%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT005-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 11:42:48 AM UTC 2026
% Result : Unsatisfiable 6.19s 1.21s
% Output : CNFRefutation 7.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of clauses : 217 ( 217 unt; 0 nHn; 51 RR)
% Number of literals : 217 ( 216 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 : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 431 ( 52 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma) ).
cnf(c2,axiom,
join(X,Y) = join(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c3,plain,
join(meet(join(X4,X3),join(X4,X2)),X4) = join(X4,meet(join(X4,X3),join(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
join(X4,meet(join(X4,X3),join(X4,X2))) = join(meet(join(X4,X3),join(X4,X2)),X4),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
meet(X2,Y2) = meet(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c6,plain,
meet(meet(X2,X4),X3) = meet(X3,meet(X2,X4)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
meet(X3,meet(X2,X4)) = meet(meet(X2,X4),X3),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c9,plain,
meet(meet(X2,X4),X3) = meet(meet(X4,X2),X3),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
meet(meet(X2,Y2),Z) = meet(X2,meet(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(c11,plain,
meet(meet(X4,X2),X3) = meet(X4,meet(X2,X3)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c13,plain,
meet(X4,meet(X2,X3)) = meet(X4,meet(X3,X2)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
meet(meet(X4,X2),X3) = meet(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
meet(meet(X2,X4),X3) = meet(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c9,c14]) ).
cnf(c16,plain,
meet(X3,meet(X2,X4)) = meet(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c7,c15]) ).
cnf(c17,plain,
meet(X4,meet(join(X4,X3),join(X4,X2))) = meet(join(X4,X2),meet(X4,join(X4,X3))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,axiom,
meet(X2,join(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
cnf(c19,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
meet(join(X4,X2),meet(X4,join(X4,X3))) = meet(join(X4,X2),X4),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
meet(join(X3,X2),X3) = meet(X3,join(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c22,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c18]) ).
cnf(c23,plain,
meet(join(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
meet(join(X4,X2),meet(X4,join(X4,X3))) = X4,
inference(transitivity,[status(thm)],[c20,c23]) ).
cnf(c25,plain,
meet(X4,meet(join(X4,X3),join(X4,X2))) = X4,
inference(transitivity,[status(thm)],[c17,c24]) ).
cnf(c26,plain,
X4 = meet(X4,meet(join(X4,X3),join(X4,X2))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
join(meet(join(X4,X3),join(X4,X2)),X4) = join(meet(join(X4,X3),join(X4,X2)),meet(X4,meet(join(X4,X3),join(X4,X2)))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c29,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
join(X3,meet(X2,X3)) = join(X3,meet(X3,X2)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,axiom,
join(X2,meet(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
cnf(c32,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
join(X3,meet(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c30,c32]) ).
cnf(c34,plain,
join(meet(join(X4,X3),join(X4,X2)),meet(X4,meet(join(X4,X3),join(X4,X2)))) = meet(join(X4,X3),join(X4,X2)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
join(meet(join(X4,X3),join(X4,X2)),X4) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c27,c34]) ).
cnf(c36,plain,
join(X4,meet(join(X4,X3),join(X4,X2))) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c4,c35]) ).
cnf(c37,plain,
join(r1,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))) = meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))) = join(r1,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
join(meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))),r1) = join(r1,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c40,plain,
join(r1,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))) = join(meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))),r1),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,axiom,
ifeq3(meet(X2,Z2),X2,meet(Z2,join(X2,Y2)),join(X2,meet(Y2,Z2))) = join(X2,meet(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular) ).
cnf(c42,plain,
ifeq3(meet(X4,join(X4,X2)),X4,meet(join(X4,X2),join(X4,X3)),join(X4,meet(X3,join(X4,X2)))) = join(X4,meet(X3,join(X4,X2))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
join(X4,meet(X3,join(X4,X2))) = ifeq3(meet(X4,join(X4,X2)),X4,meet(join(X4,X2),join(X4,X3)),join(X4,meet(X3,join(X4,X2)))),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c18]) ).
cnf(c45,plain,
ifeq3(meet(X4,join(X4,X2)),X4,meet(join(X4,X2),join(X4,X3)),join(X4,meet(X3,join(X4,X2)))) = ifeq3(X4,X4,meet(join(X4,X2),join(X4,X3)),join(X4,meet(X3,join(X4,X2)))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
ifeq3(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c47,plain,
ifeq3(X4,X4,meet(join(X4,X2),join(X4,X3)),join(X4,meet(X3,join(X4,X2)))) = meet(join(X4,X2),join(X4,X3)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
meet(join(X4,X2),join(X4,X3)) = meet(join(X4,X3),join(X4,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c49,plain,
ifeq3(X4,X4,meet(join(X4,X2),join(X4,X3)),join(X4,meet(X3,join(X4,X2)))) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c47,c48]) ).
cnf(c50,plain,
ifeq3(meet(X4,join(X4,X2)),X4,meet(join(X4,X2),join(X4,X3)),join(X4,meet(X3,join(X4,X2)))) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c45,c49]) ).
cnf(c51,plain,
join(X4,meet(X3,join(X4,X2))) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c43,c50]) ).
cnf(c52,plain,
join(r1,meet(meet(r2,b),join(r1,a))) = meet(join(r1,meet(r2,b)),join(r1,a)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
meet(join(r1,meet(r2,b)),join(r1,a)) = join(r1,meet(meet(r2,b),join(r1,a))),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
meet(join(r1,a),meet(r2,b)) = meet(meet(r2,b),join(r1,a)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c55,plain,
meet(meet(r2,b),join(r1,a)) = meet(join(r1,a),meet(r2,b)),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
meet(r2,meet(b,join(r1,a))) = meet(join(r1,a),meet(r2,b)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c57,plain,
meet(join(r1,a),meet(r2,b)) = meet(r2,meet(b,join(r1,a))),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
meet(meet(X4,X2),X3) = meet(X3,meet(X4,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c59,plain,
meet(X3,meet(X4,X2)) = meet(meet(X4,X2),X3),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
meet(meet(X4,X2),X3) = meet(X4,meet(X2,X3)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c61,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c62,plain,
meet(X4,meet(X2,X3)) = meet(X4,meet(X3,X2)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
meet(meet(X4,X2),X3) = meet(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c60,c62]) ).
cnf(c64,plain,
meet(X3,meet(X4,X2)) = meet(X4,meet(X3,X2)),
inference(transitivity,[status(thm)],[c59,c63]) ).
cnf(c65,plain,
meet(X4,meet(X3,join(X2,X4))) = meet(X3,meet(X4,join(X2,X4))),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c67,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
meet(X3,join(X2,X3)) = meet(X3,join(X3,X2)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c18]) ).
cnf(c70,plain,
meet(X3,join(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
meet(X3,meet(X4,join(X2,X4))) = meet(X3,X4),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c73,plain,
meet(X3,meet(X4,join(X2,X4))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
meet(X4,meet(X3,join(X2,X4))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c65,c73]) ).
cnf(c75,plain,
meet(b,meet(join(r1,a),join(a,b))) = meet(b,join(r1,a)),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
meet(b,join(r1,a)) = meet(b,meet(join(r1,a),join(a,b))),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
join(a,r1) = join(r1,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c78,plain,
join(r1,a) = join(a,r1),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
meet(join(r1,a),join(a,b)) = meet(join(a,r1),join(a,b)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
join(a,meet(r1,join(a,b))) = meet(join(a,r1),join(a,b)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c81,plain,
meet(join(a,r1),join(a,b)) = join(a,meet(r1,join(a,b))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,axiom,
ifeq(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(c83,plain,
ifeq(true,true,meet(r1,join(a,b)),n0) = meet(r1,join(a,b)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
meet(r1,join(a,b)) = ifeq(true,true,meet(r1,join(a,b)),n0),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,axiom,
complement(r1,join(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c86,plain,
true = complement(r1,join(a,b)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
ifeq(true,true,meet(r1,join(a,b)),n0) = ifeq(complement(r1,join(a,b)),true,meet(r1,join(a,b)),n0),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,axiom,
ifeq(complement(X2,Y2),true,meet(X2,Y2),n0) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).
cnf(c89,plain,
ifeq(complement(r1,join(a,b)),true,meet(r1,join(a,b)),n0) = n0,
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
ifeq(true,true,meet(r1,join(a,b)),n0) = n0,
inference(transitivity,[status(thm)],[c87,c89]) ).
cnf(c91,plain,
meet(r1,join(a,b)) = n0,
inference(transitivity,[status(thm)],[c84,c90]) ).
cnf(c92,plain,
join(a,meet(r1,join(a,b))) = join(a,n0),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,axiom,
join(X2,n0) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).
cnf(c94,plain,
join(a,n0) = a,
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
join(a,meet(r1,join(a,b))) = a,
inference(transitivity,[status(thm)],[c92,c94]) ).
cnf(c96,plain,
meet(join(a,r1),join(a,b)) = a,
inference(transitivity,[status(thm)],[c81,c95]) ).
cnf(c97,plain,
meet(join(r1,a),join(a,b)) = a,
inference(transitivity,[status(thm)],[c79,c96]) ).
cnf(c98,plain,
meet(b,meet(join(r1,a),join(a,b))) = meet(b,a),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
meet(b,a) = meet(a,b),
inference(substitution,[status(thm)],[c5]) ).
cnf(c100,plain,
meet(b,meet(join(r1,a),join(a,b))) = meet(a,b),
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
meet(b,join(r1,a)) = meet(a,b),
inference(transitivity,[status(thm)],[c76,c100]) ).
cnf(c102,plain,
meet(r2,meet(b,join(r1,a))) = meet(r2,meet(a,b)),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
ifeq(true,true,meet(r2,meet(a,b)),n0) = meet(r2,meet(a,b)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c104,plain,
meet(r2,meet(a,b)) = ifeq(true,true,meet(r2,meet(a,b)),n0),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,axiom,
complement(r2,meet(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c106,plain,
true = complement(r2,meet(a,b)),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
ifeq(true,true,meet(r2,meet(a,b)),n0) = ifeq(complement(r2,meet(a,b)),true,meet(r2,meet(a,b)),n0),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
ifeq(complement(r2,meet(a,b)),true,meet(r2,meet(a,b)),n0) = n0,
inference(substitution,[status(thm)],[c88]) ).
cnf(c109,plain,
ifeq(true,true,meet(r2,meet(a,b)),n0) = n0,
inference(transitivity,[status(thm)],[c107,c108]) ).
cnf(c110,plain,
meet(r2,meet(a,b)) = n0,
inference(transitivity,[status(thm)],[c104,c109]) ).
cnf(c111,plain,
meet(r2,meet(b,join(r1,a))) = n0,
inference(transitivity,[status(thm)],[c102,c110]) ).
cnf(c112,plain,
meet(join(r1,a),meet(r2,b)) = n0,
inference(transitivity,[status(thm)],[c57,c111]) ).
cnf(c113,plain,
meet(meet(r2,b),join(r1,a)) = n0,
inference(transitivity,[status(thm)],[c55,c112]) ).
cnf(c114,plain,
join(r1,meet(meet(r2,b),join(r1,a))) = join(r1,n0),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
join(r1,n0) = r1,
inference(substitution,[status(thm)],[c93]) ).
cnf(c116,plain,
join(r1,meet(meet(r2,b),join(r1,a))) = r1,
inference(transitivity,[status(thm)],[c114,c115]) ).
cnf(c117,plain,
meet(join(r1,meet(r2,b)),join(r1,a)) = r1,
inference(transitivity,[status(thm)],[c53,c116]) ).
cnf(c118,plain,
r1 = meet(join(r1,meet(r2,b)),join(r1,a)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
join(meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))),r1) = join(meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))),meet(join(r1,meet(r2,b)),join(r1,a))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c121,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
join(meet(X4,X3),meet(X4,X2)) = join(meet(X4,X3),meet(X2,X4)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
ifeq3(meet(meet(X4,X3),X4),meet(X4,X3),meet(X4,join(meet(X4,X3),X2)),join(meet(X4,X3),meet(X2,X4))) = join(meet(X4,X3),meet(X2,X4)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c124,plain,
join(meet(X4,X3),meet(X2,X4)) = ifeq3(meet(meet(X4,X3),X4),meet(X4,X3),meet(X4,join(meet(X4,X3),X2)),join(meet(X4,X3),meet(X2,X4))),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
join(X3,meet(X3,X2)) = join(meet(X3,X2),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c126,plain,
join(meet(X3,X2),X3) = join(X3,meet(X3,X2)),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c128,plain,
join(X3,meet(X3,X2)) = join(X3,meet(X2,X3)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
join(X3,meet(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c128,c33]) ).
cnf(c130,plain,
join(meet(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c126,c129]) ).
cnf(c131,plain,
X3 = join(meet(X3,X2),X3),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
meet(meet(X3,X2),X3) = meet(meet(X3,X2),join(meet(X3,X2),X3)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
meet(meet(X3,X2),join(meet(X3,X2),X3)) = meet(X3,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c134,plain,
meet(meet(X3,X2),X3) = meet(X3,X2),
inference(transitivity,[status(thm)],[c132,c133]) ).
cnf(c135,plain,
ifeq3(meet(meet(X4,X3),X4),meet(X4,X3),meet(X4,join(meet(X4,X3),X2)),join(meet(X4,X3),meet(X2,X4))) = ifeq3(meet(X4,X3),meet(X4,X3),meet(X4,join(meet(X4,X3),X2)),join(meet(X4,X3),meet(X2,X4))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
ifeq3(meet(X4,X3),meet(X4,X3),meet(X4,join(meet(X4,X3),X2)),join(meet(X4,X3),meet(X2,X4))) = meet(X4,join(meet(X4,X3),X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c137,plain,
join(meet(X4,X3),X2) = join(X2,meet(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c138,plain,
meet(X4,join(meet(X4,X3),X2)) = meet(X4,join(X2,meet(X4,X3))),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
ifeq3(meet(X4,X3),meet(X4,X3),meet(X4,join(meet(X4,X3),X2)),join(meet(X4,X3),meet(X2,X4))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c136,c138]) ).
cnf(c140,plain,
ifeq3(meet(meet(X4,X3),X4),meet(X4,X3),meet(X4,join(meet(X4,X3),X2)),join(meet(X4,X3),meet(X2,X4))) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c135,c139]) ).
cnf(c141,plain,
join(meet(X4,X3),meet(X2,X4)) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c124,c140]) ).
cnf(c142,plain,
join(meet(X4,X3),meet(X4,X2)) = meet(X4,join(X2,meet(X4,X3))),
inference(transitivity,[status(thm)],[c122,c141]) ).
cnf(c143,plain,
join(meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))),meet(join(r1,meet(r2,b)),join(r1,a))) = meet(join(r1,meet(r2,b)),join(join(r1,a),meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))))),
inference(substitution,[status(thm)],[c142]) ).
cnf(c144,axiom,
join(join(X2,Y2),Z2) = join(X2,join(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(c145,plain,
join(join(r1,a),meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))) = join(r1,join(a,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))))),
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
meet(join(r1,meet(r2,b)),join(join(r1,a),meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))))) = meet(join(r1,meet(r2,b)),join(r1,join(a,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
join(meet(join(X4,X2),join(X4,X5)),X3) = join(X3,meet(join(X4,X2),join(X4,X5))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c148,plain,
join(X4,meet(join(X5,X3),join(X5,X2))) = join(meet(join(X5,X3),join(X5,X2)),X4),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
join(X5,join(X4,meet(join(X5,X3),join(X5,X2)))) = join(X5,join(meet(join(X5,X3),join(X5,X2)),X4)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
join(join(X5,meet(join(X5,X3),join(X5,X2))),X4) = join(X5,join(meet(join(X5,X3),join(X5,X2)),X4)),
inference(substitution,[status(thm)],[c144]) ).
cnf(c151,plain,
join(X5,join(meet(join(X5,X3),join(X5,X2)),X4)) = join(join(X5,meet(join(X5,X3),join(X5,X2))),X4),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
join(join(X5,meet(join(X5,X3),join(X5,X2))),X4) = join(meet(join(X5,X3),join(X5,X2)),X4),
inference(congruence,[status(thm)],[c36]) ).
cnf(c153,plain,
join(meet(join(X5,X3),join(X5,X2)),X4) = join(X4,meet(join(X5,X3),join(X5,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c154,plain,
join(join(X5,meet(join(X5,X3),join(X5,X2))),X4) = join(X4,meet(join(X5,X3),join(X5,X2))),
inference(transitivity,[status(thm)],[c152,c153]) ).
cnf(c155,plain,
join(X5,join(meet(join(X5,X3),join(X5,X2)),X4)) = join(X4,meet(join(X5,X3),join(X5,X2))),
inference(transitivity,[status(thm)],[c151,c154]) ).
cnf(c156,plain,
join(X5,join(X4,meet(join(X5,X3),join(X5,X2)))) = join(X4,meet(join(X5,X3),join(X5,X2))),
inference(transitivity,[status(thm)],[c149,c155]) ).
cnf(c157,plain,
join(r1,join(a,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))))) = join(a,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))),
inference(substitution,[status(thm)],[c156]) ).
cnf(c158,plain,
meet(join(r1,meet(r2,b)),join(r1,join(a,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))))) = meet(join(r1,meet(r2,b)),join(a,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
join(meet(join(X4,X3),join(X4,meet(X2,X5))),X5) = join(X5,meet(join(X4,X3),join(X4,meet(X2,X5)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c160,plain,
join(X5,meet(join(X4,X3),join(X4,meet(X2,X5)))) = join(meet(join(X4,X3),join(X4,meet(X2,X5))),X5),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
join(meet(X2,X4),X3) = join(X3,meet(X2,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c162,plain,
join(X3,meet(X2,X4)) = join(meet(X2,X4),X3),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
join(X4,join(X3,meet(X2,X4))) = join(X4,join(meet(X2,X4),X3)),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
join(join(X4,meet(X2,X4)),X3) = join(X4,join(meet(X2,X4),X3)),
inference(substitution,[status(thm)],[c144]) ).
cnf(c165,plain,
join(X4,join(meet(X2,X4),X3)) = join(join(X4,meet(X2,X4)),X3),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
join(join(X4,meet(X2,X4)),X3) = join(X4,X3),
inference(congruence,[status(thm)],[c33]) ).
cnf(c167,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c168,plain,
join(join(X4,meet(X2,X4)),X3) = join(X3,X4),
inference(transitivity,[status(thm)],[c166,c167]) ).
cnf(c169,plain,
join(X4,join(meet(X2,X4),X3)) = join(X3,X4),
inference(transitivity,[status(thm)],[c165,c168]) ).
cnf(c170,plain,
join(X4,join(X3,meet(X2,X4))) = join(X3,X4),
inference(transitivity,[status(thm)],[c163,c169]) ).
cnf(c171,plain,
join(X5,join(meet(join(X4,X3),join(X4,meet(X2,X5))),meet(X2,X5))) = join(meet(join(X4,X3),join(X4,meet(X2,X5))),X5),
inference(substitution,[status(thm)],[c170]) ).
cnf(c172,plain,
join(meet(join(X4,X3),join(X4,meet(X2,X5))),X5) = join(X5,join(meet(join(X4,X3),join(X4,meet(X2,X5))),meet(X2,X5))),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
join(X2,meet(join(X4,X3),join(X4,X2))) = join(meet(join(X4,X3),join(X4,X2)),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c174,plain,
join(meet(join(X4,X3),join(X4,X2)),X2) = join(X2,meet(join(X4,X3),join(X4,X2))),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
join(X4,join(X2,meet(join(X4,X3),join(X4,X2)))) = join(X2,meet(join(X4,X3),join(X4,X2))),
inference(substitution,[status(thm)],[c156]) ).
cnf(c176,plain,
join(X2,meet(join(X4,X3),join(X4,X2))) = join(X4,join(X2,meet(join(X4,X3),join(X4,X2)))),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
join(join(X4,X2),X3) = join(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c178,plain,
join(X3,join(X4,X2)) = join(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
join(join(X4,X2),X3) = join(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c144]) ).
cnf(c180,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c181,plain,
join(X4,join(X2,X3)) = join(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
join(join(X4,X2),X3) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c179,c181]) ).
cnf(c183,plain,
join(X3,join(X4,X2)) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c178,c182]) ).
cnf(c184,plain,
join(X2,join(X4,X3)) = join(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c183]) ).
cnf(c185,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c186,plain,
join(X4,join(X2,X3)) = join(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
join(X2,join(X4,X3)) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c184,c186]) ).
cnf(c188,plain,
join(meet(join(X4,X3),join(X4,X2)),join(X4,X2)) = join(X4,join(X2,meet(join(X4,X3),join(X4,X2)))),
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
join(X4,join(X2,meet(join(X4,X3),join(X4,X2)))) = join(meet(join(X4,X3),join(X4,X2)),join(X4,X2)),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
join(X2,meet(X3,X2)) = join(meet(X3,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c191,plain,
join(meet(X3,X2),X2) = join(X2,meet(X3,X2)),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c193,plain,
join(X2,meet(X3,X2)) = join(X2,meet(X2,X3)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
join(X2,meet(X2,X3)) = X2,
inference(substitution,[status(thm)],[c31]) ).
cnf(c195,plain,
join(X2,meet(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c193,c194]) ).
cnf(c196,plain,
join(meet(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c191,c195]) ).
cnf(c197,plain,
join(meet(join(X4,X3),join(X4,X2)),join(X4,X2)) = join(X4,X2),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
join(X4,join(X2,meet(join(X4,X3),join(X4,X2)))) = join(X4,X2),
inference(transitivity,[status(thm)],[c189,c197]) ).
cnf(c199,plain,
join(X2,meet(join(X4,X3),join(X4,X2))) = join(X4,X2),
inference(transitivity,[status(thm)],[c176,c198]) ).
cnf(c200,plain,
join(meet(join(X4,X3),join(X4,X2)),X2) = join(X4,X2),
inference(transitivity,[status(thm)],[c174,c199]) ).
cnf(c201,plain,
join(meet(join(X4,X3),join(X4,meet(X2,X5))),meet(X2,X5)) = join(X4,meet(X2,X5)),
inference(substitution,[status(thm)],[c200]) ).
cnf(c202,plain,
join(X5,join(meet(join(X4,X3),join(X4,meet(X2,X5))),meet(X2,X5))) = join(X5,join(X4,meet(X2,X5))),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
join(X5,join(meet(join(X4,X3),join(X4,meet(X2,X5))),meet(X2,X5))) = join(X4,X5),
inference(transitivity,[status(thm)],[c202,c170]) ).
cnf(c204,plain,
join(meet(join(X4,X3),join(X4,meet(X2,X5))),X5) = join(X4,X5),
inference(transitivity,[status(thm)],[c172,c203]) ).
cnf(c205,plain,
join(X5,meet(join(X4,X3),join(X4,meet(X2,X5)))) = join(X4,X5),
inference(transitivity,[status(thm)],[c160,c204]) ).
cnf(c206,plain,
join(a,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))) = join(r1,a),
inference(substitution,[status(thm)],[c205]) ).
cnf(c207,plain,
meet(join(r1,meet(r2,b)),join(a,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))))) = meet(join(r1,meet(r2,b)),join(r1,a)),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
meet(join(r1,meet(r2,b)),join(a,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))))) = r1,
inference(transitivity,[status(thm)],[c207,c117]) ).
cnf(c209,plain,
meet(join(r1,meet(r2,b)),join(r1,join(a,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))))) = r1,
inference(transitivity,[status(thm)],[c158,c208]) ).
cnf(c210,plain,
meet(join(r1,meet(r2,b)),join(join(r1,a),meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))))) = r1,
inference(transitivity,[status(thm)],[c146,c209]) ).
cnf(c211,plain,
join(meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))),meet(join(r1,meet(r2,b)),join(r1,a))) = r1,
inference(transitivity,[status(thm)],[c143,c210]) ).
cnf(c212,plain,
join(meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))),r1) = r1,
inference(transitivity,[status(thm)],[c119,c211]) ).
cnf(c213,plain,
join(r1,meet(join(r1,meet(r2,b)),join(r1,meet(X2,a)))) = r1,
inference(transitivity,[status(thm)],[c40,c212]) ).
cnf(c214,plain,
meet(join(r1,meet(r2,b)),join(r1,meet(X2,a))) = r1,
inference(transitivity,[status(thm)],[c38,c213]) ).
cnf(c215,plain,
meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) = r1,
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
r1 = meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
$false,
inference(resolution,[status(thm)],[c1,c216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT005-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 13:55:31 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.19/1.21 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 6.19/1.21
% 6.19/1.21 % SZS status Unsatisfiable
% 6.19/1.21
% 6.19/1.23 % SZS output start CNFRefutation
% See solution above
% 7.01/1.34
% 7.01/1.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------