%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET880+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 2.85s 0.74s
% Output : Proof 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 53 ( 34 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 57 ( 22 ~; 18 |; 12 &)
% ( 3 <=>; 2 =>; 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 : 6 ( 6 usr; 3 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/sandbox2/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(c1,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p17,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c1]) ).
fof(f3,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B] :
( ( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set )
& ( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( ( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set )
& ( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c8,plain,
( in(X0,X1)
| set_difference(singleton(X0),X1) != empty_set ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f6,conjecture,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A,B] :
( A != B
& set_difference(singleton(A),singleton(B)) = empty_set ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( sk3 != sk4
& set_difference(singleton(sk3),singleton(sk4)) = empty_set ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f6_nnf]) ).
cnf(c12,plain,
set_difference(singleton(sk3),singleton(sk4)) = empty_set,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p15,plain,
in(sk3,singleton(sk4)),
inference(resolution,[status(thm)],[c8,c12]) ).
cnf(p18,plain,
sk3 = sk4,
inference(resolution,[status(thm)],[p17,p15]) ).
cnf(c13,plain,
sk3 != sk4,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p19,plain,
$false,
inference(resolution,[status(thm)],[p18,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET880+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Thu Sep 24 12:18:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.85/0.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.85/0.74 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------