%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT399-2 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Sun Sep 27 07:50:32 AM UTC 2026
% Result : Unsatisfiable 30.47s 4.81s
% Output : CNFRefutation 30.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 10
% Syntax : Number of formulae : 351 ( 351 unt; 0 def)
% Number of atoms : 351 ( 350 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 29 ( 29 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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; 4 con; 0-3 aty)
% Number of variables : 910 ( 68 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = meet(VAR_1,VAR_0),
file('theBenchmark.p',commutativity) ).
cnf(c_1,plain,
meet(A,B) = meet(B,A),
inference(clausify,[status(thm)],[commutativity]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,meet(VAR_1,VAR_2)) = meet(meet(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity) ).
cnf(c_2,plain,
meet(A,meet(B,C)) = meet(meet(A,B),C),
inference(clausify,[status(thm)],[associativity]) ).
cnf(c_3,plain,
meet(meet(A,B),C) = meet(A,meet(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(commutativity_001,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_001) ).
cnf(c_4,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_001]) ).
fof(associativity_002,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,join(VAR_1,VAR_2)) = join(join(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_002) ).
cnf(c_5,plain,
join(A,join(B,C)) = join(join(A,B),C),
inference(clausify,[status(thm)],[associativity_002]) ).
cnf(c_6,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(copy,[status(thm)],[c_5]) ).
fof(absorption,axiom,
! [VAR_0,VAR_1] : join(VAR_0,meet(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption) ).
cnf(c_7,plain,
join(A,meet(A,B)) = A,
inference(clausify,[status(thm)],[absorption]) ).
fof(absorption_003,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,join(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption_003) ).
cnf(c_8,plain,
meet(A,join(A,B)) = A,
inference(clausify,[status(thm)],[absorption_003]) ).
fof(definition_of_upme,axiom,
! [VAR_0,VAR_1,VAR_2] : upme(VAR_0,VAR_1,VAR_2) = meet(VAR_0,join(VAR_1,VAR_2)),
file('theBenchmark.p',definition_of_upme) ).
cnf(c_9,plain,
upme(A,B,C) = meet(A,join(B,C)),
inference(clausify,[status(thm)],[definition_of_upme]) ).
fof(definition_of_lome,axiom,
! [VAR_0,VAR_1,VAR_2] : lome(VAR_0,VAR_1,VAR_2) = join(meet(VAR_0,VAR_1),meet(VAR_0,VAR_2)),
file('theBenchmark.p',definition_of_lome) ).
cnf(c_10,plain,
lome(A,B,C) = join(meet(A,B),meet(A,C)),
inference(clausify,[status(thm)],[definition_of_lome]) ).
fof(conjecture,axiom,
! [VAR_0,VAR_1,VAR_2] : join(upme(meet(a,VAR_0),VAR_1,VAR_2),meet(VAR_1,VAR_2)) = meet(join(meet(meet(a,VAR_0),VAR_1),VAR_2),join(meet(meet(a,VAR_0),VAR_2),VAR_1)),
file('theBenchmark.p',conjecture) ).
cnf(c_13,plain,
join(upme(meet(a,A),B,C),meet(B,C)) = meet(join(meet(meet(a,A),B),C),join(meet(meet(a,A),C),B)),
inference(clausify,[status(thm)],[conjecture]) ).
cnf(c_5391,plain,
join(meet(meet(a,A),join(B,C)),meet(B,C)) = meet(join(meet(meet(a,A),B),C),join(meet(meet(a,A),C),B)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_5392,plain,
join(meet(a,meet(A,join(B,C))),meet(B,C)) = meet(join(meet(meet(a,A),B),C),join(meet(meet(a,A),C),B)),
inference(paramod,[status(thm)],[c_3,c_5391]) ).
cnf(c_5393,plain,
join(meet(B,C),meet(a,meet(A,join(B,C)))) = meet(join(meet(meet(a,A),B),C),join(meet(meet(a,A),C),B)),
inference(paramod,[status(thm)],[c_4,c_5392]) ).
cnf(c_5394,plain,
join(meet(B,C),meet(a,meet(A,join(B,C)))) = meet(join(meet(a,meet(A,B)),C),join(meet(meet(a,A),C),B)),
inference(paramod,[status(thm)],[c_3,c_5393]) ).
cnf(c_14,plain,
join(meet(A,B),meet(a,meet(C,join(A,B)))) = meet(join(meet(a,meet(C,A)),B),join(meet(a,meet(C,B)),A)),
inference(paramod,[status(thm)],[c_3,c_5394]) ).
fof(conjecture_1,axiom,
upme(meet(a,z1),z2,z3) != lome(meet(a,z1),z2,z3),
file('theBenchmark.p',conjecture_1) ).
cnf(c_15,plain,
upme(meet(a,z1),z2,z3) != lome(meet(a,z1),z2,z3),
inference(clausify,[status(thm)],[conjecture_1]) ).
cnf(c_5395,plain,
meet(meet(a,z1),join(z2,z3)) != lome(meet(a,z1),z2,z3),
inference(paramod,[status(thm)],[c_9,c_15]) ).
cnf(c_5396,plain,
meet(a,meet(z1,join(z2,z3))) != lome(meet(a,z1),z2,z3),
inference(paramod,[status(thm)],[c_3,c_5395]) ).
cnf(c_5397,plain,
meet(a,meet(z1,join(z2,z3))) != join(meet(meet(a,z1),z2),meet(meet(a,z1),z3)),
inference(paramod,[status(thm)],[c_10,c_5396]) ).
cnf(c_5398,plain,
meet(a,meet(z1,join(z2,z3))) != join(meet(z2,meet(a,z1)),meet(meet(a,z1),z3)),
inference(paramod,[status(thm)],[c_1,c_5397]) ).
cnf(c_5399,plain,
meet(a,meet(z1,join(z2,z3))) != join(meet(z2,meet(a,z1)),meet(z3,meet(a,z1))),
inference(paramod,[status(thm)],[c_1,c_5398]) ).
cnf(c_16,plain,
join(meet(z2,meet(a,z1)),meet(z3,meet(a,z1))) != meet(a,meet(z1,join(z2,z3))),
inference(copy,[status(thm)],[c_5399]) ).
cnf(c_17,plain,
meet(A,meet(B,C)) = meet(C,meet(A,B)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_5400,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_18,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_3,c_5400]) ).
cnf(c_5401,plain,
join(meet(z1,meet(z2,a)),meet(z3,meet(a,z1))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_17,c_16]) ).
cnf(c_5402,plain,
join(meet(z1,meet(a,z2)),meet(z3,meet(a,z1))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_1,c_5401]) ).
cnf(c_5403,plain,
join(meet(a,meet(z1,z2)),meet(z3,meet(a,z1))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_18,c_5402]) ).
cnf(c_5404,plain,
join(meet(a,meet(z1,z2)),meet(z1,meet(z3,a))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_17,c_5403]) ).
cnf(c_5405,plain,
join(meet(a,meet(z1,z2)),meet(z1,meet(a,z3))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_1,c_5404]) ).
cnf(c_19,plain,
join(meet(a,meet(z1,z2)),meet(a,meet(z1,z3))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_18,c_5405]) ).
cnf(c_5406,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_21,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_6,c_5406]) ).
cnf(c_22,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_23,plain,
join(meet(A,B),meet(A,meet(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_5407,plain,
join(A,B) = join(A,join(meet(A,C),B)),
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_24,plain,
join(A,join(meet(A,B),C)) = join(A,C),
inference(copy,[status(thm)],[c_5407]) ).
cnf(c_5408,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_26,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_5408]) ).
cnf(c_28,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_29,plain,
meet(join(A,B),join(A,join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_30,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_31,plain,
meet(A,A) = A,
inference(paramod,[status(thm)],[c_7,c_8]) ).
cnf(c_32,plain,
join(meet(A,B),meet(a,meet(C,join(A,B)))) = meet(join(meet(a,meet(C,B)),A),join(meet(a,meet(C,A)),B)),
inference(paramod,[status(thm)],[c_14,c_1]) ).
cnf(c_34,plain,
join(meet(A,B),meet(a,meet(join(A,B),C))) = meet(join(meet(a,meet(C,A)),B),join(meet(a,meet(C,B)),A)),
inference(paramod,[status(thm)],[c_1,c_14]) ).
cnf(c_36,plain,
join(meet(A,B),meet(a,meet(C,join(A,B)))) = meet(join(meet(a,meet(C,A)),B),join(meet(a,meet(B,C)),A)),
inference(paramod,[status(thm)],[c_1,c_14]) ).
cnf(c_42,plain,
join(meet(A,B),meet(a,meet(C,join(A,B)))) = meet(join(B,meet(a,meet(C,A))),join(meet(a,meet(C,B)),A)),
inference(paramod,[status(thm)],[c_4,c_14]) ).
cnf(c_5409,plain,
join(meet(A,B),meet(a,A)) = meet(join(meet(a,meet(A,A)),B),join(meet(a,meet(A,B)),A)),
inference(paramod,[status(thm)],[c_8,c_14]) ).
cnf(c_5410,plain,
join(meet(A,B),meet(a,A)) = meet(join(meet(a,A),B),join(meet(a,meet(A,B)),A)),
inference(paramod,[status(thm)],[c_31,c_5409]) ).
cnf(c_5411,plain,
join(meet(A,B),meet(a,A)) = meet(join(meet(a,A),B),join(A,meet(a,meet(A,B)))),
inference(paramod,[status(thm)],[c_4,c_5410]) ).
cnf(c_51,plain,
join(meet(A,B),meet(a,A)) = meet(join(A,meet(a,meet(A,B))),join(meet(a,A),B)),
inference(paramod,[status(thm)],[c_1,c_5411]) ).
cnf(c_5412,plain,
lome(a,A,meet(B,join(a,A))) = meet(join(meet(a,meet(B,a)),A),join(meet(a,meet(B,A)),a)),
inference(paramod,[status(thm)],[c_14,c_10]) ).
cnf(c_5413,plain,
join(meet(a,A),meet(a,meet(B,join(a,A)))) = meet(join(meet(a,meet(B,a)),A),join(meet(a,meet(B,A)),a)),
inference(paramod,[status(thm)],[c_10,c_5412]) ).
cnf(c_5414,plain,
join(meet(a,A),meet(a,meet(B,join(a,A)))) = meet(join(meet(a,meet(B,a)),A),join(a,meet(a,meet(B,A)))),
inference(paramod,[status(thm)],[c_4,c_5413]) ).
cnf(c_5415,plain,
join(meet(a,A),meet(a,meet(B,join(a,A)))) = meet(join(meet(a,meet(B,a)),A),a),
inference(paramod,[status(thm)],[c_7,c_5414]) ).
cnf(c_54,plain,
join(meet(a,A),meet(a,meet(B,join(a,A)))) = meet(a,join(meet(a,meet(B,a)),A)),
inference(paramod,[status(thm)],[c_1,c_5415]) ).
cnf(c_55,plain,
join(A,meet(B,meet(A,C))) = A,
inference(paramod,[status(thm)],[c_18,c_7]) ).
cnf(c_5416,plain,
meet(A,B) = meet(B,meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_8,c_18]) ).
cnf(c_56,plain,
meet(A,meet(B,join(A,C))) = meet(B,A),
inference(copy,[status(thm)],[c_5416]) ).
cnf(c_57,plain,
join(meet(A,meet(B,C)),meet(a,meet(D,join(B,meet(A,C))))) = meet(join(meet(a,meet(D,B)),meet(A,C)),join(meet(a,meet(D,meet(A,C))),B)),
inference(paramod,[status(thm)],[c_18,c_14]) ).
cnf(c_64,plain,
join(meet(A,B),meet(a,A)) = meet(A,join(meet(a,A),B)),
inference(paramod,[status(thm)],[c_55,c_51]) ).
cnf(c_65,plain,
join(meet(a,A),meet(B,a)) = meet(a,join(meet(a,meet(B,a)),A)),
inference(paramod,[status(thm)],[c_56,c_54]) ).
cnf(c_5417,plain,
join(A,B) = join(B,join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_7,c_21]) ).
cnf(c_66,plain,
join(A,join(B,meet(A,C))) = join(B,A),
inference(copy,[status(thm)],[c_5417]) ).
cnf(c_67,plain,
meet(A,join(B,join(A,C))) = A,
inference(paramod,[status(thm)],[c_21,c_8]) ).
cnf(c_5418,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_30,c_6]) ).
cnf(c_74,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_4,c_5418]) ).
cnf(c_5419,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_31,c_3]) ).
cnf(c_77,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_5419]) ).
cnf(c_5420,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_31,c_3]) ).
cnf(c_79,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_1,c_5420]) ).
cnf(c_83,plain,
join(meet(a,A),meet(B,a)) = meet(a,join(meet(B,a),A)),
inference(paramod,[status(thm)],[c_79,c_65]) ).
cnf(c_5421,plain,
join(A,B) = join(A,join(meet(C,A),B)),
inference(paramod,[status(thm)],[c_22,c_6]) ).
cnf(c_85,plain,
join(A,join(meet(B,A),C)) = join(A,C),
inference(copy,[status(thm)],[c_5421]) ).
cnf(c_89,plain,
join(meet(A,B),meet(A,meet(C,B))) = meet(A,B),
inference(paramod,[status(thm)],[c_18,c_22]) ).
cnf(c_5422,plain,
join(A,B) = join(B,join(A,meet(C,B))),
inference(paramod,[status(thm)],[c_22,c_21]) ).
cnf(c_90,plain,
join(A,join(B,meet(C,A))) = join(B,A),
inference(copy,[status(thm)],[c_5422]) ).
cnf(c_5423,plain,
meet(A,B) = meet(A,meet(join(C,A),B)),
inference(paramod,[status(thm)],[c_28,c_3]) ).
cnf(c_91,plain,
meet(A,meet(join(B,A),C)) = meet(A,C),
inference(copy,[status(thm)],[c_5423]) ).
cnf(c_93,plain,
meet(A,join(B,join(C,A))) = A,
inference(paramod,[status(thm)],[c_6,c_28]) ).
cnf(c_5424,plain,
meet(A,B) = meet(B,meet(A,join(C,B))),
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_96,plain,
meet(A,meet(B,join(C,A))) = meet(B,A),
inference(copy,[status(thm)],[c_5424]) ).
cnf(c_5425,plain,
join(A,join(B,join(C,A))) = join(join(B,C),A),
inference(paramod,[status(thm)],[c_6,c_74]) ).
cnf(c_102,plain,
join(A,join(B,join(C,A))) = join(B,join(C,A)),
inference(paramod,[status(thm)],[c_6,c_5425]) ).
cnf(c_115,plain,
join(A,meet(join(meet(a,meet(B,A)),C),join(meet(a,meet(B,C)),A))) = join(A,meet(a,meet(B,join(A,C)))),
inference(paramod,[status(thm)],[c_14,c_24]) ).
cnf(c_116,plain,
join(A,join(meet(B,meet(A,C)),D)) = join(A,D),
inference(paramod,[status(thm)],[c_18,c_24]) ).
cnf(c_5426,plain,
meet(join(meet(A,B),C),join(A,C)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_118,plain,
meet(join(A,B),join(meet(A,C),B)) = join(meet(A,C),B),
inference(paramod,[status(thm)],[c_1,c_5426]) ).
cnf(c_5427,plain,
join(A,join(meet(A,B),join(C,A))) = join(C,A),
inference(paramod,[status(thm)],[c_74,c_24]) ).
cnf(c_119,plain,
join(meet(A,B),join(C,A)) = join(C,A),
inference(paramod,[status(thm)],[c_102,c_5427]) ).
cnf(c_5428,plain,
meet(meet(A,B),meet(B,C)) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_77,c_3]) ).
cnf(c_5429,plain,
meet(B,meet(meet(A,B),C)) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_18,c_5428]) ).
cnf(c_130,plain,
meet(A,meet(B,meet(A,C))) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_3,c_5429]) ).
cnf(c_5430,plain,
meet(A,meet(B,meet(C,A))) = meet(meet(B,C),A),
inference(paramod,[status(thm)],[c_3,c_79]) ).
cnf(c_135,plain,
meet(A,meet(B,meet(C,A))) = meet(B,meet(C,A)),
inference(paramod,[status(thm)],[c_3,c_5430]) ).
cnf(c_140,plain,
join(meet(A,B),meet(B,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_79,c_23]) ).
cnf(c_148,plain,
join(meet(A,B),join(C,B)) = join(C,B),
inference(paramod,[status(thm)],[c_1,c_119]) ).
cnf(c_156,plain,
join(meet(A,meet(B,C)),join(D,B)) = join(D,B),
inference(paramod,[status(thm)],[c_18,c_119]) ).
cnf(c_174,plain,
join(A,meet(B,meet(C,meet(A,D)))) = A,
inference(paramod,[status(thm)],[c_3,c_55]) ).
cnf(c_5431,plain,
join(A,B) = join(B,join(A,meet(C,meet(B,D)))),
inference(paramod,[status(thm)],[c_55,c_21]) ).
cnf(c_176,plain,
join(A,join(B,meet(C,meet(A,D)))) = join(B,A),
inference(copy,[status(thm)],[c_5431]) ).
cnf(c_5432,plain,
meet(meet(A,B),C) = meet(A,meet(B,meet(join(meet(A,B),D),C))),
inference(paramod,[status(thm)],[c_26,c_3]) ).
cnf(c_5433,plain,
meet(A,meet(B,C)) = meet(A,meet(B,meet(join(meet(A,B),D),C))),
inference(paramod,[status(thm)],[c_3,c_5432]) ).
cnf(c_178,plain,
meet(A,meet(B,meet(join(meet(A,B),C),D))) = meet(A,meet(B,D)),
inference(copy,[status(thm)],[c_5433]) ).
cnf(c_5434,plain,
join(meet(join(A,B),C),meet(A,C)) = meet(join(A,B),C),
inference(paramod,[status(thm)],[c_26,c_22]) ).
cnf(c_187,plain,
join(meet(A,B),meet(join(A,C),B)) = meet(join(A,C),B),
inference(paramod,[status(thm)],[c_4,c_5434]) ).
cnf(c_5435,plain,
meet(A,meet(join(A,B),meet(C,A))) = meet(C,A),
inference(paramod,[status(thm)],[c_79,c_26]) ).
cnf(c_188,plain,
meet(join(A,B),meet(C,A)) = meet(C,A),
inference(paramod,[status(thm)],[c_135,c_5435]) ).
cnf(c_217,plain,
meet(join(meet(A,B),C),join(C,B)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_148,c_29]) ).
cnf(c_232,plain,
meet(join(A,B),meet(C,B)) = meet(C,B),
inference(paramod,[status(thm)],[c_4,c_188]) ).
cnf(c_5436,plain,
join(join(A,B),meet(C,meet(D,A))) = join(A,B),
inference(paramod,[status(thm)],[c_188,c_55]) ).
cnf(c_246,plain,
join(A,join(B,meet(C,meet(D,A)))) = join(A,B),
inference(paramod,[status(thm)],[c_6,c_5436]) ).
cnf(c_257,plain,
join(meet(join(A,B),C),meet(C,B)) = meet(join(A,B),C),
inference(paramod,[status(thm)],[c_232,c_23]) ).
cnf(c_5437,plain,
meet(meet(A,B),join(C,join(D,A))) = meet(A,B),
inference(paramod,[status(thm)],[c_119,c_67]) ).
cnf(c_271,plain,
meet(A,meet(B,join(C,join(D,A)))) = meet(A,B),
inference(paramod,[status(thm)],[c_3,c_5437]) ).
cnf(c_5438,plain,
meet(meet(A,B),join(C,meet(B,A))) = meet(A,B),
inference(paramod,[status(thm)],[c_140,c_93]) ).
cnf(c_296,plain,
meet(A,meet(B,join(C,meet(B,A)))) = meet(A,B),
inference(paramod,[status(thm)],[c_3,c_5438]) ).
cnf(c_476,plain,
join(meet(A,B),meet(A,a)) = meet(A,join(meet(a,A),B)),
inference(paramod,[status(thm)],[c_1,c_64]) ).
cnf(c_482,plain,
join(meet(A,B),meet(a,A)) = meet(A,join(B,meet(a,A))),
inference(paramod,[status(thm)],[c_4,c_64]) ).
cnf(c_5439,plain,
join(meet(A,meet(a,meet(join(a,A),B))),meet(a,A)) = meet(A,meet(join(meet(a,meet(B,a)),A),join(meet(a,meet(B,A)),a))),
inference(paramod,[status(thm)],[c_34,c_64]) ).
cnf(c_5440,plain,
join(meet(A,meet(a,B)),meet(a,A)) = meet(A,meet(join(meet(a,meet(B,a)),A),join(meet(a,meet(B,A)),a))),
inference(paramod,[status(thm)],[c_26,c_5439]) ).
cnf(c_5441,plain,
meet(A,join(meet(a,B),meet(a,A))) = meet(A,meet(join(meet(a,meet(B,a)),A),join(meet(a,meet(B,A)),a))),
inference(paramod,[status(thm)],[c_482,c_5440]) ).
cnf(c_5442,plain,
meet(A,join(meet(a,B),meet(a,A))) = meet(A,meet(join(meet(B,a),A),join(meet(a,meet(B,A)),a))),
inference(paramod,[status(thm)],[c_79,c_5441]) ).
cnf(c_5443,plain,
meet(A,join(meet(a,B),meet(a,A))) = meet(A,meet(join(meet(B,a),A),join(a,meet(a,meet(B,A))))),
inference(paramod,[status(thm)],[c_4,c_5442]) ).
cnf(c_5444,plain,
meet(A,join(meet(a,B),meet(a,A))) = meet(A,meet(join(meet(B,a),A),a)),
inference(paramod,[status(thm)],[c_7,c_5443]) ).
cnf(c_5445,plain,
meet(A,join(meet(a,B),meet(a,A))) = meet(A,meet(a,join(meet(B,a),A))),
inference(paramod,[status(thm)],[c_1,c_5444]) ).
cnf(c_520,plain,
meet(A,join(meet(a,B),meet(a,A))) = meet(a,A),
inference(paramod,[status(thm)],[c_96,c_5445]) ).
cnf(c_535,plain,
meet(A,join(meet(a,B),meet(A,a))) = meet(a,A),
inference(paramod,[status(thm)],[c_1,c_520]) ).
cnf(c_571,plain,
meet(A,join(meet(A,a),meet(a,B))) = meet(a,A),
inference(paramod,[status(thm)],[c_4,c_535]) ).
cnf(c_5446,plain,
join(meet(a,A),meet(a,meet(join(A,join(meet(A,a),meet(a,B))),C))) = meet(join(meet(a,meet(C,A)),join(meet(A,a),meet(a,B))),join(meet(a,meet(C,join(meet(A,a),meet(a,B)))),A)),
inference(paramod,[status(thm)],[c_571,c_34]) ).
cnf(c_5447,plain,
join(meet(a,A),meet(a,meet(join(A,meet(a,B)),C))) = meet(join(meet(a,meet(C,A)),join(meet(A,a),meet(a,B))),join(meet(a,meet(C,join(meet(A,a),meet(a,B)))),A)),
inference(paramod,[status(thm)],[c_24,c_5446]) ).
cnf(c_5448,plain,
join(meet(a,A),meet(a,meet(join(A,meet(a,B)),C))) = meet(join(meet(a,meet(C,A)),join(meet(A,a),meet(a,B))),join(A,meet(a,meet(C,join(meet(A,a),meet(a,B)))))),
inference(paramod,[status(thm)],[c_4,c_5447]) ).
cnf(c_5449,plain,
join(meet(a,A),meet(a,meet(join(A,meet(a,B)),C))) = meet(join(A,meet(a,meet(C,join(meet(A,a),meet(a,B))))),join(meet(a,meet(C,A)),join(meet(A,a),meet(a,B)))),
inference(paramod,[status(thm)],[c_1,c_5448]) ).
cnf(c_859,plain,
meet(join(A,meet(a,meet(B,join(meet(A,a),meet(a,C))))),join(meet(a,meet(B,A)),join(meet(A,a),meet(a,C)))) = join(meet(a,A),meet(a,meet(join(A,meet(a,C)),B))),
inference(copy,[status(thm)],[c_5449]) ).
cnf(c_5450,plain,
meet(a,join(meet(A,a),B)) = join(meet(A,a),meet(a,B)),
inference(paramod,[status(thm)],[c_83,c_4]) ).
cnf(c_868,plain,
join(meet(A,a),meet(a,B)) = meet(a,join(meet(A,a),B)),
inference(copy,[status(thm)],[c_5450]) ).
cnf(c_869,plain,
join(meet(a,A),meet(B,a)) = meet(a,join(A,meet(B,a))),
inference(paramod,[status(thm)],[c_4,c_83]) ).
cnf(c_5451,plain,
join(meet(a,meet(a,meet(A,join(B,a)))),meet(B,a)) = meet(a,meet(join(meet(a,meet(A,B)),a),join(meet(a,meet(A,a)),B))),
inference(paramod,[status(thm)],[c_14,c_83]) ).
cnf(c_5452,plain,
join(meet(a,meet(A,a)),meet(B,a)) = meet(a,meet(join(meet(a,meet(A,B)),a),join(meet(a,meet(A,a)),B))),
inference(paramod,[status(thm)],[c_96,c_5451]) ).
cnf(c_5453,plain,
join(meet(A,a),meet(B,a)) = meet(a,meet(join(meet(a,meet(A,B)),a),join(meet(a,meet(A,a)),B))),
inference(paramod,[status(thm)],[c_79,c_5452]) ).
cnf(c_5454,plain,
join(meet(A,a),meet(B,a)) = meet(a,meet(join(a,meet(a,meet(A,B))),join(meet(a,meet(A,a)),B))),
inference(paramod,[status(thm)],[c_4,c_5453]) ).
cnf(c_5455,plain,
join(meet(A,a),meet(B,a)) = meet(a,meet(a,join(meet(a,meet(A,a)),B))),
inference(paramod,[status(thm)],[c_7,c_5454]) ).
cnf(c_5456,plain,
join(meet(A,a),meet(B,a)) = meet(a,meet(a,join(meet(A,a),B))),
inference(paramod,[status(thm)],[c_79,c_5455]) ).
cnf(c_876,plain,
join(meet(A,a),meet(B,a)) = meet(a,join(meet(A,a),B)),
inference(paramod,[status(thm)],[c_77,c_5456]) ).
cnf(c_5457,plain,
join(meet(a,meet(a,meet(join(A,a),B))),meet(A,a)) = meet(a,meet(join(meet(a,meet(B,A)),a),join(meet(a,meet(B,a)),A))),
inference(paramod,[status(thm)],[c_34,c_83]) ).
cnf(c_5458,plain,
join(meet(a,meet(a,B)),meet(A,a)) = meet(a,meet(join(meet(a,meet(B,A)),a),join(meet(a,meet(B,a)),A))),
inference(paramod,[status(thm)],[c_91,c_5457]) ).
cnf(c_5459,plain,
join(meet(a,B),meet(A,a)) = meet(a,meet(join(meet(a,meet(B,A)),a),join(meet(a,meet(B,a)),A))),
inference(paramod,[status(thm)],[c_77,c_5458]) ).
cnf(c_5460,plain,
meet(a,join(B,meet(A,a))) = meet(a,meet(join(meet(a,meet(B,A)),a),join(meet(a,meet(B,a)),A))),
inference(paramod,[status(thm)],[c_869,c_5459]) ).
cnf(c_5461,plain,
meet(a,join(B,meet(A,a))) = meet(a,meet(join(a,meet(a,meet(B,A))),join(meet(a,meet(B,a)),A))),
inference(paramod,[status(thm)],[c_4,c_5460]) ).
cnf(c_5462,plain,
meet(a,join(B,meet(A,a))) = meet(a,meet(a,join(meet(a,meet(B,a)),A))),
inference(paramod,[status(thm)],[c_7,c_5461]) ).
cnf(c_5463,plain,
meet(a,join(B,meet(A,a))) = meet(a,meet(a,join(meet(B,a),A))),
inference(paramod,[status(thm)],[c_79,c_5462]) ).
cnf(c_5464,plain,
meet(a,join(B,meet(A,a))) = meet(a,join(meet(B,a),A)),
inference(paramod,[status(thm)],[c_77,c_5463]) ).
cnf(c_906,plain,
meet(a,join(meet(A,a),B)) = meet(a,join(A,meet(B,a))),
inference(copy,[status(thm)],[c_5464]) ).
cnf(c_5465,plain,
join(meet(a,meet(a,meet(A,join(B,a)))),meet(B,a)) = meet(a,meet(join(meet(a,meet(A,B)),a),join(meet(a,meet(a,A)),B))),
inference(paramod,[status(thm)],[c_36,c_83]) ).
cnf(c_5466,plain,
join(meet(a,meet(A,a)),meet(B,a)) = meet(a,meet(join(meet(a,meet(A,B)),a),join(meet(a,meet(a,A)),B))),
inference(paramod,[status(thm)],[c_96,c_5465]) ).
cnf(c_5467,plain,
join(meet(A,a),meet(B,a)) = meet(a,meet(join(meet(a,meet(A,B)),a),join(meet(a,meet(a,A)),B))),
inference(paramod,[status(thm)],[c_79,c_5466]) ).
cnf(c_5468,plain,
meet(a,join(meet(A,a),B)) = meet(a,meet(join(meet(a,meet(A,B)),a),join(meet(a,meet(a,A)),B))),
inference(paramod,[status(thm)],[c_876,c_5467]) ).
cnf(c_5469,plain,
meet(a,join(A,meet(B,a))) = meet(a,meet(join(meet(a,meet(A,B)),a),join(meet(a,meet(a,A)),B))),
inference(paramod,[status(thm)],[c_906,c_5468]) ).
cnf(c_5470,plain,
meet(a,join(A,meet(B,a))) = meet(a,meet(join(a,meet(a,meet(A,B))),join(meet(a,meet(a,A)),B))),
inference(paramod,[status(thm)],[c_4,c_5469]) ).
cnf(c_5471,plain,
meet(a,join(A,meet(B,a))) = meet(a,meet(a,join(meet(a,meet(a,A)),B))),
inference(paramod,[status(thm)],[c_7,c_5470]) ).
cnf(c_5472,plain,
meet(a,join(A,meet(B,a))) = meet(a,meet(a,join(meet(a,A),B))),
inference(paramod,[status(thm)],[c_77,c_5471]) ).
cnf(c_5473,plain,
meet(a,join(A,meet(B,a))) = meet(a,join(meet(a,A),B)),
inference(paramod,[status(thm)],[c_77,c_5472]) ).
cnf(c_927,plain,
meet(a,join(meet(a,A),B)) = meet(a,join(A,meet(B,a))),
inference(copy,[status(thm)],[c_5473]) ).
cnf(c_5474,plain,
meet(join(A,meet(a,meet(B,meet(a,join(meet(A,a),C))))),join(meet(a,meet(B,A)),join(meet(A,a),meet(a,C)))) = join(meet(a,A),meet(a,meet(join(A,meet(a,C)),B))),
inference(paramod,[status(thm)],[c_868,c_859]) ).
cnf(c_5475,plain,
meet(join(A,meet(a,meet(B,meet(a,join(A,meet(C,a)))))),join(meet(a,meet(B,A)),join(meet(A,a),meet(a,C)))) = join(meet(a,A),meet(a,meet(join(A,meet(a,C)),B))),
inference(paramod,[status(thm)],[c_906,c_5474]) ).
cnf(c_5476,plain,
meet(join(A,meet(B,meet(a,join(A,meet(C,a))))),join(meet(a,meet(B,A)),join(meet(A,a),meet(a,C)))) = join(meet(a,A),meet(a,meet(join(A,meet(a,C)),B))),
inference(paramod,[status(thm)],[c_130,c_5475]) ).
cnf(c_5477,plain,
meet(join(A,meet(B,meet(a,join(A,meet(C,a))))),join(meet(a,meet(B,A)),meet(a,join(meet(A,a),C)))) = join(meet(a,A),meet(a,meet(join(A,meet(a,C)),B))),
inference(paramod,[status(thm)],[c_868,c_5476]) ).
cnf(c_941,plain,
meet(join(A,meet(B,meet(a,join(A,meet(C,a))))),join(meet(a,meet(B,A)),meet(a,join(A,meet(C,a))))) = join(meet(a,A),meet(a,meet(join(A,meet(a,C)),B))),
inference(paramod,[status(thm)],[c_906,c_5477]) ).
cnf(c_997,plain,
join(meet(A,a),meet(a,B)) = meet(a,join(A,meet(B,a))),
inference(paramod,[status(thm)],[c_906,c_868]) ).
cnf(c_5478,plain,
meet(join(A,join(B,meet(A,C))),join(B,meet(A,C))) = join(meet(A,C),join(B,meet(A,C))),
inference(paramod,[status(thm)],[c_74,c_118]) ).
cnf(c_5479,plain,
meet(join(B,A),join(B,meet(A,C))) = join(meet(A,C),join(B,meet(A,C))),
inference(paramod,[status(thm)],[c_66,c_5478]) ).
cnf(c_1043,plain,
meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_74,c_5479]) ).
cnf(c_1049,plain,
meet(A,join(meet(A,B),meet(C,meet(A,D)))) = join(meet(A,B),meet(C,meet(A,D))),
inference(paramod,[status(thm)],[c_55,c_118]) ).
cnf(c_1071,plain,
join(meet(A,B),meet(B,join(A,C))) = meet(join(A,C),B),
inference(paramod,[status(thm)],[c_1,c_187]) ).
cnf(c_5480,plain,
meet(join(A,meet(B,C)),join(join(A,meet(B,C)),C)) = join(meet(B,C),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_74,c_217]) ).
cnf(c_5481,plain,
meet(join(A,meet(B,C)),join(C,join(A,meet(B,C)))) = join(meet(B,C),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_4,c_5480]) ).
cnf(c_5482,plain,
meet(join(A,meet(B,C)),join(A,C)) = join(meet(B,C),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_90,c_5481]) ).
cnf(c_5483,plain,
meet(join(A,C),join(A,meet(B,C))) = join(meet(B,C),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_1,c_5482]) ).
cnf(c_1254,plain,
meet(join(A,B),join(A,meet(C,B))) = join(A,meet(C,B)),
inference(paramod,[status(thm)],[c_74,c_5483]) ).
cnf(c_5484,plain,
join(meet(meet(A,B),meet(A,a)),meet(a,meet(meet(A,join(meet(a,A),B)),C))) = meet(join(meet(a,meet(C,meet(A,B))),meet(A,a)),join(meet(a,meet(C,meet(A,a))),meet(A,B))),
inference(paramod,[status(thm)],[c_476,c_34]) ).
cnf(c_5485,plain,
join(meet(A,meet(meet(A,B),a)),meet(a,meet(meet(A,join(meet(a,A),B)),C))) = meet(join(meet(a,meet(C,meet(A,B))),meet(A,a)),join(meet(a,meet(C,meet(A,a))),meet(A,B))),
inference(paramod,[status(thm)],[c_18,c_5484]) ).
cnf(c_5486,plain,
join(meet(A,meet(a,meet(A,B))),meet(a,meet(meet(A,join(meet(a,A),B)),C))) = meet(join(meet(a,meet(C,meet(A,B))),meet(A,a)),join(meet(a,meet(C,meet(A,a))),meet(A,B))),
inference(paramod,[status(thm)],[c_1,c_5485]) ).
cnf(c_5487,plain,
join(meet(a,meet(A,B)),meet(a,meet(meet(A,join(meet(a,A),B)),C))) = meet(join(meet(a,meet(C,meet(A,B))),meet(A,a)),join(meet(a,meet(C,meet(A,a))),meet(A,B))),
inference(paramod,[status(thm)],[c_130,c_5486]) ).
cnf(c_5488,plain,
join(meet(a,meet(A,B)),meet(a,meet(A,meet(join(meet(a,A),B),C)))) = meet(join(meet(a,meet(C,meet(A,B))),meet(A,a)),join(meet(a,meet(C,meet(A,a))),meet(A,B))),
inference(paramod,[status(thm)],[c_3,c_5487]) ).
cnf(c_5489,plain,
join(meet(a,meet(A,B)),meet(a,meet(A,C))) = meet(join(meet(a,meet(C,meet(A,B))),meet(A,a)),join(meet(a,meet(C,meet(A,a))),meet(A,B))),
inference(paramod,[status(thm)],[c_178,c_5488]) ).
cnf(c_5490,plain,
join(meet(a,meet(A,B)),meet(a,meet(A,C))) = meet(meet(a,join(meet(C,meet(A,B)),meet(A,a))),join(meet(a,meet(C,meet(A,a))),meet(A,B))),
inference(paramod,[status(thm)],[c_869,c_5489]) ).
cnf(c_5491,plain,
join(meet(a,meet(A,B)),meet(a,meet(A,C))) = meet(meet(a,join(meet(C,meet(A,B)),meet(A,a))),join(meet(C,meet(A,a)),meet(A,B))),
inference(paramod,[status(thm)],[c_135,c_5490]) ).
cnf(c_1388,plain,
join(meet(a,meet(A,B)),meet(a,meet(A,C))) = meet(a,meet(join(meet(C,meet(A,B)),meet(A,a)),join(meet(C,meet(A,a)),meet(A,B)))),
inference(paramod,[status(thm)],[c_3,c_5491]) ).
cnf(c_5492,plain,
join(meet(meet(a,meet(A,join(a,meet(B,C)))),C),meet(a,meet(B,join(meet(a,meet(A,join(a,meet(B,C)))),C)))) = meet(join(C,meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C))))))),meet(join(meet(a,meet(A,a)),meet(B,C)),join(meet(a,meet(A,meet(B,C))),a))),
inference(paramod,[status(thm)],[c_14,c_42]) ).
cnf(c_5493,plain,
join(meet(meet(A,a),C),meet(a,meet(B,join(meet(a,meet(A,join(a,meet(B,C)))),C)))) = meet(join(C,meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C))))))),meet(join(meet(a,meet(A,a)),meet(B,C)),join(meet(a,meet(A,meet(B,C))),a))),
inference(paramod,[status(thm)],[c_56,c_5492]) ).
cnf(c_5494,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(a,meet(A,join(a,meet(B,C)))),C)))) = meet(join(C,meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C))))))),meet(join(meet(a,meet(A,a)),meet(B,C)),join(meet(a,meet(A,meet(B,C))),a))),
inference(paramod,[status(thm)],[c_3,c_5493]) ).
cnf(c_5495,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(A,a),C)))) = meet(join(C,meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C))))))),meet(join(meet(a,meet(A,a)),meet(B,C)),join(meet(a,meet(A,meet(B,C))),a))),
inference(paramod,[status(thm)],[c_56,c_5494]) ).
cnf(c_5496,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(A,a),C)))) = meet(join(C,meet(a,meet(B,meet(A,a)))),meet(join(meet(a,meet(A,a)),meet(B,C)),join(meet(a,meet(A,meet(B,C))),a))),
inference(paramod,[status(thm)],[c_56,c_5495]) ).
cnf(c_5497,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(A,a),C)))) = meet(join(C,meet(B,meet(A,a))),meet(join(meet(a,meet(A,a)),meet(B,C)),join(meet(a,meet(A,meet(B,C))),a))),
inference(paramod,[status(thm)],[c_135,c_5496]) ).
cnf(c_5498,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(A,a),C)))) = meet(join(C,meet(B,meet(A,a))),meet(join(meet(A,a),meet(B,C)),join(meet(a,meet(A,meet(B,C))),a))),
inference(paramod,[status(thm)],[c_79,c_5497]) ).
cnf(c_5499,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(A,a),C)))) = meet(join(C,meet(B,meet(A,a))),meet(join(meet(A,a),meet(B,C)),join(a,meet(a,meet(A,meet(B,C)))))),
inference(paramod,[status(thm)],[c_4,c_5498]) ).
cnf(c_5500,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(A,a),C)))) = meet(join(C,meet(B,meet(A,a))),meet(join(meet(A,a),meet(B,C)),a)),
inference(paramod,[status(thm)],[c_7,c_5499]) ).
cnf(c_5501,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(A,a),C)))) = meet(join(C,meet(B,meet(A,a))),meet(a,join(meet(A,a),meet(B,C)))),
inference(paramod,[status(thm)],[c_1,c_5500]) ).
cnf(c_5502,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(A,a),C)))) = meet(join(C,meet(B,meet(A,a))),meet(a,join(A,meet(meet(B,C),a)))),
inference(paramod,[status(thm)],[c_906,c_5501]) ).
cnf(c_5503,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(A,a),C)))) = meet(join(C,meet(B,meet(A,a))),meet(a,join(A,meet(a,meet(B,C))))),
inference(paramod,[status(thm)],[c_1,c_5502]) ).
cnf(c_1491,plain,
join(meet(A,meet(a,B)),meet(a,meet(C,join(meet(A,a),B)))) = meet(a,meet(join(B,meet(C,meet(A,a))),join(A,meet(a,meet(C,B))))),
inference(paramod,[status(thm)],[c_18,c_5503]) ).
cnf(c_5504,plain,
join(meet(meet(a,meet(A,join(a,meet(B,C)))),C),meet(a,meet(B,join(meet(a,meet(A,join(a,meet(B,C)))),C)))) = meet(meet(join(meet(B,C),meet(a,meet(A,a))),join(meet(a,meet(A,meet(B,C))),a)),join(meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C)))))),C)),
inference(paramod,[status(thm)],[c_42,c_32]) ).
cnf(c_5505,plain,
join(meet(meet(A,a),C),meet(a,meet(B,join(meet(a,meet(A,join(a,meet(B,C)))),C)))) = meet(meet(join(meet(B,C),meet(a,meet(A,a))),join(meet(a,meet(A,meet(B,C))),a)),join(meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C)))))),C)),
inference(paramod,[status(thm)],[c_56,c_5504]) ).
cnf(c_5506,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(a,meet(A,join(a,meet(B,C)))),C)))) = meet(meet(join(meet(B,C),meet(a,meet(A,a))),join(meet(a,meet(A,meet(B,C))),a)),join(meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C)))))),C)),
inference(paramod,[status(thm)],[c_3,c_5505]) ).
cnf(c_5507,plain,
join(meet(A,meet(a,C)),meet(a,meet(B,join(meet(A,a),C)))) = meet(meet(join(meet(B,C),meet(a,meet(A,a))),join(meet(a,meet(A,meet(B,C))),a)),join(meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C)))))),C)),
inference(paramod,[status(thm)],[c_56,c_5506]) ).
cnf(c_5508,plain,
meet(a,meet(join(C,meet(B,meet(A,a))),join(A,meet(a,meet(B,C))))) = meet(meet(join(meet(B,C),meet(a,meet(A,a))),join(meet(a,meet(A,meet(B,C))),a)),join(meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C)))))),C)),
inference(paramod,[status(thm)],[c_1491,c_5507]) ).
cnf(c_5509,plain,
meet(a,meet(join(C,meet(B,meet(A,a))),join(A,meet(a,meet(B,C))))) = meet(meet(join(meet(B,C),meet(A,a)),join(meet(a,meet(A,meet(B,C))),a)),join(meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C)))))),C)),
inference(paramod,[status(thm)],[c_79,c_5508]) ).
cnf(c_5510,plain,
meet(a,meet(join(C,meet(B,meet(A,a))),join(A,meet(a,meet(B,C))))) = meet(meet(join(meet(B,C),meet(A,a)),join(a,meet(a,meet(A,meet(B,C))))),join(meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C)))))),C)),
inference(paramod,[status(thm)],[c_4,c_5509]) ).
cnf(c_5511,plain,
meet(a,meet(join(C,meet(B,meet(A,a))),join(A,meet(a,meet(B,C))))) = meet(meet(join(meet(B,C),meet(A,a)),a),join(meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C)))))),C)),
inference(paramod,[status(thm)],[c_7,c_5510]) ).
cnf(c_5512,plain,
meet(a,meet(join(C,meet(B,meet(A,a))),join(A,meet(a,meet(B,C))))) = meet(meet(a,join(meet(B,C),meet(A,a))),join(meet(a,meet(B,meet(a,meet(A,join(a,meet(B,C)))))),C)),
inference(paramod,[status(thm)],[c_1,c_5511]) ).
cnf(c_5513,plain,
meet(a,meet(join(C,meet(B,meet(A,a))),join(A,meet(a,meet(B,C))))) = meet(meet(a,join(meet(B,C),meet(A,a))),join(meet(a,meet(B,meet(A,a))),C)),
inference(paramod,[status(thm)],[c_56,c_5512]) ).
cnf(c_5514,plain,
meet(a,meet(join(C,meet(B,meet(A,a))),join(A,meet(a,meet(B,C))))) = meet(meet(a,join(meet(B,C),meet(A,a))),join(meet(B,meet(A,a)),C)),
inference(paramod,[status(thm)],[c_135,c_5513]) ).
cnf(c_5515,plain,
meet(a,meet(join(C,meet(B,meet(A,a))),join(A,meet(a,meet(B,C))))) = meet(a,meet(join(meet(B,C),meet(A,a)),join(meet(B,meet(A,a)),C))),
inference(paramod,[status(thm)],[c_3,c_5514]) ).
cnf(c_1529,plain,
meet(a,meet(join(meet(A,B),meet(C,a)),join(meet(A,meet(C,a)),B))) = meet(a,meet(join(B,meet(A,meet(C,a))),join(C,meet(a,meet(A,B))))),
inference(copy,[status(thm)],[c_5515]) ).
cnf(c_5516,plain,
join(meet(a,meet(A,B)),meet(a,meet(A,C))) = meet(a,meet(join(meet(A,B),meet(C,meet(A,a))),join(A,meet(a,meet(C,meet(A,B)))))),
inference(paramod,[status(thm)],[c_1529,c_1388]) ).
cnf(c_5517,plain,
join(meet(a,meet(A,B)),meet(a,meet(A,C))) = meet(a,meet(join(meet(A,B),meet(C,meet(A,a))),A)),
inference(paramod,[status(thm)],[c_174,c_5516]) ).
cnf(c_5518,plain,
join(meet(a,meet(A,B)),meet(a,meet(A,C))) = meet(a,meet(A,join(meet(A,B),meet(C,meet(A,a))))),
inference(paramod,[status(thm)],[c_1,c_5517]) ).
cnf(c_1600,plain,
join(meet(a,meet(A,B)),meet(a,meet(A,C))) = meet(a,join(meet(A,B),meet(C,meet(A,a)))),
inference(paramod,[status(thm)],[c_1049,c_5518]) ).
cnf(c_5519,plain,
meet(a,join(meet(z1,z2),meet(z3,meet(z1,a)))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_1600,c_19]) ).
cnf(c_5520,plain,
meet(a,join(meet(z1,z2),meet(z3,meet(a,z1)))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_1,c_5519]) ).
cnf(c_5521,plain,
meet(a,join(meet(z1,z2),meet(a,meet(z3,z1)))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_18,c_5520]) ).
cnf(c_1617,plain,
meet(a,join(meet(z1,z2),meet(a,meet(z1,z3)))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_1,c_5521]) ).
cnf(c_5522,plain,
join(meet(A,meet(join(B,C),D)),meet(a,meet(B,join(join(B,C),meet(A,D))))) = meet(join(meet(a,B),meet(A,D)),join(meet(a,meet(B,meet(A,D))),join(B,C))),
inference(paramod,[status(thm)],[c_8,c_57]) ).
cnf(c_5523,plain,
join(meet(A,meet(join(B,C),D)),meet(a,meet(B,join(B,join(C,meet(A,D)))))) = meet(join(meet(a,B),meet(A,D)),join(meet(a,meet(B,meet(A,D))),join(B,C))),
inference(paramod,[status(thm)],[c_6,c_5522]) ).
cnf(c_5524,plain,
join(meet(A,meet(join(B,C),D)),meet(a,B)) = meet(join(meet(a,B),meet(A,D)),join(meet(a,meet(B,meet(A,D))),join(B,C))),
inference(paramod,[status(thm)],[c_8,c_5523]) ).
cnf(c_5525,plain,
join(meet(a,B),meet(A,meet(join(B,C),D))) = meet(join(meet(a,B),meet(A,D)),join(meet(a,meet(B,meet(A,D))),join(B,C))),
inference(paramod,[status(thm)],[c_4,c_5524]) ).
cnf(c_5526,plain,
join(meet(a,B),meet(A,meet(join(B,C),D))) = meet(join(meet(a,B),meet(A,D)),join(B,join(meet(a,meet(B,meet(A,D))),C))),
inference(paramod,[status(thm)],[c_21,c_5525]) ).
cnf(c_1830,plain,
join(meet(a,A),meet(B,meet(join(A,C),D))) = meet(join(meet(a,A),meet(B,D)),join(A,C)),
inference(paramod,[status(thm)],[c_116,c_5526]) ).
cnf(c_1860,plain,
meet(join(A,meet(B,meet(a,join(A,meet(C,a))))),join(meet(a,meet(B,A)),meet(a,join(A,meet(C,a))))) = meet(join(meet(a,A),meet(a,B)),join(A,meet(a,C))),
inference(paramod,[status(thm)],[c_1830,c_941]) ).
cnf(c_2079,plain,
join(meet(a,A),meet(a,B)) = meet(a,join(A,meet(B,a))),
inference(paramod,[status(thm)],[c_1,c_869]) ).
cnf(c_5527,plain,
meet(join(A,meet(B,meet(a,join(A,meet(C,a))))),meet(a,join(meet(B,A),meet(join(A,meet(C,a)),a)))) = meet(join(meet(a,A),meet(a,B)),join(A,meet(a,C))),
inference(paramod,[status(thm)],[c_2079,c_1860]) ).
cnf(c_5528,plain,
meet(join(A,meet(B,meet(a,join(A,meet(C,a))))),meet(a,join(meet(B,A),meet(a,join(A,meet(C,a)))))) = meet(join(meet(a,A),meet(a,B)),join(A,meet(a,C))),
inference(paramod,[status(thm)],[c_1,c_5527]) ).
cnf(c_5529,plain,
meet(a,meet(join(A,meet(B,meet(a,join(A,meet(C,a))))),join(meet(B,A),meet(a,join(A,meet(C,a)))))) = meet(join(meet(a,A),meet(a,B)),join(A,meet(a,C))),
inference(paramod,[status(thm)],[c_18,c_5528]) ).
cnf(c_5530,plain,
meet(a,meet(join(A,meet(B,meet(a,join(A,meet(C,a))))),join(meet(B,A),meet(a,join(A,meet(C,a)))))) = meet(meet(a,join(A,meet(B,a))),join(A,meet(a,C))),
inference(paramod,[status(thm)],[c_2079,c_5529]) ).
cnf(c_2110,plain,
meet(a,meet(join(A,meet(B,meet(a,join(A,meet(C,a))))),join(meet(B,A),meet(a,join(A,meet(C,a)))))) = meet(a,meet(join(A,meet(B,a)),join(A,meet(a,C)))),
inference(paramod,[status(thm)],[c_3,c_5530]) ).
cnf(c_5531,plain,
meet(A,meet(a,join(B,meet(C,a)))) = meet(a,meet(A,join(meet(a,B),C))),
inference(paramod,[status(thm)],[c_927,c_18]) ).
cnf(c_2190,plain,
meet(a,meet(A,join(meet(a,B),C))) = meet(A,meet(a,join(B,meet(C,a)))),
inference(copy,[status(thm)],[c_5531]) ).
cnf(c_5532,plain,
meet(join(A,meet(B,C)),join(A,meet(B,meet(C,D)))) = join(A,meet(meet(B,C),D)),
inference(paramod,[status(thm)],[c_3,c_1043]) ).
cnf(c_2596,plain,
meet(join(A,meet(B,C)),join(A,meet(B,meet(C,D)))) = join(A,meet(B,meet(C,D))),
inference(paramod,[status(thm)],[c_3,c_5532]) ).
cnf(c_5533,plain,
meet(meet(a,join(A,meet(B,a))),join(meet(a,A),meet(meet(B,a),C))) = join(meet(a,A),meet(meet(B,a),C)),
inference(paramod,[status(thm)],[c_869,c_1043]) ).
cnf(c_5534,plain,
meet(meet(a,join(A,meet(B,a))),join(meet(a,A),meet(B,meet(a,C)))) = join(meet(a,A),meet(meet(B,a),C)),
inference(paramod,[status(thm)],[c_3,c_5533]) ).
cnf(c_5535,plain,
meet(a,meet(join(A,meet(B,a)),join(meet(a,A),meet(B,meet(a,C))))) = join(meet(a,A),meet(meet(B,a),C)),
inference(paramod,[status(thm)],[c_3,c_5534]) ).
cnf(c_5536,plain,
meet(join(A,meet(B,a)),meet(a,join(A,meet(meet(B,meet(a,C)),a)))) = join(meet(a,A),meet(meet(B,a),C)),
inference(paramod,[status(thm)],[c_2190,c_5535]) ).
cnf(c_5537,plain,
meet(join(A,meet(B,a)),meet(a,join(A,meet(a,meet(B,meet(a,C)))))) = join(meet(a,A),meet(meet(B,a),C)),
inference(paramod,[status(thm)],[c_1,c_5536]) ).
cnf(c_5538,plain,
meet(join(A,meet(B,a)),meet(a,join(A,meet(B,meet(a,C))))) = join(meet(a,A),meet(meet(B,a),C)),
inference(paramod,[status(thm)],[c_130,c_5537]) ).
cnf(c_5539,plain,
meet(a,meet(join(A,meet(B,a)),join(A,meet(B,meet(a,C))))) = join(meet(a,A),meet(meet(B,a),C)),
inference(paramod,[status(thm)],[c_18,c_5538]) ).
cnf(c_5540,plain,
meet(a,join(A,meet(B,meet(a,C)))) = join(meet(a,A),meet(meet(B,a),C)),
inference(paramod,[status(thm)],[c_2596,c_5539]) ).
cnf(c_5541,plain,
meet(a,join(A,meet(B,meet(a,C)))) = join(meet(a,A),meet(B,meet(a,C))),
inference(paramod,[status(thm)],[c_3,c_5540]) ).
cnf(c_2616,plain,
join(meet(a,A),meet(B,meet(a,C))) = meet(a,join(A,meet(B,meet(a,C)))),
inference(copy,[status(thm)],[c_5541]) ).
cnf(c_5542,plain,
join(meet(A,meet(B,join(C,D))),meet(A,meet(B,C))) = meet(A,meet(B,join(C,D))),
inference(paramod,[status(thm)],[c_56,c_89]) ).
cnf(c_2739,plain,
join(meet(A,meet(B,C)),meet(A,meet(B,join(C,D)))) = meet(A,meet(B,join(C,D))),
inference(paramod,[status(thm)],[c_4,c_5542]) ).
cnf(c_2755,plain,
meet(join(A,B),meet(C,join(A,meet(D,B)))) = meet(C,join(A,meet(D,B))),
inference(paramod,[status(thm)],[c_90,c_232]) ).
cnf(c_5543,plain,
meet(a,join(A,meet(B,a))) = meet(a,join(B,meet(join(A,meet(C,meet(B,a))),a))),
inference(paramod,[status(thm)],[c_90,c_906]) ).
cnf(c_5544,plain,
meet(a,join(A,meet(B,a))) = meet(a,join(B,meet(a,join(A,meet(C,meet(B,a)))))),
inference(paramod,[status(thm)],[c_1,c_5543]) ).
cnf(c_2768,plain,
meet(a,join(A,meet(a,join(B,meet(C,meet(A,a)))))) = meet(a,join(B,meet(A,a))),
inference(copy,[status(thm)],[c_5544]) ).
cnf(c_2780,plain,
join(meet(A,B),meet(B,join(C,A))) = meet(join(A,C),B),
inference(paramod,[status(thm)],[c_4,c_1071]) ).
cnf(c_5545,plain,
meet(join(A,B),join(A,meet(C,meet(D,B)))) = join(A,meet(meet(C,D),B)),
inference(paramod,[status(thm)],[c_3,c_1254]) ).
cnf(c_2918,plain,
meet(join(A,B),join(A,meet(C,meet(D,B)))) = join(A,meet(C,meet(D,B))),
inference(paramod,[status(thm)],[c_3,c_5545]) ).
cnf(c_5546,plain,
join(meet(A,join(B,C)),meet(meet(A,join(D,join(B,C))),C)) = meet(join(B,C),meet(A,join(D,join(B,C)))),
inference(paramod,[status(thm)],[c_96,c_257]) ).
cnf(c_5547,plain,
join(meet(A,join(B,C)),meet(C,meet(A,join(D,join(B,C))))) = meet(join(B,C),meet(A,join(D,join(B,C)))),
inference(paramod,[status(thm)],[c_1,c_5546]) ).
cnf(c_5548,plain,
join(meet(A,join(B,C)),meet(C,A)) = meet(join(B,C),meet(A,join(D,join(B,C)))),
inference(paramod,[status(thm)],[c_271,c_5547]) ).
cnf(c_3051,plain,
join(meet(A,join(B,C)),meet(C,A)) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_96,c_5548]) ).
cnf(c_5549,plain,
join(meet(meet(A,a),B),meet(B,meet(a,join(C,meet(A,a))))) = meet(join(meet(A,a),meet(a,C)),B),
inference(paramod,[status(thm)],[c_869,c_2780]) ).
cnf(c_5550,plain,
join(meet(A,meet(a,B)),meet(B,meet(a,join(C,meet(A,a))))) = meet(join(meet(A,a),meet(a,C)),B),
inference(paramod,[status(thm)],[c_3,c_5549]) ).
cnf(c_5551,plain,
join(meet(A,meet(a,B)),meet(B,meet(a,join(C,meet(A,a))))) = meet(meet(a,join(A,meet(C,a))),B),
inference(paramod,[status(thm)],[c_997,c_5550]) ).
cnf(c_4259,plain,
join(meet(A,meet(a,B)),meet(B,meet(a,join(C,meet(A,a))))) = meet(a,meet(join(A,meet(C,a)),B)),
inference(paramod,[status(thm)],[c_3,c_5551]) ).
cnf(c_5552,plain,
join(meet(meet(A,B),C),meet(C,join(meet(B,join(D,A)),meet(A,B)))) = meet(meet(join(A,D),B),C),
inference(paramod,[status(thm)],[c_2780,c_2780]) ).
cnf(c_5553,plain,
join(meet(A,meet(B,C)),meet(C,join(meet(B,join(D,A)),meet(A,B)))) = meet(meet(join(A,D),B),C),
inference(paramod,[status(thm)],[c_3,c_5552]) ).
cnf(c_5554,plain,
join(meet(A,meet(B,C)),meet(C,meet(B,join(D,A)))) = meet(meet(join(A,D),B),C),
inference(paramod,[status(thm)],[c_3051,c_5553]) ).
cnf(c_4304,plain,
join(meet(A,meet(B,C)),meet(C,meet(B,join(D,A)))) = meet(join(A,D),meet(B,C)),
inference(paramod,[status(thm)],[c_3,c_5554]) ).
cnf(c_5555,plain,
join(A,meet(join(meet(a,meet(B,A)),join(C,B)),join(meet(a,B),A))) = join(A,meet(a,meet(B,join(A,join(C,B))))),
inference(paramod,[status(thm)],[c_28,c_115]) ).
cnf(c_5556,plain,
join(A,meet(join(C,B),join(meet(a,B),A))) = join(A,meet(a,meet(B,join(A,join(C,B))))),
inference(paramod,[status(thm)],[c_156,c_5555]) ).
cnf(c_4434,plain,
join(A,meet(join(B,C),join(meet(a,C),A))) = join(A,meet(a,C)),
inference(paramod,[status(thm)],[c_93,c_5556]) ).
cnf(c_5557,plain,
join(join(A,meet(a,meet(B,C))),meet(join(meet(a,meet(B,join(A,meet(a,meet(B,C))))),C),join(A,meet(a,meet(B,C))))) = join(join(A,meet(a,meet(B,C))),meet(a,meet(B,join(join(A,meet(a,meet(B,C))),C)))),
inference(paramod,[status(thm)],[c_74,c_115]) ).
cnf(c_5558,plain,
join(join(A,meet(a,meet(B,C))),meet(join(C,meet(a,meet(B,join(A,meet(a,meet(B,C)))))),join(A,meet(a,meet(B,C))))) = join(join(A,meet(a,meet(B,C))),meet(a,meet(B,join(join(A,meet(a,meet(B,C))),C)))),
inference(paramod,[status(thm)],[c_4,c_5557]) ).
cnf(c_5559,plain,
join(join(A,meet(a,meet(B,C))),meet(join(A,meet(a,meet(B,C))),join(C,meet(a,meet(B,join(A,meet(a,meet(B,C)))))))) = join(join(A,meet(a,meet(B,C))),meet(a,meet(B,join(join(A,meet(a,meet(B,C))),C)))),
inference(paramod,[status(thm)],[c_1,c_5558]) ).
cnf(c_5560,plain,
join(A,meet(a,meet(B,C))) = join(join(A,meet(a,meet(B,C))),meet(a,meet(B,join(join(A,meet(a,meet(B,C))),C)))),
inference(paramod,[status(thm)],[c_7,c_5559]) ).
cnf(c_5561,plain,
join(A,meet(a,meet(B,C))) = join(join(A,meet(a,meet(B,C))),meet(a,meet(B,join(C,join(A,meet(a,meet(B,C))))))),
inference(paramod,[status(thm)],[c_4,c_5560]) ).
cnf(c_5562,plain,
join(A,meet(a,meet(B,C))) = join(join(A,meet(a,meet(B,C))),meet(a,meet(B,join(C,A)))),
inference(paramod,[status(thm)],[c_246,c_5561]) ).
cnf(c_5563,plain,
join(A,meet(a,meet(B,C))) = join(A,join(meet(a,meet(B,C)),meet(a,meet(B,join(C,A))))),
inference(paramod,[status(thm)],[c_6,c_5562]) ).
cnf(c_5564,plain,
join(A,meet(a,meet(B,C))) = join(A,meet(a,meet(B,join(C,A)))),
inference(paramod,[status(thm)],[c_2739,c_5563]) ).
cnf(c_4437,plain,
join(A,meet(a,meet(B,join(C,A)))) = join(A,meet(a,meet(B,C))),
inference(copy,[status(thm)],[c_5564]) ).
cnf(c_5565,plain,
join(A,meet(join(meet(a,A),B),join(meet(a,meet(a,B)),A))) = join(A,meet(a,meet(a,join(A,B)))),
inference(paramod,[status(thm)],[c_77,c_115]) ).
cnf(c_5566,plain,
join(A,meet(join(meet(a,A),B),join(meet(a,B),A))) = join(A,meet(a,meet(a,join(A,B)))),
inference(paramod,[status(thm)],[c_77,c_5565]) ).
cnf(c_5567,plain,
join(A,meet(a,B)) = join(A,meet(a,meet(a,join(A,B)))),
inference(paramod,[status(thm)],[c_4434,c_5566]) ).
cnf(c_5568,plain,
join(A,meet(a,B)) = join(A,meet(a,join(A,B))),
inference(paramod,[status(thm)],[c_77,c_5567]) ).
cnf(c_4440,plain,
join(A,meet(a,join(A,B))) = join(A,meet(a,B)),
inference(copy,[status(thm)],[c_5568]) ).
cnf(c_5569,plain,
join(A,meet(meet(a,join(meet(B,A),meet(C,a))),join(meet(a,meet(B,meet(a,C))),A))) = join(A,meet(a,meet(B,join(A,meet(a,C))))),
inference(paramod,[status(thm)],[c_2079,c_115]) ).
cnf(c_5570,plain,
join(A,meet(meet(a,join(meet(B,A),meet(C,a))),join(meet(B,meet(a,C)),A))) = join(A,meet(a,meet(B,join(A,meet(a,C))))),
inference(paramod,[status(thm)],[c_130,c_5569]) ).
cnf(c_5571,plain,
join(A,meet(a,meet(join(meet(B,A),meet(C,a)),join(meet(B,meet(a,C)),A)))) = join(A,meet(a,meet(B,join(A,meet(a,C))))),
inference(paramod,[status(thm)],[c_3,c_5570]) ).
cnf(c_5572,plain,
join(A,meet(a,meet(join(meet(B,A),meet(C,a)),meet(B,meet(a,C))))) = join(A,meet(a,meet(B,join(A,meet(a,C))))),
inference(paramod,[status(thm)],[c_4437,c_5571]) ).
cnf(c_5573,plain,
join(A,meet(a,meet(meet(B,meet(a,C)),join(meet(B,A),meet(C,a))))) = join(A,meet(a,meet(B,join(A,meet(a,C))))),
inference(paramod,[status(thm)],[c_1,c_5572]) ).
cnf(c_5574,plain,
join(A,meet(a,meet(B,meet(meet(a,C),join(meet(B,A),meet(C,a)))))) = join(A,meet(a,meet(B,join(A,meet(a,C))))),
inference(paramod,[status(thm)],[c_3,c_5573]) ).
cnf(c_5575,plain,
join(A,meet(a,meet(B,meet(a,meet(C,join(meet(B,A),meet(C,a))))))) = join(A,meet(a,meet(B,join(A,meet(a,C))))),
inference(paramod,[status(thm)],[c_3,c_5574]) ).
cnf(c_5576,plain,
join(A,meet(a,meet(B,meet(a,C)))) = join(A,meet(a,meet(B,join(A,meet(a,C))))),
inference(paramod,[status(thm)],[c_296,c_5575]) ).
cnf(c_5577,plain,
join(A,meet(B,meet(a,C))) = join(A,meet(a,meet(B,join(A,meet(a,C))))),
inference(paramod,[status(thm)],[c_130,c_5576]) ).
cnf(c_4511,plain,
join(A,meet(a,meet(B,join(A,meet(a,C))))) = join(A,meet(B,meet(a,C))),
inference(copy,[status(thm)],[c_5577]) ).
cnf(c_5578,plain,
meet(meet(a,join(A,B)),join(A,meet(a,B))) = meet(a,join(A,B)),
inference(paramod,[status(thm)],[c_4440,c_28]) ).
cnf(c_5579,plain,
meet(a,meet(join(A,B),join(A,meet(a,B)))) = meet(a,join(A,B)),
inference(paramod,[status(thm)],[c_3,c_5578]) ).
cnf(c_4682,plain,
meet(a,join(A,meet(a,B))) = meet(a,join(A,B)),
inference(paramod,[status(thm)],[c_1254,c_5579]) ).
cnf(c_5580,plain,
meet(meet(a,join(A,B)),meet(C,join(A,meet(a,B)))) = meet(C,meet(a,join(A,B))),
inference(paramod,[status(thm)],[c_4440,c_96]) ).
cnf(c_5581,plain,
meet(a,meet(join(A,B),meet(C,join(A,meet(a,B))))) = meet(C,meet(a,join(A,B))),
inference(paramod,[status(thm)],[c_3,c_5580]) ).
cnf(c_4704,plain,
meet(a,meet(A,join(B,meet(a,C)))) = meet(A,meet(a,join(B,C))),
inference(paramod,[status(thm)],[c_2755,c_5581]) ).
cnf(c_5582,plain,
meet(a,join(A,join(B,meet(C,meet(A,a))))) = meet(a,join(B,meet(A,a))),
inference(paramod,[status(thm)],[c_4682,c_2768]) ).
cnf(c_5583,plain,
meet(a,join(B,A)) = meet(a,join(B,meet(A,a))),
inference(paramod,[status(thm)],[c_176,c_5582]) ).
cnf(c_4792,plain,
meet(a,join(A,meet(B,a))) = meet(a,join(A,B)),
inference(copy,[status(thm)],[c_5583]) ).
cnf(c_4844,plain,
meet(a,join(meet(z1,z2),meet(z1,z3))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_4682,c_1617]) ).
cnf(c_4877,plain,
join(A,meet(B,meet(a,join(A,C)))) = join(A,meet(B,meet(a,C))),
inference(paramod,[status(thm)],[c_4704,c_4511]) ).
cnf(c_5584,plain,
meet(a,meet(join(A,meet(B,meet(a,join(A,C)))),join(meet(B,A),meet(a,join(A,meet(C,a)))))) = meet(a,meet(join(A,meet(B,a)),join(A,meet(a,C)))),
inference(paramod,[status(thm)],[c_4792,c_2110]) ).
cnf(c_5585,plain,
meet(a,meet(join(A,meet(B,meet(a,C))),join(meet(B,A),meet(a,join(A,meet(C,a)))))) = meet(a,meet(join(A,meet(B,a)),join(A,meet(a,C)))),
inference(paramod,[status(thm)],[c_4877,c_5584]) ).
cnf(c_5586,plain,
meet(a,meet(join(A,meet(B,meet(a,C))),join(meet(B,A),meet(a,join(A,C))))) = meet(a,meet(join(A,meet(B,a)),join(A,meet(a,C)))),
inference(paramod,[status(thm)],[c_4792,c_5585]) ).
cnf(c_5587,plain,
meet(join(A,meet(B,meet(a,C))),meet(a,join(meet(B,A),join(A,C)))) = meet(a,meet(join(A,meet(B,a)),join(A,meet(a,C)))),
inference(paramod,[status(thm)],[c_4704,c_5586]) ).
cnf(c_5588,plain,
meet(join(A,meet(B,meet(a,C))),meet(a,join(A,join(meet(B,A),C)))) = meet(a,meet(join(A,meet(B,a)),join(A,meet(a,C)))),
inference(paramod,[status(thm)],[c_21,c_5587]) ).
cnf(c_5589,plain,
meet(join(A,meet(B,meet(a,C))),meet(a,join(A,C))) = meet(a,meet(join(A,meet(B,a)),join(A,meet(a,C)))),
inference(paramod,[status(thm)],[c_85,c_5588]) ).
cnf(c_5590,plain,
meet(meet(a,join(A,C)),join(A,meet(B,meet(a,C)))) = meet(a,meet(join(A,meet(B,a)),join(A,meet(a,C)))),
inference(paramod,[status(thm)],[c_1,c_5589]) ).
cnf(c_5591,plain,
meet(a,meet(join(A,C),join(A,meet(B,meet(a,C))))) = meet(a,meet(join(A,meet(B,a)),join(A,meet(a,C)))),
inference(paramod,[status(thm)],[c_3,c_5590]) ).
cnf(c_5592,plain,
meet(a,join(A,meet(B,meet(a,C)))) = meet(a,meet(join(A,meet(B,a)),join(A,meet(a,C)))),
inference(paramod,[status(thm)],[c_2918,c_5591]) ).
cnf(c_5593,plain,
meet(a,join(A,meet(B,meet(a,C)))) = meet(join(A,meet(B,a)),meet(a,join(A,C))),
inference(paramod,[status(thm)],[c_4704,c_5592]) ).
cnf(c_4894,plain,
meet(a,join(A,meet(B,meet(a,C)))) = meet(a,meet(join(A,meet(B,a)),join(A,C))),
inference(paramod,[status(thm)],[c_18,c_5593]) ).
cnf(c_5594,plain,
join(meet(A,meet(a,B)),meet(B,meet(a,join(C,A)))) = meet(a,meet(join(A,meet(C,a)),B)),
inference(paramod,[status(thm)],[c_4792,c_4259]) ).
cnf(c_5595,plain,
meet(join(A,C),meet(a,B)) = meet(a,meet(join(A,meet(C,a)),B)),
inference(paramod,[status(thm)],[c_4304,c_5594]) ).
cnf(c_5596,plain,
meet(a,meet(join(A,C),B)) = meet(a,meet(join(A,meet(C,a)),B)),
inference(paramod,[status(thm)],[c_18,c_5595]) ).
cnf(c_4931,plain,
meet(a,meet(join(A,meet(B,a)),C)) = meet(a,meet(join(A,B),C)),
inference(copy,[status(thm)],[c_5596]) ).
cnf(c_4999,plain,
join(meet(a,A),meet(a,B)) = meet(a,join(A,B)),
inference(paramod,[status(thm)],[c_4792,c_2079]) ).
cnf(c_5597,plain,
join(meet(a,A),meet(B,meet(a,C))) = meet(a,meet(join(A,meet(B,a)),join(A,C))),
inference(paramod,[status(thm)],[c_4894,c_2616]) ).
cnf(c_5049,plain,
join(meet(a,A),meet(B,meet(a,C))) = meet(a,meet(join(A,B),join(A,C))),
inference(paramod,[status(thm)],[c_4931,c_5597]) ).
cnf(c_5598,plain,
join(meet(a,A),meet(B,meet(a,C))) = meet(a,join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_18,c_4999]) ).
cnf(c_5599,plain,
meet(a,meet(join(A,B),join(A,C))) = meet(a,join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_5049,c_5598]) ).
cnf(c_5077,plain,
meet(a,join(A,meet(B,C))) = meet(a,meet(join(A,B),join(A,C))),
inference(copy,[status(thm)],[c_5599]) ).
cnf(c_5600,plain,
meet(a,meet(join(meet(z1,z2),z1),join(meet(z1,z2),z3))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_5077,c_4844]) ).
cnf(c_5601,plain,
meet(a,meet(join(z1,meet(z1,z2)),join(meet(z1,z2),z3))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_4,c_5600]) ).
cnf(c_5602,plain,
meet(a,meet(z1,join(meet(z1,z2),z3))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_7,c_5601]) ).
cnf(c_5105,plain,
meet(a,meet(z1,join(z3,meet(z1,z2)))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_4,c_5602]) ).
cnf(c_5603,plain,
meet(z1,meet(a,join(z3,meet(z1,z2)))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_18,c_5105]) ).
cnf(c_5604,plain,
meet(z1,meet(a,meet(join(z3,z1),join(z3,z2)))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_5077,c_5603]) ).
cnf(c_5605,plain,
meet(z1,meet(a,meet(join(z1,z3),join(z3,z2)))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_4,c_5604]) ).
cnf(c_5606,plain,
meet(z1,meet(a,meet(join(z1,z3),join(z2,z3)))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_4,c_5605]) ).
cnf(c_5607,plain,
meet(a,meet(z1,meet(join(z1,z3),join(z2,z3)))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_18,c_5606]) ).
cnf(c_5608,plain,
meet(a,meet(z1,join(z2,z3))) != meet(a,meet(z1,join(z2,z3))),
inference(paramod,[status(thm)],[c_26,c_5607]) ).
cnf(c_5390,plain,
$false,
inference(copy,[status(thm)],[c_5608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT399-2 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 21:36:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3252844 was started by sandbox2 on n017,
% 0.08/0.35 % Fri Sep 25 21:36:47 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 30.47/4.81
% 30.47/4.81 % SZS status Unsatisfiable for theBenchmark
% 30.47/4.81
% 30.47/4.81 % Proof 1 at 3.75 (+ 0.65) seconds.
% 30.47/4.81 % Length of proof is 123.
% 30.47/4.81 % Level of proof is 17.
% 30.47/4.81 % Maximum clause weight is 96.000.
% 30.47/4.81 % Given clauses 160.
% 30.47/4.81
% 30.47/4.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------