%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU240+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 : n019.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 3.02s 6.05s
% Output : Proof 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 11 unt; 0 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 233 ( 88 ~; 99 |; 33 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 5 sgn 41 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_transitive_in(A,B)
<=> ! [C,D,E] :
( ( in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
=> in(ordered_pair(C,E),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
fof(f8_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C,D,E] :
( ~ in(ordered_pair(C,E),A)
& in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
| is_transitive_in(A,B) )
& ( ! [C,D,E] :
( in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E] :
( ( ( ( ~ in(ordered_pair(sk0(A,B),sk2(A,B)),A)
& in(ordered_pair(sk1(A,B),sk2(A,B)),A)
& in(ordered_pair(sk0(A,B),sk1(A,B)),A)
& in(sk2(A,B),B)
& in(sk1(A,B),B)
& in(sk0(A,B),B) )
| is_transitive_in(A,B) )
& ( in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B)
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f8_nnf]) ).
cnf(c17,plain,
( ~ in(ordered_pair(sk0(X0,X1),sk2(X0,X1)),X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f24,conjecture,
! [A] :
( relation(A)
=> ( transitive(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
=> in(ordered_pair(B,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
fof(f24_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( transitive(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
=> in(ordered_pair(B,D),A) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f24_nnf,plain,
? [A] :
( ( ( ! [B,C,D] :
( in(ordered_pair(B,D),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) )
& ~ transitive(A) )
| ( ? [B,C,D] :
( ~ in(ordered_pair(B,D),A)
& in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
& transitive(A) ) )
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f24_neg]) ).
fof(f24_sk,plain,
! [B,C,D] :
( ( ( ( in(ordered_pair(B,D),sk4)
| ~ in(ordered_pair(C,D),sk4)
| ~ in(ordered_pair(B,C),sk4) )
& ~ transitive(sk4) )
| ( ~ in(ordered_pair(sk5,sk7),sk4)
& in(ordered_pair(sk6,sk7),sk4)
& in(ordered_pair(sk5,sk6),sk4)
& transitive(sk4) ) )
& relation(sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7])],[f24_nnf]) ).
cnf(c33,plain,
relation(sk4),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p148,plain,
( ~ in(ordered_pair(sk0(sk4,X0),sk2(sk4,X0)),sk4)
| is_transitive_in(sk4,X0) ),
inference(resolution,[status(thm)],[c17,c33]) ).
cnf(c16,plain,
( in(ordered_pair(sk1(X0,X1),sk2(X0,X1)),X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p134,plain,
( in(ordered_pair(sk1(sk4,X0),sk2(sk4,X0)),sk4)
| is_transitive_in(sk4,X0) ),
inference(resolution,[status(thm)],[c16,c33]) ).
cnf(c15,plain,
( in(ordered_pair(sk0(X0,X1),sk1(X0,X1)),X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p125,plain,
( in(ordered_pair(sk0(sk4,X0),sk1(sk4,X0)),sk4)
| is_transitive_in(sk4,X0) ),
inference(resolution,[status(thm)],[c15,c33]) ).
cnf(c35,plain,
( in(ordered_pair(X1,X3),sk4)
| ~ in(ordered_pair(X2,X3),sk4)
| ~ in(ordered_pair(X1,X2),sk4)
| transitive(sk4) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p132,plain,
( in(ordered_pair(sk0(sk4,X0),X1),sk4)
| ~ in(ordered_pair(sk1(sk4,X0),X1),sk4)
| transitive(sk4)
| is_transitive_in(sk4,X0) ),
inference(resolution,[status(thm)],[p125,c35]) ).
cnf(p142,plain,
( in(ordered_pair(sk0(sk4,X0),sk2(sk4,X0)),sk4)
| transitive(sk4)
| is_transitive_in(sk4,X0)
| is_transitive_in(sk4,X0) ),
inference(resolution,[status(thm)],[p134,p132]) ).
cnf(p143,plain,
( in(ordered_pair(sk0(sk4,X0),sk2(sk4,X0)),sk4)
| transitive(sk4)
| is_transitive_in(sk4,X0) ),
inference(factoring,[status(thm)],[p142]) ).
cnf(p152,plain,
( transitive(sk4)
| is_transitive_in(sk4,X0)
| is_transitive_in(sk4,X0) ),
inference(resolution,[status(thm)],[p148,p143]) ).
cnf(p153,plain,
( transitive(sk4)
| is_transitive_in(sk4,X0) ),
inference(factoring,[status(thm)],[p152]) ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f5_nnf,plain,
! [A] :
( ( ( ~ is_transitive_in(A,relation_field(A))
| transitive(A) )
& ( is_transitive_in(A,relation_field(A))
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( ( ( ~ is_transitive_in(A,relation_field(A))
| transitive(A) )
& ( is_transitive_in(A,relation_field(A))
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c8,plain,
( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p74,plain,
( ~ is_transitive_in(sk4,relation_field(sk4))
| transitive(sk4) ),
inference(resolution,[status(thm)],[c8,c33]) ).
cnf(p154,plain,
( transitive(sk4)
| transitive(sk4) ),
inference(resolution,[status(thm)],[p153,p74]) ).
cnf(p155,plain,
transitive(sk4),
inference(factoring,[status(thm)],[p154]) ).
cnf(c7,plain,
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p70,plain,
( is_transitive_in(sk4,relation_field(sk4))
| ~ transitive(sk4) ),
inference(resolution,[status(thm)],[c7,c33]) ).
cnf(p159,plain,
is_transitive_in(sk4,relation_field(sk4)),
inference(resolution,[status(thm)],[p155,p70]) ).
cnf(c11,plain,
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| ~ is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p99,plain,
( in(ordered_pair(X1,X3),sk4)
| ~ in(ordered_pair(X2,X3),sk4)
| ~ in(ordered_pair(X1,X2),sk4)
| ~ in(X3,X0)
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ is_transitive_in(sk4,X0) ),
inference(resolution,[status(thm)],[c11,c33]) ).
cnf(p160,plain,
( in(ordered_pair(X0,X2),sk4)
| ~ in(ordered_pair(X1,X2),sk4)
| ~ in(ordered_pair(X0,X1),sk4)
| ~ in(X2,relation_field(sk4))
| ~ in(X1,relation_field(sk4))
| ~ in(X0,relation_field(sk4)) ),
inference(resolution,[status(thm)],[p159,p99]) ).
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/sandbox2/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(c55,plain,
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p174,plain,
( in(X0,relation_field(sk4))
| ~ in(ordered_pair(X0,X1),sk4) ),
inference(resolution,[status(thm)],[c55,c33]) ).
cnf(c36,plain,
( ~ transitive(sk4)
| in(ordered_pair(sk5,sk6),sk4) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p158,plain,
in(ordered_pair(sk5,sk6),sk4),
inference(resolution,[status(thm)],[p155,c36]) ).
cnf(p181,plain,
in(sk5,relation_field(sk4)),
inference(resolution,[status(thm)],[p174,p158]) ).
cnf(p232,plain,
( in(ordered_pair(sk5,X1),sk4)
| ~ in(ordered_pair(X0,X1),sk4)
| ~ in(ordered_pair(sk5,X0),sk4)
| ~ in(X1,relation_field(sk4))
| ~ in(X0,relation_field(sk4)) ),
inference(resolution,[status(thm)],[p160,p181]) ).
cnf(c38,plain,
( ~ transitive(sk4)
| in(ordered_pair(sk6,sk7),sk4) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p157,plain,
in(ordered_pair(sk6,sk7),sk4),
inference(resolution,[status(thm)],[p155,c38]) ).
cnf(p180,plain,
in(sk6,relation_field(sk4)),
inference(resolution,[status(thm)],[p174,p157]) ).
cnf(p255,plain,
( in(ordered_pair(sk5,X0),sk4)
| ~ in(ordered_pair(sk6,X0),sk4)
| ~ in(ordered_pair(sk5,sk6),sk4)
| ~ in(X0,relation_field(sk4)) ),
inference(resolution,[status(thm)],[p232,p180]) ).
cnf(c56,plain,
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p187,plain,
( in(X1,relation_field(sk4))
| ~ in(ordered_pair(X0,X1),sk4) ),
inference(resolution,[status(thm)],[c56,c33]) ).
cnf(p197,plain,
in(sk7,relation_field(sk4)),
inference(resolution,[status(thm)],[p187,p157]) ).
cnf(p261,plain,
( in(ordered_pair(sk5,sk7),sk4)
| ~ in(ordered_pair(sk6,sk7),sk4)
| ~ in(ordered_pair(sk5,sk6),sk4) ),
inference(resolution,[status(thm)],[p255,p197]) ).
cnf(p263,plain,
( in(ordered_pair(sk5,sk7),sk4)
| ~ in(ordered_pair(sk6,sk7),sk4) ),
inference(resolution,[status(thm)],[p261,p158]) ).
cnf(p264,plain,
in(ordered_pair(sk5,sk7),sk4),
inference(resolution,[status(thm)],[p263,p157]) ).
cnf(c40,plain,
( ~ transitive(sk4)
| ~ in(ordered_pair(sk5,sk7),sk4) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p268,plain,
~ transitive(sk4),
inference(resolution,[status(thm)],[p264,c40]) ).
cnf(p270,plain,
$false,
inference(resolution,[status(thm)],[p268,p155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU240+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.60 % Computer : n019.cluster.edu
% 0.11/5.60 % Model : x86_64 x86_64
% 0.11/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.60 % Memory : 8046.5625MB
% 0.11/5.60 % OS : Linux 6.8.0-71-generic
% 0.11/5.60 % CPULimit : 300
% 0.11/5.60 % WCLimit : 300
% 0.11/5.60 % DateTime : Thu Sep 24 13:22:25 UTC 2026
% 0.14/5.60 % CPUTime :
% 0.14/5.60 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.02/6.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.02/6.05 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------