%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU270+2 : 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 : n010.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 12:48:06 PM UTC 2026
% Result : Theorem 8.60s 2.10s
% Output : Refutation 9.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 108 ( 28 unt; 3 def)
% Number of atoms : 397 ( 57 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 491 ( 202 ~; 204 |; 62 &)
% ( 13 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 131 ( 0 sgn 118 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f34,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(X2,X0)
& in(X3,X0) )
=> ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord2) ).
fof(f38,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f51,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f61,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(f86,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f169,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X1,X2] :
~ ( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f247,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f250,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X0,X1)
& X0 != X1
& ~ in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f302,conjecture,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f303,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
inference(negated_conjecture,[status(cth)],[f302]) ).
fof(f323,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f394,plain,
! [X0,X1] :
( ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f395,plain,
! [X0,X1] :
( ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) ) )
| ~ relation(X1) ),
inference(flattening,[],[f394]) ).
fof(f397,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f498,plain,
! [X0] :
( ( connected(X0)
<=> ! [X1,X2] :
( ~ in(X1,relation_field(X0))
| ~ in(X2,relation_field(X0))
| X1 = X2
| in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X2,X1),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f169]) ).
fof(f576,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f247]) ).
fof(f577,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f576]) ).
fof(f581,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f250]) ).
fof(f582,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f581]) ).
fof(f637,plain,
? [X0] :
( ~ connected(inclusion_relation(X0))
& ordinal(X0) ),
inference(ennf_transformation,[],[f303]) ).
fof(f751,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f395]) ).
fof(f752,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f751]) ).
fof(f753,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ in(X4,X0)
| ~ in(X5,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f752]) ).
fof(f754,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ( ( ~ subset(sK31(X0,X1),sK32(X0,X1))
| ~ in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X1) )
& ( subset(sK31(X0,X1),sK32(X0,X1))
| in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X1) )
& in(sK31(X0,X1),X0)
& in(sK32(X0,X1),X0) ) )
& ( ( relation_field(X1) = X0
& ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ in(X4,X0)
| ~ in(X5,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31,sK32]),skolemize(X2,sK31(X0,X1)),skolemize(X3,sK32(X0,X1))],[f753]) ).
fof(f764,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f397]) ).
fof(f765,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f764]) ).
fof(f766,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK37(X0),X0)
& in(sK37(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(X1,sK37(X0))],[f765]) ).
fof(f802,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) )
& ( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f803,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) )
& ( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ) ),
inference(flattening,[],[f802]) ).
fof(f869,plain,
! [X0] :
( ( ( connected(X0)
| ? [X1,X2] :
( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) ) )
& ( ! [X1,X2] :
( ~ in(X1,relation_field(X0))
| ~ in(X2,relation_field(X0))
| X1 = X2
| in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X2,X1),X0) )
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f498]) ).
fof(f870,plain,
! [X0] :
( ( ( connected(X0)
| ? [X1,X2] :
( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) ) )
& ( ! [X3,X4] :
( ~ in(X3,relation_field(X0))
| ~ in(X4,relation_field(X0))
| X3 = X4
| in(ordered_pair(X3,X4),X0)
| in(ordered_pair(X4,X3),X0) )
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f869]) ).
fof(f871,plain,
! [X0] :
( ( ( connected(X0)
| ( in(sK97(X0),relation_field(X0))
& in(sK98(X0),relation_field(X0))
& sK97(X0) != sK98(X0)
& ~ in(ordered_pair(sK97(X0),sK98(X0)),X0)
& ~ in(ordered_pair(sK98(X0),sK97(X0)),X0) ) )
& ( ! [X3,X4] :
( ~ in(X3,relation_field(X0))
| ~ in(X4,relation_field(X0))
| X3 = X4
| in(ordered_pair(X3,X4),X0)
| in(ordered_pair(X4,X3),X0) )
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97,sK98]),skolemize(X1,sK97(X0)),skolemize(X2,sK98(X0))],[f870]) ).
fof(f938,plain,
( ~ connected(inclusion_relation(sK128))
& ordinal(sK128) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(X0,sK128)],[f637]) ).
fof(f1075,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f754]) ).
fof(f1076,plain,
! [X0,X1] :
( relation_field(X1) = X0
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f754]) ).
fof(f1090,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f766]) ).
fof(f1154,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f803]) ).
fof(f1196,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f61]) ).
fof(f1260,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f1366,plain,
! [X0] :
( connected(X0)
| ~ in(ordered_pair(sK98(X0),sK97(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f871]) ).
fof(f1367,plain,
! [X0] :
( connected(X0)
| ~ in(ordered_pair(sK97(X0),sK98(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f871]) ).
fof(f1368,plain,
! [X0] :
( sK97(X0) != sK98(X0)
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f871]) ).
fof(f1369,plain,
! [X0] :
( in(sK98(X0),relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f871]) ).
fof(f1370,plain,
! [X0] :
( in(sK97(X0),relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f871]) ).
fof(f1503,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f577]) ).
fof(f1508,plain,
! [X0,X1] :
( in(X1,X0)
| in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f582]) ).
fof(f1587,plain,
ordinal(sK128),
inference(cnf_transformation,[],[f938]) ).
fof(f1588,plain,
~ connected(inclusion_relation(sK128)),
inference(cnf_transformation,[],[f938]) ).
fof(f1634,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f323]) ).
fof(f1675,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1196,f1634]) ).
fof(f1720,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1075,f1675]) ).
fof(f1808,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(sK97(X0),sK98(X0)),unordered_pair(sK97(X0),sK97(X0))),X0)
| connected(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1367,f1675]) ).
fof(f1809,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(sK98(X0),sK97(X0)),unordered_pair(sK98(X0),sK98(X0))),X0)
| connected(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1366,f1675]) ).
fof(f1930,plain,
! [X0] :
( relation_field(inclusion_relation(X0)) = X0
| ~ relation(inclusion_relation(X0)) ),
inference(equality_resolution,[],[f1076]) ).
fof(f1931,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),inclusion_relation(X0))
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(equality_resolution,[],[f1720]) ).
fof(f2003,definition,
sF138 = inclusion_relation(sK128),
introduced(definition,[new_symbols(definition,[sF138])],[function_definition]) ).
fof(f2004,plain,
inclusion_relation(sK128) = sF138,
inference(reorient_equations,[],[f2003]) ).
fof(f2005,plain,
~ connected(sF138),
inference(definition_folding,[],[f1588,f2004]) ).
fof(f2028,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),inclusion_relation(X0))
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0) ),
inference(forward_subsumption_resolution,[],[f1931,f1260]) ).
fof(f2029,plain,
! [X0] : relation_field(inclusion_relation(X0)) = X0,
inference(forward_subsumption_resolution,[],[f1930,f1260]) ).
fof(f2042,plain,
relation(sF138),
inference(superposition,[],[f1260,f2004]) ).
fof(f2049,plain,
sK128 = relation_field(sF138),
inference(superposition,[],[f2029,f2004]) ).
fof(f2054,plain,
( in(sK97(sF138),sK128)
| connected(sF138)
| ~ relation(sF138) ),
inference(superposition,[],[f1370,f2049]) ).
fof(f2055,plain,
( in(sK98(sF138),sK128)
| connected(sF138)
| ~ relation(sF138) ),
inference(superposition,[],[f1369,f2049]) ).
fof(f2056,plain,
( in(sK98(sF138),sK128)
| ~ relation(sF138) ),
inference(forward_subsumption_resolution,[],[f2055,f2005]) ).
fof(f2057,plain,
( in(sK97(sF138),sK128)
| ~ relation(sF138) ),
inference(forward_subsumption_resolution,[],[f2054,f2005]) ).
fof(f2058,plain,
in(sK98(sF138),sK128),
inference(forward_subsumption_resolution,[],[f2056,f2042]) ).
fof(f2059,plain,
in(sK97(sF138),sK128),
inference(forward_subsumption_resolution,[],[f2057,f2042]) ).
fof(f2064,plain,
( ordinal(sK98(sF138))
| ~ ordinal(sK128) ),
inference(resolution,[],[f1503,f2058]) ).
fof(f2065,plain,
( ordinal(sK97(sF138))
| ~ ordinal(sK128) ),
inference(resolution,[],[f1503,f2059]) ).
fof(f2068,plain,
ordinal(sK97(sF138)),
inference(forward_subsumption_resolution,[],[f2065,f1587]) ).
fof(f2069,plain,
ordinal(sK98(sF138)),
inference(forward_subsumption_resolution,[],[f2064,f1587]) ).
fof(f2077,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF138)
| ~ subset(X0,X1)
| ~ in(X0,sK128)
| ~ in(X1,sK128) ),
inference(superposition,[],[f2028,f2004]) ).
fof(f2084,plain,
( ~ subset(sK97(sF138),sK98(sF138))
| ~ in(sK97(sF138),sK128)
| ~ in(sK98(sF138),sK128)
| connected(sF138)
| ~ relation(sF138) ),
inference(resolution,[],[f2077,f1808]) ).
fof(f2085,plain,
( ~ subset(sK98(sF138),sK97(sF138))
| ~ in(sK98(sF138),sK128)
| ~ in(sK97(sF138),sK128)
| connected(sF138)
| ~ relation(sF138) ),
inference(resolution,[],[f2077,f1809]) ).
fof(f2099,plain,
( ~ subset(sK98(sF138),sK97(sF138))
| ~ in(sK97(sF138),sK128)
| connected(sF138)
| ~ relation(sF138) ),
inference(forward_subsumption_resolution,[],[f2085,f2058]) ).
fof(f2100,plain,
( ~ subset(sK97(sF138),sK98(sF138))
| ~ in(sK98(sF138),sK128)
| connected(sF138)
| ~ relation(sF138) ),
inference(forward_subsumption_resolution,[],[f2084,f2059]) ).
fof(f2101,plain,
( ~ subset(sK98(sF138),sK97(sF138))
| connected(sF138)
| ~ relation(sF138) ),
inference(forward_subsumption_resolution,[],[f2099,f2059]) ).
fof(f2102,plain,
( ~ subset(sK97(sF138),sK98(sF138))
| connected(sF138)
| ~ relation(sF138) ),
inference(forward_subsumption_resolution,[],[f2100,f2058]) ).
fof(f2103,plain,
( ~ subset(sK98(sF138),sK97(sF138))
| ~ relation(sF138) ),
inference(forward_subsumption_resolution,[],[f2101,f2005]) ).
fof(f2104,plain,
( ~ subset(sK97(sF138),sK98(sF138))
| ~ relation(sF138) ),
inference(forward_subsumption_resolution,[],[f2102,f2005]) ).
fof(f2105,plain,
~ subset(sK98(sF138),sK97(sF138)),
inference(forward_subsumption_resolution,[],[f2103,f2042]) ).
fof(f2106,plain,
~ subset(sK97(sF138),sK98(sF138)),
inference(forward_subsumption_resolution,[],[f2104,f2042]) ).
fof(f2438,plain,
epsilon_transitive(sK97(sF138)),
inference(resolution,[],[f1154,f2068]) ).
fof(f2656,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(resolution,[],[f1090,f1508]) ).
fof(f2700,plain,
! [X0,X1] :
( subset(X0,X1)
| in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(forward_subsumption_resolution,[],[f2656,f1154]) ).
fof(f2732,plain,
( in(sK98(sF138),sK97(sF138))
| sK97(sF138) = sK98(sF138)
| ~ ordinal(sK97(sF138))
| ~ ordinal(sK98(sF138)) ),
inference(resolution,[],[f2700,f2106]) ).
fof(f2740,plain,
( in(sK98(sF138),sK97(sF138))
| sK97(sF138) = sK98(sF138)
| ~ ordinal(sK98(sF138)) ),
inference(forward_subsumption_resolution,[],[f2732,f2068]) ).
fof(f2742,plain,
( in(sK98(sF138),sK97(sF138))
| sK97(sF138) = sK98(sF138) ),
inference(forward_subsumption_resolution,[],[f2740,f2069]) ).
fof(f2744,definition,
( spl139_31
<=> sK97(sF138) = sK98(sF138) ),
introduced(definition,[new_symbols(definition,[spl139_31])],[avatar_definition]) ).
fof(f2746,plain,
( sK97(sF138) = sK98(sF138)
| ~ spl139_31 ),
inference(avatar_component_clause,[],[f2744]) ).
fof(f2753,definition,
( spl139_33
<=> in(sK98(sF138),sK97(sF138)) ),
introduced(definition,[new_symbols(definition,[spl139_33])],[avatar_definition]) ).
fof(f2755,plain,
( in(sK98(sF138),sK97(sF138))
| ~ spl139_33 ),
inference(avatar_component_clause,[],[f2753]) ).
fof(f2756,plain,
( spl139_31
| spl139_33 ),
inference(avatar_split_clause,[],[f2742,f2753,f2744]) ).
fof(f2769,plain,
( sK97(sF138) != sK97(sF138)
| connected(sF138)
| ~ relation(sF138)
| ~ spl139_31 ),
inference(superposition,[],[f1368,f2746]) ).
fof(f2770,plain,
( connected(sF138)
| ~ relation(sF138)
| ~ spl139_31 ),
inference(trivial_inequality_removal,[],[f2769]) ).
fof(f2771,plain,
( ~ relation(sF138)
| ~ spl139_31 ),
inference(forward_subsumption_resolution,[],[f2770,f2005]) ).
fof(f2780,plain,
( $false
| ~ spl139_31 ),
inference(forward_subsumption_resolution,[],[f2771,f2042]) ).
fof(f2781,plain,
~ spl139_31,
inference(avatar_contradiction_clause,[],[f2780]) ).
fof(f2786,plain,
( subset(sK98(sF138),sK97(sF138))
| ~ epsilon_transitive(sK97(sF138))
| ~ spl139_33 ),
inference(resolution,[],[f2755,f1090]) ).
fof(f2789,plain,
( ~ epsilon_transitive(sK97(sF138))
| ~ spl139_33 ),
inference(forward_subsumption_resolution,[],[f2786,f2105]) ).
fof(f2790,plain,
( $false
| ~ spl139_33 ),
inference(forward_subsumption_resolution,[],[f2789,f2438]) ).
fof(f2791,plain,
~ spl139_33,
inference(avatar_contradiction_clause,[],[f2790]) ).
cnf(s23,plain,
( spl139_31
| spl139_33 ),
inference(sat_conversion,[],[f2756]) ).
cnf(s26,plain,
~ spl139_31,
inference(sat_conversion,[],[f2781]) ).
cnf(s27,plain,
~ spl139_33,
inference(sat_conversion,[],[f2791]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s23,s27,s26]) ).
fof(f2792,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU270+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n010.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 04:26:03 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.44 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
% 8.60/2.10 % (1553377)Detected formulas, will run a generic FOF schedule.
% 8.60/2.10 % (1553388)dis-21_1_sil=8000:lcm=predicate:random_seed=2295379283: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)
% 8.60/2.10 % (1553386)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=510647888:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.60/2.10 % (1553385)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=420658007:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.60/2.10 % (1553382)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=4046614110:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.60/2.10 % (1553384)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=447636581:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.60/2.10 % (1553383)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=1661285548:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.60/2.10 % (1553387)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=926781345:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.60/2.10 % (1553388)Instruction limit reached!
% 8.60/2.10 % (1553388)------------------------------
% 8.60/2.10 % (1553388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553388)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553388)Termination reason: Instruction limit
% 8.60/2.10 % (1553388)Termination phase: Saturation
% 8.60/2.10 % (1553388)Time elapsed: 0.042 s
% 8.60/2.10 % (1553388)Peak memory usage: 90 MB
% 8.60/2.10 % (1553388)Instructions burned: 131 (million)
% 8.60/2.10 % (1553385)Instruction limit reached!
% 8.60/2.10 % (1553385)------------------------------
% 8.60/2.10 % (1553385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553385)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553385)Termination reason: Instruction limit
% 8.60/2.10 % (1553385)Termination phase: Saturation
% 8.60/2.10 % (1553385)Time elapsed: 0.069 s
% 8.60/2.10 % (1553385)Peak memory usage: 90 MB
% 8.60/2.10 % (1553385)Instructions burned: 110 (million)
% 8.60/2.10 % (1553386)Instruction limit reached!
% 8.60/2.10 % (1553386)------------------------------
% 8.60/2.10 % (1553386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553386)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553386)Termination reason: Instruction limit
% 8.60/2.10 % (1553386)Termination phase: Saturation
% 8.60/2.10 % (1553386)Time elapsed: 0.080 s
% 8.60/2.10 % (1553386)Peak memory usage: 89 MB
% 8.60/2.10 % (1553386)Instructions burned: 120 (million)
% 8.60/2.10 % (1553396)lrs+10_1_sil=8000:sp=occurrence:random_seed=1992266855:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.60/2.10 % (1553387)Instruction limit reached!
% 8.60/2.10 % (1553387)------------------------------
% 8.60/2.10 % (1553387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553387)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553387)Termination reason: Instruction limit
% 8.60/2.10 % (1553387)Termination phase: Saturation
% 8.60/2.10 % (1553387)Time elapsed: 0.102 s
% 8.60/2.10 % (1553387)Peak memory usage: 90 MB
% 8.60/2.10 % (1553387)Instructions burned: 140 (million)
% 8.60/2.10 % (1553396)Instruction limit reached!
% 8.60/2.10 % (1553396)------------------------------
% 8.60/2.10 % (1553396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553396)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553396)Termination reason: Instruction limit
% 8.60/2.10 % (1553396)Termination phase: Saturation
% 8.60/2.10 % (1553396)Time elapsed: 0.102 s
% 8.60/2.10 % (1553396)Peak memory usage: 93 MB
% 8.60/2.10 % (1553396)Instructions burned: 287 (million)
% 8.60/2.10 % (1553397)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3297428071:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.60/2.10 % (1553397)Refutation not found, incomplete strategy
% 8.60/2.10 % (1553397)------------------------------
% 8.60/2.10 % (1553397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553397)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553397)Termination reason: Refutation not found, incomplete strategy
% 8.60/2.10 % (1553397)Time elapsed: 0.006 s
% 8.60/2.10 % (1553397)Peak memory usage: 89 MB
% 8.60/2.10 % (1553397)Instructions burned: 7 (million)
% 8.60/2.10 % (1553398)lrs+1011_1_sil=32000:sp=occurrence:random_seed=715939652:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.60/2.10 % (1553400)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=4153997216:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 8.60/2.10 % (1553402)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1236987558:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 8.60/2.10 % (1553402)Instruction limit reached!
% 8.60/2.10 % (1553402)------------------------------
% 8.60/2.10 % (1553402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553402)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553402)Termination reason: Instruction limit
% 8.60/2.10 % (1553402)Termination phase: Saturation
% 8.60/2.10 % (1553402)Time elapsed: 0.098 s
% 8.60/2.10 % (1553402)Peak memory usage: 91 MB
% 8.60/2.10 % (1553402)Instructions burned: 295 (million)
% 8.60/2.10 % (1553400)Instruction limit reached!
% 8.60/2.10 % (1553400)------------------------------
% 8.60/2.10 % (1553400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553400)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553400)Termination reason: Instruction limit
% 8.60/2.10 % (1553400)Termination phase: Saturation
% 8.60/2.10 % (1553400)Time elapsed: 0.147 s
% 8.60/2.10 % (1553400)Peak memory usage: 93 MB
% 8.60/2.10 % (1553400)Instructions burned: 249 (million)
% 8.60/2.10 % (1553398)Instruction limit reached!
% 8.60/2.10 % (1553398)------------------------------
% 8.60/2.10 % (1553398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553398)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553398)Termination reason: Instruction limit
% 8.60/2.10 % (1553398)Termination phase: Saturation
% 8.60/2.10 % (1553398)Time elapsed: 0.229 s
% 8.60/2.10 % (1553398)Peak memory usage: 93 MB
% 8.60/2.10 % (1553398)Instructions burned: 325 (million)
% 8.60/2.10 % (1553397)------------------------------
% 8.60/2.10 % (1553397)------------------------------
% 8.60/2.10 % (1553406)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=353725490:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.60/2.10 % (1553407)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2336719584:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.60/2.10 % (1553408)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4039542946:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.60/2.10 % (1553407)Instruction limit reached!
% 8.60/2.10 % (1553407)------------------------------
% 8.60/2.10 % (1553407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553407)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553407)Termination reason: Instruction limit
% 8.60/2.10 % (1553407)Termination phase: Saturation
% 8.60/2.10 % (1553407)Time elapsed: 0.071 s
% 8.60/2.10 % (1553407)Peak memory usage: 90 MB
% 8.60/2.10 % (1553407)Instructions burned: 114 (million)
% 8.60/2.10 % (1553409)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3016734107:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 8.60/2.10 % (1553408)Instruction limit reached!
% 8.60/2.10 % (1553408)------------------------------
% 8.60/2.10 % (1553408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553408)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553408)Termination reason: Instruction limit
% 8.60/2.10 % (1553408)Termination phase: Saturation
% 8.60/2.10 % (1553408)Time elapsed: 0.070 s
% 8.60/2.10 % (1553408)Peak memory usage: 90 MB
% 8.60/2.10 % (1553408)Instructions burned: 127 (million)
% 8.60/2.10 % (1553409)Instruction limit reached!
% 8.60/2.10 % (1553409)------------------------------
% 8.60/2.10 % (1553409)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553409)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553409)Termination reason: Instruction limit
% 8.60/2.10 % (1553409)Termination phase: Saturation
% 8.60/2.10 % (1553409)Time elapsed: 0.069 s
% 8.60/2.10 % (1553409)Peak memory usage: 89 MB
% 8.60/2.10 % (1553409)Instructions burned: 115 (million)
% 8.60/2.10 % (1553413)lrs+10_1_sil=8000:sp=occurrence:random_seed=2739602327:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.60/2.10 % (1553415)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2480665889:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 8.60/2.10 % (1553416)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=428440207:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 8.60/2.10 % (1553382)First to succeed.
% 8.60/2.10 % (1553382)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1553377"
% 8.60/2.10 % (1553383)Also succeeded, but the first one will report.
% 8.60/2.10 % (1553406)Also succeeded, but the first one will report.
% 8.60/2.10 % (1553415)Instruction limit reached!
% 8.60/2.10 % (1553415)------------------------------
% 8.60/2.10 % (1553415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.60/2.10 % (1553415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.60/2.10 % (1553415)CaDiCaL version: 2.1.3
% 8.60/2.10 % (1553415)Termination reason: Instruction limit
% 8.60/2.10 % (1553415)Termination phase: Saturation
% 8.60/2.10 % (1553415)Time elapsed: 0.265 s
% 8.60/2.10 % (1553415)Peak memory usage: 93 MB
% 8.60/2.10 % (1553415)Instructions burned: 439 (million)
% 8.60/2.10 % (1553382)Refutation found. Thanks to Tanya!
% 8.60/2.10 % SZS status Theorem for theBenchmark
% 8.60/2.10 % SZS output start Proof for theBenchmark
% See solution above
% 9.12/2.20 % (1553382)------------------------------
% 9.12/2.20 % (1553382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.12/2.20 % (1553382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.12/2.20 % (1553382)CaDiCaL version: 2.1.3
% 9.12/2.20 % (1553382)Termination reason: Refutation
% 9.12/2.20 % (1553382)Time elapsed: 0.809 s
% 9.12/2.20 % (1553382)Peak memory usage: 135 MB
% 9.12/2.20 % (1553382)Instructions burned: 1255 (million)
% 9.12/2.20 % (1553382)------------------------------
% 9.12/2.20 % (1553382)------------------------------
% 9.12/2.20 % (1553377)Success in time 1.222 s
% 9.12/2.20 % Vampire exiting
%------------------------------------------------------------------------------