%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT257-1 : 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 : n009.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 07:49:54 AM UTC 2026
% Result : Unsatisfiable 11.68s 2.16s
% Output : CNFRefutation 11.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 76 ( 72 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 110 ( 16 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_H82,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(meet(VAR_1,join(VAR_0,VAR_2)),meet(VAR_2,join(VAR_0,VAR_1)))) = join(meet(VAR_0,VAR_1),meet(VAR_0,VAR_2)),
file('theBenchmark.p',equation_H82) ).
cnf(c_12,plain,
meet(A,join(meet(B,join(A,C)),meet(C,join(A,B)))) = join(meet(A,B),meet(A,C)),
inference(clausify,[status(thm)],[equation_H82]) ).
fof(prove_distributivity_hypothesis,axiom,
meet(b,a) = a,
file('theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(c_13,plain,
meet(b,a) = a,
inference(clausify,[status(thm)],[prove_distributivity_hypothesis]) ).
cnf(c_14,plain,
meet(a,b) = a,
inference(paramod,[status(thm)],[c_5,c_13]) ).
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,
join(complement(a),complement(b)) != complement(a),
inference(paramod,[status(thm)],[c_6,c_15]) ).
cnf(c_17,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_18,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_1555,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_1555]) ).
cnf(c_1556,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_26,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_7,c_1556]) ).
cnf(c_1557,plain,
join(A,B) = join(A,join(meet(A,C),B)),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_32,plain,
join(A,join(meet(A,B),C)) = join(A,C),
inference(copy,[status(thm)],[c_1557]) ).
cnf(c_35,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_1558,plain,
join(one,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_36,plain,
join(A,join(complement(A),B)) = join(one,B),
inference(copy,[status(thm)],[c_1558]) ).
cnf(c_38,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_44,plain,
( complement(B) = A
| join(B,A) != one
| meet(A,B) != zero ),
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_1559,plain,
meet(A,join(meet(B,one),meet(complement(A),join(A,B)))) = join(meet(A,B),meet(A,complement(A))),
inference(paramod,[status(thm)],[c_9,c_12]) ).
cnf(c_1560,plain,
meet(A,join(B,meet(complement(A),join(A,B)))) = join(meet(A,B),meet(A,complement(A))),
inference(paramod,[status(thm)],[c_35,c_1559]) ).
cnf(c_1561,plain,
meet(A,join(B,meet(complement(A),join(A,B)))) = join(meet(A,B),zero),
inference(paramod,[status(thm)],[c_10,c_1560]) ).
cnf(c_50,plain,
meet(A,join(B,meet(complement(A),join(A,B)))) = join(zero,meet(A,B)),
inference(paramod,[status(thm)],[c_6,c_1561]) ).
cnf(c_1562,plain,
meet(a,A) = meet(a,meet(b,A)),
inference(paramod,[status(thm)],[c_14,c_7]) ).
cnf(c_51,plain,
meet(a,meet(b,A)) = meet(a,A),
inference(copy,[status(thm)],[c_1562]) ).
cnf(c_1563,plain,
A = meet(one,A),
inference(paramod,[status(thm)],[c_35,c_5]) ).
cnf(c_70,plain,
meet(one,A) = A,
inference(copy,[status(thm)],[c_1563]) ).
cnf(c_72,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_35,c_17]) ).
cnf(c_73,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_72,c_36]) ).
cnf(c_1564,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_38,c_6]) ).
cnf(c_74,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_1564]) ).
cnf(c_79,plain,
meet(A,join(B,meet(complement(A),join(A,B)))) = meet(A,B),
inference(paramod,[status(thm)],[c_74,c_50]) ).
cnf(c_88,plain,
join(A,one) = one,
inference(paramod,[status(thm)],[c_70,c_18]) ).
cnf(c_1565,plain,
meet(A,zero) = meet(A,complement(A)),
inference(paramod,[status(thm)],[c_10,c_20]) ).
cnf(c_91,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_10,c_1565]) ).
cnf(c_1566,plain,
meet(A,zero) = meet(B,meet(A,complement(B))),
inference(paramod,[status(thm)],[c_10,c_26]) ).
cnf(c_1567,plain,
zero = meet(B,meet(A,complement(B))),
inference(paramod,[status(thm)],[c_91,c_1566]) ).
cnf(c_111,plain,
meet(A,meet(B,complement(A))) = zero,
inference(copy,[status(thm)],[c_1567]) ).
cnf(c_1568,plain,
join(A,one) = join(A,complement(meet(A,B))),
inference(paramod,[status(thm)],[c_9,c_32]) ).
cnf(c_1569,plain,
one = join(A,complement(meet(A,B))),
inference(paramod,[status(thm)],[c_88,c_1568]) ).
cnf(c_173,plain,
join(A,complement(meet(A,B))) = one,
inference(copy,[status(thm)],[c_1569]) ).
cnf(c_188,plain,
join(A,complement(meet(B,A))) = one,
inference(paramod,[status(thm)],[c_5,c_173]) ).
cnf(c_200,plain,
join(b,complement(a)) = one,
inference(paramod,[status(thm)],[c_14,c_188]) ).
cnf(c_1570,plain,
( complement(A) = join(complement(A),B)
| meet(join(complement(A),B),A) != zero ),
inference(resolve,[status(thm)],[c_44,c_73]) ).
cnf(c_1571,plain,
complement(a) != join(complement(a),complement(b)),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_1572,plain,
meet(join(complement(a),complement(b)),a) != zero,
inference(resolve,[status(thm)],[c_1570,c_1571]) ).
cnf(c_577,plain,
meet(a,join(complement(a),complement(b))) != zero,
inference(paramod,[status(thm)],[c_5,c_1572]) ).
cnf(c_1573,plain,
meet(b,join(complement(a),meet(complement(b),one))) = meet(b,complement(a)),
inference(paramod,[status(thm)],[c_200,c_79]) ).
cnf(c_1574,plain,
meet(b,join(complement(a),meet(one,complement(b)))) = meet(b,complement(a)),
inference(paramod,[status(thm)],[c_5,c_1573]) ).
cnf(c_595,plain,
meet(b,join(complement(a),complement(b))) = meet(b,complement(a)),
inference(paramod,[status(thm)],[c_70,c_1574]) ).
cnf(c_1575,plain,
meet(a,meet(b,complement(a))) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_595,c_51]) ).
cnf(c_1576,plain,
zero = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_111,c_1575]) ).
cnf(c_1553,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(copy,[status(thm)],[c_1576]) ).
cnf(c_1554,plain,
$false,
inference(resolve,[status(thm)],[c_1553,c_577]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT257-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 20:20:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2453591 was started by sandbox on n009,
% 0.08/0.36 % Fri Sep 25 20:20:43 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 11.68/2.16
% 11.68/2.16 % SZS status Unsatisfiable for theBenchmark
% 11.68/2.16
% 11.68/2.16 % Proof 1 at 1.02 (+ 0.32) seconds.
% 11.68/2.16 % Length of proof is 41.
% 11.68/2.16 % Level of proof is 9.
% 11.68/2.16 % Maximum clause weight is 31.000.
% 11.68/2.16 % Given clauses 270.
% 11.68/2.16
% 11.68/2.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------