%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU195+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 : n001.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 12:47:40 PM UTC 2026
% Result : Theorem 2.72s 1.25s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 116 ( 19 unt; 9 def)
% Number of atoms : 432 ( 36 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 555 ( 239 ~; 248 |; 40 &)
% ( 19 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 182 ( 0 sgn 170 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
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(f13,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f30,axiom,
! [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(f33,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f37,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) ) ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f40,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f50,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(f53,plain,
? [X0,X1] :
( relation_dom_restriction(X1,X0) != relation_composition(identity_relation(X0),X1)
& relation(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f54,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f37]) ).
fof(f55,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ? [X3,X4] :
( ( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0) )
& ( ( in(X5,X1)
& in(ordered_pair(X5,X6),X0) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = relation_dom_restriction(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),X1)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) )
& ( ( in(sK0(X0,X1,X2),X1)
& in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0) )
| in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0) )
& ( ( in(X5,X1)
& in(ordered_pair(X5,X6),X0) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X4,sK1(X0,X1,X2))],[f56]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f38]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X5),X1) )
& ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1)
| ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0) )
& ( in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1)
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X5),X1) )
& ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f59]) ).
fof(f66,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) )
& ( ( 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,[],[f50]) ).
fof(f67,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) )
& ( ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) )
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) )
| ~ relation(X3) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
( relation_dom_restriction(sK10,sK9) != relation_composition(identity_relation(sK9),sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f53]) ).
fof(f72,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f73,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f74,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f80,plain,
! [X0,X1] :
( X0 = X1
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1)
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f81,plain,
! [X0,X1] :
( X0 = X1
| ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1)
| ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f83,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f84,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f85,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f67]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f67]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),X3)
| ~ relation(X3) ),
inference(cnf_transformation,[],[f67]) ).
fof(f111,plain,
relation(sK10),
inference(cnf_transformation,[],[f68]) ).
fof(f112,plain,
relation_dom_restriction(sK10,sK9) != relation_composition(identity_relation(sK9),sK10),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f74,f82,f82]) ).
fof(f117,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f73,f82]) ).
fof(f118,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f72,f82,f82]) ).
fof(f119,plain,
! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f81,f82,f82]) ).
fof(f120,plain,
! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f80,f82,f82]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(identity_relation(X2),X3))
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3)
| ~ relation(X3) ),
inference(definition_unfolding,[],[f108,f82,f82]) ).
fof(f125,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(identity_relation(X2),X3))
| in(X0,X2)
| ~ relation(X3) ),
inference(definition_unfolding,[],[f107,f82]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_composition(identity_relation(X2),X3))
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X3)
| ~ relation(X3) ),
inference(definition_unfolding,[],[f106,f82,f82]) ).
fof(f127,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f116]) ).
fof(f128,plain,
! [X0,X1,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| in(X5,X1)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f117]) ).
fof(f129,plain,
! [X0,X1,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f118]) ).
fof(f132,definition,
! [X0,X1] :
( sQ11_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ11_eqProxy])],[equality_proxy_definition]) ).
fof(f137,plain,
! [X0,X1] :
( sQ11_eqProxy(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f119,f132]) ).
fof(f138,plain,
! [X0,X1] :
( sQ11_eqProxy(X0,X1)
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f120,f132]) ).
fof(f141,plain,
~ sQ11_eqProxy(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),
inference(equality_proxy_replacement,[],[f112,f132]) ).
fof(f210,definition,
( spl12_3
<=> relation(sK10) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f211,plain,
( ~ relation(sK10)
| spl12_3 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f213,definition,
( spl12_4
<=> relation(relation_composition(identity_relation(sK9),sK10)) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f214,plain,
( ~ relation(relation_composition(identity_relation(sK9),sK10))
| spl12_4 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f222,plain,
( $false
| spl12_3 ),
inference(resolution,[],[f211,f111]) ).
fof(f223,plain,
spl12_3,
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f224,plain,
( ~ relation(identity_relation(sK9))
| ~ relation(sK10)
| spl12_4 ),
inference(resolution,[],[f214,f83]) ).
fof(f226,definition,
( spl12_7
<=> relation(identity_relation(sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f227,plain,
( ~ relation(identity_relation(sK9))
| spl12_7 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f228,plain,
( ~ spl12_3
| ~ spl12_7
| spl12_4 ),
inference(avatar_split_clause,[],[f224,f213,f226,f210]) ).
fof(f229,plain,
( $false
| spl12_7 ),
inference(resolution,[],[f227,f84]) ).
fof(f230,plain,
spl12_7,
inference(avatar_contradiction_clause,[],[f229]) ).
fof(f242,plain,
( ~ in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_composition(identity_relation(sK9),sK10))
| ~ in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_dom_restriction(sK10,sK9))
| ~ relation(relation_composition(identity_relation(sK9),sK10))
| ~ relation(relation_dom_restriction(sK10,sK9)) ),
inference(resolution,[],[f137,f141]) ).
fof(f245,definition,
( spl12_9
<=> relation(relation_dom_restriction(sK10,sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f246,plain,
( ~ relation(relation_dom_restriction(sK10,sK9))
| spl12_9 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f255,definition,
( spl12_12
<=> in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_dom_restriction(sK10,sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
fof(f256,plain,
( ~ in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_dom_restriction(sK10,sK9))
| spl12_12 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f258,definition,
( spl12_13
<=> in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_composition(identity_relation(sK9),sK10)) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
fof(f259,plain,
( ~ in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_composition(identity_relation(sK9),sK10))
| spl12_13 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f260,plain,
( ~ spl12_9
| ~ spl12_4
| ~ spl12_12
| ~ spl12_13 ),
inference(avatar_split_clause,[],[f242,f258,f255,f213,f245]) ).
fof(f261,plain,
( ~ relation(sK10)
| spl12_9 ),
inference(resolution,[],[f246,f85]) ).
fof(f262,plain,
( ~ spl12_3
| spl12_9 ),
inference(avatar_split_clause,[],[f261,f245,f210]) ).
fof(f263,plain,
( ~ in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9)
| ~ in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),sK10)
| ~ relation(sK10)
| spl12_13 ),
inference(resolution,[],[f259,f124]) ).
fof(f265,definition,
( spl12_14
<=> in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),sK10) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
fof(f268,definition,
( spl12_15
<=> in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
fof(f270,plain,
( ~ spl12_3
| ~ spl12_14
| ~ spl12_15
| spl12_13 ),
inference(avatar_split_clause,[],[f263,f258,f268,f265,f210]) ).
fof(f279,plain,
( in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_composition(identity_relation(sK9),sK10))
| in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_dom_restriction(sK10,sK9))
| ~ relation(relation_composition(identity_relation(sK9),sK10))
| ~ relation(relation_dom_restriction(sK10,sK9)) ),
inference(resolution,[],[f138,f141]) ).
fof(f284,plain,
( in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_dom_restriction(sK10,sK9))
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f285,plain,
( in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),relation_composition(identity_relation(sK9),sK10))
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f286,plain,
( ~ spl12_9
| ~ spl12_4
| spl12_12
| spl12_13 ),
inference(avatar_split_clause,[],[f279,f258,f255,f213,f245]) ).
fof(f287,plain,
( in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),sK10)
| ~ relation(relation_dom_restriction(sK10,sK9))
| ~ relation(sK10)
| ~ spl12_12 ),
inference(resolution,[],[f284,f129]) ).
fof(f288,plain,
( in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9)
| ~ relation(relation_dom_restriction(sK10,sK9))
| ~ relation(sK10)
| ~ spl12_12 ),
inference(resolution,[],[f284,f128]) ).
fof(f292,plain,
( ~ spl12_3
| ~ spl12_9
| spl12_15
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f288,f255,f268,f245,f210]) ).
fof(f294,plain,
( ~ spl12_3
| ~ spl12_9
| spl12_14
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f287,f255,f265,f245,f210]) ).
fof(f295,plain,
( ~ in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9)
| ~ in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),sK10)
| ~ relation(relation_dom_restriction(sK10,sK9))
| ~ relation(sK10)
| spl12_12 ),
inference(resolution,[],[f256,f127]) ).
fof(f297,plain,
( in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK3(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10))),singleton(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)))),sK10)
| ~ relation(sK10)
| ~ spl12_13 ),
inference(resolution,[],[f285,f126]) ).
fof(f298,plain,
( in(sK2(relation_dom_restriction(sK10,sK9),relation_composition(identity_relation(sK9),sK10)),sK9)
| ~ relation(sK10)
| ~ spl12_13 ),
inference(resolution,[],[f285,f125]) ).
fof(f301,plain,
( ~ spl12_3
| spl12_15
| ~ spl12_13 ),
inference(avatar_split_clause,[],[f298,f258,f268,f210]) ).
fof(f302,plain,
( ~ spl12_3
| spl12_14
| ~ spl12_13 ),
inference(avatar_split_clause,[],[f297,f258,f265,f210]) ).
fof(f303,plain,
( ~ spl12_3
| ~ spl12_9
| ~ spl12_14
| ~ spl12_15
| spl12_12 ),
inference(avatar_split_clause,[],[f295,f255,f268,f265,f245,f210]) ).
cnf(s4,plain,
spl12_3,
inference(sat_conversion,[],[f223]) ).
cnf(s5,plain,
( ~ spl12_3
| spl12_4
| ~ spl12_7 ),
inference(sat_conversion,[],[f228]) ).
cnf(s6,plain,
spl12_7,
inference(sat_conversion,[],[f230]) ).
cnf(s10,plain,
( ~ spl12_4
| ~ spl12_9
| ~ spl12_12
| ~ spl12_13 ),
inference(sat_conversion,[],[f260]) ).
cnf(s11,plain,
( ~ spl12_3
| spl12_9 ),
inference(sat_conversion,[],[f262]) ).
cnf(s12,plain,
( ~ spl12_3
| spl12_13
| ~ spl12_14
| ~ spl12_15 ),
inference(sat_conversion,[],[f270]) ).
cnf(s15,plain,
( ~ spl12_4
| ~ spl12_9
| spl12_12
| spl12_13 ),
inference(sat_conversion,[],[f286]) ).
cnf(s16,plain,
( ~ spl12_3
| ~ spl12_9
| ~ spl12_12
| spl12_15 ),
inference(sat_conversion,[],[f292]) ).
cnf(s17,plain,
( ~ spl12_3
| ~ spl12_9
| ~ spl12_12
| spl12_14 ),
inference(sat_conversion,[],[f294]) ).
cnf(s18,plain,
( ~ spl12_3
| ~ spl12_13
| spl12_15 ),
inference(sat_conversion,[],[f301]) ).
cnf(s19,plain,
( ~ spl12_3
| ~ spl12_13
| spl12_14 ),
inference(sat_conversion,[],[f302]) ).
cnf(s20,plain,
( ~ spl12_3
| ~ spl12_9
| spl12_12
| ~ spl12_14
| ~ spl12_15 ),
inference(sat_conversion,[],[f303]) ).
cnf(s21,plain,
( ~ spl12_3
| spl12_4 ),
inference(rat,[],[s5,s6]) ).
cnf(s22,plain,
spl12_9,
inference(rat,[],[s11,s4]) ).
cnf(s23,plain,
spl12_4,
inference(rat,[],[s21,s4]) ).
cnf(s25,plain,
spl12_12,
inference(rat,[],[s20,s18,s19,s15,s4,s22,s23]) ).
cnf(s26,plain,
spl12_14,
inference(rat,[],[s17,s22,s4,s25]) ).
cnf(s27,plain,
spl12_15,
inference(rat,[],[s16,s22,s4,s25]) ).
cnf(s28,plain,
~ spl12_13,
inference(rat,[],[s10,s23,s22,s25]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s12,s27,s4,s26,s28]) ).
fof(f304,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU195+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 04:05:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 2.72/1.25 % (4914)Detected formulas, will run a generic FOF schedule.
% 2.72/1.25 % (4921)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=2666696818:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.25 % (4922)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=962844217:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.25 % (4923)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1924876901:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.25 % (4919)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=1892995964:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.25 % (4924)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2862070822:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.25 % (4920)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=4199497733:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.25 % (4925)dis-21_1_sil=8000:lcm=predicate:random_seed=2028722117: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)
% 2.72/1.25 % (4922)Refutation not found, incomplete strategy
% 2.72/1.25 % (4922)------------------------------
% 2.72/1.25 % (4922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.25 % (4922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.25 % (4922)CaDiCaL version: 2.1.3
% 2.72/1.25 % (4922)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.25 % (4922)Time elapsed: 0.002 s
% 2.72/1.25 % (4922)Peak memory usage: 88 MB
% 2.72/1.25 % (4922)Instructions burned: 1 (million)
% 2.72/1.25 % (4925)First to succeed.
% 2.72/1.25 % (4925)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4914"
% 2.72/1.25 % (4923)Instruction limit reached!
% 2.72/1.25 % (4923)------------------------------
% 2.72/1.25 % (4923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.25 % (4923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.25 % (4923)CaDiCaL version: 2.1.3
% 2.72/1.25 % (4923)Termination reason: Instruction limit
% 2.72/1.25 % (4923)Termination phase: Saturation
% 2.72/1.25 % (4923)Time elapsed: 0.066 s
% 2.72/1.25 % (4923)Peak memory usage: 88 MB
% 2.72/1.25 % (4923)Instructions burned: 120 (million)
% 2.72/1.25 % (4924)Instruction limit reached!
% 2.72/1.25 % (4924)------------------------------
% 2.72/1.25 % (4924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.25 % (4924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.25 % (4924)CaDiCaL version: 2.1.3
% 2.72/1.25 % (4924)Termination reason: Instruction limit
% 2.72/1.25 % (4924)Termination phase: Saturation
% 2.72/1.25 % (4924)Time elapsed: 0.097 s
% 2.72/1.25 % (4924)Peak memory usage: 90 MB
% 2.72/1.25 % (4924)Instructions burned: 139 (million)
% 2.72/1.25 % (4933)lrs+10_1_sil=8000:sp=occurrence:random_seed=2819060962:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.72/1.25 % (4934)lrs+10_1_sil=32000:urr=on:br=off:random_seed=179842539:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.72/1.25 % (4922)------------------------------
% 2.72/1.25 % (4922)------------------------------
% 2.72/1.25 % (4925)Refutation found. Thanks to Tanya!
% 2.72/1.25 % SZS status Theorem for theBenchmark
% 2.72/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.35 % (4925)------------------------------
% 3.41/1.35 % (4925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.35 % (4925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.35 % (4925)CaDiCaL version: 2.1.3
% 3.41/1.35 % (4925)Termination reason: Refutation
% 3.41/1.35 % (4925)Time elapsed: 0.007 s
% 3.41/1.35 % (4925)Peak memory usage: 89 MB
% 3.41/1.35 % (4925)Instructions burned: 9 (million)
% 3.41/1.35 % (4925)------------------------------
% 3.41/1.35 % (4925)------------------------------
% 3.41/1.35 % (4914)Success in time 0.412 s
% 3.41/1.35 % Vampire exiting
%------------------------------------------------------------------------------