%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET975+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 : 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 02:44:23 PM UTC 2026
% Result : Theorem 4.35s 0.96s
% Output : Proof 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 96 ( 32 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 105 ( 40 ~; 39 |; 21 &)
% ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 4 sgn 29 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c12,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f5_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(p59,plain,
( X0 != X1
| in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(c2,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p52,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(c10,plain,
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f8,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( in(B,D)
& A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( in(B,D)
& A = C ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B,C,D] :
( ( in(B,D)
& A = C
& ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) )
| ( ( ~ in(B,D)
| A != C )
& in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) ) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( ( in(sk4,sk6)
& sk3 = sk5
& ~ in(ordered_pair(sk3,sk4),cartesian_product2(singleton(sk5),sk6)) )
| ( ( ~ in(sk4,sk6)
| sk3 != sk5 )
& in(ordered_pair(sk3,sk4),cartesian_product2(singleton(sk5),sk6)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5,sk6])],[f8_nnf]) ).
cnf(c16,plain,
( sk3 = sk5
| in(ordered_pair(sk3,sk4),cartesian_product2(singleton(sk5),sk6)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p43,plain,
( sk3 = sk5
| in(sk3,singleton(sk5)) ),
inference(resolution,[status(thm)],[c10,c16]) ).
cnf(p53,plain,
( sk3 = sk5
| sk3 = sk5 ),
inference(resolution,[status(thm)],[p52,p43]) ).
cnf(p54,plain,
sk3 = sk5,
inference(factoring,[status(thm)],[p53]) ).
cnf(p63,plain,
in(sk3,singleton(sk5)),
inference(resolution,[status(thm)],[p59,p54]) ).
cnf(p92,plain,
( ~ in(X0,X1)
| in(ordered_pair(sk3,X0),cartesian_product2(singleton(sk5),X1)) ),
inference(resolution,[status(thm)],[c12,p63]) ).
cnf(c11,plain,
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(c17,plain,
( in(sk4,sk6)
| in(ordered_pair(sk3,sk4),cartesian_product2(singleton(sk5),sk6)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p48,plain,
( in(sk4,sk6)
| in(sk4,sk6) ),
inference(resolution,[status(thm)],[c11,c17]) ).
cnf(p50,plain,
in(sk4,sk6),
inference(factoring,[status(thm)],[p48]) ).
cnf(p115,plain,
in(ordered_pair(sk3,sk4),cartesian_product2(singleton(sk5),sk6)),
inference(resolution,[status(thm)],[p92,p50]) ).
cnf(c18,plain,
( ~ in(ordered_pair(sk3,sk4),cartesian_product2(singleton(sk5),sk6))
| ~ in(sk4,sk6)
| sk3 != sk5 ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p55,plain,
( ~ in(ordered_pair(sk3,sk4),cartesian_product2(singleton(sk5),sk6))
| ~ in(sk4,sk6) ),
inference(resolution,[status(thm)],[p54,c18]) ).
cnf(p57,plain,
~ in(ordered_pair(sk3,sk4),cartesian_product2(singleton(sk5),sk6)),
inference(resolution,[status(thm)],[p55,p50]) ).
cnf(p127,plain,
$false,
inference(resolution,[status(thm)],[p115,p57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET975+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 : n012.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 12:29:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.35/0.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.35/0.96 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------