%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET024+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 : n001.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 02:41:33 PM UTC 2026
% Result : Theorem 27.11s 3.99s
% Output : Proof 27.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 42 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 39 ( 15 ~; 12 |; 9 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 3 sgn 14 !; 1 ?)
% 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(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(c9,plain,
( X0 != X1
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f43,conjecture,
! [X] :
( member(X,universal_class)
=> member(X,singleton(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_in_its_singleton) ).
fof(f43_neg,negated_conjecture,
~ ! [X] :
( member(X,universal_class)
=> member(X,singleton(X)) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
? [X] :
( ~ member(X,singleton(X))
& member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
( ~ member(sk7,singleton(sk7))
& member(sk7,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f43_nnf]) ).
cnf(c89,plain,
member(sk7,universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p131,plain,
( sk7 != X0
| member(sk7,unordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[c9,c89]) ).
cnf(p137,plain,
member(sk7,unordered_pair(sk7,X0)),
inference(equality_resolution,[status(thm)],[p131]) ).
cnf(p138,plain,
member(sk7,singleton(sk7)),
inference(superposition,[status(thm)],[c12,p137]) ).
cnf(c90,plain,
~ member(sk7,singleton(sk7)),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p139,plain,
$false,
inference(resolution,[status(thm)],[p138,c90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET024+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 09:20:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.11/3.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.11/3.99 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------