%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU241+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 : n018.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 02:51:28 PM UTC 2026
% Result : Theorem 3.58s 1.09s
% Output : Proof 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 181 ( 25 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 206 ( 76 ~; 87 |; 30 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 3 sgn 34 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f33_nnf,plain,
! [A,B,C] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [C,A,B] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c54,plain,
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f24,conjecture,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f24_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f24_nnf,plain,
? [A] :
( ( ( ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) )
& ~ antisymmetric(A) )
| ( ? [B,C] :
( B != C
& in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
& antisymmetric(A) ) )
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f24_neg]) ).
fof(f24_sk,plain,
! [B,C] :
( ( ( ( B = C
| ~ in(ordered_pair(C,B),sk3)
| ~ in(ordered_pair(B,C),sk3) )
& ~ antisymmetric(sk3) )
| ( sk4 != sk5
& in(ordered_pair(sk5,sk4),sk3)
& in(ordered_pair(sk4,sk5),sk3)
& antisymmetric(sk3) ) )
& relation(sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f24_nnf]) ).
cnf(c32,plain,
relation(sk3),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p152,plain,
( in(X0,relation_field(sk3))
| ~ in(ordered_pair(X0,X1),sk3) ),
inference(resolution,[status(thm)],[c54,c32]) ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_antisymmetric_in(A,B)
<=> ! [C,D] :
( ( in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) )
=> C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f6_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( C != D
& in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) )
| is_antisymmetric_in(A,B) )
& ( ! [C,D] :
( C = D
| ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_antisymmetric_in(A,B) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( ( ( ( sk0(A,B) != sk1(A,B)
& in(ordered_pair(sk1(A,B),sk0(A,B)),A)
& in(ordered_pair(sk0(A,B),sk1(A,B)),A)
& in(sk1(A,B),B)
& in(sk0(A,B),B) )
| is_antisymmetric_in(A,B) )
& ( C = D
| ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(D,B)
| ~ in(C,B)
| ~ is_antisymmetric_in(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f6_nnf]) ).
cnf(c14,plain,
( sk0(X0,X1) != sk1(X0,X1)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p119,plain,
( sk0(sk3,X0) != sk1(sk3,X0)
| is_antisymmetric_in(sk3,X0) ),
inference(resolution,[status(thm)],[c14,c32]) ).
cnf(c13,plain,
( in(ordered_pair(sk1(X0,X1),sk0(X0,X1)),X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p107,plain,
( in(ordered_pair(sk1(sk3,X0),sk0(sk3,X0)),sk3)
| is_antisymmetric_in(sk3,X0) ),
inference(resolution,[status(thm)],[c13,c32]) ).
cnf(c12,plain,
( in(ordered_pair(sk0(X0,X1),sk1(X0,X1)),X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p98,plain,
( in(ordered_pair(sk0(sk3,X0),sk1(sk3,X0)),sk3)
| is_antisymmetric_in(sk3,X0) ),
inference(resolution,[status(thm)],[c12,c32]) ).
cnf(c34,plain,
( X1 = X2
| ~ in(ordered_pair(X2,X1),sk3)
| ~ in(ordered_pair(X1,X2),sk3)
| antisymmetric(sk3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p103,plain,
( sk0(sk3,X0) = sk1(sk3,X0)
| ~ in(ordered_pair(sk1(sk3,X0),sk0(sk3,X0)),sk3)
| antisymmetric(sk3)
| is_antisymmetric_in(sk3,X0) ),
inference(resolution,[status(thm)],[p98,c34]) ).
cnf(p115,plain,
( sk0(sk3,X0) = sk1(sk3,X0)
| antisymmetric(sk3)
| is_antisymmetric_in(sk3,X0)
| is_antisymmetric_in(sk3,X0) ),
inference(resolution,[status(thm)],[p107,p103]) ).
cnf(p116,plain,
( sk0(sk3,X0) = sk1(sk3,X0)
| antisymmetric(sk3)
| is_antisymmetric_in(sk3,X0) ),
inference(factoring,[status(thm)],[p115]) ).
cnf(p123,plain,
( antisymmetric(sk3)
| is_antisymmetric_in(sk3,X0)
| is_antisymmetric_in(sk3,X0) ),
inference(resolution,[status(thm)],[p119,p116]) ).
cnf(p124,plain,
( antisymmetric(sk3)
| is_antisymmetric_in(sk3,X0) ),
inference(factoring,[status(thm)],[p123]) ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f5_nnf,plain,
! [A] :
( ( ( ~ is_antisymmetric_in(A,relation_field(A))
| antisymmetric(A) )
& ( is_antisymmetric_in(A,relation_field(A))
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( ( ( ~ is_antisymmetric_in(A,relation_field(A))
| antisymmetric(A) )
& ( is_antisymmetric_in(A,relation_field(A))
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c8,plain,
( ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p69,plain,
( ~ is_antisymmetric_in(sk3,relation_field(sk3))
| antisymmetric(sk3) ),
inference(resolution,[status(thm)],[c8,c32]) ).
cnf(p125,plain,
( antisymmetric(sk3)
| antisymmetric(sk3) ),
inference(resolution,[status(thm)],[p124,p69]) ).
cnf(p126,plain,
antisymmetric(sk3),
inference(factoring,[status(thm)],[p125]) ).
cnf(c35,plain,
( ~ antisymmetric(sk3)
| in(ordered_pair(sk4,sk5),sk3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p131,plain,
in(ordered_pair(sk4,sk5),sk3),
inference(resolution,[status(thm)],[p126,c35]) ).
cnf(p158,plain,
in(sk4,relation_field(sk3)),
inference(resolution,[status(thm)],[p152,p131]) ).
cnf(c7,plain,
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p65,plain,
( is_antisymmetric_in(sk3,relation_field(sk3))
| ~ antisymmetric(sk3) ),
inference(resolution,[status(thm)],[c7,c32]) ).
cnf(p133,plain,
is_antisymmetric_in(sk3,relation_field(sk3)),
inference(resolution,[status(thm)],[p126,p65]) ).
cnf(c9,plain,
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p81,plain,
( X1 = X2
| ~ in(ordered_pair(X2,X1),sk3)
| ~ in(ordered_pair(X1,X2),sk3)
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ is_antisymmetric_in(sk3,X0) ),
inference(resolution,[status(thm)],[c9,c32]) ).
cnf(p134,plain,
( X0 = X1
| ~ in(ordered_pair(X1,X0),sk3)
| ~ in(ordered_pair(X0,X1),sk3)
| ~ in(X1,relation_field(sk3))
| ~ in(X0,relation_field(sk3)) ),
inference(resolution,[status(thm)],[p133,p81]) ).
cnf(p162,plain,
( sk4 = X0
| ~ in(ordered_pair(X0,sk4),sk3)
| ~ in(ordered_pair(sk4,X0),sk3)
| ~ in(X0,relation_field(sk3)) ),
inference(resolution,[status(thm)],[p158,p134]) ).
cnf(c37,plain,
( ~ antisymmetric(sk3)
| in(ordered_pair(sk5,sk4),sk3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p132,plain,
in(ordered_pair(sk5,sk4),sk3),
inference(resolution,[status(thm)],[p126,c37]) ).
cnf(p159,plain,
in(sk5,relation_field(sk3)),
inference(resolution,[status(thm)],[p152,p132]) ).
cnf(p178,plain,
( sk4 = sk5
| ~ in(ordered_pair(sk5,sk4),sk3)
| ~ in(ordered_pair(sk4,sk5),sk3) ),
inference(resolution,[status(thm)],[p162,p159]) ).
cnf(p181,plain,
( sk4 = sk5
| ~ in(ordered_pair(sk5,sk4),sk3) ),
inference(resolution,[status(thm)],[p178,p131]) ).
cnf(p182,plain,
sk4 = sk5,
inference(resolution,[status(thm)],[p181,p132]) ).
cnf(c39,plain,
( ~ antisymmetric(sk3)
| sk4 != sk5 ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p183,plain,
~ antisymmetric(sk3),
inference(resolution,[status(thm)],[p182,c39]) ).
cnf(p188,plain,
$false,
inference(resolution,[status(thm)],[p183,p126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU241+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n018.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 13:24:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.58/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.58/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------