%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : MVA009-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 102.19s 13.31s
% Output : CNFRefutation 105.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 18
% Syntax : Number of clauses : 637 ( 637 unt; 0 nHn; 10 RR)
% Number of literals : 637 ( 636 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 1199 ( 73 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
at(unit,op(x,ld(x,unit))) != unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
op(unit,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_monoid_unit) ).
cnf(c3,plain,
op(unit,ld(ld(X2,unit),unit)) = ld(ld(X2,unit),unit),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
ld(ld(X2,unit),unit) = op(unit,ld(ld(X2,unit),unit)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
op(unit,op(unit,ld(ld(X2,unit),unit))) = op(unit,ld(ld(X2,unit),unit)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
op(unit,ld(ld(X2,unit),unit)) = op(unit,op(unit,ld(ld(X2,unit),unit))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
join(X2,Y) = join(Y,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c8,plain,
join(ld(unit,X2),X2) = join(X2,ld(unit,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
join(X2,ld(unit,X2)) = join(ld(unit,X2),X2),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
X2 = op(unit,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c11,plain,
ld(unit,X2) = ld(unit,op(unit,X2)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
meet(X2,ld(unit,X2)) = meet(X2,ld(unit,op(unit,X2))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,axiom,
join(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
cnf(c14,plain,
join(op(X3,X2),op(X3,X2)) = op(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
op(X2,X3) = join(op(X2,X3),op(X2,X3)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
ld(X2,op(X2,X3)) = ld(X2,join(op(X2,X3),op(X2,X3))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
meet(X3,ld(X2,op(X2,X3))) = meet(X3,ld(X2,join(op(X2,X3),op(X2,X3)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,axiom,
meet(X2,Y2) = meet(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c19,plain,
meet(ld(X2,join(op(X2,X3),X4)),X3) = meet(X3,ld(X2,join(op(X2,X3),X4))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
meet(X4,ld(X3,join(op(X3,X4),X2))) = meet(ld(X3,join(op(X3,X4),X2)),X4),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
meet(ld(X2,join(op(X2,Y2),Z)),Y2) = Y2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',residual_c) ).
cnf(c22,plain,
meet(ld(X3,join(op(X3,X4),X2)),X4) = X4,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
meet(X4,ld(X3,join(op(X3,X4),X2))) = X4,
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
meet(X3,ld(X2,join(op(X2,X3),op(X2,X3)))) = X3,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
meet(X3,ld(X2,op(X2,X3))) = X3,
inference(transitivity,[status(thm)],[c17,c24]) ).
cnf(c26,plain,
meet(X2,ld(unit,op(unit,X2))) = X2,
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
meet(X2,ld(unit,X2)) = X2,
inference(transitivity,[status(thm)],[c12,c26]) ).
cnf(c28,plain,
X2 = meet(X2,ld(unit,X2)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
join(ld(unit,X2),X2) = join(ld(unit,X2),meet(X2,ld(unit,X2))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c31,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
join(X3,meet(X2,X3)) = join(X3,meet(X3,X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
join(meet(X3,X2),X3) = join(X3,meet(X3,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c34,plain,
join(X3,meet(X3,X2)) = join(meet(X3,X2),X3),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,axiom,
join(meet(X2,Y2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption_a) ).
cnf(c36,plain,
join(meet(X3,X2),X3) = X3,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
join(X3,meet(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c34,c36]) ).
cnf(c38,plain,
join(X3,meet(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c32,c37]) ).
cnf(c39,plain,
join(ld(unit,X2),meet(X2,ld(unit,X2))) = ld(unit,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
join(ld(unit,X2),X2) = ld(unit,X2),
inference(transitivity,[status(thm)],[c29,c39]) ).
cnf(c41,plain,
join(X2,ld(unit,X2)) = ld(unit,X2),
inference(transitivity,[status(thm)],[c9,c40]) ).
cnf(c42,plain,
ld(unit,X2) = join(X2,ld(unit,X2)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
op(unit,ld(unit,X2)) = ld(unit,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c44,plain,
ld(unit,X2) = op(unit,ld(unit,X2)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
join(X2,ld(unit,X2)) = join(X2,op(unit,ld(unit,X2))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
meet(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
cnf(c47,plain,
meet(ld(X2,X3),ld(X2,X3)) = ld(X2,X3),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
ld(X2,X3) = meet(ld(X2,X3),ld(X2,X3)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
op(X2,ld(X2,X3)) = op(X2,meet(ld(X2,X3),ld(X2,X3))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
join(X3,op(X2,ld(X2,X3))) = join(X3,op(X2,meet(ld(X2,X3),ld(X2,X3)))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
join(op(X3,meet(ld(X3,X4),X2)),X4) = join(X4,op(X3,meet(ld(X3,X4),X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c52,plain,
join(X4,op(X3,meet(ld(X3,X4),X2))) = join(op(X3,meet(ld(X3,X4),X2)),X4),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,axiom,
join(op(X2,meet(ld(X2,Z2),Y2)),Z2) = Z2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',residual_a) ).
cnf(c54,plain,
join(op(X3,meet(ld(X3,X4),X2)),X4) = X4,
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
join(X4,op(X3,meet(ld(X3,X4),X2))) = X4,
inference(transitivity,[status(thm)],[c52,c54]) ).
cnf(c56,plain,
join(X3,op(X2,meet(ld(X2,X3),ld(X2,X3)))) = X3,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
join(X3,op(X2,ld(X2,X3))) = X3,
inference(transitivity,[status(thm)],[c50,c56]) ).
cnf(c58,plain,
join(X2,op(unit,ld(unit,X2))) = X2,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
join(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(unit,ld(ld(X2,unit),unit)) = op(ld(unit,unit),ld(ld(X2,unit),unit)),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
op(unit,op(unit,ld(ld(X2,unit),unit))) = op(unit,op(ld(unit,unit),ld(ld(X2,unit),unit))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,axiom,
op(op(X2,Y2),Z2) = op(X2,op(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoid_associativity) ).
cnf(c66,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)],[c65]) ).
cnf(c67,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)],[c66]) ).
cnf(c68,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(c69,plain,
at(X3,X2) = op(op(X3,ld(X3,unit)),ld(ld(X2,unit),unit)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
op(op(X3,ld(X3,unit)),ld(ld(X2,unit),unit)) = at(X3,X2),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
op(X3,op(ld(X3,unit),ld(ld(X2,unit),unit))) = at(X3,X2),
inference(transitivity,[status(thm)],[c67,c70]) ).
cnf(c72,plain,
op(unit,op(ld(unit,unit),ld(ld(X2,unit),unit))) = at(unit,X2),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
op(unit,op(unit,ld(ld(X2,unit),unit))) = at(unit,X2),
inference(transitivity,[status(thm)],[c64,c72]) ).
cnf(c74,plain,
op(unit,ld(ld(X2,unit),unit)) = at(unit,X2),
inference(transitivity,[status(thm)],[c6,c73]) ).
cnf(c75,plain,
ld(ld(X2,unit),unit) = at(unit,X2),
inference(transitivity,[status(thm)],[c4,c74]) ).
cnf(c76,plain,
ld(ld(op(X2,ld(X2,unit)),unit),unit) = at(unit,op(X2,ld(X2,unit))),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
at(unit,op(X2,ld(X2,unit))) = ld(ld(op(X2,ld(X2,unit)),unit),unit),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
rd(unit,at(unit,op(X2,ld(X2,unit)))) = rd(unit,ld(ld(op(X2,ld(X2,unit)),unit),unit)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
join(X2,op(X3,ld(X3,X2))) = join(op(X3,ld(X3,X2)),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c80,plain,
join(op(X3,ld(X3,X2)),X2) = join(X2,op(X3,ld(X3,X2))),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
join(X2,op(X3,ld(X3,X2))) = X2,
inference(substitution,[status(thm)],[c57]) ).
cnf(c82,plain,
join(op(X3,ld(X3,X2)),X2) = X2,
inference(transitivity,[status(thm)],[c80,c81]) ).
cnf(c83,plain,
X2 = join(op(X3,ld(X3,X2)),X2),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
ld(op(X3,ld(X3,X2)),X2) = ld(op(X3,ld(X3,X2)),join(op(X3,ld(X3,X2)),X2)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
meet(unit,ld(op(X3,ld(X3,X2)),X2)) = meet(unit,ld(op(X3,ld(X3,X2)),join(op(X3,ld(X3,X2)),X2))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,axiom,
op(X2,unit) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c87,plain,
X2 = op(X2,unit),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
join(X3,X2) = join(op(X3,unit),X2),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
ld(X3,join(X3,X2)) = ld(X3,join(op(X3,unit),X2)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
meet(unit,ld(X3,join(X3,X2))) = meet(unit,ld(X3,join(op(X3,unit),X2))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
meet(unit,ld(X3,join(op(X3,unit),X2))) = unit,
inference(substitution,[status(thm)],[c23]) ).
cnf(c92,plain,
meet(unit,ld(X3,join(X3,X2))) = unit,
inference(transitivity,[status(thm)],[c90,c91]) ).
cnf(c93,plain,
meet(unit,ld(op(X3,ld(X3,X2)),join(op(X3,ld(X3,X2)),X2))) = unit,
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
meet(unit,ld(op(X3,ld(X3,X2)),X2)) = unit,
inference(transitivity,[status(thm)],[c85,c93]) ).
cnf(c95,plain,
meet(unit,ld(op(X2,ld(X2,unit)),unit)) = unit,
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
unit = meet(unit,ld(op(X2,ld(X2,unit)),unit)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
ld(ld(op(X2,ld(X2,unit)),unit),unit) = ld(ld(op(X2,ld(X2,unit)),unit),meet(unit,ld(op(X2,ld(X2,unit)),unit))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
rd(unit,ld(ld(op(X2,ld(X2,unit)),unit),unit)) = rd(unit,ld(ld(op(X2,ld(X2,unit)),unit),meet(unit,ld(op(X2,ld(X2,unit)),unit)))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
meet(unit,ld(op(X2,ld(X2,unit)),unit)) = unit,
inference(substitution,[status(thm)],[c94]) ).
cnf(c100,plain,
unit = meet(unit,ld(op(X2,ld(X2,unit)),unit)),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
rd(unit,ld(ld(op(X2,ld(X2,unit)),unit),meet(unit,ld(op(X2,ld(X2,unit)),unit)))) = rd(meet(unit,ld(op(X2,ld(X2,unit)),unit)),ld(ld(op(X2,ld(X2,unit)),unit),meet(unit,ld(op(X2,ld(X2,unit)),unit)))),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c103,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
ld(X2,meet(X3,X2)) = ld(X2,meet(X2,X3)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
rd(meet(X3,X2),ld(X2,meet(X3,X2))) = rd(meet(X3,X2),ld(X2,meet(X2,X3))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c107,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
rd(meet(X3,X2),ld(X2,meet(X2,X3))) = rd(meet(X2,X3),ld(X2,meet(X2,X3))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
X3 = join(X3,meet(X3,X2)),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c110,plain,
ld(X3,meet(X3,X2)) = ld(join(X3,meet(X3,X2)),meet(X3,X2)),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
rd(meet(X3,X2),ld(X3,meet(X3,X2))) = rd(meet(X3,X2),ld(join(X3,meet(X3,X2)),meet(X3,X2))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c113,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
ld(join(X2,X3),X3) = ld(join(X3,X2),X3),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
rd(X3,ld(join(X2,X3),X3)) = rd(X3,ld(join(X3,X2),X3)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,axiom,
join(X2,Y2) = rd(X2,ld(join(X2,Y2),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',generalized_mv_algebra_a) ).
cnf(c117,plain,
join(X3,X2) = rd(X3,ld(join(X3,X2),X3)),
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
rd(X3,ld(join(X3,X2),X3)) = join(X3,X2),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
rd(X3,ld(join(X2,X3),X3)) = join(X3,X2),
inference(transitivity,[status(thm)],[c115,c118]) ).
cnf(c120,plain,
rd(meet(X3,X2),ld(join(X3,meet(X3,X2)),meet(X3,X2))) = join(meet(X3,X2),X3),
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
join(meet(X3,X2),X3) = join(X3,meet(X3,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c122,plain,
join(meet(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c121,c37]) ).
cnf(c123,plain,
rd(meet(X3,X2),ld(join(X3,meet(X3,X2)),meet(X3,X2))) = X3,
inference(transitivity,[status(thm)],[c120,c122]) ).
cnf(c124,plain,
rd(meet(X3,X2),ld(X3,meet(X3,X2))) = X3,
inference(transitivity,[status(thm)],[c111,c123]) ).
cnf(c125,plain,
rd(meet(X2,X3),ld(X2,meet(X2,X3))) = X2,
inference(substitution,[status(thm)],[c124]) ).
cnf(c126,plain,
rd(meet(X3,X2),ld(X2,meet(X2,X3))) = X2,
inference(transitivity,[status(thm)],[c108,c125]) ).
cnf(c127,plain,
rd(meet(X3,X2),ld(X2,meet(X3,X2))) = X2,
inference(transitivity,[status(thm)],[c105,c126]) ).
cnf(c128,plain,
rd(meet(unit,ld(op(X2,ld(X2,unit)),unit)),ld(ld(op(X2,ld(X2,unit)),unit),meet(unit,ld(op(X2,ld(X2,unit)),unit)))) = ld(op(X2,ld(X2,unit)),unit),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
rd(unit,ld(ld(op(X2,ld(X2,unit)),unit),meet(unit,ld(op(X2,ld(X2,unit)),unit)))) = ld(op(X2,ld(X2,unit)),unit),
inference(transitivity,[status(thm)],[c101,c128]) ).
cnf(c130,plain,
rd(unit,ld(ld(op(X2,ld(X2,unit)),unit),unit)) = ld(op(X2,ld(X2,unit)),unit),
inference(transitivity,[status(thm)],[c98,c129]) ).
cnf(c131,plain,
rd(unit,at(unit,op(X2,ld(X2,unit)))) = ld(op(X2,ld(X2,unit)),unit),
inference(transitivity,[status(thm)],[c78,c130]) ).
cnf(c132,plain,
ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit) = ld(ld(op(X2,ld(X2,unit)),unit),unit),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
ld(ld(op(X2,ld(X2,unit)),unit),unit) = at(unit,op(X2,ld(X2,unit))),
inference(substitution,[status(thm)],[c75]) ).
cnf(c134,plain,
ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit) = at(unit,op(X2,ld(X2,unit))),
inference(transitivity,[status(thm)],[c132,c133]) ).
cnf(c135,plain,
at(unit,op(X2,ld(X2,unit))) = ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),X3) = meet(X3,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c137,plain,
meet(X3,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3)) = meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),X3),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
X2 = ld(unit,X2),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c139,plain,
meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),X3) = meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),ld(unit,X3)),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
join(rd(X2,X2),unit) = join(unit,rd(X2,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c141,plain,
join(unit,rd(X2,X2)) = join(rd(X2,X2),unit),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
X2 = op(unit,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c143,plain,
rd(X2,X2) = rd(op(unit,X2),X2),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
meet(unit,rd(X2,X2)) = meet(unit,rd(op(unit,X2),X2)),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
join(op(X3,X2),op(X3,X2)) = op(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c146,plain,
op(X3,X2) = join(op(X3,X2),op(X3,X2)),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
rd(op(X3,X2),X2) = rd(join(op(X3,X2),op(X3,X2)),X2),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
meet(X3,rd(op(X3,X2),X2)) = meet(X3,rd(join(op(X3,X2),op(X3,X2)),X2)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
meet(rd(join(op(X4,X3),X2),X3),X4) = meet(X4,rd(join(op(X4,X3),X2),X3)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c150,plain,
meet(X4,rd(join(op(X4,X3),X2),X3)) = meet(rd(join(op(X4,X3),X2),X3),X4),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,axiom,
meet(rd(join(op(Y2,X2),Z2),X2),Y2) = Y2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',residual_d) ).
cnf(c152,plain,
meet(rd(join(op(X4,X3),X2),X3),X4) = X4,
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
meet(X4,rd(join(op(X4,X3),X2),X3)) = X4,
inference(transitivity,[status(thm)],[c150,c152]) ).
cnf(c154,plain,
meet(X3,rd(join(op(X3,X2),op(X3,X2)),X2)) = X3,
inference(substitution,[status(thm)],[c153]) ).
cnf(c155,plain,
meet(X3,rd(op(X3,X2),X2)) = X3,
inference(transitivity,[status(thm)],[c148,c154]) ).
cnf(c156,plain,
meet(unit,rd(op(unit,X2),X2)) = unit,
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
meet(unit,rd(X2,X2)) = unit,
inference(transitivity,[status(thm)],[c144,c156]) ).
cnf(c158,plain,
unit = meet(unit,rd(X2,X2)),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
join(rd(X2,X2),unit) = join(rd(X2,X2),meet(unit,rd(X2,X2))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
join(rd(X2,X2),meet(unit,rd(X2,X2))) = rd(X2,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c161,plain,
join(rd(X2,X2),unit) = rd(X2,X2),
inference(transitivity,[status(thm)],[c159,c160]) ).
cnf(c162,plain,
join(unit,rd(X2,X2)) = rd(X2,X2),
inference(transitivity,[status(thm)],[c141,c161]) ).
cnf(c163,plain,
rd(X2,X2) = join(unit,rd(X2,X2)),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
join(rd(X2,X2),unit) = join(unit,rd(X2,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c165,plain,
join(unit,rd(X2,X2)) = join(rd(X2,X2),unit),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
op(ld(X2,unit),unit) = ld(X2,unit),
inference(substitution,[status(thm)],[c86]) ).
cnf(c167,plain,
ld(X2,unit) = op(ld(X2,unit),unit),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
op(X2,ld(X2,unit)) = op(X2,op(ld(X2,unit),unit)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
ld(unit,unit) = unit,
inference(substitution,[status(thm)],[c60]) ).
cnf(c170,plain,
unit = ld(unit,unit),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
op(ld(X2,unit),unit) = op(ld(X2,unit),ld(unit,unit)),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
op(X2,op(ld(X2,unit),unit)) = op(X2,op(ld(X2,unit),ld(unit,unit))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
ld(unit,unit) = unit,
inference(substitution,[status(thm)],[c60]) ).
cnf(c174,plain,
unit = ld(unit,unit),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
ld(unit,unit) = ld(ld(unit,unit),unit),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
op(ld(X2,unit),ld(unit,unit)) = op(ld(X2,unit),ld(ld(unit,unit),unit)),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,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)],[c176]) ).
cnf(c178,plain,
op(X2,op(ld(X2,unit),ld(ld(unit,unit),unit))) = at(X2,unit),
inference(substitution,[status(thm)],[c71]) ).
cnf(c179,plain,
op(X2,op(ld(X2,unit),ld(unit,unit))) = at(X2,unit),
inference(transitivity,[status(thm)],[c177,c178]) ).
cnf(c180,plain,
op(X2,op(ld(X2,unit),unit)) = at(X2,unit),
inference(transitivity,[status(thm)],[c172,c179]) ).
cnf(c181,plain,
op(X2,ld(X2,unit)) = at(X2,unit),
inference(transitivity,[status(thm)],[c168,c180]) ).
cnf(c182,plain,
at(X2,unit) = op(X2,ld(X2,unit)),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
meet(unit,at(X2,unit)) = meet(unit,op(X2,ld(X2,unit))),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
meet(op(X2,ld(X2,X3)),X3) = meet(X3,op(X2,ld(X2,X3))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c185,plain,
meet(X3,op(X2,ld(X2,X3))) = meet(op(X2,ld(X2,X3)),X3),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
X3 = join(X3,op(X2,ld(X2,X3))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c187,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)],[c186]) ).
cnf(c188,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c189,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
meet(X3,join(X2,X3)) = meet(X3,join(X3,X2)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
meet(join(X3,X2),X3) = meet(X3,join(X3,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c192,plain,
meet(X3,join(X3,X2)) = meet(join(X3,X2),X3),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,axiom,
meet(join(X2,Y2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption_b) ).
cnf(c194,plain,
meet(join(X3,X2),X3) = X3,
inference(substitution,[status(thm)],[c193]) ).
cnf(c195,plain,
meet(X3,join(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c192,c194]) ).
cnf(c196,plain,
meet(X3,join(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c190,c195]) ).
cnf(c197,plain,
meet(op(X2,ld(X2,X3)),join(X3,op(X2,ld(X2,X3)))) = op(X2,ld(X2,X3)),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
meet(op(X2,ld(X2,X3)),X3) = op(X2,ld(X2,X3)),
inference(transitivity,[status(thm)],[c187,c197]) ).
cnf(c199,plain,
meet(X3,op(X2,ld(X2,X3))) = op(X2,ld(X2,X3)),
inference(transitivity,[status(thm)],[c185,c198]) ).
cnf(c200,plain,
meet(unit,op(X2,ld(X2,unit))) = op(X2,ld(X2,unit)),
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
meet(unit,op(X2,ld(X2,unit))) = at(X2,unit),
inference(transitivity,[status(thm)],[c200,c181]) ).
cnf(c202,plain,
meet(unit,at(X2,unit)) = at(X2,unit),
inference(transitivity,[status(thm)],[c183,c201]) ).
cnf(c203,plain,
at(X2,unit) = meet(unit,at(X2,unit)),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
rd(at(X2,unit),at(X2,unit)) = rd(at(X2,unit),meet(unit,at(X2,unit))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
ld(unit,meet(unit,at(X2,unit))) = meet(unit,at(X2,unit)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c206,plain,
meet(unit,at(X2,unit)) = ld(unit,meet(unit,at(X2,unit))),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
rd(at(X2,unit),meet(unit,at(X2,unit))) = rd(at(X2,unit),ld(unit,meet(unit,at(X2,unit)))),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
at(X2,unit) = meet(unit,at(X2,unit)),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c209,plain,
rd(at(X2,unit),ld(unit,meet(unit,at(X2,unit)))) = rd(meet(unit,at(X2,unit)),ld(unit,meet(unit,at(X2,unit)))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
rd(meet(unit,at(X2,unit)),ld(unit,meet(unit,at(X2,unit)))) = unit,
inference(substitution,[status(thm)],[c124]) ).
cnf(c211,plain,
rd(at(X2,unit),ld(unit,meet(unit,at(X2,unit)))) = unit,
inference(transitivity,[status(thm)],[c209,c210]) ).
cnf(c212,plain,
rd(at(X2,unit),meet(unit,at(X2,unit))) = unit,
inference(transitivity,[status(thm)],[c207,c211]) ).
cnf(c213,plain,
rd(at(X2,unit),at(X2,unit)) = unit,
inference(transitivity,[status(thm)],[c204,c212]) ).
cnf(c214,plain,
unit = rd(at(X2,unit),at(X2,unit)),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
join(rd(X2,X2),unit) = join(rd(X2,X2),rd(at(X2,unit),at(X2,unit))),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
at(X2,unit) = op(X2,ld(X2,unit)),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c217,plain,
op(rd(X2,X2),at(X2,unit)) = op(rd(X2,X2),op(X2,ld(X2,unit))),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
op(op(rd(X3,X3),X3),X2) = op(rd(X3,X3),op(X3,X2)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c219,plain,
op(rd(X3,X3),op(X3,X2)) = op(op(rd(X3,X3),X3),X2),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
meet(op(rd(X3,X2),X2),X3) = meet(X3,op(rd(X3,X2),X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c221,plain,
meet(X3,op(rd(X3,X2),X2)) = meet(op(rd(X3,X2),X2),X3),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
meet(rd(X3,X2),rd(X3,X2)) = rd(X3,X2),
inference(substitution,[status(thm)],[c46]) ).
cnf(c223,plain,
rd(X3,X2) = meet(rd(X3,X2),rd(X3,X2)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
op(rd(X3,X2),X2) = op(meet(rd(X3,X2),rd(X3,X2)),X2),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
join(X3,op(rd(X3,X2),X2)) = join(X3,op(meet(rd(X3,X2),rd(X3,X2)),X2)),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
join(op(meet(X3,rd(X4,X2)),X2),X4) = join(X4,op(meet(X3,rd(X4,X2)),X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c227,plain,
join(X4,op(meet(X3,rd(X4,X2)),X2)) = join(op(meet(X3,rd(X4,X2)),X2),X4),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,axiom,
join(op(meet(Y2,rd(Z2,X2)),X2),Z2) = Z2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',residual_b) ).
cnf(c229,plain,
join(op(meet(X3,rd(X4,X2)),X2),X4) = X4,
inference(substitution,[status(thm)],[c228]) ).
cnf(c230,plain,
join(X4,op(meet(X3,rd(X4,X2)),X2)) = X4,
inference(transitivity,[status(thm)],[c227,c229]) ).
cnf(c231,plain,
join(X3,op(meet(rd(X3,X2),rd(X3,X2)),X2)) = X3,
inference(substitution,[status(thm)],[c230]) ).
cnf(c232,plain,
join(X3,op(rd(X3,X2),X2)) = X3,
inference(transitivity,[status(thm)],[c225,c231]) ).
cnf(c233,plain,
X3 = join(X3,op(rd(X3,X2),X2)),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
meet(op(rd(X3,X2),X2),X3) = meet(op(rd(X3,X2),X2),join(X3,op(rd(X3,X2),X2))),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
meet(op(rd(X3,X2),X2),join(X3,op(rd(X3,X2),X2))) = op(rd(X3,X2),X2),
inference(substitution,[status(thm)],[c196]) ).
cnf(c236,plain,
meet(op(rd(X3,X2),X2),X3) = op(rd(X3,X2),X2),
inference(transitivity,[status(thm)],[c234,c235]) ).
cnf(c237,plain,
meet(X3,op(rd(X3,X2),X2)) = op(rd(X3,X2),X2),
inference(transitivity,[status(thm)],[c221,c236]) ).
cnf(c238,plain,
meet(X2,op(rd(X2,X2),X2)) = op(rd(X2,X2),X2),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
op(rd(X2,X2),X2) = meet(X2,op(rd(X2,X2),X2)),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
ld(unit,op(rd(X2,X2),X3)) = op(rd(X2,X2),X3),
inference(substitution,[status(thm)],[c60]) ).
cnf(c241,plain,
op(rd(X2,X2),X3) = ld(unit,op(rd(X2,X2),X3)),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
meet(X3,op(rd(X2,X2),X3)) = meet(X3,ld(unit,op(rd(X2,X2),X3))),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
rd(X2,X2) = join(unit,rd(X2,X2)),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c244,plain,
op(rd(X2,X2),X3) = op(join(unit,rd(X2,X2)),X3),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
ld(unit,op(rd(X2,X2),X3)) = ld(unit,op(join(unit,rd(X2,X2)),X3)),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
meet(X3,ld(unit,op(rd(X2,X2),X3))) = meet(X3,ld(unit,op(join(unit,rd(X2,X2)),X3))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
meet(X2,join(X4,X3)) = meet(join(X4,X3),X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c248,plain,
meet(join(X4,X3),X2) = meet(X2,join(X4,X3)),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
meet(X4,meet(join(X4,X3),X2)) = meet(X4,meet(X2,join(X4,X3))),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
meet(join(X4,X2),X3) = meet(X3,join(X4,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c251,plain,
meet(X3,join(X4,X2)) = meet(join(X4,X2),X3),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
meet(X4,meet(X3,join(X4,X2))) = meet(X4,meet(join(X4,X2),X3)),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,axiom,
meet(meet(X2,Y2),Z2) = meet(X2,meet(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(c254,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,meet(join(X4,X2),X3)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c255,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(meet(X4,join(X4,X2)),X3),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
meet(meet(X4,join(X4,X2)),X3) = meet(X4,X3),
inference(congruence,[status(thm)],[c195]) ).
cnf(c257,plain,
meet(X4,meet(join(X4,X2),X3)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
meet(X4,meet(X3,join(X4,X2))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c252,c257]) ).
cnf(c259,plain,
meet(X4,meet(X2,join(X4,X3))) = meet(X4,X2),
inference(substitution,[status(thm)],[c258]) ).
cnf(c260,plain,
meet(X4,meet(join(X4,X3),X2)) = meet(X4,X2),
inference(transitivity,[status(thm)],[c249,c259]) ).
cnf(c261,plain,
meet(X4,meet(join(X4,X3),rd(op(join(X4,X3),X2),X2))) = meet(X4,rd(op(join(X4,X3),X2),X2)),
inference(substitution,[status(thm)],[c260]) ).
cnf(c262,plain,
meet(X4,rd(op(join(X4,X3),X2),X2)) = meet(X4,meet(join(X4,X3),rd(op(join(X4,X3),X2),X2))),
inference(symmetry,[status(thm)],[c261]) ).
cnf(c263,plain,
meet(join(X4,X3),rd(op(join(X4,X3),X2),X2)) = join(X4,X3),
inference(substitution,[status(thm)],[c155]) ).
cnf(c264,plain,
meet(X4,meet(join(X4,X3),rd(op(join(X4,X3),X2),X2))) = meet(X4,join(X4,X3)),
inference(congruence,[status(thm)],[c263]) ).
cnf(c265,plain,
meet(X4,meet(join(X4,X3),rd(op(join(X4,X3),X2),X2))) = X4,
inference(transitivity,[status(thm)],[c264,c195]) ).
cnf(c266,plain,
meet(X4,rd(op(join(X4,X3),X2),X2)) = X4,
inference(transitivity,[status(thm)],[c262,c265]) ).
cnf(c267,plain,
meet(X3,rd(op(join(X3,X2),X4),X4)) = X3,
inference(substitution,[status(thm)],[c266]) ).
cnf(c268,plain,
X3 = meet(X3,rd(op(join(X3,X2),X4),X4)),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c269,plain,
ld(X3,op(join(X3,X2),X4)) = ld(meet(X3,rd(op(join(X3,X2),X4),X4)),op(join(X3,X2),X4)),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
meet(X4,ld(X3,op(join(X3,X2),X4))) = meet(X4,ld(meet(X3,rd(op(join(X3,X2),X4),X4)),op(join(X3,X2),X4))),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
join(X2,op(meet(X3,rd(X2,X4)),X4)) = X2,
inference(substitution,[status(thm)],[c230]) ).
cnf(c272,plain,
X2 = join(X2,op(meet(X3,rd(X2,X4)),X4)),
inference(symmetry,[status(thm)],[c271]) ).
cnf(c273,plain,
ld(meet(X3,rd(X2,X4)),X2) = ld(meet(X3,rd(X2,X4)),join(X2,op(meet(X3,rd(X2,X4)),X4))),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
meet(X4,ld(meet(X3,rd(X2,X4)),X2)) = meet(X4,ld(meet(X3,rd(X2,X4)),join(X2,op(meet(X3,rd(X2,X4)),X4)))),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
join(op(X3,X4),X2) = join(X2,op(X3,X4)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c276,plain,
join(X2,op(X3,X4)) = join(op(X3,X4),X2),
inference(symmetry,[status(thm)],[c275]) ).
cnf(c277,plain,
ld(X3,join(X2,op(X3,X4))) = ld(X3,join(op(X3,X4),X2)),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
meet(X4,ld(X3,join(X2,op(X3,X4)))) = meet(X4,ld(X3,join(op(X3,X4),X2))),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
meet(X4,ld(X3,join(X2,op(X3,X4)))) = X4,
inference(transitivity,[status(thm)],[c278,c23]) ).
cnf(c280,plain,
meet(X4,ld(meet(X3,rd(X2,X4)),join(X2,op(meet(X3,rd(X2,X4)),X4)))) = X4,
inference(substitution,[status(thm)],[c279]) ).
cnf(c281,plain,
meet(X4,ld(meet(X3,rd(X2,X4)),X2)) = X4,
inference(transitivity,[status(thm)],[c274,c280]) ).
cnf(c282,plain,
meet(X4,ld(meet(X3,rd(op(join(X3,X2),X4),X4)),op(join(X3,X2),X4))) = X4,
inference(substitution,[status(thm)],[c281]) ).
cnf(c283,plain,
meet(X4,ld(X3,op(join(X3,X2),X4))) = X4,
inference(transitivity,[status(thm)],[c270,c282]) ).
cnf(c284,plain,
meet(X3,ld(unit,op(join(unit,rd(X2,X2)),X3))) = X3,
inference(substitution,[status(thm)],[c283]) ).
cnf(c285,plain,
meet(X3,ld(unit,op(rd(X2,X2),X3))) = X3,
inference(transitivity,[status(thm)],[c246,c284]) ).
cnf(c286,plain,
meet(X3,op(rd(X2,X2),X3)) = X3,
inference(transitivity,[status(thm)],[c242,c285]) ).
cnf(c287,plain,
meet(X2,op(rd(X2,X2),X2)) = X2,
inference(substitution,[status(thm)],[c286]) ).
cnf(c288,plain,
op(rd(X2,X2),X2) = X2,
inference(transitivity,[status(thm)],[c239,c287]) ).
cnf(c289,plain,
op(op(rd(X3,X3),X3),X2) = op(X3,X2),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
op(rd(X3,X3),op(X3,X2)) = op(X3,X2),
inference(transitivity,[status(thm)],[c219,c289]) ).
cnf(c291,plain,
op(rd(X2,X2),op(X2,ld(X2,unit))) = op(X2,ld(X2,unit)),
inference(substitution,[status(thm)],[c290]) ).
cnf(c292,plain,
op(rd(X2,X2),op(X2,ld(X2,unit))) = at(X2,unit),
inference(transitivity,[status(thm)],[c291,c181]) ).
cnf(c293,plain,
op(rd(X2,X2),at(X2,unit)) = at(X2,unit),
inference(transitivity,[status(thm)],[c217,c292]) ).
cnf(c294,plain,
at(X2,unit) = op(rd(X2,X2),at(X2,unit)),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
rd(at(X2,unit),at(X2,unit)) = rd(op(rd(X2,X2),at(X2,unit)),at(X2,unit)),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
join(rd(X2,X2),rd(at(X2,unit),at(X2,unit))) = join(rd(X2,X2),rd(op(rd(X2,X2),at(X2,unit)),at(X2,unit))),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
join(rd(op(X3,X2),X2),X3) = join(X3,rd(op(X3,X2),X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c298,plain,
join(X3,rd(op(X3,X2),X2)) = join(rd(op(X3,X2),X2),X3),
inference(symmetry,[status(thm)],[c297]) ).
cnf(c299,plain,
X3 = meet(X3,rd(op(X3,X2),X2)),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c300,plain,
join(rd(op(X3,X2),X2),X3) = join(rd(op(X3,X2),X2),meet(X3,rd(op(X3,X2),X2))),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
join(rd(op(X3,X2),X2),meet(X3,rd(op(X3,X2),X2))) = rd(op(X3,X2),X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c302,plain,
join(rd(op(X3,X2),X2),X3) = rd(op(X3,X2),X2),
inference(transitivity,[status(thm)],[c300,c301]) ).
cnf(c303,plain,
join(X3,rd(op(X3,X2),X2)) = rd(op(X3,X2),X2),
inference(transitivity,[status(thm)],[c298,c302]) ).
cnf(c304,plain,
join(rd(X2,X2),rd(op(rd(X2,X2),at(X2,unit)),at(X2,unit))) = rd(op(rd(X2,X2),at(X2,unit)),at(X2,unit)),
inference(substitution,[status(thm)],[c303]) ).
cnf(c305,plain,
rd(op(rd(X2,X2),at(X2,unit)),at(X2,unit)) = rd(at(X2,unit),at(X2,unit)),
inference(congruence,[status(thm)],[c293]) ).
cnf(c306,plain,
rd(op(rd(X2,X2),at(X2,unit)),at(X2,unit)) = unit,
inference(transitivity,[status(thm)],[c305,c213]) ).
cnf(c307,plain,
join(rd(X2,X2),rd(op(rd(X2,X2),at(X2,unit)),at(X2,unit))) = unit,
inference(transitivity,[status(thm)],[c304,c306]) ).
cnf(c308,plain,
join(rd(X2,X2),rd(at(X2,unit),at(X2,unit))) = unit,
inference(transitivity,[status(thm)],[c296,c307]) ).
cnf(c309,plain,
join(rd(X2,X2),unit) = unit,
inference(transitivity,[status(thm)],[c215,c308]) ).
cnf(c310,plain,
join(unit,rd(X2,X2)) = unit,
inference(transitivity,[status(thm)],[c165,c309]) ).
cnf(c311,plain,
rd(X2,X2) = unit,
inference(transitivity,[status(thm)],[c163,c310]) ).
cnf(c312,plain,
rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))) = unit,
inference(substitution,[status(thm)],[c311]) ).
cnf(c313,plain,
unit = rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(symmetry,[status(thm)],[c312]) ).
cnf(c314,plain,
ld(unit,X3) = ld(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),X3),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),ld(unit,X3)) = meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),ld(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),X3)),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
meet(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),rd(unit,at(unit,op(X2,ld(X2,unit))))) = meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c317,plain,
meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))) = meet(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(symmetry,[status(thm)],[c316]) ).
cnf(c318,plain,
op(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit) = rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(substitution,[status(thm)],[c86]) ).
cnf(c319,plain,
rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))) = op(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
join(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))) = join(rd(unit,at(unit,op(X2,ld(X2,unit)))),op(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit)),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
join(rd(unit,at(unit,op(X2,ld(X2,unit)))),op(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit)) = join(ld(op(X2,ld(X2,unit)),unit),op(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c322,plain,
rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))) = rd(ld(op(X2,ld(X2,unit)),unit),rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c323,plain,
op(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit) = op(rd(ld(op(X2,ld(X2,unit)),unit),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
join(ld(op(X2,ld(X2,unit)),unit),op(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit)) = join(ld(op(X2,ld(X2,unit)),unit),op(rd(ld(op(X2,ld(X2,unit)),unit),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit)),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
rd(ld(op(X2,ld(X2,unit)),unit),rd(unit,at(unit,op(X2,ld(X2,unit))))) = rd(ld(op(X2,ld(X2,unit)),unit),ld(op(X2,ld(X2,unit)),unit)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c326,plain,
op(rd(ld(op(X2,ld(X2,unit)),unit),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit) = op(rd(ld(op(X2,ld(X2,unit)),unit),ld(op(X2,ld(X2,unit)),unit)),unit),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
join(ld(op(X2,ld(X2,unit)),unit),op(rd(ld(op(X2,ld(X2,unit)),unit),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit)) = join(ld(op(X2,ld(X2,unit)),unit),op(rd(ld(op(X2,ld(X2,unit)),unit),ld(op(X2,ld(X2,unit)),unit)),unit)),
inference(congruence,[status(thm)],[c326]) ).
cnf(c328,plain,
meet(unit,ld(op(X2,ld(X2,unit)),unit)) = unit,
inference(substitution,[status(thm)],[c94]) ).
cnf(c329,plain,
unit = meet(unit,ld(op(X2,ld(X2,unit)),unit)),
inference(symmetry,[status(thm)],[c328]) ).
cnf(c330,plain,
op(rd(ld(op(X2,ld(X2,unit)),unit),ld(op(X2,ld(X2,unit)),unit)),unit) = op(rd(ld(op(X2,ld(X2,unit)),unit),ld(op(X2,ld(X2,unit)),unit)),meet(unit,ld(op(X2,ld(X2,unit)),unit))),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
join(ld(op(X2,ld(X2,unit)),unit),op(rd(ld(op(X2,ld(X2,unit)),unit),ld(op(X2,ld(X2,unit)),unit)),unit)) = join(ld(op(X2,ld(X2,unit)),unit),op(rd(ld(op(X2,ld(X2,unit)),unit),ld(op(X2,ld(X2,unit)),unit)),meet(unit,ld(op(X2,ld(X2,unit)),unit)))),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c333,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
op(rd(X3,X3),meet(X2,X3)) = op(rd(X3,X3),meet(X3,X2)),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
join(X3,op(rd(X3,X3),meet(X2,X3))) = join(X3,op(rd(X3,X3),meet(X3,X2))),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
X2 = join(X2,X2),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c337,plain,
rd(X2,X2) = rd(X2,join(X2,X2)),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
ld(rd(X2,X2),X2) = ld(rd(X2,join(X2,X2)),X2),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,axiom,
join(X2,Y2) = ld(rd(X2,join(X2,Y2)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',generalized_mv_algebra_b) ).
cnf(c340,plain,
join(X2,X2) = ld(rd(X2,join(X2,X2)),X2),
inference(substitution,[status(thm)],[c339]) ).
cnf(c341,plain,
ld(rd(X2,join(X2,X2)),X2) = join(X2,X2),
inference(symmetry,[status(thm)],[c340]) ).
cnf(c342,plain,
ld(rd(X2,join(X2,X2)),X2) = X2,
inference(transitivity,[status(thm)],[c341,c13]) ).
cnf(c343,plain,
ld(rd(X2,X2),X2) = X2,
inference(transitivity,[status(thm)],[c338,c342]) ).
cnf(c344,plain,
X2 = ld(rd(X2,X2),X2),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
meet(X3,X2) = meet(ld(rd(X3,X3),X3),X2),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
op(rd(X3,X3),meet(X3,X2)) = op(rd(X3,X3),meet(ld(rd(X3,X3),X3),X2)),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
join(X3,op(rd(X3,X3),meet(X3,X2))) = join(X3,op(rd(X3,X3),meet(ld(rd(X3,X3),X3),X2))),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
join(X3,op(rd(X3,X3),meet(ld(rd(X3,X3),X3),X2))) = X3,
inference(substitution,[status(thm)],[c55]) ).
cnf(c349,plain,
join(X3,op(rd(X3,X3),meet(X3,X2))) = X3,
inference(transitivity,[status(thm)],[c347,c348]) ).
cnf(c350,plain,
join(X3,op(rd(X3,X3),meet(X2,X3))) = X3,
inference(transitivity,[status(thm)],[c335,c349]) ).
cnf(c351,plain,
join(ld(op(X2,ld(X2,unit)),unit),op(rd(ld(op(X2,ld(X2,unit)),unit),ld(op(X2,ld(X2,unit)),unit)),meet(unit,ld(op(X2,ld(X2,unit)),unit)))) = ld(op(X2,ld(X2,unit)),unit),
inference(substitution,[status(thm)],[c350]) ).
cnf(c352,plain,
ld(op(X2,ld(X2,unit)),unit) = rd(unit,at(unit,op(X2,ld(X2,unit)))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c353,plain,
join(ld(op(X2,ld(X2,unit)),unit),op(rd(ld(op(X2,ld(X2,unit)),unit),ld(op(X2,ld(X2,unit)),unit)),meet(unit,ld(op(X2,ld(X2,unit)),unit)))) = rd(unit,at(unit,op(X2,ld(X2,unit)))),
inference(transitivity,[status(thm)],[c351,c352]) ).
cnf(c354,plain,
join(ld(op(X2,ld(X2,unit)),unit),op(rd(ld(op(X2,ld(X2,unit)),unit),ld(op(X2,ld(X2,unit)),unit)),unit)) = rd(unit,at(unit,op(X2,ld(X2,unit)))),
inference(transitivity,[status(thm)],[c331,c353]) ).
cnf(c355,plain,
join(ld(op(X2,ld(X2,unit)),unit),op(rd(ld(op(X2,ld(X2,unit)),unit),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit)) = rd(unit,at(unit,op(X2,ld(X2,unit)))),
inference(transitivity,[status(thm)],[c327,c354]) ).
cnf(c356,plain,
join(ld(op(X2,ld(X2,unit)),unit),op(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit)) = rd(unit,at(unit,op(X2,ld(X2,unit)))),
inference(transitivity,[status(thm)],[c324,c355]) ).
cnf(c357,plain,
join(rd(unit,at(unit,op(X2,ld(X2,unit)))),op(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),unit)) = rd(unit,at(unit,op(X2,ld(X2,unit)))),
inference(transitivity,[status(thm)],[c321,c356]) ).
cnf(c358,plain,
join(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))) = rd(unit,at(unit,op(X2,ld(X2,unit)))),
inference(transitivity,[status(thm)],[c320,c357]) ).
cnf(c359,plain,
rd(unit,at(unit,op(X2,ld(X2,unit)))) = join(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c360,plain,
meet(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),rd(unit,at(unit,op(X2,ld(X2,unit))))) = meet(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),join(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))))),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
meet(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),join(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))))) = rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(substitution,[status(thm)],[c196]) ).
cnf(c362,plain,
meet(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),rd(unit,at(unit,op(X2,ld(X2,unit))))) = rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(transitivity,[status(thm)],[c360,c361]) ).
cnf(c363,plain,
meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))) = rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(transitivity,[status(thm)],[c317,c362]) ).
cnf(c364,plain,
rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))) = meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))),
inference(symmetry,[status(thm)],[c363]) ).
cnf(c365,plain,
ld(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),X3) = ld(meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))),X3),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),ld(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),X3)) = meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),ld(meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))),X3)),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c368,plain,
meet(X3,X2) = meet(X2,X3),
inference(symmetry,[status(thm)],[c367]) ).
cnf(c369,plain,
ld(meet(X4,X2),X3) = ld(meet(X2,X4),X3),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
meet(ld(X4,X3),ld(meet(X4,X2),X3)) = meet(ld(X4,X3),ld(meet(X2,X4),X3)),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
join(X2,op(X3,ld(X3,X2))) = X2,
inference(substitution,[status(thm)],[c57]) ).
cnf(c372,plain,
X2 = join(X2,op(X3,ld(X3,X2))),
inference(symmetry,[status(thm)],[c371]) ).
cnf(c373,plain,
rd(X2,ld(X3,X2)) = rd(join(X2,op(X3,ld(X3,X2))),ld(X3,X2)),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
meet(X3,rd(X2,ld(X3,X2))) = meet(X3,rd(join(X2,op(X3,ld(X3,X2))),ld(X3,X2))),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
join(op(X4,X2),X3) = join(X3,op(X4,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c376,plain,
join(X3,op(X4,X2)) = join(op(X4,X2),X3),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
rd(join(X3,op(X4,X2)),X2) = rd(join(op(X4,X2),X3),X2),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
meet(X4,rd(join(X3,op(X4,X2)),X2)) = meet(X4,rd(join(op(X4,X2),X3),X2)),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
meet(X4,rd(join(op(X4,X2),X3),X2)) = X4,
inference(substitution,[status(thm)],[c153]) ).
cnf(c380,plain,
meet(X4,rd(join(X3,op(X4,X2)),X2)) = X4,
inference(transitivity,[status(thm)],[c378,c379]) ).
cnf(c381,plain,
meet(X3,rd(join(X2,op(X3,ld(X3,X2))),ld(X3,X2))) = X3,
inference(substitution,[status(thm)],[c380]) ).
cnf(c382,plain,
meet(X3,rd(X2,ld(X3,X2))) = X3,
inference(transitivity,[status(thm)],[c374,c381]) ).
cnf(c383,plain,
X3 = meet(X3,rd(X2,ld(X3,X2))),
inference(symmetry,[status(thm)],[c382]) ).
cnf(c384,plain,
meet(X2,X4) = meet(X2,meet(X4,rd(X3,ld(X4,X3)))),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,plain,
ld(meet(X2,X4),X3) = ld(meet(X2,meet(X4,rd(X3,ld(X4,X3)))),X3),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
meet(ld(X4,X3),ld(meet(X2,X4),X3)) = meet(ld(X4,X3),ld(meet(X2,meet(X4,rd(X3,ld(X4,X3)))),X3)),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
meet(meet(X3,X2),rd(X4,X5)) = meet(X3,meet(X2,rd(X4,X5))),
inference(substitution,[status(thm)],[c253]) ).
cnf(c388,plain,
meet(X4,meet(X3,rd(X5,X2))) = meet(meet(X4,X3),rd(X5,X2)),
inference(symmetry,[status(thm)],[c387]) ).
cnf(c389,plain,
op(meet(X4,meet(X3,rd(X5,X2))),X2) = op(meet(meet(X4,X3),rd(X5,X2)),X2),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
join(X5,op(meet(X4,meet(X3,rd(X5,X2))),X2)) = join(X5,op(meet(meet(X4,X3),rd(X5,X2)),X2)),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
join(X5,op(meet(meet(X4,X3),rd(X5,X2)),X2)) = X5,
inference(substitution,[status(thm)],[c230]) ).
cnf(c392,plain,
join(X5,op(meet(X4,meet(X3,rd(X5,X2))),X2)) = X5,
inference(transitivity,[status(thm)],[c390,c391]) ).
cnf(c393,plain,
join(X2,op(meet(X4,meet(X3,rd(X2,X5))),X5)) = X2,
inference(substitution,[status(thm)],[c392]) ).
cnf(c394,plain,
X2 = join(X2,op(meet(X4,meet(X3,rd(X2,X5))),X5)),
inference(symmetry,[status(thm)],[c393]) ).
cnf(c395,plain,
ld(meet(X4,meet(X3,rd(X2,X5))),X2) = ld(meet(X4,meet(X3,rd(X2,X5))),join(X2,op(meet(X4,meet(X3,rd(X2,X5))),X5))),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
meet(X5,ld(meet(X4,meet(X3,rd(X2,X5))),X2)) = meet(X5,ld(meet(X4,meet(X3,rd(X2,X5))),join(X2,op(meet(X4,meet(X3,rd(X2,X5))),X5)))),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
meet(X5,ld(meet(X4,meet(X3,rd(X2,X5))),join(X2,op(meet(X4,meet(X3,rd(X2,X5))),X5)))) = X5,
inference(substitution,[status(thm)],[c279]) ).
cnf(c398,plain,
meet(X5,ld(meet(X4,meet(X3,rd(X2,X5))),X2)) = X5,
inference(transitivity,[status(thm)],[c396,c397]) ).
cnf(c399,plain,
meet(ld(X4,X3),ld(meet(X2,meet(X4,rd(X3,ld(X4,X3)))),X3)) = ld(X4,X3),
inference(substitution,[status(thm)],[c398]) ).
cnf(c400,plain,
meet(ld(X4,X3),ld(meet(X2,X4),X3)) = ld(X4,X3),
inference(transitivity,[status(thm)],[c386,c399]) ).
cnf(c401,plain,
meet(ld(X4,X3),ld(meet(X4,X2),X3)) = ld(X4,X3),
inference(transitivity,[status(thm)],[c370,c400]) ).
cnf(c402,plain,
meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),ld(meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))),X3)) = ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),
inference(substitution,[status(thm)],[c401]) ).
cnf(c403,plain,
meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),ld(rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),X3)) = ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),
inference(transitivity,[status(thm)],[c366,c402]) ).
cnf(c404,plain,
meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),ld(unit,X3)) = ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),
inference(transitivity,[status(thm)],[c315,c403]) ).
cnf(c405,plain,
meet(ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),X3) = ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),
inference(transitivity,[status(thm)],[c139,c404]) ).
cnf(c406,plain,
meet(X3,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3)) = ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),X3),
inference(transitivity,[status(thm)],[c137,c405]) ).
cnf(c407,plain,
meet(unit,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit)) = ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit),
inference(substitution,[status(thm)],[c406]) ).
cnf(c408,plain,
ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit) = meet(unit,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit)),
inference(symmetry,[status(thm)],[c407]) ).
cnf(c409,plain,
join(ld(X2,X2),unit) = join(unit,ld(X2,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c410,plain,
join(unit,ld(X2,X2)) = join(ld(X2,X2),unit),
inference(symmetry,[status(thm)],[c409]) ).
cnf(c411,plain,
X2 = op(X2,unit),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c412,plain,
ld(X2,X2) = ld(X2,op(X2,unit)),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
meet(unit,ld(X2,X2)) = meet(unit,ld(X2,op(X2,unit))),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
meet(unit,ld(X2,op(X2,unit))) = unit,
inference(substitution,[status(thm)],[c25]) ).
cnf(c415,plain,
meet(unit,ld(X2,X2)) = unit,
inference(transitivity,[status(thm)],[c413,c414]) ).
cnf(c416,plain,
unit = meet(unit,ld(X2,X2)),
inference(symmetry,[status(thm)],[c415]) ).
cnf(c417,plain,
join(ld(X2,X2),unit) = join(ld(X2,X2),meet(unit,ld(X2,X2))),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
join(ld(X2,X2),meet(unit,ld(X2,X2))) = ld(X2,X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c419,plain,
join(ld(X2,X2),unit) = ld(X2,X2),
inference(transitivity,[status(thm)],[c417,c418]) ).
cnf(c420,plain,
join(unit,ld(X2,X2)) = ld(X2,X2),
inference(transitivity,[status(thm)],[c410,c419]) ).
cnf(c421,plain,
join(unit,ld(ld(X2,unit),ld(X2,unit))) = ld(ld(X2,unit),ld(X2,unit)),
inference(substitution,[status(thm)],[c420]) ).
cnf(c422,plain,
ld(ld(X2,unit),ld(X2,unit)) = join(unit,ld(ld(X2,unit),ld(X2,unit))),
inference(symmetry,[status(thm)],[c421]) ).
cnf(c423,plain,
join(ld(ld(X2,unit),ld(X2,unit)),unit) = join(unit,ld(ld(X2,unit),ld(X2,unit))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c424,plain,
join(unit,ld(ld(X2,unit),ld(X2,unit))) = join(ld(ld(X2,unit),ld(X2,unit)),unit),
inference(symmetry,[status(thm)],[c423]) ).
cnf(c425,plain,
join(rd(X2,unit),X2) = join(X2,rd(X2,unit)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c426,plain,
join(X2,rd(X2,unit)) = join(rd(X2,unit),X2),
inference(symmetry,[status(thm)],[c425]) ).
cnf(c427,plain,
X2 = op(X2,unit),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c428,plain,
rd(X2,unit) = rd(op(X2,unit),unit),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
meet(X2,rd(X2,unit)) = meet(X2,rd(op(X2,unit),unit)),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
meet(X2,rd(op(X2,unit),unit)) = X2,
inference(substitution,[status(thm)],[c155]) ).
cnf(c431,plain,
meet(X2,rd(X2,unit)) = X2,
inference(transitivity,[status(thm)],[c429,c430]) ).
cnf(c432,plain,
X2 = meet(X2,rd(X2,unit)),
inference(symmetry,[status(thm)],[c431]) ).
cnf(c433,plain,
join(rd(X2,unit),X2) = join(rd(X2,unit),meet(X2,rd(X2,unit))),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
join(rd(X2,unit),meet(X2,rd(X2,unit))) = rd(X2,unit),
inference(substitution,[status(thm)],[c38]) ).
cnf(c435,plain,
join(rd(X2,unit),X2) = rd(X2,unit),
inference(transitivity,[status(thm)],[c433,c434]) ).
cnf(c436,plain,
join(X2,rd(X2,unit)) = rd(X2,unit),
inference(transitivity,[status(thm)],[c426,c435]) ).
cnf(c437,plain,
join(op(X2,ld(X2,unit)),rd(op(X2,ld(X2,unit)),unit)) = rd(op(X2,ld(X2,unit)),unit),
inference(substitution,[status(thm)],[c436]) ).
cnf(c438,plain,
rd(op(X2,ld(X2,unit)),unit) = join(op(X2,ld(X2,unit)),rd(op(X2,ld(X2,unit)),unit)),
inference(symmetry,[status(thm)],[c437]) ).
cnf(c439,plain,
op(rd(op(X2,ld(X2,unit)),unit),unit) = rd(op(X2,ld(X2,unit)),unit),
inference(substitution,[status(thm)],[c86]) ).
cnf(c440,plain,
rd(op(X2,ld(X2,unit)),unit) = op(rd(op(X2,ld(X2,unit)),unit),unit),
inference(symmetry,[status(thm)],[c439]) ).
cnf(c441,plain,
join(op(X2,ld(X2,unit)),rd(op(X2,ld(X2,unit)),unit)) = join(op(X2,ld(X2,unit)),op(rd(op(X2,ld(X2,unit)),unit),unit)),
inference(congruence,[status(thm)],[c440]) ).
cnf(c442,plain,
X2 = join(op(X3,ld(X3,X2)),X2),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c443,plain,
rd(op(X3,ld(X3,X2)),X2) = rd(op(X3,ld(X3,X2)),join(op(X3,ld(X3,X2)),X2)),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
ld(rd(op(X3,ld(X3,X2)),X2),op(X3,ld(X3,X2))) = ld(rd(op(X3,ld(X3,X2)),join(op(X3,ld(X3,X2)),X2)),op(X3,ld(X3,X2))),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
join(op(X3,ld(X3,X2)),X2) = ld(rd(op(X3,ld(X3,X2)),join(op(X3,ld(X3,X2)),X2)),op(X3,ld(X3,X2))),
inference(substitution,[status(thm)],[c339]) ).
cnf(c446,plain,
ld(rd(op(X3,ld(X3,X2)),join(op(X3,ld(X3,X2)),X2)),op(X3,ld(X3,X2))) = join(op(X3,ld(X3,X2)),X2),
inference(symmetry,[status(thm)],[c445]) ).
cnf(c447,plain,
ld(rd(op(X3,ld(X3,X2)),join(op(X3,ld(X3,X2)),X2)),op(X3,ld(X3,X2))) = X2,
inference(transitivity,[status(thm)],[c446,c82]) ).
cnf(c448,plain,
ld(rd(op(X3,ld(X3,X2)),X2),op(X3,ld(X3,X2))) = X2,
inference(transitivity,[status(thm)],[c444,c447]) ).
cnf(c449,plain,
ld(rd(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit))) = unit,
inference(substitution,[status(thm)],[c448]) ).
cnf(c450,plain,
unit = ld(rd(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit))),
inference(symmetry,[status(thm)],[c449]) ).
cnf(c451,plain,
op(rd(op(X2,ld(X2,unit)),unit),unit) = op(rd(op(X2,ld(X2,unit)),unit),ld(rd(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit)))),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
join(op(X2,ld(X2,unit)),op(rd(op(X2,ld(X2,unit)),unit),unit)) = join(op(X2,ld(X2,unit)),op(rd(op(X2,ld(X2,unit)),unit),ld(rd(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit))))),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
join(op(X2,ld(X2,unit)),op(rd(op(X2,ld(X2,unit)),unit),ld(rd(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit))))) = op(X2,ld(X2,unit)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c454,plain,
join(op(X2,ld(X2,unit)),op(rd(op(X2,ld(X2,unit)),unit),unit)) = op(X2,ld(X2,unit)),
inference(transitivity,[status(thm)],[c452,c453]) ).
cnf(c455,plain,
join(op(X2,ld(X2,unit)),rd(op(X2,ld(X2,unit)),unit)) = op(X2,ld(X2,unit)),
inference(transitivity,[status(thm)],[c441,c454]) ).
cnf(c456,plain,
rd(op(X2,ld(X2,unit)),unit) = op(X2,ld(X2,unit)),
inference(transitivity,[status(thm)],[c438,c455]) ).
cnf(c457,plain,
op(X2,ld(X2,unit)) = rd(op(X2,ld(X2,unit)),unit),
inference(symmetry,[status(thm)],[c456]) ).
cnf(c458,plain,
ld(op(X2,ld(X2,unit)),op(X2,ld(X2,unit))) = ld(rd(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit))),
inference(congruence,[status(thm)],[c457]) ).
cnf(c459,plain,
ld(rd(op(X2,ld(X2,unit)),unit),op(X2,ld(X2,unit))) = unit,
inference(substitution,[status(thm)],[c448]) ).
cnf(c460,plain,
ld(op(X2,ld(X2,unit)),op(X2,ld(X2,unit))) = unit,
inference(transitivity,[status(thm)],[c458,c459]) ).
cnf(c461,plain,
unit = ld(op(X2,ld(X2,unit)),op(X2,ld(X2,unit))),
inference(symmetry,[status(thm)],[c460]) ).
cnf(c462,plain,
join(ld(ld(X2,unit),ld(X2,unit)),unit) = join(ld(ld(X2,unit),ld(X2,unit)),ld(op(X2,ld(X2,unit)),op(X2,ld(X2,unit)))),
inference(congruence,[status(thm)],[c461]) ).
cnf(c463,plain,
op(op(X3,X2),ld(X2,X2)) = op(X3,op(X2,ld(X2,X2))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c464,plain,
meet(X2,op(X2,ld(X2,X2))) = op(X2,ld(X2,X2)),
inference(substitution,[status(thm)],[c199]) ).
cnf(c465,plain,
op(X2,ld(X2,X2)) = meet(X2,op(X2,ld(X2,X2))),
inference(symmetry,[status(thm)],[c464]) ).
cnf(c466,plain,
rd(X2,unit) = join(X2,rd(X2,unit)),
inference(symmetry,[status(thm)],[c436]) ).
cnf(c467,plain,
op(rd(X2,unit),unit) = rd(X2,unit),
inference(substitution,[status(thm)],[c86]) ).
cnf(c468,plain,
rd(X2,unit) = op(rd(X2,unit),unit),
inference(symmetry,[status(thm)],[c467]) ).
cnf(c469,plain,
join(X2,rd(X2,unit)) = join(X2,op(rd(X2,unit),unit)),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
join(X2,op(rd(X2,unit),unit)) = X2,
inference(substitution,[status(thm)],[c232]) ).
cnf(c471,plain,
join(X2,rd(X2,unit)) = X2,
inference(transitivity,[status(thm)],[c469,c470]) ).
cnf(c472,plain,
rd(X2,unit) = X2,
inference(transitivity,[status(thm)],[c466,c471]) ).
cnf(c473,plain,
rd(op(X3,ld(X2,X2)),unit) = op(X3,ld(X2,X2)),
inference(substitution,[status(thm)],[c472]) ).
cnf(c474,plain,
op(X3,ld(X2,X2)) = rd(op(X3,ld(X2,X2)),unit),
inference(symmetry,[status(thm)],[c473]) ).
cnf(c475,plain,
meet(X3,op(X3,ld(X2,X2))) = meet(X3,rd(op(X3,ld(X2,X2)),unit)),
inference(congruence,[status(thm)],[c474]) ).
cnf(c476,plain,
ld(X2,X2) = join(unit,ld(X2,X2)),
inference(symmetry,[status(thm)],[c420]) ).
cnf(c477,plain,
op(X3,ld(X2,X2)) = op(X3,join(unit,ld(X2,X2))),
inference(congruence,[status(thm)],[c476]) ).
cnf(c478,plain,
rd(op(X3,ld(X2,X2)),unit) = rd(op(X3,join(unit,ld(X2,X2))),unit),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
meet(X3,rd(op(X3,ld(X2,X2)),unit)) = meet(X3,rd(op(X3,join(unit,ld(X2,X2))),unit)),
inference(congruence,[status(thm)],[c478]) ).
cnf(c480,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)],[c260]) ).
cnf(c481,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)],[c480]) ).
cnf(c482,plain,
meet(join(X4,X2),ld(X3,op(X3,join(X4,X2)))) = join(X4,X2),
inference(substitution,[status(thm)],[c25]) ).
cnf(c483,plain,
meet(X4,meet(join(X4,X2),ld(X3,op(X3,join(X4,X2))))) = meet(X4,join(X4,X2)),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
meet(X4,meet(join(X4,X2),ld(X3,op(X3,join(X4,X2))))) = X4,
inference(transitivity,[status(thm)],[c483,c195]) ).
cnf(c485,plain,
meet(X4,ld(X3,op(X3,join(X4,X2)))) = X4,
inference(transitivity,[status(thm)],[c481,c484]) ).
cnf(c486,plain,
meet(X3,ld(X4,op(X4,join(X3,X2)))) = X3,
inference(substitution,[status(thm)],[c485]) ).
cnf(c487,plain,
X3 = meet(X3,ld(X4,op(X4,join(X3,X2)))),
inference(symmetry,[status(thm)],[c486]) ).
cnf(c488,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)],[c487]) ).
cnf(c489,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)],[c488]) ).
cnf(c490,plain,
meet(ld(X4,X3),X2) = meet(X2,ld(X4,X3)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c491,plain,
meet(X2,ld(X4,X3)) = meet(ld(X4,X3),X2),
inference(symmetry,[status(thm)],[c490]) ).
cnf(c492,plain,
rd(X3,meet(X2,ld(X4,X3))) = rd(X3,meet(ld(X4,X3),X2)),
inference(congruence,[status(thm)],[c491]) ).
cnf(c493,plain,
meet(X4,rd(X3,meet(X2,ld(X4,X3)))) = meet(X4,rd(X3,meet(ld(X4,X3),X2))),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
join(X3,op(X4,meet(ld(X4,X3),X2))) = X3,
inference(substitution,[status(thm)],[c55]) ).
cnf(c495,plain,
X3 = join(X3,op(X4,meet(ld(X4,X3),X2))),
inference(symmetry,[status(thm)],[c494]) ).
cnf(c496,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)],[c495]) ).
cnf(c497,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)],[c496]) ).
cnf(c498,plain,
meet(X4,rd(join(X3,op(X4,meet(ld(X4,X3),X2))),meet(ld(X4,X3),X2))) = X4,
inference(substitution,[status(thm)],[c380]) ).
cnf(c499,plain,
meet(X4,rd(X3,meet(ld(X4,X3),X2))) = X4,
inference(transitivity,[status(thm)],[c497,c498]) ).
cnf(c500,plain,
meet(X4,rd(X3,meet(X2,ld(X4,X3)))) = X4,
inference(transitivity,[status(thm)],[c493,c499]) ).
cnf(c501,plain,
meet(X4,rd(op(X4,join(X3,X2)),meet(X3,ld(X4,op(X4,join(X3,X2)))))) = X4,
inference(substitution,[status(thm)],[c500]) ).
cnf(c502,plain,
meet(X4,rd(op(X4,join(X3,X2)),X3)) = X4,
inference(transitivity,[status(thm)],[c489,c501]) ).
cnf(c503,plain,
meet(X3,rd(op(X3,join(unit,ld(X2,X2))),unit)) = X3,
inference(substitution,[status(thm)],[c502]) ).
cnf(c504,plain,
meet(X3,rd(op(X3,ld(X2,X2)),unit)) = X3,
inference(transitivity,[status(thm)],[c479,c503]) ).
cnf(c505,plain,
meet(X3,op(X3,ld(X2,X2))) = X3,
inference(transitivity,[status(thm)],[c475,c504]) ).
cnf(c506,plain,
meet(X2,op(X2,ld(X2,X2))) = X2,
inference(substitution,[status(thm)],[c505]) ).
cnf(c507,plain,
op(X2,ld(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c465,c506]) ).
cnf(c508,plain,
op(X3,op(X2,ld(X2,X2))) = op(X3,X2),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
op(op(X3,X2),ld(X2,X2)) = op(X3,X2),
inference(transitivity,[status(thm)],[c463,c508]) ).
cnf(c510,plain,
op(op(X2,ld(X2,unit)),ld(ld(X2,unit),ld(X2,unit))) = op(X2,ld(X2,unit)),
inference(substitution,[status(thm)],[c509]) ).
cnf(c511,plain,
op(X2,ld(X2,unit)) = op(op(X2,ld(X2,unit)),ld(ld(X2,unit),ld(X2,unit))),
inference(symmetry,[status(thm)],[c510]) ).
cnf(c512,plain,
ld(op(X2,ld(X2,unit)),op(X2,ld(X2,unit))) = ld(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(ld(X2,unit),ld(X2,unit)))),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
join(ld(ld(X2,unit),ld(X2,unit)),ld(op(X2,ld(X2,unit)),op(X2,ld(X2,unit)))) = join(ld(ld(X2,unit),ld(X2,unit)),ld(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(ld(X2,unit),ld(X2,unit))))),
inference(congruence,[status(thm)],[c512]) ).
cnf(c514,plain,
join(ld(X2,op(X2,X3)),X3) = join(X3,ld(X2,op(X2,X3))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c515,plain,
join(X3,ld(X2,op(X2,X3))) = join(ld(X2,op(X2,X3)),X3),
inference(symmetry,[status(thm)],[c514]) ).
cnf(c516,plain,
X3 = meet(X3,ld(X2,op(X2,X3))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c517,plain,
join(ld(X2,op(X2,X3)),X3) = join(ld(X2,op(X2,X3)),meet(X3,ld(X2,op(X2,X3)))),
inference(congruence,[status(thm)],[c516]) ).
cnf(c518,plain,
join(ld(X2,op(X2,X3)),meet(X3,ld(X2,op(X2,X3)))) = ld(X2,op(X2,X3)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c519,plain,
join(ld(X2,op(X2,X3)),X3) = ld(X2,op(X2,X3)),
inference(transitivity,[status(thm)],[c517,c518]) ).
cnf(c520,plain,
join(X3,ld(X2,op(X2,X3))) = ld(X2,op(X2,X3)),
inference(transitivity,[status(thm)],[c515,c519]) ).
cnf(c521,plain,
join(ld(ld(X2,unit),ld(X2,unit)),ld(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(ld(X2,unit),ld(X2,unit))))) = ld(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(ld(X2,unit),ld(X2,unit)))),
inference(substitution,[status(thm)],[c520]) ).
cnf(c522,plain,
op(op(X2,ld(X2,unit)),ld(ld(X2,unit),ld(X2,unit))) = op(X2,ld(X2,unit)),
inference(substitution,[status(thm)],[c509]) ).
cnf(c523,plain,
ld(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(ld(X2,unit),ld(X2,unit)))) = ld(op(X2,ld(X2,unit)),op(X2,ld(X2,unit))),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
ld(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(ld(X2,unit),ld(X2,unit)))) = unit,
inference(transitivity,[status(thm)],[c523,c460]) ).
cnf(c525,plain,
join(ld(ld(X2,unit),ld(X2,unit)),ld(op(X2,ld(X2,unit)),op(op(X2,ld(X2,unit)),ld(ld(X2,unit),ld(X2,unit))))) = unit,
inference(transitivity,[status(thm)],[c521,c524]) ).
cnf(c526,plain,
join(ld(ld(X2,unit),ld(X2,unit)),ld(op(X2,ld(X2,unit)),op(X2,ld(X2,unit)))) = unit,
inference(transitivity,[status(thm)],[c513,c525]) ).
cnf(c527,plain,
join(ld(ld(X2,unit),ld(X2,unit)),unit) = unit,
inference(transitivity,[status(thm)],[c462,c526]) ).
cnf(c528,plain,
join(unit,ld(ld(X2,unit),ld(X2,unit))) = unit,
inference(transitivity,[status(thm)],[c424,c527]) ).
cnf(c529,plain,
ld(ld(X2,unit),ld(X2,unit)) = unit,
inference(transitivity,[status(thm)],[c422,c528]) ).
cnf(c530,plain,
unit = ld(ld(X2,unit),ld(X2,unit)),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c531,plain,
ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit) = ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),ld(ld(X2,unit),ld(X2,unit))),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
meet(unit,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit)) = meet(unit,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),ld(ld(X2,unit),ld(X2,unit)))),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),X3) = join(X3,op(X3,rd(unit,at(unit,op(X2,ld(X2,unit)))))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c534,plain,
join(X3,op(X3,rd(unit,at(unit,op(X2,ld(X2,unit)))))) = join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),X3),
inference(symmetry,[status(thm)],[c533]) ).
cnf(c535,plain,
X2 = op(X2,unit),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c536,plain,
join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),X3) = join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),op(X3,unit)),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))) = unit,
inference(substitution,[status(thm)],[c311]) ).
cnf(c538,plain,
unit = rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(symmetry,[status(thm)],[c537]) ).
cnf(c539,plain,
op(X3,unit) = op(X3,rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),op(X3,unit)) = join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),op(X3,rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))))),
inference(congruence,[status(thm)],[c539]) ).
cnf(c541,plain,
rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))) = meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))),
inference(symmetry,[status(thm)],[c363]) ).
cnf(c542,plain,
op(X3,rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))) = op(X3,meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))))),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),op(X3,rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))))) = join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),op(X3,meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))))),
inference(congruence,[status(thm)],[c542]) ).
cnf(c544,plain,
meet(X2,ld(X3,op(X3,X4))) = meet(ld(X3,op(X3,X4)),X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c545,plain,
meet(ld(X3,op(X3,X4)),X2) = meet(X2,ld(X3,op(X3,X4))),
inference(symmetry,[status(thm)],[c544]) ).
cnf(c546,plain,
meet(X4,meet(ld(X3,op(X3,X4)),X2)) = meet(X4,meet(X2,ld(X3,op(X3,X4)))),
inference(congruence,[status(thm)],[c545]) ).
cnf(c547,plain,
meet(ld(X2,op(X2,X4)),X3) = meet(X3,ld(X2,op(X2,X4))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c548,plain,
meet(X3,ld(X2,op(X2,X4))) = meet(ld(X2,op(X2,X4)),X3),
inference(symmetry,[status(thm)],[c547]) ).
cnf(c549,plain,
meet(X4,meet(X3,ld(X2,op(X2,X4)))) = meet(X4,meet(ld(X2,op(X2,X4)),X3)),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
meet(meet(X4,ld(X2,op(X2,X4))),X3) = meet(X4,meet(ld(X2,op(X2,X4)),X3)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c551,plain,
meet(X4,meet(ld(X2,op(X2,X4)),X3)) = meet(meet(X4,ld(X2,op(X2,X4))),X3),
inference(symmetry,[status(thm)],[c550]) ).
cnf(c552,plain,
meet(meet(X4,ld(X2,op(X2,X4))),X3) = meet(X4,X3),
inference(congruence,[status(thm)],[c25]) ).
cnf(c553,plain,
meet(X4,meet(ld(X2,op(X2,X4)),X3)) = meet(X4,X3),
inference(transitivity,[status(thm)],[c551,c552]) ).
cnf(c554,plain,
meet(X4,meet(X3,ld(X2,op(X2,X4)))) = meet(X4,X3),
inference(transitivity,[status(thm)],[c549,c553]) ).
cnf(c555,plain,
meet(X4,meet(X2,ld(X3,op(X3,X4)))) = meet(X4,X2),
inference(substitution,[status(thm)],[c554]) ).
cnf(c556,plain,
meet(X4,meet(ld(X3,op(X3,X4)),X2)) = meet(X4,X2),
inference(transitivity,[status(thm)],[c546,c555]) ).
cnf(c557,plain,
meet(X3,meet(ld(X4,op(X4,X3)),X2)) = meet(X3,X2),
inference(substitution,[status(thm)],[c556]) ).
cnf(c558,plain,
meet(X3,X2) = meet(X3,meet(ld(X4,op(X4,X3)),X2)),
inference(symmetry,[status(thm)],[c557]) ).
cnf(c559,plain,
op(X4,meet(X3,X2)) = op(X4,meet(X3,meet(ld(X4,op(X4,X3)),X2))),
inference(congruence,[status(thm)],[c558]) ).
cnf(c560,plain,
join(op(X4,X3),op(X4,meet(X3,X2))) = join(op(X4,X3),op(X4,meet(X3,meet(ld(X4,op(X4,X3)),X2)))),
inference(congruence,[status(thm)],[c559]) ).
cnf(c561,plain,
meet(meet(X3,X2),X4) = meet(X4,meet(X3,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c562,plain,
meet(X4,meet(X3,X2)) = meet(meet(X3,X2),X4),
inference(symmetry,[status(thm)],[c561]) ).
cnf(c563,plain,
meet(meet(X3,X2),X4) = meet(X3,meet(X2,X4)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c564,plain,
meet(X2,X3) = meet(X3,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c565,plain,
meet(X3,meet(X2,X4)) = meet(X3,meet(X4,X2)),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
meet(meet(X3,X2),X4) = meet(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c563,c565]) ).
cnf(c567,plain,
meet(X4,meet(X3,X2)) = meet(X3,meet(X4,X2)),
inference(transitivity,[status(thm)],[c562,c566]) ).
cnf(c568,plain,
meet(ld(X4,X5),meet(X3,X2)) = meet(X3,meet(ld(X4,X5),X2)),
inference(substitution,[status(thm)],[c567]) ).
cnf(c569,plain,
meet(X3,meet(ld(X4,X5),X2)) = meet(ld(X4,X5),meet(X3,X2)),
inference(symmetry,[status(thm)],[c568]) ).
cnf(c570,plain,
op(X4,meet(X3,meet(ld(X4,X5),X2))) = op(X4,meet(ld(X4,X5),meet(X3,X2))),
inference(congruence,[status(thm)],[c569]) ).
cnf(c571,plain,
join(X5,op(X4,meet(X3,meet(ld(X4,X5),X2)))) = join(X5,op(X4,meet(ld(X4,X5),meet(X3,X2)))),
inference(congruence,[status(thm)],[c570]) ).
cnf(c572,plain,
join(X5,op(X4,meet(ld(X4,X5),meet(X3,X2)))) = X5,
inference(substitution,[status(thm)],[c55]) ).
cnf(c573,plain,
join(X5,op(X4,meet(X3,meet(ld(X4,X5),X2)))) = X5,
inference(transitivity,[status(thm)],[c571,c572]) ).
cnf(c574,plain,
join(op(X4,X3),op(X4,meet(X3,meet(ld(X4,op(X4,X3)),X2)))) = op(X4,X3),
inference(substitution,[status(thm)],[c573]) ).
cnf(c575,plain,
join(op(X4,X3),op(X4,meet(X3,X2))) = op(X4,X3),
inference(transitivity,[status(thm)],[c560,c574]) ).
cnf(c576,plain,
join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),op(X3,meet(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit)))))))) = op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(substitution,[status(thm)],[c575]) ).
cnf(c577,plain,
join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),op(X3,rd(rd(unit,at(unit,op(X2,ld(X2,unit)))),rd(unit,at(unit,op(X2,ld(X2,unit))))))) = op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(transitivity,[status(thm)],[c543,c576]) ).
cnf(c578,plain,
join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),op(X3,unit)) = op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(transitivity,[status(thm)],[c540,c577]) ).
cnf(c579,plain,
join(op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),X3) = op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(transitivity,[status(thm)],[c536,c578]) ).
cnf(c580,plain,
join(X3,op(X3,rd(unit,at(unit,op(X2,ld(X2,unit)))))) = op(X3,rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(transitivity,[status(thm)],[c534,c579]) ).
cnf(c581,plain,
join(ld(X2,unit),op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit)))))) = op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(substitution,[status(thm)],[c580]) ).
cnf(c582,plain,
op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit))))) = join(ld(X2,unit),op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit)))))),
inference(symmetry,[status(thm)],[c581]) ).
cnf(c583,plain,
op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit))))) = op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c584,plain,
join(ld(X2,unit),op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit)))))) = join(ld(X2,unit),op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit))),
inference(congruence,[status(thm)],[c583]) ).
cnf(c585,plain,
join(op(X2,ld(op(X4,X2),X3)),ld(X4,X3)) = join(ld(X4,X3),op(X2,ld(op(X4,X2),X3))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c586,plain,
join(ld(X4,X3),op(X2,ld(op(X4,X2),X3))) = join(op(X2,ld(op(X4,X2),X3)),ld(X4,X3)),
inference(symmetry,[status(thm)],[c585]) ).
cnf(c587,plain,
join(X3,op(op(X4,X2),ld(op(X4,X2),X3))) = X3,
inference(substitution,[status(thm)],[c57]) ).
cnf(c588,plain,
X3 = join(X3,op(op(X4,X2),ld(op(X4,X2),X3))),
inference(symmetry,[status(thm)],[c587]) ).
cnf(c589,plain,
rd(X3,op(X2,ld(op(X4,X2),X3))) = rd(join(X3,op(op(X4,X2),ld(op(X4,X2),X3))),op(X2,ld(op(X4,X2),X3))),
inference(congruence,[status(thm)],[c588]) ).
cnf(c590,plain,
meet(X4,rd(X3,op(X2,ld(op(X4,X2),X3)))) = meet(X4,rd(join(X3,op(op(X4,X2),ld(op(X4,X2),X3))),op(X2,ld(op(X4,X2),X3)))),
inference(congruence,[status(thm)],[c589]) ).
cnf(c591,plain,
join(op(op(X5,X3),X2),X4) = join(X4,op(op(X5,X3),X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c592,plain,
join(X4,op(op(X5,X3),X2)) = join(op(op(X5,X3),X2),X4),
inference(symmetry,[status(thm)],[c591]) ).
cnf(c593,plain,
rd(join(X4,op(op(X5,X3),X2)),op(X3,X2)) = rd(join(op(op(X5,X3),X2),X4),op(X3,X2)),
inference(congruence,[status(thm)],[c592]) ).
cnf(c594,plain,
meet(X5,rd(join(X4,op(op(X5,X3),X2)),op(X3,X2))) = meet(X5,rd(join(op(op(X5,X3),X2),X4),op(X3,X2))),
inference(congruence,[status(thm)],[c593]) ).
cnf(c595,plain,
op(op(X4,X3),X2) = op(X4,op(X3,X2)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c596,plain,
join(op(op(X5,X3),X2),X4) = join(op(X5,op(X3,X2)),X4),
inference(congruence,[status(thm)],[c595]) ).
cnf(c597,plain,
rd(join(op(op(X5,X3),X2),X4),op(X3,X2)) = rd(join(op(X5,op(X3,X2)),X4),op(X3,X2)),
inference(congruence,[status(thm)],[c596]) ).
cnf(c598,plain,
meet(X5,rd(join(op(op(X5,X3),X2),X4),op(X3,X2))) = meet(X5,rd(join(op(X5,op(X3,X2)),X4),op(X3,X2))),
inference(congruence,[status(thm)],[c597]) ).
cnf(c599,plain,
meet(X5,rd(join(op(X5,op(X3,X2)),X4),op(X3,X2))) = X5,
inference(substitution,[status(thm)],[c153]) ).
cnf(c600,plain,
meet(X5,rd(join(op(op(X5,X3),X2),X4),op(X3,X2))) = X5,
inference(transitivity,[status(thm)],[c598,c599]) ).
cnf(c601,plain,
meet(X5,rd(join(X4,op(op(X5,X3),X2)),op(X3,X2))) = X5,
inference(transitivity,[status(thm)],[c594,c600]) ).
cnf(c602,plain,
meet(X4,rd(join(X3,op(op(X4,X2),ld(op(X4,X2),X3))),op(X2,ld(op(X4,X2),X3)))) = X4,
inference(substitution,[status(thm)],[c601]) ).
cnf(c603,plain,
meet(X4,rd(X3,op(X2,ld(op(X4,X2),X3)))) = X4,
inference(transitivity,[status(thm)],[c590,c602]) ).
cnf(c604,plain,
X4 = meet(X4,rd(X3,op(X2,ld(op(X4,X2),X3)))),
inference(symmetry,[status(thm)],[c603]) ).
cnf(c605,plain,
ld(X4,X3) = ld(meet(X4,rd(X3,op(X2,ld(op(X4,X2),X3)))),X3),
inference(congruence,[status(thm)],[c604]) ).
cnf(c606,plain,
join(op(X2,ld(op(X4,X2),X3)),ld(X4,X3)) = join(op(X2,ld(op(X4,X2),X3)),ld(meet(X4,rd(X3,op(X2,ld(op(X4,X2),X3)))),X3)),
inference(congruence,[status(thm)],[c605]) ).
cnf(c607,plain,
join(ld(meet(X3,rd(X2,X4)),X2),X4) = join(X4,ld(meet(X3,rd(X2,X4)),X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c608,plain,
join(X4,ld(meet(X3,rd(X2,X4)),X2)) = join(ld(meet(X3,rd(X2,X4)),X2),X4),
inference(symmetry,[status(thm)],[c607]) ).
cnf(c609,plain,
X4 = meet(X4,ld(meet(X3,rd(X2,X4)),X2)),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c610,plain,
join(ld(meet(X3,rd(X2,X4)),X2),X4) = join(ld(meet(X3,rd(X2,X4)),X2),meet(X4,ld(meet(X3,rd(X2,X4)),X2))),
inference(congruence,[status(thm)],[c609]) ).
cnf(c611,plain,
join(ld(meet(X3,rd(X2,X4)),X2),meet(X4,ld(meet(X3,rd(X2,X4)),X2))) = ld(meet(X3,rd(X2,X4)),X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c612,plain,
join(ld(meet(X3,rd(X2,X4)),X2),X4) = ld(meet(X3,rd(X2,X4)),X2),
inference(transitivity,[status(thm)],[c610,c611]) ).
cnf(c613,plain,
join(X4,ld(meet(X3,rd(X2,X4)),X2)) = ld(meet(X3,rd(X2,X4)),X2),
inference(transitivity,[status(thm)],[c608,c612]) ).
cnf(c614,plain,
join(op(X2,ld(op(X4,X2),X3)),ld(meet(X4,rd(X3,op(X2,ld(op(X4,X2),X3)))),X3)) = ld(meet(X4,rd(X3,op(X2,ld(op(X4,X2),X3)))),X3),
inference(substitution,[status(thm)],[c613]) ).
cnf(c615,plain,
ld(meet(X4,rd(X3,op(X2,ld(op(X4,X2),X3)))),X3) = ld(X4,X3),
inference(congruence,[status(thm)],[c603]) ).
cnf(c616,plain,
join(op(X2,ld(op(X4,X2),X3)),ld(meet(X4,rd(X3,op(X2,ld(op(X4,X2),X3)))),X3)) = ld(X4,X3),
inference(transitivity,[status(thm)],[c614,c615]) ).
cnf(c617,plain,
join(op(X2,ld(op(X4,X2),X3)),ld(X4,X3)) = ld(X4,X3),
inference(transitivity,[status(thm)],[c606,c616]) ).
cnf(c618,plain,
join(ld(X4,X3),op(X2,ld(op(X4,X2),X3))) = ld(X4,X3),
inference(transitivity,[status(thm)],[c586,c617]) ).
cnf(c619,plain,
join(ld(X2,unit),op(ld(X2,unit),ld(op(X2,ld(X2,unit)),unit))) = ld(X2,unit),
inference(substitution,[status(thm)],[c618]) ).
cnf(c620,plain,
join(ld(X2,unit),op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit)))))) = ld(X2,unit),
inference(transitivity,[status(thm)],[c584,c619]) ).
cnf(c621,plain,
op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit))))) = ld(X2,unit),
inference(transitivity,[status(thm)],[c582,c620]) ).
cnf(c622,plain,
ld(X2,unit) = op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit))))),
inference(symmetry,[status(thm)],[c621]) ).
cnf(c623,plain,
ld(ld(X2,unit),ld(X2,unit)) = ld(ld(X2,unit),op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit)))))),
inference(congruence,[status(thm)],[c622]) ).
cnf(c624,plain,
ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),ld(ld(X2,unit),ld(X2,unit))) = ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),ld(ld(X2,unit),op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit))))))),
inference(congruence,[status(thm)],[c623]) ).
cnf(c625,plain,
meet(unit,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),ld(ld(X2,unit),ld(X2,unit)))) = meet(unit,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),ld(ld(X2,unit),op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit)))))))),
inference(congruence,[status(thm)],[c624]) ).
cnf(c626,plain,
ld(X2,op(X2,X3)) = join(X3,ld(X2,op(X2,X3))),
inference(symmetry,[status(thm)],[c520]) ).
cnf(c627,plain,
ld(X3,ld(X2,op(X2,X3))) = ld(X3,join(X3,ld(X2,op(X2,X3)))),
inference(congruence,[status(thm)],[c626]) ).
cnf(c628,plain,
meet(unit,ld(X3,ld(X2,op(X2,X3)))) = meet(unit,ld(X3,join(X3,ld(X2,op(X2,X3))))),
inference(congruence,[status(thm)],[c627]) ).
cnf(c629,plain,
meet(unit,ld(X3,join(X3,ld(X2,op(X2,X3))))) = unit,
inference(substitution,[status(thm)],[c92]) ).
cnf(c630,plain,
meet(unit,ld(X3,ld(X2,op(X2,X3)))) = unit,
inference(transitivity,[status(thm)],[c628,c629]) ).
cnf(c631,plain,
meet(unit,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),ld(ld(X2,unit),op(ld(X2,unit),rd(unit,at(unit,op(X2,ld(X2,unit)))))))) = unit,
inference(substitution,[status(thm)],[c630]) ).
cnf(c632,plain,
meet(unit,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),ld(ld(X2,unit),ld(X2,unit)))) = unit,
inference(transitivity,[status(thm)],[c625,c631]) ).
cnf(c633,plain,
meet(unit,ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit)) = unit,
inference(transitivity,[status(thm)],[c532,c632]) ).
cnf(c634,plain,
ld(rd(unit,at(unit,op(X2,ld(X2,unit)))),unit) = unit,
inference(transitivity,[status(thm)],[c408,c633]) ).
cnf(c635,plain,
at(unit,op(X2,ld(X2,unit))) = unit,
inference(transitivity,[status(thm)],[c135,c634]) ).
cnf(c636,plain,
at(unit,op(x,ld(x,unit))) = unit,
inference(substitution,[status(thm)],[c635]) ).
cnf(c637,plain,
$false,
inference(resolution,[status(thm)],[c1,c636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MVA009-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 17:50:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 102.19/13.31 Command-line arguments: --flatten --complete-subsets
% 102.19/13.31
% 102.19/13.31 % SZS status Unsatisfiable
% 102.19/13.31
% 102.19/13.39 % SZS output start CNFRefutation
% See solution above
% 105.13/13.75
% 105.13/13.75 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------