%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT240-1 : 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 : n004.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 07:49:52 AM UTC 2026
% Result : Unsatisfiable 182.11s 24.53s
% Output : CNFRefutation 182.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 83 ( 76 unt; 0 def)
% Number of atoms : 92 ( 91 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 116 ( 11 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_H50,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_0,meet(VAR_2,join(VAR_1,VAR_3)))))),
file('theBenchmark.p',equation_H50) ).
cnf(c_12,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(A,meet(C,join(B,D)))))),
inference(clausify,[status(thm)],[equation_H50]) ).
cnf(c_13,plain,
meet(A,join(B,meet(C,join(A,meet(C,join(B,D)))))) = meet(A,join(B,meet(C,join(A,D)))),
inference(copy,[status(thm)],[c_12]) ).
fof(prove_distributivity_hypothesis,axiom,
meet(b,a) = a,
file('theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(c_14,plain,
meet(b,a) = a,
inference(clausify,[status(thm)],[prove_distributivity_hypothesis]) ).
fof(prove_distributivity,axiom,
join(complement(b),complement(a)) != complement(a),
file('theBenchmark.p',prove_distributivity) ).
cnf(c_15,plain,
join(complement(b),complement(a)) != complement(a),
inference(clausify,[status(thm)],[prove_distributivity]) ).
cnf(c_16,plain,
meet(join(A,B),A) = A,
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_18,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_18142,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_20,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_18142]) ).
cnf(c_26,plain,
meet(A,meet(B,C)) = meet(C,meet(A,B)),
inference(paramod,[status(thm)],[c_7,c_5]) ).
cnf(c_45,plain,
join(join(A,B),C) = join(A,join(C,B)),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_52,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_18143,plain,
one = join(complement(A),A),
inference(paramod,[status(thm)],[c_9,c_6]) ).
cnf(c_53,plain,
join(complement(A),A) = one,
inference(copy,[status(thm)],[c_18143]) ).
cnf(c_18144,plain,
join(one,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_18145,plain,
join(one,A) = join(join(B,A),complement(B)),
inference(paramod,[status(thm)],[c_45,c_18144]) ).
cnf(c_54,plain,
join(join(A,B),complement(A)) = join(one,B),
inference(copy,[status(thm)],[c_18145]) ).
cnf(c_56,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_18146,plain,
zero = meet(complement(A),A),
inference(paramod,[status(thm)],[c_10,c_5]) ).
cnf(c_57,plain,
meet(complement(A),A) = zero,
inference(copy,[status(thm)],[c_18146]) ).
cnf(c_84,plain,
join(b,a) = b,
inference(paramod,[status(thm)],[c_14,c_4]) ).
cnf(c_88,plain,
join(complement(a),complement(b)) != complement(a),
inference(paramod,[status(thm)],[c_6,c_15]) ).
cnf(c_109,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_52,c_16]) ).
cnf(c_110,plain,
join(join(A,B),complement(A)) = one,
inference(paramod,[status(thm)],[c_109,c_54]) ).
cnf(c_18147,plain,
b = join(a,b),
inference(paramod,[status(thm)],[c_84,c_6]) ).
cnf(c_118,plain,
join(a,b) = b,
inference(copy,[status(thm)],[c_18147]) ).
cnf(c_18148,plain,
join(b,A) = join(b,join(a,A)),
inference(paramod,[status(thm)],[c_84,c_8]) ).
cnf(c_119,plain,
join(b,join(a,A)) = join(b,A),
inference(copy,[status(thm)],[c_18148]) ).
cnf(c_18149,plain,
meet(A,zero) = meet(A,complement(A)),
inference(paramod,[status(thm)],[c_10,c_20]) ).
cnf(c_135,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_10,c_18149]) ).
cnf(c_18150,plain,
( complement(complement(A)) = A
| meet(complement(A),A) != zero ),
inference(resolve,[status(thm)],[c_53,c_11]) ).
cnf(c_18151,plain,
( complement(complement(A)) = A
| zero != zero ),
inference(paramod,[status(thm)],[c_57,c_18150]) ).
cnf(c_178,plain,
complement(complement(A)) = A,
inference(copy,[status(thm)],[c_18151]) ).
cnf(c_18152,plain,
join(one,A) = join(complement(B),join(B,A)),
inference(paramod,[status(thm)],[c_53,c_8]) ).
cnf(c_18153,plain,
one = join(complement(B),join(B,A)),
inference(paramod,[status(thm)],[c_109,c_18152]) ).
cnf(c_179,plain,
join(complement(A),join(A,B)) = one,
inference(copy,[status(thm)],[c_18153]) ).
cnf(c_18154,plain,
meet(A,zero) = meet(complement(B),meet(A,B)),
inference(paramod,[status(thm)],[c_10,c_26]) ).
cnf(c_18155,plain,
zero = meet(complement(B),meet(A,B)),
inference(paramod,[status(thm)],[c_135,c_18154]) ).
cnf(c_198,plain,
meet(complement(A),meet(B,A)) = zero,
inference(copy,[status(thm)],[c_18155]) ).
cnf(c_301,plain,
join(b,complement(a)) = one,
inference(paramod,[status(thm)],[c_118,c_110]) ).
cnf(c_18156,plain,
one = join(complement(a),b),
inference(paramod,[status(thm)],[c_301,c_6]) ).
cnf(c_307,plain,
join(complement(a),b) = one,
inference(copy,[status(thm)],[c_18156]) ).
cnf(c_18157,plain,
meet(A,join(complement(a),meet(B,join(A,meet(B,one))))) = meet(A,join(complement(a),meet(B,join(A,b)))),
inference(paramod,[status(thm)],[c_307,c_13]) ).
cnf(c_18158,plain,
meet(A,join(complement(a),meet(B,join(A,B)))) = meet(A,join(complement(a),meet(B,join(A,b)))),
inference(paramod,[status(thm)],[c_52,c_18157]) ).
cnf(c_18159,plain,
meet(A,join(complement(a),B)) = meet(A,join(complement(a),meet(B,join(A,b)))),
inference(paramod,[status(thm)],[c_18,c_18158]) ).
cnf(c_313,plain,
meet(A,join(complement(a),meet(B,join(A,b)))) = meet(A,join(complement(a),B)),
inference(copy,[status(thm)],[c_18159]) ).
cnf(c_18160,plain,
( complement(complement(A)) = join(A,B)
| meet(complement(A),join(A,B)) != zero ),
inference(resolve,[status(thm)],[c_179,c_11]) ).
cnf(c_18161,plain,
( A = join(A,B)
| meet(complement(A),join(A,B)) != zero ),
inference(paramod,[status(thm)],[c_178,c_18160]) ).
cnf(c_470,plain,
( join(A,B) = A
| meet(complement(A),join(A,B)) != zero ),
inference(copy,[status(thm)],[c_18161]) ).
cnf(c_772,plain,
meet(join(a,A),join(b,A)) = join(a,A),
inference(paramod,[status(thm)],[c_119,c_18]) ).
cnf(c_1216,plain,
meet(complement(join(b,A)),join(a,A)) = zero,
inference(paramod,[status(thm)],[c_772,c_198]) ).
cnf(c_18162,plain,
meet(complement(complement(a)),join(complement(a),complement(b))) != zero,
inference(resolve,[status(thm)],[c_470,c_88]) ).
cnf(c_3457,plain,
meet(a,join(complement(a),complement(b))) != zero,
inference(paramod,[status(thm)],[c_178,c_18162]) ).
cnf(c_18163,plain,
meet(a,join(complement(a),zero)) = meet(a,join(complement(a),complement(join(b,b)))),
inference(paramod,[status(thm)],[c_1216,c_313]) ).
cnf(c_18164,plain,
meet(a,complement(a)) = meet(a,join(complement(a),complement(join(b,b)))),
inference(paramod,[status(thm)],[c_56,c_18163]) ).
cnf(c_18165,plain,
zero = meet(a,join(complement(a),complement(join(b,b)))),
inference(paramod,[status(thm)],[c_10,c_18164]) ).
cnf(c_18166,plain,
zero = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_2,c_18165]) ).
cnf(c_18167,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(copy,[status(thm)],[c_18166]) ).
cnf(c_18141,plain,
$false,
inference(resolve,[status(thm)],[c_3457,c_18167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT240-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n004.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 20:19:06 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 4003857 was started by sandbox2 on n004,
% 0.16/0.44 % Fri Sep 25 20:19:06 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 182.11/24.53
% 182.11/24.53 % given #500 (T,wt=32): 17059 meet(join(A,meet(B,C)),complement(join(B,A))) = zero. [para(6(a,1),15683(a,1,2,1))].
% 182.11/24.53
% 182.11/24.53 % SZS status Unsatisfiable for theBenchmark
% 182.11/24.53
% 182.11/24.53 % Proof 1 at 6.77 (+ 1.20) seconds.
% 182.11/24.53 % Length of proof is 43.
% 182.11/24.53 % Level of proof is 7.
% 182.11/24.53 % Maximum clause weight is 58.000.
% 182.11/24.53 % Given clauses 506.
% 182.11/24.53
% 182.11/24.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------