%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 11:49:11 AM UTC 2026
% Result : Unsatisfiable 1.95s 0.80s
% Output : CNFRefutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 13
% Syntax : Number of clauses : 270 ( 270 unt; 0 nHn; 9 RR)
% Number of literals : 270 ( 269 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; 5 con; 0-2 aty)
% Number of variables : 531 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
implies(implies(x,y),implies(implies(y,z),implies(x,z))) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
cnf(c2,axiom,
not(X) = xor(X,truth),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
cnf(c3,plain,
not(not(X2)) = xor(not(X2),truth),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
xor(X2,xor(truth,Y)) = xor(xor(X2,truth),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
cnf(c5,plain,
xor(X2,xor(truth,X3)) = xor(xor(X2,truth),X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
xor(X2,truth) = not(X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c7,plain,
xor(xor(X3,truth),X2) = xor(not(X3),X2),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
xor(X3,xor(truth,X2)) = xor(not(X3),X2),
inference(transitivity,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
xor(X2,xor(truth,truth)) = xor(not(X2),truth),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
xor(not(X2),truth) = xor(X2,xor(truth,truth)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
xor(X2,X2) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c12,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c13,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
xor(X2,X2) = not(truth),
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
xor(truth,truth) = not(truth),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
xor(X2,xor(truth,truth)) = xor(X2,not(truth)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
xor(X2,not(truth)) = xor(X2,falsehood),
inference(congruence,[status(thm)],[c12]) ).
cnf(c18,axiom,
xor(X2,falsehood) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c19,plain,
xor(X2,not(truth)) = X2,
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
xor(X2,xor(truth,truth)) = X2,
inference(transitivity,[status(thm)],[c16,c19]) ).
cnf(c21,plain,
xor(not(X2),truth) = X2,
inference(transitivity,[status(thm)],[c10,c20]) ).
cnf(c22,plain,
not(not(X2)) = X2,
inference(transitivity,[status(thm)],[c3,c21]) ).
cnf(c23,plain,
not(not(implies(X3,X2))) = implies(X3,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
implies(X3,X2) = not(not(implies(X3,X2))),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
implies(implies(X3,X2),implies(implies(X2,X4),implies(X3,X4))) = implies(not(not(implies(X3,X2))),implies(implies(X2,X4),implies(X3,X4))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c27,plain,
implies(X3,X2) = implies(X3,not(not(X2))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
not(implies(X3,X2)) = not(implies(X3,not(not(X2)))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
X2 = xor(X2,not(truth)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c30,plain,
and_star(X3,X2) = and_star(X3,xor(X2,not(truth))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
not(and_star(X3,X2)) = not(and_star(X3,xor(X2,not(truth)))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,axiom,
xor(X2,Y2) = xor(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(c33,plain,
xor(X2,truth) = xor(truth,X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
xor(truth,X2) = xor(X2,truth),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
xor(X2,truth) = not(X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c36,plain,
xor(truth,X2) = not(X2),
inference(transitivity,[status(thm)],[c34,c35]) ).
cnf(c37,plain,
xor(truth,and_star(X3,xor(X2,not(truth)))) = not(and_star(X3,xor(X2,not(truth)))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
not(and_star(X3,xor(X2,not(truth)))) = xor(truth,and_star(X3,xor(X2,not(truth)))),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
xor(not(X2),X3) = xor(X3,not(X2)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c40,plain,
xor(X3,not(X2)) = xor(not(X2),X3),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
xor(X2,xor(truth,X3)) = xor(not(X2),X3),
inference(substitution,[status(thm)],[c8]) ).
cnf(c42,plain,
xor(not(X2),X3) = xor(X2,xor(truth,X3)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
xor(truth,X2) = xor(X2,truth),
inference(substitution,[status(thm)],[c32]) ).
cnf(c44,plain,
xor(X2,xor(truth,X3)) = xor(X2,xor(X3,truth)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
xor(X2,truth) = not(X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c46,plain,
xor(X2,xor(X3,truth)) = xor(X2,not(X3)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
xor(X2,xor(truth,X3)) = xor(X2,not(X3)),
inference(transitivity,[status(thm)],[c44,c46]) ).
cnf(c48,plain,
xor(not(X2),X3) = xor(X2,not(X3)),
inference(transitivity,[status(thm)],[c42,c47]) ).
cnf(c49,plain,
xor(X3,not(X2)) = xor(X2,not(X3)),
inference(transitivity,[status(thm)],[c40,c48]) ).
cnf(c50,plain,
xor(truth,not(X2)) = xor(X2,not(truth)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
xor(X2,not(truth)) = xor(truth,not(X2)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
and_star(X3,xor(X2,not(truth))) = and_star(X3,xor(truth,not(X2))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
xor(truth,and_star(X3,xor(X2,not(truth)))) = xor(truth,and_star(X3,xor(truth,not(X2)))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,axiom,
implies(X2,Y2) = xor(truth,and_star(X2,xor(truth,Y2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
cnf(c55,plain,
implies(X3,not(X2)) = xor(truth,and_star(X3,xor(truth,not(X2)))),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
xor(truth,and_star(X3,xor(truth,not(X2)))) = implies(X3,not(X2)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
xor(truth,and_star(X3,xor(X2,not(truth)))) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c53,c56]) ).
cnf(c58,plain,
not(and_star(X3,xor(X2,not(truth)))) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c38,c57]) ).
cnf(c59,plain,
not(and_star(X3,X2)) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c31,c58]) ).
cnf(c60,plain,
not(and_star(X2,X3)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
implies(X2,not(X3)) = not(and_star(X2,X3)),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,axiom,
and_star(X2,Y2) = and_star(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(c63,plain,
and_star(X3,X2) = and_star(X2,X3),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
and_star(X2,X3) = and_star(X3,X2),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
not(and_star(X2,X3)) = not(and_star(X3,X2)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
not(and_star(X2,X3)) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c65,c59]) ).
cnf(c67,plain,
implies(X2,not(X3)) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c61,c66]) ).
cnf(c68,plain,
implies(X3,not(X2)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
not(implies(X3,not(X2))) = not(implies(X2,not(X3))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
not(and_star(X2,X3)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c71,plain,
implies(X2,not(X3)) = not(and_star(X2,X3)),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
not(implies(X2,not(X3))) = not(not(and_star(X2,X3))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
not(not(and_star(X2,X3))) = and_star(X2,X3),
inference(substitution,[status(thm)],[c22]) ).
cnf(c74,plain,
and_star(X2,X3) = and_star(X3,X2),
inference(substitution,[status(thm)],[c62]) ).
cnf(c75,plain,
not(not(and_star(X2,X3))) = and_star(X3,X2),
inference(transitivity,[status(thm)],[c73,c74]) ).
cnf(c76,plain,
not(implies(X2,not(X3))) = and_star(X3,X2),
inference(transitivity,[status(thm)],[c72,c75]) ).
cnf(c77,plain,
not(implies(X3,not(X2))) = and_star(X3,X2),
inference(transitivity,[status(thm)],[c69,c76]) ).
cnf(c78,plain,
not(implies(X3,not(not(X2)))) = and_star(X3,not(X2)),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
not(implies(X3,X2)) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c28,c78]) ).
cnf(c80,plain,
not(implies(X2,X3)) = and_star(X2,not(X3)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
and_star(X2,not(X3)) = not(implies(X2,X3)),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
implies(not(implies(X4,X3)),and_star(X2,not(X3))) = implies(not(implies(X4,X3)),not(implies(X2,X3))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
implies(not(X3),not(X2)) = implies(X2,not(not(X3))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c84,plain,
implies(X2,not(not(X3))) = implies(X2,X3),
inference(congruence,[status(thm)],[c22]) ).
cnf(c85,plain,
implies(not(X3),not(X2)) = implies(X2,X3),
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
implies(not(implies(X4,X3)),not(implies(X2,X3))) = implies(implies(X2,X3),implies(X4,X3)),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c88,plain,
implies(X2,X3) = implies(X2,not(not(X3))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
implies(implies(X2,X3),implies(X4,X3)) = implies(implies(X2,not(not(X3))),implies(X4,X3)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
not(and_star(X2,not(X3))) = implies(X2,not(not(X3))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c91,plain,
implies(X2,not(not(X3))) = not(and_star(X2,not(X3))),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
implies(implies(X2,not(not(X3))),implies(X4,X3)) = implies(not(and_star(X2,not(X3))),implies(X4,X3)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
implies(X3,not(X2)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c94,plain,
implies(X2,implies(X4,not(X3))) = implies(X2,implies(X3,not(X4))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
not(and_star(X2,X3)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c96,plain,
implies(X2,not(X3)) = not(and_star(X2,X3)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
implies(X2,implies(X3,not(X4))) = implies(X2,not(and_star(X3,X4))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
not(and_star(X2,and_star(X3,X4))) = implies(X2,not(and_star(X3,X4))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c99,plain,
implies(X2,not(and_star(X3,X4))) = not(and_star(X2,and_star(X3,X4))),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,axiom,
and_star(and_star(X2,Y2),Z) = and_star(X2,and_star(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_associativity) ).
cnf(c101,plain,
and_star(and_star(X2,X3),X4) = and_star(X2,and_star(X3,X4)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
and_star(X2,and_star(X3,X4)) = and_star(and_star(X2,X3),X4),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
not(and_star(X2,and_star(X3,X4))) = not(and_star(and_star(X2,X3),X4)),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
not(and_star(and_star(X2,X3),X4)) = implies(and_star(X2,X3),not(X4)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c105,plain,
implies(X4,not(and_star(X2,X3))) = implies(and_star(X2,X3),not(X4)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c106,plain,
implies(and_star(X2,X3),not(X4)) = implies(X4,not(and_star(X2,X3))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
not(and_star(X2,X3)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c108,plain,
implies(X4,not(and_star(X2,X3))) = implies(X4,implies(X2,not(X3))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
implies(X3,not(X2)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c110,plain,
implies(X2,not(X3)) = implies(X3,not(X2)),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
implies(X4,implies(X2,not(X3))) = implies(X4,implies(X3,not(X2))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
implies(X4,not(and_star(X2,X3))) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c108,c111]) ).
cnf(c113,plain,
implies(and_star(X2,X3),not(X4)) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c106,c112]) ).
cnf(c114,plain,
not(and_star(and_star(X2,X3),X4)) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c104,c113]) ).
cnf(c115,plain,
not(and_star(X2,and_star(X3,X4))) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c103,c114]) ).
cnf(c116,plain,
implies(X2,not(and_star(X3,X4))) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c99,c115]) ).
cnf(c117,plain,
implies(X2,implies(X3,not(X4))) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c97,c116]) ).
cnf(c118,plain,
implies(X2,implies(X4,not(X3))) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c94,c117]) ).
cnf(c119,plain,
implies(not(X4),implies(X3,not(X2))) = implies(X3,implies(X2,not(not(X4)))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
implies(X2,not(not(X3))) = implies(X2,X3),
inference(congruence,[status(thm)],[c22]) ).
cnf(c121,plain,
implies(X3,implies(X2,not(not(X4)))) = implies(X3,implies(X2,X4)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
implies(not(X4),implies(X3,not(X2))) = implies(X3,implies(X2,X4)),
inference(transitivity,[status(thm)],[c119,c121]) ).
cnf(c123,plain,
implies(not(X3),implies(X2,not(X4))) = implies(X2,implies(X4,X3)),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
implies(X2,implies(X4,X3)) = implies(not(X3),implies(X2,not(X4))),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
implies(X4,implies(not(X3),not(X2))) = implies(not(X3),implies(X2,not(X4))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c126,plain,
implies(not(X3),implies(X2,not(X4))) = implies(X4,implies(not(X3),not(X2))),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
implies(X2,implies(X4,X3)) = implies(X4,implies(not(X3),not(X2))),
inference(transitivity,[status(thm)],[c124,c126]) ).
cnf(c128,plain,
implies(not(X2),implies(X4,X3)) = implies(X4,implies(not(X3),not(not(X2)))),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
implies(not(X3),not(not(X2))) = implies(not(X3),X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c130,plain,
implies(X4,implies(not(X3),not(not(X2)))) = implies(X4,implies(not(X3),X2)),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
implies(not(X2),implies(X4,X3)) = implies(X4,implies(not(X3),X2)),
inference(transitivity,[status(thm)],[c128,c130]) ).
cnf(c132,plain,
implies(not(and_star(X2,not(X3))),implies(X4,X3)) = implies(X4,implies(not(X3),and_star(X2,not(X3)))),
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c134,plain,
implies(implies(X3,X2),X2) = implies(implies(X3,X2),not(not(X2))),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
not(and_star(implies(X3,X2),not(X2))) = implies(implies(X3,X2),not(not(X2))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c136,plain,
implies(implies(X3,X2),not(not(X2))) = not(and_star(implies(X3,X2),not(X2))),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
and_star(not(X2),implies(X3,X2)) = and_star(implies(X3,X2),not(X2)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c138,plain,
and_star(implies(X3,X2),not(X2)) = and_star(not(X2),implies(X3,X2)),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c140,plain,
implies(X3,X2) = implies(X3,not(not(X2))),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
and_star(not(X2),implies(X3,X2)) = and_star(not(X2),implies(X3,not(not(X2)))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
implies(X3,not(not(X2))) = implies(not(X2),not(X3)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c143,plain,
and_star(not(X2),implies(X3,not(not(X2)))) = and_star(not(X2),implies(not(X2),not(X3))),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
implies(X2,X3) = implies(not(X3),not(X2)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c145,plain,
and_star(X2,implies(X2,X3)) = and_star(X2,implies(not(X3),not(X2))),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
not(and_star(not(X3),X2)) = implies(not(X3),not(X2)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c147,plain,
implies(not(X3),not(X2)) = not(and_star(not(X3),X2)),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
and_star(X2,implies(not(X3),not(X2))) = and_star(X2,not(and_star(not(X3),X2))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
not(X2) = xor(truth,X2),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c150,plain,
and_star(not(X3),X2) = and_star(xor(truth,X3),X2),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
not(and_star(not(X3),X2)) = not(and_star(xor(truth,X3),X2)),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
and_star(X2,not(and_star(not(X3),X2))) = and_star(X2,not(and_star(xor(truth,X3),X2))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
and_star(not(and_star(xor(truth,X2),X3)),X3) = and_star(X3,not(and_star(xor(truth,X2),X3))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c154,plain,
and_star(X3,not(and_star(xor(truth,X2),X3))) = and_star(not(and_star(xor(truth,X2),X3)),X3),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
not(and_star(xor(truth,X2),X3)) = xor(and_star(xor(truth,X2),X3),truth),
inference(substitution,[status(thm)],[c2]) ).
cnf(c156,plain,
and_star(not(and_star(xor(truth,X2),X3)),X3) = and_star(xor(and_star(xor(truth,X2),X3),truth),X3),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,axiom,
and_star(xor(and_star(xor(truth,X2),Y2),truth),Y2) = and_star(xor(and_star(xor(truth,Y2),X2),truth),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
cnf(c158,plain,
and_star(xor(and_star(xor(truth,X2),X3),truth),X3) = and_star(xor(and_star(xor(truth,X3),X2),truth),X2),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
not(and_star(xor(truth,X3),X2)) = xor(and_star(xor(truth,X3),X2),truth),
inference(substitution,[status(thm)],[c2]) ).
cnf(c160,plain,
xor(and_star(xor(truth,X3),X2),truth) = not(and_star(xor(truth,X3),X2)),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
and_star(xor(and_star(xor(truth,X3),X2),truth),X2) = and_star(not(and_star(xor(truth,X3),X2)),X2),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
and_star(not(and_star(xor(truth,X3),X2)),X2) = and_star(X2,not(and_star(xor(truth,X3),X2))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c163,plain,
and_star(xor(and_star(xor(truth,X3),X2),truth),X2) = and_star(X2,not(and_star(xor(truth,X3),X2))),
inference(transitivity,[status(thm)],[c161,c162]) ).
cnf(c164,plain,
and_star(xor(and_star(xor(truth,X2),X3),truth),X3) = and_star(X2,not(and_star(xor(truth,X3),X2))),
inference(transitivity,[status(thm)],[c158,c163]) ).
cnf(c165,plain,
and_star(not(and_star(xor(truth,X2),X3)),X3) = and_star(X2,not(and_star(xor(truth,X3),X2))),
inference(transitivity,[status(thm)],[c156,c164]) ).
cnf(c166,plain,
and_star(X3,not(and_star(xor(truth,X2),X3))) = and_star(X2,not(and_star(xor(truth,X3),X2))),
inference(transitivity,[status(thm)],[c154,c165]) ).
cnf(c167,plain,
and_star(X2,not(and_star(xor(truth,X3),X2))) = and_star(X3,not(and_star(xor(truth,X2),X3))),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
not(and_star(xor(truth,X2),X3)) = implies(xor(truth,X2),not(X3)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c169,plain,
and_star(X3,not(and_star(xor(truth,X2),X3))) = and_star(X3,implies(xor(truth,X2),not(X3))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
implies(xor(truth,X2),not(X3)) = implies(not(X2),not(X3)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c171,plain,
and_star(X3,implies(xor(truth,X2),not(X3))) = and_star(X3,implies(not(X2),not(X3))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
and_star(X3,not(and_star(xor(truth,X2),X3))) = and_star(X3,implies(not(X2),not(X3))),
inference(transitivity,[status(thm)],[c169,c171]) ).
cnf(c173,plain,
and_star(X2,not(and_star(xor(truth,X3),X2))) = and_star(X3,implies(not(X2),not(X3))),
inference(transitivity,[status(thm)],[c167,c172]) ).
cnf(c174,plain,
and_star(X2,not(and_star(not(X3),X2))) = and_star(X3,implies(not(X2),not(X3))),
inference(transitivity,[status(thm)],[c152,c173]) ).
cnf(c175,plain,
and_star(X2,implies(not(X3),not(X2))) = and_star(X3,implies(not(X2),not(X3))),
inference(transitivity,[status(thm)],[c148,c174]) ).
cnf(c176,plain,
and_star(X2,implies(X2,X3)) = and_star(X3,implies(not(X2),not(X3))),
inference(transitivity,[status(thm)],[c145,c175]) ).
cnf(c177,plain,
and_star(not(X3),implies(not(X3),X2)) = and_star(X2,implies(not(not(X3)),not(X2))),
inference(substitution,[status(thm)],[c176]) ).
cnf(c178,plain,
implies(not(not(X3)),not(X2)) = implies(X3,not(X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c179,plain,
and_star(X2,implies(not(not(X3)),not(X2))) = and_star(X2,implies(X3,not(X2))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
and_star(not(X3),implies(not(X3),X2)) = and_star(X2,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c177,c179]) ).
cnf(c181,plain,
and_star(not(X2),implies(not(X2),not(X3))) = and_star(not(X3),implies(X2,not(not(X3)))),
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
implies(X2,not(not(X3))) = implies(X2,X3),
inference(congruence,[status(thm)],[c22]) ).
cnf(c183,plain,
and_star(not(X3),implies(X2,not(not(X3)))) = and_star(not(X3),implies(X2,X3)),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
and_star(not(X2),implies(not(X2),not(X3))) = and_star(not(X3),implies(X2,X3)),
inference(transitivity,[status(thm)],[c181,c183]) ).
cnf(c185,plain,
and_star(not(X2),implies(X3,not(not(X2)))) = and_star(not(X3),implies(X2,X3)),
inference(transitivity,[status(thm)],[c143,c184]) ).
cnf(c186,plain,
and_star(not(X2),implies(X3,X2)) = and_star(not(X3),implies(X2,X3)),
inference(transitivity,[status(thm)],[c141,c185]) ).
cnf(c187,plain,
and_star(not(X3),implies(X2,X3)) = and_star(not(X2),implies(X3,X2)),
inference(substitution,[status(thm)],[c186]) ).
cnf(c188,plain,
and_star(not(X2),implies(X3,X2)) = and_star(not(X3),implies(X2,X3)),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
and_star(implies(X3,X2),not(X2)) = and_star(not(X3),implies(X2,X3)),
inference(transitivity,[status(thm)],[c138,c188]) ).
cnf(c190,plain,
not(and_star(implies(X3,X2),not(X2))) = not(and_star(not(X3),implies(X2,X3))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
not(and_star(not(X3),implies(X2,X3))) = implies(not(X3),not(implies(X2,X3))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c192,plain,
not(implies(X2,X3)) = and_star(X2,not(X3)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c193,plain,
implies(not(X3),not(implies(X2,X3))) = implies(not(X3),and_star(X2,not(X3))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
not(and_star(not(X3),implies(X2,X3))) = implies(not(X3),and_star(X2,not(X3))),
inference(transitivity,[status(thm)],[c191,c193]) ).
cnf(c195,plain,
not(and_star(implies(X3,X2),not(X2))) = implies(not(X3),and_star(X2,not(X3))),
inference(transitivity,[status(thm)],[c190,c194]) ).
cnf(c196,plain,
implies(implies(X3,X2),not(not(X2))) = implies(not(X3),and_star(X2,not(X3))),
inference(transitivity,[status(thm)],[c136,c195]) ).
cnf(c197,plain,
implies(implies(X3,X2),X2) = implies(not(X3),and_star(X2,not(X3))),
inference(transitivity,[status(thm)],[c134,c196]) ).
cnf(c198,plain,
implies(not(X3),and_star(X2,not(X3))) = implies(implies(X3,X2),X2),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
implies(X4,implies(not(X3),and_star(X2,not(X3)))) = implies(X4,implies(implies(X3,X2),X2)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
implies(not(X2),not(X3)) = implies(X3,X2),
inference(substitution,[status(thm)],[c85]) ).
cnf(c201,plain,
implies(X3,X2) = implies(not(X2),not(X3)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
implies(X3,implies(X4,X2)) = implies(X3,implies(not(X2),not(X4))),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
implies(X4,implies(X3,not(not(X2)))) = implies(X3,implies(not(X2),not(X4))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c204,plain,
implies(X3,implies(not(X2),not(X4))) = implies(X4,implies(X3,not(not(X2)))),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
implies(X3,not(not(X2))) = implies(X3,X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c206,plain,
implies(X4,implies(X3,not(not(X2)))) = implies(X4,implies(X3,X2)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
implies(X3,implies(not(X2),not(X4))) = implies(X4,implies(X3,X2)),
inference(transitivity,[status(thm)],[c204,c206]) ).
cnf(c208,plain,
implies(X3,implies(X4,X2)) = implies(X4,implies(X3,X2)),
inference(transitivity,[status(thm)],[c202,c207]) ).
cnf(c209,plain,
implies(X4,implies(implies(X3,X2),X2)) = implies(implies(X3,X2),implies(X4,X2)),
inference(substitution,[status(thm)],[c208]) ).
cnf(c210,plain,
implies(X4,implies(not(X3),and_star(X2,not(X3)))) = implies(implies(X3,X2),implies(X4,X2)),
inference(transitivity,[status(thm)],[c199,c209]) ).
cnf(c211,plain,
implies(not(and_star(X2,not(X3))),implies(X4,X3)) = implies(implies(X3,X2),implies(X4,X2)),
inference(transitivity,[status(thm)],[c132,c210]) ).
cnf(c212,plain,
implies(implies(X2,not(not(X3))),implies(X4,X3)) = implies(implies(X3,X2),implies(X4,X2)),
inference(transitivity,[status(thm)],[c92,c211]) ).
cnf(c213,plain,
implies(implies(X2,X3),implies(X4,X3)) = implies(implies(X3,X2),implies(X4,X2)),
inference(transitivity,[status(thm)],[c89,c212]) ).
cnf(c214,plain,
implies(not(implies(X4,X3)),not(implies(X2,X3))) = implies(implies(X3,X2),implies(X4,X2)),
inference(transitivity,[status(thm)],[c86,c213]) ).
cnf(c215,plain,
implies(not(implies(X4,X3)),and_star(X2,not(X3))) = implies(implies(X3,X2),implies(X4,X2)),
inference(transitivity,[status(thm)],[c82,c214]) ).
cnf(c216,plain,
implies(implies(X3,X2),implies(X4,X2)) = implies(not(implies(X4,X3)),and_star(X2,not(X3))),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
implies(not(not(implies(X4,X3))),implies(implies(X3,X2),implies(X4,X2))) = implies(not(not(implies(X4,X3))),implies(not(implies(X4,X3)),and_star(X2,not(X3)))),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
implies(not(X2),not(X3)) = implies(X3,X2),
inference(substitution,[status(thm)],[c85]) ).
cnf(c219,plain,
implies(X3,X2) = implies(not(X2),not(X3)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
implies(not(X3),implies(X3,X2)) = implies(not(X3),implies(not(X2),not(X3))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c222,plain,
implies(X2,X3) = implies(X2,not(not(X3))),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
implies(X3,implies(X2,X3)) = implies(X3,implies(X2,not(not(X3)))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
not(and_star(X2,not(X3))) = implies(X2,not(not(X3))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c225,plain,
implies(X2,not(not(X3))) = not(and_star(X2,not(X3))),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
implies(X3,implies(X2,not(not(X3)))) = implies(X3,not(and_star(X2,not(X3)))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
not(and_star(X3,and_star(X2,not(X3)))) = implies(X3,not(and_star(X2,not(X3)))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c228,plain,
implies(X3,not(and_star(X2,not(X3)))) = not(and_star(X3,and_star(X2,not(X3)))),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
and_star(not(X3),X2) = and_star(X2,not(X3)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c230,plain,
and_star(X2,not(X3)) = and_star(not(X3),X2),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
and_star(X3,and_star(X2,not(X3))) = and_star(X3,and_star(not(X3),X2)),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
and_star(and_star(X3,not(X3)),X2) = and_star(X3,and_star(not(X3),X2)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c233,plain,
and_star(X3,and_star(not(X3),X2)) = and_star(and_star(X3,not(X3)),X2),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
and_star(X2,not(X2)) = and_star(X2,xor(X2,truth)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c235,plain,
xor(truth,X2) = xor(X2,truth),
inference(substitution,[status(thm)],[c32]) ).
cnf(c236,plain,
xor(X2,truth) = xor(truth,X2),
inference(symmetry,[status(thm)],[c235]) ).
cnf(c237,plain,
and_star(X2,xor(X2,truth)) = and_star(X2,xor(truth,X2)),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
and_star(xor(truth,X2),X2) = and_star(X2,xor(truth,X2)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c239,plain,
and_star(X2,xor(truth,X2)) = and_star(xor(truth,X2),X2),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,axiom,
and_star(xor(truth,X2),X2) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c241,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c242,plain,
and_star(xor(truth,X2),X2) = not(truth),
inference(transitivity,[status(thm)],[c240,c241]) ).
cnf(c243,plain,
and_star(X2,xor(truth,X2)) = not(truth),
inference(transitivity,[status(thm)],[c239,c242]) ).
cnf(c244,plain,
and_star(X2,xor(X2,truth)) = not(truth),
inference(transitivity,[status(thm)],[c237,c243]) ).
cnf(c245,plain,
and_star(X2,not(X2)) = not(truth),
inference(transitivity,[status(thm)],[c234,c244]) ).
cnf(c246,plain,
and_star(and_star(X3,not(X3)),X2) = and_star(not(truth),X2),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
and_star(X2,not(truth)) = and_star(not(truth),X2),
inference(substitution,[status(thm)],[c62]) ).
cnf(c248,plain,
and_star(not(truth),X2) = and_star(X2,not(truth)),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
and_star(X2,not(truth)) = and_star(X2,falsehood),
inference(congruence,[status(thm)],[c12]) ).
cnf(c250,axiom,
and_star(X2,falsehood) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c251,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c252,plain,
and_star(X2,falsehood) = not(truth),
inference(transitivity,[status(thm)],[c250,c251]) ).
cnf(c253,plain,
and_star(X2,not(truth)) = not(truth),
inference(transitivity,[status(thm)],[c249,c252]) ).
cnf(c254,plain,
and_star(not(truth),X2) = not(truth),
inference(transitivity,[status(thm)],[c248,c253]) ).
cnf(c255,plain,
and_star(and_star(X3,not(X3)),X2) = not(truth),
inference(transitivity,[status(thm)],[c246,c254]) ).
cnf(c256,plain,
and_star(X3,and_star(not(X3),X2)) = not(truth),
inference(transitivity,[status(thm)],[c233,c255]) ).
cnf(c257,plain,
and_star(X3,and_star(X2,not(X3))) = not(truth),
inference(transitivity,[status(thm)],[c231,c256]) ).
cnf(c258,plain,
not(and_star(X3,and_star(X2,not(X3)))) = not(not(truth)),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
not(not(truth)) = truth,
inference(substitution,[status(thm)],[c22]) ).
cnf(c260,plain,
not(and_star(X3,and_star(X2,not(X3)))) = truth,
inference(transitivity,[status(thm)],[c258,c259]) ).
cnf(c261,plain,
implies(X3,not(and_star(X2,not(X3)))) = truth,
inference(transitivity,[status(thm)],[c228,c260]) ).
cnf(c262,plain,
implies(X3,implies(X2,not(not(X3)))) = truth,
inference(transitivity,[status(thm)],[c226,c261]) ).
cnf(c263,plain,
implies(X3,implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c223,c262]) ).
cnf(c264,plain,
implies(not(X3),implies(not(X2),not(X3))) = truth,
inference(substitution,[status(thm)],[c263]) ).
cnf(c265,plain,
implies(not(X3),implies(X3,X2)) = truth,
inference(transitivity,[status(thm)],[c220,c264]) ).
cnf(c266,plain,
implies(not(not(implies(X4,X3))),implies(not(implies(X4,X3)),and_star(X2,not(X3)))) = truth,
inference(substitution,[status(thm)],[c265]) ).
cnf(c267,plain,
implies(not(not(implies(X4,X3))),implies(implies(X3,X2),implies(X4,X2))) = truth,
inference(transitivity,[status(thm)],[c217,c266]) ).
cnf(c268,plain,
implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2))) = truth,
inference(transitivity,[status(thm)],[c25,c267]) ).
cnf(c269,plain,
implies(implies(x,y),implies(implies(y,z),implies(x,z))) = truth,
inference(substitution,[status(thm)],[c268]) ).
cnf(c270,plain,
$false,
inference(resolution,[status(thm)],[c1,c269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 15:24:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.95/0.80 Command-line arguments: --flatten --complete-subsets
% 1.95/0.80
% 1.95/0.80 % SZS status Unsatisfiable
% 1.95/0.80
% 2.74/0.82 % SZS output start CNFRefutation
% See solution above
% 3.43/0.93
% 3.43/0.93 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------