%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT241-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 11:44:36 AM UTC 2026
% Result : Unsatisfiable 2.38s 0.70s
% Output : CNFRefutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of clauses : 166 ( 166 unt; 0 nHn; 32 RR)
% Number of literals : 166 ( 165 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 263 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c2,axiom,
ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_join_complement) ).
cnf(c3,plain,
ifeq(join(a,join(complement(b),complement(a))),one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = join(complement(b),complement(a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
join(complement(b),complement(a)) = ifeq(join(a,join(complement(b),complement(a))),one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
join(X2,Y2) = join(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c6,plain,
join(meet(X4,X2),X3) = join(X3,meet(X4,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
join(X3,meet(X4,X2)) = join(meet(X4,X2),X3),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
join(X4,join(X3,meet(X4,X2))) = join(X4,join(meet(X4,X2),X3)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
join(join(X2,Y2),Z) = join(X2,join(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(c10,plain,
join(join(X4,meet(X4,X2)),X3) = join(X4,join(meet(X4,X2),X3)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
join(X4,join(meet(X4,X2),X3)) = join(join(X4,meet(X4,X2)),X3),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,axiom,
join(X2,meet(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
cnf(c13,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
join(join(X4,meet(X4,X2)),X3) = join(X4,X3),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
join(X4,join(meet(X4,X2),X3)) = join(X4,X3),
inference(transitivity,[status(thm)],[c11,c14]) ).
cnf(c16,plain,
join(X4,join(X3,meet(X4,X2))) = join(X4,X3),
inference(transitivity,[status(thm)],[c8,c15]) ).
cnf(c17,plain,
join(X4,X3) = join(X4,join(X3,meet(X4,X2))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
meet(X2,join(X4,X3)) = meet(X2,join(X4,join(X3,meet(X4,X2)))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
join(X3,meet(X2,join(X4,X3))) = join(X3,meet(X2,join(X4,join(X3,meet(X4,X2))))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
meet(X4,join(X3,meet(X2,join(X4,X3)))) = meet(X4,join(X3,meet(X2,join(X4,join(X3,meet(X4,X2)))))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,axiom,
meet(X2,join(Y2,meet(Z2,join(X2,U)))) = meet(X2,join(Y2,join(meet(X2,Z2),meet(Z2,U)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H51) ).
cnf(c22,plain,
meet(X4,join(X3,meet(X2,join(X4,join(X3,meet(X4,X2)))))) = meet(X4,join(X3,join(meet(X4,X2),meet(X2,join(X3,meet(X4,X2)))))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c24,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
meet(X2,join(X4,X3)) = meet(X2,join(X3,X4)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
join(X3,meet(X2,join(X4,X3))) = join(X3,meet(X2,join(X3,X4))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
join(X4,join(X3,meet(X2,join(X4,X3)))) = join(X4,join(X3,meet(X2,join(X3,X4)))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,axiom,
meet(X2,Y2) = meet(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c29,plain,
meet(join(X3,X4),X2) = meet(X2,join(X3,X4)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
meet(X2,join(X3,X4)) = meet(join(X3,X4),X2),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
join(X3,meet(X2,join(X3,X4))) = join(X3,meet(join(X3,X4),X2)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
join(X4,join(X3,meet(X2,join(X3,X4)))) = join(X4,join(X3,meet(join(X3,X4),X2))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
join(join(X3,X2),X4) = join(X4,join(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c34,plain,
join(X4,join(X3,X2)) = join(join(X3,X2),X4),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
join(join(X3,X2),X4) = join(X3,join(X2,X4)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c36,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c37,plain,
join(X3,join(X2,X4)) = join(X3,join(X4,X2)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
join(join(X3,X2),X4) = join(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
join(X4,join(X3,X2)) = join(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c34,c38]) ).
cnf(c40,plain,
join(X3,join(X4,meet(join(X3,X4),X2))) = join(X4,join(X3,meet(join(X3,X4),X2))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
join(X4,join(X3,meet(join(X3,X4),X2))) = join(X3,join(X4,meet(join(X3,X4),X2))),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
join(join(X3,X4),meet(join(X3,X4),X2)) = join(X3,join(X4,meet(join(X3,X4),X2))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c43,plain,
join(X3,join(X4,meet(join(X3,X4),X2))) = join(join(X3,X4),meet(join(X3,X4),X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
join(join(X3,X4),meet(join(X3,X4),X2)) = join(X3,X4),
inference(substitution,[status(thm)],[c12]) ).
cnf(c45,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c46,plain,
join(join(X3,X4),meet(join(X3,X4),X2)) = join(X4,X3),
inference(transitivity,[status(thm)],[c44,c45]) ).
cnf(c47,plain,
join(X3,join(X4,meet(join(X3,X4),X2))) = join(X4,X3),
inference(transitivity,[status(thm)],[c43,c46]) ).
cnf(c48,plain,
join(X4,join(X3,meet(join(X3,X4),X2))) = join(X4,X3),
inference(transitivity,[status(thm)],[c41,c47]) ).
cnf(c49,plain,
join(X4,join(X3,meet(X2,join(X3,X4)))) = join(X4,X3),
inference(transitivity,[status(thm)],[c32,c48]) ).
cnf(c50,plain,
join(X4,join(X3,meet(X2,join(X4,X3)))) = join(X4,X3),
inference(transitivity,[status(thm)],[c27,c49]) ).
cnf(c51,plain,
join(X3,join(meet(X4,X2),meet(X2,join(X3,meet(X4,X2))))) = join(X3,meet(X4,X2)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
meet(X4,join(X3,join(meet(X4,X2),meet(X2,join(X3,meet(X4,X2)))))) = meet(X4,join(X3,meet(X4,X2))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
meet(X4,join(X3,meet(X2,join(X4,join(X3,meet(X4,X2)))))) = meet(X4,join(X3,meet(X4,X2))),
inference(transitivity,[status(thm)],[c22,c52]) ).
cnf(c54,plain,
meet(X4,join(X3,meet(X2,join(X4,X3)))) = meet(X4,join(X3,meet(X4,X2))),
inference(transitivity,[status(thm)],[c20,c53]) ).
cnf(c55,plain,
meet(X3,join(complement(X3),meet(X2,join(X3,complement(X3))))) = meet(X3,join(complement(X3),meet(X3,X2))),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
meet(X3,join(complement(X3),meet(X3,X2))) = meet(X3,join(complement(X3),meet(X2,join(X3,complement(X3))))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,axiom,
join(X2,complement(X2)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c58,plain,
meet(X2,join(X3,complement(X3))) = meet(X2,one),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
join(complement(X3),meet(X2,join(X3,complement(X3)))) = join(complement(X3),meet(X2,one)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
meet(X3,join(complement(X3),meet(X2,join(X3,complement(X3))))) = meet(X3,join(complement(X3),meet(X2,one))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
one = join(X2,complement(X2)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c62,plain,
meet(X2,one) = meet(X2,join(X2,complement(X2))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,axiom,
meet(X2,join(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
cnf(c64,plain,
meet(X2,join(X2,complement(X2))) = X2,
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
meet(X2,one) = X2,
inference(transitivity,[status(thm)],[c62,c64]) ).
cnf(c66,plain,
join(complement(X3),meet(X2,one)) = join(complement(X3),X2),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
meet(X3,join(complement(X3),meet(X2,one))) = meet(X3,join(complement(X3),X2)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
join(complement(X3),X2) = join(X2,complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c69,plain,
meet(X3,join(complement(X3),X2)) = meet(X3,join(X2,complement(X3))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
meet(X3,join(complement(X3),meet(X2,one))) = meet(X3,join(X2,complement(X3))),
inference(transitivity,[status(thm)],[c67,c69]) ).
cnf(c71,plain,
meet(X3,join(complement(X3),meet(X2,join(X3,complement(X3))))) = meet(X3,join(X2,complement(X3))),
inference(transitivity,[status(thm)],[c60,c70]) ).
cnf(c72,plain,
meet(X3,join(complement(X3),meet(X3,X2))) = meet(X3,join(X2,complement(X3))),
inference(transitivity,[status(thm)],[c56,c71]) ).
cnf(c73,plain,
meet(a,join(complement(a),meet(a,complement(b)))) = meet(a,join(complement(b),complement(a))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(a),meet(a,complement(b)))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
meet(complement(b),a) = meet(a,complement(b)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c76,plain,
meet(a,complement(b)) = meet(complement(b),a),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
meet(X2,a) = meet(a,X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c78,plain,
meet(a,X2) = meet(X2,a),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
meet(b,meet(a,X2)) = meet(b,meet(X2,a)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
meet(a,X2) = meet(X2,a),
inference(substitution,[status(thm)],[c28]) ).
cnf(c81,plain,
meet(X2,a) = meet(a,X2),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
meet(b,meet(X2,a)) = meet(b,meet(a,X2)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,axiom,
meet(meet(X2,Y2),Z2) = meet(X2,meet(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(c84,plain,
meet(meet(b,a),X2) = meet(b,meet(a,X2)),
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
meet(b,meet(a,X2)) = meet(meet(b,a),X2),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,axiom,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c87,plain,
meet(meet(b,a),X2) = meet(a,X2),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
meet(a,X2) = meet(X2,a),
inference(substitution,[status(thm)],[c28]) ).
cnf(c89,plain,
meet(meet(b,a),X2) = meet(X2,a),
inference(transitivity,[status(thm)],[c87,c88]) ).
cnf(c90,plain,
meet(b,meet(a,X2)) = meet(X2,a),
inference(transitivity,[status(thm)],[c85,c89]) ).
cnf(c91,plain,
meet(b,meet(X2,a)) = meet(X2,a),
inference(transitivity,[status(thm)],[c82,c90]) ).
cnf(c92,plain,
meet(b,meet(a,X2)) = meet(X2,a),
inference(transitivity,[status(thm)],[c79,c91]) ).
cnf(c93,plain,
meet(b,meet(a,complement(b))) = meet(complement(b),a),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
meet(complement(b),a) = meet(b,meet(a,complement(b))),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
meet(complement(X3),X2) = meet(X2,complement(X3)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c96,plain,
meet(X2,complement(X3)) = meet(complement(X3),X2),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
meet(X3,meet(X2,complement(X3))) = meet(X3,meet(complement(X3),X2)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
meet(meet(X3,complement(X3)),X2) = meet(X3,meet(complement(X3),X2)),
inference(substitution,[status(thm)],[c83]) ).
cnf(c99,plain,
meet(X3,meet(complement(X3),X2)) = meet(meet(X3,complement(X3)),X2),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,axiom,
meet(X2,complement(X2)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c101,plain,
meet(meet(X3,complement(X3)),X2) = meet(zero,X2),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
meet(X2,zero) = meet(zero,X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c103,plain,
meet(zero,X2) = meet(X2,zero),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
meet(zero,X2) = meet(X2,zero),
inference(substitution,[status(thm)],[c28]) ).
cnf(c105,plain,
meet(X2,zero) = meet(zero,X2),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
join(X2,zero) = join(zero,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c107,plain,
join(zero,X2) = join(X2,zero),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
zero = meet(X2,complement(X2)),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c109,plain,
join(X2,zero) = join(X2,meet(X2,complement(X2))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
join(X2,meet(X2,complement(X2))) = X2,
inference(substitution,[status(thm)],[c12]) ).
cnf(c111,plain,
join(X2,zero) = X2,
inference(transitivity,[status(thm)],[c109,c110]) ).
cnf(c112,plain,
join(zero,X2) = X2,
inference(transitivity,[status(thm)],[c107,c111]) ).
cnf(c113,plain,
join(zero,meet(zero,X2)) = meet(zero,X2),
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
meet(zero,X2) = join(zero,meet(zero,X2)),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
join(zero,meet(zero,X2)) = zero,
inference(substitution,[status(thm)],[c12]) ).
cnf(c116,plain,
meet(zero,X2) = zero,
inference(transitivity,[status(thm)],[c114,c115]) ).
cnf(c117,plain,
meet(X2,zero) = zero,
inference(transitivity,[status(thm)],[c105,c116]) ).
cnf(c118,plain,
meet(zero,X2) = zero,
inference(transitivity,[status(thm)],[c103,c117]) ).
cnf(c119,plain,
meet(meet(X3,complement(X3)),X2) = zero,
inference(transitivity,[status(thm)],[c101,c118]) ).
cnf(c120,plain,
meet(X3,meet(complement(X3),X2)) = zero,
inference(transitivity,[status(thm)],[c99,c119]) ).
cnf(c121,plain,
meet(X3,meet(X2,complement(X3))) = zero,
inference(transitivity,[status(thm)],[c97,c120]) ).
cnf(c122,plain,
meet(b,meet(a,complement(b))) = zero,
inference(substitution,[status(thm)],[c121]) ).
cnf(c123,plain,
meet(complement(b),a) = zero,
inference(transitivity,[status(thm)],[c94,c122]) ).
cnf(c124,plain,
meet(a,complement(b)) = zero,
inference(transitivity,[status(thm)],[c76,c123]) ).
cnf(c125,plain,
join(complement(a),meet(a,complement(b))) = join(complement(a),zero),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
meet(a,join(complement(a),meet(a,complement(b)))) = meet(a,join(complement(a),zero)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
join(complement(a),zero) = complement(a),
inference(substitution,[status(thm)],[c111]) ).
cnf(c128,plain,
meet(a,join(complement(a),zero)) = meet(a,complement(a)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
meet(a,complement(a)) = zero,
inference(substitution,[status(thm)],[c100]) ).
cnf(c130,plain,
meet(a,join(complement(a),zero)) = zero,
inference(transitivity,[status(thm)],[c128,c129]) ).
cnf(c131,plain,
meet(a,join(complement(a),meet(a,complement(b)))) = zero,
inference(transitivity,[status(thm)],[c126,c130]) ).
cnf(c132,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(transitivity,[status(thm)],[c74,c131]) ).
cnf(c133,plain,
ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))) = ifeq(zero,zero,complement(a),join(complement(b),complement(a))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
ifeq(join(a,join(complement(b),complement(a))),one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = ifeq(join(a,join(complement(b),complement(a))),one,ifeq(zero,zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
join(complement(X3),X2) = join(X2,complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c136,plain,
join(X2,complement(X3)) = join(complement(X3),X2),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
join(X3,join(X2,complement(X3))) = join(X3,join(complement(X3),X2)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
join(join(X3,complement(X3)),X2) = join(X3,join(complement(X3),X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c139,plain,
join(X3,join(complement(X3),X2)) = join(join(X3,complement(X3)),X2),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
join(join(X3,complement(X3)),X2) = join(one,X2),
inference(congruence,[status(thm)],[c57]) ).
cnf(c141,plain,
join(X2,one) = join(one,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c142,plain,
join(one,X2) = join(X2,one),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
join(one,X2) = join(X2,one),
inference(substitution,[status(thm)],[c5]) ).
cnf(c144,plain,
join(X2,one) = join(one,X2),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
meet(X2,one) = meet(one,X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c146,plain,
meet(one,X2) = meet(X2,one),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
meet(one,X2) = X2,
inference(transitivity,[status(thm)],[c146,c65]) ).
cnf(c148,plain,
X2 = meet(one,X2),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
join(one,X2) = join(one,meet(one,X2)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
join(one,meet(one,X2)) = one,
inference(substitution,[status(thm)],[c12]) ).
cnf(c151,plain,
join(one,X2) = one,
inference(transitivity,[status(thm)],[c149,c150]) ).
cnf(c152,plain,
join(X2,one) = one,
inference(transitivity,[status(thm)],[c144,c151]) ).
cnf(c153,plain,
join(one,X2) = one,
inference(transitivity,[status(thm)],[c142,c152]) ).
cnf(c154,plain,
join(join(X3,complement(X3)),X2) = one,
inference(transitivity,[status(thm)],[c140,c153]) ).
cnf(c155,plain,
join(X3,join(complement(X3),X2)) = one,
inference(transitivity,[status(thm)],[c139,c154]) ).
cnf(c156,plain,
join(X3,join(X2,complement(X3))) = one,
inference(transitivity,[status(thm)],[c137,c155]) ).
cnf(c157,plain,
join(a,join(complement(b),complement(a))) = one,
inference(substitution,[status(thm)],[c156]) ).
cnf(c158,plain,
ifeq(join(a,join(complement(b),complement(a))),one,ifeq(zero,zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = ifeq(one,one,ifeq(zero,zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c160,plain,
ifeq(one,one,ifeq(zero,zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = ifeq(zero,zero,complement(a),join(complement(b),complement(a))),
inference(substitution,[status(thm)],[c159]) ).
cnf(c161,plain,
ifeq(zero,zero,complement(a),join(complement(b),complement(a))) = complement(a),
inference(substitution,[status(thm)],[c159]) ).
cnf(c162,plain,
ifeq(one,one,ifeq(zero,zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = complement(a),
inference(transitivity,[status(thm)],[c160,c161]) ).
cnf(c163,plain,
ifeq(join(a,join(complement(b),complement(a))),one,ifeq(zero,zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = complement(a),
inference(transitivity,[status(thm)],[c158,c162]) ).
cnf(c164,plain,
ifeq(join(a,join(complement(b),complement(a))),one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = complement(a),
inference(transitivity,[status(thm)],[c134,c163]) ).
cnf(c165,plain,
join(complement(b),complement(a)) = complement(a),
inference(transitivity,[status(thm)],[c4,c164]) ).
cnf(c166,plain,
$false,
inference(resolution,[status(thm)],[c1,c165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT241-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sun Sep 27 14:07:34 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.38/0.70 Command-line arguments: --no-flatten-goal
% 2.38/0.70
% 2.38/0.70 % SZS status Unsatisfiable
% 2.38/0.70
% 2.38/0.70 % SZS output start CNFRefutation
% See solution above
% 2.89/0.74
% 2.89/0.74 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------