%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 07:49:30 AM UTC 2026
% Result : Unsatisfiable 92.30s 12.42s
% Output : CNFRefutation 92.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 19
% Syntax : Number of formulae : 183 ( 154 unt; 0 def)
% Number of atoms : 215 ( 198 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 38 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 327 ( 35 sgn 29 !; 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(x_meet_0,axiom,
! [VAR_0] : meet(VAR_0,n0) = n0,
file('theBenchmark.p',x_meet_0) ).
cnf(c_9,plain,
meet(A,n0) = n0,
inference(clausify,[status(thm)],[x_meet_0]) ).
fof(x_join_0,axiom,
! [VAR_0] : join(VAR_0,n0) = VAR_0,
file('theBenchmark.p',x_join_0) ).
cnf(c_10,plain,
join(A,n0) = A,
inference(clausify,[status(thm)],[x_join_0]) ).
fof(x_meet_1,axiom,
! [VAR_0] : meet(VAR_0,n1) = VAR_0,
file('theBenchmark.p',x_meet_1) ).
cnf(c_11,plain,
meet(A,n1) = A,
inference(clausify,[status(thm)],[x_meet_1]) ).
fof(x_join_1,axiom,
! [VAR_0] : join(VAR_0,n1) = n1,
file('theBenchmark.p',x_join_1) ).
cnf(c_12,plain,
join(A,n1) = n1,
inference(clausify,[status(thm)],[x_join_1]) ).
fof(modular,axiom,
! [VAR_0,VAR_1,VAR_2] :
( meet(VAR_1,join(VAR_0,VAR_2)) = join(VAR_0,meet(VAR_2,VAR_1))
| meet(VAR_0,VAR_1) != VAR_0 ),
file('theBenchmark.p',modular) ).
cnf(c_13,plain,
( meet(B,join(A,C)) = join(A,meet(C,B))
| meet(A,B) != A ),
inference(clausify,[status(thm)],[modular]) ).
cnf(c_14,plain,
( join(A,meet(C,B)) = meet(B,join(A,C))
| meet(A,B) != A ),
inference(copy,[status(thm)],[c_13]) ).
fof(complement_meet,axiom,
! [VAR_0,VAR_1] :
( meet(VAR_0,VAR_1) = n0
| ~ complement(VAR_0,VAR_1) ),
file('theBenchmark.p',complement_meet) ).
cnf(c_15,plain,
( meet(A,B) = n0
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[complement_meet]) ).
fof(complement_join,axiom,
! [VAR_0,VAR_1] :
( join(VAR_0,VAR_1) = n1
| ~ complement(VAR_0,VAR_1) ),
file('theBenchmark.p',complement_join) ).
cnf(c_16,plain,
( join(A,B) = n1
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[complement_join]) ).
fof(meet_join_complement,axiom,
! [VAR_0,VAR_1] :
( complement(VAR_0,VAR_1)
| join(VAR_0,VAR_1) != n1
| meet(VAR_0,VAR_1) != n0 ),
file('theBenchmark.p',meet_join_complement) ).
cnf(c_17,plain,
( complement(A,B)
| join(A,B) != n1
| meet(A,B) != n0 ),
inference(clausify,[status(thm)],[meet_join_complement]) ).
fof(complement_of_a_join_b,axiom,
complement(r1,join(a,b)),
file('theBenchmark.p',complement_of_a_join_b) ).
cnf(c_18,plain,
complement(r1,join(a,b)),
inference(clausify,[status(thm)],[complement_of_a_join_b]) ).
fof(complement_of_a_meet_b,axiom,
complement(r2,meet(a,b)),
file('theBenchmark.p',complement_of_a_meet_b) ).
cnf(c_19,plain,
complement(r2,meet(a,b)),
inference(clausify,[status(thm)],[complement_of_a_meet_b]) ).
fof(prove_complememt,axiom,
~ complement(a,join(r1,meet(r2,b))),
file('theBenchmark.p',prove_complememt) ).
cnf(c_20,plain,
~ complement(a,join(r1,meet(r2,b))),
inference(clausify,[status(thm)],[prove_complememt]) ).
cnf(c_21,plain,
~ complement(a,join(r1,meet(b,r2))),
inference(paramod,[status(thm)],[c_5,c_20]) ).
cnf(c_22,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_23,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_10751,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_25,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_10751]) ).
cnf(c_10752,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_26,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_5,c_10752]) ).
cnf(c_10753,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_28,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_10753]) ).
cnf(c_10754,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_31,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_7,c_10754]) ).
cnf(c_10755,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_33,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_10755]) ).
cnf(c_10756,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_34,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_6,c_10756]) ).
cnf(c_35,plain,
meet(join(A,B),join(A,join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_10757,plain,
join(A,B) = join(A,join(meet(A,C),B)),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_37,plain,
join(A,join(meet(A,B),C)) = join(A,C),
inference(copy,[status(thm)],[c_10757]) ).
cnf(c_10758,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_39,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_8,c_10758]) ).
cnf(c_10759,plain,
A = join(n0,A),
inference(paramod,[status(thm)],[c_10,c_6]) ).
cnf(c_41,plain,
join(n0,A) = A,
inference(copy,[status(thm)],[c_10759]) ).
cnf(c_10760,plain,
A = meet(n1,A),
inference(paramod,[status(thm)],[c_11,c_5]) ).
cnf(c_42,plain,
meet(n1,A) = A,
inference(copy,[status(thm)],[c_10760]) ).
cnf(c_10761,plain,
n1 = join(n1,A),
inference(paramod,[status(thm)],[c_12,c_6]) ).
cnf(c_43,plain,
join(n1,A) = n1,
inference(copy,[status(thm)],[c_10761]) ).
cnf(c_44,plain,
join(A,meet(B,join(A,C))) = meet(join(A,C),join(A,B)),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_45,plain,
( join(B,meet(C,A)) = meet(A,join(B,C))
| meet(A,B) != B ),
inference(paramod,[status(thm)],[c_5,c_14]) ).
cnf(c_57,plain,
( complement(B,A)
| join(B,A) != n1
| meet(A,B) != n0 ),
inference(paramod,[status(thm)],[c_5,c_17]) ).
cnf(c_10762,plain,
join(r1,join(a,b)) = n1,
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_10763,plain,
join(a,join(r1,b)) = n1,
inference(paramod,[status(thm)],[c_39,c_10762]) ).
cnf(c_61,plain,
join(a,join(b,r1)) = n1,
inference(paramod,[status(thm)],[c_6,c_10763]) ).
cnf(c_62,plain,
meet(r1,join(a,b)) = n0,
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_63,plain,
join(r2,meet(a,b)) = n1,
inference(resolve,[status(thm)],[c_19,c_16]) ).
cnf(c_10764,plain,
meet(r2,meet(a,b)) = n0,
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_10765,plain,
meet(a,meet(r2,b)) = n0,
inference(paramod,[status(thm)],[c_31,c_10764]) ).
cnf(c_64,plain,
meet(a,meet(b,r2)) = n0,
inference(paramod,[status(thm)],[c_5,c_10765]) ).
cnf(c_65,plain,
join(A,meet(B,meet(C,A))) = A,
inference(paramod,[status(thm)],[c_7,c_22]) ).
cnf(c_10766,plain,
join(A,B) = join(A,join(meet(C,A),B)),
inference(paramod,[status(thm)],[c_22,c_8]) ).
cnf(c_66,plain,
join(A,join(meet(B,A),C)) = join(A,C),
inference(copy,[status(thm)],[c_10766]) ).
cnf(c_69,plain,
join(A,meet(B,join(C,A))) = meet(join(C,A),join(A,B)),
inference(resolve,[status(thm)],[c_23,c_14]) ).
cnf(c_10767,plain,
join(join(A,a),join(b,r1)) = join(A,n1),
inference(paramod,[status(thm)],[c_61,c_8]) ).
cnf(c_10768,plain,
join(b,join(join(A,a),r1)) = join(A,n1),
inference(paramod,[status(thm)],[c_39,c_10767]) ).
cnf(c_10769,plain,
join(b,join(r1,join(A,a))) = join(A,n1),
inference(paramod,[status(thm)],[c_6,c_10768]) ).
cnf(c_131,plain,
join(b,join(r1,join(A,a))) = n1,
inference(paramod,[status(thm)],[c_12,c_10769]) ).
cnf(c_10770,plain,
meet(meet(A,B),meet(B,C)) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_25,c_7]) ).
cnf(c_10771,plain,
meet(B,meet(meet(A,B),C)) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_31,c_10770]) ).
cnf(c_142,plain,
meet(A,meet(B,meet(A,C))) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_7,c_10771]) ).
cnf(c_10772,plain,
meet(A,meet(B,meet(C,A))) = meet(meet(B,C),A),
inference(paramod,[status(thm)],[c_7,c_26]) ).
cnf(c_146,plain,
meet(A,meet(B,meet(C,A))) = meet(B,meet(C,A)),
inference(paramod,[status(thm)],[c_7,c_10772]) ).
cnf(c_10773,plain,
meet(A,B) = meet(B,meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_3,c_31]) ).
cnf(c_182,plain,
meet(A,meet(B,join(A,C))) = meet(B,A),
inference(copy,[status(thm)],[c_10773]) ).
cnf(c_10774,plain,
meet(A,n0) = meet(r1,meet(A,join(a,b))),
inference(paramod,[status(thm)],[c_62,c_31]) ).
cnf(c_10775,plain,
n0 = meet(r1,meet(A,join(a,b))),
inference(paramod,[status(thm)],[c_9,c_10774]) ).
cnf(c_188,plain,
meet(r1,meet(A,join(a,b))) = n0,
inference(copy,[status(thm)],[c_10775]) ).
cnf(c_240,plain,
join(meet(A,B),meet(C,B)) = meet(B,join(meet(A,B),C)),
inference(resolve,[status(thm)],[c_45,c_26]) ).
cnf(c_241,plain,
join(meet(A,B),meet(C,A)) = meet(A,join(meet(A,B),C)),
inference(resolve,[status(thm)],[c_45,c_25]) ).
cnf(c_10776,plain,
join(A,B) = join(B,join(A,meet(C,meet(D,B)))),
inference(paramod,[status(thm)],[c_65,c_39]) ).
cnf(c_255,plain,
join(A,join(B,meet(C,meet(D,A)))) = join(B,A),
inference(copy,[status(thm)],[c_10776]) ).
cnf(c_10777,plain,
meet(r1,b) = n0,
inference(paramod,[status(thm)],[c_23,c_188]) ).
cnf(c_333,plain,
meet(b,r1) = n0,
inference(paramod,[status(thm)],[c_5,c_10777]) ).
cnf(c_10778,plain,
meet(A,meet(join(A,B),meet(C,A))) = meet(C,A),
inference(paramod,[status(thm)],[c_26,c_28]) ).
cnf(c_563,plain,
meet(join(A,B),meet(C,A)) = meet(C,A),
inference(paramod,[status(thm)],[c_146,c_10778]) ).
cnf(c_10779,plain,
( join(join(B,C),meet(D,meet(A,B))) = meet(meet(A,B),join(join(B,C),D))
| meet(A,B) != join(B,C) ),
inference(paramod,[status(thm)],[c_563,c_14]) ).
cnf(c_10780,plain,
( join(B,join(C,meet(D,meet(A,B)))) = meet(meet(A,B),join(join(B,C),D))
| meet(A,B) != join(B,C) ),
inference(paramod,[status(thm)],[c_8,c_10779]) ).
cnf(c_10781,plain,
( join(C,B) = meet(meet(A,B),join(join(B,C),D))
| meet(A,B) != join(B,C) ),
inference(paramod,[status(thm)],[c_255,c_10780]) ).
cnf(c_10782,plain,
( join(C,B) = meet(meet(A,B),join(B,join(C,D)))
| meet(A,B) != join(B,C) ),
inference(paramod,[status(thm)],[c_8,c_10781]) ).
cnf(c_10783,plain,
( join(C,B) = meet(A,meet(B,join(B,join(C,D))))
| meet(A,B) != join(B,C) ),
inference(paramod,[status(thm)],[c_7,c_10782]) ).
cnf(c_10784,plain,
( join(C,B) = meet(A,B)
| meet(A,B) != join(B,C) ),
inference(paramod,[status(thm)],[c_3,c_10783]) ).
cnf(c_572,plain,
( join(B,A) = meet(C,A)
| join(A,B) != meet(C,A) ),
inference(copy,[status(thm)],[c_10784]) ).
cnf(c_581,plain,
( join(B,A) = meet(C,A)
| join(A,B) != meet(A,C) ),
inference(paramod,[status(thm)],[c_5,c_572]) ).
cnf(c_10785,plain,
( join(n1,A) = meet(B,A)
| n1 != meet(A,B) ),
inference(paramod,[status(thm)],[c_12,c_581]) ).
cnf(c_10786,plain,
( n1 = meet(B,A)
| n1 != meet(A,B) ),
inference(paramod,[status(thm)],[c_43,c_10785]) ).
cnf(c_10787,plain,
( n1 = meet(B,A)
| meet(A,B) != n1 ),
inference(copy,[status(thm)],[c_10786]) ).
cnf(c_597,plain,
( meet(B,A) = n1
| meet(A,B) != n1 ),
inference(copy,[status(thm)],[c_10787]) ).
cnf(c_10788,plain,
meet(join(meet(A,B),C),join(A,C)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_37,c_23]) ).
cnf(c_926,plain,
meet(join(A,B),join(meet(A,C),B)) = join(meet(A,C),B),
inference(paramod,[status(thm)],[c_5,c_10788]) ).
cnf(c_10789,plain,
meet(join(meet(A,B),C),join(B,C)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_66,c_23]) ).
cnf(c_978,plain,
meet(join(A,B),join(meet(C,A),B)) = join(meet(C,A),B),
inference(paramod,[status(thm)],[c_5,c_10789]) ).
cnf(c_10790,plain,
join(b,join(A,join(r1,a))) = n1,
inference(paramod,[status(thm)],[c_39,c_131]) ).
cnf(c_1055,plain,
join(b,join(A,join(a,r1))) = n1,
inference(paramod,[status(thm)],[c_6,c_10790]) ).
cnf(c_2235,plain,
meet(join(A,B),join(B,A)) = join(A,B),
inference(paramod,[status(thm)],[c_34,c_35]) ).
cnf(c_10791,plain,
( meet(join(B,A),join(A,B)) = n1
| join(A,B) != n1 ),
inference(paramod,[status(thm)],[c_2235,c_597]) ).
cnf(c_2276,plain,
( join(B,A) = n1
| join(A,B) != n1 ),
inference(paramod,[status(thm)],[c_2235,c_10791]) ).
cnf(c_2349,plain,
( join(C,join(A,B)) = n1
| join(A,join(B,C)) != n1 ),
inference(paramod,[status(thm)],[c_8,c_2276]) ).
cnf(c_2599,plain,
( join(C,join(B,A)) = n1
| join(A,join(B,C)) != n1 ),
inference(paramod,[status(thm)],[c_39,c_2349]) ).
cnf(c_10792,plain,
join(join(a,r1),join(A,b)) = n1,
inference(resolve,[status(thm)],[c_2599,c_1055]) ).
cnf(c_2695,plain,
join(a,join(r1,join(A,b))) = n1,
inference(paramod,[status(thm)],[c_8,c_10792]) ).
cnf(c_2775,plain,
join(A,meet(B,meet(C,join(A,D)))) = meet(join(A,D),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_7,c_44]) ).
cnf(c_10793,plain,
join(b,n0) = meet(join(a,b),join(b,r1)),
inference(paramod,[status(thm)],[c_62,c_69]) ).
cnf(c_10794,plain,
join(n0,b) = meet(join(a,b),join(b,r1)),
inference(paramod,[status(thm)],[c_6,c_10793]) ).
cnf(c_10795,plain,
b = meet(join(a,b),join(b,r1)),
inference(paramod,[status(thm)],[c_41,c_10794]) ).
cnf(c_3168,plain,
meet(join(a,b),join(b,r1)) = b,
inference(copy,[status(thm)],[c_10795]) ).
cnf(c_10796,plain,
meet(b,A) = meet(join(a,b),meet(join(b,r1),A)),
inference(paramod,[status(thm)],[c_3168,c_7]) ).
cnf(c_3305,plain,
meet(join(a,b),meet(join(b,r1),A)) = meet(b,A),
inference(copy,[status(thm)],[c_10796]) ).
cnf(c_10797,plain,
join(meet(A,B),meet(C,meet(A,join(B,D)))) = meet(meet(A,join(B,D)),join(meet(B,meet(A,join(B,D))),C)),
inference(paramod,[status(thm)],[c_182,c_240]) ).
cnf(c_10798,plain,
join(meet(A,B),meet(C,meet(A,join(B,D)))) = meet(meet(A,join(B,D)),join(meet(A,B),C)),
inference(paramod,[status(thm)],[c_182,c_10797]) ).
cnf(c_3585,plain,
join(meet(A,B),meet(C,meet(A,join(B,D)))) = meet(A,meet(join(B,D),join(meet(A,B),C))),
inference(paramod,[status(thm)],[c_7,c_10798]) ).
cnf(c_10799,plain,
join(meet(A,meet(B,join(C,D))),meet(B,C)) = meet(meet(B,join(C,D)),join(meet(A,meet(B,join(C,D))),C)),
inference(paramod,[status(thm)],[c_182,c_240]) ).
cnf(c_10800,plain,
join(meet(B,C),meet(A,meet(B,join(C,D)))) = meet(meet(B,join(C,D)),join(meet(A,meet(B,join(C,D))),C)),
inference(paramod,[status(thm)],[c_6,c_10799]) ).
cnf(c_10801,plain,
meet(B,meet(join(C,D),join(meet(B,C),A))) = meet(meet(B,join(C,D)),join(meet(A,meet(B,join(C,D))),C)),
inference(paramod,[status(thm)],[c_3585,c_10800]) ).
cnf(c_10802,plain,
meet(B,meet(join(C,D),join(meet(B,C),A))) = meet(meet(B,join(C,D)),join(C,meet(A,meet(B,join(C,D))))),
inference(paramod,[status(thm)],[c_6,c_10801]) ).
cnf(c_10803,plain,
meet(B,meet(join(C,D),join(meet(B,C),A))) = meet(meet(B,join(C,D)),meet(join(C,D),join(C,meet(A,B)))),
inference(paramod,[status(thm)],[c_2775,c_10802]) ).
cnf(c_10804,plain,
meet(B,meet(join(C,D),join(meet(B,C),A))) = meet(join(C,D),meet(meet(B,join(C,D)),join(C,meet(A,B)))),
inference(paramod,[status(thm)],[c_31,c_10803]) ).
cnf(c_10805,plain,
meet(B,meet(join(C,D),join(meet(B,C),A))) = meet(join(C,D),meet(B,meet(join(C,D),join(C,meet(A,B))))),
inference(paramod,[status(thm)],[c_7,c_10804]) ).
cnf(c_3586,plain,
meet(A,meet(join(B,C),join(meet(A,B),D))) = meet(A,meet(join(B,C),join(B,meet(D,A)))),
inference(paramod,[status(thm)],[c_142,c_10805]) ).
cnf(c_10806,plain,
meet(join(A,meet(B,C)),meet(C,join(meet(C,A),B))) = join(meet(C,A),meet(B,C)),
inference(paramod,[status(thm)],[c_241,c_978]) ).
cnf(c_10807,plain,
meet(C,meet(join(A,meet(B,C)),join(meet(C,A),B))) = join(meet(C,A),meet(B,C)),
inference(paramod,[status(thm)],[c_31,c_10806]) ).
cnf(c_10808,plain,
meet(C,meet(join(A,meet(B,C)),join(A,meet(B,C)))) = join(meet(C,A),meet(B,C)),
inference(paramod,[status(thm)],[c_3586,c_10807]) ).
cnf(c_10809,plain,
meet(C,join(A,meet(B,C))) = join(meet(C,A),meet(B,C)),
inference(paramod,[status(thm)],[c_1,c_10808]) ).
cnf(c_10810,plain,
meet(C,join(A,meet(B,C))) = meet(C,join(meet(C,A),B)),
inference(paramod,[status(thm)],[c_241,c_10809]) ).
cnf(c_5874,plain,
meet(A,join(meet(A,B),C)) = meet(A,join(B,meet(C,A))),
inference(copy,[status(thm)],[c_10810]) ).
cnf(c_10811,plain,
meet(join(a,b),join(meet(b,A),r1)) = meet(b,join(meet(b,A),r1)),
inference(paramod,[status(thm)],[c_926,c_3305]) ).
cnf(c_10812,plain,
meet(join(a,b),join(r1,meet(b,A))) = meet(b,join(meet(b,A),r1)),
inference(paramod,[status(thm)],[c_6,c_10811]) ).
cnf(c_8716,plain,
meet(join(a,b),join(r1,meet(b,A))) = meet(b,join(r1,meet(b,A))),
inference(paramod,[status(thm)],[c_6,c_10812]) ).
cnf(c_10813,plain,
meet(b,join(meet(b,r2),a)) = meet(b,n1),
inference(paramod,[status(thm)],[c_63,c_5874]) ).
cnf(c_10814,plain,
meet(b,join(a,meet(b,r2))) = meet(b,n1),
inference(paramod,[status(thm)],[c_6,c_10813]) ).
cnf(c_10815,plain,
meet(b,join(a,meet(b,r2))) = meet(n1,b),
inference(paramod,[status(thm)],[c_5,c_10814]) ).
cnf(c_9115,plain,
meet(b,join(a,meet(b,r2))) = b,
inference(paramod,[status(thm)],[c_42,c_10815]) ).
cnf(c_10816,plain,
meet(b,join(n0,A)) = meet(b,join(r1,meet(A,b))),
inference(paramod,[status(thm)],[c_333,c_5874]) ).
cnf(c_10817,plain,
meet(b,A) = meet(b,join(r1,meet(A,b))),
inference(paramod,[status(thm)],[c_41,c_10816]) ).
cnf(c_9129,plain,
meet(b,join(r1,meet(A,b))) = meet(b,A),
inference(copy,[status(thm)],[c_10817]) ).
cnf(c_10818,plain,
join(join(a,meet(b,r2)),b) = join(a,meet(b,r2)),
inference(paramod,[status(thm)],[c_9115,c_22]) ).
cnf(c_10819,plain,
join(b,join(a,meet(b,r2))) = join(a,meet(b,r2)),
inference(paramod,[status(thm)],[c_6,c_10818]) ).
cnf(c_10820,plain,
join(a,join(b,meet(b,r2))) = join(a,meet(b,r2)),
inference(paramod,[status(thm)],[c_39,c_10819]) ).
cnf(c_10821,plain,
join(a,b) = join(a,meet(b,r2)),
inference(paramod,[status(thm)],[c_4,c_10820]) ).
cnf(c_9430,plain,
join(a,meet(b,r2)) = join(a,b),
inference(copy,[status(thm)],[c_10821]) ).
cnf(c_10822,plain,
join(join(A,a),meet(b,r2)) = join(A,join(a,b)),
inference(paramod,[status(thm)],[c_9430,c_8]) ).
cnf(c_9450,plain,
join(meet(b,r2),join(A,a)) = join(A,join(a,b)),
inference(paramod,[status(thm)],[c_6,c_10822]) ).
cnf(c_9563,plain,
meet(b,join(r1,meet(b,A))) = meet(b,A),
inference(paramod,[status(thm)],[c_5,c_9129]) ).
cnf(c_9624,plain,
meet(join(a,b),join(r1,meet(b,A))) = meet(b,A),
inference(paramod,[status(thm)],[c_9563,c_8716]) ).
cnf(c_10823,plain,
join(a,join(meet(b,r2),join(r1,a))) = n1,
inference(paramod,[status(thm)],[c_9450,c_2695]) ).
cnf(c_10824,plain,
join(a,join(meet(b,r2),join(a,r1))) = n1,
inference(paramod,[status(thm)],[c_6,c_10823]) ).
cnf(c_10825,plain,
join(a,join(a,join(meet(b,r2),r1))) = n1,
inference(paramod,[status(thm)],[c_39,c_10824]) ).
cnf(c_10826,plain,
join(a,join(a,join(r1,meet(b,r2)))) = n1,
inference(paramod,[status(thm)],[c_6,c_10825]) ).
cnf(c_9774,plain,
join(a,join(r1,meet(b,r2))) = n1,
inference(paramod,[status(thm)],[c_33,c_10826]) ).
cnf(c_10827,plain,
( complement(a,join(r1,meet(b,r2)))
| meet(join(r1,meet(b,r2)),a) != n0 ),
inference(resolve,[status(thm)],[c_9774,c_57]) ).
cnf(c_10828,plain,
( complement(a,join(r1,meet(b,r2)))
| meet(a,join(r1,meet(b,r2))) != n0 ),
inference(paramod,[status(thm)],[c_5,c_10827]) ).
cnf(c_9815,plain,
meet(a,join(r1,meet(b,r2))) != n0,
inference(resolve,[status(thm)],[c_21,c_10828]) ).
cnf(c_10829,plain,
meet(a,meet(b,A)) = meet(a,join(r1,meet(b,A))),
inference(paramod,[status(thm)],[c_9624,c_28]) ).
cnf(c_10739,plain,
meet(a,join(r1,meet(b,A))) = meet(a,meet(b,A)),
inference(copy,[status(thm)],[c_10829]) ).
cnf(c_10830,plain,
meet(a,meet(b,r2)) != n0,
inference(paramod,[status(thm)],[c_10739,c_9815]) ).
cnf(c_10831,plain,
n0 != n0,
inference(paramod,[status(thm)],[c_64,c_10830]) ).
cnf(c_10750,plain,
$false,
inference(copy,[status(thm)],[c_10831]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 25 19:53:20 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.29 % Process 2847947 was started by sandbox2 on n012,
% 0.03/0.29 % Fri Sep 25 19:53:20 2026
% 0.03/0.29 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 92.30/12.42
% 92.30/12.42 % given #500 (T,wt=33): 1433 meet(A,meet(B,C)) != B | meet(B,meet(A,C)) = B. [para(5(a,1),632(a,1,2))].
% 92.30/12.42
% 92.30/12.42 % given #1000 (T,wt=33): 6498 join(A,meet(B,C)) != join(A,C) | join(A,meet(C,B)) = join(A,C). [para(6(a,1),6472(a,2))].
% 92.30/12.42
% 92.30/12.42 % SZS status Unsatisfiable for theBenchmark
% 92.30/12.42
% 92.30/12.42 % Proof 1 at 3.21 (+ 0.87) seconds.
% 92.30/12.42 % Length of proof is 83.
% 92.30/12.42 % Level of proof is 13.
% 92.30/12.42 % Maximum clause weight is 52.000.
% 92.30/12.42 % Given clauses 1188.
% 92.30/12.42
% 92.30/12.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------