%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL109-6 : 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 11:49:03 AM UTC 2026
% Result : Unsatisfiable 3.83s 0.98s
% Output : CNFRefutation 5.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 14
% Syntax : Number of clauses : 371 ( 371 unt; 0 nHn; 39 RR)
% Number of literals : 371 ( 370 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 637 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(c2,axiom,
xor(X2,falsehood) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = xor(X2,falsehood),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
and_star(X3,X2) = and_star(X3,xor(X2,falsehood)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
not(and_star(X3,X2)) = not(and_star(X3,xor(X2,falsehood))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c7,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
xor(X2,falsehood) = xor(X2,not(truth)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
and_star(X3,xor(X2,falsehood)) = and_star(X3,xor(X2,not(truth))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
not(and_star(X3,xor(X2,falsehood))) = not(and_star(X3,xor(X2,not(truth)))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
xor(X,Y) = xor(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(c12,plain,
xor(X2,truth) = xor(truth,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
xor(truth,X2) = xor(X2,truth),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
not(X2) = xor(X2,truth),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
xor(X2,truth) = not(X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
xor(truth,X2) = not(X2),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
xor(truth,and_star(X3,xor(X2,not(truth)))) = not(and_star(X3,xor(X2,not(truth)))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
not(and_star(X3,xor(X2,not(truth)))) = xor(truth,and_star(X3,xor(X2,not(truth)))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
xor(not(X2),X3) = xor(X3,not(X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c20,plain,
xor(X3,not(X2)) = xor(not(X2),X3),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
xor(X2,xor(truth,Y2)) = xor(xor(X2,truth),Y2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
cnf(c22,plain,
xor(X3,xor(truth,X2)) = xor(xor(X3,truth),X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
xor(X2,truth) = not(X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c24,plain,
xor(xor(X3,truth),X2) = xor(not(X3),X2),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
xor(X3,xor(truth,X2)) = xor(not(X3),X2),
inference(transitivity,[status(thm)],[c22,c24]) ).
cnf(c26,plain,
xor(X2,xor(truth,X3)) = xor(not(X2),X3),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
xor(not(X2),X3) = xor(X2,xor(truth,X3)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
xor(truth,X2) = xor(X2,truth),
inference(substitution,[status(thm)],[c11]) ).
cnf(c29,plain,
xor(X2,xor(truth,X3)) = xor(X2,xor(X3,truth)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
xor(X2,truth) = not(X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c31,plain,
xor(X2,xor(X3,truth)) = xor(X2,not(X3)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
xor(X2,xor(truth,X3)) = xor(X2,not(X3)),
inference(transitivity,[status(thm)],[c29,c31]) ).
cnf(c33,plain,
xor(not(X2),X3) = xor(X2,not(X3)),
inference(transitivity,[status(thm)],[c27,c32]) ).
cnf(c34,plain,
xor(X3,not(X2)) = xor(X2,not(X3)),
inference(transitivity,[status(thm)],[c20,c33]) ).
cnf(c35,plain,
xor(truth,not(X2)) = xor(X2,not(truth)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
xor(X2,not(truth)) = xor(truth,not(X2)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
and_star(X3,xor(X2,not(truth))) = and_star(X3,xor(truth,not(X2))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
xor(truth,and_star(X3,xor(X2,not(truth)))) = xor(truth,and_star(X3,xor(truth,not(X2)))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
implies(X2,Y2) = xor(truth,and_star(X2,xor(truth,Y2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
cnf(c40,plain,
implies(X3,not(X2)) = xor(truth,and_star(X3,xor(truth,not(X2)))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
xor(truth,and_star(X3,xor(truth,not(X2)))) = implies(X3,not(X2)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
xor(truth,and_star(X3,xor(X2,not(truth)))) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c38,c41]) ).
cnf(c43,plain,
not(and_star(X3,xor(X2,not(truth)))) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c18,c42]) ).
cnf(c44,plain,
not(and_star(X3,xor(X2,falsehood))) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c10,c43]) ).
cnf(c45,plain,
not(and_star(X3,X2)) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c5,c44]) ).
cnf(c46,plain,
not(and_star(X2,X3)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
implies(X2,not(X3)) = not(and_star(X2,X3)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,axiom,
and_star(X2,Y2) = and_star(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(c49,plain,
and_star(X3,X2) = and_star(X2,X3),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
and_star(X2,X3) = and_star(X3,X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
not(and_star(X2,X3)) = not(and_star(X3,X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
not(and_star(X2,X3)) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c51,c45]) ).
cnf(c53,plain,
implies(X2,not(X3)) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c47,c52]) ).
cnf(c54,plain,
implies(not(X3),not(X2)) = implies(X2,not(not(X3))),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
not(not(X2)) = xor(not(X2),truth),
inference(substitution,[status(thm)],[c14]) ).
cnf(c56,plain,
xor(X2,xor(truth,truth)) = xor(not(X2),truth),
inference(substitution,[status(thm)],[c25]) ).
cnf(c57,plain,
xor(not(X2),truth) = xor(X2,xor(truth,truth)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,axiom,
xor(X2,X2) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
cnf(c59,plain,
xor(truth,truth) = falsehood,
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
xor(X2,xor(truth,truth)) = xor(X2,falsehood),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
xor(X2,xor(truth,truth)) = X2,
inference(transitivity,[status(thm)],[c60,c2]) ).
cnf(c62,plain,
xor(not(X2),truth) = X2,
inference(transitivity,[status(thm)],[c57,c61]) ).
cnf(c63,plain,
not(not(X2)) = X2,
inference(transitivity,[status(thm)],[c55,c62]) ).
cnf(c64,plain,
implies(X2,not(not(X3))) = implies(X2,X3),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
implies(not(X3),not(X2)) = implies(X2,X3),
inference(transitivity,[status(thm)],[c54,c64]) ).
cnf(c66,plain,
implies(not(implies(b,a)),not(implies(implies(a,b),implies(b,a)))) = implies(implies(implies(a,b),implies(b,a)),implies(b,a)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(not(implies(b,a)),not(implies(implies(a,b),implies(b,a)))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c69,plain,
implies(X3,X2) = implies(X3,not(not(X2))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
not(implies(X3,X2)) = not(implies(X3,not(not(X2)))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
implies(X3,not(X2)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c72,plain,
not(implies(X3,not(X2))) = not(implies(X2,not(X3))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
not(and_star(X2,X3)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c74,plain,
implies(X2,not(X3)) = not(and_star(X2,X3)),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
not(implies(X2,not(X3))) = not(not(and_star(X2,X3))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
not(not(and_star(X2,X3))) = and_star(X2,X3),
inference(substitution,[status(thm)],[c63]) ).
cnf(c77,plain,
and_star(X2,X3) = and_star(X3,X2),
inference(substitution,[status(thm)],[c48]) ).
cnf(c78,plain,
not(not(and_star(X2,X3))) = and_star(X3,X2),
inference(transitivity,[status(thm)],[c76,c77]) ).
cnf(c79,plain,
not(implies(X2,not(X3))) = and_star(X3,X2),
inference(transitivity,[status(thm)],[c75,c78]) ).
cnf(c80,plain,
not(implies(X3,not(X2))) = and_star(X3,X2),
inference(transitivity,[status(thm)],[c72,c79]) ).
cnf(c81,plain,
not(implies(X3,not(not(X2)))) = and_star(X3,not(X2)),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
not(implies(X3,X2)) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c70,c81]) ).
cnf(c83,plain,
not(implies(b,a)) = and_star(b,not(a)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
implies(not(implies(b,a)),not(implies(implies(a,b),implies(b,a)))) = implies(and_star(b,not(a)),not(implies(implies(a,b),implies(b,a)))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
not(implies(implies(a,b),implies(b,a))) = and_star(implies(a,b),not(implies(b,a))),
inference(substitution,[status(thm)],[c82]) ).
cnf(c86,plain,
implies(and_star(b,not(a)),not(implies(implies(a,b),implies(b,a)))) = implies(and_star(b,not(a)),and_star(implies(a,b),not(implies(b,a)))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
not(implies(b,a)) = and_star(b,not(a)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c88,plain,
and_star(implies(a,b),not(implies(b,a))) = and_star(implies(a,b),and_star(b,not(a))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
implies(and_star(b,not(a)),and_star(implies(a,b),not(implies(b,a)))) = implies(and_star(b,not(a)),and_star(implies(a,b),and_star(b,not(a)))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
and_star(and_star(X3,X4),X2) = and_star(X2,and_star(X3,X4)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c91,plain,
and_star(X3,and_star(X4,X2)) = and_star(and_star(X4,X2),X3),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,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(c93,plain,
and_star(and_star(X4,X2),X3) = and_star(X4,and_star(X2,X3)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
and_star(X2,X3) = and_star(X3,X2),
inference(substitution,[status(thm)],[c48]) ).
cnf(c95,plain,
and_star(X4,and_star(X2,X3)) = and_star(X4,and_star(X3,X2)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
and_star(and_star(X4,X2),X3) = and_star(X4,and_star(X3,X2)),
inference(transitivity,[status(thm)],[c93,c95]) ).
cnf(c97,plain,
and_star(X3,and_star(X4,X2)) = and_star(X4,and_star(X3,X2)),
inference(transitivity,[status(thm)],[c91,c96]) ).
cnf(c98,plain,
and_star(b,and_star(implies(a,b),not(a))) = and_star(implies(a,b),and_star(b,not(a))),
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
and_star(implies(a,b),and_star(b,not(a))) = and_star(b,and_star(implies(a,b),not(a))),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
implies(and_star(b,not(a)),and_star(implies(a,b),and_star(b,not(a)))) = implies(and_star(b,not(a)),and_star(b,and_star(implies(a,b),not(a)))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
and_star(implies(a,b),not(a)) = and_star(not(a),implies(a,b)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c102,plain,
and_star(b,and_star(implies(a,b),not(a))) = and_star(b,and_star(not(a),implies(a,b))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
implies(and_star(b,not(a)),and_star(b,and_star(implies(a,b),not(a)))) = implies(and_star(b,not(a)),and_star(b,and_star(not(a),implies(a,b)))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
and_star(X3,X2) = not(implies(X3,not(X2))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c105,plain,
implies(and_star(X4,X3),X2) = implies(not(implies(X4,not(X3))),X2),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c107,plain,
implies(not(X2),X3) = implies(not(X2),not(not(X3))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
implies(not(X2),not(not(X3))) = implies(not(X3),X2),
inference(substitution,[status(thm)],[c65]) ).
cnf(c109,plain,
implies(not(X2),X3) = implies(not(X3),X2),
inference(transitivity,[status(thm)],[c107,c108]) ).
cnf(c110,plain,
implies(not(implies(X4,not(X3))),X2) = implies(not(X2),implies(X4,not(X3))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
implies(X3,not(X2)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c112,plain,
implies(X2,implies(X4,not(X3))) = implies(X2,implies(X3,not(X4))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
not(and_star(X2,X3)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c114,plain,
implies(X2,not(X3)) = not(and_star(X2,X3)),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
implies(X2,implies(X3,not(X4))) = implies(X2,not(and_star(X3,X4))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
not(and_star(X2,and_star(X3,X4))) = implies(X2,not(and_star(X3,X4))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c117,plain,
implies(X2,not(and_star(X3,X4))) = not(and_star(X2,and_star(X3,X4))),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
and_star(and_star(X2,X3),X4) = and_star(X2,and_star(X3,X4)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c119,plain,
and_star(X2,and_star(X3,X4)) = and_star(and_star(X2,X3),X4),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
not(and_star(X2,and_star(X3,X4))) = not(and_star(and_star(X2,X3),X4)),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
not(and_star(and_star(X2,X3),X4)) = implies(and_star(X2,X3),not(X4)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c122,plain,
implies(X4,not(and_star(X2,X3))) = implies(and_star(X2,X3),not(X4)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c123,plain,
implies(and_star(X2,X3),not(X4)) = implies(X4,not(and_star(X2,X3))),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
not(and_star(X2,X3)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c125,plain,
implies(X4,not(and_star(X2,X3))) = implies(X4,implies(X2,not(X3))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
implies(X3,not(X2)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c127,plain,
implies(X2,not(X3)) = implies(X3,not(X2)),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
implies(X4,implies(X2,not(X3))) = implies(X4,implies(X3,not(X2))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
implies(X4,not(and_star(X2,X3))) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c125,c128]) ).
cnf(c130,plain,
implies(and_star(X2,X3),not(X4)) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c123,c129]) ).
cnf(c131,plain,
not(and_star(and_star(X2,X3),X4)) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c121,c130]) ).
cnf(c132,plain,
not(and_star(X2,and_star(X3,X4))) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c120,c131]) ).
cnf(c133,plain,
implies(X2,not(and_star(X3,X4))) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c117,c132]) ).
cnf(c134,plain,
implies(X2,implies(X3,not(X4))) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c115,c133]) ).
cnf(c135,plain,
implies(X2,implies(X4,not(X3))) = implies(X4,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c112,c134]) ).
cnf(c136,plain,
implies(not(X2),implies(X4,not(X3))) = implies(X4,implies(X3,not(not(X2)))),
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
implies(X3,not(not(X2))) = implies(X3,X2),
inference(congruence,[status(thm)],[c63]) ).
cnf(c138,plain,
implies(X4,implies(X3,not(not(X2)))) = implies(X4,implies(X3,X2)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
implies(not(X2),implies(X4,not(X3))) = implies(X4,implies(X3,X2)),
inference(transitivity,[status(thm)],[c136,c138]) ).
cnf(c140,plain,
implies(not(implies(X4,not(X3))),X2) = implies(X4,implies(X3,X2)),
inference(transitivity,[status(thm)],[c110,c139]) ).
cnf(c141,plain,
implies(and_star(X4,X3),X2) = implies(X4,implies(X3,X2)),
inference(transitivity,[status(thm)],[c105,c140]) ).
cnf(c142,plain,
implies(and_star(b,not(a)),and_star(b,and_star(not(a),implies(a,b)))) = implies(b,implies(not(a),and_star(b,and_star(not(a),implies(a,b))))),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
and_star(X3,and_star(not(X2),implies(X2,X3))) = and_star(not(X2),and_star(X3,implies(X2,X3))),
inference(substitution,[status(thm)],[c97]) ).
cnf(c144,plain,
and_star(implies(X2,X3),X3) = and_star(X3,implies(X2,X3)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c145,plain,
and_star(X3,implies(X2,X3)) = and_star(implies(X2,X3),X3),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
and_star(not(X2),and_star(X3,implies(X2,X3))) = and_star(not(X2),and_star(implies(X2,X3),X3)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
and_star(not(X2),and_star(implies(X2,X3),X3)) = and_star(implies(X2,X3),and_star(not(X2),X3)),
inference(substitution,[status(thm)],[c97]) ).
cnf(c148,axiom,
and_star(X2,truth) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c149,plain,
X2 = and_star(X2,truth),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
and_star(not(X2),X3) = and_star(not(X2),and_star(X3,truth)),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
and_star(implies(X2,X3),and_star(not(X2),X3)) = and_star(implies(X2,X3),and_star(not(X2),and_star(X3,truth))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
implies(not(X3),X2) = implies(not(X2),X3),
inference(substitution,[status(thm)],[c109]) ).
cnf(c153,plain,
implies(X3,implies(not(X3),X2)) = implies(X3,implies(not(X2),X3)),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c155,plain,
implies(X2,X3) = implies(X2,not(not(X3))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
implies(X3,implies(X2,X3)) = implies(X3,implies(X2,not(not(X3)))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
not(and_star(X2,not(X3))) = implies(X2,not(not(X3))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c158,plain,
implies(X2,not(not(X3))) = not(and_star(X2,not(X3))),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
implies(X3,implies(X2,not(not(X3)))) = implies(X3,not(and_star(X2,not(X3)))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
not(and_star(X3,and_star(X2,not(X3)))) = implies(X3,not(and_star(X2,not(X3)))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c161,plain,
implies(X3,not(and_star(X2,not(X3)))) = not(and_star(X3,and_star(X2,not(X3)))),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
and_star(not(X3),X2) = and_star(X2,not(X3)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c163,plain,
and_star(X2,not(X3)) = and_star(not(X3),X2),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
and_star(X3,and_star(X2,not(X3))) = and_star(X3,and_star(not(X3),X2)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
and_star(and_star(X3,not(X3)),X2) = and_star(X3,and_star(not(X3),X2)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c166,plain,
and_star(X3,and_star(not(X3),X2)) = and_star(and_star(X3,not(X3)),X2),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
and_star(X2,not(X2)) = and_star(X2,xor(X2,truth)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c168,plain,
xor(truth,X2) = xor(X2,truth),
inference(substitution,[status(thm)],[c11]) ).
cnf(c169,plain,
xor(X2,truth) = xor(truth,X2),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
and_star(X2,xor(X2,truth)) = and_star(X2,xor(truth,X2)),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
and_star(xor(truth,X2),X2) = and_star(X2,xor(truth,X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c172,plain,
and_star(X2,xor(truth,X2)) = and_star(xor(truth,X2),X2),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,axiom,
and_star(xor(truth,X2),X2) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c174,plain,
and_star(X2,xor(truth,X2)) = falsehood,
inference(transitivity,[status(thm)],[c172,c173]) ).
cnf(c175,plain,
and_star(X2,xor(X2,truth)) = falsehood,
inference(transitivity,[status(thm)],[c170,c174]) ).
cnf(c176,plain,
and_star(X2,not(X2)) = falsehood,
inference(transitivity,[status(thm)],[c167,c175]) ).
cnf(c177,plain,
and_star(and_star(X3,not(X3)),X2) = and_star(falsehood,X2),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
and_star(X2,falsehood) = and_star(falsehood,X2),
inference(substitution,[status(thm)],[c48]) ).
cnf(c179,plain,
and_star(falsehood,X2) = and_star(X2,falsehood),
inference(symmetry,[status(thm)],[c178]) ).
cnf(c180,axiom,
and_star(X2,falsehood) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c181,plain,
and_star(falsehood,X2) = falsehood,
inference(transitivity,[status(thm)],[c179,c180]) ).
cnf(c182,plain,
and_star(and_star(X3,not(X3)),X2) = falsehood,
inference(transitivity,[status(thm)],[c177,c181]) ).
cnf(c183,plain,
and_star(X3,and_star(not(X3),X2)) = falsehood,
inference(transitivity,[status(thm)],[c166,c182]) ).
cnf(c184,plain,
and_star(X3,and_star(X2,not(X3))) = falsehood,
inference(transitivity,[status(thm)],[c164,c183]) ).
cnf(c185,plain,
not(and_star(X3,and_star(X2,not(X3)))) = not(falsehood),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
not(falsehood) = xor(falsehood,truth),
inference(substitution,[status(thm)],[c14]) ).
cnf(c187,plain,
xor(X2,falsehood) = xor(falsehood,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c188,plain,
xor(falsehood,X2) = xor(X2,falsehood),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
xor(falsehood,X2) = X2,
inference(transitivity,[status(thm)],[c188,c2]) ).
cnf(c190,plain,
xor(falsehood,truth) = truth,
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
not(falsehood) = truth,
inference(transitivity,[status(thm)],[c186,c190]) ).
cnf(c192,plain,
not(and_star(X3,and_star(X2,not(X3)))) = truth,
inference(transitivity,[status(thm)],[c185,c191]) ).
cnf(c193,plain,
implies(X3,not(and_star(X2,not(X3)))) = truth,
inference(transitivity,[status(thm)],[c161,c192]) ).
cnf(c194,plain,
implies(X3,implies(X2,not(not(X3)))) = truth,
inference(transitivity,[status(thm)],[c159,c193]) ).
cnf(c195,plain,
implies(X3,implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c156,c194]) ).
cnf(c196,plain,
implies(X3,implies(not(X2),X3)) = truth,
inference(substitution,[status(thm)],[c195]) ).
cnf(c197,plain,
implies(X3,implies(not(X3),X2)) = truth,
inference(transitivity,[status(thm)],[c153,c196]) ).
cnf(c198,plain,
implies(X2,implies(not(X2),not(X3))) = truth,
inference(substitution,[status(thm)],[c197]) ).
cnf(c199,plain,
truth = implies(X2,implies(not(X2),not(X3))),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
and_star(X3,truth) = and_star(X3,implies(X2,implies(not(X2),not(X3)))),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
and_star(not(X2),and_star(X3,truth)) = and_star(not(X2),and_star(X3,implies(X2,implies(not(X2),not(X3))))),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
and_star(implies(X2,X3),and_star(not(X2),and_star(X3,truth))) = and_star(implies(X2,X3),and_star(not(X2),and_star(X3,implies(X2,implies(not(X2),not(X3)))))),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
not(and_star(not(X2),X3)) = implies(not(X2),not(X3)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c204,plain,
implies(not(X2),not(X3)) = not(and_star(not(X2),X3)),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
implies(X2,implies(not(X2),not(X3))) = implies(X2,not(and_star(not(X2),X3))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
and_star(X3,implies(X2,implies(not(X2),not(X3)))) = and_star(X3,implies(X2,not(and_star(not(X2),X3)))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
and_star(not(X2),and_star(X3,implies(X2,implies(not(X2),not(X3))))) = and_star(not(X2),and_star(X3,implies(X2,not(and_star(not(X2),X3))))),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
and_star(implies(X2,X3),and_star(not(X2),and_star(X3,implies(X2,implies(not(X2),not(X3)))))) = and_star(implies(X2,X3),and_star(not(X2),and_star(X3,implies(X2,not(and_star(not(X2),X3)))))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
and_star(and_star(not(X2),X3),implies(X2,not(and_star(not(X2),X3)))) = and_star(not(X2),and_star(X3,implies(X2,not(and_star(not(X2),X3))))),
inference(substitution,[status(thm)],[c92]) ).
cnf(c210,plain,
and_star(not(X2),and_star(X3,implies(X2,not(and_star(not(X2),X3))))) = and_star(and_star(not(X2),X3),implies(X2,not(and_star(not(X2),X3)))),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
and_star(implies(X2,X3),and_star(not(X2),and_star(X3,implies(X2,not(and_star(not(X2),X3)))))) = and_star(implies(X2,X3),and_star(and_star(not(X2),X3),implies(X2,not(and_star(not(X2),X3))))),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c213,plain,
implies(X2,X3) = implies(not(not(X2)),X3),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
and_star(implies(X2,X3),and_star(and_star(not(X2),X3),implies(X2,not(and_star(not(X2),X3))))) = and_star(implies(not(not(X2)),X3),and_star(and_star(not(X2),X3),implies(X2,not(and_star(not(X2),X3))))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
and_star(not(X4),and_star(X3,implies(not(X4),X2))) = and_star(X3,and_star(not(X4),implies(not(X4),X2))),
inference(substitution,[status(thm)],[c97]) ).
cnf(c216,plain,
implies(X2,X3) = implies(not(X3),not(X2)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c217,plain,
and_star(X2,implies(X2,X3)) = and_star(X2,implies(not(X3),not(X2))),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
not(and_star(not(X3),X2)) = implies(not(X3),not(X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c219,plain,
implies(not(X3),not(X2)) = not(and_star(not(X3),X2)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
and_star(X2,implies(not(X3),not(X2))) = and_star(X2,not(and_star(not(X3),X2))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
not(X2) = xor(truth,X2),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c222,plain,
and_star(not(X3),X2) = and_star(xor(truth,X3),X2),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
not(and_star(not(X3),X2)) = not(and_star(xor(truth,X3),X2)),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
and_star(X2,not(and_star(not(X3),X2))) = and_star(X2,not(and_star(xor(truth,X3),X2))),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,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)],[c48]) ).
cnf(c226,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)],[c225]) ).
cnf(c227,plain,
not(and_star(xor(truth,X2),X3)) = xor(and_star(xor(truth,X2),X3),truth),
inference(substitution,[status(thm)],[c14]) ).
cnf(c228,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)],[c227]) ).
cnf(c229,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(c230,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)],[c229]) ).
cnf(c231,plain,
not(and_star(xor(truth,X3),X2)) = xor(and_star(xor(truth,X3),X2),truth),
inference(substitution,[status(thm)],[c14]) ).
cnf(c232,plain,
xor(and_star(xor(truth,X3),X2),truth) = not(and_star(xor(truth,X3),X2)),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,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)],[c232]) ).
cnf(c234,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)],[c48]) ).
cnf(c235,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)],[c233,c234]) ).
cnf(c236,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)],[c230,c235]) ).
cnf(c237,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)],[c228,c236]) ).
cnf(c238,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)],[c226,c237]) ).
cnf(c239,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)],[c238]) ).
cnf(c240,plain,
not(and_star(xor(truth,X2),X3)) = implies(xor(truth,X2),not(X3)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c241,plain,
and_star(X3,not(and_star(xor(truth,X2),X3))) = and_star(X3,implies(xor(truth,X2),not(X3))),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
implies(xor(truth,X2),not(X3)) = implies(not(X2),not(X3)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c243,plain,
and_star(X3,implies(xor(truth,X2),not(X3))) = and_star(X3,implies(not(X2),not(X3))),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
and_star(X3,not(and_star(xor(truth,X2),X3))) = and_star(X3,implies(not(X2),not(X3))),
inference(transitivity,[status(thm)],[c241,c243]) ).
cnf(c245,plain,
and_star(X2,not(and_star(xor(truth,X3),X2))) = and_star(X3,implies(not(X2),not(X3))),
inference(transitivity,[status(thm)],[c239,c244]) ).
cnf(c246,plain,
and_star(X2,not(and_star(not(X3),X2))) = and_star(X3,implies(not(X2),not(X3))),
inference(transitivity,[status(thm)],[c224,c245]) ).
cnf(c247,plain,
and_star(X2,implies(not(X3),not(X2))) = and_star(X3,implies(not(X2),not(X3))),
inference(transitivity,[status(thm)],[c220,c246]) ).
cnf(c248,plain,
and_star(X2,implies(X2,X3)) = and_star(X3,implies(not(X2),not(X3))),
inference(transitivity,[status(thm)],[c217,c247]) ).
cnf(c249,plain,
and_star(not(X3),implies(not(X3),X2)) = and_star(X2,implies(not(not(X3)),not(X2))),
inference(substitution,[status(thm)],[c248]) ).
cnf(c250,plain,
implies(not(not(X3)),not(X2)) = implies(X3,not(X2)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c251,plain,
and_star(X2,implies(not(not(X3)),not(X2))) = and_star(X2,implies(X3,not(X2))),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
and_star(not(X3),implies(not(X3),X2)) = and_star(X2,implies(X3,not(X2))),
inference(transitivity,[status(thm)],[c249,c251]) ).
cnf(c253,plain,
and_star(X3,and_star(not(X4),implies(not(X4),X2))) = and_star(X3,and_star(X2,implies(X4,not(X2)))),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
and_star(not(X4),and_star(X3,implies(not(X4),X2))) = and_star(X3,and_star(X2,implies(X4,not(X2)))),
inference(transitivity,[status(thm)],[c215,c253]) ).
cnf(c255,plain,
and_star(not(X2),and_star(implies(not(not(X2)),X3),implies(not(X2),and_star(not(X2),X3)))) = and_star(implies(not(not(X2)),X3),and_star(and_star(not(X2),X3),implies(X2,not(and_star(not(X2),X3))))),
inference(substitution,[status(thm)],[c254]) ).
cnf(c256,plain,
and_star(implies(not(not(X2)),X3),and_star(and_star(not(X2),X3),implies(X2,not(and_star(not(X2),X3))))) = and_star(not(X2),and_star(implies(not(not(X2)),X3),implies(not(X2),and_star(not(X2),X3)))),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c257,plain,
and_star(X3,X2) = not(implies(X3,not(X2))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c258,plain,
implies(X3,and_star(X3,X2)) = implies(X3,not(implies(X3,not(X2)))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
and_star(implies(not(X3),X2),implies(X3,and_star(X3,X2))) = and_star(implies(not(X3),X2),implies(X3,not(implies(X3,not(X2))))),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
not(and_star(X3,implies(X3,not(X2)))) = implies(X3,not(implies(X3,not(X2)))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c261,plain,
implies(X3,not(implies(X3,not(X2)))) = not(and_star(X3,implies(X3,not(X2)))),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c262,plain,
and_star(implies(not(X3),X2),implies(X3,not(implies(X3,not(X2))))) = and_star(implies(not(X3),X2),not(and_star(X3,implies(X3,not(X2))))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
X2 = not(not(X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c264,plain,
implies(not(X3),X2) = implies(not(X3),not(not(X2))),
inference(congruence,[status(thm)],[c263]) ).
cnf(c265,plain,
and_star(implies(not(X3),X2),not(and_star(X3,implies(X3,not(X2))))) = and_star(implies(not(X3),not(not(X2))),not(and_star(X3,implies(X3,not(X2))))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
not(X2) = xor(truth,X2),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c267,plain,
not(not(X2)) = not(xor(truth,X2)),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
implies(not(X3),not(not(X2))) = implies(not(X3),not(xor(truth,X2))),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
and_star(implies(not(X3),not(not(X2))),not(and_star(X3,implies(X3,not(X2))))) = and_star(implies(not(X3),not(xor(truth,X2))),not(and_star(X3,implies(X3,not(X2))))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
not(X2) = xor(truth,X2),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c271,plain,
implies(X3,not(X2)) = implies(X3,xor(truth,X2)),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
and_star(X3,implies(X3,not(X2))) = and_star(X3,implies(X3,xor(truth,X2))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
not(and_star(X3,implies(X3,not(X2)))) = not(and_star(X3,implies(X3,xor(truth,X2)))),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
and_star(implies(not(X3),not(xor(truth,X2))),not(and_star(X3,implies(X3,not(X2))))) = and_star(implies(not(X3),not(xor(truth,X2))),not(and_star(X3,implies(X3,xor(truth,X2))))),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
and_star(X3,implies(X3,xor(truth,X2))) = and_star(xor(truth,X2),implies(not(X3),not(xor(truth,X2)))),
inference(substitution,[status(thm)],[c248]) ).
cnf(c276,plain,
not(and_star(X3,implies(X3,xor(truth,X2)))) = not(and_star(xor(truth,X2),implies(not(X3),not(xor(truth,X2))))),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
and_star(implies(not(X3),not(xor(truth,X2))),not(and_star(X3,implies(X3,xor(truth,X2))))) = and_star(implies(not(X3),not(xor(truth,X2))),not(and_star(xor(truth,X2),implies(not(X3),not(xor(truth,X2)))))),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
and_star(implies(not(X3),not(xor(truth,X2))),not(and_star(xor(truth,X2),implies(not(X3),not(xor(truth,X2)))))) = and_star(X2,not(and_star(xor(truth,implies(not(X3),not(xor(truth,X2)))),X2))),
inference(substitution,[status(thm)],[c238]) ).
cnf(c279,plain,
not(and_star(xor(truth,implies(not(X3),not(xor(truth,X2)))),X2)) = implies(xor(truth,implies(not(X3),not(xor(truth,X2)))),not(X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c280,plain,
and_star(X2,not(and_star(xor(truth,implies(not(X3),not(xor(truth,X2)))),X2))) = and_star(X2,implies(xor(truth,implies(not(X3),not(xor(truth,X2)))),not(X2))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
xor(truth,implies(not(X3),not(xor(truth,X2)))) = not(implies(not(X3),not(xor(truth,X2)))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c282,plain,
implies(xor(truth,implies(not(X3),not(xor(truth,X2)))),not(X2)) = implies(not(implies(not(X3),not(xor(truth,X2)))),not(X2)),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
and_star(X2,implies(xor(truth,implies(not(X3),not(xor(truth,X2)))),not(X2))) = and_star(X2,implies(not(implies(not(X3),not(xor(truth,X2)))),not(X2))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
not(implies(not(X3),not(xor(truth,X2)))) = and_star(not(X3),xor(truth,X2)),
inference(substitution,[status(thm)],[c80]) ).
cnf(c285,plain,
implies(not(implies(not(X3),not(xor(truth,X2)))),not(X2)) = implies(and_star(not(X3),xor(truth,X2)),not(X2)),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
and_star(X2,implies(not(implies(not(X3),not(xor(truth,X2)))),not(X2))) = and_star(X2,implies(and_star(not(X3),xor(truth,X2)),not(X2))),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
implies(and_star(not(X3),xor(truth,X2)),not(X2)) = implies(not(X3),implies(xor(truth,X2),not(X2))),
inference(substitution,[status(thm)],[c141]) ).
cnf(c288,plain,
and_star(X2,implies(and_star(not(X3),xor(truth,X2)),not(X2))) = and_star(X2,implies(not(X3),implies(xor(truth,X2),not(X2)))),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
implies(xor(truth,X2),not(X2)) = implies(not(X2),not(X2)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c290,plain,
implies(not(X3),implies(xor(truth,X2),not(X2))) = implies(not(X3),implies(not(X2),not(X2))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
and_star(X2,implies(not(X3),implies(xor(truth,X2),not(X2)))) = and_star(X2,implies(not(X3),implies(not(X2),not(X2)))),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
implies(X2,X2) = xor(truth,and_star(X2,xor(truth,X2))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c293,plain,
xor(truth,and_star(X2,xor(truth,X2))) = xor(truth,falsehood),
inference(congruence,[status(thm)],[c174]) ).
cnf(c294,plain,
xor(truth,falsehood) = truth,
inference(substitution,[status(thm)],[c2]) ).
cnf(c295,plain,
xor(truth,and_star(X2,xor(truth,X2))) = truth,
inference(transitivity,[status(thm)],[c293,c294]) ).
cnf(c296,plain,
implies(X2,X2) = truth,
inference(transitivity,[status(thm)],[c292,c295]) ).
cnf(c297,plain,
implies(not(X2),not(X2)) = truth,
inference(substitution,[status(thm)],[c296]) ).
cnf(c298,plain,
implies(not(X3),implies(not(X2),not(X2))) = implies(not(X3),truth),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
and_star(X2,implies(not(X3),implies(not(X2),not(X2)))) = and_star(X2,implies(not(X3),truth)),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
implies(X2,truth) = xor(truth,and_star(X2,xor(truth,truth))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c301,plain,
xor(truth,truth) = falsehood,
inference(substitution,[status(thm)],[c58]) ).
cnf(c302,plain,
and_star(X2,xor(truth,truth)) = and_star(X2,falsehood),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
xor(truth,and_star(X2,xor(truth,truth))) = xor(truth,and_star(X2,falsehood)),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
xor(truth,and_star(X2,falsehood)) = xor(truth,falsehood),
inference(congruence,[status(thm)],[c180]) ).
cnf(c305,plain,
xor(truth,falsehood) = truth,
inference(substitution,[status(thm)],[c2]) ).
cnf(c306,plain,
xor(truth,and_star(X2,falsehood)) = truth,
inference(transitivity,[status(thm)],[c304,c305]) ).
cnf(c307,plain,
xor(truth,and_star(X2,xor(truth,truth))) = truth,
inference(transitivity,[status(thm)],[c303,c306]) ).
cnf(c308,plain,
implies(X2,truth) = truth,
inference(transitivity,[status(thm)],[c300,c307]) ).
cnf(c309,plain,
implies(not(X2),truth) = truth,
inference(substitution,[status(thm)],[c308]) ).
cnf(c310,plain,
and_star(X2,implies(not(X3),truth)) = and_star(X2,truth),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
and_star(X2,implies(not(X3),truth)) = X2,
inference(transitivity,[status(thm)],[c310,c148]) ).
cnf(c312,plain,
and_star(X2,implies(not(X3),implies(not(X2),not(X2)))) = X2,
inference(transitivity,[status(thm)],[c299,c311]) ).
cnf(c313,plain,
and_star(X2,implies(not(X3),implies(xor(truth,X2),not(X2)))) = X2,
inference(transitivity,[status(thm)],[c291,c312]) ).
cnf(c314,plain,
and_star(X2,implies(and_star(not(X3),xor(truth,X2)),not(X2))) = X2,
inference(transitivity,[status(thm)],[c288,c313]) ).
cnf(c315,plain,
and_star(X2,implies(not(implies(not(X3),not(xor(truth,X2)))),not(X2))) = X2,
inference(transitivity,[status(thm)],[c286,c314]) ).
cnf(c316,plain,
and_star(X2,implies(xor(truth,implies(not(X3),not(xor(truth,X2)))),not(X2))) = X2,
inference(transitivity,[status(thm)],[c283,c315]) ).
cnf(c317,plain,
and_star(X2,not(and_star(xor(truth,implies(not(X3),not(xor(truth,X2)))),X2))) = X2,
inference(transitivity,[status(thm)],[c280,c316]) ).
cnf(c318,plain,
and_star(implies(not(X3),not(xor(truth,X2))),not(and_star(xor(truth,X2),implies(not(X3),not(xor(truth,X2)))))) = X2,
inference(transitivity,[status(thm)],[c278,c317]) ).
cnf(c319,plain,
and_star(implies(not(X3),not(xor(truth,X2))),not(and_star(X3,implies(X3,xor(truth,X2))))) = X2,
inference(transitivity,[status(thm)],[c277,c318]) ).
cnf(c320,plain,
and_star(implies(not(X3),not(xor(truth,X2))),not(and_star(X3,implies(X3,not(X2))))) = X2,
inference(transitivity,[status(thm)],[c274,c319]) ).
cnf(c321,plain,
and_star(implies(not(X3),not(not(X2))),not(and_star(X3,implies(X3,not(X2))))) = X2,
inference(transitivity,[status(thm)],[c269,c320]) ).
cnf(c322,plain,
and_star(implies(not(X3),X2),not(and_star(X3,implies(X3,not(X2))))) = X2,
inference(transitivity,[status(thm)],[c265,c321]) ).
cnf(c323,plain,
and_star(implies(not(X3),X2),implies(X3,not(implies(X3,not(X2))))) = X2,
inference(transitivity,[status(thm)],[c262,c322]) ).
cnf(c324,plain,
and_star(implies(not(X3),X2),implies(X3,and_star(X3,X2))) = X2,
inference(transitivity,[status(thm)],[c259,c323]) ).
cnf(c325,plain,
and_star(implies(not(not(X2)),X3),implies(not(X2),and_star(not(X2),X3))) = X3,
inference(substitution,[status(thm)],[c324]) ).
cnf(c326,plain,
and_star(not(X2),and_star(implies(not(not(X2)),X3),implies(not(X2),and_star(not(X2),X3)))) = and_star(not(X2),X3),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
and_star(not(X2),X3) = and_star(X3,not(X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c328,plain,
and_star(not(X2),and_star(implies(not(not(X2)),X3),implies(not(X2),and_star(not(X2),X3)))) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c326,c327]) ).
cnf(c329,plain,
and_star(implies(not(not(X2)),X3),and_star(and_star(not(X2),X3),implies(X2,not(and_star(not(X2),X3))))) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c256,c328]) ).
cnf(c330,plain,
and_star(implies(X2,X3),and_star(and_star(not(X2),X3),implies(X2,not(and_star(not(X2),X3))))) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c214,c329]) ).
cnf(c331,plain,
and_star(implies(X2,X3),and_star(not(X2),and_star(X3,implies(X2,not(and_star(not(X2),X3)))))) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c211,c330]) ).
cnf(c332,plain,
and_star(implies(X2,X3),and_star(not(X2),and_star(X3,implies(X2,implies(not(X2),not(X3)))))) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c208,c331]) ).
cnf(c333,plain,
and_star(implies(X2,X3),and_star(not(X2),and_star(X3,truth))) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c202,c332]) ).
cnf(c334,plain,
and_star(implies(X2,X3),and_star(not(X2),X3)) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c151,c333]) ).
cnf(c335,plain,
and_star(not(X2),and_star(implies(X2,X3),X3)) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c147,c334]) ).
cnf(c336,plain,
and_star(not(X2),and_star(X3,implies(X2,X3))) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c146,c335]) ).
cnf(c337,plain,
and_star(X3,and_star(not(X2),implies(X2,X3))) = and_star(X3,not(X2)),
inference(transitivity,[status(thm)],[c143,c336]) ).
cnf(c338,plain,
and_star(b,and_star(not(a),implies(a,b))) = and_star(b,not(a)),
inference(substitution,[status(thm)],[c337]) ).
cnf(c339,plain,
implies(not(a),and_star(b,and_star(not(a),implies(a,b)))) = implies(not(a),and_star(b,not(a))),
inference(congruence,[status(thm)],[c338]) ).
cnf(c340,plain,
implies(b,implies(not(a),and_star(b,and_star(not(a),implies(a,b))))) = implies(b,implies(not(a),and_star(b,not(a)))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
and_star(X3,X2) = not(implies(X3,not(X2))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c342,plain,
implies(X2,and_star(X3,X2)) = implies(X2,not(implies(X3,not(X2)))),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
implies(X3,implies(X2,and_star(X3,X2))) = implies(X3,implies(X2,not(implies(X3,not(X2))))),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,plain,
not(and_star(X2,implies(X3,not(X2)))) = implies(X2,not(implies(X3,not(X2)))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c345,plain,
implies(X2,not(implies(X3,not(X2)))) = not(and_star(X2,implies(X3,not(X2)))),
inference(symmetry,[status(thm)],[c344]) ).
cnf(c346,plain,
implies(X3,implies(X2,not(implies(X3,not(X2))))) = implies(X3,not(and_star(X2,implies(X3,not(X2))))),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
not(and_star(X3,and_star(X2,implies(X3,not(X2))))) = implies(X3,not(and_star(X2,implies(X3,not(X2))))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c348,plain,
implies(X3,not(and_star(X2,implies(X3,not(X2))))) = not(and_star(X3,and_star(X2,implies(X3,not(X2))))),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c349,plain,
implies(X3,not(X2)) = not(and_star(X3,X2)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c350,plain,
and_star(X2,implies(X3,not(X2))) = and_star(X2,not(and_star(X3,X2))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
and_star(X3,and_star(X2,implies(X3,not(X2)))) = and_star(X3,and_star(X2,not(and_star(X3,X2)))),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
and_star(and_star(X3,X2),not(and_star(X3,X2))) = and_star(X3,and_star(X2,not(and_star(X3,X2)))),
inference(substitution,[status(thm)],[c92]) ).
cnf(c353,plain,
and_star(X3,and_star(X2,not(and_star(X3,X2)))) = and_star(and_star(X3,X2),not(and_star(X3,X2))),
inference(symmetry,[status(thm)],[c352]) ).
cnf(c354,plain,
and_star(and_star(X3,X2),not(and_star(X3,X2))) = falsehood,
inference(substitution,[status(thm)],[c176]) ).
cnf(c355,plain,
and_star(X3,and_star(X2,not(and_star(X3,X2)))) = falsehood,
inference(transitivity,[status(thm)],[c353,c354]) ).
cnf(c356,plain,
and_star(X3,and_star(X2,implies(X3,not(X2)))) = falsehood,
inference(transitivity,[status(thm)],[c351,c355]) ).
cnf(c357,plain,
not(and_star(X3,and_star(X2,implies(X3,not(X2))))) = not(falsehood),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
not(and_star(X3,and_star(X2,implies(X3,not(X2))))) = truth,
inference(transitivity,[status(thm)],[c357,c191]) ).
cnf(c359,plain,
implies(X3,not(and_star(X2,implies(X3,not(X2))))) = truth,
inference(transitivity,[status(thm)],[c348,c358]) ).
cnf(c360,plain,
implies(X3,implies(X2,not(implies(X3,not(X2))))) = truth,
inference(transitivity,[status(thm)],[c346,c359]) ).
cnf(c361,plain,
implies(X3,implies(X2,and_star(X3,X2))) = truth,
inference(transitivity,[status(thm)],[c343,c360]) ).
cnf(c362,plain,
implies(b,implies(not(a),and_star(b,not(a)))) = truth,
inference(substitution,[status(thm)],[c361]) ).
cnf(c363,plain,
implies(b,implies(not(a),and_star(b,and_star(not(a),implies(a,b))))) = truth,
inference(transitivity,[status(thm)],[c340,c362]) ).
cnf(c364,plain,
implies(and_star(b,not(a)),and_star(b,and_star(not(a),implies(a,b)))) = truth,
inference(transitivity,[status(thm)],[c142,c363]) ).
cnf(c365,plain,
implies(and_star(b,not(a)),and_star(b,and_star(implies(a,b),not(a)))) = truth,
inference(transitivity,[status(thm)],[c103,c364]) ).
cnf(c366,plain,
implies(and_star(b,not(a)),and_star(implies(a,b),and_star(b,not(a)))) = truth,
inference(transitivity,[status(thm)],[c100,c365]) ).
cnf(c367,plain,
implies(and_star(b,not(a)),and_star(implies(a,b),not(implies(b,a)))) = truth,
inference(transitivity,[status(thm)],[c89,c366]) ).
cnf(c368,plain,
implies(and_star(b,not(a)),not(implies(implies(a,b),implies(b,a)))) = truth,
inference(transitivity,[status(thm)],[c86,c367]) ).
cnf(c369,plain,
implies(not(implies(b,a)),not(implies(implies(a,b),implies(b,a)))) = truth,
inference(transitivity,[status(thm)],[c84,c368]) ).
cnf(c370,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth,
inference(transitivity,[status(thm)],[c67,c369]) ).
cnf(c371,plain,
$false,
inference(resolution,[status(thm)],[c1,c370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL109-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.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 15:22:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.83/0.98 Command-line arguments: --no-flatten-goal
% 3.83/0.98
% 3.83/0.98 % SZS status Unsatisfiable
% 3.83/0.98
% 3.83/1.00 % SZS output start CNFRefutation
% See solution above
% 5.17/1.17
% 5.17/1.17 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------