%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET875+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:44:12 PM UTC 2026
% Result : Theorem 0.14s 5.80s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 49 ( 22 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 55 ( 24 ~; 16 |; 13 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
& ~ in(C,B) )
| ( C != A
& in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,A,C] :
( ( ( sk0(A,B) = A
& ~ in(sk0(A,B),B) )
| ( sk0(A,B) != A
& in(sk0(A,B),B) )
| B = singleton(A) )
& ( ( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c2,plain,
( X2 != X0
| in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p15,plain,
( X0 != X1
| in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
fof(f6,conjecture,
! [A,B] :
~ ( A = B
& disjoint(singleton(A),singleton(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B] :
~ ( A = B
& disjoint(singleton(A),singleton(B)) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A,B] :
( A = B
& disjoint(singleton(A),singleton(B)) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( sk3 = sk4
& disjoint(singleton(sk3),singleton(sk4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f6_nnf]) ).
cnf(c12,plain,
sk3 = sk4,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p27,plain,
in(sk3,singleton(sk4)),
inference(resolution,[status(thm)],[p15,c12]) ).
cnf(c11,plain,
disjoint(singleton(sk3),singleton(sk4)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f2,axiom,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f2_nnf,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c7,plain,
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p21,plain,
~ in(sk3,singleton(sk4)),
inference(resolution,[status(thm)],[c11,c7]) ).
cnf(p57,plain,
$false,
inference(resolution,[status(thm)],[p27,p21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET875+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n015.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 12:22:01 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/5.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.80 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------