%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET949+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 : n020.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 02:44:21 PM UTC 2026
% Result : Theorem 6.00s 1.43s
% Output : Proof 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 59 ( 24 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 75 ( 30 ~; 21 |; 22 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 51 ( 2 sgn 32 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
& ~ in(D,C) )
| ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(D,C) ) )
| C = cartesian_product2(A,B) )
& ( ! [D] :
( ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
| in(D,C) )
& ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [C,A,B,D,E,F] :
( ( ( sk2(A,B,C) = ordered_pair(sk3(A,B,C),sk4(A,B,C))
& in(sk4(A,B,C),B)
& in(sk3(A,B,C),A)
& ~ in(sk2(A,B,C),C) )
| ( ( sk2(A,B,C) != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(sk2(A,B,C),C) )
| C = cartesian_product2(A,B) )
& ( ( ( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A)
| in(D,C) )
& ( ( D = ordered_pair(sk0(A,B,C,D),sk1(A,B,C,D))
& in(sk1(A,B,C,D),B)
& in(sk0(A,B,C,D),A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4])],[f2_nnf]) ).
cnf(c4,plain,
( X3 = ordered_pair(sk0(X0,X1,X2,X3),sk1(X0,X1,X2,X3))
| ~ in(X3,X2)
| X2 != cartesian_product2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p57,plain,
( X0 = ordered_pair(sk0(X1,X2,cartesian_product2(X1,X2),X0),sk1(X1,X2,cartesian_product2(X1,X2),X0))
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c4]) ).
fof(f7,conjecture,
! [A,B,C] :
~ ( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B,C] :
( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
! [D,E] :
( ordered_pair(D,E) != sk7
& in(sk7,cartesian_product2(sk8,sk9)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8,sk9])],[f7_nnf]) ).
cnf(c18,plain,
in(sk7,cartesian_product2(sk8,sk9)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p341,plain,
sk7 = ordered_pair(sk0(sk8,sk9,cartesian_product2(sk8,sk9),sk7),sk1(sk8,sk9,cartesian_product2(sk8,sk9),sk7)),
inference(resolution,[status(thm)],[p57,c18]) ).
cnf(c19,plain,
ordered_pair(X3,X4) != sk7,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p346,plain,
sk7 != sk7,
inference(superposition,[status(thm)],[p341,c19]) ).
cnf(p352,plain,
$false,
inference(equality_resolution,[status(thm)],[p346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET949+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:26:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.00/1.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.00/1.43 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------