%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET921+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 : n009.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 02:44:17 PM UTC 2026
% Result : Theorem 3.29s 0.91s
% Output : Proof 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 6 unt; 0 def)
% Number of atoms : 123 ( 41 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 145 ( 56 ~; 54 |; 29 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 64 ( 4 sgn 27 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ~ in(D,B)
& in(D,A)
& ~ in(D,C) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk1(A,B,C),B)
& in(sk1(A,B,C),A)
& ~ in(sk1(A,B,C),C) )
| ( ( in(sk1(A,B,C),B)
| ~ in(sk1(A,B,C),A) )
& in(sk1(A,B,C),C) )
| C = set_difference(A,B) )
& ( ( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f2_nnf]) ).
cnf(c9,plain,
( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p50,plain,
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(c7,plain,
( in(X3,X0)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p31,plain,
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c7]) ).
fof(f5,conjecture,
! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<=> ( A != C
& in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
fof(f5_neg,negated_conjecture,
~ ! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<=> ( A != C
& in(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [A,B,C] :
( ( A != C
& in(A,B)
& ~ in(A,set_difference(B,singleton(C))) )
| ( ( A = C
| ~ in(A,B) )
& in(A,set_difference(B,singleton(C))) ) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( ( sk4 != sk6
& in(sk4,sk5)
& ~ in(sk4,set_difference(sk5,singleton(sk6))) )
| ( ( sk4 = sk6
| ~ in(sk4,sk5) )
& in(sk4,set_difference(sk5,singleton(sk6))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f5_nnf]) ).
cnf(c19,plain,
( in(sk4,sk5)
| in(sk4,set_difference(sk5,singleton(sk6))) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p32,plain,
( in(sk4,sk5)
| in(sk4,sk5) ),
inference(resolution,[status(thm)],[p31,c19]) ).
cnf(p42,plain,
in(sk4,sk5),
inference(factoring,[status(thm)],[p32]) ).
cnf(p54,plain,
( in(sk4,X0)
| in(sk4,set_difference(sk5,X0)) ),
inference(resolution,[status(thm)],[p50,p42]) ).
cnf(c21,plain,
( ~ in(sk4,set_difference(sk5,singleton(sk6)))
| sk4 = sk6
| ~ in(sk4,sk5) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p48,plain,
( ~ in(sk4,set_difference(sk5,singleton(sk6)))
| sk4 = sk6 ),
inference(resolution,[status(thm)],[c21,p42]) ).
cnf(p56,plain,
( sk4 = sk6
| in(sk4,singleton(sk6)) ),
inference(resolution,[status(thm)],[p54,p48]) ).
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(p25,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(p59,plain,
( sk4 = sk6
| sk4 = sk6 ),
inference(resolution,[status(thm)],[p56,p25]) ).
cnf(p61,plain,
sk4 = sk6,
inference(factoring,[status(thm)],[p59]) ).
cnf(c20,plain,
( sk4 != sk6
| in(sk4,set_difference(sk5,singleton(sk6))) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p73,plain,
in(sk4,set_difference(sk5,singleton(sk6))),
inference(resolution,[status(thm)],[p61,c20]) ).
cnf(c8,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p45,plain,
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(p78,plain,
~ in(sk4,singleton(sk6)),
inference(resolution,[status(thm)],[p73,p45]) ).
cnf(c2,plain,
( X2 != X0
| in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p27,plain,
( X0 != X1
| in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p74,plain,
in(sk4,singleton(sk6)),
inference(resolution,[status(thm)],[p61,p27]) ).
cnf(p83,plain,
$false,
inference(resolution,[status(thm)],[p78,p74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET921+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n009.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 12:22:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.29/0.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.29/0.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------