(X2),falsehood),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
implies(not(X2),falsehood) = implies(truth,implies(not(X2),falsehood)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
implies(not(X3),X2) = implies(not(X2),X3),
inference(substitution,[status(thm)],[c36]) ).
cnf(c44,plain,
implies(X3,implies(not(X3),X2)) = implies(X3,implies(not(X2),X3)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
implies(truth,implies(X3,implies(X2,X3))) = implies(X3,implies(X2,X3)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c46,plain,
implies(X3,implies(X2,X3)) = implies(truth,implies(X3,implies(X2,X3))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,axiom,
implies(implies(X2,Y2),Y2) = implies(implies(Y2,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
cnf(c48,plain,
implies(implies(truth,X2),X2) = implies(implies(X2,truth),truth),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
implies(implies(X2,truth),truth) = implies(implies(truth,X2),X2),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
implies(implies(truth,X2),X2) = implies(X2,X2),
inference(congruence,[status(thm)],[c40]) ).
cnf(c51,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c52,plain,
implies(X2,X2) = implies(implies(truth,X2),X2),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
implies(truth,implies(implies(truth,X2),X2)) = implies(implies(truth,X2),X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c54,plain,
implies(implies(truth,X2),X2) = implies(truth,implies(implies(truth,X2),X2)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c56,plain,
implies(implies(X3,X2),X2) = implies(implies(X3,X2),implies(truth,X2)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
implies(X3,implies(implies(X3,X2),X2)) = implies(X3,implies(implies(X3,X2),implies(truth,X2))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c59,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)],[c58]) ).
cnf(c60,axiom,
implies(implies(X2,Y2),implies(implies(Y2,Z),implies(X2,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
cnf(c61,plain,
implies(implies(truth,X3),implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
implies(X3,implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(transitivity,[status(thm)],[c59,c61]) ).
cnf(c63,plain,
implies(X3,implies(implies(X3,X2),X2)) = truth,
inference(transitivity,[status(thm)],[c57,c62]) ).
cnf(c64,plain,
implies(truth,implies(implies(truth,X2),X2)) = truth,
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
implies(implies(truth,X2),X2) = truth,
inference(transitivity,[status(thm)],[c54,c64]) ).
cnf(c66,plain,
implies(X2,X2) = truth,
inference(transitivity,[status(thm)],[c52,c65]) ).
cnf(c67,plain,
implies(implies(truth,X2),X2) = truth,
inference(transitivity,[status(thm)],[c50,c66]) ).
cnf(c68,plain,
implies(implies(X2,truth),truth) = truth,
inference(transitivity,[status(thm)],[c49,c67]) ).
cnf(c69,plain,
truth = implies(implies(X2,truth),truth),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
implies(X2,truth) = implies(X2,implies(implies(X2,truth),truth)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
implies(X2,implies(implies(X2,truth),truth)) = truth,
inference(substitution,[status(thm)],[c63]) ).
cnf(c72,plain,
implies(X2,truth) = truth,
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
truth = implies(X2,truth),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
implies(truth,implies(X3,implies(X2,X3))) = implies(implies(X2,truth),implies(X3,implies(X2,X3))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c76,plain,
implies(X3,implies(X2,X3)) = implies(implies(truth,X3),implies(X2,X3)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
implies(implies(X2,truth),implies(X3,implies(X2,X3))) = implies(implies(X2,truth),implies(implies(truth,X3),implies(X2,X3))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
implies(implies(X2,truth),implies(implies(truth,X3),implies(X2,X3))) = truth,
inference(substitution,[status(thm)],[c60]) ).
cnf(c79,plain,
implies(implies(X2,truth),implies(X3,implies(X2,X3))) = truth,
inference(transitivity,[status(thm)],[c77,c78]) ).
cnf(c80,plain,
implies(truth,implies(X3,implies(X2,X3))) = truth,
inference(transitivity,[status(thm)],[c74,c79]) ).
cnf(c81,plain,
implies(X3,implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c46,c80]) ).
cnf(c82,plain,
implies(X3,implies(not(X2),X3)) = truth,
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,plain,
implies(X3,implies(not(X3),X2)) = truth,
inference(transitivity,[status(thm)],[c44,c82]) ).
cnf(c84,plain,
implies(X2,implies(not(X2),falsehood)) = truth,
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
truth = implies(X2,implies(not(X2),falsehood)),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
implies(truth,implies(not(X2),falsehood)) = implies(implies(X2,implies(not(X2),falsehood)),implies(not(X2),falsehood)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
implies(implies(implies(not(X2),falsehood),X2),X2) = implies(implies(X2,implies(not(X2),falsehood)),implies(not(X2),falsehood)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c88,plain,
implies(implies(X2,implies(not(X2),falsehood)),implies(not(X2),falsehood)) = implies(implies(implies(not(X2),falsehood),X2),X2),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c90,plain,
implies(implies(not(X2),falsehood),X2) = implies(implies(not(X2),falsehood),implies(truth,X2)),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c92,plain,
implies(not(X2),falsehood) = implies(not(X2),not(truth)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
implies(implies(not(X2),falsehood),implies(truth,X2)) = implies(implies(not(X2),not(truth)),implies(truth,X2)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,axiom,
implies(implies(not(X2),not(Y2)),implies(Y2,X2)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
cnf(c95,plain,
implies(implies(not(X2),not(truth)),implies(truth,X2)) = truth,
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
implies(implies(not(X2),falsehood),implies(truth,X2)) = truth,
inference(transitivity,[status(thm)],[c93,c95]) ).
cnf(c97,plain,
implies(implies(not(X2),falsehood),X2) = truth,
inference(transitivity,[status(thm)],[c90,c96]) ).
cnf(c98,plain,
implies(implies(implies(not(X2),falsehood),X2),X2) = implies(truth,X2),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
implies(implies(implies(not(X2),falsehood),X2),X2) = X2,
inference(transitivity,[status(thm)],[c98,c40]) ).
cnf(c100,plain,
implies(implies(X2,implies(not(X2),falsehood)),implies(not(X2),falsehood)) = X2,
inference(transitivity,[status(thm)],[c88,c99]) ).
cnf(c101,plain,
implies(truth,implies(not(X2),falsehood)) = X2,
inference(transitivity,[status(thm)],[c86,c100]) ).
cnf(c102,plain,
implies(not(X2),falsehood) = X2,
inference(transitivity,[status(thm)],[c42,c101]) ).
cnf(c103,plain,
implies(not(not(X2)),falsehood) = not(X2),
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
not(implies(not(not(X2)),falsehood)) = not(not(X2)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
X2 = implies(not(X2),falsehood),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c106,plain,
implies(X2,falsehood) = implies(implies(not(X2),falsehood),falsehood),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
implies(implies(not(X2),falsehood),falsehood) = implies(implies(falsehood,not(X2)),not(X2)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c108,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c109,plain,
implies(falsehood,X2) = implies(not(truth),X2),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
implies(not(truth),X2) = implies(not(X2),truth),
inference(substitution,[status(thm)],[c36]) ).
cnf(c111,plain,
implies(not(X2),truth) = truth,
inference(substitution,[status(thm)],[c72]) ).
cnf(c112,plain,
implies(not(truth),X2) = truth,
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
implies(falsehood,X2) = truth,
inference(transitivity,[status(thm)],[c109,c112]) ).
cnf(c114,plain,
implies(falsehood,not(X2)) = truth,
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
implies(implies(falsehood,not(X2)),not(X2)) = implies(truth,not(X2)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
implies(truth,not(X2)) = not(X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c117,plain,
implies(implies(falsehood,not(X2)),not(X2)) = not(X2),
inference(transitivity,[status(thm)],[c115,c116]) ).
cnf(c118,plain,
implies(implies(not(X2),falsehood),falsehood) = not(X2),
inference(transitivity,[status(thm)],[c107,c117]) ).
cnf(c119,plain,
implies(X2,falsehood) = not(X2),
inference(transitivity,[status(thm)],[c106,c118]) ).
cnf(c120,plain,
implies(not(X2),falsehood) = not(not(X2)),
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
not(not(X2)) = implies(not(X2),falsehood),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
implies(not(falsehood),X2) = implies(not(X2),falsehood),
inference(substitution,[status(thm)],[c36]) ).
cnf(c123,plain,
implies(not(X2),falsehood) = implies(not(falsehood),X2),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(substitution,[status(thm)],[c40]) ).
cnf(c125,plain,
not(falsehood) = implies(truth,not(falsehood)),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
implies(implies(not(not(falsehood)),falsehood),not(falsehood)) = truth,
inference(substitution,[status(thm)],[c97]) ).
cnf(c127,plain,
truth = implies(implies(not(not(falsehood)),falsehood),not(falsehood)),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
implies(truth,not(falsehood)) = implies(implies(implies(not(not(falsehood)),falsehood),not(falsehood)),not(falsehood)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
implies(implies(not(falsehood),X2),X2) = implies(implies(X2,not(falsehood)),not(falsehood)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c130,plain,
implies(implies(X2,not(falsehood)),not(falsehood)) = implies(implies(not(falsehood),X2),X2),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
implies(not(falsehood),X2) = implies(not(X2),falsehood),
inference(substitution,[status(thm)],[c36]) ).
cnf(c132,plain,
implies(implies(not(falsehood),X2),X2) = implies(implies(not(X2),falsehood),X2),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
implies(implies(not(falsehood),X2),X2) = truth,
inference(transitivity,[status(thm)],[c132,c97]) ).
cnf(c134,plain,
implies(implies(X2,not(falsehood)),not(falsehood)) = truth,
inference(transitivity,[status(thm)],[c130,c133]) ).
cnf(c135,plain,
implies(implies(implies(not(not(falsehood)),falsehood),not(falsehood)),not(falsehood)) = truth,
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
implies(truth,not(falsehood)) = truth,
inference(transitivity,[status(thm)],[c128,c135]) ).
cnf(c137,plain,
not(falsehood) = truth,
inference(transitivity,[status(thm)],[c125,c136]) ).
cnf(c138,plain,
implies(not(falsehood),X2) = implies(truth,X2),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
implies(not(falsehood),X2) = X2,
inference(transitivity,[status(thm)],[c138,c40]) ).
cnf(c140,plain,
implies(not(X2),falsehood) = X2,
inference(transitivity,[status(thm)],[c123,c139]) ).
cnf(c141,plain,
not(not(X2)) = X2,
inference(transitivity,[status(thm)],[c121,c140]) ).
cnf(c142,plain,
not(implies(not(not(X2)),falsehood)) = X2,
inference(transitivity,[status(thm)],[c104,c141]) ).
cnf(c143,plain,
not(implies(not(falsehood),not(X2))) = X2,
inference(transitivity,[status(thm)],[c39,c142]) ).
cnf(c144,plain,
and(X2,truth) = X2,
inference(transitivity,[status(thm)],[c28,c143]) ).
cnf(c145,plain,
and(not(X2),truth) = not(X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
implies(not(and(X2,not(truth))),and(not(X2),truth)) = implies(not(and(X2,not(truth))),not(X2)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
and(X2,not(truth)) = and(X2,falsehood),
inference(congruence,[status(thm)],[c11]) ).
cnf(c148,plain,
not(and(X2,not(truth))) = not(and(X2,falsehood)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
implies(not(and(X2,not(truth))),not(X2)) = implies(not(and(X2,falsehood)),not(X2)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
and(falsehood,X2) = and(X2,falsehood),
inference(substitution,[status(thm)],[c24]) ).
cnf(c151,plain,
and(X2,falsehood) = and(falsehood,X2),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
not(implies(not(not(falsehood)),not(X2))) = and(falsehood,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c153,plain,
and(falsehood,X2) = not(implies(not(not(falsehood)),not(X2))),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
not(not(falsehood)) = not(truth),
inference(congruence,[status(thm)],[c137]) ).
cnf(c155,plain,
implies(not(not(falsehood)),not(X2)) = implies(not(truth),not(X2)),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
not(implies(not(not(falsehood)),not(X2))) = not(implies(not(truth),not(X2))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
implies(not(truth),not(X2)) = implies(falsehood,not(X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c158,plain,
not(implies(not(truth),not(X2))) = not(implies(falsehood,not(X2))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
implies(falsehood,not(X2)) = truth,
inference(substitution,[status(thm)],[c113]) ).
cnf(c160,plain,
not(implies(falsehood,not(X2))) = not(truth),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
not(implies(falsehood,not(X2))) = falsehood,
inference(transitivity,[status(thm)],[c160,c11]) ).
cnf(c162,plain,
not(implies(not(truth),not(X2))) = falsehood,
inference(transitivity,[status(thm)],[c158,c161]) ).
cnf(c163,plain,
not(implies(not(not(falsehood)),not(X2))) = falsehood,
inference(transitivity,[status(thm)],[c156,c162]) ).
cnf(c164,plain,
and(falsehood,X2) = falsehood,
inference(transitivity,[status(thm)],[c153,c163]) ).
cnf(c165,plain,
and(X2,falsehood) = falsehood,
inference(transitivity,[status(thm)],[c151,c164]) ).
cnf(c166,plain,
not(and(X2,falsehood)) = not(falsehood),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
implies(not(and(X2,falsehood)),not(X2)) = implies(not(falsehood),not(X2)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
implies(not(falsehood),not(X2)) = implies(truth,not(X2)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c169,plain,
implies(truth,not(X2)) = not(X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c170,plain,
implies(not(falsehood),not(X2)) = not(X2),
inference(transitivity,[status(thm)],[c168,c169]) ).
cnf(c171,plain,
implies(not(and(X2,falsehood)),not(X2)) = not(X2),
inference(transitivity,[status(thm)],[c167,c170]) ).
cnf(c172,plain,
implies(not(and(X2,not(truth))),not(X2)) = not(X2),
inference(transitivity,[status(thm)],[c149,c171]) ).
cnf(c173,plain,
implies(not(and(X2,not(truth))),and(not(X2),truth)) = not(X2),
inference(transitivity,[status(thm)],[c146,c172]) ).
cnf(c174,plain,
xor(X2,truth) = not(X2),
inference(transitivity,[status(thm)],[c10,c173]) ).
cnf(c175,plain,
xor(x,truth) = not(x),
inference(substitution,[status(thm)],[c174]) ).
cnf(c176,plain,
not(x) = xor(x,truth),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
$false,
inference(resolution,[status(thm)],[c1,c176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL153-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.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
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 15:21:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.47 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
% 0.13/0.47
% 0.13/0.47 % SZS status Unsatisfiable
% 0.13/0.47
% 0.13/0.48 % SZS output start CNFRefutation
% See solution above
% 0.66/0.54
% 0.66/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------