%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT235-1 : 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 : n014.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 07:49:51 AM UTC 2026
% Result : Unsatisfiable 23.93s 3.67s
% Output : CNFRefutation 23.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 69 unt; 0 def)
% Number of atoms : 77 ( 76 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 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 : 98 ( 7 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(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_H34,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : meet(VAR_0,join(VAR_1,meet(VAR_2,VAR_3))) = meet(VAR_0,join(VAR_1,meet(VAR_2,join(VAR_1,meet(VAR_3,join(VAR_1,VAR_2)))))),
file('theBenchmark.p',equation_H34) ).
cnf(c_12,plain,
meet(A,join(B,meet(C,D))) = meet(A,join(B,meet(C,join(B,meet(D,join(B,C)))))),
inference(clausify,[status(thm)],[equation_H34]) ).
cnf(c_13,plain,
meet(A,join(B,meet(C,join(B,meet(D,join(B,C)))))) = meet(A,join(B,meet(C,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_5492,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_27,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_7,c_5492]) ).
cnf(c_36,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_40,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_5493,plain,
meet(join(A,meet(B,join(A,meet(C,join(A,B))))),join(A,meet(B,C))) = join(A,meet(B,join(A,meet(C,join(A,B))))),
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_5494,plain,
meet(join(A,meet(B,C)),join(A,meet(B,join(A,meet(C,join(A,B)))))) = join(A,meet(B,join(A,meet(C,join(A,B))))),
inference(paramod,[status(thm)],[c_5,c_5493]) ).
cnf(c_5495,plain,
meet(join(A,meet(B,C)),join(A,meet(B,C))) = join(A,meet(B,join(A,meet(C,join(A,B))))),
inference(paramod,[status(thm)],[c_13,c_5494]) ).
cnf(c_5496,plain,
join(A,meet(B,C)) = join(A,meet(B,join(A,meet(C,join(A,B))))),
inference(paramod,[status(thm)],[c_1,c_5495]) ).
cnf(c_44,plain,
join(A,meet(B,join(A,meet(C,join(A,B))))) = join(A,meet(B,C)),
inference(copy,[status(thm)],[c_5496]) ).
cnf(c_5497,plain,
join(b,a) = b,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_59,plain,
join(a,b) = b,
inference(paramod,[status(thm)],[c_6,c_5497]) ).
cnf(c_5498,plain,
A = meet(one,A),
inference(paramod,[status(thm)],[c_36,c_5]) ).
cnf(c_60,plain,
meet(one,A) = A,
inference(copy,[status(thm)],[c_5498]) ).
cnf(c_5499,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_40,c_6]) ).
cnf(c_63,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_5499]) ).
cnf(c_5500,plain,
join(join(A,a),b) = join(A,b),
inference(paramod,[status(thm)],[c_59,c_8]) ).
cnf(c_65,plain,
join(b,join(A,a)) = join(A,b),
inference(paramod,[status(thm)],[c_6,c_5500]) ).
cnf(c_75,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_63,c_18]) ).
cnf(c_133,plain,
meet(join(A,a),join(A,b)) = join(A,a),
inference(paramod,[status(thm)],[c_65,c_19]) ).
cnf(c_149,plain,
meet(join(a,A),join(A,b)) = join(A,a),
inference(paramod,[status(thm)],[c_6,c_133]) ).
cnf(c_5501,plain,
meet(one,join(complement(a),b)) = join(complement(a),a),
inference(paramod,[status(thm)],[c_9,c_149]) ).
cnf(c_5502,plain,
meet(one,join(b,complement(a))) = join(complement(a),a),
inference(paramod,[status(thm)],[c_6,c_5501]) ).
cnf(c_5503,plain,
join(b,complement(a)) = join(complement(a),a),
inference(paramod,[status(thm)],[c_60,c_5502]) ).
cnf(c_5504,plain,
join(b,complement(a)) = join(a,complement(a)),
inference(paramod,[status(thm)],[c_6,c_5503]) ).
cnf(c_182,plain,
join(b,complement(a)) = one,
inference(paramod,[status(thm)],[c_9,c_5504]) ).
cnf(c_5505,plain,
meet(A,zero) = meet(B,meet(A,complement(B))),
inference(paramod,[status(thm)],[c_10,c_27]) ).
cnf(c_5506,plain,
zero = meet(B,meet(A,complement(B))),
inference(paramod,[status(thm)],[c_75,c_5505]) ).
cnf(c_191,plain,
meet(A,meet(B,complement(A))) = zero,
inference(copy,[status(thm)],[c_5506]) ).
cnf(c_5507,plain,
join(A,meet(complement(A),join(A,meet(B,one)))) = join(A,meet(complement(A),B)),
inference(paramod,[status(thm)],[c_9,c_44]) ).
cnf(c_504,plain,
join(A,meet(complement(A),join(A,B))) = join(A,meet(complement(A),B)),
inference(paramod,[status(thm)],[c_36,c_5507]) ).
cnf(c_5508,plain,
join(b,meet(complement(b),one)) = join(b,meet(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_182,c_504]) ).
cnf(c_5509,plain,
join(b,meet(one,complement(b))) = join(b,meet(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_5,c_5508]) ).
cnf(c_5510,plain,
join(b,complement(b)) = join(b,meet(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_60,c_5509]) ).
cnf(c_5511,plain,
one = join(b,meet(complement(b),complement(a))),
inference(paramod,[status(thm)],[c_9,c_5510]) ).
cnf(c_5512,plain,
one = join(b,meet(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_5,c_5511]) ).
cnf(c_5320,plain,
join(b,meet(complement(a),complement(b))) = one,
inference(copy,[status(thm)],[c_5512]) ).
cnf(c_5513,plain,
( complement(A) = meet(B,complement(A))
| join(A,meet(B,complement(A))) != one ),
inference(resolve,[status(thm)],[c_11,c_191]) ).
cnf(c_5514,plain,
complement(b) = meet(complement(a),complement(b)),
inference(resolve,[status(thm)],[c_5513,c_5320]) ).
cnf(c_5490,plain,
meet(complement(a),complement(b)) = complement(b),
inference(copy,[status(thm)],[c_5514]) ).
cnf(c_5515,plain,
join(complement(a),complement(b)) = complement(a),
inference(paramod,[status(thm)],[c_5490,c_4]) ).
cnf(c_5491,plain,
$false,
inference(resolve,[status(thm)],[c_17,c_5515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.23 % Problem : LAT235-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.24 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.59 % Computer : n014.cluster.edu
% 0.10/0.59 % Model : x86_64 x86_64
% 0.10/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.59 % Memory : 8046.5625MB
% 0.10/0.59 % OS : Linux 6.8.0-71-generic
% 0.10/0.59 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Fri Sep 25 20:18:34 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.59 % Process 1009720 was started by sandbox on n014,
% 0.10/0.59 % Fri Sep 25 20:18:34 2026
% 0.10/0.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.60
% 0.10/0.60 % From the command line: assign(max_seconds, 300).
% 23.93/3.67
% 23.93/3.67 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 23.93/3.67
% 23.93/3.67 % SZS status Unsatisfiable for theBenchmark
% 23.93/3.67
% 23.93/3.67 % Proof 1 at 2.31 (+ 0.73) seconds.
% 23.93/3.67 % Length of proof is 35.
% 23.93/3.67 % Level of proof is 9.
% 23.93/3.67 % Maximum clause weight is 56.000.
% 23.93/3.67 % Given clauses 313.
% 23.93/3.67
% 23.93/3.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------