%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET096+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:35:45 AM UTC 2026
% Result : Theorem 34.40s 5.01s
% Output : CNFRefutation 34.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 18 unt; 0 def)
% Number of atoms : 105 ( 37 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 94 ( 33 ~; 34 |; 20 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 32 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
fof(extensionality,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('theBenchmark.p',extensionality) ).
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(two_subsets_of_singleton,conjecture,
! [X,Y] :
( subclass(X,singleton(Y))
=> ( singleton(Y) = X
| X = null_class ) ),
file('theBenchmark.p',two_subsets_of_singleton) ).
fof(two_subsets_of_singleton_neg,negated_conjecture,
~ ! [X,Y] :
( subclass(X,singleton(Y))
=> ( singleton(Y) = X
| X = null_class ) ),
inference(assume_negation,[status(cth)],[two_subsets_of_singleton]) ).
fof(nnf_42,plain,
? [X,Y] :
( singleton(Y) != X
& null_class != X
& subclass(X,singleton(Y)) ),
inference(fof_nnf,[status(thm)],[two_subsets_of_singleton_neg]) ).
fof(sk_two_subsets_of_singleton_neg,plain,
( singleton(sK0) != sK1
& null_class != sK1
& subclass(sK1,singleton(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X,sK1),skolemize(Y,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
singleton(sK0) != sK1,
inference(split_conjunct,[status(thm)],[sk_two_subsets_of_singleton_neg]) ).
cnf(c_65,negated_conjecture,
null_class != sK1,
inference(split_conjunct,[status(thm)],[sk_two_subsets_of_singleton_neg]) ).
cnf(c_66,negated_conjecture,
sK1 != null_class,
inference(copy,[status(thm)],[c_65]) ).
cnf(c_67,negated_conjecture,
subclass(sK1,singleton(sK0)),
inference(split_conjunct,[status(thm)],[sk_two_subsets_of_singleton_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_70,plain,
( member(sK2(A),A)
| null_class = A ),
inference(split_conjunct,[status(thm)],[sk_regularity]) ).
cnf(c_130,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_134,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_136,plain,
( ~ subclass(A,B)
| ~ subclass(B,A)
| A = B ),
inference(clausify,[status(thm)],[extensionality]) ).
fof(nnf_1,plain,
! [X,Y] :
( ( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ( ! [X0] :
( member(X0,Y)
| ~ member(X0,X) )
| ~ subclass(X,Y) ) ),
inference(fof_nnf,[status(thm)],[subclass_defn]) ).
fof(sk_subclass_defn_sk,plain,
! [X,Y] :
( ( ( ~ member(sK3(X,Y),Y)
& member(sK3(X,Y),X) )
| subclass(X,Y) )
& ( ! [X0] :
( member(X0,Y)
| ~ member(X0,X) )
| ~ subclass(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U,sK3(X,Y))],[nnf_1]) ).
fof(sk_subclass_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(VAR_0,VAR_1),VAR_1)
| subclass(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK3(VAR_0,VAR_1),VAR_0)
| subclass(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subclass_defn_sk]) ).
cnf(c_140,plain,
( ~ member(sK3(A,B),B)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_141,plain,
( member(sK3(A,B),A)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_142,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_195,negated_conjecture,
subclass(sK1,unordered_pair(sK0,sK0)),
inference(paramod,[status(thm)],[c_130,c_67]) ).
cnf(c_196,negated_conjecture,
unordered_pair(sK0,sK0) != sK1,
inference(paramod,[status(thm)],[c_130,c_64]) ).
cnf(c_197,plain,
( A = B
| ~ member(A,unordered_pair(B,B)) ),
inference(factor,[status(thm)],[c_134]) ).
cnf(c_15526,negated_conjecture,
null_class != sK1,
inference(copy,[status(thm)],[c_66]) ).
cnf(c_203,negated_conjecture,
member(sK2(sK1),sK1),
inference(resolve,[status(thm)],[c_70,c_15526]) ).
cnf(c_403,plain,
( sK3(unordered_pair(A,B),C) = B
| sK3(unordered_pair(A,B),C) = A
| subclass(unordered_pair(A,B),C) ),
inference(resolve,[status(thm)],[c_141,c_134]) ).
cnf(c_15527,negated_conjecture,
( ~ subclass(unordered_pair(sK0,sK0),sK1)
| sK1 = unordered_pair(sK0,sK0) ),
inference(resolve,[status(thm)],[c_195,c_136]) ).
cnf(c_15528,negated_conjecture,
( ~ subclass(unordered_pair(sK0,sK0),sK1)
| unordered_pair(sK0,sK0) = sK1 ),
inference(copy,[status(thm)],[c_15527]) ).
cnf(c_542,negated_conjecture,
~ subclass(unordered_pair(sK0,sK0),sK1),
inference(resolve,[status(thm)],[c_196,c_15528]) ).
cnf(c_600,plain,
( member(sK2(sK1),A)
| ~ subclass(sK1,A) ),
inference(resolve,[status(thm)],[c_203,c_142]) ).
cnf(c_1679,plain,
~ member(sK3(unordered_pair(sK0,sK0),sK1),sK1),
inference(resolve,[status(thm)],[c_140,c_542]) ).
cnf(c_7405,plain,
member(sK2(sK1),unordered_pair(sK0,sK0)),
inference(resolve,[status(thm)],[c_600,c_195]) ).
cnf(c_7416,plain,
sK2(sK1) = sK0,
inference(resolve,[status(thm)],[c_7405,c_197]) ).
cnf(c_7762,negated_conjecture,
member(sK0,sK1),
inference(paramod,[status(thm)],[c_7416,c_203]) ).
cnf(c_15529,plain,
( sK3(unordered_pair(sK0,sK0),sK1) = sK0
| sK3(unordered_pair(sK0,sK0),sK1) = sK0 ),
inference(resolve,[status(thm)],[c_403,c_542]) ).
cnf(c_15520,plain,
sK3(unordered_pair(sK0,sK0),sK1) = sK0,
inference(copy,[status(thm)],[c_15529]) ).
cnf(c_15530,plain,
~ member(sK0,sK1),
inference(paramod,[status(thm)],[c_15520,c_1679]) ).
cnf(c_15525,plain,
$false,
inference(resolve,[status(thm)],[c_7762,c_15530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET096+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n015.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sat Sep 26 07:09:29 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.08/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.57 % Process 3399713 was started by sandbox on n015,
% 0.08/0.57 % Sat Sep 26 07:09:29 2026
% 0.08/0.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.58
% 0.08/0.58 % From the command line: assign(max_seconds, 300).
% 34.40/5.01
% 34.40/5.01 % given #500 (F,wt=9): 7667 -member(c3,unordered_pair(c4,c4)). [back_rewrite(2874),rewrite([7416(3),7416(4)])].
% 34.40/5.01
% 34.40/5.01 % SZS status Theorem for theBenchmark
% 34.40/5.01
% 34.40/5.01 % Proof 1 at 3.24 (+ 1.13) seconds.
% 34.40/5.01 % Length of proof is 30.
% 34.40/5.01 % Level of proof is 8.
% 34.40/5.01 % Maximum clause weight is 25.000.
% 34.40/5.01 % Given clauses 771.
% 34.40/5.01
% 34.40/5.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------