%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU178+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 02:51:14 PM UTC 2026
% Result : Theorem 16.34s 2.73s
% Output : Proof 16.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 4 unt; 0 def)
% Number of atoms : 172 ( 22 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 194 ( 69 ~; 81 |; 32 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 1 con; 0-3 aty)
% Number of variables : 116 ( 6 sgn 59 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk3(A,B),B)
& in(sk3(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f3_nnf]) ).
cnf(c6,plain,
( in(sk3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f2,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f2_nnf,plain,
! [A] :
( ( ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) )
| relation(A) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( ( ( sk2(A) != ordered_pair(C,D)
& in(sk2(A),A) )
| relation(A) )
& ( B = ordered_pair(sk0(A,B),sk1(A,B))
| ~ in(B,A)
| ~ relation(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f2_nnf]) ).
cnf(c2,plain,
( X1 = ordered_pair(sk0(X0,X1),sk1(X0,X1))
| ~ in(X1,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f31,conjecture,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f31_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f31_nnf,plain,
? [A] :
( ~ subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f31_neg]) ).
fof(f31_sk,plain,
( ~ subset(sk16,cartesian_product2(relation_dom(sk16),relation_rng(sk16)))
& relation(sk16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f31_nnf]) ).
cnf(c50,plain,
relation(sk16),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p61,plain,
( X0 = ordered_pair(sk0(sk16,X0),sk1(sk16,X0))
| ~ in(X0,sk16) ),
inference(resolution,[status(thm)],[c2,c50]) ).
cnf(p71,plain,
( sk3(sk16,X0) = ordered_pair(sk0(sk16,sk3(sk16,X0)),sk1(sk16,sk3(sk16,X0)))
| subset(sk16,X0) ),
inference(resolution,[status(thm)],[c6,p61]) ).
fof(f29,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f29_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)],[f29]) ).
fof(f29_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)],[f29_nnf]) ).
cnf(c48,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f4_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
& ~ in(C,B) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk5(A,B),sk6(A,B)),A)
& ~ in(sk5(A,B),B) )
| ( ~ in(ordered_pair(sk5(A,B),D),A)
& in(sk5(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk4(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f4_nnf]) ).
cnf(c9,plain,
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p83,plain,
( ~ in(ordered_pair(X1,X2),sk16)
| in(X1,X0)
| X0 != relation_dom(sk16) ),
inference(resolution,[status(thm)],[c9,c50]) ).
cnf(p85,plain,
( ~ in(ordered_pair(X0,X1),sk16)
| in(X0,relation_dom(sk16)) ),
inference(equality_resolution,[status(thm)],[p83]) ).
cnf(p86,plain,
( ~ in(sk3(sk16,X0),sk16)
| in(sk0(sk16,sk3(sk16,X0)),relation_dom(sk16))
| subset(sk16,X0) ),
inference(superposition,[status(thm)],[p71,p85]) ).
cnf(p87,plain,
( subset(sk16,X0)
| in(sk0(sk16,sk3(sk16,X0)),relation_dom(sk16))
| subset(sk16,X0) ),
inference(resolution,[status(thm)],[p86,c6]) ).
cnf(p88,plain,
( in(sk0(sk16,sk3(sk16,X0)),relation_dom(sk16))
| subset(sk16,X0) ),
inference(factoring,[status(thm)],[p87]) ).
cnf(p201,plain,
( subset(sk16,X0)
| ~ in(X1,X2)
| in(ordered_pair(sk0(sk16,sk3(sk16,X0)),X1),cartesian_product2(relation_dom(sk16),X2)) ),
inference(resolution,[status(thm)],[c48,p88]) ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f5_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
& ~ in(C,B) )
| ( ! [D] : ~ in(ordered_pair(D,C),A)
& in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk9(A,B),sk8(A,B)),A)
& ~ in(sk8(A,B),B) )
| ( ~ in(ordered_pair(D,sk8(A,B)),A)
& in(sk8(A,B),B) )
| B = relation_rng(A) )
& ( ( ( ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( in(ordered_pair(sk7(A,B,C),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8,sk9])],[f5_nnf]) ).
cnf(c15,plain,
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p124,plain,
( ~ in(ordered_pair(X2,X1),sk16)
| in(X1,X0)
| X0 != relation_rng(sk16) ),
inference(resolution,[status(thm)],[c15,c50]) ).
cnf(p128,plain,
( ~ in(ordered_pair(X1,X0),sk16)
| in(X0,relation_rng(sk16)) ),
inference(equality_resolution,[status(thm)],[p124]) ).
cnf(p129,plain,
( ~ in(sk3(sk16,X0),sk16)
| in(sk1(sk16,sk3(sk16,X0)),relation_rng(sk16))
| subset(sk16,X0) ),
inference(superposition,[status(thm)],[p71,p128]) ).
cnf(p151,plain,
( subset(sk16,X0)
| in(sk1(sk16,sk3(sk16,X0)),relation_rng(sk16))
| subset(sk16,X0) ),
inference(resolution,[status(thm)],[p129,c6]) ).
cnf(p152,plain,
( in(sk1(sk16,sk3(sk16,X0)),relation_rng(sk16))
| subset(sk16,X0) ),
inference(factoring,[status(thm)],[p151]) ).
cnf(p244,plain,
( subset(sk16,X1)
| subset(sk16,X0)
| in(ordered_pair(sk0(sk16,sk3(sk16,X0)),sk1(sk16,sk3(sk16,X1))),cartesian_product2(relation_dom(sk16),relation_rng(sk16))) ),
inference(resolution,[status(thm)],[p201,p152]) ).
cnf(p6092,plain,
( subset(sk16,X0)
| in(ordered_pair(sk0(sk16,sk3(sk16,X0)),sk1(sk16,sk3(sk16,X0))),cartesian_product2(relation_dom(sk16),relation_rng(sk16))) ),
inference(factoring,[status(thm)],[p244]) ).
cnf(p6189,plain,
( subset(sk16,X0)
| in(sk3(sk16,X0),cartesian_product2(relation_dom(sk16),relation_rng(sk16)))
| subset(sk16,X0) ),
inference(superposition,[status(thm)],[p71,p6092]) ).
cnf(p6265,plain,
( in(sk3(sk16,X0),cartesian_product2(relation_dom(sk16),relation_rng(sk16)))
| subset(sk16,X0) ),
inference(factoring,[status(thm)],[p6189]) ).
cnf(c7,plain,
( ~ in(sk3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p6267,plain,
( subset(sk16,cartesian_product2(relation_dom(sk16),relation_rng(sk16)))
| subset(sk16,cartesian_product2(relation_dom(sk16),relation_rng(sk16))) ),
inference(resolution,[status(thm)],[p6265,c7]) ).
cnf(p6343,plain,
subset(sk16,cartesian_product2(relation_dom(sk16),relation_rng(sk16))),
inference(factoring,[status(thm)],[p6267]) ).
cnf(c51,plain,
~ subset(sk16,cartesian_product2(relation_dom(sk16),relation_rng(sk16))),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p6344,plain,
$false,
inference(resolution,[status(thm)],[p6343,c51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU178+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.41 % Computer : n009.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Thu Sep 24 13:04:14 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.34/2.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.34/2.73 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------