%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT237-1 : 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 : n013.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 5.58s 1.20s
% Output : CNFRefutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 64 unt; 0 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 5 |; 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 : 100 ( 19 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_H40,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_3,meet(VAR_2,join(VAR_0,VAR_1)))))),
file('theBenchmark.p',equation_H40) ).
cnf(c_12,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(D,meet(C,join(A,B)))))),
inference(clausify,[status(thm)],[equation_H40]) ).
cnf(c_13,plain,
meet(A,join(B,meet(C,join(D,meet(C,join(A,B)))))) = 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]) ).
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_19,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_1920,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_1920]) ).
cnf(c_36,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_1921,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_1921]) ).
cnf(c_39,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_1922,plain,
meet(A,join(complement(A),meet(B,join(C,meet(B,one))))) = meet(A,join(complement(A),meet(B,join(A,C)))),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_1923,plain,
meet(A,join(complement(A),meet(B,join(C,B)))) = meet(A,join(complement(A),meet(B,join(A,C)))),
inference(paramod,[status(thm)],[c_36,c_1922]) ).
cnf(c_1924,plain,
meet(A,join(complement(A),B)) = meet(A,join(complement(A),meet(B,join(A,C)))),
inference(paramod,[status(thm)],[c_19,c_1923]) ).
cnf(c_64,plain,
meet(A,join(complement(A),meet(B,join(A,C)))) = meet(A,join(complement(A),B)),
inference(copy,[status(thm)],[c_1924]) ).
cnf(c_1925,plain,
join(b,a) = b,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_76,plain,
join(a,b) = b,
inference(paramod,[status(thm)],[c_6,c_1925]) ).
cnf(c_78,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_36,c_18]) ).
cnf(c_79,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_78,c_37]) ).
cnf(c_1926,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_39,c_6]) ).
cnf(c_80,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_1926]) ).
cnf(c_1927,plain,
join(join(A,a),b) = join(A,b),
inference(paramod,[status(thm)],[c_76,c_8]) ).
cnf(c_83,plain,
join(b,join(A,a)) = join(A,b),
inference(paramod,[status(thm)],[c_6,c_1927]) ).
cnf(c_93,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_80,c_18]) ).
cnf(c_1928,plain,
( complement(A) = join(complement(A),B)
| meet(A,join(complement(A),B)) != zero ),
inference(resolve,[status(thm)],[c_11,c_79]) ).
cnf(c_1929,plain,
complement(a) != join(complement(a),complement(b)),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_100,plain,
meet(a,join(complement(a),complement(b))) != zero,
inference(resolve,[status(thm)],[c_1928,c_1929]) ).
cnf(c_1930,plain,
meet(A,zero) = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_10,c_24]) ).
cnf(c_1931,plain,
zero = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_93,c_1930]) ).
cnf(c_134,plain,
meet(A,complement(join(A,B))) = zero,
inference(copy,[status(thm)],[c_1931]) ).
cnf(c_156,plain,
meet(A,complement(join(B,A))) = zero,
inference(paramod,[status(thm)],[c_6,c_134]) ).
cnf(c_228,plain,
join(b,join(A,a)) = join(b,A),
inference(paramod,[status(thm)],[c_83,c_6]) ).
cnf(c_327,plain,
meet(join(A,a),complement(join(b,A))) = zero,
inference(paramod,[status(thm)],[c_228,c_156]) ).
cnf(c_1932,plain,
meet(join(meet(b,A),a),complement(b)) = zero,
inference(paramod,[status(thm)],[c_4,c_327]) ).
cnf(c_1124,plain,
meet(join(a,meet(b,A)),complement(b)) = zero,
inference(paramod,[status(thm)],[c_6,c_1932]) ).
cnf(c_1933,plain,
zero = meet(complement(b),join(a,meet(b,A))),
inference(paramod,[status(thm)],[c_1124,c_5]) ).
cnf(c_1621,plain,
meet(complement(b),join(a,meet(b,A))) = zero,
inference(copy,[status(thm)],[c_1933]) ).
cnf(c_1934,plain,
meet(a,join(complement(a),zero)) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_1621,c_64]) ).
cnf(c_1935,plain,
meet(a,join(zero,complement(a))) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_6,c_1934]) ).
cnf(c_1936,plain,
meet(a,complement(a)) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_80,c_1935]) ).
cnf(c_1937,plain,
zero = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_10,c_1936]) ).
cnf(c_1918,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(copy,[status(thm)],[c_1937]) ).
cnf(c_1919,plain,
$false,
inference(resolve,[status(thm)],[c_1918,c_100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT237-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 20:18:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1107860 was started by sandbox on n013,
% 0.11/0.37 % Fri Sep 25 20:18:22 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 5.58/1.20
% 5.58/1.20 % SZS status Unsatisfiable for theBenchmark
% 5.58/1.20
% 5.58/1.20 % Proof 1 at 0.59 (+ 0.18) seconds.
% 5.58/1.20 % Length of proof is 37.
% 5.58/1.20 % Level of proof is 10.
% 5.58/1.20 % Maximum clause weight is 23.000.
% 5.58/1.20 % Given clauses 189.
% 5.58/1.20
% 5.58/1.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------