%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT214-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:49:49 AM UTC 2026
% Result : Unsatisfiable 152.78s 20.77s
% Output : CNFRefutation 152.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 13
% Syntax : Number of formulae : 151 ( 136 unt; 0 def)
% Number of atoms : 178 ( 177 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 34 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 7 ( 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 : 323 ( 62 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_H79,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(meet(VAR_0,join(VAR_1,meet(VAR_0,VAR_2))),meet(VAR_2,VAR_3))),
file('theBenchmark.p',equation_H79) ).
cnf(c_12,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(meet(A,join(B,meet(A,C))),meet(C,D))),
inference(clausify,[status(thm)],[equation_H79]) ).
cnf(c_13,plain,
meet(A,join(meet(A,join(B,meet(A,C))),meet(C,D))) = 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(meet(a,b),meet(a,c)) != meet(a,join(b,c)),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_16,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_17,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_27457,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_20,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_5,c_27457]) ).
cnf(c_27458,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_22,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_27458]) ).
cnf(c_27459,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_28,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_6,c_27459]) ).
cnf(c_29,plain,
meet(join(A,B),join(A,join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_30,plain,
join(A,join(B,meet(join(A,B),C))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_27460,plain,
join(A,B) = join(A,join(meet(A,C),B)),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_31,plain,
join(A,join(meet(A,B),C)) = join(A,C),
inference(copy,[status(thm)],[c_27460]) ).
cnf(c_34,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_27461,plain,
join(one,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_35,plain,
join(A,join(complement(A),B)) = join(one,B),
inference(copy,[status(thm)],[c_27461]) ).
cnf(c_37,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_27462,plain,
meet(zero,A) = meet(B,meet(complement(B),A)),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_38,plain,
meet(A,meet(complement(A),B)) = meet(zero,B),
inference(copy,[status(thm)],[c_27462]) ).
cnf(c_42,plain,
( complement(A) = B
| join(B,A) != one
| meet(A,B) != zero ),
inference(paramod,[status(thm)],[c_6,c_11]) ).
cnf(c_27463,plain,
meet(A,join(meet(A,join(B,meet(A,C))),C)) = meet(A,join(B,meet(C,join(A,C)))),
inference(paramod,[status(thm)],[c_1,c_13]) ).
cnf(c_27464,plain,
meet(A,join(C,meet(A,join(B,meet(A,C))))) = meet(A,join(B,meet(C,join(A,C)))),
inference(paramod,[status(thm)],[c_6,c_27463]) ).
cnf(c_44,plain,
meet(A,join(B,meet(A,join(C,meet(A,B))))) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_17,c_27464]) ).
cnf(c_54,plain,
meet(A,join(meet(B,C),meet(A,join(D,meet(A,B))))) = meet(A,join(D,meet(B,join(A,C)))),
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_27465,plain,
join(A,B) = join(A,join(meet(C,A),B)),
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_65,plain,
join(A,join(meet(B,A),C)) = join(A,C),
inference(copy,[status(thm)],[c_27465]) ).
cnf(c_27466,plain,
A = meet(one,A),
inference(paramod,[status(thm)],[c_34,c_5]) ).
cnf(c_70,plain,
meet(one,A) = A,
inference(copy,[status(thm)],[c_27466]) ).
cnf(c_72,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_34,c_16]) ).
cnf(c_73,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_72,c_35]) ).
cnf(c_27467,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_37,c_6]) ).
cnf(c_74,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_27467]) ).
cnf(c_83,plain,
meet(zero,A) = zero,
inference(paramod,[status(thm)],[c_37,c_17]) ).
cnf(c_27468,plain,
one = join(A,one),
inference(paramod,[status(thm)],[c_17,c_70]) ).
cnf(c_84,plain,
join(A,one) = one,
inference(copy,[status(thm)],[c_27468]) ).
cnf(c_85,plain,
meet(A,meet(complement(A),B)) = zero,
inference(paramod,[status(thm)],[c_83,c_38]) ).
cnf(c_88,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_74,c_16]) ).
cnf(c_27469,plain,
meet(A,meet(B,meet(C,A))) = meet(meet(B,C),A),
inference(paramod,[status(thm)],[c_7,c_20]) ).
cnf(c_97,plain,
meet(A,meet(B,meet(C,A))) = meet(B,meet(C,A)),
inference(paramod,[status(thm)],[c_7,c_27469]) ).
cnf(c_27470,plain,
( complement(A) = join(complement(A),B)
| one != one
| meet(A,join(complement(A),B)) != zero ),
inference(paramod,[status(thm)],[c_73,c_11]) ).
cnf(c_27471,plain,
( join(complement(A),B) = complement(A)
| one != one
| meet(A,join(complement(A),B)) != zero ),
inference(copy,[status(thm)],[c_27470]) ).
cnf(c_102,plain,
( join(complement(A),B) = complement(A)
| meet(A,join(complement(A),B)) != zero ),
inference(copy,[status(thm)],[c_27471]) ).
cnf(c_103,plain,
meet(A,meet(B,complement(A))) = zero,
inference(paramod,[status(thm)],[c_5,c_85]) ).
cnf(c_27472,plain,
zero = meet(A,meet(B,meet(complement(meet(A,B)),C))),
inference(paramod,[status(thm)],[c_85,c_7]) ).
cnf(c_104,plain,
meet(A,meet(B,meet(complement(meet(A,B)),C))) = zero,
inference(copy,[status(thm)],[c_27472]) ).
cnf(c_27473,plain,
meet(A,zero) = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_10,c_22]) ).
cnf(c_27474,plain,
zero = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_88,c_27473]) ).
cnf(c_143,plain,
meet(A,complement(join(A,B))) = zero,
inference(copy,[status(thm)],[c_27474]) ).
cnf(c_27475,plain,
meet(A,meet(join(A,B),meet(C,A))) = meet(C,A),
inference(paramod,[status(thm)],[c_20,c_22]) ).
cnf(c_148,plain,
meet(join(A,B),meet(C,A)) = meet(C,A),
inference(paramod,[status(thm)],[c_97,c_27475]) ).
cnf(c_153,plain,
meet(A,complement(join(B,A))) = zero,
inference(paramod,[status(thm)],[c_6,c_143]) ).
cnf(c_27476,plain,
meet(A,join(meet(A,join(B,zero)),meet(complement(join(A,C)),D))) = meet(A,join(B,meet(complement(join(A,C)),join(A,D)))),
inference(paramod,[status(thm)],[c_143,c_13]) ).
cnf(c_156,plain,
meet(A,join(meet(A,B),meet(complement(join(A,C)),D))) = meet(A,join(B,meet(complement(join(A,C)),join(A,D)))),
inference(paramod,[status(thm)],[c_37,c_27476]) ).
cnf(c_232,plain,
meet(join(A,B),join(B,A)) = join(A,B),
inference(paramod,[status(thm)],[c_28,c_29]) ).
cnf(c_27477,plain,
meet(join(A,meet(join(B,A),C)),join(B,A)) = join(A,meet(join(B,A),C)),
inference(paramod,[status(thm)],[c_30,c_17]) ).
cnf(c_261,plain,
meet(join(A,B),join(B,meet(join(A,B),C))) = join(B,meet(join(A,B),C)),
inference(paramod,[status(thm)],[c_5,c_27477]) ).
cnf(c_27478,plain,
join(A,one) = join(A,complement(meet(A,B))),
inference(paramod,[status(thm)],[c_9,c_31]) ).
cnf(c_27479,plain,
one = join(A,complement(meet(A,B))),
inference(paramod,[status(thm)],[c_84,c_27478]) ).
cnf(c_282,plain,
join(A,complement(meet(A,B))) = one,
inference(copy,[status(thm)],[c_27479]) ).
cnf(c_316,plain,
join(A,complement(meet(B,A))) = one,
inference(paramod,[status(thm)],[c_5,c_282]) ).
cnf(c_321,plain,
join(A,complement(meet(B,meet(C,A)))) = one,
inference(paramod,[status(thm)],[c_7,c_316]) ).
cnf(c_27480,plain,
( complement(complement(A)) = A
| one != one
| meet(complement(A),A) != zero ),
inference(paramod,[status(thm)],[c_9,c_42]) ).
cnf(c_27481,plain,
( complement(complement(A)) = A
| one != one
| meet(A,complement(A)) != zero ),
inference(paramod,[status(thm)],[c_5,c_27480]) ).
cnf(c_27482,plain,
( complement(complement(A)) = A
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_10,c_27481]) ).
cnf(c_27483,plain,
( complement(complement(A)) = A
| one != one ),
inference(copy,[status(thm)],[c_27482]) ).
cnf(c_370,plain,
complement(complement(A)) = A,
inference(copy,[status(thm)],[c_27483]) ).
cnf(c_27484,plain,
meet(A,join(meet(B,complement(A)),meet(A,join(C,zero)))) = meet(A,join(C,meet(B,complement(A)))),
inference(paramod,[status(thm)],[c_103,c_44]) ).
cnf(c_500,plain,
meet(A,join(meet(B,complement(A)),meet(A,C))) = meet(A,join(C,meet(B,complement(A)))),
inference(paramod,[status(thm)],[c_37,c_27484]) ).
cnf(c_658,plain,
meet(join(meet(A,B),C),complement(join(B,C))) = zero,
inference(paramod,[status(thm)],[c_65,c_153]) ).
cnf(c_27485,plain,
join(join(A,B),complement(meet(C,join(B,A)))) = one,
inference(paramod,[status(thm)],[c_232,c_321]) ).
cnf(c_1020,plain,
join(A,join(B,complement(meet(C,join(B,A))))) = one,
inference(paramod,[status(thm)],[c_8,c_27485]) ).
cnf(c_27486,plain,
meet(A,join(meet(B,complement(A)),meet(A,join(C,meet(A,B))))) = meet(A,join(C,meet(B,one))),
inference(paramod,[status(thm)],[c_9,c_54]) ).
cnf(c_1341,plain,
meet(A,join(meet(B,complement(A)),meet(A,join(C,meet(A,B))))) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_34,c_27486]) ).
cnf(c_27487,plain,
meet(A,meet(complement(meet(A,join(B,C))),B)) = zero,
inference(paramod,[status(thm)],[c_148,c_104]) ).
cnf(c_1704,plain,
meet(A,meet(B,complement(meet(A,join(B,C))))) = zero,
inference(paramod,[status(thm)],[c_5,c_27487]) ).
cnf(c_27488,plain,
zero = meet(complement(join(A,B)),join(meet(C,A),B)),
inference(paramod,[status(thm)],[c_658,c_5]) ).
cnf(c_4988,plain,
meet(complement(join(A,B)),join(meet(C,A),B)) = zero,
inference(copy,[status(thm)],[c_27488]) ).
cnf(c_8660,plain,
meet(complement(A),join(meet(B,A),meet(C,A))) = zero,
inference(paramod,[status(thm)],[c_16,c_4988]) ).
cnf(c_27489,plain,
meet(complement(A),join(A,meet(complement(join(complement(A),B)),join(complement(A),A)))) = zero,
inference(paramod,[status(thm)],[c_156,c_8660]) ).
cnf(c_27490,plain,
meet(complement(A),join(A,meet(complement(join(complement(A),B)),join(A,complement(A))))) = zero,
inference(paramod,[status(thm)],[c_6,c_27489]) ).
cnf(c_27491,plain,
meet(complement(A),join(A,meet(complement(join(complement(A),B)),one))) = zero,
inference(paramod,[status(thm)],[c_9,c_27490]) ).
cnf(c_27492,plain,
meet(complement(A),join(A,meet(one,complement(join(complement(A),B))))) = zero,
inference(paramod,[status(thm)],[c_5,c_27491]) ).
cnf(c_12436,plain,
meet(complement(A),join(A,complement(join(complement(A),B)))) = zero,
inference(paramod,[status(thm)],[c_70,c_27492]) ).
cnf(c_27493,plain,
meet(A,join(complement(A),complement(join(complement(complement(A)),B)))) = zero,
inference(paramod,[status(thm)],[c_370,c_12436]) ).
cnf(c_12470,plain,
meet(A,join(complement(A),complement(join(A,B)))) = zero,
inference(paramod,[status(thm)],[c_370,c_27493]) ).
cnf(c_12654,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(resolve,[status(thm)],[c_102,c_12470]) ).
cnf(c_12832,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_6,c_12654]) ).
cnf(c_27494,plain,
join(complement(meet(A,B)),complement(A)) = complement(meet(A,B)),
inference(paramod,[status(thm)],[c_4,c_12832]) ).
cnf(c_13033,plain,
join(complement(A),complement(meet(A,B))) = complement(meet(A,B)),
inference(paramod,[status(thm)],[c_6,c_27494]) ).
cnf(c_15468,plain,
meet(complement(A),complement(meet(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_13033,c_3]) ).
cnf(c_15499,plain,
join(A,complement(meet(B,join(complement(B),A)))) = one,
inference(paramod,[status(thm)],[c_13033,c_1020]) ).
cnf(c_27495,plain,
meet(A,complement(meet(complement(A),B))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_370,c_15468]) ).
cnf(c_15669,plain,
meet(A,complement(meet(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_370,c_27495]) ).
cnf(c_15699,plain,
meet(A,complement(meet(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_5,c_15669]) ).
cnf(c_27496,plain,
meet(A,B) = meet(A,meet(complement(meet(C,complement(A))),B)),
inference(paramod,[status(thm)],[c_15699,c_7]) ).
cnf(c_15766,plain,
meet(A,meet(complement(meet(B,complement(A))),C)) = meet(A,C),
inference(copy,[status(thm)],[c_27496]) ).
cnf(c_27497,plain,
join(meet(A,join(B,meet(A,complement(A)))),complement(meet(A,join(B,complement(A))))) = one,
inference(paramod,[status(thm)],[c_44,c_15499]) ).
cnf(c_27498,plain,
join(meet(A,join(B,zero)),complement(meet(A,join(B,complement(A))))) = one,
inference(paramod,[status(thm)],[c_10,c_27497]) ).
cnf(c_15961,plain,
join(meet(A,B),complement(meet(A,join(B,complement(A))))) = one,
inference(paramod,[status(thm)],[c_37,c_27498]) ).
cnf(c_27499,plain,
meet(A,join(meet(A,B),meet(join(A,meet(A,B)),C))) = join(meet(A,B),meet(join(A,meet(A,B)),C)),
inference(paramod,[status(thm)],[c_4,c_261]) ).
cnf(c_27500,plain,
meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(join(A,meet(A,B)),C)),
inference(paramod,[status(thm)],[c_4,c_27499]) ).
cnf(c_25892,plain,
meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_4,c_27500]) ).
cnf(c_27501,plain,
( complement(meet(A,B)) = complement(meet(A,join(B,complement(A))))
| one != one
| meet(meet(A,B),complement(meet(A,join(B,complement(A))))) != zero ),
inference(paramod,[status(thm)],[c_15961,c_11]) ).
cnf(c_27502,plain,
( complement(meet(A,B)) = complement(meet(A,join(B,complement(A))))
| one != one
| meet(A,meet(B,complement(meet(A,join(B,complement(A)))))) != zero ),
inference(paramod,[status(thm)],[c_7,c_27501]) ).
cnf(c_27503,plain,
( complement(meet(A,B)) = complement(meet(A,join(B,complement(A))))
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_1704,c_27502]) ).
cnf(c_27504,plain,
( complement(meet(A,join(B,complement(A)))) = complement(meet(A,B))
| one != one
| zero != zero ),
inference(copy,[status(thm)],[c_27503]) ).
cnf(c_27505,plain,
( complement(meet(A,join(B,complement(A)))) = complement(meet(A,B))
| one != one ),
inference(copy,[status(thm)],[c_27504]) ).
cnf(c_26987,plain,
complement(meet(A,join(B,complement(A)))) = complement(meet(A,B)),
inference(copy,[status(thm)],[c_27505]) ).
cnf(c_27506,plain,
complement(complement(meet(A,B))) = meet(A,join(B,complement(A))),
inference(paramod,[status(thm)],[c_26987,c_370]) ).
cnf(c_27507,plain,
meet(A,B) = meet(A,join(B,complement(A))),
inference(paramod,[status(thm)],[c_370,c_27506]) ).
cnf(c_27021,plain,
meet(A,join(B,complement(A))) = meet(A,B),
inference(copy,[status(thm)],[c_27507]) ).
cnf(c_27508,plain,
meet(A,meet(complement(meet(B,complement(A))),C)) = meet(A,join(C,complement(complement(meet(B,complement(A)))))),
inference(paramod,[status(thm)],[c_27021,c_15766]) ).
cnf(c_27509,plain,
meet(A,C) = meet(A,join(C,complement(complement(meet(B,complement(A)))))),
inference(paramod,[status(thm)],[c_15766,c_27508]) ).
cnf(c_27510,plain,
meet(A,C) = meet(A,join(C,meet(B,complement(A)))),
inference(paramod,[status(thm)],[c_370,c_27509]) ).
cnf(c_27141,plain,
meet(A,join(B,meet(C,complement(A)))) = meet(A,B),
inference(copy,[status(thm)],[c_27510]) ).
cnf(c_27213,plain,
meet(A,join(meet(B,complement(A)),meet(A,C))) = meet(A,C),
inference(paramod,[status(thm)],[c_27141,c_500]) ).
cnf(c_27225,plain,
meet(A,join(B,meet(A,C))) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_27213,c_1341]) ).
cnf(c_27511,plain,
meet(A,join(meet(A,B),C)) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_27225,c_25892]) ).
cnf(c_27252,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(meet(A,B),C)),
inference(copy,[status(thm)],[c_27511]) ).
cnf(c_27512,plain,
meet(a,join(meet(a,b),c)) != meet(a,join(b,c)),
inference(paramod,[status(thm)],[c_27252,c_15]) ).
cnf(c_27513,plain,
meet(a,join(c,meet(a,b))) != meet(a,join(b,c)),
inference(paramod,[status(thm)],[c_6,c_27512]) ).
cnf(c_27514,plain,
meet(a,join(c,b)) != meet(a,join(b,c)),
inference(paramod,[status(thm)],[c_27225,c_27513]) ).
cnf(c_27515,plain,
meet(a,join(b,c)) != meet(a,join(b,c)),
inference(paramod,[status(thm)],[c_6,c_27514]) ).
cnf(c_27456,plain,
$false,
inference(copy,[status(thm)],[c_27515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT214-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 20:18:58 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2132429 was started by sandbox2 on n015,
% 0.11/0.37 % Fri Sep 25 20:18:58 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 152.78/20.77
% 152.78/20.77 % given #500 (T,wt=13): 7614 meet(A,join(meet(complement(A),B),meet(C,complement(A)))) = zero. [para(370(a,1),3306(a,1,2)),rewrite([5(6)])].
% 152.78/20.77
% 152.78/20.77 % SZS status Unsatisfiable for theBenchmark
% 152.78/20.77
% 152.78/20.77 % Proof 1 at 16.80 (+ 3.48) seconds.
% 152.78/20.77 % Length of proof is 79.
% 152.78/20.77 % Level of proof is 22.
% 152.78/20.77 % Maximum clause weight is 25.000.
% 152.78/20.77 % Given clauses 637.
% 152.78/20.77
% 152.78/20.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------