%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL160-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.66s 0.51s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 15
% Syntax : Number of clauses : 323 ( 323 unt; 0 nHn; 106 RR)
% Number of literals : 323 ( 322 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 346 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
and_star(xor(and_star(xor(truth,x),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
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(and_star(xor(truth,x),y),truth) = xor(truth,and_star(xor(truth,x),y)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
and_star(xor(and_star(xor(truth,x),y),truth),y) = and_star(xor(truth,and_star(xor(truth,x),y)),y),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
xor(truth,x) = xor(x,truth),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
and_star(xor(truth,x),y) = and_star(xor(x,truth),y),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
xor(truth,and_star(xor(truth,x),y)) = xor(truth,and_star(xor(x,truth),y)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
and_star(xor(truth,and_star(xor(truth,x),y)),y) = and_star(xor(truth,and_star(xor(x,truth),y)),y),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
and_star(X2,Y2) = and_star(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(c10,plain,
and_star(xor(truth,and_star(xor(x,truth),y)),y) = and_star(y,xor(truth,and_star(xor(x,truth),y))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
and_star(xor(x,truth),y) = and_star(y,xor(x,truth)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c12,plain,
xor(truth,and_star(xor(x,truth),y)) = xor(truth,and_star(y,xor(x,truth))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
and_star(y,xor(truth,and_star(xor(x,truth),y))) = and_star(y,xor(truth,and_star(y,xor(x,truth)))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
and_star(X2,Y2) = not(or(not(X2),not(Y2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_definition) ).
cnf(c15,plain,
and_star(X3,X2) = not(or(not(X3),not(X2))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,axiom,
and(X2,Y2) = not(or(not(X2),not(Y2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition) ).
cnf(c17,plain,
and(X3,X2) = not(or(not(X3),not(X2))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
not(or(not(X3),not(X2))) = and(X3,X2),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
and_star(X3,X2) = and(X3,X2),
inference(transitivity,[status(thm)],[c15,c18]) ).
cnf(c20,plain,
and_star(y,xor(truth,and_star(y,xor(x,truth)))) = and(y,xor(truth,and_star(y,xor(x,truth)))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
and_star(y,xor(x,truth)) = and(y,xor(x,truth)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c22,plain,
xor(truth,and_star(y,xor(x,truth))) = xor(truth,and(y,xor(x,truth))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
and(y,xor(truth,and_star(y,xor(x,truth)))) = and(y,xor(truth,and(y,xor(x,truth)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
xor(X2,Y2) = or(and(X2,not(Y2)),and(not(X2),Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition) ).
cnf(c25,plain,
xor(X2,truth) = or(and(X2,not(truth)),and(not(X2),truth)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c27,plain,
and(X2,not(truth)) = and(X2,falsehood),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
or(and(X2,not(truth)),and(not(X2),truth)) = or(and(X2,falsehood),and(not(X2),truth)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,axiom,
and(X2,Y2) = and(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutativity) ).
cnf(c30,plain,
and(falsehood,X2) = and(X2,falsehood),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
and(X2,falsehood) = and(falsehood,X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
and(falsehood,X2) = not(or(not(falsehood),not(X2))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c33,axiom,
implies(truth,X2) = X2,
file('/export/starexec/sandbox/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/sandbox/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)],[c26]) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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,c26]) ).
cnf(c113,plain,
not(or(not(falsehood),not(X2))) = falsehood,
inference(transitivity,[status(thm)],[c77,c112]) ).
cnf(c114,plain,
and(falsehood,X2) = falsehood,
inference(transitivity,[status(thm)],[c32,c113]) ).
cnf(c115,plain,
and(X2,falsehood) = falsehood,
inference(transitivity,[status(thm)],[c31,c114]) ).
cnf(c116,plain,
or(and(X2,falsehood),and(not(X2),truth)) = or(falsehood,and(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(not(X2),truth)) = and(not(X2),truth),
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c26]) ).
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(truth,X2) = not(or(not(truth),not(X2))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c125,plain,
not(or(not(truth),not(X2))) = and(truth,X2),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
and(truth,X2) = and(X2,truth),
inference(substitution,[status(thm)],[c29]) ).
cnf(c127,plain,
not(or(not(truth),not(X2))) = and(X2,truth),
inference(transitivity,[status(thm)],[c125,c126]) ).
cnf(c128,plain,
not(or(falsehood,not(X2))) = and(X2,truth),
inference(transitivity,[status(thm)],[c123,c127]) ).
cnf(c129,plain,
and(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(X2,truth) = not(not(X2)),
inference(transitivity,[status(thm)],[c129,c131]) ).
cnf(c133,plain,
and(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)],[c26]) ).
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(not(X2),truth) = not(X2),
inference(transitivity,[status(thm)],[c133,c161]) ).
cnf(c163,plain,
or(falsehood,and(not(X2),truth)) = not(X2),
inference(transitivity,[status(thm)],[c120,c162]) ).
cnf(c164,plain,
or(and(X2,falsehood),and(not(X2),truth)) = not(X2),
inference(transitivity,[status(thm)],[c116,c163]) ).
cnf(c165,plain,
or(and(X2,not(truth)),and(not(X2),truth)) = not(X2),
inference(transitivity,[status(thm)],[c28,c164]) ).
cnf(c166,plain,
xor(X2,truth) = not(X2),
inference(transitivity,[status(thm)],[c25,c165]) ).
cnf(c167,plain,
xor(x,truth) = not(x),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
and(y,xor(x,truth)) = and(y,not(x)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
xor(truth,and(y,xor(x,truth))) = xor(truth,and(y,not(x))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
and(y,xor(truth,and(y,xor(x,truth)))) = and(y,xor(truth,and(y,not(x)))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
xor(X2,truth) = xor(truth,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c172,plain,
xor(truth,X2) = xor(X2,truth),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
xor(truth,X2) = not(X2),
inference(transitivity,[status(thm)],[c172,c166]) ).
cnf(c174,plain,
xor(truth,and(y,not(x))) = not(and(y,not(x))),
inference(substitution,[status(thm)],[c173]) ).
cnf(c175,plain,
and(y,xor(truth,and(y,not(x)))) = and(y,not(and(y,not(x)))),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
and(X2,X3) = and(X3,X2),
inference(substitution,[status(thm)],[c29]) ).
cnf(c177,plain,
and(X3,X2) = and(X2,X3),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
not(and(X3,X2)) = not(and(X2,X3)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
or(falsehood,not(and(X2,X3))) = not(and(X2,X3)),
inference(substitution,[status(thm)],[c119]) ).
cnf(c180,plain,
not(and(X2,X3)) = or(falsehood,not(and(X2,X3))),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
and(X3,X2) = and(X2,X3),
inference(substitution,[status(thm)],[c29]) ).
cnf(c182,plain,
and(X3,X2) = and(X2,X3),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
not(and(X3,X2)) = not(and(X2,X3)),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
or(X4,not(and(X3,X2))) = or(X4,not(and(X2,X3))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c186,plain,
implies(X3,X2) = implies(not(not(X3)),X2),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
or(not(X3),X2) = implies(not(not(X3)),X2),
inference(substitution,[status(thm)],[c45]) ).
cnf(c188,plain,
implies(not(not(X3)),X2) = or(not(X3),X2),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
or(not(X3),X2) = or(X2,not(X3)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c190,plain,
implies(not(not(X3)),X2) = or(X2,not(X3)),
inference(transitivity,[status(thm)],[c188,c189]) ).
cnf(c191,plain,
implies(X3,X2) = or(X2,not(X3)),
inference(transitivity,[status(thm)],[c186,c190]) ).
cnf(c192,plain,
implies(and(X2,X3),X4) = or(X4,not(and(X2,X3))),
inference(substitution,[status(thm)],[c191]) ).
cnf(c193,plain,
or(X4,not(and(X2,X3))) = implies(and(X2,X3),X4),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
and(X2,X3) = not(or(not(X2),not(X3))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c195,plain,
implies(and(X2,X3),X4) = implies(not(or(not(X2),not(X3))),X4),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
or(or(not(X2),not(X3)),X4) = implies(not(or(not(X2),not(X3))),X4),
inference(substitution,[status(thm)],[c45]) ).
cnf(c197,plain,
implies(not(or(not(X2),not(X3))),X4) = or(or(not(X2),not(X3)),X4),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,axiom,
or(or(X2,Y2),Z2) = or(X2,or(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_associativity) ).
cnf(c199,plain,
or(or(not(X2),not(X3)),X4) = or(not(X2),or(not(X3),X4)),
inference(substitution,[status(thm)],[c198]) ).
cnf(c200,plain,
or(or(X4,X2),X3) = or(X3,or(X4,X2)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c201,plain,
or(X3,or(X4,X2)) = or(or(X4,X2),X3),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
or(or(X4,X2),X3) = or(X4,or(X2,X3)),
inference(substitution,[status(thm)],[c198]) ).
cnf(c203,plain,
or(X2,X3) = or(X3,X2),
inference(substitution,[status(thm)],[c36]) ).
cnf(c204,plain,
or(X4,or(X2,X3)) = or(X4,or(X3,X2)),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
or(or(X4,X2),X3) = or(X4,or(X3,X2)),
inference(transitivity,[status(thm)],[c202,c204]) ).
cnf(c206,plain,
or(X3,or(X4,X2)) = or(X4,or(X3,X2)),
inference(transitivity,[status(thm)],[c201,c205]) ).
cnf(c207,plain,
or(not(X3),or(not(X2),X4)) = or(not(X2),or(not(X3),X4)),
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
or(not(X2),or(not(X3),X4)) = or(not(X3),or(not(X2),X4)),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
or(not(X2),X3) = or(X3,not(X2)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c210,plain,
or(not(X3),or(not(X2),X4)) = or(not(X3),or(X4,not(X2))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
or(X4,or(not(X3),not(X2))) = or(not(X3),or(X4,not(X2))),
inference(substitution,[status(thm)],[c206]) ).
cnf(c212,plain,
or(not(X3),or(X4,not(X2))) = or(X4,or(not(X3),not(X2))),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
or(not(X3),or(not(X2),X4)) = or(X4,or(not(X3),not(X2))),
inference(transitivity,[status(thm)],[c210,c212]) ).
cnf(c214,plain,
or(not(X2),or(not(X3),X4)) = or(X4,or(not(X3),not(X2))),
inference(transitivity,[status(thm)],[c208,c213]) ).
cnf(c215,plain,
or(or(not(X2),not(X3)),X4) = or(X4,or(not(X3),not(X2))),
inference(transitivity,[status(thm)],[c199,c214]) ).
cnf(c216,plain,
implies(not(or(not(X2),not(X3))),X4) = or(X4,or(not(X3),not(X2))),
inference(transitivity,[status(thm)],[c197,c215]) ).
cnf(c217,plain,
implies(and(X2,X3),X4) = or(X4,or(not(X3),not(X2))),
inference(transitivity,[status(thm)],[c195,c216]) ).
cnf(c218,plain,
or(X4,not(and(X2,X3))) = or(X4,or(not(X3),not(X2))),
inference(transitivity,[status(thm)],[c193,c217]) ).
cnf(c219,plain,
or(X4,not(and(X3,X2))) = or(X4,or(not(X3),not(X2))),
inference(transitivity,[status(thm)],[c184,c218]) ).
cnf(c220,plain,
or(falsehood,not(and(X2,X3))) = or(falsehood,or(not(X2),not(X3))),
inference(substitution,[status(thm)],[c219]) ).
cnf(c221,plain,
or(falsehood,or(not(X2),not(X3))) = or(not(X2),not(X3)),
inference(substitution,[status(thm)],[c119]) ).
cnf(c222,plain,
or(not(X2),not(X3)) = or(not(X3),not(X2)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c223,plain,
or(falsehood,or(not(X2),not(X3))) = or(not(X3),not(X2)),
inference(transitivity,[status(thm)],[c221,c222]) ).
cnf(c224,plain,
or(falsehood,not(and(X2,X3))) = or(not(X3),not(X2)),
inference(transitivity,[status(thm)],[c220,c223]) ).
cnf(c225,plain,
not(and(X2,X3)) = or(not(X3),not(X2)),
inference(transitivity,[status(thm)],[c180,c224]) ).
cnf(c226,plain,
not(and(X3,X2)) = or(not(X3),not(X2)),
inference(transitivity,[status(thm)],[c178,c225]) ).
cnf(c227,plain,
not(and(y,not(x))) = or(not(y),not(not(x))),
inference(substitution,[status(thm)],[c226]) ).
cnf(c228,plain,
and(y,not(and(y,not(x)))) = and(y,or(not(y),not(not(x)))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
not(not(x)) = x,
inference(substitution,[status(thm)],[c160]) ).
cnf(c230,plain,
or(not(y),not(not(x))) = or(not(y),x),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
and(y,or(not(y),not(not(x)))) = and(y,or(not(y),x)),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
or(not(y),x) = or(x,not(y)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c233,plain,
and(y,or(not(y),x)) = and(y,or(x,not(y))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
and(X2,or(X3,not(X2))) = not(or(not(X2),not(or(X3,not(X2))))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c235,plain,
implies(or(X3,not(X2)),not(X2)) = or(not(X2),not(or(X3,not(X2)))),
inference(substitution,[status(thm)],[c191]) ).
cnf(c236,plain,
or(not(X2),not(or(X3,not(X2)))) = implies(or(X3,not(X2)),not(X2)),
inference(symmetry,[status(thm)],[c235]) ).
cnf(c237,plain,
or(X3,not(X2)) = implies(not(X3),not(X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c238,plain,
implies(or(X3,not(X2)),not(X2)) = implies(implies(not(X3),not(X2)),not(X2)),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
implies(implies(not(X2),X3),X3) = implies(implies(X3,not(X2)),not(X2)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c240,plain,
implies(implies(X3,not(X2)),not(X2)) = implies(implies(not(X2),X3),X3),
inference(symmetry,[status(thm)],[c239]) ).
cnf(c241,plain,
or(X2,X3) = implies(not(X2),X3),
inference(substitution,[status(thm)],[c45]) ).
cnf(c242,plain,
implies(not(X2),X3) = or(X2,X3),
inference(symmetry,[status(thm)],[c241]) ).
cnf(c243,plain,
implies(implies(not(X2),X3),X3) = implies(or(X2,X3),X3),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
or(X2,X3) = or(X3,X2),
inference(substitution,[status(thm)],[c36]) ).
cnf(c245,plain,
implies(or(X2,X3),X3) = implies(or(X3,X2),X3),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
implies(implies(not(X2),X3),X3) = implies(or(X3,X2),X3),
inference(transitivity,[status(thm)],[c243,c245]) ).
cnf(c247,plain,
implies(implies(X3,not(X2)),not(X2)) = implies(or(X3,X2),X3),
inference(transitivity,[status(thm)],[c240,c246]) ).
cnf(c248,plain,
implies(implies(not(X3),not(X2)),not(X2)) = implies(or(not(X3),X2),not(X3)),
inference(substitution,[status(thm)],[c247]) ).
cnf(c249,plain,
implies(or(not(X3),X2),not(X3)) = or(not(X3),not(or(not(X3),X2))),
inference(substitution,[status(thm)],[c191]) ).
cnf(c250,plain,
implies(implies(not(X3),not(X2)),not(X2)) = or(not(X3),not(or(not(X3),X2))),
inference(transitivity,[status(thm)],[c248,c249]) ).
cnf(c251,plain,
implies(or(X3,not(X2)),not(X2)) = or(not(X3),not(or(not(X3),X2))),
inference(transitivity,[status(thm)],[c238,c250]) ).
cnf(c252,plain,
or(not(X2),not(or(X3,not(X2)))) = or(not(X3),not(or(not(X3),X2))),
inference(transitivity,[status(thm)],[c236,c251]) ).
cnf(c253,plain,
not(or(not(X2),not(or(X3,not(X2))))) = not(or(not(X3),not(or(not(X3),X2)))),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
and(X3,or(not(X3),X2)) = not(or(not(X3),not(or(not(X3),X2)))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c255,plain,
not(or(not(X3),not(or(not(X3),X2)))) = and(X3,or(not(X3),X2)),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
or(not(X3),X2) = or(X2,not(X3)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c257,plain,
and(X3,or(not(X3),X2)) = and(X3,or(X2,not(X3))),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
not(or(not(X3),not(or(not(X3),X2)))) = and(X3,or(X2,not(X3))),
inference(transitivity,[status(thm)],[c255,c257]) ).
cnf(c259,plain,
not(or(not(X2),not(or(X3,not(X2))))) = and(X3,or(X2,not(X3))),
inference(transitivity,[status(thm)],[c253,c258]) ).
cnf(c260,plain,
and(X2,or(X3,not(X2))) = and(X3,or(X2,not(X3))),
inference(transitivity,[status(thm)],[c234,c259]) ).
cnf(c261,plain,
and(x,or(y,not(x))) = and(y,or(x,not(y))),
inference(substitution,[status(thm)],[c260]) ).
cnf(c262,plain,
and(y,or(x,not(y))) = and(x,or(y,not(x))),
inference(symmetry,[status(thm)],[c261]) ).
cnf(c263,plain,
or(not(x),y) = or(y,not(x)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c264,plain,
or(y,not(x)) = or(not(x),y),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
and(x,or(y,not(x))) = and(x,or(not(x),y)),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
not(not(y)) = y,
inference(substitution,[status(thm)],[c160]) ).
cnf(c267,plain,
y = not(not(y)),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
or(not(x),y) = or(not(x),not(not(y))),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
and(x,or(not(x),y)) = and(x,or(not(x),not(not(y)))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
not(and(x,not(y))) = or(not(x),not(not(y))),
inference(substitution,[status(thm)],[c226]) ).
cnf(c271,plain,
or(not(x),not(not(y))) = not(and(x,not(y))),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
and(x,or(not(x),not(not(y)))) = and(x,not(and(x,not(y)))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
xor(truth,and(x,not(y))) = not(and(x,not(y))),
inference(substitution,[status(thm)],[c173]) ).
cnf(c274,plain,
not(and(x,not(y))) = xor(truth,and(x,not(y))),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
and(x,not(and(x,not(y)))) = and(x,xor(truth,and(x,not(y)))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
xor(y,truth) = not(y),
inference(substitution,[status(thm)],[c166]) ).
cnf(c277,plain,
not(y) = xor(y,truth),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
and(x,not(y)) = and(x,xor(y,truth)),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
xor(truth,and(x,not(y))) = xor(truth,and(x,xor(y,truth))),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
and(x,xor(truth,and(x,not(y)))) = and(x,xor(truth,and(x,xor(y,truth)))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
and_star(x,xor(y,truth)) = and(x,xor(y,truth)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c282,plain,
and(x,xor(y,truth)) = and_star(x,xor(y,truth)),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
xor(truth,and(x,xor(y,truth))) = xor(truth,and_star(x,xor(y,truth))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
and(x,xor(truth,and(x,xor(y,truth)))) = and(x,xor(truth,and_star(x,xor(y,truth)))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
and_star(x,xor(truth,and_star(x,xor(y,truth)))) = and(x,xor(truth,and_star(x,xor(y,truth)))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c286,plain,
and(x,xor(truth,and_star(x,xor(y,truth)))) = and_star(x,xor(truth,and_star(x,xor(y,truth)))),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
and_star(xor(y,truth),x) = and_star(x,xor(y,truth)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c288,plain,
and_star(x,xor(y,truth)) = and_star(xor(y,truth),x),
inference(symmetry,[status(thm)],[c287]) ).
cnf(c289,plain,
xor(truth,and_star(x,xor(y,truth))) = xor(truth,and_star(xor(y,truth),x)),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
and_star(x,xor(truth,and_star(x,xor(y,truth)))) = and_star(x,xor(truth,and_star(xor(y,truth),x))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
and_star(xor(truth,and_star(xor(y,truth),x)),x) = and_star(x,xor(truth,and_star(xor(y,truth),x))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c292,plain,
and_star(x,xor(truth,and_star(xor(y,truth),x))) = and_star(xor(truth,and_star(xor(y,truth),x)),x),
inference(symmetry,[status(thm)],[c291]) ).
cnf(c293,plain,
xor(truth,y) = xor(y,truth),
inference(substitution,[status(thm)],[c2]) ).
cnf(c294,plain,
xor(y,truth) = xor(truth,y),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
and_star(xor(y,truth),x) = and_star(xor(truth,y),x),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
xor(truth,and_star(xor(y,truth),x)) = xor(truth,and_star(xor(truth,y),x)),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
and_star(xor(truth,and_star(xor(y,truth),x)),x) = and_star(xor(truth,and_star(xor(truth,y),x)),x),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
xor(and_star(xor(truth,y),x),truth) = xor(truth,and_star(xor(truth,y),x)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c299,plain,
xor(truth,and_star(xor(truth,y),x)) = xor(and_star(xor(truth,y),x),truth),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
and_star(xor(truth,and_star(xor(truth,y),x)),x) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
and_star(xor(truth,and_star(xor(y,truth),x)),x) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c297,c300]) ).
cnf(c302,plain,
and_star(x,xor(truth,and_star(xor(y,truth),x))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c292,c301]) ).
cnf(c303,plain,
and_star(x,xor(truth,and_star(x,xor(y,truth)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c290,c302]) ).
cnf(c304,plain,
and(x,xor(truth,and_star(x,xor(y,truth)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c286,c303]) ).
cnf(c305,plain,
and(x,xor(truth,and(x,xor(y,truth)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c284,c304]) ).
cnf(c306,plain,
and(x,xor(truth,and(x,not(y)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c280,c305]) ).
cnf(c307,plain,
and(x,not(and(x,not(y)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c275,c306]) ).
cnf(c308,plain,
and(x,or(not(x),not(not(y)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c272,c307]) ).
cnf(c309,plain,
and(x,or(not(x),y)) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c269,c308]) ).
cnf(c310,plain,
and(x,or(y,not(x))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c265,c309]) ).
cnf(c311,plain,
and(y,or(x,not(y))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c262,c310]) ).
cnf(c312,plain,
and(y,or(not(y),x)) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c233,c311]) ).
cnf(c313,plain,
and(y,or(not(y),not(not(x)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c231,c312]) ).
cnf(c314,plain,
and(y,not(and(y,not(x)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c228,c313]) ).
cnf(c315,plain,
and(y,xor(truth,and(y,not(x)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c175,c314]) ).
cnf(c316,plain,
and(y,xor(truth,and(y,xor(x,truth)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c170,c315]) ).
cnf(c317,plain,
and(y,xor(truth,and_star(y,xor(x,truth)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c23,c316]) ).
cnf(c318,plain,
and_star(y,xor(truth,and_star(y,xor(x,truth)))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c20,c317]) ).
cnf(c319,plain,
and_star(y,xor(truth,and_star(xor(x,truth),y))) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c13,c318]) ).
cnf(c320,plain,
and_star(xor(truth,and_star(xor(x,truth),y)),y) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c10,c319]) ).
cnf(c321,plain,
and_star(xor(truth,and_star(xor(truth,x),y)),y) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c8,c320]) ).
cnf(c322,plain,
and_star(xor(and_star(xor(truth,x),y),truth),y) = and_star(xor(and_star(xor(truth,y),x),truth),x),
inference(transitivity,[status(thm)],[c4,c321]) ).
cnf(c323,plain,
$false,
inference(resolution,[status(thm)],[c1,c322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL160-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.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 15:24:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.66/0.51 Command-line arguments: --no-flatten-goal
% 0.66/0.51
% 0.66/0.51 % SZS status Unsatisfiable
% 0.66/0.51
% 0.66/0.53 % SZS output start CNFRefutation
% See solution above
% 1.66/0.66
% 1.66/0.66 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------