%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU242+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 : n006.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 0.14s 10.81s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of formulae : 56 ( 8 unt; 0 def)
% Number of atoms : 217 ( 31 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 247 ( 86 ~; 115 |; 38 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 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 : 60 ( 0 sgn 25 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_connected_in(A,B)
<=> ! [C,D] :
~ ( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
fof(f8_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) )
| is_connected_in(A,B) )
& ( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D] :
( ( ( ( ~ in(ordered_pair(sk1(A,B),sk0(A,B)),A)
& ~ in(ordered_pair(sk0(A,B),sk1(A,B)),A)
& sk0(A,B) != sk1(A,B)
& in(sk1(A,B),B)
& in(sk0(A,B),B) )
| is_connected_in(A,B) )
& ( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B)
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f8_nnf]) ).
cnf(c12,plain,
( in(sk0(X0,X1),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f24,conjecture,
! [A] :
( relation(A)
=> ( connected(A)
<=> ! [B,C] :
~ ( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f24_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( connected(A)
<=> ! [B,C] :
~ ( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f24_nnf,plain,
? [A] :
( ( ( ! [B,C] :
( in(ordered_pair(C,B),A)
| in(ordered_pair(B,C),A)
| B = C
| ~ in(C,relation_field(A))
| ~ in(B,relation_field(A)) )
& ~ connected(A) )
| ( ? [B,C] :
( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) )
& connected(A) ) )
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f24_neg]) ).
fof(f24_sk,plain,
! [B,C] :
( ( ( ( in(ordered_pair(C,B),sk3)
| in(ordered_pair(B,C),sk3)
| B = C
| ~ in(C,relation_field(sk3))
| ~ in(B,relation_field(sk3)) )
& ~ connected(sk3) )
| ( ~ in(ordered_pair(sk5,sk4),sk3)
& ~ in(ordered_pair(sk4,sk5),sk3)
& sk4 != sk5
& in(sk5,relation_field(sk3))
& in(sk4,relation_field(sk3))
& connected(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(p96,plain,
( in(sk0(sk3,X0),X0)
| is_connected_in(sk3,X0) ),
inference(resolution,[status(thm)],[c12,c32]) ).
cnf(c34,plain,
( in(ordered_pair(X2,X1),sk3)
| in(ordered_pair(X1,X2),sk3)
| X1 = X2
| ~ in(X2,relation_field(sk3))
| ~ in(X1,relation_field(sk3))
| connected(sk3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p101,plain,
( in(ordered_pair(X0,sk0(sk3,relation_field(sk3))),sk3)
| in(ordered_pair(sk0(sk3,relation_field(sk3)),X0),sk3)
| sk0(sk3,relation_field(sk3)) = X0
| ~ in(X0,relation_field(sk3))
| connected(sk3)
| is_connected_in(sk3,relation_field(sk3)) ),
inference(resolution,[status(thm)],[p96,c34]) ).
cnf(c13,plain,
( in(sk1(X0,X1),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p107,plain,
( in(sk1(sk3,X0),X0)
| is_connected_in(sk3,X0) ),
inference(resolution,[status(thm)],[c13,c32]) ).
cnf(p115,plain,
( is_connected_in(sk3,relation_field(sk3))
| in(ordered_pair(sk1(sk3,relation_field(sk3)),sk0(sk3,relation_field(sk3))),sk3)
| in(ordered_pair(sk0(sk3,relation_field(sk3)),sk1(sk3,relation_field(sk3))),sk3)
| sk0(sk3,relation_field(sk3)) = sk1(sk3,relation_field(sk3))
| connected(sk3)
| is_connected_in(sk3,relation_field(sk3)) ),
inference(resolution,[status(thm)],[p101,p107]) ).
cnf(p129,plain,
( in(ordered_pair(sk1(sk3,relation_field(sk3)),sk0(sk3,relation_field(sk3))),sk3)
| in(ordered_pair(sk0(sk3,relation_field(sk3)),sk1(sk3,relation_field(sk3))),sk3)
| sk0(sk3,relation_field(sk3)) = sk1(sk3,relation_field(sk3))
| connected(sk3)
| is_connected_in(sk3,relation_field(sk3)) ),
inference(factoring,[status(thm)],[p115]) ).
cnf(c16,plain,
( ~ in(ordered_pair(sk1(X0,X1),sk0(X0,X1)),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p130,plain,
( ~ in(ordered_pair(sk1(sk3,X0),sk0(sk3,X0)),sk3)
| is_connected_in(sk3,X0) ),
inference(resolution,[status(thm)],[c16,c32]) ).
cnf(p136,plain,
( is_connected_in(sk3,relation_field(sk3))
| in(ordered_pair(sk0(sk3,relation_field(sk3)),sk1(sk3,relation_field(sk3))),sk3)
| sk0(sk3,relation_field(sk3)) = sk1(sk3,relation_field(sk3))
| connected(sk3)
| is_connected_in(sk3,relation_field(sk3)) ),
inference(resolution,[status(thm)],[p129,p130]) ).
cnf(p137,plain,
( in(ordered_pair(sk0(sk3,relation_field(sk3)),sk1(sk3,relation_field(sk3))),sk3)
| sk0(sk3,relation_field(sk3)) = sk1(sk3,relation_field(sk3))
| connected(sk3)
| is_connected_in(sk3,relation_field(sk3)) ),
inference(factoring,[status(thm)],[p136]) ).
cnf(c15,plain,
( ~ in(ordered_pair(sk0(X0,X1),sk1(X0,X1)),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p123,plain,
( ~ in(ordered_pair(sk0(sk3,X0),sk1(sk3,X0)),sk3)
| is_connected_in(sk3,X0) ),
inference(resolution,[status(thm)],[c15,c32]) ).
cnf(p141,plain,
( is_connected_in(sk3,relation_field(sk3))
| sk0(sk3,relation_field(sk3)) = sk1(sk3,relation_field(sk3))
| connected(sk3)
| is_connected_in(sk3,relation_field(sk3)) ),
inference(resolution,[status(thm)],[p137,p123]) ).
cnf(p142,plain,
( sk0(sk3,relation_field(sk3)) = sk1(sk3,relation_field(sk3))
| connected(sk3)
| is_connected_in(sk3,relation_field(sk3)) ),
inference(factoring,[status(thm)],[p141]) ).
cnf(c14,plain,
( sk0(X0,X1) != sk1(X0,X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p116,plain,
( sk0(sk3,X0) != sk1(sk3,X0)
| is_connected_in(sk3,X0) ),
inference(resolution,[status(thm)],[c14,c32]) ).
cnf(p144,plain,
( is_connected_in(sk3,relation_field(sk3))
| connected(sk3)
| is_connected_in(sk3,relation_field(sk3)) ),
inference(resolution,[status(thm)],[p142,p116]) ).
cnf(p145,plain,
( connected(sk3)
| is_connected_in(sk3,relation_field(sk3)) ),
inference(factoring,[status(thm)],[p144]) ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f5_nnf,plain,
! [A] :
( ( ( ~ is_connected_in(A,relation_field(A))
| connected(A) )
& ( is_connected_in(A,relation_field(A))
| ~ connected(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( ( ( ~ is_connected_in(A,relation_field(A))
| connected(A) )
& ( is_connected_in(A,relation_field(A))
| ~ connected(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c8,plain,
( ~ is_connected_in(X0,relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p71,plain,
( ~ is_connected_in(sk3,relation_field(sk3))
| connected(sk3) ),
inference(resolution,[status(thm)],[c8,c32]) ).
cnf(p146,plain,
( connected(sk3)
| connected(sk3) ),
inference(resolution,[status(thm)],[p145,p71]) ).
cnf(p149,plain,
connected(sk3),
inference(factoring,[status(thm)],[p146]) ).
cnf(c7,plain,
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p67,plain,
( is_connected_in(sk3,relation_field(sk3))
| ~ connected(sk3) ),
inference(resolution,[status(thm)],[c7,c32]) ).
cnf(p152,plain,
is_connected_in(sk3,relation_field(sk3)),
inference(resolution,[status(thm)],[p149,p67]) ).
cnf(c11,plain,
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1)
| ~ is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p92,plain,
( in(ordered_pair(X2,X1),sk3)
| in(ordered_pair(X1,X2),sk3)
| X1 = X2
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ is_connected_in(sk3,X0) ),
inference(resolution,[status(thm)],[c11,c32]) ).
cnf(p159,plain,
( in(ordered_pair(X1,X0),sk3)
| in(ordered_pair(X0,X1),sk3)
| X0 = X1
| ~ in(X1,relation_field(sk3))
| ~ in(X0,relation_field(sk3)) ),
inference(resolution,[status(thm)],[p152,p92]) ).
cnf(c35,plain,
( ~ connected(sk3)
| in(sk4,relation_field(sk3)) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p150,plain,
in(sk4,relation_field(sk3)),
inference(resolution,[status(thm)],[p149,c35]) ).
cnf(p161,plain,
( in(ordered_pair(X0,sk4),sk3)
| in(ordered_pair(sk4,X0),sk3)
| sk4 = X0
| ~ in(X0,relation_field(sk3)) ),
inference(resolution,[status(thm)],[p159,p150]) ).
cnf(c37,plain,
( ~ connected(sk3)
| in(sk5,relation_field(sk3)) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p151,plain,
in(sk5,relation_field(sk3)),
inference(resolution,[status(thm)],[p149,c37]) ).
cnf(p163,plain,
( in(ordered_pair(sk5,sk4),sk3)
| in(ordered_pair(sk4,sk5),sk3)
| sk4 = sk5 ),
inference(resolution,[status(thm)],[p161,p151]) ).
cnf(c43,plain,
( ~ connected(sk3)
| ~ in(ordered_pair(sk5,sk4),sk3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p165,plain,
( ~ connected(sk3)
| in(ordered_pair(sk4,sk5),sk3)
| sk4 = sk5 ),
inference(resolution,[status(thm)],[p163,c43]) ).
cnf(p168,plain,
( in(ordered_pair(sk4,sk5),sk3)
| sk4 = sk5 ),
inference(resolution,[status(thm)],[p165,p149]) ).
cnf(c41,plain,
( ~ connected(sk3)
| ~ in(ordered_pair(sk4,sk5),sk3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p170,plain,
( ~ connected(sk3)
| sk4 = sk5 ),
inference(resolution,[status(thm)],[p168,c41]) ).
cnf(p173,plain,
sk4 = sk5,
inference(resolution,[status(thm)],[p170,p149]) ).
cnf(c39,plain,
( ~ connected(sk3)
| sk4 != sk5 ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p174,plain,
~ connected(sk3),
inference(resolution,[status(thm)],[p173,c39]) ).
cnf(p175,plain,
$false,
inference(resolution,[status(thm)],[p174,p149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU242+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/10.38 % Computer : n006.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Thu Sep 24 13:22:25 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/10.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/10.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------