%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT224-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 11:44:34 AM UTC 2026
% Result : Unsatisfiable 77.84s 10.41s
% Output : CNFRefutation 78.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 13
% Syntax : Number of clauses : 224 ( 224 unt; 0 nHn; 45 RR)
% Number of literals : 224 ( 223 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; 0-4 aty)
% Number of variables : 404 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c2,axiom,
join(X,Y) = join(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c3,plain,
join(complement(a),complement(b)) = join(complement(b),complement(a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
join(complement(b),complement(a)) = join(complement(a),complement(b)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
ifeq(join(X2,Y2),one,ifeq(meet(X2,Y2),zero,complement(X2),Y2),Y2) = Y2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_join_complement) ).
cnf(c6,plain,
ifeq(join(b,meet(complement(a),complement(meet(b,complement(a))))),one,ifeq(meet(b,meet(complement(a),complement(meet(b,complement(a))))),zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))),meet(complement(a),complement(meet(b,complement(a))))) = meet(complement(a),complement(meet(b,complement(a)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
meet(complement(a),complement(meet(b,complement(a)))) = ifeq(join(b,meet(complement(a),complement(meet(b,complement(a))))),one,ifeq(meet(b,meet(complement(a),complement(meet(b,complement(a))))),zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))),meet(complement(a),complement(meet(b,complement(a))))),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
meet(join(X3,X2),complement(meet(X3,X2))) = meet(join(X2,X3),complement(meet(X3,X2))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
join(X3,meet(join(X3,X2),complement(meet(X3,X2)))) = join(X3,meet(join(X2,X3),complement(meet(X3,X2)))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
meet(X2,Y2) = meet(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c13,plain,
meet(complement(meet(X3,X2)),join(X2,X3)) = meet(join(X2,X3),complement(meet(X3,X2))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
meet(join(X2,X3),complement(meet(X3,X2))) = meet(complement(meet(X3,X2)),join(X2,X3)),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
join(X3,meet(join(X2,X3),complement(meet(X3,X2)))) = join(X3,meet(complement(meet(X3,X2)),join(X2,X3))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
meet(X2,join(X4,X3)) = meet(join(X4,X3),X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c17,plain,
meet(join(X2,X4),X3) = meet(X3,join(X2,X4)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
join(meet(X4,X3),meet(join(X2,X4),X3)) = join(meet(X4,X3),meet(X3,join(X2,X4))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c20,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
join(meet(X4,X3),meet(X3,join(X2,X4))) = join(meet(X3,X4),meet(X3,join(X2,X4))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c23,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
join(meet(X4,X3),meet(X4,join(X2,X3))) = join(meet(X3,X4),meet(X4,join(X2,X3))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
join(meet(X4,join(X2,X3)),meet(X3,X4)) = join(meet(X3,X4),meet(X4,join(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
join(meet(X3,X4),meet(X4,join(X2,X3))) = join(meet(X4,join(X2,X3)),meet(X3,X4)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
meet(meet(X3,X2),X4) = meet(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c28,plain,
meet(X4,meet(X3,X2)) = meet(meet(X3,X2),X4),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,axiom,
meet(meet(X2,Y2),Z) = meet(X2,meet(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(c30,plain,
meet(meet(X3,X2),X4) = meet(X3,meet(X2,X4)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c32,plain,
meet(X3,meet(X2,X4)) = meet(X3,meet(X4,X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
meet(meet(X3,X2),X4) = meet(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c30,c32]) ).
cnf(c34,plain,
meet(X4,meet(X3,X2)) = meet(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c28,c33]) ).
cnf(c35,plain,
meet(X3,meet(X4,join(X2,X4))) = meet(X4,meet(X3,join(X2,X4))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
meet(X4,meet(X3,join(X2,X4))) = meet(X3,meet(X4,join(X2,X4))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c38,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
meet(X3,join(X2,X3)) = meet(X3,join(X3,X2)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,axiom,
meet(X2,join(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
cnf(c41,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
meet(X3,join(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c39,c41]) ).
cnf(c43,plain,
meet(X3,meet(X4,join(X2,X4))) = meet(X3,X4),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c45,plain,
meet(X3,meet(X4,join(X2,X4))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
meet(X4,meet(X3,join(X2,X4))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c36,c45]) ).
cnf(c47,plain,
meet(X3,meet(X4,join(X2,X3))) = meet(X3,X4),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
meet(X3,X4) = meet(X3,meet(X4,join(X2,X3))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
join(meet(X4,join(X2,X3)),meet(X3,X4)) = join(meet(X4,join(X2,X3)),meet(X3,meet(X4,join(X2,X3)))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c12]) ).
cnf(c51,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
join(X3,meet(X2,X3)) = join(X3,meet(X3,X2)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,axiom,
join(X2,meet(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
cnf(c54,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
join(X3,meet(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c52,c54]) ).
cnf(c56,plain,
join(meet(X4,join(X2,X3)),meet(X3,meet(X4,join(X2,X3)))) = meet(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
join(meet(X4,join(X2,X3)),meet(X3,X4)) = meet(X4,join(X2,X3)),
inference(transitivity,[status(thm)],[c49,c56]) ).
cnf(c58,plain,
join(meet(X3,X4),meet(X4,join(X2,X3))) = meet(X4,join(X2,X3)),
inference(transitivity,[status(thm)],[c26,c57]) ).
cnf(c59,plain,
join(meet(X4,X3),meet(X4,join(X2,X3))) = meet(X4,join(X2,X3)),
inference(transitivity,[status(thm)],[c24,c58]) ).
cnf(c60,plain,
join(meet(X3,X4),meet(X3,join(X2,X4))) = meet(X3,join(X2,X4)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c62,plain,
meet(X3,join(X2,X4)) = meet(X3,join(X4,X2)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
join(meet(X3,X4),meet(X3,join(X2,X4))) = meet(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c60,c62]) ).
cnf(c64,plain,
join(meet(X4,X3),meet(X3,join(X2,X4))) = meet(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c21,c63]) ).
cnf(c65,plain,
join(meet(X4,X3),meet(join(X2,X4),X3)) = meet(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c18,c64]) ).
cnf(c66,plain,
join(meet(X2,complement(meet(X3,X2))),meet(join(X3,X2),complement(meet(X3,X2)))) = meet(complement(meet(X3,X2)),join(X2,X3)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
meet(complement(meet(X3,X2)),join(X2,X3)) = join(meet(X2,complement(meet(X3,X2))),meet(join(X3,X2),complement(meet(X3,X2)))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
join(X3,meet(complement(meet(X3,X2)),join(X2,X3))) = join(X3,join(meet(X2,complement(meet(X3,X2))),meet(join(X3,X2),complement(meet(X3,X2))))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,axiom,
join(join(X2,Y2),Z2) = join(X2,join(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(c70,plain,
join(join(X3,meet(X2,complement(meet(X3,X2)))),meet(join(X3,X2),complement(meet(X3,X2)))) = join(X3,join(meet(X2,complement(meet(X3,X2))),meet(join(X3,X2),complement(meet(X3,X2))))),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
join(X3,join(meet(X2,complement(meet(X3,X2))),meet(join(X3,X2),complement(meet(X3,X2))))) = join(join(X3,meet(X2,complement(meet(X3,X2)))),meet(join(X3,X2),complement(meet(X3,X2)))),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
meet(complement(meet(X3,X2)),X2) = meet(X2,complement(meet(X3,X2))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c73,plain,
meet(X2,complement(meet(X3,X2))) = meet(complement(meet(X3,X2)),X2),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
join(X3,meet(X2,complement(meet(X3,X2)))) = join(X3,meet(complement(meet(X3,X2)),X2)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
meet(complement(meet(X3,X2)),join(X3,meet(X2,complement(meet(X3,X2))))) = meet(complement(meet(X3,X2)),join(X3,meet(complement(meet(X3,X2)),X2))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
join(X4,meet(X3,X2)) = join(meet(X3,X2),X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c77,plain,
join(meet(X3,X2),X4) = join(X4,meet(X3,X2)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
meet(X2,join(meet(X3,X2),X4)) = meet(X2,join(X4,meet(X3,X2))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
join(X3,meet(X2,join(meet(X3,X2),X4))) = join(X3,meet(X2,join(X4,meet(X3,X2)))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
meet(X4,join(X3,meet(X2,join(meet(X3,X2),X4)))) = meet(X4,join(X3,meet(X2,join(X4,meet(X3,X2))))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c82,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
join(meet(X4,X3),meet(X4,join(X3,X2))) = join(meet(X3,X4),meet(X4,join(X3,X2))),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
join(meet(X4,join(X3,X2)),meet(X3,X4)) = join(meet(X3,X4),meet(X4,join(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c85,plain,
join(meet(X3,X4),meet(X4,join(X3,X2))) = join(meet(X4,join(X3,X2)),meet(X3,X4)),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
meet(join(X4,X2),X3) = meet(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c87,plain,
meet(X3,join(X4,X2)) = meet(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
meet(X4,meet(X3,join(X4,X2))) = meet(X4,meet(join(X4,X2),X3)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,meet(join(X4,X2),X3)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c90,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(meet(X4,join(X4,X2)),X3),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c40]) ).
cnf(c92,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,X3),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c90,c92]) ).
cnf(c94,plain,
meet(X4,meet(X3,join(X4,X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c88,c93]) ).
cnf(c95,plain,
meet(X3,meet(X4,join(X3,X2))) = meet(X3,X4),
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
meet(X3,X4) = meet(X3,meet(X4,join(X3,X2))),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
join(meet(X4,join(X3,X2)),meet(X3,X4)) = join(meet(X4,join(X3,X2)),meet(X3,meet(X4,join(X3,X2)))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
join(meet(X4,join(X3,X2)),meet(X3,meet(X4,join(X3,X2)))) = meet(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c99,plain,
join(meet(X4,join(X3,X2)),meet(X3,X4)) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c97,c98]) ).
cnf(c100,plain,
join(meet(X3,X4),meet(X4,join(X3,X2))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c85,c99]) ).
cnf(c101,plain,
join(meet(X4,X3),meet(X4,join(X3,X2))) = meet(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c83,c100]) ).
cnf(c102,plain,
join(meet(X4,X3),meet(X4,join(X3,meet(X2,join(X4,meet(X3,X2)))))) = meet(X4,join(X3,meet(X2,join(X4,meet(X3,X2))))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
meet(X4,join(X3,meet(X2,join(X4,meet(X3,X2))))) = join(meet(X4,X3),meet(X4,join(X3,meet(X2,join(X4,meet(X3,X2)))))),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,axiom,
meet(X2,join(Y2,meet(X2,Z2))) = join(meet(X2,Y2),meet(X2,join(Y2,meet(Z2,join(X2,meet(Y2,Z2)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H8) ).
cnf(c105,plain,
meet(X4,join(X3,meet(X4,X2))) = join(meet(X4,X3),meet(X4,join(X3,meet(X2,join(X4,meet(X3,X2)))))),
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
join(meet(X4,X3),meet(X4,join(X3,meet(X2,join(X4,meet(X3,X2)))))) = meet(X4,join(X3,meet(X4,X2))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
meet(X4,join(X3,meet(X2,join(X4,meet(X3,X2))))) = meet(X4,join(X3,meet(X4,X2))),
inference(transitivity,[status(thm)],[c103,c106]) ).
cnf(c108,plain,
meet(X4,join(X3,meet(X2,join(meet(X3,X2),X4)))) = meet(X4,join(X3,meet(X4,X2))),
inference(transitivity,[status(thm)],[c80,c107]) ).
cnf(c109,plain,
meet(complement(meet(X3,X2)),join(X3,meet(X2,join(meet(X3,X2),complement(meet(X3,X2)))))) = meet(complement(meet(X3,X2)),join(X3,meet(complement(meet(X3,X2)),X2))),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
meet(complement(meet(X3,X2)),join(X3,meet(complement(meet(X3,X2)),X2))) = meet(complement(meet(X3,X2)),join(X3,meet(X2,join(meet(X3,X2),complement(meet(X3,X2)))))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,axiom,
join(X2,complement(X2)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_join) ).
cnf(c112,plain,
join(meet(X3,X2),complement(meet(X3,X2))) = one,
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
meet(X2,join(meet(X3,X2),complement(meet(X3,X2)))) = meet(X2,one),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
join(X3,meet(X2,join(meet(X3,X2),complement(meet(X3,X2))))) = join(X3,meet(X2,one)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
meet(complement(meet(X3,X2)),join(X3,meet(X2,join(meet(X3,X2),complement(meet(X3,X2)))))) = meet(complement(meet(X3,X2)),join(X3,meet(X2,one))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
one = join(X2,complement(X2)),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c117,plain,
meet(X2,one) = meet(X2,join(X2,complement(X2))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
meet(X2,join(X2,complement(X2))) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c119,plain,
meet(X2,one) = X2,
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
join(X3,meet(X2,one)) = join(X3,X2),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
meet(complement(meet(X3,X2)),join(X3,meet(X2,one))) = meet(complement(meet(X3,X2)),join(X3,X2)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
meet(complement(meet(X3,X2)),join(X3,X2)) = meet(join(X3,X2),complement(meet(X3,X2))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c123,plain,
meet(complement(meet(X3,X2)),join(X3,meet(X2,one))) = meet(join(X3,X2),complement(meet(X3,X2))),
inference(transitivity,[status(thm)],[c121,c122]) ).
cnf(c124,plain,
meet(complement(meet(X3,X2)),join(X3,meet(X2,join(meet(X3,X2),complement(meet(X3,X2)))))) = meet(join(X3,X2),complement(meet(X3,X2))),
inference(transitivity,[status(thm)],[c115,c123]) ).
cnf(c125,plain,
meet(complement(meet(X3,X2)),join(X3,meet(complement(meet(X3,X2)),X2))) = meet(join(X3,X2),complement(meet(X3,X2))),
inference(transitivity,[status(thm)],[c110,c124]) ).
cnf(c126,plain,
meet(complement(meet(X3,X2)),join(X3,meet(X2,complement(meet(X3,X2))))) = meet(join(X3,X2),complement(meet(X3,X2))),
inference(transitivity,[status(thm)],[c75,c125]) ).
cnf(c127,plain,
meet(join(X3,X2),complement(meet(X3,X2))) = meet(complement(meet(X3,X2)),join(X3,meet(X2,complement(meet(X3,X2))))),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
join(join(X3,meet(X2,complement(meet(X3,X2)))),meet(join(X3,X2),complement(meet(X3,X2)))) = join(join(X3,meet(X2,complement(meet(X3,X2)))),meet(complement(meet(X3,X2)),join(X3,meet(X2,complement(meet(X3,X2)))))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
join(join(X3,meet(X2,complement(meet(X3,X2)))),meet(complement(meet(X3,X2)),join(X3,meet(X2,complement(meet(X3,X2)))))) = join(X3,meet(X2,complement(meet(X3,X2)))),
inference(substitution,[status(thm)],[c55]) ).
cnf(c130,plain,
join(join(X3,meet(X2,complement(meet(X3,X2)))),meet(join(X3,X2),complement(meet(X3,X2)))) = join(X3,meet(X2,complement(meet(X3,X2)))),
inference(transitivity,[status(thm)],[c128,c129]) ).
cnf(c131,plain,
join(X3,join(meet(X2,complement(meet(X3,X2))),meet(join(X3,X2),complement(meet(X3,X2))))) = join(X3,meet(X2,complement(meet(X3,X2)))),
inference(transitivity,[status(thm)],[c71,c130]) ).
cnf(c132,plain,
join(X3,meet(complement(meet(X3,X2)),join(X2,X3))) = join(X3,meet(X2,complement(meet(X3,X2)))),
inference(transitivity,[status(thm)],[c68,c131]) ).
cnf(c133,plain,
join(X3,meet(join(X2,X3),complement(meet(X3,X2)))) = join(X3,meet(X2,complement(meet(X3,X2)))),
inference(transitivity,[status(thm)],[c15,c132]) ).
cnf(c134,plain,
join(X3,meet(join(X3,X2),complement(meet(X3,X2)))) = join(X3,meet(X2,complement(meet(X3,X2)))),
inference(transitivity,[status(thm)],[c11,c133]) ).
cnf(c135,plain,
join(b,meet(join(b,complement(a)),complement(meet(b,complement(a))))) = join(b,meet(complement(a),complement(meet(b,complement(a))))),
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
join(b,meet(complement(a),complement(meet(b,complement(a))))) = join(b,meet(join(b,complement(a)),complement(meet(b,complement(a))))),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
join(complement(a),b) = join(b,complement(a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c138,plain,
join(b,complement(a)) = join(complement(a),b),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
join(X2,a) = join(a,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c140,plain,
join(a,X2) = join(X2,a),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
join(b,join(a,X2)) = join(b,join(X2,a)),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
join(a,X2) = join(X2,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c143,plain,
join(X2,a) = join(a,X2),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
join(b,join(X2,a)) = join(b,join(a,X2)),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
join(join(b,a),X2) = join(b,join(a,X2)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c146,plain,
join(b,join(a,X2)) = join(join(b,a),X2),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,axiom,
meet(b,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c148,plain,
a = meet(b,a),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
join(b,a) = join(b,meet(b,a)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
join(b,meet(b,a)) = b,
inference(substitution,[status(thm)],[c53]) ).
cnf(c151,plain,
join(b,a) = b,
inference(transitivity,[status(thm)],[c149,c150]) ).
cnf(c152,plain,
join(join(b,a),X2) = join(b,X2),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
join(b,X2) = join(X2,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c154,plain,
join(join(b,a),X2) = join(X2,b),
inference(transitivity,[status(thm)],[c152,c153]) ).
cnf(c155,plain,
join(b,join(a,X2)) = join(X2,b),
inference(transitivity,[status(thm)],[c146,c154]) ).
cnf(c156,plain,
join(b,join(X2,a)) = join(X2,b),
inference(transitivity,[status(thm)],[c144,c155]) ).
cnf(c157,plain,
join(b,join(a,X2)) = join(X2,b),
inference(transitivity,[status(thm)],[c141,c156]) ).
cnf(c158,plain,
join(b,join(a,complement(a))) = join(complement(a),b),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
join(complement(a),b) = join(b,join(a,complement(a))),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
join(a,complement(a)) = one,
inference(substitution,[status(thm)],[c111]) ).
cnf(c161,plain,
join(b,join(a,complement(a))) = join(b,one),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
join(one,X2) = join(X2,one),
inference(substitution,[status(thm)],[c2]) ).
cnf(c163,plain,
join(X2,one) = join(one,X2),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
meet(X2,one) = meet(one,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c165,plain,
meet(one,X2) = meet(X2,one),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
meet(one,X2) = X2,
inference(transitivity,[status(thm)],[c165,c119]) ).
cnf(c167,plain,
X2 = meet(one,X2),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
join(one,X2) = join(one,meet(one,X2)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
join(one,meet(one,X2)) = one,
inference(substitution,[status(thm)],[c53]) ).
cnf(c170,plain,
join(one,X2) = one,
inference(transitivity,[status(thm)],[c168,c169]) ).
cnf(c171,plain,
join(X2,one) = one,
inference(transitivity,[status(thm)],[c163,c170]) ).
cnf(c172,plain,
join(b,one) = one,
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
join(b,join(a,complement(a))) = one,
inference(transitivity,[status(thm)],[c161,c172]) ).
cnf(c174,plain,
join(complement(a),b) = one,
inference(transitivity,[status(thm)],[c159,c173]) ).
cnf(c175,plain,
join(b,complement(a)) = one,
inference(transitivity,[status(thm)],[c138,c174]) ).
cnf(c176,plain,
meet(join(b,complement(a)),complement(meet(b,complement(a)))) = meet(one,complement(meet(b,complement(a)))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
join(b,meet(join(b,complement(a)),complement(meet(b,complement(a))))) = join(b,meet(one,complement(meet(b,complement(a))))),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
meet(one,complement(meet(b,complement(a)))) = complement(meet(b,complement(a))),
inference(substitution,[status(thm)],[c166]) ).
cnf(c179,plain,
join(b,meet(one,complement(meet(b,complement(a))))) = join(b,complement(meet(b,complement(a)))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
join(X2,meet(X4,X3)) = join(meet(X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c181,plain,
join(meet(X4,X3),X2) = join(X2,meet(X4,X3)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
join(X4,join(meet(X4,X3),X2)) = join(X4,join(X2,meet(X4,X3))),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
join(meet(X4,X2),X3) = join(X3,meet(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c184,plain,
join(X3,meet(X4,X2)) = join(meet(X4,X2),X3),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
join(X4,join(X3,meet(X4,X2))) = join(X4,join(meet(X4,X2),X3)),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
join(join(X4,meet(X4,X2)),X3) = join(X4,join(meet(X4,X2),X3)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c187,plain,
join(X4,join(meet(X4,X2),X3)) = join(join(X4,meet(X4,X2)),X3),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c53]) ).
cnf(c189,plain,
join(join(X4,meet(X4,X2)),X3) = join(X4,X3),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
join(X4,join(meet(X4,X2),X3)) = join(X4,X3),
inference(transitivity,[status(thm)],[c187,c189]) ).
cnf(c191,plain,
join(X4,join(X3,meet(X4,X2))) = join(X4,X3),
inference(transitivity,[status(thm)],[c185,c190]) ).
cnf(c192,plain,
join(X4,join(X2,meet(X4,X3))) = join(X4,X2),
inference(substitution,[status(thm)],[c191]) ).
cnf(c193,plain,
join(X4,join(meet(X4,X3),X2)) = join(X4,X2),
inference(transitivity,[status(thm)],[c182,c192]) ).
cnf(c194,plain,
join(X3,join(meet(X3,X2),complement(meet(X3,X2)))) = join(X3,complement(meet(X3,X2))),
inference(substitution,[status(thm)],[c193]) ).
cnf(c195,plain,
join(X3,complement(meet(X3,X2))) = join(X3,join(meet(X3,X2),complement(meet(X3,X2)))),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
join(meet(X3,X2),complement(meet(X3,X2))) = one,
inference(substitution,[status(thm)],[c111]) ).
cnf(c197,plain,
join(X3,join(meet(X3,X2),complement(meet(X3,X2)))) = join(X3,one),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
join(X3,join(meet(X3,X2),complement(meet(X3,X2)))) = one,
inference(transitivity,[status(thm)],[c197,c171]) ).
cnf(c199,plain,
join(X3,complement(meet(X3,X2))) = one,
inference(transitivity,[status(thm)],[c195,c198]) ).
cnf(c200,plain,
join(b,complement(meet(b,complement(a)))) = one,
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
join(b,meet(one,complement(meet(b,complement(a))))) = one,
inference(transitivity,[status(thm)],[c179,c200]) ).
cnf(c202,plain,
join(b,meet(join(b,complement(a)),complement(meet(b,complement(a))))) = one,
inference(transitivity,[status(thm)],[c177,c201]) ).
cnf(c203,plain,
join(b,meet(complement(a),complement(meet(b,complement(a))))) = one,
inference(transitivity,[status(thm)],[c136,c202]) ).
cnf(c204,plain,
ifeq(join(b,meet(complement(a),complement(meet(b,complement(a))))),one,ifeq(meet(b,meet(complement(a),complement(meet(b,complement(a))))),zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))),meet(complement(a),complement(meet(b,complement(a))))) = ifeq(one,one,ifeq(meet(b,meet(complement(a),complement(meet(b,complement(a))))),zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))),meet(complement(a),complement(meet(b,complement(a))))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c206,plain,
ifeq(one,one,ifeq(meet(b,meet(complement(a),complement(meet(b,complement(a))))),zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))),meet(complement(a),complement(meet(b,complement(a))))) = ifeq(meet(b,meet(complement(a),complement(meet(b,complement(a))))),zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))),
inference(substitution,[status(thm)],[c205]) ).
cnf(c207,plain,
meet(meet(X3,X2),complement(meet(X3,X2))) = meet(X3,meet(X2,complement(meet(X3,X2)))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c208,plain,
meet(X3,meet(X2,complement(meet(X3,X2)))) = meet(meet(X3,X2),complement(meet(X3,X2))),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,axiom,
meet(X2,complement(X2)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_meet) ).
cnf(c210,plain,
meet(meet(X3,X2),complement(meet(X3,X2))) = zero,
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
meet(X3,meet(X2,complement(meet(X3,X2)))) = zero,
inference(transitivity,[status(thm)],[c208,c210]) ).
cnf(c212,plain,
meet(b,meet(complement(a),complement(meet(b,complement(a))))) = zero,
inference(substitution,[status(thm)],[c211]) ).
cnf(c213,plain,
ifeq(meet(b,meet(complement(a),complement(meet(b,complement(a))))),zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))) = ifeq(zero,zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
ifeq(zero,zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))) = complement(b),
inference(substitution,[status(thm)],[c205]) ).
cnf(c215,plain,
ifeq(meet(b,meet(complement(a),complement(meet(b,complement(a))))),zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))) = complement(b),
inference(transitivity,[status(thm)],[c213,c214]) ).
cnf(c216,plain,
ifeq(one,one,ifeq(meet(b,meet(complement(a),complement(meet(b,complement(a))))),zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))),meet(complement(a),complement(meet(b,complement(a))))) = complement(b),
inference(transitivity,[status(thm)],[c206,c215]) ).
cnf(c217,plain,
ifeq(join(b,meet(complement(a),complement(meet(b,complement(a))))),one,ifeq(meet(b,meet(complement(a),complement(meet(b,complement(a))))),zero,complement(b),meet(complement(a),complement(meet(b,complement(a))))),meet(complement(a),complement(meet(b,complement(a))))) = complement(b),
inference(transitivity,[status(thm)],[c204,c216]) ).
cnf(c218,plain,
meet(complement(a),complement(meet(b,complement(a)))) = complement(b),
inference(transitivity,[status(thm)],[c7,c217]) ).
cnf(c219,plain,
complement(b) = meet(complement(a),complement(meet(b,complement(a)))),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
join(complement(a),complement(b)) = join(complement(a),meet(complement(a),complement(meet(b,complement(a))))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
join(complement(a),meet(complement(a),complement(meet(b,complement(a))))) = complement(a),
inference(substitution,[status(thm)],[c53]) ).
cnf(c222,plain,
join(complement(a),complement(b)) = complement(a),
inference(transitivity,[status(thm)],[c220,c221]) ).
cnf(c223,plain,
join(complement(b),complement(a)) = complement(a),
inference(transitivity,[status(thm)],[c4,c222]) ).
cnf(c224,plain,
$false,
inference(resolution,[status(thm)],[c1,c223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT224-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n010.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 14:07:16 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 77.84/10.41 Command-line arguments: --no-flatten-goal
% 77.84/10.41
% 77.84/10.41 % SZS status Unsatisfiable
% 77.84/10.41
% 77.84/10.42 % SZS output start CNFRefutation
% See solution above
% 78.54/10.52
% 78.54/10.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------