%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 0.44s 0.52s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 13
% Syntax : Number of clauses : 180 ( 180 unt; 0 nHn; 26 RR)
% Number of literals : 180 ( 179 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 189 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
and_star(xor(truth,x),x) != falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c2,axiom,
xor(X,Y) = xor(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(c3,plain,
xor(truth,x) = xor(x,truth),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
and_star(xor(truth,x),x) = and_star(xor(x,truth),x),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
and_star(X2,Y2) = and_star(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(c6,plain,
and_star(xor(x,truth),x) = and_star(x,xor(x,truth)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,axiom,
and(X2,Y2) = not(or(not(X2),not(Y2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition) ).
cnf(c8,plain,
and(X3,X2) = not(or(not(X3),not(X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,axiom,
and_star(X2,Y2) = not(or(not(X2),not(Y2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_definition) ).
cnf(c10,plain,
and_star(X3,X2) = not(or(not(X3),not(X2))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
not(or(not(X3),not(X2))) = and_star(X3,X2),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
and(X3,X2) = and_star(X3,X2),
inference(transitivity,[status(thm)],[c8,c11]) ).
cnf(c13,plain,
and(not(X3),X2) = and_star(not(X3),X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
and_star(not(X3),X2) = and(not(X3),X2),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,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)],[c14]) ).
cnf(c16,plain,
and(X3,not(X2)) = and_star(X3,not(X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c17,plain,
and_star(X3,not(X2)) = and(X3,not(X2)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
or(and_star(X3,not(X2)),and(not(X3),X2)) = or(and(X3,not(X2)),and(not(X3),X2)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
xor(X2,Y2) = or(and(X2,not(Y2)),and(not(X2),Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition) ).
cnf(c20,plain,
xor(X3,X2) = or(and(X3,not(X2)),and(not(X3),X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
or(and(X3,not(X2)),and(not(X3),X2)) = xor(X3,X2),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
or(and_star(X3,not(X2)),and(not(X3),X2)) = xor(X3,X2),
inference(transitivity,[status(thm)],[c18,c21]) ).
cnf(c23,plain,
or(and_star(X3,not(X2)),and_star(not(X3),X2)) = xor(X3,X2),
inference(transitivity,[status(thm)],[c15,c22]) ).
cnf(c24,plain,
or(and_star(X2,not(truth)),and_star(not(X2),truth)) = xor(X2,truth),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
xor(X2,truth) = or(and_star(X2,not(truth)),and_star(not(X2),truth)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c27,plain,
and_star(X2,not(truth)) = and_star(X2,falsehood),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,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)],[c27]) ).
cnf(c29,plain,
and_star(falsehood,X2) = and_star(X2,falsehood),
inference(substitution,[status(thm)],[c5]) ).
cnf(c30,plain,
and_star(X2,falsehood) = and_star(falsehood,X2),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
and_star(falsehood,X2) = not(or(not(falsehood),not(X2))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c32,axiom,
implies(truth,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
cnf(c33,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
not(falsehood) = implies(truth,not(falsehood)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,axiom,
or(X2,Y2) = or(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_commutativity) ).
cnf(c36,plain,
or(X2,falsehood) = or(falsehood,X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
or(falsehood,X2) = or(X2,falsehood),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
implies(or(falsehood,X2),X2) = implies(or(X2,falsehood),X2),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c40,plain,
implies(or(X2,falsehood),X2) = implies(or(X2,falsehood),implies(truth,X2)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c42,plain,
or(X2,falsehood) = or(X2,not(truth)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
implies(or(X2,falsehood),implies(truth,X2)) = implies(or(X2,not(truth)),implies(truth,X2)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,axiom,
or(X2,Y2) = implies(not(X2),Y2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition) ).
cnf(c45,plain,
or(X3,not(X2)) = implies(not(X3),not(X2)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
implies(or(X3,not(X2)),implies(X2,X3)) = implies(implies(not(X3),not(X2)),implies(X2,X3)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,axiom,
implies(implies(not(X2),not(Y2)),implies(Y2,X2)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
cnf(c48,plain,
implies(implies(not(X3),not(X2)),implies(X2,X3)) = truth,
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
implies(or(X3,not(X2)),implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c46,c48]) ).
cnf(c50,plain,
implies(or(X2,not(truth)),implies(truth,X2)) = truth,
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
implies(or(X2,falsehood),implies(truth,X2)) = truth,
inference(transitivity,[status(thm)],[c43,c50]) ).
cnf(c52,plain,
implies(or(X2,falsehood),X2) = truth,
inference(transitivity,[status(thm)],[c40,c51]) ).
cnf(c53,plain,
implies(or(falsehood,X2),X2) = truth,
inference(transitivity,[status(thm)],[c38,c52]) ).
cnf(c54,plain,
implies(or(falsehood,truth),truth) = truth,
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
truth = implies(or(falsehood,truth),truth),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
implies(truth,not(falsehood)) = implies(implies(or(falsehood,truth),truth),not(falsehood)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
or(X2,truth) = implies(not(X2),truth),
inference(substitution,[status(thm)],[c44]) ).
cnf(c58,plain,
implies(or(X2,truth),truth) = implies(implies(not(X2),truth),truth),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,axiom,
implies(implies(X2,Y2),Y2) = implies(implies(Y2,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
cnf(c60,plain,
implies(implies(truth,X2),X2) = implies(implies(X2,truth),truth),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
implies(implies(X2,truth),truth) = implies(implies(truth,X2),X2),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
implies(implies(truth,X2),X2) = implies(X2,X2),
inference(congruence,[status(thm)],[c32]) ).
cnf(c63,plain,
implies(implies(X2,truth),truth) = implies(X2,X2),
inference(transitivity,[status(thm)],[c61,c62]) ).
cnf(c64,plain,
implies(implies(not(X2),truth),truth) = implies(not(X2),not(X2)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
or(X2,not(X2)) = implies(not(X2),not(X2)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c66,plain,
implies(not(X2),not(X2)) = or(X2,not(X2)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
implies(implies(not(X2),truth),truth) = or(X2,not(X2)),
inference(transitivity,[status(thm)],[c64,c66]) ).
cnf(c68,plain,
implies(or(X2,truth),truth) = or(X2,not(X2)),
inference(transitivity,[status(thm)],[c58,c67]) ).
cnf(c69,plain,
implies(or(falsehood,truth),truth) = or(falsehood,not(falsehood)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
implies(implies(or(falsehood,truth),truth),not(falsehood)) = implies(or(falsehood,not(falsehood)),not(falsehood)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
implies(or(falsehood,not(falsehood)),not(falsehood)) = truth,
inference(substitution,[status(thm)],[c53]) ).
cnf(c72,plain,
implies(implies(or(falsehood,truth),truth),not(falsehood)) = truth,
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
implies(truth,not(falsehood)) = truth,
inference(transitivity,[status(thm)],[c56,c72]) ).
cnf(c74,plain,
not(falsehood) = truth,
inference(transitivity,[status(thm)],[c34,c73]) ).
cnf(c75,plain,
or(not(falsehood),not(X2)) = or(truth,not(X2)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
not(or(not(falsehood),not(X2))) = not(or(truth,not(X2))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
or(X2,truth) = or(truth,X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c78,plain,
or(truth,X2) = or(X2,truth),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
or(X2,truth) = implies(not(X2),truth),
inference(substitution,[status(thm)],[c44]) ).
cnf(c80,plain,
or(falsehood,X2) = or(X2,falsehood),
inference(substitution,[status(thm)],[c35]) ).
cnf(c81,plain,
or(X2,falsehood) = or(falsehood,X2),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
or(falsehood,X2) = implies(not(falsehood),X2),
inference(substitution,[status(thm)],[c44]) ).
cnf(c83,plain,
implies(not(falsehood),X2) = implies(truth,X2),
inference(congruence,[status(thm)],[c74]) ).
cnf(c84,plain,
implies(not(falsehood),X2) = X2,
inference(transitivity,[status(thm)],[c83,c32]) ).
cnf(c85,plain,
or(falsehood,X2) = X2,
inference(transitivity,[status(thm)],[c82,c84]) ).
cnf(c86,plain,
or(X2,falsehood) = X2,
inference(transitivity,[status(thm)],[c81,c85]) ).
cnf(c87,plain,
X2 = or(X2,falsehood),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
implies(X2,X2) = implies(or(X2,falsehood),X2),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
implies(X2,X2) = truth,
inference(transitivity,[status(thm)],[c88,c52]) ).
cnf(c90,plain,
truth = implies(X2,X2),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
implies(X2,truth) = implies(X2,implies(X2,X2)),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
implies(X2,X2) = implies(implies(X2,truth),truth),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c93,plain,
implies(X2,implies(X2,X2)) = implies(X2,implies(implies(X2,truth),truth)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c95,plain,
implies(implies(X3,X2),X2) = implies(implies(X3,X2),implies(truth,X2)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
implies(X3,implies(implies(X3,X2),X2)) = implies(X3,implies(implies(X3,X2),implies(truth,X2))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c98,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)],[c97]) ).
cnf(c99,axiom,
implies(implies(X2,Y2),implies(implies(Y2,Z),implies(X2,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
cnf(c100,plain,
implies(implies(truth,X3),implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
implies(X3,implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(transitivity,[status(thm)],[c98,c100]) ).
cnf(c102,plain,
implies(X3,implies(implies(X3,X2),X2)) = truth,
inference(transitivity,[status(thm)],[c96,c101]) ).
cnf(c103,plain,
implies(X2,implies(implies(X2,truth),truth)) = truth,
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
implies(X2,implies(X2,X2)) = truth,
inference(transitivity,[status(thm)],[c93,c103]) ).
cnf(c105,plain,
implies(X2,truth) = truth,
inference(transitivity,[status(thm)],[c91,c104]) ).
cnf(c106,plain,
implies(not(X2),truth) = truth,
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
or(X2,truth) = truth,
inference(transitivity,[status(thm)],[c79,c106]) ).
cnf(c108,plain,
or(truth,X2) = truth,
inference(transitivity,[status(thm)],[c78,c107]) ).
cnf(c109,plain,
or(truth,not(X2)) = truth,
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
not(or(truth,not(X2))) = not(truth),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
not(or(truth,not(X2))) = falsehood,
inference(transitivity,[status(thm)],[c110,c26]) ).
cnf(c112,plain,
not(or(not(falsehood),not(X2))) = falsehood,
inference(transitivity,[status(thm)],[c76,c111]) ).
cnf(c113,plain,
and_star(falsehood,X2) = falsehood,
inference(transitivity,[status(thm)],[c31,c112]) ).
cnf(c114,plain,
and_star(X2,falsehood) = falsehood,
inference(transitivity,[status(thm)],[c30,c113]) ).
cnf(c115,plain,
or(and_star(X2,falsehood),and_star(not(X2),truth)) = or(falsehood,and_star(not(X2),truth)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
or(X2,falsehood) = or(falsehood,X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c117,plain,
or(falsehood,X2) = or(X2,falsehood),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
or(falsehood,X2) = X2,
inference(transitivity,[status(thm)],[c117,c86]) ).
cnf(c119,plain,
or(falsehood,and_star(not(X2),truth)) = and_star(not(X2),truth),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c121,plain,
or(falsehood,not(X2)) = or(not(truth),not(X2)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
not(or(falsehood,not(X2))) = not(or(not(truth),not(X2))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
and_star(truth,X2) = not(or(not(truth),not(X2))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c124,plain,
not(or(not(truth),not(X2))) = and_star(truth,X2),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
and_star(truth,X2) = and_star(X2,truth),
inference(substitution,[status(thm)],[c5]) ).
cnf(c126,plain,
not(or(not(truth),not(X2))) = and_star(X2,truth),
inference(transitivity,[status(thm)],[c124,c125]) ).
cnf(c127,plain,
not(or(falsehood,not(X2))) = and_star(X2,truth),
inference(transitivity,[status(thm)],[c122,c126]) ).
cnf(c128,plain,
and_star(X2,truth) = not(or(falsehood,not(X2))),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
or(falsehood,not(X2)) = not(X2),
inference(substitution,[status(thm)],[c118]) ).
cnf(c130,plain,
not(or(falsehood,not(X2))) = not(not(X2)),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
and_star(X2,truth) = not(not(X2)),
inference(transitivity,[status(thm)],[c128,c130]) ).
cnf(c132,plain,
and_star(not(X2),truth) = not(not(not(X2))),
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
X2 = or(X2,falsehood),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c134,plain,
implies(X2,falsehood) = implies(or(X2,falsehood),falsehood),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
or(X2,falsehood) = implies(not(X2),falsehood),
inference(substitution,[status(thm)],[c44]) ).
cnf(c136,plain,
implies(or(X2,falsehood),falsehood) = implies(implies(not(X2),falsehood),falsehood),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
implies(implies(falsehood,X2),X2) = implies(implies(X2,falsehood),falsehood),
inference(substitution,[status(thm)],[c59]) ).
cnf(c138,plain,
implies(implies(X2,falsehood),falsehood) = implies(implies(falsehood,X2),X2),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c140,plain,
implies(falsehood,X2) = implies(not(truth),X2),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
or(truth,X2) = implies(not(truth),X2),
inference(substitution,[status(thm)],[c44]) ).
cnf(c142,plain,
implies(not(truth),X2) = or(truth,X2),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
or(truth,X2) = or(X2,truth),
inference(substitution,[status(thm)],[c35]) ).
cnf(c144,plain,
implies(not(truth),X2) = or(X2,truth),
inference(transitivity,[status(thm)],[c142,c143]) ).
cnf(c145,plain,
implies(falsehood,X2) = or(X2,truth),
inference(transitivity,[status(thm)],[c140,c144]) ).
cnf(c146,plain,
implies(implies(falsehood,X2),X2) = implies(or(X2,truth),X2),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
implies(implies(X2,falsehood),falsehood) = implies(or(X2,truth),X2),
inference(transitivity,[status(thm)],[c138,c146]) ).
cnf(c148,plain,
implies(or(X2,truth),X2) = implies(truth,X2),
inference(congruence,[status(thm)],[c107]) ).
cnf(c149,plain,
implies(or(X2,truth),X2) = X2,
inference(transitivity,[status(thm)],[c148,c32]) ).
cnf(c150,plain,
implies(implies(X2,falsehood),falsehood) = X2,
inference(transitivity,[status(thm)],[c147,c149]) ).
cnf(c151,plain,
implies(implies(not(X2),falsehood),falsehood) = not(X2),
inference(substitution,[status(thm)],[c150]) ).
cnf(c152,plain,
implies(or(X2,falsehood),falsehood) = not(X2),
inference(transitivity,[status(thm)],[c136,c151]) ).
cnf(c153,plain,
implies(X2,falsehood) = not(X2),
inference(transitivity,[status(thm)],[c134,c152]) ).
cnf(c154,plain,
implies(not(X2),falsehood) = not(not(X2)),
inference(substitution,[status(thm)],[c153]) ).
cnf(c155,plain,
not(not(X2)) = implies(not(X2),falsehood),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
or(X2,falsehood) = implies(not(X2),falsehood),
inference(substitution,[status(thm)],[c44]) ).
cnf(c157,plain,
implies(not(X2),falsehood) = or(X2,falsehood),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
implies(not(X2),falsehood) = X2,
inference(transitivity,[status(thm)],[c157,c86]) ).
cnf(c159,plain,
not(not(X2)) = X2,
inference(transitivity,[status(thm)],[c155,c158]) ).
cnf(c160,plain,
not(not(not(X2))) = not(X2),
inference(substitution,[status(thm)],[c159]) ).
cnf(c161,plain,
and_star(not(X2),truth) = not(X2),
inference(transitivity,[status(thm)],[c132,c160]) ).
cnf(c162,plain,
or(falsehood,and_star(not(X2),truth)) = not(X2),
inference(transitivity,[status(thm)],[c119,c161]) ).
cnf(c163,plain,
or(and_star(X2,falsehood),and_star(not(X2),truth)) = not(X2),
inference(transitivity,[status(thm)],[c115,c162]) ).
cnf(c164,plain,
or(and_star(X2,not(truth)),and_star(not(X2),truth)) = not(X2),
inference(transitivity,[status(thm)],[c28,c163]) ).
cnf(c165,plain,
xor(X2,truth) = not(X2),
inference(transitivity,[status(thm)],[c25,c164]) ).
cnf(c166,plain,
xor(x,truth) = not(x),
inference(substitution,[status(thm)],[c165]) ).
cnf(c167,plain,
and_star(x,xor(x,truth)) = and_star(x,not(x)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
and_star(X2,not(X2)) = not(or(not(X2),not(not(X2)))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c169,plain,
or(X2,not(X2)) = implies(not(X2),not(X2)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c170,plain,
implies(not(X2),not(X2)) = truth,
inference(substitution,[status(thm)],[c89]) ).
cnf(c171,plain,
or(X2,not(X2)) = truth,
inference(transitivity,[status(thm)],[c169,c170]) ).
cnf(c172,plain,
or(not(X2),not(not(X2))) = truth,
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
not(or(not(X2),not(not(X2)))) = not(truth),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
not(or(not(X2),not(not(X2)))) = falsehood,
inference(transitivity,[status(thm)],[c173,c26]) ).
cnf(c175,plain,
and_star(X2,not(X2)) = falsehood,
inference(transitivity,[status(thm)],[c168,c174]) ).
cnf(c176,plain,
and_star(x,not(x)) = falsehood,
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
and_star(x,xor(x,truth)) = falsehood,
inference(transitivity,[status(thm)],[c167,c176]) ).
cnf(c178,plain,
and_star(xor(x,truth),x) = falsehood,
inference(transitivity,[status(thm)],[c6,c177]) ).
cnf(c179,plain,
and_star(xor(truth,x),x) = falsehood,
inference(transitivity,[status(thm)],[c4,c178]) ).
cnf(c180,plain,
$false,
inference(resolution,[status(thm)],[c1,c179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:27:06 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.44/0.52 Command-line arguments: --no-flatten-goal
% 0.44/0.52
% 0.44/0.52 % SZS status Unsatisfiable
% 0.44/0.52
% 0.44/0.54 % SZS output start CNFRefutation
% See solution above
% 1.35/0.67
% 1.35/0.67 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------