%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% 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 11:49:10 AM UTC 2026
% Result : Unsatisfiable 3.57s 0.95s
% Output : CNFRefutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 13
% Syntax : Number of clauses : 220 ( 220 unt; 0 nHn; 19 RR)
% Number of literals : 220 ( 219 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 270 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c2,axiom,
and_star(X,Y) = and_star(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(c3,plain,
and_star(not(X3),X2) = and_star(X2,not(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
and_star(X2,not(X3)) = and_star(not(X3),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
or(and_star(X3,xor(truth,X2)),and_star(X2,not(X3))) = or(and_star(X3,xor(truth,X2)),and_star(not(X3),X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
xor(X2,Y2) = xor(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(c7,plain,
xor(truth,X2) = xor(X2,truth),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,axiom,
and(X2,Y2) = not(or(not(X2),not(Y2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_definition) ).
cnf(c9,plain,
and(X3,X2) = not(or(not(X3),not(X2))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,axiom,
and_star(X2,Y2) = not(or(not(X2),not(Y2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_definition) ).
cnf(c11,plain,
and_star(X3,X2) = not(or(not(X3),not(X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
not(or(not(X3),not(X2))) = and_star(X3,X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
and(X3,X2) = and_star(X3,X2),
inference(transitivity,[status(thm)],[c9,c12]) ).
cnf(c14,plain,
and(not(X3),X2) = and_star(not(X3),X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
and_star(not(X3),X2) = and(not(X3),X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
or(and_star(X3,not(X2)),and_star(not(X3),X2)) = or(and_star(X3,not(X2)),and(not(X3),X2)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
and(X3,not(X2)) = and_star(X3,not(X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c18,plain,
and_star(X3,not(X2)) = and(X3,not(X2)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
or(and_star(X3,not(X2)),and(not(X3),X2)) = or(and(X3,not(X2)),and(not(X3),X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
xor(X2,Y2) = or(and(X2,not(Y2)),and(not(X2),Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_definition) ).
cnf(c21,plain,
xor(X3,X2) = or(and(X3,not(X2)),and(not(X3),X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
or(and(X3,not(X2)),and(not(X3),X2)) = xor(X3,X2),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
or(and_star(X3,not(X2)),and(not(X3),X2)) = xor(X3,X2),
inference(transitivity,[status(thm)],[c19,c22]) ).
cnf(c24,plain,
or(and_star(X3,not(X2)),and_star(not(X3),X2)) = xor(X3,X2),
inference(transitivity,[status(thm)],[c16,c23]) ).
cnf(c25,plain,
or(and_star(X2,not(truth)),and_star(not(X2),truth)) = xor(X2,truth),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
xor(X2,truth) = or(and_star(X2,not(truth)),and_star(not(X2),truth)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c28,plain,
and_star(X2,not(truth)) = and_star(X2,falsehood),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
or(and_star(X2,not(truth)),and_star(not(X2),truth)) = or(and_star(X2,falsehood),and_star(not(X2),truth)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
and_star(falsehood,X2) = and_star(X2,falsehood),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
and_star(X2,falsehood) = and_star(falsehood,X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
and_star(falsehood,X2) = not(or(not(falsehood),not(X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c33,axiom,
implies(truth,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
cnf(c34,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
not(falsehood) = implies(truth,not(falsehood)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,axiom,
or(X2,Y2) = or(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
cnf(c37,plain,
or(X2,falsehood) = or(falsehood,X2),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
or(falsehood,X2) = or(X2,falsehood),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
implies(or(falsehood,X2),X2) = implies(or(X2,falsehood),X2),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c41,plain,
implies(or(X2,falsehood),X2) = implies(or(X2,falsehood),implies(truth,X2)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c43,plain,
or(X2,falsehood) = or(X2,not(truth)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
implies(or(X2,falsehood),implies(truth,X2)) = implies(or(X2,not(truth)),implies(truth,X2)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,axiom,
or(X2,Y2) = implies(not(X2),Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_definition) ).
cnf(c46,plain,
or(X3,not(X2)) = implies(not(X3),not(X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
implies(or(X3,not(X2)),implies(X2,X3)) = implies(implies(not(X3),not(X2)),implies(X2,X3)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,axiom,
implies(implies(not(X2),not(Y2)),implies(Y2,X2)) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).
cnf(c49,plain,
implies(implies(not(X3),not(X2)),implies(X2,X3)) = truth,
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
implies(or(X3,not(X2)),implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c47,c49]) ).
cnf(c51,plain,
implies(or(X2,not(truth)),implies(truth,X2)) = truth,
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
implies(or(X2,falsehood),implies(truth,X2)) = truth,
inference(transitivity,[status(thm)],[c44,c51]) ).
cnf(c53,plain,
implies(or(X2,falsehood),X2) = truth,
inference(transitivity,[status(thm)],[c41,c52]) ).
cnf(c54,plain,
implies(or(falsehood,X2),X2) = truth,
inference(transitivity,[status(thm)],[c39,c53]) ).
cnf(c55,plain,
implies(or(falsehood,truth),truth) = truth,
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
truth = implies(or(falsehood,truth),truth),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
implies(truth,not(falsehood)) = implies(implies(or(falsehood,truth),truth),not(falsehood)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
or(X2,truth) = implies(not(X2),truth),
inference(substitution,[status(thm)],[c45]) ).
cnf(c59,plain,
implies(or(X2,truth),truth) = implies(implies(not(X2),truth),truth),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,axiom,
implies(implies(X2,Y2),Y2) = implies(implies(Y2,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
cnf(c61,plain,
implies(implies(truth,X2),X2) = implies(implies(X2,truth),truth),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
implies(implies(X2,truth),truth) = implies(implies(truth,X2),X2),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
implies(implies(truth,X2),X2) = implies(X2,X2),
inference(congruence,[status(thm)],[c33]) ).
cnf(c64,plain,
implies(implies(X2,truth),truth) = implies(X2,X2),
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
implies(implies(not(X2),truth),truth) = implies(not(X2),not(X2)),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
or(X2,not(X2)) = implies(not(X2),not(X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c67,plain,
implies(not(X2),not(X2)) = or(X2,not(X2)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
implies(implies(not(X2),truth),truth) = or(X2,not(X2)),
inference(transitivity,[status(thm)],[c65,c67]) ).
cnf(c69,plain,
implies(or(X2,truth),truth) = or(X2,not(X2)),
inference(transitivity,[status(thm)],[c59,c68]) ).
cnf(c70,plain,
implies(or(falsehood,truth),truth) = or(falsehood,not(falsehood)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
implies(implies(or(falsehood,truth),truth),not(falsehood)) = implies(or(falsehood,not(falsehood)),not(falsehood)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
implies(or(falsehood,not(falsehood)),not(falsehood)) = truth,
inference(substitution,[status(thm)],[c54]) ).
cnf(c73,plain,
implies(implies(or(falsehood,truth),truth),not(falsehood)) = truth,
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
implies(truth,not(falsehood)) = truth,
inference(transitivity,[status(thm)],[c57,c73]) ).
cnf(c75,plain,
not(falsehood) = truth,
inference(transitivity,[status(thm)],[c35,c74]) ).
cnf(c76,plain,
or(not(falsehood),not(X2)) = or(truth,not(X2)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
not(or(not(falsehood),not(X2))) = not(or(truth,not(X2))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
or(X2,truth) = or(truth,X2),
inference(substitution,[status(thm)],[c36]) ).
cnf(c79,plain,
or(truth,X2) = or(X2,truth),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
or(X2,truth) = implies(not(X2),truth),
inference(substitution,[status(thm)],[c45]) ).
cnf(c81,plain,
or(falsehood,X2) = or(X2,falsehood),
inference(substitution,[status(thm)],[c36]) ).
cnf(c82,plain,
or(X2,falsehood) = or(falsehood,X2),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
or(falsehood,X2) = implies(not(falsehood),X2),
inference(substitution,[status(thm)],[c45]) ).
cnf(c84,plain,
implies(not(falsehood),X2) = implies(truth,X2),
inference(congruence,[status(thm)],[c75]) ).
cnf(c85,plain,
implies(not(falsehood),X2) = X2,
inference(transitivity,[status(thm)],[c84,c33]) ).
cnf(c86,plain,
or(falsehood,X2) = X2,
inference(transitivity,[status(thm)],[c83,c85]) ).
cnf(c87,plain,
or(X2,falsehood) = X2,
inference(transitivity,[status(thm)],[c82,c86]) ).
cnf(c88,plain,
X2 = or(X2,falsehood),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
implies(X2,X2) = implies(or(X2,falsehood),X2),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
implies(X2,X2) = truth,
inference(transitivity,[status(thm)],[c89,c53]) ).
cnf(c91,plain,
truth = implies(X2,X2),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
implies(X2,truth) = implies(X2,implies(X2,X2)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
implies(X2,X2) = implies(implies(X2,truth),truth),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c94,plain,
implies(X2,implies(X2,X2)) = implies(X2,implies(implies(X2,truth),truth)),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c96,plain,
implies(implies(X3,X2),X2) = implies(implies(X3,X2),implies(truth,X2)),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
implies(X3,implies(implies(X3,X2),X2)) = implies(X3,implies(implies(X3,X2),implies(truth,X2))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c99,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)],[c98]) ).
cnf(c100,axiom,
implies(implies(X2,Y2),implies(implies(Y2,Z),implies(X2,Z))) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_2) ).
cnf(c101,plain,
implies(implies(truth,X3),implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
implies(X3,implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(transitivity,[status(thm)],[c99,c101]) ).
cnf(c103,plain,
implies(X3,implies(implies(X3,X2),X2)) = truth,
inference(transitivity,[status(thm)],[c97,c102]) ).
cnf(c104,plain,
implies(X2,implies(implies(X2,truth),truth)) = truth,
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
implies(X2,implies(X2,X2)) = truth,
inference(transitivity,[status(thm)],[c94,c104]) ).
cnf(c106,plain,
implies(X2,truth) = truth,
inference(transitivity,[status(thm)],[c92,c105]) ).
cnf(c107,plain,
implies(not(X2),truth) = truth,
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
or(X2,truth) = truth,
inference(transitivity,[status(thm)],[c80,c107]) ).
cnf(c109,plain,
or(truth,X2) = truth,
inference(transitivity,[status(thm)],[c79,c108]) ).
cnf(c110,plain,
or(truth,not(X2)) = truth,
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
not(or(truth,not(X2))) = not(truth),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
not(or(truth,not(X2))) = falsehood,
inference(transitivity,[status(thm)],[c111,c27]) ).
cnf(c113,plain,
not(or(not(falsehood),not(X2))) = falsehood,
inference(transitivity,[status(thm)],[c77,c112]) ).
cnf(c114,plain,
and_star(falsehood,X2) = falsehood,
inference(transitivity,[status(thm)],[c32,c113]) ).
cnf(c115,plain,
and_star(X2,falsehood) = falsehood,
inference(transitivity,[status(thm)],[c31,c114]) ).
cnf(c116,plain,
or(and_star(X2,falsehood),and_star(not(X2),truth)) = or(falsehood,and_star(not(X2),truth)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
or(X2,falsehood) = or(falsehood,X2),
inference(substitution,[status(thm)],[c36]) ).
cnf(c118,plain,
or(falsehood,X2) = or(X2,falsehood),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
or(falsehood,X2) = X2,
inference(transitivity,[status(thm)],[c118,c87]) ).
cnf(c120,plain,
or(falsehood,and_star(not(X2),truth)) = and_star(not(X2),truth),
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c122,plain,
or(falsehood,not(X2)) = or(not(truth),not(X2)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
not(or(falsehood,not(X2))) = not(or(not(truth),not(X2))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
and_star(truth,X2) = not(or(not(truth),not(X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c125,plain,
not(or(not(truth),not(X2))) = and_star(truth,X2),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
and_star(truth,X2) = and_star(X2,truth),
inference(substitution,[status(thm)],[c2]) ).
cnf(c127,plain,
not(or(not(truth),not(X2))) = and_star(X2,truth),
inference(transitivity,[status(thm)],[c125,c126]) ).
cnf(c128,plain,
not(or(falsehood,not(X2))) = and_star(X2,truth),
inference(transitivity,[status(thm)],[c123,c127]) ).
cnf(c129,plain,
and_star(X2,truth) = not(or(falsehood,not(X2))),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
or(falsehood,not(X2)) = not(X2),
inference(substitution,[status(thm)],[c119]) ).
cnf(c131,plain,
not(or(falsehood,not(X2))) = not(not(X2)),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
and_star(X2,truth) = not(not(X2)),
inference(transitivity,[status(thm)],[c129,c131]) ).
cnf(c133,plain,
and_star(not(X2),truth) = not(not(not(X2))),
inference(substitution,[status(thm)],[c132]) ).
cnf(c134,plain,
X2 = or(X2,falsehood),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c135,plain,
implies(X2,falsehood) = implies(or(X2,falsehood),falsehood),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
or(X2,falsehood) = implies(not(X2),falsehood),
inference(substitution,[status(thm)],[c45]) ).
cnf(c137,plain,
implies(or(X2,falsehood),falsehood) = implies(implies(not(X2),falsehood),falsehood),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
implies(implies(falsehood,X2),X2) = implies(implies(X2,falsehood),falsehood),
inference(substitution,[status(thm)],[c60]) ).
cnf(c139,plain,
implies(implies(X2,falsehood),falsehood) = implies(implies(falsehood,X2),X2),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c141,plain,
implies(falsehood,X2) = implies(not(truth),X2),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
or(truth,X2) = implies(not(truth),X2),
inference(substitution,[status(thm)],[c45]) ).
cnf(c143,plain,
implies(not(truth),X2) = or(truth,X2),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
or(truth,X2) = or(X2,truth),
inference(substitution,[status(thm)],[c36]) ).
cnf(c145,plain,
implies(not(truth),X2) = or(X2,truth),
inference(transitivity,[status(thm)],[c143,c144]) ).
cnf(c146,plain,
implies(falsehood,X2) = or(X2,truth),
inference(transitivity,[status(thm)],[c141,c145]) ).
cnf(c147,plain,
implies(implies(falsehood,X2),X2) = implies(or(X2,truth),X2),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
implies(implies(X2,falsehood),falsehood) = implies(or(X2,truth),X2),
inference(transitivity,[status(thm)],[c139,c147]) ).
cnf(c149,plain,
implies(or(X2,truth),X2) = implies(truth,X2),
inference(congruence,[status(thm)],[c108]) ).
cnf(c150,plain,
implies(or(X2,truth),X2) = X2,
inference(transitivity,[status(thm)],[c149,c33]) ).
cnf(c151,plain,
implies(implies(X2,falsehood),falsehood) = X2,
inference(transitivity,[status(thm)],[c148,c150]) ).
cnf(c152,plain,
implies(implies(not(X2),falsehood),falsehood) = not(X2),
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
implies(or(X2,falsehood),falsehood) = not(X2),
inference(transitivity,[status(thm)],[c137,c152]) ).
cnf(c154,plain,
implies(X2,falsehood) = not(X2),
inference(transitivity,[status(thm)],[c135,c153]) ).
cnf(c155,plain,
implies(not(X2),falsehood) = not(not(X2)),
inference(substitution,[status(thm)],[c154]) ).
cnf(c156,plain,
not(not(X2)) = implies(not(X2),falsehood),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
or(X2,falsehood) = implies(not(X2),falsehood),
inference(substitution,[status(thm)],[c45]) ).
cnf(c158,plain,
implies(not(X2),falsehood) = or(X2,falsehood),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
implies(not(X2),falsehood) = X2,
inference(transitivity,[status(thm)],[c158,c87]) ).
cnf(c160,plain,
not(not(X2)) = X2,
inference(transitivity,[status(thm)],[c156,c159]) ).
cnf(c161,plain,
not(not(not(X2))) = not(X2),
inference(substitution,[status(thm)],[c160]) ).
cnf(c162,plain,
and_star(not(X2),truth) = not(X2),
inference(transitivity,[status(thm)],[c133,c161]) ).
cnf(c163,plain,
or(falsehood,and_star(not(X2),truth)) = not(X2),
inference(transitivity,[status(thm)],[c120,c162]) ).
cnf(c164,plain,
or(and_star(X2,falsehood),and_star(not(X2),truth)) = not(X2),
inference(transitivity,[status(thm)],[c116,c163]) ).
cnf(c165,plain,
or(and_star(X2,not(truth)),and_star(not(X2),truth)) = not(X2),
inference(transitivity,[status(thm)],[c29,c164]) ).
cnf(c166,plain,
xor(X2,truth) = not(X2),
inference(transitivity,[status(thm)],[c26,c165]) ).
cnf(c167,plain,
xor(truth,X2) = not(X2),
inference(transitivity,[status(thm)],[c7,c166]) ).
cnf(c168,plain,
and_star(X3,xor(truth,X2)) = and_star(X3,not(X2)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
or(and_star(X3,xor(truth,X2)),and_star(not(X3),X2)) = or(and_star(X3,not(X2)),and_star(not(X3),X2)),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
or(and_star(X3,xor(truth,X2)),and_star(not(X3),X2)) = xor(X3,X2),
inference(transitivity,[status(thm)],[c169,c24]) ).
cnf(c171,plain,
or(and_star(X3,xor(truth,X2)),and_star(X2,not(X3))) = xor(X3,X2),
inference(transitivity,[status(thm)],[c5,c170]) ).
cnf(c172,plain,
or(and_star(xor(X3,truth),xor(truth,X2)),and_star(X2,not(xor(X3,truth)))) = xor(xor(X3,truth),X2),
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
xor(xor(X3,truth),X2) = or(and_star(xor(X3,truth),xor(truth,X2)),and_star(X2,not(xor(X3,truth)))),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
or(falsehood,xor(X2,truth)) = xor(X2,truth),
inference(substitution,[status(thm)],[c119]) ).
cnf(c175,plain,
xor(X2,truth) = or(falsehood,xor(X2,truth)),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
not(xor(X2,truth)) = not(or(falsehood,xor(X2,truth))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
or(falsehood,xor(X2,truth)) = or(falsehood,not(X2)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c178,plain,
not(or(falsehood,xor(X2,truth))) = not(or(falsehood,not(X2))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
and_star(X2,truth) = X2,
inference(transitivity,[status(thm)],[c132,c160]) ).
cnf(c180,plain,
not(or(falsehood,not(X2))) = X2,
inference(transitivity,[status(thm)],[c128,c179]) ).
cnf(c181,plain,
not(or(falsehood,xor(X2,truth))) = X2,
inference(transitivity,[status(thm)],[c178,c180]) ).
cnf(c182,plain,
not(xor(X2,truth)) = X2,
inference(transitivity,[status(thm)],[c176,c181]) ).
cnf(c183,plain,
and_star(X2,not(xor(X3,truth))) = and_star(X2,X3),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
or(and_star(xor(X3,truth),xor(truth,X2)),and_star(X2,not(xor(X3,truth)))) = or(and_star(xor(X3,truth),xor(truth,X2)),and_star(X2,X3)),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
and_star(xor(X3,truth),xor(truth,X2)) = and_star(xor(truth,X2),xor(X3,truth)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c186,plain,
or(and_star(xor(X3,truth),xor(truth,X2)),and_star(X2,X3)) = or(and_star(xor(truth,X2),xor(X3,truth)),and_star(X2,X3)),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
and_star(X2,X3) = and_star(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c188,plain,
or(and_star(xor(truth,X2),xor(X3,truth)),and_star(X2,X3)) = or(and_star(xor(truth,X2),xor(X3,truth)),and_star(X3,X2)),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
or(falsehood,xor(truth,X2)) = xor(truth,X2),
inference(substitution,[status(thm)],[c119]) ).
cnf(c190,plain,
xor(truth,X2) = or(falsehood,xor(truth,X2)),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
not(xor(truth,X2)) = not(or(falsehood,xor(truth,X2))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
or(falsehood,xor(truth,X2)) = or(falsehood,not(X2)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c193,plain,
not(or(falsehood,xor(truth,X2))) = not(or(falsehood,not(X2))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
and_star(X2,truth) = X2,
inference(transitivity,[status(thm)],[c132,c160]) ).
cnf(c195,plain,
not(or(falsehood,not(X2))) = X2,
inference(transitivity,[status(thm)],[c128,c194]) ).
cnf(c196,plain,
not(or(falsehood,xor(truth,X2))) = X2,
inference(transitivity,[status(thm)],[c193,c195]) ).
cnf(c197,plain,
not(xor(truth,X2)) = X2,
inference(transitivity,[status(thm)],[c191,c196]) ).
cnf(c198,plain,
X2 = not(xor(truth,X2)),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
and_star(X2,X3) = and_star(X2,not(xor(truth,X3))),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
or(and_star(xor(truth,X3),xor(X2,truth)),and_star(X2,X3)) = or(and_star(xor(truth,X3),xor(X2,truth)),and_star(X2,not(xor(truth,X3)))),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
and_star(not(X3),X2) = and_star(X2,not(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c202,plain,
and_star(X2,not(X3)) = and_star(not(X3),X2),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
or(and_star(X3,xor(X2,truth)),and_star(X2,not(X3))) = or(and_star(X3,xor(X2,truth)),and_star(not(X3),X2)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
and_star(X3,xor(X2,truth)) = and_star(X3,not(X2)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c205,plain,
or(and_star(X3,xor(X2,truth)),and_star(not(X3),X2)) = or(and_star(X3,not(X2)),and_star(not(X3),X2)),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
or(and_star(X3,xor(X2,truth)),and_star(not(X3),X2)) = xor(X3,X2),
inference(transitivity,[status(thm)],[c205,c24]) ).
cnf(c207,plain,
or(and_star(X3,xor(X2,truth)),and_star(X2,not(X3))) = xor(X3,X2),
inference(transitivity,[status(thm)],[c203,c206]) ).
cnf(c208,plain,
or(and_star(xor(truth,X3),xor(X2,truth)),and_star(X2,not(xor(truth,X3)))) = xor(xor(truth,X3),X2),
inference(substitution,[status(thm)],[c207]) ).
cnf(c209,plain,
xor(X2,xor(truth,X3)) = xor(xor(truth,X3),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c210,plain,
xor(xor(truth,X3),X2) = xor(X2,xor(truth,X3)),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
or(and_star(xor(truth,X3),xor(X2,truth)),and_star(X2,not(xor(truth,X3)))) = xor(X2,xor(truth,X3)),
inference(transitivity,[status(thm)],[c208,c210]) ).
cnf(c212,plain,
or(and_star(xor(truth,X3),xor(X2,truth)),and_star(X2,X3)) = xor(X2,xor(truth,X3)),
inference(transitivity,[status(thm)],[c200,c211]) ).
cnf(c213,plain,
or(and_star(xor(truth,X2),xor(X3,truth)),and_star(X3,X2)) = xor(X3,xor(truth,X2)),
inference(substitution,[status(thm)],[c212]) ).
cnf(c214,plain,
or(and_star(xor(truth,X2),xor(X3,truth)),and_star(X2,X3)) = xor(X3,xor(truth,X2)),
inference(transitivity,[status(thm)],[c188,c213]) ).
cnf(c215,plain,
or(and_star(xor(X3,truth),xor(truth,X2)),and_star(X2,X3)) = xor(X3,xor(truth,X2)),
inference(transitivity,[status(thm)],[c186,c214]) ).
cnf(c216,plain,
or(and_star(xor(X3,truth),xor(truth,X2)),and_star(X2,not(xor(X3,truth)))) = xor(X3,xor(truth,X2)),
inference(transitivity,[status(thm)],[c184,c215]) ).
cnf(c217,plain,
xor(xor(X3,truth),X2) = xor(X3,xor(truth,X2)),
inference(transitivity,[status(thm)],[c173,c216]) ).
cnf(c218,plain,
xor(xor(x,truth),y) = xor(x,xor(truth,y)),
inference(substitution,[status(thm)],[c217]) ).
cnf(c219,plain,
xor(x,xor(truth,y)) = xor(xor(x,truth),y),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
$false,
inference(resolution,[status(thm)],[c1,c219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 15:27:06 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.57/0.95 Command-line arguments: --flatten --complete-subsets
% 3.57/0.95
% 3.57/0.95 % SZS status Unsatisfiable
% 3.57/0.95
% 3.57/0.96 % SZS output start CNFRefutation
% See solution above
% 3.57/1.05
% 3.57/1.05 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------