%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET879+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 02:44:13 PM UTC 2026
% Result : Theorem 2.65s 0.79s
% Output : Proof 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 5 unt; 0 def)
% Number of atoms : 72 ( 48 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 80 ( 33 ~; 28 |; 14 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 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(p22,plain,
( X0 != X1
| in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
fof(f2,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f2_nnf,plain,
! [A,B] :
( ( in(A,B)
| set_difference(singleton(A),B) = singleton(A) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( in(A,B)
| set_difference(singleton(A),B) = singleton(A) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c8,plain,
( in(X0,X1)
| set_difference(singleton(X0),X1) = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f5,conjecture,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
fof(f5_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [A,B] :
( ( A != B
& set_difference(singleton(A),singleton(B)) != singleton(A) )
| ( A = B
& set_difference(singleton(A),singleton(B)) = singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( ( sk3 != sk4
& set_difference(singleton(sk3),singleton(sk4)) != singleton(sk3) )
| ( sk3 = sk4
& set_difference(singleton(sk3),singleton(sk4)) = singleton(sk3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f5_nnf]) ).
cnf(c13,plain,
( set_difference(singleton(sk3),singleton(sk4)) != singleton(sk3)
| sk3 = sk4 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p17,plain,
( sk3 = sk4
| in(sk3,singleton(sk4)) ),
inference(resolution,[status(thm)],[c8,c13]) ).
cnf(c1,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p16,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(p20,plain,
( sk3 = sk4
| sk3 = sk4 ),
inference(resolution,[status(thm)],[p17,p16]) ).
cnf(p21,plain,
sk3 = sk4,
inference(factoring,[status(thm)],[p20]) ).
cnf(p32,plain,
in(sk3,singleton(sk4)),
inference(resolution,[status(thm)],[p22,p21]) ).
cnf(c12,plain,
( sk3 != sk4
| set_difference(singleton(sk3),singleton(sk4)) = singleton(sk3) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p26,plain,
set_difference(singleton(sk3),singleton(sk4)) = singleton(sk3),
inference(resolution,[status(thm)],[p21,c12]) ).
cnf(c7,plain,
( ~ in(X0,X1)
| set_difference(singleton(X0),X1) != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p27,plain,
~ in(sk3,singleton(sk4)),
inference(resolution,[status(thm)],[p26,c7]) ).
cnf(p34,plain,
$false,
inference(resolution,[status(thm)],[p32,p27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET879+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n015.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 : Thu Sep 24 12:22:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.65/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.65/0.79 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------