%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU157+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 02:51:08 PM UTC 2026
% Result : Theorem 6.17s 1.28s
% Output : Proof 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 5 unt; 0 def)
% Number of atoms : 137 ( 40 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 150 ( 54 ~; 62 |; 29 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 94 ( 4 sgn 38 !; 11 ?)
% 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/sandbox/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(c5,plain,
( X3 != ordered_pair(X4,X5)
| ~ in(X5,X1)
| ~ in(X4,X0)
| in(X3,X2)
| X2 != cartesian_product2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p60,plain,
( X0 != ordered_pair(X3,X4)
| ~ in(X4,X2)
| ~ in(X3,X1)
| in(X0,cartesian_product2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c5]) ).
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(p51,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(f9,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',l55_zfmisc_1) ).
fof(f9_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)],[f9]) ).
fof(f9_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)],[f9_neg]) ).
fof(f9_sk,plain,
( ( in(sk6,sk8)
& in(sk5,sk7)
& ~ in(ordered_pair(sk5,sk6),cartesian_product2(sk7,sk8)) )
| ( ( ~ in(sk6,sk8)
| ~ in(sk5,sk7) )
& in(ordered_pair(sk5,sk6),cartesian_product2(sk7,sk8)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6,sk7,sk8])],[f9_nnf]) ).
cnf(c21,plain,
( in(sk5,sk7)
| in(ordered_pair(sk5,sk6),cartesian_product2(sk7,sk8)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p363,plain,
( in(sk5,sk7)
| ordered_pair(sk5,sk6) = ordered_pair(sk0(sk7,sk8,cartesian_product2(sk7,sk8),ordered_pair(sk5,sk6)),sk1(sk7,sk8,cartesian_product2(sk7,sk8),ordered_pair(sk5,sk6))) ),
inference(resolution,[status(thm)],[p51,c21]) ).
fof(f12,axiom,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f12_nnf,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c28,plain,
( X0 = X2
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p370,plain,
( sk5 = sk0(sk7,sk8,cartesian_product2(sk7,sk8),ordered_pair(sk5,sk6))
| in(sk5,sk7) ),
inference(resolution,[status(thm)],[p363,c28]) ).
cnf(c2,plain,
( in(sk0(X0,X1,X2,X3),X0)
| ~ in(X3,X2)
| X2 != cartesian_product2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p33,plain,
( in(sk0(X1,X2,cartesian_product2(X1,X2),X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p107,plain,
( in(sk5,sk7)
| in(sk0(sk7,sk8,cartesian_product2(sk7,sk8),ordered_pair(sk5,sk6)),sk7) ),
inference(resolution,[status(thm)],[p33,c21]) ).
cnf(p380,plain,
( in(sk5,sk7)
| in(sk5,sk7)
| in(sk5,sk7) ),
inference(superposition,[status(thm)],[p370,p107]) ).
cnf(p385,plain,
( in(sk5,sk7)
| in(sk5,sk7) ),
inference(factoring,[status(thm)],[p380]) ).
cnf(p386,plain,
in(sk5,sk7),
inference(factoring,[status(thm)],[p385]) ).
cnf(p473,plain,
( X0 != ordered_pair(sk5,X2)
| ~ in(X2,X1)
| in(X0,cartesian_product2(sk7,X1)) ),
inference(resolution,[status(thm)],[p60,p386]) ).
cnf(p475,plain,
( ~ in(X0,X1)
| in(ordered_pair(sk5,X0),cartesian_product2(sk7,X1)) ),
inference(equality_resolution,[status(thm)],[p473]) ).
cnf(c22,plain,
( in(sk6,sk8)
| in(ordered_pair(sk5,sk6),cartesian_product2(sk7,sk8)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p364,plain,
( in(sk6,sk8)
| ordered_pair(sk5,sk6) = ordered_pair(sk0(sk7,sk8,cartesian_product2(sk7,sk8),ordered_pair(sk5,sk6)),sk1(sk7,sk8,cartesian_product2(sk7,sk8),ordered_pair(sk5,sk6))) ),
inference(resolution,[status(thm)],[p51,c22]) ).
cnf(c29,plain,
( X1 = X3
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p439,plain,
( sk6 = sk1(sk7,sk8,cartesian_product2(sk7,sk8),ordered_pair(sk5,sk6))
| in(sk6,sk8) ),
inference(resolution,[status(thm)],[p364,c29]) ).
cnf(c3,plain,
( in(sk1(X0,X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != cartesian_product2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p34,plain,
( in(sk1(X1,X2,cartesian_product2(X1,X2),X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p120,plain,
( in(sk6,sk8)
| in(sk1(sk7,sk8,cartesian_product2(sk7,sk8),ordered_pair(sk5,sk6)),sk8) ),
inference(resolution,[status(thm)],[p34,c22]) ).
cnf(p452,plain,
( in(sk6,sk8)
| in(sk6,sk8)
| in(sk6,sk8) ),
inference(superposition,[status(thm)],[p439,p120]) ).
cnf(p455,plain,
( in(sk6,sk8)
| in(sk6,sk8) ),
inference(factoring,[status(thm)],[p452]) ).
cnf(p456,plain,
in(sk6,sk8),
inference(factoring,[status(thm)],[p455]) ).
cnf(p487,plain,
in(ordered_pair(sk5,sk6),cartesian_product2(sk7,sk8)),
inference(resolution,[status(thm)],[p475,p456]) ).
cnf(c23,plain,
( ~ in(ordered_pair(sk5,sk6),cartesian_product2(sk7,sk8))
| ~ in(sk6,sk8)
| ~ in(sk5,sk7) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p391,plain,
( ~ in(ordered_pair(sk5,sk6),cartesian_product2(sk7,sk8))
| ~ in(sk6,sk8) ),
inference(resolution,[status(thm)],[p386,c23]) ).
cnf(p462,plain,
~ in(ordered_pair(sk5,sk6),cartesian_product2(sk7,sk8)),
inference(resolution,[status(thm)],[p456,p391]) ).
cnf(p513,plain,
$false,
inference(resolution,[status(thm)],[p487,p462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU157+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.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 13:04:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.17/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.17/1.28 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------