%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET882+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 5.98s 1.24s
% Output : Proof 5.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 72 ( 43 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 85 ( 35 ~; 28 |; 17 &)
% ( 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; 2 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B,C] :
( ( ( A != B
& ~ in(B,C) )
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) )
& ( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( ( ( A != B
& ~ in(B,C) )
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) )
& ( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c10,plain,
( ~ in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f2_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)],[f2]) ).
fof(f2_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])],[f2_nnf]) ).
cnf(c3,plain,
( X2 != X0
| in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p18,plain,
( X0 != X1
| in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p20,plain,
in(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[p18]) ).
cnf(p33,plain,
( in(X0,singleton(X1))
| set_difference(unordered_pair(X0,X1),singleton(X1)) = singleton(X0) ),
inference(resolution,[status(thm)],[c10,p20]) ).
fof(f6,conjecture,
! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A,B] :
( set_difference(unordered_pair(A,B),singleton(B)) != singleton(A)
& A != B ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( set_difference(unordered_pair(sk3,sk4),singleton(sk4)) != singleton(sk3)
& sk3 != sk4 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f6_nnf]) ).
cnf(c15,plain,
set_difference(unordered_pair(sk3,sk4),singleton(sk4)) != singleton(sk3),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p48,plain,
in(sk3,singleton(sk4)),
inference(resolution,[status(thm)],[p33,c15]) ).
cnf(c2,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p17,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p57,plain,
sk3 = sk4,
inference(resolution,[status(thm)],[p48,p17]) ).
cnf(c14,plain,
sk3 != sk4,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p59,plain,
$false,
inference(resolution,[status(thm)],[p57,c14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:22:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.98/1.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.98/1.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------