%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET082+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 : n007.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 08:35:41 AM UTC 2026
% Result : Theorem 25.83s 3.79s
% Output : CNFRefutation 25.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 71 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 56 ( 16 ~; 23 |; 11 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 3 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
fof(class_elements_are_sets,axiom,
! [X] : subclass(X,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
fof(unordered_pair_defn,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('theBenchmark.p',unordered_pair_defn) ).
fof(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('theBenchmark.p',singleton_set_defn) ).
fof(regularity,axiom,
! [X] :
( X != null_class
=> ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) ) ),
file('theBenchmark.p',regularity) ).
fof(singleton_is_null_class,conjecture,
! [X] :
( ~ member(X,universal_class)
=> singleton(X) = null_class ),
file('theBenchmark.p',singleton_is_null_class) ).
fof(singleton_is_null_class_neg,negated_conjecture,
~ ! [X] :
( ~ member(X,universal_class)
=> singleton(X) = null_class ),
inference(assume_negation,[status(cth)],[singleton_is_null_class]) ).
fof(nnf_42,plain,
? [X] :
( singleton(X) != null_class
& ~ member(X,universal_class) ),
inference(fof_nnf,[status(thm)],[singleton_is_null_class_neg]) ).
fof(sk_singleton_is_null_class_neg,plain,
( singleton(sK0) != null_class
& ~ member(sK0,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
singleton(sK0) != null_class,
inference(split_conjunct,[status(thm)],[sk_singleton_is_null_class_neg]) ).
cnf(c_65,negated_conjecture,
~ member(sK0,universal_class),
inference(split_conjunct,[status(thm)],[sk_singleton_is_null_class_neg]) ).
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_68,plain,
( member(sK1(A),A)
| null_class = A ),
inference(split_conjunct,[status(thm)],[sk_regularity]) ).
cnf(c_69,plain,
( member(sK1(A),universal_class)
| null_class = A ),
inference(split_conjunct,[status(thm)],[sk_regularity]) ).
cnf(c_128,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_132,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_137,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
cnf(c_140,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_defn]) ).
cnf(c_193,negated_conjecture,
unordered_pair(sK0,sK0) != null_class,
inference(paramod,[status(thm)],[c_128,c_64]) ).
cnf(c_11724,plain,
( null_class = unordered_pair(A,B)
| sK1(unordered_pair(A,B)) = B
| sK1(unordered_pair(A,B)) = A ),
inference(resolve,[status(thm)],[c_132,c_68]) ).
cnf(c_311,plain,
( unordered_pair(A,B) = null_class
| sK1(unordered_pair(A,B)) = B
| sK1(unordered_pair(A,B)) = A ),
inference(copy,[status(thm)],[c_11724]) ).
cnf(c_312,plain,
( unordered_pair(A,A) = null_class
| sK1(unordered_pair(A,A)) = A ),
inference(factor,[status(thm)],[c_311]) ).
cnf(c_11725,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_140,c_137]) ).
cnf(c_343,negated_conjecture,
~ member(sK0,A),
inference(resolve,[status(thm)],[c_11725,c_65]) ).
cnf(c_11726,plain,
( member(A,universal_class)
| null_class = unordered_pair(A,A)
| unordered_pair(A,A) = null_class ),
inference(paramod,[status(thm)],[c_312,c_69]) ).
cnf(c_11727,plain,
( member(A,universal_class)
| unordered_pair(A,A) = null_class
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_11726]) ).
cnf(c_5683,plain,
( member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_11727]) ).
cnf(c_11728,plain,
unordered_pair(sK0,sK0) = null_class,
inference(resolve,[status(thm)],[c_5683,c_343]) ).
cnf(c_11723,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_193,c_11728]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n007.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 07:02:08 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.42 % Process 3072328 was started by sandbox2 on n007,
% 0.17/0.42 % Sat Sep 26 07:02:08 2026
% 0.17/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 25.83/3.79
% 25.83/3.79 % given #500 (W,wt=16): 2090 -subclass(f2(null_class,universal_class),complement(c1)). [ur(140,b,1682,a,c,263,a)].
% 25.83/3.79
% 25.83/3.79 % SZS status Theorem for theBenchmark
% 25.83/3.79
% 25.83/3.79 % Proof 1 at 2.69 (+ 0.60) seconds.
% 25.83/3.79 % Length of proof is 20.
% 25.83/3.79 % Level of proof is 5.
% 25.83/3.79 % Maximum clause weight is 32.000.
% 25.83/3.79 % Given clauses 798.
% 25.83/3.79
% 25.83/3.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------