%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET064+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 08:35:34 AM UTC 2026
% Result : Theorem 0.24s 0.51s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 34 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 28 ( 9 ~; 8 |; 10 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 17 ( 1 sgn 10 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(regularity,axiom,
! [X] :
( X != null_class
=> ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) ) ),
file('theBenchmark.p',regularity) ).
fof(null_class_is_unique,conjecture,
! [Z] :
( ? [Y] : member(Y,Z)
| Z = null_class ),
file('theBenchmark.p',null_class_is_unique) ).
fof(null_class_is_unique_neg,negated_conjecture,
~ ! [Z] :
( ? [Y] : member(Y,Z)
| Z = null_class ),
inference(assume_negation,[status(cth)],[null_class_is_unique]) ).
fof(nnf_42,plain,
? [Z] :
( ! [Y] : ~ member(Y,Z)
& null_class != Z ),
inference(fof_nnf,[status(thm)],[null_class_is_unique_neg]) ).
fof(sk_null_class_is_unique_neg,plain,
( ! [Y] : ~ member(Y,sK0)
& null_class != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
~ member(A,sK0),
inference(split_conjunct,[status(thm)],[sk_null_class_is_unique_neg]) ).
cnf(c_65,negated_conjecture,
null_class != sK0,
inference(split_conjunct,[status(thm)],[sk_null_class_is_unique_neg]) ).
cnf(c_66,negated_conjecture,
sK0 != null_class,
inference(copy,[status(thm)],[c_65]) ).
fof(nnf_39,plain,
! [X] :
( ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) )
| null_class = X ),
inference(fof_nnf,[status(thm)],[regularity]) ).
fof(sk_regularity_sk,plain,
! [X] :
( ( disjoint(sK1(X),X)
& member(sK1(X),X)
& member(sK1(X),universal_class) )
| null_class = X ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U,sK1(X))],[nnf_39]) ).
fof(sk_regularity,plain,
( ! [VAR_0] :
( disjoint(sK1(VAR_0),VAR_0)
| null_class = VAR_0 )
& ! [VAR_0] :
( member(sK1(VAR_0),VAR_0)
| null_class = VAR_0 )
& ! [VAR_0] :
( member(sK1(VAR_0),universal_class)
| null_class = VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_regularity_sk]) ).
cnf(c_69,plain,
( member(sK1(A),A)
| null_class = A ),
inference(split_conjunct,[status(thm)],[sk_regularity]) ).
cnf(c_200,negated_conjecture,
null_class = sK0,
inference(resolve,[status(thm)],[c_69,c_64]) ).
cnf(c_201,negated_conjecture,
sK0 = null_class,
inference(copy,[status(thm)],[c_200]) ).
cnf(c_199,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_66,c_201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET064+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n005.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 07:01:34 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 1501406 was started by sandbox2 on n005,
% 0.19/0.46 % Sat Sep 26 07:01:34 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 0.24/0.51
% 0.24/0.51 % SZS status Theorem for theBenchmark
% 0.24/0.51
% 0.24/0.51 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.24/0.51 % Length of proof is 7.
% 0.24/0.51 % Level of proof is 3.
% 0.24/0.51 % Maximum clause weight is 7.000.
% 0.24/0.51 % Given clauses 8.
% 0.24/0.51
% 0.24/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------