%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU165+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 02:51:11 PM UTC 2026
% Result : Theorem 4.24s 1.09s
% Output : Proof 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 24 ~; 22 |; 13 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 4 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,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(f7_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)],[f7]) ).
fof(f7_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)],[f7_nnf]) ).
cnf(c14,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c12,plain,
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f6,conjecture,
! [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',t106_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_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)],[f6_neg]) ).
fof(f6_sk,plain,
( ( in(sk3,sk5)
& in(sk2,sk4)
& ~ in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5)) )
| ( ( ~ in(sk3,sk5)
| ~ in(sk2,sk4) )
& in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f6_nnf]) ).
cnf(c7,plain,
( in(sk2,sk4)
| in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p37,plain,
( in(sk2,sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[c12,c7]) ).
cnf(p39,plain,
in(sk2,sk4),
inference(factoring,[status(thm)],[p37]) ).
cnf(p47,plain,
( ~ in(X0,X1)
| in(ordered_pair(sk2,X0),cartesian_product2(sk4,X1)) ),
inference(resolution,[status(thm)],[c14,p39]) ).
cnf(c13,plain,
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c8,plain,
( in(sk3,sk5)
| in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p42,plain,
( in(sk3,sk5)
| in(sk3,sk5) ),
inference(resolution,[status(thm)],[c13,c8]) ).
cnf(p43,plain,
in(sk3,sk5),
inference(factoring,[status(thm)],[p42]) ).
cnf(p50,plain,
in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5)),
inference(resolution,[status(thm)],[p47,p43]) ).
cnf(c9,plain,
( ~ in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5))
| ~ in(sk3,sk5)
| ~ in(sk2,sk4) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p40,plain,
( ~ in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5))
| ~ in(sk3,sk5) ),
inference(resolution,[status(thm)],[p39,c9]) ).
cnf(p45,plain,
~ in(ordered_pair(sk2,sk3),cartesian_product2(sk4,sk5)),
inference(resolution,[status(thm)],[p43,p40]) ).
cnf(p55,plain,
$false,
inference(resolution,[status(thm)],[p50,p45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU165+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n003.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 13:01:52 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.24/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.24/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------