%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT249-1 : 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 : n016.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 2.24s 0.75s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 61 unt; 0 def)
% Number of atoms : 72 ( 71 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 : 8 ( 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 : 76 ( 6 sgn 22 !; 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(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_H64,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,VAR_2)) = meet(VAR_0,join(VAR_1,meet(VAR_0,join(VAR_2,meet(VAR_0,join(VAR_1,meet(VAR_0,VAR_2))))))),
file('theBenchmark.p',equation_H64) ).
cnf(c_12,plain,
meet(A,join(B,C)) = meet(A,join(B,meet(A,join(C,meet(A,join(B,meet(A,C))))))),
inference(clausify,[status(thm)],[equation_H64]) ).
cnf(c_13,plain,
meet(A,join(B,meet(A,join(C,meet(A,join(B,meet(A,C))))))) = 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_981,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_981]) ).
cnf(c_36,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_982,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_982]) ).
cnf(c_39,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_45,plain,
( complement(B) = A
| join(B,A) != one
| meet(A,B) != zero ),
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_983,plain,
meet(A,join(B,meet(A,join(complement(A),meet(A,join(B,zero)))))) = meet(A,join(B,complement(A))),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_55,plain,
meet(A,join(B,meet(A,join(complement(A),meet(A,B))))) = meet(A,join(B,complement(A))),
inference(paramod,[status(thm)],[c_39,c_983]) ).
cnf(c_984,plain,
meet(a,A) = meet(a,meet(b,A)),
inference(paramod,[status(thm)],[c_15,c_7]) ).
cnf(c_59,plain,
meet(a,meet(b,A)) = meet(a,A),
inference(copy,[status(thm)],[c_984]) ).
cnf(c_985,plain,
meet(A,zero) = meet(A,complement(A)),
inference(paramod,[status(thm)],[c_10,c_21]) ).
cnf(c_79,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_10,c_985]) ).
cnf(c_84,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_36,c_18]) ).
cnf(c_85,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_84,c_37]) ).
cnf(c_986,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_39,c_6]) ).
cnf(c_86,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_986]) ).
cnf(c_987,plain,
meet(a,zero) = meet(a,complement(b)),
inference(paramod,[status(thm)],[c_10,c_59]) ).
cnf(c_988,plain,
zero = meet(a,complement(b)),
inference(paramod,[status(thm)],[c_79,c_987]) ).
cnf(c_620,plain,
meet(a,complement(b)) = zero,
inference(copy,[status(thm)],[c_988]) ).
cnf(c_989,plain,
meet(a,join(complement(b),meet(a,join(complement(a),zero)))) = meet(a,join(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_620,c_55]) ).
cnf(c_990,plain,
meet(a,join(complement(b),meet(a,join(zero,complement(a))))) = meet(a,join(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_6,c_989]) ).
cnf(c_991,plain,
meet(a,join(complement(b),meet(a,complement(a)))) = meet(a,join(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_86,c_990]) ).
cnf(c_992,plain,
meet(a,join(complement(b),zero)) = meet(a,join(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_10,c_991]) ).
cnf(c_993,plain,
meet(a,join(zero,complement(b))) = meet(a,join(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_6,c_992]) ).
cnf(c_994,plain,
meet(a,complement(b)) = meet(a,join(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_86,c_993]) ).
cnf(c_995,plain,
zero = meet(a,join(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_620,c_994]) ).
cnf(c_996,plain,
zero = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_6,c_995]) ).
cnf(c_695,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(copy,[status(thm)],[c_996]) ).
cnf(c_997,plain,
( complement(A) = join(complement(A),B)
| meet(join(complement(A),B),A) != zero ),
inference(resolve,[status(thm)],[c_45,c_85]) ).
cnf(c_998,plain,
complement(a) != join(complement(a),complement(b)),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_999,plain,
meet(join(complement(a),complement(b)),a) != zero,
inference(resolve,[status(thm)],[c_997,c_998]) ).
cnf(c_1000,plain,
meet(a,join(complement(a),complement(b))) != zero,
inference(paramod,[status(thm)],[c_5,c_999]) ).
cnf(c_1001,plain,
zero != zero,
inference(paramod,[status(thm)],[c_695,c_1000]) ).
cnf(c_980,plain,
$false,
inference(copy,[status(thm)],[c_1001]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT249-1 : 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 : n016.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 20:25:14 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3207284 was started by sandbox on n016,
% 0.09/0.36 % Fri Sep 25 20:25:14 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 2.24/0.75
% 2.24/0.75 % SZS status Unsatisfiable for theBenchmark
% 2.24/0.75
% 2.24/0.75 % Proof 1 at 0.30 (+ 0.08) seconds.
% 2.24/0.75 % Length of proof is 31.
% 2.24/0.75 % Level of proof is 5.
% 2.24/0.75 % Maximum clause weight is 61.000.
% 2.24/0.75 % Given clauses 125.
% 2.24/0.75
% 2.24/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------