%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : MVA008-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:05:50 PM UTC 2026
% Result : Unsatisfiable 94.35s 12.31s
% Output : CNFRefutation 95.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 17
% Syntax : Number of clauses : 369 ( 369 unt; 0 nHn; 8 RR)
% Number of literals : 369 ( 368 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; 2 con; 0-2 aty)
% Number of variables : 744 ( 54 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
at(op(x,ld(x,unit)),unit) != op(x,ld(x,unit)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
op(X,unit) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_monoid_unit) ).
cnf(c3,plain,
op(ld(X2,unit),unit) = ld(X2,unit),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
ld(X2,unit) = op(ld(X2,unit),unit),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
op(X2,ld(X2,unit)) = op(X2,op(ld(X2,unit),unit)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
meet(X2,Y) = meet(Y,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c7,plain,
meet(ld(unit,X2),X2) = meet(X2,ld(unit,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
meet(X2,ld(unit,X2)) = meet(ld(unit,X2),X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
op(unit,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_monoid_unit) ).
cnf(c10,plain,
op(unit,ld(unit,X2)) = ld(unit,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
ld(unit,X2) = op(unit,ld(unit,X2)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
join(X2,ld(unit,X2)) = join(X2,op(unit,ld(unit,X2))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,axiom,
meet(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
cnf(c14,plain,
meet(ld(X3,X2),ld(X3,X2)) = ld(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
ld(X2,X3) = meet(ld(X2,X3),ld(X2,X3)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
op(X2,ld(X2,X3)) = op(X2,meet(ld(X2,X3),ld(X2,X3))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
join(X3,op(X2,ld(X2,X3))) = join(X3,op(X2,meet(ld(X2,X3),ld(X2,X3)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,axiom,
join(X2,Y2) = join(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c19,plain,
join(op(X2,meet(ld(X2,X3),X4)),X3) = join(X3,op(X2,meet(ld(X2,X3),X4))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
join(X4,op(X3,meet(ld(X3,X4),X2))) = join(op(X3,meet(ld(X3,X4),X2)),X4),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
join(op(X2,meet(ld(X2,Z),Y2)),Z) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',residual_a) ).
cnf(c22,plain,
join(op(X3,meet(ld(X3,X4),X2)),X4) = X4,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
join(X4,op(X3,meet(ld(X3,X4),X2))) = X4,
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
join(X3,op(X2,meet(ld(X2,X3),ld(X2,X3)))) = X3,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
join(X3,op(X2,ld(X2,X3))) = X3,
inference(transitivity,[status(thm)],[c17,c24]) ).
cnf(c26,plain,
join(X2,op(unit,ld(unit,X2))) = X2,
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
join(X2,ld(unit,X2)) = X2,
inference(transitivity,[status(thm)],[c12,c26]) ).
cnf(c28,plain,
X2 = join(X2,ld(unit,X2)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
meet(ld(unit,X2),X2) = meet(ld(unit,X2),join(X2,ld(unit,X2))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c31,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
meet(X3,join(X2,X3)) = meet(X3,join(X3,X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
meet(join(X3,X2),X3) = meet(X3,join(X3,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c34,plain,
meet(X3,join(X3,X2)) = meet(join(X3,X2),X3),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,axiom,
meet(join(X2,Y2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption_b) ).
cnf(c36,plain,
meet(join(X3,X2),X3) = X3,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
meet(X3,join(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c34,c36]) ).
cnf(c38,plain,
meet(X3,join(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c32,c37]) ).
cnf(c39,plain,
meet(ld(unit,X2),join(X2,ld(unit,X2))) = ld(unit,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
meet(ld(unit,X2),X2) = ld(unit,X2),
inference(transitivity,[status(thm)],[c29,c39]) ).
cnf(c41,plain,
meet(X2,ld(unit,X2)) = ld(unit,X2),
inference(transitivity,[status(thm)],[c8,c40]) ).
cnf(c42,plain,
ld(unit,X2) = meet(X2,ld(unit,X2)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
X2 = op(unit,X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c44,plain,
ld(unit,X2) = ld(unit,op(unit,X2)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
meet(X2,ld(unit,X2)) = meet(X2,ld(unit,op(unit,X2))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
join(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
cnf(c47,plain,
join(op(X2,X3),op(X2,X3)) = op(X2,X3),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
op(X2,X3) = join(op(X2,X3),op(X2,X3)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
ld(X2,op(X2,X3)) = ld(X2,join(op(X2,X3),op(X2,X3))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
meet(X3,ld(X2,op(X2,X3))) = meet(X3,ld(X2,join(op(X2,X3),op(X2,X3)))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
meet(ld(X3,join(op(X3,X4),X2)),X4) = meet(X4,ld(X3,join(op(X3,X4),X2))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c52,plain,
meet(X4,ld(X3,join(op(X3,X4),X2))) = meet(ld(X3,join(op(X3,X4),X2)),X4),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,axiom,
meet(ld(X2,join(op(X2,Y2),Z2)),Y2) = Y2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',residual_c) ).
cnf(c54,plain,
meet(ld(X3,join(op(X3,X4),X2)),X4) = X4,
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
meet(X4,ld(X3,join(op(X3,X4),X2))) = X4,
inference(transitivity,[status(thm)],[c52,c54]) ).
cnf(c56,plain,
meet(X3,ld(X2,join(op(X2,X3),op(X2,X3)))) = X3,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
meet(X3,ld(X2,op(X2,X3))) = X3,
inference(transitivity,[status(thm)],[c50,c56]) ).
cnf(c58,plain,
meet(X2,ld(unit,op(unit,X2))) = X2,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
meet(X2,ld(unit,X2)) = X2,
inference(transitivity,[status(thm)],[c45,c58]) ).
cnf(c60,plain,
ld(unit,X2) = X2,
inference(transitivity,[status(thm)],[c42,c59]) ).
cnf(c61,plain,
ld(unit,unit) = unit,
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
unit = ld(unit,unit),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
op(ld(X2,unit),unit) = op(ld(X2,unit),ld(unit,unit)),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
op(X2,op(ld(X2,unit),unit)) = op(X2,op(ld(X2,unit),ld(unit,unit))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
ld(unit,unit) = unit,
inference(substitution,[status(thm)],[c60]) ).
cnf(c66,plain,
unit = ld(unit,unit),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
ld(unit,unit) = ld(ld(unit,unit),unit),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
op(ld(X2,unit),ld(unit,unit)) = op(ld(X2,unit),ld(ld(unit,unit),unit)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
op(X2,op(ld(X2,unit),ld(unit,unit))) = op(X2,op(ld(X2,unit),ld(ld(unit,unit),unit))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,axiom,
op(op(X2,Y2),Z2) = op(X2,op(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoid_associativity) ).
cnf(c71,plain,
op(op(X3,ld(X3,unit)),ld(ld(X2,unit),unit)) = op(X3,op(ld(X3,unit),ld(ld(X2,unit),unit))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
op(X3,op(ld(X3,unit),ld(ld(X2,unit),unit))) = op(op(X3,ld(X3,unit)),ld(ld(X2,unit),unit)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,axiom,
at(X2,Y2) = op(op(X2,ld(X2,unit)),ld(ld(Y2,unit),unit)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_at) ).
cnf(c74,plain,
at(X3,X2) = op(op(X3,ld(X3,unit)),ld(ld(X2,unit),unit)),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
op(op(X3,ld(X3,unit)),ld(ld(X2,unit),unit)) = at(X3,X2),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
op(X3,op(ld(X3,unit),ld(ld(X2,unit),unit))) = at(X3,X2),
inference(transitivity,[status(thm)],[c72,c75]) ).
cnf(c77,plain,
op(X2,op(ld(X2,unit),ld(ld(unit,unit),unit))) = at(X2,unit),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
op(X2,op(ld(X2,unit),ld(unit,unit))) = at(X2,unit),
inference(transitivity,[status(thm)],[c69,c77]) ).
cnf(c79,plain,
op(X2,op(ld(X2,unit),unit)) = at(X2,unit),
inference(transitivity,[status(thm)],[c64,c78]) ).
cnf(c80,plain,
op(X2,ld(X2,unit)) = at(X2,unit),
inference(transitivity,[status(thm)],[c5,c79]) ).
cnf(c81,plain,
op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)) = at(op(X2,ld(X2,unit)),unit),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
at(op(X2,ld(X2,unit)),unit) = op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)) = op(X2,op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c84,plain,
op(op(X2,X4),X3) = op(X2,op(X4,X3)),
inference(substitution,[status(thm)],[c70]) ).
cnf(c85,plain,
ld(X2,op(op(X2,X4),X3)) = ld(X2,op(X2,op(X4,X3))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
meet(op(X4,X3),ld(X2,op(op(X2,X4),X3))) = meet(op(X4,X3),ld(X2,op(X2,op(X4,X3)))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
meet(op(X4,X3),ld(X2,op(X2,op(X4,X3)))) = op(X4,X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c88,plain,
meet(op(X4,X3),ld(X2,op(op(X2,X4),X3))) = op(X4,X3),
inference(transitivity,[status(thm)],[c86,c87]) ).
cnf(c89,plain,
meet(op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),ld(X2,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)))) = op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)) = meet(op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),ld(X2,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)))),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)) = at(op(X2,ld(X2,unit)),unit),
inference(substitution,[status(thm)],[c80]) ).
cnf(c92,plain,
ld(X2,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))) = ld(X2,at(op(X2,ld(X2,unit)),unit)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
meet(op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),ld(X2,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)))) = meet(op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),ld(X2,at(op(X2,ld(X2,unit)),unit))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
meet(ld(X3,at(X2,unit)),ld(X3,unit)) = meet(ld(X3,unit),ld(X3,at(X2,unit))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c95,plain,
meet(ld(X3,unit),ld(X3,at(X2,unit))) = meet(ld(X3,at(X2,unit)),ld(X3,unit)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
join(op(X3,ld(X3,at(X2,unit))),unit) = join(unit,op(X3,ld(X3,at(X2,unit)))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c97,plain,
join(unit,op(X3,ld(X3,at(X2,unit)))) = join(op(X3,ld(X3,at(X2,unit))),unit),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
join(X2,at(X3,unit)) = join(at(X3,unit),X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c99,plain,
join(at(X3,unit),X2) = join(X2,at(X3,unit)),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
join(unit,join(at(X3,unit),X2)) = join(unit,join(X2,at(X3,unit))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
join(at(X2,unit),X3) = join(X3,at(X2,unit)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c102,plain,
join(X3,at(X2,unit)) = join(at(X2,unit),X3),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
join(unit,join(X3,at(X2,unit))) = join(unit,join(at(X2,unit),X3)),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,axiom,
join(join(X2,Y2),Z2) = join(X2,join(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(c105,plain,
join(join(unit,at(X2,unit)),X3) = join(unit,join(at(X2,unit),X3)),
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
join(unit,join(at(X2,unit),X3)) = join(join(unit,at(X2,unit)),X3),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
at(X2,unit) = op(X2,ld(X2,unit)),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c108,plain,
join(unit,at(X2,unit)) = join(unit,op(X2,ld(X2,unit))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
join(unit,op(X2,ld(X2,unit))) = unit,
inference(substitution,[status(thm)],[c25]) ).
cnf(c110,plain,
join(unit,at(X2,unit)) = unit,
inference(transitivity,[status(thm)],[c108,c109]) ).
cnf(c111,plain,
join(join(unit,at(X2,unit)),X3) = join(unit,X3),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
join(unit,X2) = join(X2,unit),
inference(substitution,[status(thm)],[c18]) ).
cnf(c113,plain,
join(join(unit,at(X2,unit)),X3) = join(X3,unit),
inference(transitivity,[status(thm)],[c111,c112]) ).
cnf(c114,plain,
join(unit,join(at(X2,unit),X3)) = join(X3,unit),
inference(transitivity,[status(thm)],[c106,c113]) ).
cnf(c115,plain,
join(unit,join(X3,at(X2,unit))) = join(X3,unit),
inference(transitivity,[status(thm)],[c103,c114]) ).
cnf(c116,plain,
join(unit,join(X2,at(X3,unit))) = join(X2,unit),
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
join(unit,join(at(X3,unit),X2)) = join(X2,unit),
inference(transitivity,[status(thm)],[c100,c116]) ).
cnf(c118,plain,
join(unit,join(at(X2,unit),op(X3,ld(X3,at(X2,unit))))) = join(op(X3,ld(X3,at(X2,unit))),unit),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
join(op(X3,ld(X3,at(X2,unit))),unit) = join(unit,join(at(X2,unit),op(X3,ld(X3,at(X2,unit))))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
join(at(X2,unit),op(X3,ld(X3,at(X2,unit)))) = at(X2,unit),
inference(substitution,[status(thm)],[c25]) ).
cnf(c121,plain,
join(unit,join(at(X2,unit),op(X3,ld(X3,at(X2,unit))))) = join(unit,at(X2,unit)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
join(unit,join(at(X2,unit),op(X3,ld(X3,at(X2,unit))))) = unit,
inference(transitivity,[status(thm)],[c121,c110]) ).
cnf(c123,plain,
join(op(X3,ld(X3,at(X2,unit))),unit) = unit,
inference(transitivity,[status(thm)],[c119,c122]) ).
cnf(c124,plain,
join(unit,op(X3,ld(X3,at(X2,unit)))) = unit,
inference(transitivity,[status(thm)],[c97,c123]) ).
cnf(c125,plain,
unit = join(unit,op(X3,ld(X3,at(X2,unit)))),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
ld(X3,unit) = ld(X3,join(unit,op(X3,ld(X3,at(X2,unit))))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
meet(ld(X3,at(X2,unit)),ld(X3,unit)) = meet(ld(X3,at(X2,unit)),ld(X3,join(unit,op(X3,ld(X3,at(X2,unit)))))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
join(op(X3,X4),X2) = join(X2,op(X3,X4)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c129,plain,
join(X2,op(X3,X4)) = join(op(X3,X4),X2),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
ld(X3,join(X2,op(X3,X4))) = ld(X3,join(op(X3,X4),X2)),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
meet(X4,ld(X3,join(X2,op(X3,X4)))) = meet(X4,ld(X3,join(op(X3,X4),X2))),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
meet(X4,ld(X3,join(X2,op(X3,X4)))) = X4,
inference(transitivity,[status(thm)],[c131,c55]) ).
cnf(c133,plain,
meet(ld(X3,at(X2,unit)),ld(X3,join(unit,op(X3,ld(X3,at(X2,unit)))))) = ld(X3,at(X2,unit)),
inference(substitution,[status(thm)],[c132]) ).
cnf(c134,plain,
meet(ld(X3,at(X2,unit)),ld(X3,unit)) = ld(X3,at(X2,unit)),
inference(transitivity,[status(thm)],[c127,c133]) ).
cnf(c135,plain,
meet(ld(X3,unit),ld(X3,at(X2,unit))) = ld(X3,at(X2,unit)),
inference(transitivity,[status(thm)],[c95,c134]) ).
cnf(c136,plain,
meet(ld(X2,unit),ld(X2,at(op(X2,ld(X2,unit)),unit))) = ld(X2,at(op(X2,ld(X2,unit)),unit)),
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
ld(X2,at(op(X2,ld(X2,unit)),unit)) = meet(ld(X2,unit),ld(X2,at(op(X2,ld(X2,unit)),unit))),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
join(at(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit))) = join(op(X2,ld(X2,unit)),at(op(X2,ld(X2,unit)),unit)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c139,plain,
join(op(X2,ld(X2,unit)),at(op(X2,ld(X2,unit)),unit)) = join(at(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit))),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)) = at(op(X2,ld(X2,unit)),unit),
inference(substitution,[status(thm)],[c80]) ).
cnf(c141,plain,
at(op(X2,ld(X2,unit)),unit) = op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
join(at(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit))) = join(op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)),op(X2,ld(X2,unit))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
meet(op(X2,ld(X2,X3)),X3) = meet(X3,op(X2,ld(X2,X3))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c144,plain,
meet(X3,op(X2,ld(X2,X3))) = meet(op(X2,ld(X2,X3)),X3),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
X3 = join(X3,op(X2,ld(X2,X3))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c146,plain,
meet(op(X2,ld(X2,X3)),X3) = meet(op(X2,ld(X2,X3)),join(X3,op(X2,ld(X2,X3)))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
meet(op(X2,ld(X2,X3)),join(X3,op(X2,ld(X2,X3)))) = op(X2,ld(X2,X3)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c148,plain,
meet(op(X2,ld(X2,X3)),X3) = op(X2,ld(X2,X3)),
inference(transitivity,[status(thm)],[c146,c147]) ).
cnf(c149,plain,
meet(X3,op(X2,ld(X2,X3))) = op(X2,ld(X2,X3)),
inference(transitivity,[status(thm)],[c144,c148]) ).
cnf(c150,plain,
meet(unit,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))) = op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)),
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)) = meet(unit,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
join(op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)),op(X2,ld(X2,unit))) = join(meet(unit,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))),op(X2,ld(X2,unit))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
meet(rd(X2,unit),X2) = meet(X2,rd(X2,unit)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c154,plain,
meet(X2,rd(X2,unit)) = meet(rd(X2,unit),X2),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
op(rd(X2,unit),unit) = rd(X2,unit),
inference(substitution,[status(thm)],[c2]) ).
cnf(c156,plain,
rd(X2,unit) = op(rd(X2,unit),unit),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
join(X2,rd(X2,unit)) = join(X2,op(rd(X2,unit),unit)),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
meet(rd(X3,X2),rd(X3,X2)) = rd(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c159,plain,
rd(X3,X2) = meet(rd(X3,X2),rd(X3,X2)),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
op(rd(X3,X2),X2) = op(meet(rd(X3,X2),rd(X3,X2)),X2),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
join(X3,op(rd(X3,X2),X2)) = join(X3,op(meet(rd(X3,X2),rd(X3,X2)),X2)),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
join(op(meet(X3,rd(X4,X2)),X2),X4) = join(X4,op(meet(X3,rd(X4,X2)),X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c163,plain,
join(X4,op(meet(X3,rd(X4,X2)),X2)) = join(op(meet(X3,rd(X4,X2)),X2),X4),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,axiom,
join(op(meet(Y2,rd(Z2,X2)),X2),Z2) = Z2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',residual_b) ).
cnf(c165,plain,
join(op(meet(X3,rd(X4,X2)),X2),X4) = X4,
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
join(X4,op(meet(X3,rd(X4,X2)),X2)) = X4,
inference(transitivity,[status(thm)],[c163,c165]) ).
cnf(c167,plain,
join(X3,op(meet(rd(X3,X2),rd(X3,X2)),X2)) = X3,
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
join(X3,op(rd(X3,X2),X2)) = X3,
inference(transitivity,[status(thm)],[c161,c167]) ).
cnf(c169,plain,
join(X2,op(rd(X2,unit),unit)) = X2,
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
join(X2,rd(X2,unit)) = X2,
inference(transitivity,[status(thm)],[c157,c169]) ).
cnf(c171,plain,
X2 = join(X2,rd(X2,unit)),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
meet(rd(X2,unit),X2) = meet(rd(X2,unit),join(X2,rd(X2,unit))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
meet(rd(X2,unit),join(X2,rd(X2,unit))) = rd(X2,unit),
inference(substitution,[status(thm)],[c38]) ).
cnf(c174,plain,
meet(rd(X2,unit),X2) = rd(X2,unit),
inference(transitivity,[status(thm)],[c172,c173]) ).
cnf(c175,plain,
meet(X2,rd(X2,unit)) = rd(X2,unit),
inference(transitivity,[status(thm)],[c154,c174]) ).
cnf(c176,plain,
rd(X2,unit) = meet(X2,rd(X2,unit)),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
X2 = op(X2,unit),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c178,plain,
rd(X2,unit) = rd(op(X2,unit),unit),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
meet(X2,rd(X2,unit)) = meet(X2,rd(op(X2,unit),unit)),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
join(op(X3,X2),op(X3,X2)) = op(X3,X2),
inference(substitution,[status(thm)],[c46]) ).
cnf(c181,plain,
op(X3,X2) = join(op(X3,X2),op(X3,X2)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
rd(op(X3,X2),X2) = rd(join(op(X3,X2),op(X3,X2)),X2),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
meet(X3,rd(op(X3,X2),X2)) = meet(X3,rd(join(op(X3,X2),op(X3,X2)),X2)),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
meet(rd(join(op(X4,X3),X2),X3),X4) = meet(X4,rd(join(op(X4,X3),X2),X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c185,plain,
meet(X4,rd(join(op(X4,X3),X2),X3)) = meet(rd(join(op(X4,X3),X2),X3),X4),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,axiom,
meet(rd(join(op(Y2,X2),Z2),X2),Y2) = Y2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',residual_d) ).
cnf(c187,plain,
meet(rd(join(op(X4,X3),X2),X3),X4) = X4,
inference(substitution,[status(thm)],[c186]) ).
cnf(c188,plain,
meet(X4,rd(join(op(X4,X3),X2),X3)) = X4,
inference(transitivity,[status(thm)],[c185,c187]) ).
cnf(c189,plain,
meet(X3,rd(join(op(X3,X2),op(X3,X2)),X2)) = X3,
inference(substitution,[status(thm)],[c188]) ).
cnf(c190,plain,
meet(X3,rd(op(X3,X2),X2)) = X3,
inference(transitivity,[status(thm)],[c183,c189]) ).
cnf(c191,plain,
meet(X2,rd(op(X2,unit),unit)) = X2,
inference(substitution,[status(thm)],[c190]) ).
cnf(c192,plain,
meet(X2,rd(X2,unit)) = X2,
inference(transitivity,[status(thm)],[c179,c191]) ).
cnf(c193,plain,
rd(X2,unit) = X2,
inference(transitivity,[status(thm)],[c176,c192]) ).
cnf(c194,plain,
rd(op(X3,ld(X3,X2)),unit) = op(X3,ld(X3,X2)),
inference(substitution,[status(thm)],[c193]) ).
cnf(c195,plain,
op(X3,ld(X3,X2)) = rd(op(X3,ld(X3,X2)),unit),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
ld(op(X3,ld(X3,X2)),X2) = ld(rd(op(X3,ld(X3,X2)),unit),X2),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
op(X4,ld(op(X3,ld(X3,X2)),X2)) = op(X4,ld(rd(op(X3,ld(X3,X2)),unit),X2)),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
meet(X4,op(X4,ld(op(X3,ld(X3,X2)),X2))) = meet(X4,op(X4,ld(rd(op(X3,ld(X3,X2)),unit),X2))),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
join(ld(rd(op(X3,ld(X3,X2)),X4),X2),X4) = join(X4,ld(rd(op(X3,ld(X3,X2)),X4),X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c200,plain,
join(X4,ld(rd(op(X3,ld(X3,X2)),X4),X2)) = join(ld(rd(op(X3,ld(X3,X2)),X4),X2),X4),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
join(op(rd(op(X3,ld(X3,X4)),X2),X2),X4) = join(X4,op(rd(op(X3,ld(X3,X4)),X2),X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c202,plain,
join(X4,op(rd(op(X3,ld(X3,X4)),X2),X2)) = join(op(rd(op(X3,ld(X3,X4)),X2),X2),X4),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
join(X2,op(X3,ld(X3,X4))) = join(op(X3,ld(X3,X4)),X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c204,plain,
join(op(X3,ld(X3,X4)),X2) = join(X2,op(X3,ld(X3,X4))),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
join(X4,join(op(X3,ld(X3,X4)),X2)) = join(X4,join(X2,op(X3,ld(X3,X4)))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
join(op(X2,ld(X2,X4)),X3) = join(X3,op(X2,ld(X2,X4))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c207,plain,
join(X3,op(X2,ld(X2,X4))) = join(op(X2,ld(X2,X4)),X3),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
join(X4,join(X3,op(X2,ld(X2,X4)))) = join(X4,join(op(X2,ld(X2,X4)),X3)),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
join(join(X4,op(X2,ld(X2,X4))),X3) = join(X4,join(op(X2,ld(X2,X4)),X3)),
inference(substitution,[status(thm)],[c104]) ).
cnf(c210,plain,
join(X4,join(op(X2,ld(X2,X4)),X3)) = join(join(X4,op(X2,ld(X2,X4))),X3),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
join(join(X4,op(X2,ld(X2,X4))),X3) = join(X4,X3),
inference(congruence,[status(thm)],[c25]) ).
cnf(c212,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c213,plain,
join(join(X4,op(X2,ld(X2,X4))),X3) = join(X3,X4),
inference(transitivity,[status(thm)],[c211,c212]) ).
cnf(c214,plain,
join(X4,join(op(X2,ld(X2,X4)),X3)) = join(X3,X4),
inference(transitivity,[status(thm)],[c210,c213]) ).
cnf(c215,plain,
join(X4,join(X3,op(X2,ld(X2,X4)))) = join(X3,X4),
inference(transitivity,[status(thm)],[c208,c214]) ).
cnf(c216,plain,
join(X4,join(X2,op(X3,ld(X3,X4)))) = join(X2,X4),
inference(substitution,[status(thm)],[c215]) ).
cnf(c217,plain,
join(X4,join(op(X3,ld(X3,X4)),X2)) = join(X2,X4),
inference(transitivity,[status(thm)],[c205,c216]) ).
cnf(c218,plain,
join(X4,join(op(X3,ld(X3,X4)),op(rd(op(X3,ld(X3,X4)),X2),X2))) = join(op(rd(op(X3,ld(X3,X4)),X2),X2),X4),
inference(substitution,[status(thm)],[c217]) ).
cnf(c219,plain,
join(op(rd(op(X3,ld(X3,X4)),X2),X2),X4) = join(X4,join(op(X3,ld(X3,X4)),op(rd(op(X3,ld(X3,X4)),X2),X2))),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
join(op(X3,ld(X3,X4)),op(rd(op(X3,ld(X3,X4)),X2),X2)) = op(X3,ld(X3,X4)),
inference(substitution,[status(thm)],[c168]) ).
cnf(c221,plain,
join(X4,join(op(X3,ld(X3,X4)),op(rd(op(X3,ld(X3,X4)),X2),X2))) = join(X4,op(X3,ld(X3,X4))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
join(X4,join(op(X3,ld(X3,X4)),op(rd(op(X3,ld(X3,X4)),X2),X2))) = X4,
inference(transitivity,[status(thm)],[c221,c25]) ).
cnf(c223,plain,
join(op(rd(op(X3,ld(X3,X4)),X2),X2),X4) = X4,
inference(transitivity,[status(thm)],[c219,c222]) ).
cnf(c224,plain,
join(X4,op(rd(op(X3,ld(X3,X4)),X2),X2)) = X4,
inference(transitivity,[status(thm)],[c202,c223]) ).
cnf(c225,plain,
join(X2,op(rd(op(X3,ld(X3,X2)),X4),X4)) = X2,
inference(substitution,[status(thm)],[c224]) ).
cnf(c226,plain,
X2 = join(X2,op(rd(op(X3,ld(X3,X2)),X4),X4)),
inference(symmetry,[status(thm)],[c225]) ).
cnf(c227,plain,
ld(rd(op(X3,ld(X3,X2)),X4),X2) = ld(rd(op(X3,ld(X3,X2)),X4),join(X2,op(rd(op(X3,ld(X3,X2)),X4),X4))),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
meet(X4,ld(rd(op(X3,ld(X3,X2)),X4),X2)) = meet(X4,ld(rd(op(X3,ld(X3,X2)),X4),join(X2,op(rd(op(X3,ld(X3,X2)),X4),X4)))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
meet(X4,ld(rd(op(X3,ld(X3,X2)),X4),join(X2,op(rd(op(X3,ld(X3,X2)),X4),X4)))) = X4,
inference(substitution,[status(thm)],[c132]) ).
cnf(c230,plain,
meet(X4,ld(rd(op(X3,ld(X3,X2)),X4),X2)) = X4,
inference(transitivity,[status(thm)],[c228,c229]) ).
cnf(c231,plain,
X4 = meet(X4,ld(rd(op(X3,ld(X3,X2)),X4),X2)),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
join(ld(rd(op(X3,ld(X3,X2)),X4),X2),X4) = join(ld(rd(op(X3,ld(X3,X2)),X4),X2),meet(X4,ld(rd(op(X3,ld(X3,X2)),X4),X2))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c234,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
join(X3,meet(X2,X3)) = join(X3,meet(X3,X2)),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
join(meet(X3,X2),X3) = join(X3,meet(X3,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c237,plain,
join(X3,meet(X3,X2)) = join(meet(X3,X2),X3),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,axiom,
join(meet(X2,Y2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption_a) ).
cnf(c239,plain,
join(meet(X3,X2),X3) = X3,
inference(substitution,[status(thm)],[c238]) ).
cnf(c240,plain,
join(X3,meet(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c237,c239]) ).
cnf(c241,plain,
join(X3,meet(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c235,c240]) ).
cnf(c242,plain,
join(ld(rd(op(X3,ld(X3,X2)),X4),X2),meet(X4,ld(rd(op(X3,ld(X3,X2)),X4),X2))) = ld(rd(op(X3,ld(X3,X2)),X4),X2),
inference(substitution,[status(thm)],[c241]) ).
cnf(c243,plain,
join(ld(rd(op(X3,ld(X3,X2)),X4),X2),X4) = ld(rd(op(X3,ld(X3,X2)),X4),X2),
inference(transitivity,[status(thm)],[c232,c242]) ).
cnf(c244,plain,
join(X4,ld(rd(op(X3,ld(X3,X2)),X4),X2)) = ld(rd(op(X3,ld(X3,X2)),X4),X2),
inference(transitivity,[status(thm)],[c200,c243]) ).
cnf(c245,plain,
join(unit,ld(rd(op(X3,ld(X3,X2)),unit),X2)) = ld(rd(op(X3,ld(X3,X2)),unit),X2),
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
ld(rd(op(X3,ld(X3,X2)),unit),X2) = join(unit,ld(rd(op(X3,ld(X3,X2)),unit),X2)),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
op(X4,ld(rd(op(X3,ld(X3,X2)),unit),X2)) = op(X4,join(unit,ld(rd(op(X3,ld(X3,X2)),unit),X2))),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
meet(X4,op(X4,ld(rd(op(X3,ld(X3,X2)),unit),X2))) = meet(X4,op(X4,join(unit,ld(rd(op(X3,ld(X3,X2)),unit),X2)))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
join(X2,unit) = join(unit,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c250,plain,
join(unit,X2) = join(X2,unit),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
op(X3,join(unit,X2)) = op(X3,join(X2,unit)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
meet(X3,op(X3,join(unit,X2))) = meet(X3,op(X3,join(X2,unit))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
rd(op(X3,join(X2,unit)),unit) = op(X3,join(X2,unit)),
inference(substitution,[status(thm)],[c193]) ).
cnf(c254,plain,
op(X3,join(X2,unit)) = rd(op(X3,join(X2,unit)),unit),
inference(symmetry,[status(thm)],[c253]) ).
cnf(c255,plain,
meet(X3,op(X3,join(X2,unit))) = meet(X3,rd(op(X3,join(X2,unit)),unit)),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
join(unit,join(X3,op(X2,ld(X2,unit)))) = join(X3,unit),
inference(substitution,[status(thm)],[c215]) ).
cnf(c257,plain,
join(X3,unit) = join(unit,join(X3,op(X2,ld(X2,unit)))),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
op(X4,join(X3,unit)) = op(X4,join(unit,join(X3,op(X2,ld(X2,unit))))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
rd(op(X4,join(X3,unit)),unit) = rd(op(X4,join(unit,join(X3,op(X2,ld(X2,unit))))),unit),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
meet(X4,rd(op(X4,join(X3,unit)),unit)) = meet(X4,rd(op(X4,join(unit,join(X3,op(X2,ld(X2,unit))))),unit)),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
meet(X2,join(X4,X3)) = meet(join(X4,X3),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c262,plain,
meet(join(X4,X3),X2) = meet(X2,join(X4,X3)),
inference(symmetry,[status(thm)],[c261]) ).
cnf(c263,plain,
meet(X4,meet(join(X4,X3),X2)) = meet(X4,meet(X2,join(X4,X3))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
meet(join(X4,X2),X3) = meet(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c265,plain,
meet(X3,join(X4,X2)) = meet(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
meet(X4,meet(X3,join(X4,X2))) = meet(X4,meet(join(X4,X2),X3)),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,axiom,
meet(meet(X2,Y2),Z2) = meet(X2,meet(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(c268,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,meet(join(X4,X2),X3)),
inference(substitution,[status(thm)],[c267]) ).
cnf(c269,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(meet(X4,join(X4,X2)),X3),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,X3),
inference(congruence,[status(thm)],[c37]) ).
cnf(c271,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c269,c270]) ).
cnf(c272,plain,
meet(X4,meet(X3,join(X4,X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c266,c271]) ).
cnf(c273,plain,
meet(X4,meet(X2,join(X4,X3))) = meet(X4,X2),
inference(substitution,[status(thm)],[c272]) ).
cnf(c274,plain,
meet(X4,meet(join(X4,X3),X2)) = meet(X4,X2),
inference(transitivity,[status(thm)],[c263,c273]) ).
cnf(c275,plain,
meet(X4,meet(join(X4,X2),ld(X3,op(X3,join(X4,X2))))) = meet(X4,ld(X3,op(X3,join(X4,X2)))),
inference(substitution,[status(thm)],[c274]) ).
cnf(c276,plain,
meet(X4,ld(X3,op(X3,join(X4,X2)))) = meet(X4,meet(join(X4,X2),ld(X3,op(X3,join(X4,X2))))),
inference(symmetry,[status(thm)],[c275]) ).
cnf(c277,plain,
meet(join(X4,X2),ld(X3,op(X3,join(X4,X2)))) = join(X4,X2),
inference(substitution,[status(thm)],[c57]) ).
cnf(c278,plain,
meet(X4,meet(join(X4,X2),ld(X3,op(X3,join(X4,X2))))) = meet(X4,join(X4,X2)),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
meet(X4,meet(join(X4,X2),ld(X3,op(X3,join(X4,X2))))) = X4,
inference(transitivity,[status(thm)],[c278,c37]) ).
cnf(c280,plain,
meet(X4,ld(X3,op(X3,join(X4,X2)))) = X4,
inference(transitivity,[status(thm)],[c276,c279]) ).
cnf(c281,plain,
meet(X3,ld(X4,op(X4,join(X3,X2)))) = X3,
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
X3 = meet(X3,ld(X4,op(X4,join(X3,X2)))),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
rd(op(X4,join(X3,X2)),X3) = rd(op(X4,join(X3,X2)),meet(X3,ld(X4,op(X4,join(X3,X2))))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
meet(X4,rd(op(X4,join(X3,X2)),X3)) = meet(X4,rd(op(X4,join(X3,X2)),meet(X3,ld(X4,op(X4,join(X3,X2)))))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
meet(ld(X4,X3),X2) = meet(X2,ld(X4,X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c286,plain,
meet(X2,ld(X4,X3)) = meet(ld(X4,X3),X2),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
rd(X3,meet(X2,ld(X4,X3))) = rd(X3,meet(ld(X4,X3),X2)),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
meet(X4,rd(X3,meet(X2,ld(X4,X3)))) = meet(X4,rd(X3,meet(ld(X4,X3),X2))),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
join(X3,op(X4,meet(ld(X4,X3),X2))) = X3,
inference(substitution,[status(thm)],[c23]) ).
cnf(c290,plain,
X3 = join(X3,op(X4,meet(ld(X4,X3),X2))),
inference(symmetry,[status(thm)],[c289]) ).
cnf(c291,plain,
rd(X3,meet(ld(X4,X3),X2)) = rd(join(X3,op(X4,meet(ld(X4,X3),X2))),meet(ld(X4,X3),X2)),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
meet(X4,rd(X3,meet(ld(X4,X3),X2))) = meet(X4,rd(join(X3,op(X4,meet(ld(X4,X3),X2))),meet(ld(X4,X3),X2))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
join(op(X4,X2),X3) = join(X3,op(X4,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c294,plain,
join(X3,op(X4,X2)) = join(op(X4,X2),X3),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
rd(join(X3,op(X4,X2)),X2) = rd(join(op(X4,X2),X3),X2),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
meet(X4,rd(join(X3,op(X4,X2)),X2)) = meet(X4,rd(join(op(X4,X2),X3),X2)),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
meet(X4,rd(join(op(X4,X2),X3),X2)) = X4,
inference(substitution,[status(thm)],[c188]) ).
cnf(c298,plain,
meet(X4,rd(join(X3,op(X4,X2)),X2)) = X4,
inference(transitivity,[status(thm)],[c296,c297]) ).
cnf(c299,plain,
meet(X4,rd(join(X3,op(X4,meet(ld(X4,X3),X2))),meet(ld(X4,X3),X2))) = X4,
inference(substitution,[status(thm)],[c298]) ).
cnf(c300,plain,
meet(X4,rd(X3,meet(ld(X4,X3),X2))) = X4,
inference(transitivity,[status(thm)],[c292,c299]) ).
cnf(c301,plain,
meet(X4,rd(X3,meet(X2,ld(X4,X3)))) = X4,
inference(transitivity,[status(thm)],[c288,c300]) ).
cnf(c302,plain,
meet(X4,rd(op(X4,join(X3,X2)),meet(X3,ld(X4,op(X4,join(X3,X2)))))) = X4,
inference(substitution,[status(thm)],[c301]) ).
cnf(c303,plain,
meet(X4,rd(op(X4,join(X3,X2)),X3)) = X4,
inference(transitivity,[status(thm)],[c284,c302]) ).
cnf(c304,plain,
meet(X4,rd(op(X4,join(unit,join(X3,op(X2,ld(X2,unit))))),unit)) = X4,
inference(substitution,[status(thm)],[c303]) ).
cnf(c305,plain,
meet(X3,rd(op(X3,join(X2,unit)),unit)) = X3,
inference(transitivity,[status(thm)],[c260,c304]) ).
cnf(c306,plain,
meet(X3,op(X3,join(X2,unit))) = X3,
inference(transitivity,[status(thm)],[c255,c305]) ).
cnf(c307,plain,
meet(X3,op(X3,join(unit,X2))) = X3,
inference(transitivity,[status(thm)],[c252,c306]) ).
cnf(c308,plain,
meet(X4,op(X4,join(unit,ld(rd(op(X3,ld(X3,X2)),unit),X2)))) = X4,
inference(substitution,[status(thm)],[c307]) ).
cnf(c309,plain,
meet(X4,op(X4,ld(rd(op(X3,ld(X3,X2)),unit),X2))) = X4,
inference(transitivity,[status(thm)],[c248,c308]) ).
cnf(c310,plain,
meet(X4,op(X4,ld(op(X3,ld(X3,X2)),X2))) = X4,
inference(transitivity,[status(thm)],[c198,c309]) ).
cnf(c311,plain,
meet(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))) = op(X2,ld(X2,unit)),
inference(substitution,[status(thm)],[c310]) ).
cnf(c312,plain,
op(X2,ld(X2,unit)) = meet(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))),
inference(symmetry,[status(thm)],[c311]) ).
cnf(c313,plain,
join(meet(unit,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))),op(X2,ld(X2,unit))) = join(meet(unit,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))),meet(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)))),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
meet(X3,op(X2,ld(X2,X4))) = meet(op(X2,ld(X2,X4)),X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c315,plain,
meet(op(X2,ld(X2,X4)),X3) = meet(X3,op(X2,ld(X2,X4))),
inference(symmetry,[status(thm)],[c314]) ).
cnf(c316,plain,
join(meet(X4,X3),meet(op(X2,ld(X2,X4)),X3)) = join(meet(X4,X3),meet(X3,op(X2,ld(X2,X4)))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c318,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c317]) ).
cnf(c319,plain,
join(meet(X4,X3),meet(X3,op(X2,ld(X2,X4)))) = join(meet(X3,X4),meet(X3,op(X2,ld(X2,X4)))),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
op(X2,ld(X2,X3)) = meet(X3,op(X2,ld(X2,X3))),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c321,plain,
meet(X4,op(X2,ld(X2,X3))) = meet(X4,meet(X3,op(X2,ld(X2,X3)))),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
join(meet(X4,X3),meet(X4,op(X2,ld(X2,X3)))) = join(meet(X4,X3),meet(X4,meet(X3,op(X2,ld(X2,X3))))),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
meet(meet(X4,X3),X2) = meet(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c267]) ).
cnf(c324,plain,
meet(X4,meet(X3,X2)) = meet(meet(X4,X3),X2),
inference(symmetry,[status(thm)],[c323]) ).
cnf(c325,plain,
join(meet(X4,X3),meet(X4,meet(X3,X2))) = join(meet(X4,X3),meet(meet(X4,X3),X2)),
inference(congruence,[status(thm)],[c324]) ).
cnf(c326,plain,
join(meet(X4,X3),meet(meet(X4,X3),X2)) = meet(X4,X3),
inference(substitution,[status(thm)],[c240]) ).
cnf(c327,plain,
join(meet(X4,X3),meet(X4,meet(X3,X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c325,c326]) ).
cnf(c328,plain,
join(meet(X4,X3),meet(X4,meet(X3,op(X2,ld(X2,X3))))) = meet(X4,X3),
inference(substitution,[status(thm)],[c327]) ).
cnf(c329,plain,
join(meet(X4,X3),meet(X4,op(X2,ld(X2,X3)))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c322,c328]) ).
cnf(c330,plain,
join(meet(X3,X4),meet(X3,op(X2,ld(X2,X4)))) = meet(X3,X4),
inference(substitution,[status(thm)],[c329]) ).
cnf(c331,plain,
join(meet(X4,X3),meet(X3,op(X2,ld(X2,X4)))) = meet(X3,X4),
inference(transitivity,[status(thm)],[c319,c330]) ).
cnf(c332,plain,
join(meet(X4,X3),meet(op(X2,ld(X2,X4)),X3)) = meet(X3,X4),
inference(transitivity,[status(thm)],[c316,c331]) ).
cnf(c333,plain,
join(meet(unit,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))),meet(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)))) = meet(op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)),unit),
inference(substitution,[status(thm)],[c332]) ).
cnf(c334,plain,
op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)) = at(op(X2,ld(X2,unit)),unit),
inference(substitution,[status(thm)],[c80]) ).
cnf(c335,plain,
meet(op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)),unit) = meet(at(op(X2,ld(X2,unit)),unit),unit),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
meet(at(op(X2,ld(X2,unit)),unit),unit) = meet(unit,at(op(X2,ld(X2,unit)),unit)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c337,plain,
meet(at(X2,unit),unit) = meet(unit,at(X2,unit)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c338,plain,
meet(unit,at(X2,unit)) = meet(at(X2,unit),unit),
inference(symmetry,[status(thm)],[c337]) ).
cnf(c339,plain,
unit = join(unit,at(X2,unit)),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c340,plain,
meet(at(X2,unit),unit) = meet(at(X2,unit),join(unit,at(X2,unit))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
meet(at(X2,unit),join(unit,at(X2,unit))) = at(X2,unit),
inference(substitution,[status(thm)],[c38]) ).
cnf(c342,plain,
meet(at(X2,unit),unit) = at(X2,unit),
inference(transitivity,[status(thm)],[c340,c341]) ).
cnf(c343,plain,
meet(unit,at(X2,unit)) = at(X2,unit),
inference(transitivity,[status(thm)],[c338,c342]) ).
cnf(c344,plain,
meet(unit,at(op(X2,ld(X2,unit)),unit)) = at(op(X2,ld(X2,unit)),unit),
inference(substitution,[status(thm)],[c343]) ).
cnf(c345,plain,
meet(at(op(X2,ld(X2,unit)),unit),unit) = at(op(X2,ld(X2,unit)),unit),
inference(transitivity,[status(thm)],[c336,c344]) ).
cnf(c346,plain,
meet(op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)),unit) = at(op(X2,ld(X2,unit)),unit),
inference(transitivity,[status(thm)],[c335,c345]) ).
cnf(c347,plain,
join(meet(unit,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))),meet(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)))) = at(op(X2,ld(X2,unit)),unit),
inference(transitivity,[status(thm)],[c333,c346]) ).
cnf(c348,plain,
join(meet(unit,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit))),op(X2,ld(X2,unit))) = at(op(X2,ld(X2,unit)),unit),
inference(transitivity,[status(thm)],[c313,c347]) ).
cnf(c349,plain,
join(op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)),op(X2,ld(X2,unit))) = at(op(X2,ld(X2,unit)),unit),
inference(transitivity,[status(thm)],[c152,c348]) ).
cnf(c350,plain,
join(at(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit))) = at(op(X2,ld(X2,unit)),unit),
inference(transitivity,[status(thm)],[c142,c349]) ).
cnf(c351,plain,
join(op(X2,ld(X2,unit)),at(op(X2,ld(X2,unit)),unit)) = at(op(X2,ld(X2,unit)),unit),
inference(transitivity,[status(thm)],[c139,c350]) ).
cnf(c352,plain,
at(op(X2,ld(X2,unit)),unit) = join(op(X2,ld(X2,unit)),at(op(X2,ld(X2,unit)),unit)),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
ld(X2,at(op(X2,ld(X2,unit)),unit)) = ld(X2,join(op(X2,ld(X2,unit)),at(op(X2,ld(X2,unit)),unit))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
meet(ld(X2,unit),ld(X2,at(op(X2,ld(X2,unit)),unit))) = meet(ld(X2,unit),ld(X2,join(op(X2,ld(X2,unit)),at(op(X2,ld(X2,unit)),unit)))),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
meet(ld(X2,unit),ld(X2,join(op(X2,ld(X2,unit)),at(op(X2,ld(X2,unit)),unit)))) = ld(X2,unit),
inference(substitution,[status(thm)],[c55]) ).
cnf(c356,plain,
meet(ld(X2,unit),ld(X2,at(op(X2,ld(X2,unit)),unit))) = ld(X2,unit),
inference(transitivity,[status(thm)],[c354,c355]) ).
cnf(c357,plain,
ld(X2,at(op(X2,ld(X2,unit)),unit)) = ld(X2,unit),
inference(transitivity,[status(thm)],[c137,c356]) ).
cnf(c358,plain,
meet(op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),ld(X2,at(op(X2,ld(X2,unit)),unit))) = meet(op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),ld(X2,unit)),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
meet(op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),ld(X2,unit)) = meet(ld(X2,unit),op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c360,plain,
meet(ld(X2,unit),op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit))) = ld(X2,unit),
inference(substitution,[status(thm)],[c310]) ).
cnf(c361,plain,
meet(op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),ld(X2,unit)) = ld(X2,unit),
inference(transitivity,[status(thm)],[c359,c360]) ).
cnf(c362,plain,
meet(op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),ld(X2,at(op(X2,ld(X2,unit)),unit))) = ld(X2,unit),
inference(transitivity,[status(thm)],[c358,c361]) ).
cnf(c363,plain,
meet(op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),ld(X2,op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)))) = ld(X2,unit),
inference(transitivity,[status(thm)],[c93,c362]) ).
cnf(c364,plain,
op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)) = ld(X2,unit),
inference(transitivity,[status(thm)],[c90,c363]) ).
cnf(c365,plain,
op(X2,op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit))) = op(X2,ld(X2,unit)),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
op(op(X2,ld(X2,unit)),ld(op(X2,ld(X2,unit)),unit)) = op(X2,ld(X2,unit)),
inference(transitivity,[status(thm)],[c83,c365]) ).
cnf(c367,plain,
at(op(X2,ld(X2,unit)),unit) = op(X2,ld(X2,unit)),
inference(transitivity,[status(thm)],[c82,c366]) ).
cnf(c368,plain,
at(op(x,ld(x,unit)),unit) = op(x,ld(x,unit)),
inference(substitution,[status(thm)],[c367]) ).
cnf(c369,plain,
$false,
inference(resolution,[status(thm)],[c1,c368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MVA008-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n009.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 27 17:45:59 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 94.35/12.31 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 94.35/12.31
% 94.35/12.31 % SZS status Unsatisfiable
% 94.35/12.31
% 94.35/12.33 % SZS output start CNFRefutation
% See solution above
% 95.95/12.51
% 95.95/12.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------