%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT038-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 11:42:53 AM UTC 2026
% Result : Unsatisfiable 0.76s 0.57s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of clauses : 171 ( 171 unt; 0 nHn; 68 RR)
% Number of literals : 171 ( 170 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 209 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
f(aa,dd) != f(cc,dd),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rhs) ).
cnf(c2,axiom,
meet(X,Y) = meet(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c3,plain,
meet(f(cc,dd),f(join(aa,bb),dd)) = meet(f(join(aa,bb),dd),f(cc,dd)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
meet(f(join(aa,bb),dd),f(cc,dd)) = meet(f(cc,dd),f(join(aa,bb),dd)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
join(X2,Y2) = join(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c6,plain,
join(f(cc,dd),f(join(aa,bb),dd)) = join(f(join(aa,bb),dd),f(cc,dd)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
join(f(join(aa,bb),dd),f(cc,dd)) = join(f(cc,dd),f(join(aa,bb),dd)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
f(join(aa,bb),dd) = f(join(cc,bb),dd),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c9,plain,
join(f(cc,dd),f(join(aa,bb),dd)) = join(f(cc,dd),f(join(cc,bb),dd)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
f(join(U,V),W) = join(f(U,W),f(V,W)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_left_join) ).
cnf(c11,plain,
f(join(X3,X4),X2) = join(f(X3,X2),f(X4,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
join(f(X3,X2),f(X4,X2)) = f(join(X3,X4),X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c14,plain,
f(join(X3,X4),X2) = f(join(X4,X3),X2),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
join(f(X3,X2),f(X4,X2)) = f(join(X4,X3),X2),
inference(transitivity,[status(thm)],[c12,c14]) ).
cnf(c16,plain,
join(f(cc,dd),f(join(cc,bb),dd)) = f(join(join(cc,bb),cc),dd),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
meet(X3,join(X3,X2)) = meet(join(X3,X2),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
meet(join(X3,X2),X3) = meet(X3,join(X3,X2)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,axiom,
meet(X2,join(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
cnf(c20,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
meet(join(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
X3 = meet(join(X3,X2),X3),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
join(join(X3,X2),X3) = join(join(X3,X2),meet(join(X3,X2),X3)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
join(X2,meet(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
cnf(c25,plain,
join(join(X3,X2),meet(join(X3,X2),X3)) = join(X3,X2),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
join(join(X3,X2),X3) = join(X3,X2),
inference(transitivity,[status(thm)],[c23,c25]) ).
cnf(c27,plain,
join(join(cc,bb),cc) = join(cc,bb),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
f(join(join(cc,bb),cc),dd) = f(join(cc,bb),dd),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
f(join(cc,bb),dd) = f(join(aa,bb),dd),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c30,plain,
f(join(join(cc,bb),cc),dd) = f(join(aa,bb),dd),
inference(transitivity,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
join(f(cc,dd),f(join(cc,bb),dd)) = f(join(aa,bb),dd),
inference(transitivity,[status(thm)],[c16,c30]) ).
cnf(c32,plain,
join(f(cc,dd),f(join(aa,bb),dd)) = f(join(aa,bb),dd),
inference(transitivity,[status(thm)],[c9,c31]) ).
cnf(c33,plain,
join(f(join(aa,bb),dd),f(cc,dd)) = f(join(aa,bb),dd),
inference(transitivity,[status(thm)],[c7,c32]) ).
cnf(c34,plain,
f(join(aa,bb),dd) = join(f(join(aa,bb),dd),f(cc,dd)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
meet(f(cc,dd),f(join(aa,bb),dd)) = meet(f(cc,dd),join(f(join(aa,bb),dd),f(cc,dd))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c37,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
meet(X3,join(X2,X3)) = meet(X3,join(X3,X2)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c19]) ).
cnf(c40,plain,
meet(X3,join(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c38,c39]) ).
cnf(c41,plain,
meet(f(cc,dd),join(f(join(aa,bb),dd),f(cc,dd))) = f(cc,dd),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
meet(f(cc,dd),f(join(aa,bb),dd)) = f(cc,dd),
inference(transitivity,[status(thm)],[c35,c41]) ).
cnf(c43,plain,
meet(f(join(aa,bb),dd),f(cc,dd)) = f(cc,dd),
inference(transitivity,[status(thm)],[c4,c42]) ).
cnf(c44,plain,
f(cc,dd) = meet(f(join(aa,bb),dd),f(cc,dd)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
meet(f(cc,dd),f(join(aa,bb),dd)) = meet(f(join(aa,bb),dd),f(cc,dd)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c46,plain,
meet(f(join(aa,bb),dd),f(cc,dd)) = meet(f(cc,dd),f(join(aa,bb),dd)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
f(join(aa,bb),dd) = join(f(aa,dd),f(bb,dd)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c48,plain,
meet(f(cc,dd),f(join(aa,bb),dd)) = meet(f(cc,dd),join(f(aa,dd),f(bb,dd))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
meet(f(cc,dd),X2) = meet(X2,f(cc,dd)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c50,plain,
meet(X2,f(cc,dd)) = meet(f(cc,dd),X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(X2,f(cc,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,hypothesis,
join(X2,meet(Y2,Z)) = meet(join(X2,Y2),join(X2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_join) ).
cnf(c53,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X2)) = meet(join(meet(f(aa,dd),f(bb,dd)),f(cc,dd)),join(meet(f(aa,dd),f(bb,dd)),X2)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),f(cc,dd)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c55,plain,
join(meet(f(aa,dd),f(bb,dd)),f(cc,dd)) = join(f(cc,dd),meet(f(aa,dd),f(bb,dd))),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,axiom,
meet(f(aa,dd),f(bb,dd)) = meet(f(cc,dd),f(bb,dd)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c57,plain,
join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) = join(f(cc,dd),meet(f(cc,dd),f(bb,dd))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
meet(f(cc,dd),f(bb,dd)) = meet(f(bb,dd),f(cc,dd)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
join(f(cc,dd),meet(f(cc,dd),f(bb,dd))) = join(f(cc,dd),meet(f(bb,dd),f(cc,dd))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c61,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
join(X3,meet(X2,X3)) = join(X3,meet(X3,X2)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c64,plain,
join(X3,meet(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
join(f(cc,dd),meet(f(bb,dd),f(cc,dd))) = f(cc,dd),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
join(f(cc,dd),meet(f(cc,dd),f(bb,dd))) = f(cc,dd),
inference(transitivity,[status(thm)],[c59,c65]) ).
cnf(c67,plain,
join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) = f(cc,dd),
inference(transitivity,[status(thm)],[c57,c66]) ).
cnf(c68,plain,
join(meet(f(aa,dd),f(bb,dd)),f(cc,dd)) = f(cc,dd),
inference(transitivity,[status(thm)],[c55,c67]) ).
cnf(c69,plain,
meet(join(meet(f(aa,dd),f(bb,dd)),f(cc,dd)),join(meet(f(aa,dd),f(bb,dd)),X2)) = meet(f(cc,dd),join(meet(f(aa,dd),f(bb,dd)),X2)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
join(meet(f(aa,dd),f(bb,dd)),X2) = join(X2,meet(f(aa,dd),f(bb,dd))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c71,plain,
meet(f(cc,dd),join(meet(f(aa,dd),f(bb,dd)),X2)) = meet(f(cc,dd),join(X2,meet(f(aa,dd),f(bb,dd)))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
meet(join(meet(f(aa,dd),f(bb,dd)),f(cc,dd)),join(meet(f(aa,dd),f(bb,dd)),X2)) = meet(f(cc,dd),join(X2,meet(f(aa,dd),f(bb,dd)))),
inference(transitivity,[status(thm)],[c69,c71]) ).
cnf(c73,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X2)) = meet(f(cc,dd),join(X2,meet(f(aa,dd),f(bb,dd)))),
inference(transitivity,[status(thm)],[c53,c72]) ).
cnf(c74,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(X2,f(cc,dd))) = meet(f(cc,dd),join(X2,meet(f(aa,dd),f(bb,dd)))),
inference(transitivity,[status(thm)],[c51,c73]) ).
cnf(c75,plain,
meet(f(cc,dd),join(X2,meet(f(aa,dd),f(bb,dd)))) = join(meet(f(aa,dd),f(bb,dd)),meet(X2,f(cc,dd))),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
meet(f(cc,dd),X2) = meet(X2,f(cc,dd)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c77,plain,
meet(X2,f(cc,dd)) = meet(f(cc,dd),X2),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(X2,f(cc,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X2)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X2)) = join(meet(f(cc,dd),f(bb,dd)),meet(f(cc,dd),X2)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c80,plain,
meet(f(cc,dd),f(bb,dd)) = meet(f(bb,dd),f(cc,dd)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c81,plain,
join(meet(f(cc,dd),f(bb,dd)),meet(f(cc,dd),X2)) = join(meet(f(bb,dd),f(cc,dd)),meet(f(cc,dd),X2)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c83,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
join(meet(X4,X3),meet(X3,X2)) = join(meet(X3,X4),meet(X3,X2)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,hypothesis,
meet(X2,join(Y2,Z2)) = join(meet(X2,Y2),meet(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_meet) ).
cnf(c86,plain,
meet(X3,join(X4,X2)) = join(meet(X3,X4),meet(X3,X2)),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
join(meet(X3,X4),meet(X3,X2)) = meet(X3,join(X4,X2)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
join(meet(X4,X3),meet(X3,X2)) = meet(X3,join(X4,X2)),
inference(transitivity,[status(thm)],[c84,c87]) ).
cnf(c89,plain,
join(meet(f(bb,dd),f(cc,dd)),meet(f(cc,dd),X2)) = meet(f(cc,dd),join(f(bb,dd),X2)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
join(f(bb,dd),X2) = join(X2,f(bb,dd)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c91,plain,
meet(f(cc,dd),join(f(bb,dd),X2)) = meet(f(cc,dd),join(X2,f(bb,dd))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
join(meet(f(bb,dd),f(cc,dd)),meet(f(cc,dd),X2)) = meet(f(cc,dd),join(X2,f(bb,dd))),
inference(transitivity,[status(thm)],[c89,c91]) ).
cnf(c93,plain,
join(meet(f(cc,dd),f(bb,dd)),meet(f(cc,dd),X2)) = meet(f(cc,dd),join(X2,f(bb,dd))),
inference(transitivity,[status(thm)],[c81,c92]) ).
cnf(c94,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X2)) = meet(f(cc,dd),join(X2,f(bb,dd))),
inference(transitivity,[status(thm)],[c79,c93]) ).
cnf(c95,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(X2,f(cc,dd))) = meet(f(cc,dd),join(X2,f(bb,dd))),
inference(transitivity,[status(thm)],[c78,c94]) ).
cnf(c96,plain,
meet(f(cc,dd),join(X2,meet(f(aa,dd),f(bb,dd)))) = meet(f(cc,dd),join(X2,f(bb,dd))),
inference(transitivity,[status(thm)],[c75,c95]) ).
cnf(c97,plain,
meet(f(cc,dd),join(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) = meet(f(cc,dd),join(f(aa,dd),f(bb,dd))),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
meet(f(cc,dd),join(f(aa,dd),f(bb,dd))) = meet(f(cc,dd),join(f(aa,dd),meet(f(aa,dd),f(bb,dd)))),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
join(f(aa,dd),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),f(aa,dd)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c100,plain,
meet(f(cc,dd),join(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) = meet(f(cc,dd),join(meet(f(aa,dd),f(bb,dd)),f(aa,dd))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
join(X3,meet(X3,X2)) = join(meet(X3,X2),X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c102,plain,
join(meet(X3,X2),X3) = join(X3,meet(X3,X2)),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c104,plain,
join(meet(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c102,c103]) ).
cnf(c105,plain,
join(meet(f(aa,dd),f(bb,dd)),f(aa,dd)) = f(aa,dd),
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
meet(f(cc,dd),join(meet(f(aa,dd),f(bb,dd)),f(aa,dd))) = meet(f(cc,dd),f(aa,dd)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
meet(f(cc,dd),f(aa,dd)) = meet(f(aa,dd),f(cc,dd)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c108,plain,
join(f(cc,dd),X2) = join(X2,f(cc,dd)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c109,plain,
join(X2,f(cc,dd)) = join(f(cc,dd),X2),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
meet(f(join(aa,bb),dd),join(X2,f(cc,dd))) = meet(f(join(aa,bb),dd),join(f(cc,dd),X2)),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
join(f(bb,dd),f(cc,dd)) = f(join(cc,bb),dd),
inference(substitution,[status(thm)],[c15]) ).
cnf(c112,plain,
f(join(cc,bb),dd) = f(join(aa,bb),dd),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c113,plain,
join(f(bb,dd),f(cc,dd)) = f(join(aa,bb),dd),
inference(transitivity,[status(thm)],[c111,c112]) ).
cnf(c114,plain,
f(join(aa,bb),dd) = join(f(bb,dd),f(cc,dd)),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
meet(f(join(aa,bb),dd),join(f(cc,dd),X2)) = meet(join(f(bb,dd),f(cc,dd)),join(f(cc,dd),X2)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c117,plain,
join(X3,X2) = join(X2,X3),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
meet(join(X4,X3),join(X3,X2)) = meet(join(X3,X4),join(X3,X2)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
join(X3,meet(X4,X2)) = meet(join(X3,X4),join(X3,X2)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c120,plain,
meet(join(X3,X4),join(X3,X2)) = join(X3,meet(X4,X2)),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
meet(join(X4,X3),join(X3,X2)) = join(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c118,c120]) ).
cnf(c122,plain,
meet(join(f(bb,dd),f(cc,dd)),join(f(cc,dd),X2)) = join(f(cc,dd),meet(f(bb,dd),X2)),
inference(substitution,[status(thm)],[c121]) ).
cnf(c123,plain,
meet(f(bb,dd),X2) = meet(X2,f(bb,dd)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c124,plain,
join(f(cc,dd),meet(f(bb,dd),X2)) = join(f(cc,dd),meet(X2,f(bb,dd))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
meet(join(f(bb,dd),f(cc,dd)),join(f(cc,dd),X2)) = join(f(cc,dd),meet(X2,f(bb,dd))),
inference(transitivity,[status(thm)],[c122,c124]) ).
cnf(c126,plain,
meet(f(join(aa,bb),dd),join(f(cc,dd),X2)) = join(f(cc,dd),meet(X2,f(bb,dd))),
inference(transitivity,[status(thm)],[c115,c125]) ).
cnf(c127,plain,
meet(f(join(aa,bb),dd),join(X2,f(cc,dd))) = join(f(cc,dd),meet(X2,f(bb,dd))),
inference(transitivity,[status(thm)],[c110,c126]) ).
cnf(c128,plain,
meet(f(join(aa,bb),dd),join(f(aa,dd),f(cc,dd))) = join(f(cc,dd),meet(f(aa,dd),f(bb,dd))),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),f(cc,dd)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c130,plain,
join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) = f(cc,dd),
inference(transitivity,[status(thm)],[c129,c68]) ).
cnf(c131,plain,
meet(f(join(aa,bb),dd),join(f(aa,dd),f(cc,dd))) = f(cc,dd),
inference(transitivity,[status(thm)],[c128,c130]) ).
cnf(c132,plain,
f(cc,dd) = meet(f(join(aa,bb),dd),join(f(aa,dd),f(cc,dd))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
meet(f(aa,dd),f(cc,dd)) = meet(f(aa,dd),meet(f(join(aa,bb),dd),join(f(aa,dd),f(cc,dd)))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
meet(join(X4,X2),X3) = meet(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c135,plain,
meet(X3,join(X4,X2)) = meet(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
meet(X4,meet(X3,join(X4,X2))) = meet(X4,meet(join(X4,X2),X3)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,axiom,
meet(meet(X2,Y2),Z2) = meet(X2,meet(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(c138,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,meet(join(X4,X2),X3)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(meet(X4,join(X4,X2)),X3),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
meet(X3,join(X3,X2)) = X3,
inference(substitution,[status(thm)],[c19]) ).
cnf(c141,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,X3),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c139,c141]) ).
cnf(c143,plain,
meet(X4,meet(X3,join(X4,X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c136,c142]) ).
cnf(c144,plain,
meet(f(aa,dd),meet(f(join(aa,bb),dd),join(f(aa,dd),f(cc,dd)))) = meet(f(aa,dd),f(join(aa,bb),dd)),
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
meet(f(aa,dd),f(join(aa,bb),dd)) = meet(f(join(aa,bb),dd),f(aa,dd)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c146,plain,
meet(f(X4,X2),f(join(X4,X3),X2)) = meet(f(join(X4,X3),X2),f(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c147,plain,
meet(f(join(X4,X3),X2),f(X4,X2)) = meet(f(X4,X2),f(join(X4,X3),X2)),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
join(f(X4,X2),f(join(X4,X3),X2)) = join(f(join(X4,X3),X2),f(X4,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c149,plain,
join(f(join(X4,X3),X2),f(X4,X2)) = join(f(X4,X2),f(join(X4,X3),X2)),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
join(f(X4,X2),f(join(X4,X3),X2)) = f(join(join(X4,X3),X4),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c151,plain,
f(join(join(X4,X3),X4),X2) = f(join(X4,X3),X2),
inference(congruence,[status(thm)],[c26]) ).
cnf(c152,plain,
join(f(X4,X2),f(join(X4,X3),X2)) = f(join(X4,X3),X2),
inference(transitivity,[status(thm)],[c150,c151]) ).
cnf(c153,plain,
join(f(join(X4,X3),X2),f(X4,X2)) = f(join(X4,X3),X2),
inference(transitivity,[status(thm)],[c149,c152]) ).
cnf(c154,plain,
f(join(X4,X3),X2) = join(f(join(X4,X3),X2),f(X4,X2)),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
meet(f(X4,X2),f(join(X4,X3),X2)) = meet(f(X4,X2),join(f(join(X4,X3),X2),f(X4,X2))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
meet(f(X4,X2),join(f(join(X4,X3),X2),f(X4,X2))) = f(X4,X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c157,plain,
meet(f(X4,X2),f(join(X4,X3),X2)) = f(X4,X2),
inference(transitivity,[status(thm)],[c155,c156]) ).
cnf(c158,plain,
meet(f(join(X4,X3),X2),f(X4,X2)) = f(X4,X2),
inference(transitivity,[status(thm)],[c147,c157]) ).
cnf(c159,plain,
meet(f(join(aa,bb),dd),f(aa,dd)) = f(aa,dd),
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
meet(f(aa,dd),f(join(aa,bb),dd)) = f(aa,dd),
inference(transitivity,[status(thm)],[c145,c159]) ).
cnf(c161,plain,
meet(f(aa,dd),meet(f(join(aa,bb),dd),join(f(aa,dd),f(cc,dd)))) = f(aa,dd),
inference(transitivity,[status(thm)],[c144,c160]) ).
cnf(c162,plain,
meet(f(aa,dd),f(cc,dd)) = f(aa,dd),
inference(transitivity,[status(thm)],[c133,c161]) ).
cnf(c163,plain,
meet(f(cc,dd),f(aa,dd)) = f(aa,dd),
inference(transitivity,[status(thm)],[c107,c162]) ).
cnf(c164,plain,
meet(f(cc,dd),join(meet(f(aa,dd),f(bb,dd)),f(aa,dd))) = f(aa,dd),
inference(transitivity,[status(thm)],[c106,c163]) ).
cnf(c165,plain,
meet(f(cc,dd),join(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) = f(aa,dd),
inference(transitivity,[status(thm)],[c100,c164]) ).
cnf(c166,plain,
meet(f(cc,dd),join(f(aa,dd),f(bb,dd))) = f(aa,dd),
inference(transitivity,[status(thm)],[c98,c165]) ).
cnf(c167,plain,
meet(f(cc,dd),f(join(aa,bb),dd)) = f(aa,dd),
inference(transitivity,[status(thm)],[c48,c166]) ).
cnf(c168,plain,
meet(f(join(aa,bb),dd),f(cc,dd)) = f(aa,dd),
inference(transitivity,[status(thm)],[c46,c167]) ).
cnf(c169,plain,
f(cc,dd) = f(aa,dd),
inference(transitivity,[status(thm)],[c44,c168]) ).
cnf(c170,plain,
f(aa,dd) = f(cc,dd),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
$false,
inference(resolution,[status(thm)],[c1,c170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT038-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 13:58:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.76/0.57 Command-line arguments: --flatten --complete-subsets
% 0.76/0.57
% 0.76/0.57 % SZS status Unsatisfiable
% 0.76/0.57
% 0.76/0.57 % SZS output start CNFRefutation
% See solution above
% 0.76/0.62
% 0.76/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------