%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU191+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 : Tue Sep 29 12:47:39 PM UTC 2026
% Result : Theorem 3.10s 1.06s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 71 ( 8 unt; 0 def)
% Number of atoms : 345 ( 52 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 484 ( 210 ~; 203 |; 53 &)
% ( 10 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 190 ( 162 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( in(X2,X0)
& X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f12,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
? [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<~> ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) ) )
& relation(X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( in(X2,X0)
& X2 = X3 ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f43,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f44,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f43]) ).
fof(f46,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) )
& ( ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) )
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) )
& relation(X3) ),
inference(nnf_transformation,[],[f33]) ).
fof(f47,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) )
& ( ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) )
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) )
& relation(X3) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
( ( ~ in(sK0,sK2)
| ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3)) )
& ( ( in(sK0,sK2)
& in(ordered_pair(sK0,sK1),sK3) )
| in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3)) )
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ? [X2,X3] :
( ( ~ in(X2,X0)
| X2 != X3
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( in(X2,X0)
& X2 = X3 )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(X2,X0)
| X2 != X3 )
& ( ( in(X2,X0)
& X2 = X3 )
| ~ in(ordered_pair(X2,X3),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f36]) ).
fof(f50,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ? [X2,X3] :
( ( ~ in(X2,X0)
| X2 != X3
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( in(X2,X0)
& X2 = X3 )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(X2,X0)
| X2 != X3 )
& ( ( in(X2,X0)
& X2 = X3 )
| ~ in(ordered_pair(X2,X3),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ? [X2,X3] :
( ( ~ in(X2,X0)
| X2 != X3
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( in(X2,X0)
& X2 = X3 )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(X4,X0)
| X4 != X5 )
& ( ( in(X4,X0)
& X4 = X5 )
| ~ in(ordered_pair(X4,X5),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ( ( ~ in(sK4(X0,X1),X0)
| sK4(X0,X1) != sK5(X0,X1)
| ~ in(ordered_pair(sK4(X0,X1),sK5(X0,X1)),X1) )
& ( ( in(sK4(X0,X1),X0)
& sK4(X0,X1) = sK5(X0,X1) )
| in(ordered_pair(sK4(X0,X1),sK5(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(X4,X0)
| X4 != X5 )
& ( ( in(X4,X0)
& X4 = X5 )
| ~ in(ordered_pair(X4,X5),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1))],[f51]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) ) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ( ( ! [X5] :
( ~ in(ordered_pair(sK6(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK7(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK6(X0,X1,X2),sK7(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK6(X0,X1,X2),sK8(X0,X1,X2)),X0)
& in(ordered_pair(sK8(X0,X1,X2),sK7(X0,X1,X2)),X1) )
| in(ordered_pair(sK6(X0,X1,X2),sK7(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ( in(ordered_pair(X7,sK9(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK9(X0,X1,X7,X8),X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X4,sK7(X0,X1,X2)),skolemize(X6,sK8(X0,X1,X2)),skolemize(X10,sK9(X0,X1,X7,X8))],[f54]) ).
fof(f60,plain,
relation(sK3),
inference(cnf_transformation,[],[f48]) ).
fof(f61,plain,
( in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| in(ordered_pair(sK0,sK1),sK3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f62,plain,
( in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| in(sK0,sK2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f63,plain,
( ~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(sK0,sK2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f66,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f67,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f68,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f69,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(X4,X0)
| X4 != X5
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f74,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK9(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f75,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK9(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f76,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),X2)
| ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f89,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f93,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,X5),X1)
| ~ in(X5,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(equality_resolution,[],[f69]) ).
fof(f94,plain,
! [X0,X5] :
( in(ordered_pair(X5,X5),identity_relation(X0))
| ~ in(X5,X0)
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f93]) ).
fof(f95,plain,
! [X0,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f68]) ).
fof(f96,plain,
! [X0,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f67]) ).
fof(f97,plain,
! [X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1)
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f76]) ).
fof(f98,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(X7,sK9(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f75]) ).
fof(f99,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(sK9(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f74]) ).
fof(f124,plain,
! [X0,X5] :
( in(ordered_pair(X5,X5),identity_relation(X0))
| ~ in(X5,X0) ),
inference(forward_subsumption_resolution,[],[f94,f66]) ).
fof(f127,plain,
! [X0,X4,X5] :
( ~ in(ordered_pair(X4,X5),identity_relation(X0))
| in(X4,X0) ),
inference(forward_subsumption_resolution,[],[f95,f66]) ).
fof(f129,plain,
! [X0,X4,X5] :
( ~ in(ordered_pair(X4,X5),identity_relation(X0))
| X4 = X5 ),
inference(forward_subsumption_resolution,[],[f96,f66]) ).
fof(f174,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(X7,sK9(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f98,f89]) ).
fof(f176,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3)
| ~ relation(identity_relation(X2))
| sK9(identity_relation(X2),X3,X0,X1) = X0 ),
inference(resolution,[],[f174,f129]) ).
fof(f182,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3)
| sK9(identity_relation(X2),X3,X0,X1) = X0 ),
inference(forward_subsumption_resolution,[],[f176,f66]) ).
fof(f183,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(sK9(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f99,f89]) ).
fof(f191,plain,
! [X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f97,f89]) ).
fof(f192,plain,
! [X0] :
( ~ in(ordered_pair(sK0,X0),identity_relation(sK2))
| ~ in(ordered_pair(X0,sK1),sK3)
| ~ relation(sK3)
| ~ relation(identity_relation(sK2))
| ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(sK0,sK2) ),
inference(resolution,[],[f191,f63]) ).
fof(f195,plain,
! [X0] :
( ~ in(ordered_pair(sK0,X0),identity_relation(sK2))
| ~ in(ordered_pair(X0,sK1),sK3)
| ~ relation(sK3)
| ~ relation(identity_relation(sK2))
| ~ in(ordered_pair(sK0,sK1),sK3) ),
inference(forward_subsumption_resolution,[],[f192,f127]) ).
fof(f196,plain,
! [X0] :
( ~ in(ordered_pair(sK0,X0),identity_relation(sK2))
| ~ in(ordered_pair(X0,sK1),sK3)
| ~ relation(identity_relation(sK2))
| ~ in(ordered_pair(sK0,sK1),sK3) ),
inference(forward_subsumption_resolution,[],[f195,f60]) ).
fof(f197,plain,
! [X0] :
( ~ in(ordered_pair(sK0,X0),identity_relation(sK2))
| ~ in(ordered_pair(X0,sK1),sK3)
| ~ in(ordered_pair(sK0,sK1),sK3) ),
inference(forward_subsumption_resolution,[],[f196,f66]) ).
fof(f198,plain,
( ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(sK0,sK2) ),
inference(resolution,[],[f197,f124]) ).
fof(f199,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK9(identity_relation(sK2),X0,sK0,X1),sK1),sK3)
| ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(ordered_pair(sK0,X1),relation_composition(identity_relation(sK2),X0))
| ~ relation(X0)
| ~ relation(identity_relation(sK2)) ),
inference(resolution,[],[f197,f174]) ).
fof(f201,plain,
( ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(sK0,sK2) ),
inference(duplicate_literal_removal,[],[f198]) ).
fof(f202,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK9(identity_relation(sK2),X0,sK0,X1),sK1),sK3)
| ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(ordered_pair(sK0,X1),relation_composition(identity_relation(sK2),X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f199,f66]) ).
fof(f225,plain,
( ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| ~ relation(sK3)
| ~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| ~ relation(sK3)
| ~ relation(identity_relation(sK2)) ),
inference(resolution,[],[f202,f183]) ).
fof(f227,plain,
( ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| ~ relation(sK3)
| ~ relation(identity_relation(sK2)) ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f228,plain,
( ~ in(ordered_pair(sK0,sK1),sK3)
| ~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| ~ relation(identity_relation(sK2)) ),
inference(forward_subsumption_resolution,[],[f227,f60]) ).
fof(f229,plain,
( ~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| ~ in(ordered_pair(sK0,sK1),sK3) ),
inference(forward_subsumption_resolution,[],[f228,f66]) ).
fof(f237,plain,
( ~ in(ordered_pair(sK0,sK1),sK3)
| in(sK0,sK2) ),
inference(resolution,[],[f229,f62]) ).
fof(f240,plain,
~ in(ordered_pair(sK0,sK1),sK3),
inference(forward_subsumption_resolution,[],[f237,f201]) ).
fof(f326,plain,
( ~ relation(sK3)
| sK0 = sK9(identity_relation(sK2),sK3,sK0,sK1)
| in(ordered_pair(sK0,sK1),sK3) ),
inference(resolution,[],[f182,f61]) ).
fof(f335,plain,
( sK0 = sK9(identity_relation(sK2),sK3,sK0,sK1)
| in(ordered_pair(sK0,sK1),sK3) ),
inference(forward_subsumption_resolution,[],[f326,f60]) ).
fof(f337,plain,
sK0 = sK9(identity_relation(sK2),sK3,sK0,sK1),
inference(forward_subsumption_resolution,[],[f335,f240]) ).
fof(f340,plain,
( in(ordered_pair(sK0,sK1),sK3)
| ~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| ~ relation(sK3)
| ~ relation(identity_relation(sK2)) ),
inference(superposition,[],[f183,f337]) ).
fof(f344,plain,
( ~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| ~ relation(sK3)
| ~ relation(identity_relation(sK2)) ),
inference(forward_subsumption_resolution,[],[f340,f229]) ).
fof(f346,plain,
( ~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3))
| ~ relation(identity_relation(sK2)) ),
inference(forward_subsumption_resolution,[],[f344,f60]) ).
fof(f347,plain,
~ in(ordered_pair(sK0,sK1),relation_composition(identity_relation(sK2),sK3)),
inference(forward_subsumption_resolution,[],[f346,f66]) ).
fof(f351,plain,
in(ordered_pair(sK0,sK1),sK3),
inference(resolution,[],[f347,f61]) ).
fof(f356,plain,
$false,
inference(forward_subsumption_resolution,[],[f351,f240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU191+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:57:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.10/1.06 % (1419116)Detected formulas, will run a generic FOF schedule.
% 3.10/1.06 % (1419124)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1860288781:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.10/1.06 % (1419125)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2991005048:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.10/1.06 % (1419127)dis-21_1_sil=8000:lcm=predicate:random_seed=2208510648:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.10/1.06 % (1419123)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1633265618:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.10/1.06 % (1419122)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1573609330:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.10/1.06 % (1419121)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1096446869:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.10/1.06 % (1419126)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1886770266:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.10/1.06 % (1419124)Refutation not found, incomplete strategy
% 3.10/1.06 % (1419124)------------------------------
% 3.10/1.06 % (1419124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.06 % (1419124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.06 % (1419124)CaDiCaL version: 2.1.3
% 3.10/1.06 % (1419124)Termination reason: Refutation not found, incomplete strategy
% 3.10/1.06 % (1419124)Time elapsed: 0.003 s
% 3.10/1.06 % (1419124)Peak memory usage: 88 MB
% 3.10/1.06 % (1419124)Instructions burned: 3 (million)
% 3.10/1.06 % (1419125)First to succeed.
% 3.10/1.06 % (1419125)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1419116"
% 3.10/1.06 % (1419126)Also succeeded, but the first one will report.
% 3.10/1.06 % (1419127)Instruction limit reached!
% 3.10/1.06 % (1419127)------------------------------
% 3.10/1.06 % (1419127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.06 % (1419127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.06 % (1419127)CaDiCaL version: 2.1.3
% 3.10/1.06 % (1419127)Termination reason: Instruction limit
% 3.10/1.06 % (1419127)Termination phase: Saturation
% 3.10/1.06 % (1419127)Time elapsed: 0.062 s
% 3.10/1.06 % (1419127)Peak memory usage: 90 MB
% 3.10/1.06 % (1419127)Instructions burned: 130 (million)
% 3.10/1.06 % (1419135)lrs+10_1_sil=8000:sp=occurrence:random_seed=3764723454:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.10/1.06 % (1419124)------------------------------
% 3.10/1.06 % (1419124)------------------------------
% 3.10/1.06 % (1419125)Refutation found. Thanks to Tanya!
% 3.10/1.06 % SZS status Theorem for theBenchmark
% 3.10/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.25 % (1419125)------------------------------
% 3.47/1.25 % (1419125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.25 % (1419125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.25 % (1419125)CaDiCaL version: 2.1.3
% 3.47/1.25 % (1419125)Termination reason: Refutation
% 3.47/1.25 % (1419125)Time elapsed: 0.011 s
% 3.47/1.25 % (1419125)Peak memory usage: 88 MB
% 3.47/1.25 % (1419125)Instructions burned: 15 (million)
% 3.47/1.25 % (1419125)------------------------------
% 3.47/1.25 % (1419125)------------------------------
% 3.47/1.25 % (1419116)Success in time 0.436 s
% 3.47/1.25 % Vampire exiting
%------------------------------------------------------------------------------