%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT244-1 : 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 : n011.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 07:49:53 AM UTC 2026
% Result : Unsatisfiable 55.69s 8.93s
% Output : CNFRefutation 55.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 57 unt; 0 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 75 ( 9 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_H58,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,VAR_2)) = meet(VAR_0,join(VAR_1,meet(join(VAR_0,VAR_1),join(VAR_2,meet(VAR_0,VAR_1))))),
file('theBenchmark.p',equation_H58) ).
cnf(c_12,plain,
meet(A,join(B,C)) = meet(A,join(B,meet(join(A,B),join(C,meet(A,B))))),
inference(clausify,[status(thm)],[equation_H58]) ).
cnf(c_13,plain,
meet(A,join(B,meet(join(A,B),join(C,meet(A,B))))) = meet(A,join(B,C)),
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]) ).
cnf(c_15,plain,
meet(a,b) = a,
inference(paramod,[status(thm)],[c_5,c_14]) ).
fof(prove_distributivity,axiom,
join(complement(b),complement(a)) != complement(a),
file('theBenchmark.p',prove_distributivity) ).
cnf(c_16,plain,
join(complement(b),complement(a)) != complement(a),
inference(clausify,[status(thm)],[prove_distributivity]) ).
cnf(c_17,plain,
join(complement(a),complement(b)) != complement(a),
inference(paramod,[status(thm)],[c_6,c_16]) ).
cnf(c_18,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_20028,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_24,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_20028]) ).
cnf(c_20029,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_29,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_20029]) ).
cnf(c_20030,plain,
one = join(A,join(B,complement(join(A,B)))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_38,plain,
join(A,join(B,complement(join(A,B)))) = one,
inference(copy,[status(thm)],[c_20030]) ).
cnf(c_39,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_20031,plain,
join(b,a) = b,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_69,plain,
join(a,b) = b,
inference(paramod,[status(thm)],[c_6,c_20031]) ).
cnf(c_20032,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_39,c_6]) ).
cnf(c_75,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_20032]) ).
cnf(c_90,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_75,c_18]) ).
cnf(c_20033,plain,
meet(A,zero) = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_10,c_24]) ).
cnf(c_20034,plain,
zero = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_90,c_20033]) ).
cnf(c_132,plain,
meet(A,complement(join(A,B))) = zero,
inference(copy,[status(thm)],[c_20034]) ).
cnf(c_144,plain,
meet(a,complement(b)) = zero,
inference(paramod,[status(thm)],[c_69,c_132]) ).
cnf(c_20035,plain,
meet(a,join(complement(b),meet(join(a,complement(b)),join(A,zero)))) = meet(a,join(complement(b),A)),
inference(paramod,[status(thm)],[c_144,c_13]) ).
cnf(c_146,plain,
meet(a,join(complement(b),meet(join(a,complement(b)),A))) = meet(a,join(complement(b),A)),
inference(paramod,[status(thm)],[c_39,c_20035]) ).
cnf(c_20036,plain,
meet(a,join(complement(b),zero)) = meet(a,join(complement(b),complement(join(a,complement(b))))),
inference(paramod,[status(thm)],[c_10,c_146]) ).
cnf(c_20037,plain,
meet(a,join(zero,complement(b))) = meet(a,join(complement(b),complement(join(a,complement(b))))),
inference(paramod,[status(thm)],[c_6,c_20036]) ).
cnf(c_20038,plain,
meet(a,complement(b)) = meet(a,join(complement(b),complement(join(a,complement(b))))),
inference(paramod,[status(thm)],[c_75,c_20037]) ).
cnf(c_20039,plain,
zero = meet(a,join(complement(b),complement(join(a,complement(b))))),
inference(paramod,[status(thm)],[c_144,c_20038]) ).
cnf(c_5819,plain,
meet(a,join(complement(b),complement(join(a,complement(b))))) = zero,
inference(copy,[status(thm)],[c_20039]) ).
cnf(c_20040,plain,
( complement(a) = join(complement(b),complement(join(a,complement(b))))
| join(a,join(complement(b),complement(join(a,complement(b))))) != one ),
inference(resolve,[status(thm)],[c_11,c_5819]) ).
cnf(c_20041,plain,
complement(a) = join(complement(b),complement(join(a,complement(b)))),
inference(resolve,[status(thm)],[c_20040,c_38]) ).
cnf(c_20020,plain,
join(complement(b),complement(join(a,complement(b)))) = complement(a),
inference(copy,[status(thm)],[c_20041]) ).
cnf(c_20042,plain,
join(complement(b),complement(a)) = join(complement(b),complement(join(a,complement(b)))),
inference(paramod,[status(thm)],[c_20020,c_29]) ).
cnf(c_20043,plain,
join(complement(a),complement(b)) = join(complement(b),complement(join(a,complement(b)))),
inference(paramod,[status(thm)],[c_6,c_20042]) ).
cnf(c_20026,plain,
join(complement(a),complement(b)) = complement(a),
inference(paramod,[status(thm)],[c_20020,c_20043]) ).
cnf(c_20027,plain,
$false,
inference(resolve,[status(thm)],[c_20026,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT244-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 20:19:29 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 2791155 was started by sandbox on n011,
% 0.12/0.36 % Fri Sep 25 20:19:29 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 55.69/8.93
% 55.69/8.93 % given #500 (T,wt=12): 2493 join(A,join(B,join(b,complement(join(A,a))))) = one. [para(1535(a,1),35(a,1,2)),rewrite([87(2)]),flip(a)].
% 55.69/8.93
% 55.69/8.93 % SZS status Unsatisfiable for theBenchmark
% 55.69/8.93
% 55.69/8.93 % Proof 1 at 6.87 (+ 1.65) seconds.
% 55.69/8.93 % Length of proof is 31.
% 55.69/8.93 % Level of proof is 10.
% 55.69/8.93 % Maximum clause weight is 19.000.
% 55.69/8.93 % Given clauses 681.
% 55.69/8.93
% 55.69/8.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------