%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET071+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 : n012.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 08:35:37 AM UTC 2026
% Result : Theorem 15.30s 2.50s
% Output : CNFRefutation 15.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 22 unt; 0 def)
% Number of atoms : 114 ( 48 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 29 ~; 40 |; 15 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 13 sgn 18 !; 4 ?)
% 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(null_class_defn,axiom,
! [X] : ~ member(X,null_class),
file('theBenchmark.p',null_class_defn) ).
fof(regularity,axiom,
! [X] :
( X != null_class
=> ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) ) ),
file('theBenchmark.p',regularity) ).
fof(null_unordered_pair,conjecture,
! [X,Y] :
( ( ~ member(Y,universal_class)
& ~ member(X,universal_class) )
=> unordered_pair(X,Y) = null_class ),
file('theBenchmark.p',null_unordered_pair) ).
fof(null_unordered_pair_neg,negated_conjecture,
~ ! [X,Y] :
( ( ~ member(Y,universal_class)
& ~ member(X,universal_class) )
=> unordered_pair(X,Y) = null_class ),
inference(assume_negation,[status(cth)],[null_unordered_pair]) ).
fof(nnf_42,plain,
? [X,Y] :
( unordered_pair(X,Y) != null_class
& ~ member(Y,universal_class)
& ~ member(X,universal_class) ),
inference(fof_nnf,[status(thm)],[null_unordered_pair_neg]) ).
fof(sk_null_unordered_pair_neg,plain,
( unordered_pair(sK0,sK1) != null_class
& ~ member(sK1,universal_class)
& ~ member(sK0,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
unordered_pair(sK0,sK1) != null_class,
inference(split_conjunct,[status(thm)],[sk_null_unordered_pair_neg]) ).
cnf(c_65,negated_conjecture,
~ member(sK1,universal_class),
inference(split_conjunct,[status(thm)],[sk_null_unordered_pair_neg]) ).
cnf(c_66,negated_conjecture,
~ member(sK0,universal_class),
inference(split_conjunct,[status(thm)],[sk_null_unordered_pair_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(sK2(X),X)
& member(sK2(X),X)
& member(sK2(X),universal_class) )
| null_class = X ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U,sK2(X))],[nnf_39]) ).
fof(sk_regularity,plain,
( ! [VAR_0] :
( disjoint(sK2(VAR_0),VAR_0)
| null_class = VAR_0 )
& ! [VAR_0] :
( member(sK2(VAR_0),VAR_0)
| null_class = VAR_0 )
& ! [VAR_0] :
( member(sK2(VAR_0),universal_class)
| null_class = VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_regularity_sk]) ).
cnf(c_69,plain,
( member(sK2(A),A)
| null_class = A ),
inference(split_conjunct,[status(thm)],[sk_regularity]) ).
cnf(c_70,plain,
( member(sK2(A),universal_class)
| null_class = A ),
inference(split_conjunct,[status(thm)],[sk_regularity]) ).
cnf(c_110,plain,
~ member(A,null_class),
inference(clausify,[status(thm)],[null_class_defn]) ).
cnf(c_132,plain,
( A != B
| ~ member(A,universal_class)
| member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_133,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_138,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
cnf(c_141,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_defn]) ).
cnf(c_14394,negated_conjecture,
null_class != unordered_pair(sK0,sK1),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_200,negated_conjecture,
member(sK2(unordered_pair(sK0,sK1)),unordered_pair(sK0,sK1)),
inference(resolve,[status(thm)],[c_69,c_14394]) ).
cnf(c_14395,negated_conjecture,
null_class != unordered_pair(sK0,sK1),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_218,negated_conjecture,
member(sK2(unordered_pair(sK0,sK1)),universal_class),
inference(resolve,[status(thm)],[c_70,c_14395]) ).
cnf(c_397,plain,
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
inference(xxres,[status(thm)],[c_132]) ).
cnf(c_14396,plain,
( null_class = unordered_pair(A,B)
| sK2(unordered_pair(A,B)) = B
| sK2(unordered_pair(A,B)) = A ),
inference(resolve,[status(thm)],[c_133,c_69]) ).
cnf(c_398,plain,
( unordered_pair(A,B) = null_class
| sK2(unordered_pair(A,B)) = B
| sK2(unordered_pair(A,B)) = A ),
inference(copy,[status(thm)],[c_14396]) ).
cnf(c_14397,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_141,c_138]) ).
cnf(c_477,negated_conjecture,
~ member(sK0,A),
inference(resolve,[status(thm)],[c_14397,c_66]) ).
cnf(c_14398,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_141,c_138]) ).
cnf(c_478,negated_conjecture,
~ member(sK1,A),
inference(resolve,[status(thm)],[c_14398,c_65]) ).
cnf(c_14360,plain,
member(sK2(unordered_pair(sK0,sK1)),unordered_pair(sK2(unordered_pair(sK0,sK1)),A)),
inference(resolve,[status(thm)],[c_397,c_218]) ).
cnf(c_14399,plain,
( member(sK0,unordered_pair(sK0,sK1))
| unordered_pair(sK0,sK1) = null_class
| sK2(unordered_pair(sK0,sK1)) = sK1 ),
inference(paramod,[status(thm)],[c_398,c_200]) ).
cnf(c_14400,negated_conjecture,
( member(sK0,unordered_pair(sK0,sK1))
| sK2(unordered_pair(sK0,sK1)) = sK1 ),
inference(resolve,[status(thm)],[c_64,c_14399]) ).
cnf(c_14375,negated_conjecture,
sK2(unordered_pair(sK0,sK1)) = sK1,
inference(resolve,[status(thm)],[c_477,c_14400]) ).
cnf(c_14401,plain,
( member(sK1,unordered_pair(sK0,sK1))
| unordered_pair(sK0,sK1) = null_class
| sK2(unordered_pair(sK0,sK1)) = sK0 ),
inference(paramod,[status(thm)],[c_398,c_200]) ).
cnf(c_14402,plain,
( member(sK1,unordered_pair(sK0,sK1))
| unordered_pair(sK0,sK1) = null_class
| sK1 = sK0 ),
inference(paramod,[status(thm)],[c_14375,c_14401]) ).
cnf(c_14403,negated_conjecture,
( member(sK1,unordered_pair(sK0,sK1))
| sK1 = sK0 ),
inference(resolve,[status(thm)],[c_64,c_14402]) ).
cnf(c_14376,negated_conjecture,
sK1 = sK0,
inference(resolve,[status(thm)],[c_478,c_14403]) ).
cnf(c_14404,plain,
( member(sK2(unordered_pair(sK0,sK1)),null_class)
| sK2(unordered_pair(sK0,sK1)) = sK1
| sK2(unordered_pair(sK0,sK1)) = sK0 ),
inference(paramod,[status(thm)],[c_398,c_200]) ).
cnf(c_14405,plain,
( member(sK2(unordered_pair(sK0,sK1)),null_class)
| sK2(unordered_pair(sK0,sK1)) = sK1
| sK2(unordered_pair(sK0,sK0)) = sK0 ),
inference(paramod,[status(thm)],[c_14376,c_14404]) ).
cnf(c_14406,plain,
( member(sK2(unordered_pair(sK0,sK1)),null_class)
| sK2(unordered_pair(sK0,sK0)) = sK1
| sK2(unordered_pair(sK0,sK0)) = sK0 ),
inference(paramod,[status(thm)],[c_14376,c_14405]) ).
cnf(c_14407,plain,
( member(sK2(unordered_pair(sK0,sK1)),null_class)
| sK2(unordered_pair(sK0,sK0)) = sK0
| sK2(unordered_pair(sK0,sK0)) = sK0 ),
inference(paramod,[status(thm)],[c_14376,c_14406]) ).
cnf(c_14408,plain,
( member(sK2(unordered_pair(sK0,sK0)),null_class)
| sK2(unordered_pair(sK0,sK0)) = sK0
| sK2(unordered_pair(sK0,sK0)) = sK0 ),
inference(paramod,[status(thm)],[c_14376,c_14407]) ).
cnf(c_14409,plain,
( member(sK2(unordered_pair(sK0,sK0)),null_class)
| sK2(unordered_pair(sK0,sK0)) = sK0 ),
inference(copy,[status(thm)],[c_14408]) ).
cnf(c_14378,plain,
sK2(unordered_pair(sK0,sK0)) = sK0,
inference(resolve,[status(thm)],[c_110,c_14409]) ).
cnf(c_14410,plain,
member(sK2(unordered_pair(sK0,sK0)),unordered_pair(sK2(unordered_pair(sK0,sK1)),A)),
inference(paramod,[status(thm)],[c_14376,c_14360]) ).
cnf(c_14411,plain,
member(sK0,unordered_pair(sK2(unordered_pair(sK0,sK1)),A)),
inference(paramod,[status(thm)],[c_14378,c_14410]) ).
cnf(c_14412,plain,
member(sK0,unordered_pair(sK2(unordered_pair(sK0,sK0)),A)),
inference(paramod,[status(thm)],[c_14376,c_14411]) ).
cnf(c_14413,plain,
member(sK0,unordered_pair(sK0,A)),
inference(paramod,[status(thm)],[c_14378,c_14412]) ).
cnf(c_14393,plain,
$false,
inference(resolve,[status(thm)],[c_477,c_14413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET071+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 07:02:07 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 4147880 was started by sandbox2 on n012,
% 0.03/0.30 % Sat Sep 26 07:02:07 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 15.30/2.50
% 15.30/2.50 % given #500 (F,wt=9): 6442 complement(c1) != sum_class(universal_class). [ur(137,b,3664,a)].
% 15.30/2.50
% 15.30/2.50 % SZS status Theorem for theBenchmark
% 15.30/2.50
% 15.30/2.50 % Proof 1 at 1.59 (+ 0.57) seconds.
% 15.30/2.50 % Length of proof is 27.
% 15.30/2.50 % Level of proof is 6.
% 15.30/2.50 % Maximum clause weight is 23.000.
% 15.30/2.50 % Given clauses 706.
% 15.30/2.50
% 15.30/2.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------