%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT197-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 07:49:48 AM UTC 2026
% Result : Unsatisfiable 278.33s 37.19s
% Output : CNFRefutation 278.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 86
% Number of leaves : 13
% Syntax : Number of formulae : 293 ( 265 unt; 0 def)
% Number of atoms : 338 ( 337 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 49 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 5 con; 0-2 aty)
% Number of variables : 708 ( 151 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(idempotence_of_meet,axiom,
! [VAR_0] : meet(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_meet) ).
cnf(c_1,plain,
meet(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_meet]) ).
fof(idempotence_of_join,axiom,
! [VAR_0] : join(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_join) ).
cnf(c_2,plain,
join(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_join]) ).
fof(absorption1,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,join(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption1) ).
cnf(c_3,plain,
meet(A,join(A,B)) = A,
inference(clausify,[status(thm)],[absorption1]) ).
fof(absorption2,axiom,
! [VAR_0,VAR_1] : join(VAR_0,meet(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption2) ).
cnf(c_4,plain,
join(A,meet(A,B)) = A,
inference(clausify,[status(thm)],[absorption2]) ).
fof(commutativity_of_meet,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = meet(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_meet) ).
cnf(c_5,plain,
meet(A,B) = meet(B,A),
inference(clausify,[status(thm)],[commutativity_of_meet]) ).
fof(commutativity_of_join,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_join) ).
cnf(c_6,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
fof(associativity_of_meet,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(VAR_0,VAR_1),VAR_2) = meet(VAR_0,meet(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_meet) ).
cnf(c_7,plain,
meet(meet(A,B),C) = meet(A,meet(B,C)),
inference(clausify,[status(thm)],[associativity_of_meet]) ).
fof(associativity_of_join,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(VAR_0,VAR_1),VAR_2) = join(VAR_0,join(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_join) ).
cnf(c_8,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[associativity_of_join]) ).
fof(complement_join,axiom,
! [VAR_0] : join(VAR_0,complement(VAR_0)) = one,
file('theBenchmark.p',complement_join) ).
cnf(c_9,plain,
join(A,complement(A)) = one,
inference(clausify,[status(thm)],[complement_join]) ).
fof(complement_meet,axiom,
! [VAR_0] : meet(VAR_0,complement(VAR_0)) = zero,
file('theBenchmark.p',complement_meet) ).
cnf(c_10,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[complement_meet]) ).
fof(meet_join_complement,axiom,
! [VAR_0,VAR_1] :
( complement(VAR_0) = VAR_1
| join(VAR_0,VAR_1) != one
| meet(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',meet_join_complement) ).
cnf(c_11,plain,
( complement(A) = B
| join(A,B) != one
| meet(A,B) != zero ),
inference(clausify,[status(thm)],[meet_join_complement]) ).
fof(equation_H40,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : meet(VAR_0,join(VAR_1,meet(VAR_2,join(VAR_0,VAR_3)))) = meet(VAR_0,join(VAR_1,meet(VAR_2,join(VAR_3,meet(VAR_2,join(VAR_0,VAR_1)))))),
file('theBenchmark.p',equation_H40) ).
cnf(c_12,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(D,meet(C,join(A,B)))))),
inference(clausify,[status(thm)],[equation_H40]) ).
cnf(c_13,plain,
meet(A,join(B,meet(C,join(D,meet(C,join(A,B)))))) = meet(A,join(B,meet(C,join(A,D)))),
inference(copy,[status(thm)],[c_12]) ).
fof(prove_distributivity,axiom,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('theBenchmark.p',prove_distributivity) ).
cnf(c_14,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(clausify,[status(thm)],[prove_distributivity]) ).
cnf(c_15,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_16,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_32920,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_18,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_32920]) ).
cnf(c_32921,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_19,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_5,c_32921]) ).
cnf(c_32922,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_21,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_32922]) ).
cnf(c_22,plain,
join(meet(A,B),meet(A,meet(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_32923,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_24,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_7,c_32923]) ).
cnf(c_28,plain,
meet(join(A,B),join(A,join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_32924,plain,
join(A,B) = join(A,join(meet(A,C),B)),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_30,plain,
join(A,join(meet(A,B),C)) = join(A,C),
inference(copy,[status(thm)],[c_32924]) ).
cnf(c_32925,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_32,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_8,c_32925]) ).
cnf(c_33,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_32926,plain,
join(one,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_34,plain,
join(A,join(complement(A),B)) = join(one,B),
inference(copy,[status(thm)],[c_32926]) ).
cnf(c_32927,plain,
one = join(A,join(B,complement(join(A,B)))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_35,plain,
join(A,join(B,complement(join(A,B)))) = one,
inference(copy,[status(thm)],[c_32927]) ).
cnf(c_36,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_41,plain,
( complement(B) = A
| join(B,A) != one
| meet(A,B) != zero ),
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_32928,plain,
meet(A,join(B,meet(C,meet(C,join(A,B))))) = meet(A,join(B,meet(C,join(A,meet(C,join(A,B)))))),
inference(paramod,[status(thm)],[c_2,c_13]) ).
cnf(c_32929,plain,
meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(C,join(A,meet(C,join(A,B)))))),
inference(paramod,[status(thm)],[c_18,c_32928]) ).
cnf(c_45,plain,
meet(A,join(B,meet(C,join(A,meet(C,join(A,B)))))) = meet(A,join(B,meet(C,join(A,B)))),
inference(copy,[status(thm)],[c_32929]) ).
cnf(c_32930,plain,
meet(A,join(B,meet(C,join(A,meet(C,join(A,B)))))) = meet(A,join(B,meet(C,A))),
inference(paramod,[status(thm)],[c_2,c_13]) ).
cnf(c_46,plain,
meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(C,A))),
inference(paramod,[status(thm)],[c_45,c_32930]) ).
cnf(c_32931,plain,
meet(A,join(complement(A),meet(B,join(C,meet(B,one))))) = meet(A,join(complement(A),meet(B,join(A,C)))),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_32932,plain,
meet(A,join(complement(A),meet(B,join(C,B)))) = meet(A,join(complement(A),meet(B,join(A,C)))),
inference(paramod,[status(thm)],[c_33,c_32931]) ).
cnf(c_32933,plain,
meet(A,join(complement(A),B)) = meet(A,join(complement(A),meet(B,join(A,C)))),
inference(paramod,[status(thm)],[c_16,c_32932]) ).
cnf(c_61,plain,
meet(A,join(complement(A),meet(B,join(A,C)))) = meet(A,join(complement(A),B)),
inference(copy,[status(thm)],[c_32933]) ).
cnf(c_68,plain,
join(A,meet(B,meet(C,A))) = A,
inference(paramod,[status(thm)],[c_7,c_15]) ).
cnf(c_32934,plain,
join(A,B) = join(A,join(meet(C,A),B)),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_69,plain,
join(A,join(meet(B,A),C)) = join(A,C),
inference(copy,[status(thm)],[c_32934]) ).
cnf(c_32935,plain,
A = meet(one,A),
inference(paramod,[status(thm)],[c_33,c_5]) ).
cnf(c_72,plain,
meet(one,A) = A,
inference(copy,[status(thm)],[c_32935]) ).
cnf(c_74,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_33,c_15]) ).
cnf(c_75,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_74,c_34]) ).
cnf(c_32936,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_36,c_6]) ).
cnf(c_76,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_32936]) ).
cnf(c_32937,plain,
meet(A,B) = meet(A,meet(join(C,A),B)),
inference(paramod,[status(thm)],[c_16,c_7]) ).
cnf(c_78,plain,
meet(A,meet(join(B,A),C)) = meet(A,C),
inference(copy,[status(thm)],[c_32937]) ).
cnf(c_80,plain,
meet(A,join(B,join(C,A))) = A,
inference(paramod,[status(thm)],[c_8,c_16]) ).
cnf(c_82,plain,
meet(zero,A) = zero,
inference(paramod,[status(thm)],[c_36,c_16]) ).
cnf(c_32938,plain,
one = join(A,one),
inference(paramod,[status(thm)],[c_16,c_72]) ).
cnf(c_83,plain,
join(A,one) = one,
inference(copy,[status(thm)],[c_32938]) ).
cnf(c_87,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_76,c_15]) ).
cnf(c_32939,plain,
( complement(B) = meet(A,B)
| join(B,meet(A,B)) != one
| meet(A,B) != zero ),
inference(paramod,[status(thm)],[c_19,c_11]) ).
cnf(c_32940,plain,
( complement(B) = meet(A,B)
| B != one
| meet(A,B) != zero ),
inference(paramod,[status(thm)],[c_15,c_32939]) ).
cnf(c_94,plain,
( complement(B) = meet(A,B)
| one != B
| meet(A,B) != zero ),
inference(copy,[status(thm)],[c_32940]) ).
cnf(c_95,plain,
join(A,join(B,complement(A))) = one,
inference(paramod,[status(thm)],[c_6,c_75]) ).
cnf(c_32941,plain,
join(join(A,B),meet(C,A)) = join(A,B),
inference(paramod,[status(thm)],[c_3,c_68]) ).
cnf(c_116,plain,
join(A,join(B,meet(C,A))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_32941]) ).
cnf(c_123,plain,
meet(A,join(B,join(A,C))) = A,
inference(paramod,[status(thm)],[c_6,c_80]) ).
cnf(c_130,plain,
meet(join(A,B),meet(join(A,join(B,C)),D)) = meet(join(A,B),D),
inference(paramod,[status(thm)],[c_8,c_21]) ).
cnf(c_32942,plain,
meet(A,zero) = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_10,c_21]) ).
cnf(c_32943,plain,
zero = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_87,c_32942]) ).
cnf(c_131,plain,
meet(A,complement(join(A,B))) = zero,
inference(copy,[status(thm)],[c_32943]) ).
cnf(c_132,plain,
( complement(A) = meet(join(A,C),B)
| join(A,meet(join(A,C),B)) != one
| meet(A,B) != zero ),
inference(paramod,[status(thm)],[c_21,c_11]) ).
cnf(c_32944,plain,
meet(A,join(A,B)) = meet(A,join(C,join(D,join(A,B)))),
inference(paramod,[status(thm)],[c_80,c_21]) ).
cnf(c_32945,plain,
A = meet(A,join(C,join(D,join(A,B)))),
inference(paramod,[status(thm)],[c_3,c_32944]) ).
cnf(c_139,plain,
meet(A,join(B,join(C,join(A,D)))) = A,
inference(copy,[status(thm)],[c_32945]) ).
cnf(c_141,plain,
meet(A,complement(join(B,A))) = zero,
inference(paramod,[status(thm)],[c_6,c_131]) ).
cnf(c_32946,plain,
zero = meet(A,meet(B,complement(join(meet(A,B),C)))),
inference(paramod,[status(thm)],[c_131,c_7]) ).
cnf(c_142,plain,
meet(A,meet(B,complement(join(meet(A,B),C)))) = zero,
inference(copy,[status(thm)],[c_32946]) ).
cnf(c_32947,plain,
meet(A,B) = meet(A,meet(join(C,join(A,D)),B)),
inference(paramod,[status(thm)],[c_123,c_7]) ).
cnf(c_155,plain,
meet(A,meet(join(B,join(A,C)),D)) = meet(A,D),
inference(copy,[status(thm)],[c_32947]) ).
cnf(c_164,plain,
join(meet(A,B),meet(B,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_19,c_22]) ).
cnf(c_166,plain,
join(A,join(B,complement(join(B,A)))) = one,
inference(paramod,[status(thm)],[c_6,c_35]) ).
cnf(c_174,plain,
( complement(B) = meet(A,C)
| join(B,meet(A,C)) != one
| meet(A,meet(B,C)) != zero ),
inference(paramod,[status(thm)],[c_24,c_11]) ).
cnf(c_32948,plain,
meet(A,B) = meet(B,meet(A,join(C,join(D,B)))),
inference(paramod,[status(thm)],[c_80,c_24]) ).
cnf(c_178,plain,
meet(A,meet(B,join(C,join(D,A)))) = meet(B,A),
inference(copy,[status(thm)],[c_32948]) ).
cnf(c_32949,plain,
meet(A,B) = meet(B,meet(A,join(C,join(B,D)))),
inference(paramod,[status(thm)],[c_123,c_24]) ).
cnf(c_181,plain,
meet(A,meet(B,join(C,join(A,D)))) = meet(B,A),
inference(copy,[status(thm)],[c_32949]) ).
cnf(c_32950,plain,
meet(A,join(B,C)) = meet(join(B,C),meet(A,join(B,join(C,D)))),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_206,plain,
meet(join(A,B),meet(C,join(A,join(B,D)))) = meet(C,join(A,B)),
inference(copy,[status(thm)],[c_32950]) ).
cnf(c_32951,plain,
join(A,one) = join(A,complement(meet(A,B))),
inference(paramod,[status(thm)],[c_9,c_30]) ).
cnf(c_32952,plain,
one = join(A,complement(meet(A,B))),
inference(paramod,[status(thm)],[c_83,c_32951]) ).
cnf(c_246,plain,
join(A,complement(meet(A,B))) = one,
inference(copy,[status(thm)],[c_32952]) ).
cnf(c_278,plain,
join(A,complement(meet(B,A))) = one,
inference(paramod,[status(thm)],[c_5,c_246]) ).
cnf(c_32953,plain,
one = join(A,join(B,complement(meet(C,join(A,B))))),
inference(paramod,[status(thm)],[c_278,c_8]) ).
cnf(c_284,plain,
join(A,join(B,complement(meet(C,join(A,B))))) = one,
inference(copy,[status(thm)],[c_32953]) ).
cnf(c_286,plain,
join(meet(join(A,B),C),complement(meet(A,C))) = one,
inference(paramod,[status(thm)],[c_21,c_278]) ).
cnf(c_32954,plain,
( complement(complement(A)) = A
| join(complement(A),A) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_10,c_41]) ).
cnf(c_32955,plain,
( complement(complement(A)) = A
| join(A,complement(A)) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_6,c_32954]) ).
cnf(c_32956,plain,
( complement(complement(A)) = A
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_9,c_32955]) ).
cnf(c_32957,plain,
( complement(complement(A)) = A
| one != one ),
inference(copy,[status(thm)],[c_32956]) ).
cnf(c_320,plain,
complement(complement(A)) = A,
inference(copy,[status(thm)],[c_32957]) ).
cnf(c_344,plain,
join(complement(A),join(B,A)) = one,
inference(paramod,[status(thm)],[c_320,c_95]) ).
cnf(c_32958,plain,
meet(A,join(complement(A),meet(B,one))) = meet(A,join(complement(A),meet(B,A))),
inference(paramod,[status(thm)],[c_9,c_46]) ).
cnf(c_32959,plain,
meet(A,join(complement(A),B)) = meet(A,join(complement(A),meet(B,A))),
inference(paramod,[status(thm)],[c_33,c_32958]) ).
cnf(c_474,plain,
meet(A,join(complement(A),meet(B,A))) = meet(A,join(complement(A),B)),
inference(copy,[status(thm)],[c_32959]) ).
cnf(c_524,plain,
join(meet(A,B),join(meet(A,meet(C,B)),D)) = join(meet(A,B),D),
inference(paramod,[status(thm)],[c_24,c_69]) ).
cnf(c_552,plain,
join(meet(join(A,B),C),complement(meet(B,C))) = one,
inference(paramod,[status(thm)],[c_78,c_278]) ).
cnf(c_570,plain,
meet(join(A,meet(B,C)),complement(join(C,A))) = zero,
inference(paramod,[status(thm)],[c_116,c_141]) ).
cnf(c_32960,plain,
meet(A,B) = meet(B,meet(A,join(C,join(D,join(B,E))))),
inference(paramod,[status(thm)],[c_139,c_24]) ).
cnf(c_943,plain,
meet(A,meet(B,join(C,join(D,join(A,E))))) = meet(B,A),
inference(copy,[status(thm)],[c_32960]) ).
cnf(c_32961,plain,
join(complement(meet(A,B)),meet(B,A)) = one,
inference(paramod,[status(thm)],[c_164,c_344]) ).
cnf(c_978,plain,
join(meet(A,B),complement(meet(B,A))) = one,
inference(paramod,[status(thm)],[c_6,c_32961]) ).
cnf(c_32962,plain,
join(one,A) = join(meet(B,C),join(complement(meet(C,B)),A)),
inference(paramod,[status(thm)],[c_978,c_8]) ).
cnf(c_32963,plain,
one = join(meet(B,C),join(complement(meet(C,B)),A)),
inference(paramod,[status(thm)],[c_74,c_32962]) ).
cnf(c_1088,plain,
join(meet(A,B),join(complement(meet(B,A)),C)) = one,
inference(copy,[status(thm)],[c_32963]) ).
cnf(c_1574,plain,
meet(A,meet(B,complement(join(meet(B,A),C)))) = zero,
inference(paramod,[status(thm)],[c_5,c_142]) ).
cnf(c_32964,plain,
one = join(complement(meet(A,B)),meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_286,c_6]) ).
cnf(c_2431,plain,
join(complement(meet(A,B)),meet(join(A,C),B)) = one,
inference(copy,[status(thm)],[c_32964]) ).
cnf(c_32965,plain,
one = join(complement(meet(A,B)),meet(join(C,A),B)),
inference(paramod,[status(thm)],[c_552,c_6]) ).
cnf(c_3439,plain,
join(complement(meet(A,B)),meet(join(C,A),B)) = one,
inference(copy,[status(thm)],[c_32965]) ).
cnf(c_32966,plain,
zero = meet(complement(join(A,B)),join(B,meet(C,A))),
inference(paramod,[status(thm)],[c_570,c_5]) ).
cnf(c_3479,plain,
meet(complement(join(A,B)),join(B,meet(C,A))) = zero,
inference(copy,[status(thm)],[c_32966]) ).
cnf(c_5517,plain,
join(complement(A),meet(join(A,B),join(C,A))) = one,
inference(paramod,[status(thm)],[c_16,c_2431]) ).
cnf(c_5913,plain,
join(complement(A),meet(join(B,A),join(C,A))) = one,
inference(paramod,[status(thm)],[c_16,c_3439]) ).
cnf(c_32967,plain,
( complement(complement(meet(A,B))) = meet(join(complement(meet(A,B)),A),B)
| one != one
| meet(complement(meet(A,B)),B) != zero ),
inference(paramod,[status(thm)],[c_3439,c_132]) ).
cnf(c_32968,plain,
( complement(complement(meet(A,B))) = meet(join(complement(meet(A,B)),A),B)
| one != one
| meet(B,complement(meet(A,B))) != zero ),
inference(paramod,[status(thm)],[c_5,c_32967]) ).
cnf(c_32969,plain,
( meet(A,B) = meet(join(complement(meet(A,B)),A),B)
| one != one
| meet(B,complement(meet(A,B))) != zero ),
inference(paramod,[status(thm)],[c_320,c_32968]) ).
cnf(c_32970,plain,
( meet(A,B) = meet(join(A,complement(meet(A,B))),B)
| one != one
| meet(B,complement(meet(A,B))) != zero ),
inference(paramod,[status(thm)],[c_6,c_32969]) ).
cnf(c_32971,plain,
( meet(A,B) = meet(one,B)
| one != one
| meet(B,complement(meet(A,B))) != zero ),
inference(paramod,[status(thm)],[c_246,c_32970]) ).
cnf(c_32972,plain,
( meet(A,B) = B
| one != one
| meet(B,complement(meet(A,B))) != zero ),
inference(paramod,[status(thm)],[c_72,c_32971]) ).
cnf(c_5949,plain,
( meet(B,A) = A
| meet(A,complement(meet(B,A))) != zero ),
inference(copy,[status(thm)],[c_32972]) ).
cnf(c_32973,plain,
meet(A,join(complement(A),zero)) = meet(A,join(complement(A),complement(join(B,A)))),
inference(paramod,[status(thm)],[c_3479,c_61]) ).
cnf(c_32974,plain,
meet(A,join(zero,complement(A))) = meet(A,join(complement(A),complement(join(B,A)))),
inference(paramod,[status(thm)],[c_6,c_32973]) ).
cnf(c_32975,plain,
meet(A,complement(A)) = meet(A,join(complement(A),complement(join(B,A)))),
inference(paramod,[status(thm)],[c_76,c_32974]) ).
cnf(c_32976,plain,
zero = meet(A,join(complement(A),complement(join(B,A)))),
inference(paramod,[status(thm)],[c_10,c_32975]) ).
cnf(c_6091,plain,
meet(A,join(complement(A),complement(join(B,A)))) = zero,
inference(copy,[status(thm)],[c_32976]) ).
cnf(c_32977,plain,
( complement(A) = join(complement(A),complement(join(B,A)))
| join(A,join(complement(A),complement(join(B,A)))) != one ),
inference(resolve,[status(thm)],[c_11,c_6091]) ).
cnf(c_32978,plain,
complement(meet(A,A)) = join(complement(meet(A,A)),complement(join(B,meet(A,A)))),
inference(resolve,[status(thm)],[c_32977,c_1088]) ).
cnf(c_32979,plain,
complement(A) = join(complement(meet(A,A)),complement(join(B,meet(A,A)))),
inference(paramod,[status(thm)],[c_1,c_32978]) ).
cnf(c_32980,plain,
complement(A) = join(complement(A),complement(join(B,meet(A,A)))),
inference(paramod,[status(thm)],[c_1,c_32979]) ).
cnf(c_32981,plain,
complement(A) = join(complement(A),complement(join(B,A))),
inference(paramod,[status(thm)],[c_1,c_32980]) ).
cnf(c_6104,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(copy,[status(thm)],[c_32981]) ).
cnf(c_32982,plain,
join(complement(meet(A,B)),complement(A)) = complement(meet(A,B)),
inference(paramod,[status(thm)],[c_4,c_6104]) ).
cnf(c_6132,plain,
join(complement(A),complement(meet(A,B))) = complement(meet(A,B)),
inference(paramod,[status(thm)],[c_6,c_32982]) ).
cnf(c_6133,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_6,c_6104]) ).
cnf(c_32983,plain,
join(complement(meet(A,B)),complement(B)) = complement(meet(A,B)),
inference(paramod,[status(thm)],[c_15,c_6104]) ).
cnf(c_6136,plain,
join(complement(A),complement(meet(B,A))) = complement(meet(B,A)),
inference(paramod,[status(thm)],[c_6,c_32983]) ).
cnf(c_32984,plain,
meet(complement(join(A,B)),complement(B)) = complement(join(A,B)),
inference(paramod,[status(thm)],[c_6104,c_16]) ).
cnf(c_6137,plain,
meet(complement(A),complement(join(B,A))) = complement(join(B,A)),
inference(paramod,[status(thm)],[c_5,c_32984]) ).
cnf(c_32985,plain,
join(A,complement(B)) = join(complement(B),join(A,complement(join(C,B)))),
inference(paramod,[status(thm)],[c_6104,c_32]) ).
cnf(c_6145,plain,
join(complement(A),join(B,complement(join(C,A)))) = join(B,complement(A)),
inference(copy,[status(thm)],[c_32985]) ).
cnf(c_32986,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_320,c_6104]) ).
cnf(c_6148,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_320,c_32986]) ).
cnf(c_6286,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_6,c_6148]) ).
cnf(c_32987,plain,
join(A,B) = join(B,join(A,complement(join(C,complement(B))))),
inference(paramod,[status(thm)],[c_6148,c_32]) ).
cnf(c_6294,plain,
join(A,join(B,complement(join(C,complement(A))))) = join(B,A),
inference(copy,[status(thm)],[c_32987]) ).
cnf(c_32988,plain,
join(A,complement(B)) = join(complement(B),join(A,complement(join(B,C)))),
inference(paramod,[status(thm)],[c_6133,c_32]) ).
cnf(c_6405,plain,
join(complement(A),join(B,complement(join(A,C)))) = join(B,complement(A)),
inference(copy,[status(thm)],[c_32988]) ).
cnf(c_8010,plain,
meet(complement(A),complement(meet(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_6132,c_3]) ).
cnf(c_8032,plain,
join(A,complement(meet(B,join(A,complement(B))))) = one,
inference(paramod,[status(thm)],[c_6132,c_284]) ).
cnf(c_32989,plain,
meet(A,complement(meet(complement(A),B))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_320,c_8010]) ).
cnf(c_8074,plain,
meet(A,complement(meet(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_320,c_32989]) ).
cnf(c_8112,plain,
meet(A,complement(meet(B,meet(complement(A),C)))) = A,
inference(paramod,[status(thm)],[c_24,c_8074]) ).
cnf(c_32990,plain,
join(one,A) = join(B,join(complement(meet(C,join(B,complement(C)))),A)),
inference(paramod,[status(thm)],[c_8032,c_8]) ).
cnf(c_32991,plain,
one = join(B,join(complement(meet(C,join(B,complement(C)))),A)),
inference(paramod,[status(thm)],[c_74,c_32990]) ).
cnf(c_8433,plain,
join(A,join(complement(meet(B,join(A,complement(B)))),C)) = one,
inference(copy,[status(thm)],[c_32991]) ).
cnf(c_8437,plain,
join(A,complement(meet(complement(B),join(A,B)))) = one,
inference(paramod,[status(thm)],[c_320,c_8032]) ).
cnf(c_32992,plain,
meet(A,join(B,A)) = meet(A,complement(meet(C,meet(complement(join(B,A)),D)))),
inference(paramod,[status(thm)],[c_8112,c_78]) ).
cnf(c_32993,plain,
A = meet(A,complement(meet(C,meet(complement(join(B,A)),D)))),
inference(paramod,[status(thm)],[c_16,c_32992]) ).
cnf(c_8679,plain,
meet(A,complement(meet(B,meet(complement(join(C,A)),D)))) = A,
inference(copy,[status(thm)],[c_32993]) ).
cnf(c_9288,plain,
join(A,complement(meet(join(A,B),complement(B)))) = one,
inference(paramod,[status(thm)],[c_5,c_8437]) ).
cnf(c_32994,plain,
meet(A,complement(join(meet(complement(B),A),B))) = zero,
inference(paramod,[status(thm)],[c_6137,c_1574]) ).
cnf(c_9548,plain,
meet(A,complement(join(B,meet(complement(B),A)))) = zero,
inference(paramod,[status(thm)],[c_6,c_32994]) ).
cnf(c_32995,plain,
meet(join(A,B),meet(C,join(A,join(B,D)))) = meet(join(A,B),meet(C,join(E,join(F,join(A,join(B,D)))))),
inference(paramod,[status(thm)],[c_178,c_130]) ).
cnf(c_32996,plain,
meet(C,join(A,B)) = meet(join(A,B),meet(C,join(E,join(F,join(A,join(B,D)))))),
inference(paramod,[status(thm)],[c_206,c_32995]) ).
cnf(c_10787,plain,
meet(join(A,B),meet(C,join(D,join(E,join(A,join(B,F)))))) = meet(C,join(A,B)),
inference(copy,[status(thm)],[c_32996]) ).
cnf(c_32997,plain,
meet(A,meet(B,join(C,join(A,D)))) = meet(A,meet(B,join(E,join(F,join(C,join(A,D)))))),
inference(paramod,[status(thm)],[c_178,c_155]) ).
cnf(c_32998,plain,
meet(B,A) = meet(A,meet(B,join(E,join(F,join(C,join(A,D)))))),
inference(paramod,[status(thm)],[c_181,c_32997]) ).
cnf(c_10808,plain,
meet(A,meet(B,join(C,join(D,join(E,join(A,F)))))) = meet(B,A),
inference(copy,[status(thm)],[c_32998]) ).
cnf(c_32999,plain,
( meet(A,join(A,B)) = join(A,B)
| meet(join(A,B),complement(A)) != zero ),
inference(paramod,[status(thm)],[c_3,c_5949]) ).
cnf(c_33000,plain,
( A = join(A,B)
| meet(join(A,B),complement(A)) != zero ),
inference(paramod,[status(thm)],[c_3,c_32999]) ).
cnf(c_14831,plain,
( join(A,B) = A
| meet(join(A,B),complement(A)) != zero ),
inference(copy,[status(thm)],[c_33000]) ).
cnf(c_18534,plain,
join(A,complement(meet(B,meet(C,join(A,complement(C)))))) = one,
inference(paramod,[status(thm)],[c_6136,c_8433]) ).
cnf(c_21682,plain,
( join(B,A) = B
| meet(join(A,B),complement(B)) != zero ),
inference(paramod,[status(thm)],[c_6,c_14831]) ).
cnf(c_33001,plain,
one = complement(meet(A,meet(B,join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_18534,c_6132]) ).
cnf(c_22199,plain,
complement(meet(A,meet(B,join(complement(A),complement(B))))) = one,
inference(copy,[status(thm)],[c_33001]) ).
cnf(c_33002,plain,
( complement(complement(meet(A,meet(complement(join(B,zero)),C)))) = meet(zero,complement(meet(A,meet(complement(join(B,zero)),C))))
| one != complement(meet(A,meet(complement(join(B,zero)),C))) ),
inference(resolve,[status(thm)],[c_94,c_8679]) ).
cnf(c_33003,plain,
one = complement(meet(A,meet(B,join(complement(A),complement(B))))),
inference(copy,[status(thm)],[c_22199]) ).
cnf(c_33004,plain,
complement(complement(meet(A,meet(complement(join(B,zero)),join(complement(A),complement(complement(join(B,zero)))))))) = meet(zero,complement(meet(A,meet(complement(join(B,zero)),join(complement(A),complement(complement(join(B,zero)))))))),
inference(resolve,[status(thm)],[c_33002,c_33003]) ).
cnf(c_33005,plain,
complement(complement(meet(A,meet(complement(B),join(complement(A),complement(complement(join(B,zero)))))))) = meet(zero,complement(meet(A,meet(complement(join(B,zero)),join(complement(A),complement(complement(join(B,zero)))))))),
inference(paramod,[status(thm)],[c_36,c_33004]) ).
cnf(c_33006,plain,
complement(complement(meet(A,meet(complement(B),join(complement(A),complement(complement(B))))))) = meet(zero,complement(meet(A,meet(complement(join(B,zero)),join(complement(A),complement(complement(join(B,zero)))))))),
inference(paramod,[status(thm)],[c_36,c_33005]) ).
cnf(c_33007,plain,
complement(complement(meet(A,meet(complement(B),join(complement(A),B))))) = meet(zero,complement(meet(A,meet(complement(join(B,zero)),join(complement(A),complement(complement(join(B,zero)))))))),
inference(paramod,[status(thm)],[c_320,c_33006]) ).
cnf(c_33008,plain,
meet(A,meet(complement(B),join(complement(A),B))) = meet(zero,complement(meet(A,meet(complement(join(B,zero)),join(complement(A),complement(complement(join(B,zero)))))))),
inference(paramod,[status(thm)],[c_320,c_33007]) ).
cnf(c_33009,plain,
meet(A,meet(complement(B),join(complement(A),B))) = meet(zero,complement(meet(A,meet(complement(B),join(complement(A),complement(complement(join(B,zero)))))))),
inference(paramod,[status(thm)],[c_36,c_33008]) ).
cnf(c_33010,plain,
meet(A,meet(complement(B),join(complement(A),B))) = meet(zero,complement(meet(A,meet(complement(B),join(complement(A),complement(complement(B))))))),
inference(paramod,[status(thm)],[c_36,c_33009]) ).
cnf(c_33011,plain,
meet(A,meet(complement(B),join(complement(A),B))) = meet(zero,complement(meet(A,meet(complement(B),join(complement(A),B))))),
inference(paramod,[status(thm)],[c_320,c_33010]) ).
cnf(c_22218,plain,
meet(A,meet(complement(B),join(complement(A),B))) = zero,
inference(paramod,[status(thm)],[c_82,c_33011]) ).
cnf(c_33012,plain,
( complement(complement(A)) = meet(B,join(complement(B),A))
| join(complement(A),meet(B,join(complement(B),A))) != one ),
inference(resolve,[status(thm)],[c_174,c_22218]) ).
cnf(c_33013,plain,
complement(complement(A)) = meet(join(B,A),join(complement(join(B,A)),A)),
inference(resolve,[status(thm)],[c_33012,c_5913]) ).
cnf(c_33014,plain,
A = meet(join(B,A),join(complement(join(B,A)),A)),
inference(paramod,[status(thm)],[c_320,c_33013]) ).
cnf(c_33015,plain,
A = meet(join(B,A),join(A,complement(join(B,A)))),
inference(paramod,[status(thm)],[c_6,c_33014]) ).
cnf(c_22287,plain,
meet(join(A,B),join(B,complement(join(A,B)))) = B,
inference(copy,[status(thm)],[c_33015]) ).
cnf(c_33016,plain,
( complement(complement(A)) = meet(B,join(complement(B),A))
| join(complement(A),meet(B,join(complement(B),A))) != one ),
inference(resolve,[status(thm)],[c_174,c_22218]) ).
cnf(c_33017,plain,
complement(complement(A)) = meet(join(A,B),join(complement(join(A,B)),A)),
inference(resolve,[status(thm)],[c_33016,c_5517]) ).
cnf(c_33018,plain,
A = meet(join(A,B),join(complement(join(A,B)),A)),
inference(paramod,[status(thm)],[c_320,c_33017]) ).
cnf(c_33019,plain,
A = meet(join(A,B),join(A,complement(join(A,B)))),
inference(paramod,[status(thm)],[c_6,c_33018]) ).
cnf(c_22288,plain,
meet(join(A,B),join(A,complement(join(A,B)))) = A,
inference(copy,[status(thm)],[c_33019]) ).
cnf(c_22305,plain,
meet(complement(A),meet(complement(B),join(A,B))) = zero,
inference(paramod,[status(thm)],[c_320,c_22218]) ).
cnf(c_33020,plain,
meet(complement(A),meet(complement(join(B,complement(join(A,B)))),one)) = zero,
inference(paramod,[status(thm)],[c_35,c_22305]) ).
cnf(c_33021,plain,
meet(complement(A),meet(one,complement(join(B,complement(join(A,B)))))) = zero,
inference(paramod,[status(thm)],[c_5,c_33020]) ).
cnf(c_22535,plain,
meet(complement(A),complement(join(B,complement(join(A,B))))) = zero,
inference(paramod,[status(thm)],[c_72,c_33021]) ).
cnf(c_33022,plain,
meet(complement(A),meet(complement(join(B,complement(join(B,A)))),one)) = zero,
inference(paramod,[status(thm)],[c_166,c_22305]) ).
cnf(c_33023,plain,
meet(complement(A),meet(one,complement(join(B,complement(join(B,A)))))) = zero,
inference(paramod,[status(thm)],[c_5,c_33022]) ).
cnf(c_22537,plain,
meet(complement(A),complement(join(B,complement(join(B,A))))) = zero,
inference(paramod,[status(thm)],[c_72,c_33023]) ).
cnf(c_22720,plain,
meet(join(A,B),join(B,complement(join(B,A)))) = B,
inference(paramod,[status(thm)],[c_6,c_22287]) ).
cnf(c_33024,plain,
meet(A,join(meet(B,A),complement(join(A,meet(B,A))))) = meet(B,A),
inference(paramod,[status(thm)],[c_15,c_22287]) ).
cnf(c_22724,plain,
meet(A,join(meet(B,A),complement(A))) = meet(B,A),
inference(paramod,[status(thm)],[c_15,c_33024]) ).
cnf(c_33025,plain,
meet(A,B) = meet(A,join(B,complement(join(B,A)))),
inference(paramod,[status(thm)],[c_22288,c_78]) ).
cnf(c_22748,plain,
meet(A,join(B,complement(join(B,A)))) = meet(A,B),
inference(copy,[status(thm)],[c_33025]) ).
cnf(c_33026,plain,
meet(A,join(complement(A),meet(B,A))) = meet(B,A),
inference(paramod,[status(thm)],[c_6,c_22724]) ).
cnf(c_22930,plain,
meet(A,join(complement(A),B)) = meet(B,A),
inference(paramod,[status(thm)],[c_474,c_33026]) ).
cnf(c_22949,plain,
meet(A,join(complement(A),B)) = meet(A,B),
inference(paramod,[status(thm)],[c_22930,c_5]) ).
cnf(c_33027,plain,
meet(A,join(B,complement(A))) = meet(join(B,complement(join(C,complement(complement(A))))),A),
inference(paramod,[status(thm)],[c_6294,c_22930]) ).
cnf(c_33028,plain,
meet(A,join(B,complement(A))) = meet(join(B,complement(join(C,A))),A),
inference(paramod,[status(thm)],[c_320,c_33027]) ).
cnf(c_33029,plain,
meet(A,join(B,complement(A))) = meet(A,join(B,complement(join(C,A)))),
inference(paramod,[status(thm)],[c_5,c_33028]) ).
cnf(c_23059,plain,
meet(A,join(B,complement(join(C,A)))) = meet(A,join(B,complement(A))),
inference(copy,[status(thm)],[c_33029]) ).
cnf(c_23142,plain,
meet(A,join(B,complement(A))) = meet(A,B),
inference(paramod,[status(thm)],[c_23059,c_22748]) ).
cnf(c_23168,plain,
meet(complement(A),join(A,B)) = meet(complement(A),B),
inference(paramod,[status(thm)],[c_320,c_22949]) ).
cnf(c_23236,plain,
meet(complement(A),join(B,A)) = meet(complement(A),B),
inference(paramod,[status(thm)],[c_320,c_23142]) ).
cnf(c_33030,plain,
meet(meet(join(A,B),complement(B)),one) = meet(meet(join(A,B),complement(B)),A),
inference(paramod,[status(thm)],[c_9288,c_23142]) ).
cnf(c_33031,plain,
meet(one,meet(join(A,B),complement(B))) = meet(meet(join(A,B),complement(B)),A),
inference(paramod,[status(thm)],[c_5,c_33030]) ).
cnf(c_33032,plain,
meet(join(A,B),complement(B)) = meet(meet(join(A,B),complement(B)),A),
inference(paramod,[status(thm)],[c_72,c_33031]) ).
cnf(c_33033,plain,
meet(join(A,B),complement(B)) = meet(A,meet(join(A,B),complement(B))),
inference(paramod,[status(thm)],[c_5,c_33032]) ).
cnf(c_23255,plain,
meet(join(A,B),complement(B)) = meet(A,complement(B)),
inference(paramod,[status(thm)],[c_21,c_33033]) ).
cnf(c_23282,plain,
( join(B,A) = B
| meet(A,complement(B)) != zero ),
inference(paramod,[status(thm)],[c_23255,c_21682]) ).
cnf(c_33034,plain,
meet(meet(complement(A),B),C) = meet(complement(A),meet(join(B,A),C)),
inference(paramod,[status(thm)],[c_23236,c_7]) ).
cnf(c_33035,plain,
meet(complement(A),meet(B,C)) = meet(complement(A),meet(join(B,A),C)),
inference(paramod,[status(thm)],[c_7,c_33034]) ).
cnf(c_23540,plain,
meet(complement(A),meet(join(B,A),C)) = meet(complement(A),meet(B,C)),
inference(copy,[status(thm)],[c_33035]) ).
cnf(c_33036,plain,
join(join(A,complement(join(A,B))),complement(B)) = join(A,complement(join(A,B))),
inference(resolve,[status(thm)],[c_23282,c_22537]) ).
cnf(c_33037,plain,
join(complement(B),join(A,complement(join(A,B)))) = join(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_6,c_33036]) ).
cnf(c_33038,plain,
join(A,complement(B)) = join(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_6145,c_33037]) ).
cnf(c_23774,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(copy,[status(thm)],[c_33038]) ).
cnf(c_33039,plain,
join(join(A,complement(join(B,A))),complement(B)) = join(A,complement(join(B,A))),
inference(resolve,[status(thm)],[c_23282,c_22535]) ).
cnf(c_33040,plain,
join(complement(B),join(A,complement(join(B,A)))) = join(A,complement(join(B,A))),
inference(paramod,[status(thm)],[c_6,c_33039]) ).
cnf(c_33041,plain,
join(A,complement(B)) = join(A,complement(join(B,A))),
inference(paramod,[status(thm)],[c_6405,c_33040]) ).
cnf(c_23775,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(copy,[status(thm)],[c_33041]) ).
cnf(c_33042,plain,
join(join(A,meet(complement(A),B)),B) = join(A,meet(complement(A),B)),
inference(resolve,[status(thm)],[c_23282,c_9548]) ).
cnf(c_33043,plain,
join(B,join(A,meet(complement(A),B))) = join(A,meet(complement(A),B)),
inference(paramod,[status(thm)],[c_6,c_33042]) ).
cnf(c_33044,plain,
join(B,A) = join(A,meet(complement(A),B)),
inference(paramod,[status(thm)],[c_116,c_33043]) ).
cnf(c_23784,plain,
join(A,meet(complement(A),B)) = join(B,A),
inference(copy,[status(thm)],[c_33044]) ).
cnf(c_23799,plain,
meet(join(A,B),join(B,complement(A))) = B,
inference(paramod,[status(thm)],[c_23774,c_22720]) ).
cnf(c_33045,plain,
join(complement(join(complement(A),B)),meet(complement(complement(join(complement(A),B))),A)) = A,
inference(paramod,[status(thm)],[c_6286,c_23784]) ).
cnf(c_33046,plain,
join(complement(join(complement(A),B)),meet(join(complement(A),B),A)) = A,
inference(paramod,[status(thm)],[c_320,c_33045]) ).
cnf(c_33047,plain,
join(complement(join(complement(A),B)),meet(A,join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_5,c_33046]) ).
cnf(c_33048,plain,
join(complement(join(complement(A),B)),meet(A,B)) = A,
inference(paramod,[status(thm)],[c_22949,c_33047]) ).
cnf(c_23870,plain,
join(meet(A,B),complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_6,c_33048]) ).
cnf(c_33049,plain,
meet(complement(A),join(complement(join(B,A)),complement(complement(A)))) = complement(join(B,A)),
inference(paramod,[status(thm)],[c_6104,c_23799]) ).
cnf(c_33050,plain,
meet(complement(A),join(complement(join(B,A)),A)) = complement(join(B,A)),
inference(paramod,[status(thm)],[c_320,c_33049]) ).
cnf(c_33051,plain,
meet(complement(A),join(A,complement(join(B,A)))) = complement(join(B,A)),
inference(paramod,[status(thm)],[c_6,c_33050]) ).
cnf(c_33052,plain,
meet(complement(A),join(A,complement(B))) = complement(join(B,A)),
inference(paramod,[status(thm)],[c_23775,c_33051]) ).
cnf(c_33053,plain,
meet(complement(A),complement(B)) = complement(join(B,A)),
inference(paramod,[status(thm)],[c_23168,c_33052]) ).
cnf(c_24097,plain,
complement(join(A,B)) = meet(complement(B),complement(A)),
inference(copy,[status(thm)],[c_33053]) ).
cnf(c_33054,plain,
join(meet(A,B),meet(complement(B),complement(complement(A)))) = A,
inference(paramod,[status(thm)],[c_24097,c_23870]) ).
cnf(c_24226,plain,
join(meet(A,B),meet(complement(B),A)) = A,
inference(paramod,[status(thm)],[c_320,c_33054]) ).
cnf(c_27114,plain,
join(meet(A,B),meet(complement(A),B)) = B,
inference(paramod,[status(thm)],[c_5,c_24226]) ).
cnf(c_33055,plain,
join(meet(A,B),meet(complement(A),meet(join(C,A),B))) = meet(join(C,A),B),
inference(paramod,[status(thm)],[c_78,c_27114]) ).
cnf(c_29941,plain,
join(meet(A,B),meet(complement(A),meet(C,B))) = meet(join(C,A),B),
inference(paramod,[status(thm)],[c_23540,c_33055]) ).
cnf(c_33056,plain,
join(meet(A,B),meet(C,B)) = join(meet(A,B),meet(complement(A),meet(C,B))),
inference(paramod,[status(thm)],[c_27114,c_524]) ).
cnf(c_31116,plain,
join(meet(A,B),meet(complement(A),meet(C,B))) = join(meet(A,B),meet(C,B)),
inference(copy,[status(thm)],[c_33056]) ).
cnf(c_33057,plain,
join(meet(A,B),meet(C,B)) = meet(join(C,A),B),
inference(paramod,[status(thm)],[c_31116,c_29941]) ).
cnf(c_31127,plain,
meet(join(A,B),C) = join(meet(B,C),meet(A,C)),
inference(copy,[status(thm)],[c_33057]) ).
cnf(c_33058,plain,
join(meet(B,meet(C,join(D,join(E,join(A,join(B,F)))))),meet(A,meet(C,join(D,join(E,join(A,join(B,F))))))) = meet(C,join(A,B)),
inference(paramod,[status(thm)],[c_31127,c_10787]) ).
cnf(c_33059,plain,
join(meet(C,B),meet(A,meet(C,join(D,join(E,join(A,join(B,F))))))) = meet(C,join(A,B)),
inference(paramod,[status(thm)],[c_10808,c_33058]) ).
cnf(c_33060,plain,
join(meet(C,B),meet(C,A)) = meet(C,join(A,B)),
inference(paramod,[status(thm)],[c_943,c_33059]) ).
cnf(c_32000,plain,
meet(A,join(B,C)) = join(meet(A,C),meet(A,B)),
inference(copy,[status(thm)],[c_33060]) ).
cnf(c_33061,plain,
join(meet(a,c),meet(a,b)) != join(meet(a,b),meet(a,c)),
inference(paramod,[status(thm)],[c_32000,c_14]) ).
cnf(c_33062,plain,
join(meet(a,b),meet(a,c)) != join(meet(a,b),meet(a,c)),
inference(paramod,[status(thm)],[c_6,c_33061]) ).
cnf(c_32919,plain,
$false,
inference(copy,[status(thm)],[c_33062]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT197-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.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 20:13:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.03/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.36 % Process 1099797 was started by sandbox on n013,
% 0.03/0.36 % Fri Sep 25 20:13:21 2026
% 0.03/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.36
% 0.03/0.36 % From the command line: assign(max_seconds, 300).
% 278.33/37.19
% 278.33/37.19 % given #500 (T,wt=13): 6325 join(A,complement(join(B,complement(meet(C,meet(D,A)))))) = A. [para(6148(a,1),119(a,1,2)),rewrite([68(3)]),flip(a)].
% 278.33/37.19
% 278.33/37.19 % SZS status Unsatisfiable for theBenchmark
% 278.33/37.19
% 278.33/37.19 % Proof 1 at 28.34 (+ 7.72) seconds.
% 278.33/37.19 % Length of proof is 137.
% 278.33/37.19 % Level of proof is 31.
% 278.33/37.19 % Maximum clause weight is 23.000.
% 278.33/37.19 % Given clauses 814.
% 278.33/37.19
% 278.33/37.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------