%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU060+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 12:47:10 PM UTC 2026
% Result : Theorem 8.52s 2.20s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 134 ( 18 unt; 6 def)
% Number of atoms : 549 ( 64 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 721 ( 306 ~; 320 |; 73 &)
% ( 15 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 314 ( 0 sgn 292 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f8,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/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f10,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f11,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f12,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f13,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f37,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> relation_inverse_image(relation_dom_restriction(X2,X0),X1) = set_intersection2(X0,relation_inverse_image(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> relation_inverse_image(relation_dom_restriction(X2,X0),X1) = set_intersection2(X0,relation_inverse_image(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f58,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,[],[f8]) ).
fof(f59,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f60,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f61,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f69,plain,
? [X0,X1,X2] :
( relation_inverse_image(relation_dom_restriction(X2,X0),X1) != set_intersection2(X0,relation_inverse_image(X2,X1))
& relation(X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f81,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f80]) ).
fof(f82,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,[],[f58]) ).
fof(f83,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,[],[f82]) ).
fof(f84,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,[],[f83]) ).
fof(f85,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))],[f84]) ).
fof(f86,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f59]) ).
fof(f87,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X6,X8),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(sK2(X0,X1,X2),X4),X0)
| ~ in(X4,X1) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X0)
& in(sK3(X0,X1,X2),X1) )
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(X6,sK4(X0,X1,X6)),X0)
& in(sK4(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X5,sK3(X0,X1,X2)),skolemize(X8,sK4(X0,X1,X6))],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f90,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK6(X0,X1,X2),X0)
| ~ in(sK6(X0,X1,X2),X1)
| ~ in(sK6(X0,X1,X2),X2) )
& ( ( in(sK6(X0,X1,X2),X0)
& in(sK6(X0,X1,X2),X1) )
| in(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f94]) ).
fof(f107,plain,
( relation_inverse_image(relation_dom_restriction(sK20,sK18),sK19) != set_intersection2(sK18,relation_inverse_image(sK20,sK19))
& relation(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X0,sK18),skolemize(X1,sK19),skolemize(X2,sK20)],[f69]) ).
fof(f118,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f119,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,[],[f85]) ).
fof(f120,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,[],[f85]) ).
fof(f121,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,[],[f85]) ).
fof(f125,plain,
! [X2,X0,X1,X6] :
( in(sK4(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f126,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(X6,sK4(X0,X1,X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f127,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f132,plain,
! [X0,X1] :
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f133,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f134,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f135,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f136,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f140,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f141,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f179,plain,
relation(sK20),
inference(cnf_transformation,[],[f107]) ).
fof(f180,plain,
relation_inverse_image(relation_dom_restriction(sK20,sK18),sK19) != set_intersection2(sK18,relation_inverse_image(sK20,sK19)),
inference(cnf_transformation,[],[f107]) ).
fof(f195,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,[],[f121,f140,f140]) ).
fof(f196,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,[],[f120,f140]) ).
fof(f197,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,[],[f119,f140,f140]) ).
fof(f200,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f127,f140]) ).
fof(f201,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK4(X0,X1,X6)),singleton(X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f126,f140]) ).
fof(f205,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,[],[f195]) ).
fof(f206,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f196]) ).
fof(f207,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f197]) ).
fof(f208,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| in(X6,relation_inverse_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f200]) ).
fof(f209,plain,
! [X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK4(X0,X1,X6)),singleton(X6)),X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f201]) ).
fof(f210,plain,
! [X0,X1,X6] :
( in(sK4(X0,X1,X6),X1)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f211,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f136]) ).
fof(f212,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f135]) ).
fof(f213,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f134]) ).
fof(f214,definition,
sF21 = relation_dom_restriction(sK20,sK18),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f215,plain,
relation_dom_restriction(sK20,sK18) = sF21,
inference(reorient_equations,[],[f214]) ).
fof(f216,definition,
sF22 = relation_inverse_image(sF21,sK19),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f217,plain,
relation_inverse_image(sF21,sK19) = sF22,
inference(reorient_equations,[],[f216]) ).
fof(f218,definition,
sF23 = relation_inverse_image(sK20,sK19),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f219,plain,
relation_inverse_image(sK20,sK19) = sF23,
inference(reorient_equations,[],[f218]) ).
fof(f220,definition,
sF24 = set_intersection2(sK18,sF23),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f221,plain,
set_intersection2(sK18,sF23) = sF24,
inference(reorient_equations,[],[f220]) ).
fof(f222,plain,
sF22 != sF24,
inference(definition_folding,[],[f180,f221,f219,f217,f215]) ).
fof(f223,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(X0) ),
inference(forward_subsumption_resolution,[],[f207,f141]) ).
fof(f224,plain,
! [X0,X1,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),relation_dom_restriction(X0,X1))
| in(X5,X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f206,f141]) ).
fof(f225,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(X0) ),
inference(forward_subsumption_resolution,[],[f205,f141]) ).
fof(f226,plain,
! [X0] :
( ~ in(X0,sF24)
| in(X0,sK18) ),
inference(superposition,[],[f212,f221]) ).
fof(f227,plain,
! [X0] :
( ~ in(X0,sF24)
| in(X0,sF23) ),
inference(superposition,[],[f213,f221]) ).
fof(f247,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF21)
| in(X0,sK18)
| ~ relation(sK20) ),
inference(superposition,[],[f224,f215]) ).
fof(f248,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF21)
| in(X0,sK18) ),
inference(forward_subsumption_resolution,[],[f247,f179]) ).
fof(f251,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF21)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK20)
| ~ relation(sK20) ),
inference(superposition,[],[f223,f215]) ).
fof(f252,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF21)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK20) ),
inference(forward_subsumption_resolution,[],[f251,f179]) ).
fof(f257,plain,
! [X0] :
( ~ in(X0,sF23)
| ~ in(X0,sK18)
| in(X0,sF24) ),
inference(superposition,[],[f211,f221]) ).
fof(f267,plain,
! [X0,X1] :
( in(X0,sK18)
| ~ in(X0,relation_inverse_image(sF21,X1))
| ~ relation(sF21) ),
inference(resolution,[],[f248,f209]) ).
fof(f269,definition,
( spl25_6
<=> relation(sF21) ),
introduced(definition,[new_symbols(definition,[spl25_6])],[avatar_definition]) ).
fof(f270,plain,
( relation(sF21)
| ~ spl25_6 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f271,plain,
( ~ relation(sF21)
| spl25_6 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f273,definition,
( spl25_7
<=> ! [X0,X1] :
( in(X0,sK18)
| ~ in(X0,relation_inverse_image(sF21,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl25_7])],[avatar_definition]) ).
fof(f274,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sF21,X1))
| in(X0,sK18) )
| ~ spl25_7 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f275,plain,
( ~ spl25_6
| spl25_7 ),
inference(avatar_split_clause,[],[f267,f273,f269]) ).
fof(f280,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF21)
| ~ in(X0,sK18)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK20)
| ~ relation(sK20) ),
inference(superposition,[],[f225,f215]) ).
fof(f283,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK20)
| ~ in(X0,sK18)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sF21) ),
inference(forward_subsumption_resolution,[],[f280,f179]) ).
fof(f285,plain,
! [X0,X1] :
( ~ in(X0,sK18)
| in(unordered_pair(unordered_pair(X0,sK4(sK20,X1,X0)),singleton(X0)),sF21)
| ~ in(X0,relation_inverse_image(sK20,X1))
| ~ relation(sK20) ),
inference(resolution,[],[f283,f209]) ).
fof(f286,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK4(sK20,X1,X0)),singleton(X0)),sF21)
| ~ in(X0,sK18)
| ~ in(X0,relation_inverse_image(sK20,X1)) ),
inference(forward_subsumption_resolution,[],[f285,f179]) ).
fof(f288,plain,
! [X2,X0,X1] :
( ~ in(X0,sK18)
| ~ in(X0,relation_inverse_image(sK20,X1))
| in(X0,relation_inverse_image(sF21,X2))
| ~ in(sK4(sK20,X1,X0),X2)
| ~ relation(sF21) ),
inference(resolution,[],[f286,f208]) ).
fof(f290,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK4(sF21,X1,X0)),singleton(X0)),sK20)
| ~ in(X0,relation_inverse_image(sF21,X1))
| ~ relation(sF21) ),
inference(resolution,[],[f252,f209]) ).
fof(f365,plain,
( relation(sF21)
| ~ relation(sK20) ),
inference(superposition,[],[f141,f215]) ).
fof(f366,plain,
( ~ relation(sK20)
| spl25_6 ),
inference(forward_subsumption_resolution,[],[f365,f271]) ).
fof(f367,plain,
( $false
| spl25_6 ),
inference(forward_subsumption_resolution,[],[f366,f179]) ).
fof(f368,plain,
spl25_6,
inference(avatar_contradiction_clause,[],[f367]) ).
fof(f369,plain,
( ! [X2,X0,X1] :
( ~ in(sK4(sK20,X1,X0),X2)
| ~ in(X0,relation_inverse_image(sK20,X1))
| in(X0,relation_inverse_image(sF21,X2))
| ~ in(X0,sK18) )
| ~ spl25_6 ),
inference(forward_subsumption_resolution,[],[f288,f270]) ).
fof(f370,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK4(sF21,X1,X0)),singleton(X0)),sK20)
| ~ in(X0,relation_inverse_image(sF21,X1)) )
| ~ spl25_6 ),
inference(forward_subsumption_resolution,[],[f290,f270]) ).
fof(f375,plain,
( ! [X0] :
( ~ in(X0,sF22)
| in(X0,sK18) )
| ~ spl25_7 ),
inference(superposition,[],[f274,f217]) ).
fof(f392,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(sF21,X1))
| in(X0,relation_inverse_image(sK20,X2))
| ~ in(sK4(sF21,X1,X0),X2)
| ~ relation(sK20) )
| ~ spl25_6 ),
inference(resolution,[],[f370,f208]) ).
fof(f395,plain,
( ! [X2,X0,X1] :
( ~ in(sK4(sF21,X1,X0),X2)
| in(X0,relation_inverse_image(sK20,X2))
| ~ in(X0,relation_inverse_image(sF21,X1)) )
| ~ spl25_6 ),
inference(forward_subsumption_resolution,[],[f392,f179]) ).
fof(f397,plain,
( ! [X0,X1] :
( in(X0,relation_inverse_image(sK20,X1))
| ~ in(X0,relation_inverse_image(sF21,X1))
| ~ in(X0,relation_inverse_image(sF21,X1))
| ~ relation(sF21) )
| ~ spl25_6 ),
inference(resolution,[],[f395,f210]) ).
fof(f399,plain,
( ! [X0,X1] :
( in(X0,relation_inverse_image(sK20,X1))
| ~ in(X0,relation_inverse_image(sF21,X1))
| ~ relation(sF21) )
| ~ spl25_6 ),
inference(duplicate_literal_removal,[],[f397]) ).
fof(f400,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sF21,X1))
| in(X0,relation_inverse_image(sK20,X1)) )
| ~ spl25_6 ),
inference(forward_subsumption_resolution,[],[f399,f270]) ).
fof(f404,plain,
( ! [X0] :
( ~ in(X0,sF22)
| in(X0,relation_inverse_image(sK20,sK19)) )
| ~ spl25_6 ),
inference(superposition,[],[f400,f217]) ).
fof(f405,plain,
( ! [X0] :
( ~ in(X0,sF22)
| in(X0,sF23) )
| ~ spl25_6 ),
inference(forward_demodulation,[],[f404,f219]) ).
fof(f414,plain,
( ! [X0] :
( in(sK5(sF22,X0),sF23)
| subset(sF22,X0) )
| ~ spl25_6 ),
inference(resolution,[],[f132,f405]) ).
fof(f415,plain,
( ! [X0] :
( in(sK5(sF22,X0),sK18)
| subset(sF22,X0) )
| ~ spl25_7 ),
inference(resolution,[],[f132,f375]) ).
fof(f417,plain,
! [X0] :
( in(sK5(sF24,X0),sF23)
| subset(sF24,X0) ),
inference(resolution,[],[f132,f227]) ).
fof(f418,plain,
! [X0] :
( in(sK5(sF24,X0),sK18)
| subset(sF24,X0) ),
inference(resolution,[],[f132,f226]) ).
fof(f421,plain,
( ! [X0] :
( subset(sF22,X0)
| ~ in(sK5(sF22,X0),sK18)
| in(sK5(sF22,X0),sF24) )
| ~ spl25_6 ),
inference(resolution,[],[f414,f257]) ).
fof(f423,plain,
( ! [X0] :
( in(sK5(sF22,X0),sF24)
| subset(sF22,X0) )
| ~ spl25_6
| ~ spl25_7 ),
inference(forward_subsumption_resolution,[],[f421,f415]) ).
fof(f424,plain,
( subset(sF22,sF24)
| subset(sF22,sF24)
| ~ spl25_6
| ~ spl25_7 ),
inference(resolution,[],[f423,f133]) ).
fof(f427,plain,
( subset(sF22,sF24)
| ~ spl25_6
| ~ spl25_7 ),
inference(duplicate_literal_removal,[],[f424]) ).
fof(f435,plain,
( ~ subset(sF24,sF22)
| sF22 = sF24
| ~ spl25_6
| ~ spl25_7 ),
inference(resolution,[],[f427,f118]) ).
fof(f436,plain,
( ~ subset(sF24,sF22)
| ~ spl25_6
| ~ spl25_7 ),
inference(forward_subsumption_resolution,[],[f435,f222]) ).
fof(f472,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK20,X1))
| in(X0,relation_inverse_image(sF21,X1))
| ~ in(X0,sK18)
| ~ in(X0,relation_inverse_image(sK20,X1))
| ~ relation(sK20) )
| ~ spl25_6 ),
inference(resolution,[],[f369,f210]) ).
fof(f474,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK20,X1))
| in(X0,relation_inverse_image(sF21,X1))
| ~ in(X0,sK18)
| ~ relation(sK20) )
| ~ spl25_6 ),
inference(duplicate_literal_removal,[],[f472]) ).
fof(f475,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK20,X1))
| in(X0,relation_inverse_image(sF21,X1))
| ~ in(X0,sK18) )
| ~ spl25_6 ),
inference(forward_subsumption_resolution,[],[f474,f179]) ).
fof(f480,plain,
( ! [X0] :
( ~ in(X0,sF23)
| in(X0,relation_inverse_image(sF21,sK19))
| ~ in(X0,sK18) )
| ~ spl25_6 ),
inference(superposition,[],[f475,f219]) ).
fof(f481,plain,
( ! [X0] :
( ~ in(X0,sF23)
| in(X0,sF22)
| ~ in(X0,sK18) )
| ~ spl25_6 ),
inference(forward_demodulation,[],[f480,f217]) ).
fof(f486,plain,
( ! [X0] :
( in(sK5(sF24,X0),sF22)
| ~ in(sK5(sF24,X0),sK18)
| subset(sF24,X0) )
| ~ spl25_6 ),
inference(resolution,[],[f481,f417]) ).
fof(f488,plain,
( ! [X0] :
( in(sK5(sF24,X0),sF22)
| subset(sF24,X0) )
| ~ spl25_6 ),
inference(forward_subsumption_resolution,[],[f486,f418]) ).
fof(f489,plain,
( subset(sF24,sF22)
| subset(sF24,sF22)
| ~ spl25_6 ),
inference(resolution,[],[f488,f133]) ).
fof(f492,plain,
( subset(sF24,sF22)
| ~ spl25_6 ),
inference(duplicate_literal_removal,[],[f489]) ).
fof(f493,plain,
( $false
| ~ spl25_6
| ~ spl25_7 ),
inference(forward_subsumption_resolution,[],[f492,f436]) ).
fof(f494,plain,
( ~ spl25_6
| ~ spl25_7 ),
inference(avatar_contradiction_clause,[],[f493]) ).
cnf(s4,plain,
( ~ spl25_6
| spl25_7 ),
inference(sat_conversion,[],[f275]) ).
cnf(s5,plain,
spl25_6,
inference(sat_conversion,[],[f368]) ).
cnf(s8,plain,
( ~ spl25_6
| ~ spl25_7 ),
inference(sat_conversion,[],[f494]) ).
cnf(s9,plain,
~ spl25_7,
inference(rat,[],[s8,s5]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s4,s9,s5]) ).
fof(f495,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU060+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:29:36 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.40/2.20 % (3634913)Detected formulas, will run a generic FOF schedule.
% 9.40/2.20 % (3634997)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2664117996:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.40/2.20 % (3634997)Refutation not found, incomplete strategy
% 9.40/2.20 % (3634997)------------------------------
% 9.40/2.20 % (3634997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3634997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3634997)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3634997)Termination reason: Refutation not found, incomplete strategy
% 9.40/2.20 % (3634997)Time elapsed: 0.002 s
% 9.40/2.20 % (3634997)Peak memory usage: 88 MB
% 9.40/2.20 % (3634997)Instructions burned: 2 (million)
% 9.40/2.20 % (3634996)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=3851292364:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.40/2.20 % (3634999)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=190682691:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.52/2.20 % (3634994)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=2917295207:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.52/2.20 % (3634998)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2543800016:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.52/2.20 % (3635000)dis-21_1_sil=8000:lcm=predicate:random_seed=551875847: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)
% 8.52/2.20 % (3634995)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=3079387225:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.52/2.20 % (3634998)Instruction limit reached!
% 8.52/2.20 % (3634998)------------------------------
% 8.52/2.20 % (3634998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3634998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3634998)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3634998)Termination reason: Instruction limit
% 8.52/2.20 % (3634998)Termination phase: Saturation
% 8.52/2.20 % (3634998)Time elapsed: 0.070 s
% 8.52/2.20 % (3634998)Peak memory usage: 88 MB
% 8.52/2.20 % (3634998)Instructions burned: 119 (million)
% 8.52/2.20 % (3635000)Instruction limit reached!
% 8.52/2.20 % (3635000)------------------------------
% 8.52/2.20 % (3635000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3635000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3635000)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3635000)Termination reason: Instruction limit
% 8.52/2.20 % (3635000)Termination phase: Saturation
% 8.52/2.20 % (3635000)Time elapsed: 0.076 s
% 8.52/2.20 % (3635000)Peak memory usage: 89 MB
% 8.52/2.20 % (3635000)Instructions burned: 130 (million)
% 8.52/2.20 % (3634999)Instruction limit reached!
% 8.52/2.20 % (3634999)------------------------------
% 8.52/2.20 % (3634999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3634999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3634999)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3634999)Termination reason: Instruction limit
% 8.52/2.20 % (3634999)Termination phase: Saturation
% 8.52/2.20 % (3634999)Time elapsed: 0.093 s
% 8.52/2.20 % (3634999)Peak memory usage: 89 MB
% 8.52/2.20 % (3634999)Instructions burned: 139 (million)
% 8.52/2.20 % (3634997)------------------------------
% 8.52/2.20 % (3634997)------------------------------
% 8.52/2.20 % (3635021)lrs+10_1_sil=8000:sp=occurrence:random_seed=3963829855:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.52/2.20 % (3635022)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1368815273:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.52/2.20 % (3635023)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2806183641:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.52/2.20 % (3635022)Instruction limit reached!
% 8.52/2.20 % (3635022)------------------------------
% 8.52/2.20 % (3635022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3635022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3635022)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3635022)Termination reason: Instruction limit
% 8.52/2.20 % (3635022)Termination phase: Saturation
% 8.52/2.20 % (3635022)Time elapsed: 0.081 s
% 8.52/2.20 % (3635022)Peak memory usage: 90 MB
% 8.52/2.20 % (3635022)Instructions burned: 158 (million)
% 8.52/2.20 % (3635024)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1547576247:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 8.52/2.20 % (3635021)Instruction limit reached!
% 8.52/2.20 % (3635021)------------------------------
% 8.52/2.20 % (3635021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3635021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3635021)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3635021)Termination reason: Instruction limit
% 8.52/2.20 % (3635021)Termination phase: Saturation
% 8.52/2.20 % (3635021)Time elapsed: 0.177 s
% 8.52/2.20 % (3635021)Peak memory usage: 91 MB
% 8.52/2.20 % (3635021)Instructions burned: 286 (million)
% 8.52/2.20 % (3635024)Instruction limit reached!
% 8.52/2.20 % (3635024)------------------------------
% 8.52/2.20 % (3635024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3635024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3635024)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3635024)Termination reason: Instruction limit
% 8.52/2.20 % (3635024)Termination phase: Saturation
% 8.52/2.20 % (3635024)Time elapsed: 0.085 s
% 8.52/2.20 % (3635024)Peak memory usage: 95 MB
% 8.52/2.20 % (3635024)Instructions burned: 249 (million)
% 8.52/2.20 % (3635023)Instruction limit reached!
% 8.52/2.20 % (3635023)------------------------------
% 8.52/2.20 % (3635023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3635023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3635023)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3635023)Termination reason: Instruction limit
% 8.52/2.20 % (3635023)Termination phase: Saturation
% 8.52/2.20 % (3635023)Time elapsed: 0.211 s
% 8.52/2.20 % (3635023)Peak memory usage: 91 MB
% 8.52/2.20 % (3635023)Instructions burned: 325 (million)
% 8.52/2.20 % (3635028)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2944395648:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.52/2.20 % (3635028)Refutation not found, incomplete strategy
% 8.52/2.20 % (3635028)------------------------------
% 8.52/2.20 % (3635028)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3635028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3635028)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3635028)Termination reason: Refutation not found, incomplete strategy
% 8.52/2.20 % (3635028)Time elapsed: 0.005 s
% 8.52/2.20 % (3635028)Peak memory usage: 88 MB
% 8.52/2.20 % (3635028)Instructions burned: 3 (million)
% 8.52/2.20 % (3635039)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1071994632:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.52/2.20 % (3635040)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1505114515:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.52/2.20 % (3635038)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3395142736:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.52/2.20 % (3635039)Instruction limit reached!
% 8.52/2.20 % (3635039)------------------------------
% 8.52/2.20 % (3635039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3635039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3635039)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3635039)Termination reason: Instruction limit
% 8.52/2.20 % (3635039)Termination phase: Saturation
% 8.52/2.20 % (3635039)Time elapsed: 0.066 s
% 8.52/2.20 % (3635039)Peak memory usage: 90 MB
% 8.52/2.20 % (3635039)Instructions burned: 114 (million)
% 8.52/2.20 % (3635040)Instruction limit reached!
% 8.52/2.20 % (3635040)------------------------------
% 8.52/2.20 % (3635040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3635040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3635040)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3635040)Termination reason: Instruction limit
% 8.52/2.20 % (3635040)Termination phase: Saturation
% 8.52/2.20 % (3635040)Time elapsed: 0.114 s
% 8.52/2.20 % (3635040)Peak memory usage: 89 MB
% 8.52/2.20 % (3635040)Instructions burned: 127 (million)
% 8.52/2.20 % (3634994)First to succeed.
% 8.52/2.20 % (3634994)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3634913"
% 8.52/2.20 % (3635054)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2823145880:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 8.52/2.20 % (3635028)------------------------------
% 8.52/2.20 % (3635028)------------------------------
% 8.52/2.20 % (3635054)Instruction limit reached!
% 8.52/2.20 % (3635054)------------------------------
% 8.52/2.20 % (3635054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3635054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3635054)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3635054)Termination reason: Instruction limit
% 8.52/2.20 % (3635054)Termination phase: Saturation
% 8.52/2.20 % (3635054)Time elapsed: 0.061 s
% 8.52/2.20 % (3635054)Peak memory usage: 89 MB
% 8.52/2.20 % (3635054)Instructions burned: 115 (million)
% 8.52/2.20 % (3635055)lrs+10_1_sil=8000:sp=occurrence:random_seed=2304090816:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 8.52/2.20 % (3635060)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=680591463:i=437:sd=1:aac=none:ss=included_2988 on theBenchmark for (2988ds/437Mi)
% 8.52/2.20 % (3635060)Refutation not found, incomplete strategy
% 8.52/2.20 % (3635060)------------------------------
% 8.52/2.20 % (3635060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.52/2.20 % (3635060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.52/2.20 % (3635060)CaDiCaL version: 2.1.3
% 8.52/2.20 % (3635060)Termination reason: Refutation not found, incomplete strategy
% 8.52/2.20 % (3635060)Time elapsed: 0.003 s
% 8.52/2.20 % (3635060)Peak memory usage: 88 MB
% 8.52/2.20 % (3635060)Instructions burned: 3 (million)
% 8.52/2.20 % (3634994)Refutation found. Thanks to Tanya!
% 8.52/2.20 % SZS status Theorem for theBenchmark
% 8.52/2.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/2.30 % (3634994)------------------------------
% 0.16/2.30 % (3634994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.30 % (3634994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.30 % (3634994)CaDiCaL version: 2.1.3
% 0.16/2.30 % (3634994)Termination reason: Refutation
% 0.16/2.30 % (3634994)Time elapsed: 0.835 s
% 0.16/2.30 % (3634994)Peak memory usage: 129 MB
% 0.16/2.30 % (3634994)Instructions burned: 996 (million)
% 0.16/2.30 % (3634994)------------------------------
% 0.16/2.30 % (3634994)------------------------------
% 0.16/2.30 % (3634913)Success in time 1.331 s
% 0.16/2.30 % Vampire exiting
%------------------------------------------------------------------------------