%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET081+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 : Fri Sep 25 02:42:02 PM UTC 2026
% Result : Theorem 55.39s 13.54s
% Output : Proof 55.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 92 ( 35 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 84 ( 32 ~; 29 |; 17 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 4 sgn 40 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f5_nnf,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c12,plain,
singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f8,axiom,
! [X,Y] :
( ( member(Y,universal_class)
& member(X,universal_class) )
=> ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_second) ).
fof(f8_nnf,plain,
! [X,Y] :
( ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X )
| ~ member(Y,universal_class)
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X )
| ~ member(Y,universal_class)
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c18,plain,
( second(ordered_pair(X0,X1)) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f0,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,U] :
( ( ( ~ member(sk0(X,Y),Y)
& member(sk0(X,Y),X) )
| subclass(X,Y) )
& ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f1_nnf,plain,
! [X] : subclass(X,universal_class),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : subclass(X,universal_class),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p91,plain,
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c0,c3]) ).
fof(f43,conjecture,
! [X,Y] :
( member(Y,singleton(X))
=> Y = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f43_neg,negated_conjecture,
~ ! [X,Y] :
( member(Y,singleton(X))
=> Y = X ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
? [X,Y] :
( Y != X
& member(Y,singleton(X)) ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
( sk8 != sk7
& member(sk8,singleton(sk7)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8])],[f43_nnf]) ).
cnf(c89,plain,
member(sk8,singleton(sk7)),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p117,plain,
member(sk8,universal_class),
inference(resolution,[status(thm)],[p91,c89]) ).
cnf(p250,plain,
( second(ordered_pair(sk8,X0)) = X0
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[c18,p117]) ).
fof(f4,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
fof(f4_nnf,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c11,plain,
member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p262,plain,
second(ordered_pair(sk8,unordered_pair(X0,X1))) = unordered_pair(X0,X1),
inference(resolution,[status(thm)],[p250,c11]) ).
cnf(p275,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(superposition,[status(thm)],[c12,p262]) ).
fof(f3,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f3_nnf,plain,
! [U,X,Y] :
( ( ( U != Y
& U != X )
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,X,Y] :
( ( ( U != Y
& U != X )
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p121,plain,
( X0 = X1
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(factoring,[status(thm)],[c8]) ).
cnf(p276,plain,
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(demodulation,[status(thm)],[p275,p121]) ).
cnf(p280,plain,
sk8 = sk7,
inference(resolution,[status(thm)],[p276,c89]) ).
cnf(c90,plain,
sk8 != sk7,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p282,plain,
sk7 != sk7,
inference(demodulation,[status(thm)],[p280,c90]) ).
cnf(p378,plain,
$false,
inference(equality_resolution,[status(thm)],[p282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET081+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.39 % Computer : n019.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Thu Sep 24 09:39:26 UTC 2026
% 0.10/5.40 % CPUTime :
% 0.10/5.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 55.39/13.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.39/13.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------