%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 02:44:22 PM UTC 2026
% Result : Theorem 5.35s 1.11s
% Output : Proof 5.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 4 unt; 0 def)
% Number of atoms : 76 ( 27 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 23 ~; 31 |; 11 &)
% ( 2 <=>; 3 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 3 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
! [A,B] :
( cartesian_product2(A,A) = cartesian_product2(B,B)
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B] :
( cartesian_product2(A,A) = cartesian_product2(B,B)
=> A = B ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B] :
( A != B
& cartesian_product2(A,A) = cartesian_product2(B,B) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( sk2 != sk3
& cartesian_product2(sk2,sk2) = cartesian_product2(sk3,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f7_nnf]) ).
cnf(c9,plain,
cartesian_product2(sk2,sk2) = cartesian_product2(sk3,sk3),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f8,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f8_nnf,plain,
! [A,B] :
( A = B
| ? [C] :
( ( in(C,B)
& ~ in(C,A) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( A = B
| ( in(sk4(A,B),B)
& ~ in(sk4(A,B),A) )
| ( ~ in(sk4(A,B),B)
& in(sk4(A,B),A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f8_nnf]) ).
cnf(c12,plain,
( X0 = X1
| in(sk4(X0,X1),X1)
| in(sk4(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f4,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(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c6,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p41,plain,
( ~ in(X0,X1)
| in(ordered_pair(X0,X0),cartesian_product2(X1,X1)) ),
inference(factoring,[status(thm)],[c6]) ).
cnf(p78,plain,
( in(ordered_pair(sk4(X0,X1),sk4(X0,X1)),cartesian_product2(X0,X0))
| X0 = X1
| in(sk4(X0,X1),X1) ),
inference(resolution,[status(thm)],[c12,p41]) ).
cnf(c4,plain,
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p20,plain,
( in(X0,sk3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(sk2,sk2)) ),
inference(superposition,[status(thm)],[c9,c4]) ).
cnf(p419,plain,
( in(sk4(sk2,X0),sk3)
| sk2 = X0
| in(sk4(sk2,X0),X0) ),
inference(resolution,[status(thm)],[p78,p20]) ).
cnf(p424,plain,
( sk2 = sk3
| in(sk4(sk2,sk3),sk3) ),
inference(factoring,[status(thm)],[p419]) ).
cnf(p438,plain,
( in(ordered_pair(sk4(sk2,sk3),sk4(sk2,sk3)),cartesian_product2(sk3,sk3))
| sk2 = sk3 ),
inference(resolution,[status(thm)],[p424,p41]) ).
cnf(p450,plain,
( in(ordered_pair(sk4(sk2,sk3),sk4(sk2,sk3)),cartesian_product2(sk2,sk2))
| sk2 = sk3 ),
inference(superposition,[status(thm)],[c9,p438]) ).
cnf(p518,plain,
( in(sk4(sk2,sk3),sk2)
| sk2 = sk3 ),
inference(resolution,[status(thm)],[p450,c4]) ).
cnf(c13,plain,
( X0 = X1
| ~ in(sk4(X0,X1),X0)
| ~ in(sk4(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p439,plain,
( sk2 = sk3
| ~ in(sk4(sk2,sk3),sk2)
| sk2 = sk3 ),
inference(resolution,[status(thm)],[p424,c13]) ).
cnf(p442,plain,
( ~ in(sk4(sk2,sk3),sk2)
| sk2 = sk3 ),
inference(factoring,[status(thm)],[p439]) ).
cnf(p563,plain,
( sk2 = sk3
| sk2 = sk3 ),
inference(resolution,[status(thm)],[p518,p442]) ).
cnf(p564,plain,
sk2 = sk3,
inference(factoring,[status(thm)],[p563]) ).
cnf(c10,plain,
sk2 != sk3,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p565,plain,
$false,
inference(resolution,[status(thm)],[p564,c10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:28:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.35/1.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.35/1.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------