%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET103+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 : n016.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 08:35:47 AM UTC 2026
% Result : Theorem 26.19s 3.76s
% Output : CNFRefutation 26.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 18 unt; 0 def)
% Number of atoms : 92 ( 41 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 23 ~; 31 |; 12 &)
% ( 3 <=>; 2 =>; 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 4 sgn 22 !; 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(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('theBenchmark.p',singleton_set_defn) ).
fof(ordered_pair_defn,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
file('theBenchmark.p',ordered_pair_defn) ).
fof(complement,axiom,
! [X,Z] :
( member(Z,complement(X))
<=> ( ~ member(Z,X)
& member(Z,universal_class) ) ),
file('theBenchmark.p',complement) ).
fof(regularity,axiom,
! [X] :
( X != null_class
=> ? [U] :
( disjoint(U,X)
& member(U,X)
& member(U,universal_class) ) ),
file('theBenchmark.p',regularity) ).
fof(property_1_of_ordered_pair,conjecture,
! [X,Y] :
( member(Y,universal_class)
| unordered_pair(singleton(X),unordered_pair(X,null_class)) = ordered_pair(X,Y) ),
file('theBenchmark.p',property_1_of_ordered_pair) ).
fof(property_1_of_ordered_pair_neg,negated_conjecture,
~ ! [X,Y] :
( member(Y,universal_class)
| unordered_pair(singleton(X),unordered_pair(X,null_class)) = ordered_pair(X,Y) ),
inference(assume_negation,[status(cth)],[property_1_of_ordered_pair]) ).
fof(nnf_42,plain,
? [X,Y] :
( ~ member(Y,universal_class)
& ordered_pair(X,Y) != unordered_pair(singleton(X),unordered_pair(X,null_class)) ),
inference(fof_nnf,[status(thm)],[property_1_of_ordered_pair_neg]) ).
fof(sk_property_1_of_ordered_pair_neg,plain,
( ~ member(sK0,universal_class)
& ordered_pair(sK1,sK0) != unordered_pair(singleton(sK1),unordered_pair(sK1,null_class)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X,sK1),skolemize(Y,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
~ member(sK0,universal_class),
inference(split_conjunct,[status(thm)],[sk_property_1_of_ordered_pair_neg]) ).
cnf(c_65,negated_conjecture,
ordered_pair(sK1,sK0) != unordered_pair(singleton(sK1),unordered_pair(sK1,null_class)),
inference(split_conjunct,[status(thm)],[sk_property_1_of_ordered_pair_neg]) ).
cnf(c_66,negated_conjecture,
unordered_pair(singleton(sK1),unordered_pair(sK1,null_class)) != ordered_pair(sK1,sK0),
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(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_112,plain,
( member(A,B)
| ~ member(A,universal_class)
| member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement]) ).
cnf(c_128,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(clausify,[status(thm)],[ordered_pair_defn]) ).
cnf(c_129,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_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_12940,negated_conjecture,
unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,null_class)) != ordered_pair(sK1,sK0),
inference(paramod,[status(thm)],[c_129,c_66]) ).
cnf(c_12941,negated_conjecture,
unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,null_class)) != unordered_pair(singleton(sK1),unordered_pair(sK1,singleton(sK0))),
inference(paramod,[status(thm)],[c_128,c_12940]) ).
cnf(c_12942,negated_conjecture,
unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,null_class)) != unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,singleton(sK0))),
inference(paramod,[status(thm)],[c_129,c_12941]) ).
cnf(c_12943,negated_conjecture,
unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,null_class)) != unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),
inference(paramod,[status(thm)],[c_129,c_12942]) ).
cnf(c_192,negated_conjecture,
unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))) != unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,null_class)),
inference(copy,[status(thm)],[c_12943]) ).
cnf(c_312,plain,
( null_class = A
| member(sK2(A),B)
| member(sK2(A),complement(B)) ),
inference(resolve,[status(thm)],[c_112,c_70]) ).
cnf(c_12944,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_381,plain,
( unordered_pair(A,B) = null_class
| sK2(unordered_pair(A,B)) = B
| sK2(unordered_pair(A,B)) = A ),
inference(copy,[status(thm)],[c_12944]) ).
cnf(c_12945,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_141,c_138]) ).
cnf(c_457,negated_conjecture,
~ member(sK0,A),
inference(resolve,[status(thm)],[c_12945,c_64]) ).
cnf(c_12946,plain,
( unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,null_class)) != unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,null_class))
| member(sK2(unordered_pair(sK0,sK0)),A)
| member(sK2(unordered_pair(sK0,sK0)),complement(A)) ),
inference(paramod,[status(thm)],[c_312,c_192]) ).
cnf(c_8242,plain,
( member(sK2(unordered_pair(sK0,sK0)),A)
| member(sK2(unordered_pair(sK0,sK0)),complement(A)) ),
inference(copy,[status(thm)],[c_12946]) ).
cnf(c_12947,plain,
( unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,null_class)) != unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,null_class))
| sK2(unordered_pair(sK0,sK0)) = sK0
| sK2(unordered_pair(sK0,sK0)) = sK0 ),
inference(paramod,[status(thm)],[c_381,c_192]) ).
cnf(c_12948,plain,
( sK2(unordered_pair(sK0,sK0)) = sK0
| sK2(unordered_pair(sK0,sK0)) = sK0 ),
inference(copy,[status(thm)],[c_12947]) ).
cnf(c_12917,plain,
sK2(unordered_pair(sK0,sK0)) = sK0,
inference(copy,[status(thm)],[c_12948]) ).
cnf(c_12949,plain,
( member(sK2(unordered_pair(sK0,sK0)),A)
| member(sK0,complement(A)) ),
inference(paramod,[status(thm)],[c_12917,c_8242]) ).
cnf(c_12950,plain,
( member(sK0,A)
| member(sK0,complement(A)) ),
inference(paramod,[status(thm)],[c_12917,c_12949]) ).
cnf(c_12951,plain,
member(sK0,A),
inference(resolve,[status(thm)],[c_457,c_12950]) ).
cnf(c_12939,plain,
$false,
inference(resolve,[status(thm)],[c_457,c_12951]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET103+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:12:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 261326 was started by sandbox2 on n016,
% 0.09/0.36 % Sat Sep 26 07:12:44 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 26.19/3.76
% 26.19/3.76 % given #500 (F,wt=10): 1382 -member(f5(c1),unordered_pair(universal_class,universal_class)). [ur(195,b,964,a)].
% 26.19/3.76
% 26.19/3.76 % SZS status Theorem for theBenchmark
% 26.19/3.76
% 26.19/3.76 % Proof 1 at 2.44 (+ 0.85) seconds.
% 26.19/3.76 % Length of proof is 26.
% 26.19/3.76 % Level of proof is 5.
% 26.19/3.76 % Maximum clause weight is 35.000.
% 26.19/3.76 % Given clauses 683.
% 26.19/3.76
% 26.19/3.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------