%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT251-1 : 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 0.22s 5.77s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 68 ( 64 unt; 0 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 14 ~; 7 |; 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 : 86 ( 11 sgn 23 !; 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_H69,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,VAR_2)) = join(meet(VAR_0,join(VAR_2,meet(VAR_0,VAR_1))),meet(VAR_0,join(VAR_1,meet(VAR_0,VAR_2)))),
file('theBenchmark.p',equation_H69) ).
cnf(c_12,plain,
meet(A,join(B,C)) = join(meet(A,join(C,meet(A,B))),meet(A,join(B,meet(A,C)))),
inference(clausify,[status(thm)],[equation_H69]) ).
cnf(c_13,plain,
join(meet(A,join(B,meet(A,C))),meet(A,join(C,meet(A,B)))) = meet(A,join(C,B)),
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_492,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_21,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_492]) ).
cnf(c_493,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_493]) ).
cnf(c_36,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_494,plain,
join(one,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_37,plain,
join(A,join(complement(A),B)) = join(one,B),
inference(copy,[status(thm)],[c_494]) ).
cnf(c_39,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_46,plain,
( complement(A) = B
| join(B,A) != one
| meet(A,B) != zero ),
inference(paramod,[status(thm)],[c_6,c_11]) ).
cnf(c_495,plain,
join(meet(A,join(B,zero)),meet(A,join(complement(A),meet(A,B)))) = meet(A,join(complement(A),B)),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_50,plain,
join(meet(A,B),meet(A,join(complement(A),meet(A,B)))) = meet(A,join(complement(A),B)),
inference(paramod,[status(thm)],[c_39,c_495]) ).
cnf(c_496,plain,
join(b,a) = b,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_62,plain,
join(a,b) = b,
inference(paramod,[status(thm)],[c_6,c_496]) ).
cnf(c_73,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_36,c_18]) ).
cnf(c_74,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_73,c_37]) ).
cnf(c_497,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_497]) ).
cnf(c_498,plain,
meet(A,zero) = meet(A,complement(A)),
inference(paramod,[status(thm)],[c_10,c_21]) ).
cnf(c_86,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_10,c_498]) ).
cnf(c_499,plain,
meet(A,zero) = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_10,c_24]) ).
cnf(c_500,plain,
zero = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_86,c_499]) ).
cnf(c_93,plain,
meet(A,complement(join(A,B))) = zero,
inference(copy,[status(thm)],[c_500]) ).
cnf(c_124,plain,
meet(a,complement(b)) = zero,
inference(paramod,[status(thm)],[c_62,c_93]) ).
cnf(c_501,plain,
join(zero,meet(a,join(complement(a),meet(a,complement(b))))) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_124,c_50]) ).
cnf(c_502,plain,
join(zero,meet(a,join(complement(a),zero))) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_124,c_501]) ).
cnf(c_503,plain,
join(zero,meet(a,join(zero,complement(a)))) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_6,c_502]) ).
cnf(c_504,plain,
join(zero,meet(a,complement(a))) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_75,c_503]) ).
cnf(c_505,plain,
join(zero,zero) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_10,c_504]) ).
cnf(c_506,plain,
zero = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_2,c_505]) ).
cnf(c_438,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(copy,[status(thm)],[c_506]) ).
cnf(c_507,plain,
( complement(a) = join(complement(a),complement(b))
| join(join(complement(a),complement(b)),a) != one ),
inference(resolve,[status(thm)],[c_46,c_438]) ).
cnf(c_508,plain,
complement(a) != join(complement(a),complement(b)),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_509,plain,
join(join(complement(a),complement(b)),a) != one,
inference(resolve,[status(thm)],[c_507,c_508]) ).
cnf(c_510,plain,
join(a,join(complement(a),complement(b))) != one,
inference(paramod,[status(thm)],[c_6,c_509]) ).
cnf(c_511,plain,
one != one,
inference(paramod,[status(thm)],[c_74,c_510]) ).
cnf(c_491,plain,
$false,
inference(copy,[status(thm)],[c_511]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT251-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.45 % Computer : n011.cluster.edu
% 0.15/5.45 % Model : x86_64 x86_64
% 0.15/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.45 % Memory : 8046.5625MB
% 0.15/5.45 % OS : Linux 6.8.0-71-generic
% 0.15/5.46 % CPULimit : 300
% 0.15/5.46 % WCLimit : 300
% 0.15/5.46 % DateTime : Fri Sep 25 20:20:19 UTC 2026
% 0.15/5.46 % CPUTime :
% 0.15/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.46 % Process 2792253 was started by sandbox on n011,
% 0.15/5.46 % Fri Sep 25 20:20:19 2026
% 0.15/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.47
% 0.15/5.47 % From the command line: assign(max_seconds, 300).
% 0.22/5.77
% 0.22/5.77 % SZS status Unsatisfiable for theBenchmark
% 0.22/5.77
% 0.22/5.77 % Proof 1 at 0.20 (+ 0.09) seconds.
% 0.22/5.77 % Length of proof is 34.
% 0.22/5.77 % Level of proof is 6.
% 0.22/5.77 % Maximum clause weight is 31.000.
% 0.22/5.77 % Given clauses 104.
% 0.22/5.77
% 0.22/5.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------