%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM401+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:15:03 PM UTC 2026
% Result : Theorem 3.99s 1.53s
% Output : Refutation 5.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 136 ( 15 unt; 6 def)
% Number of atoms : 455 ( 61 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 521 ( 202 ~; 234 |; 57 &)
% ( 18 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 133 ( 0 sgn 120 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f10,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f11,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f13,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f39,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f46,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(f48,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,succ(X1))
<=> ordinal_subset(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_ordinal1) ).
fof(f49,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,succ(X1))
<=> ordinal_subset(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f66,plain,
? [X0] :
( ? [X1] :
( ( in(X0,succ(X1))
<~> ordinal_subset(X0,X1) )
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f72,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f73,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f72]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f77]) ).
fof(f82,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f87,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) ),
inference(nnf_transformation,[],[f66]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
( ( ~ ordinal_subset(sK0,sK1)
| ~ in(sK0,succ(sK1)) )
& ( ordinal_subset(sK0,sK1)
| in(sK0,succ(sK1)) )
& ordinal(sK1)
& ordinal(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f73]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f109]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK7(X0,X1,X2),X0)
& ~ in(sK7(X0,X1,X2),X1) )
| ~ in(sK7(X0,X1,X2),X2) )
& ( in(sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X1)
| in(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f113,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f112]) ).
fof(f114,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK8(X0,X1) != X0
| ~ in(sK8(X0,X1),X1) )
& ( sK8(X0,X1) = X0
| in(sK8(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f113]) ).
fof(f116,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,[],[f87]) ).
fof(f117,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f116]) ).
fof(f118,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK9(X0),X0)
& in(sK9(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f120,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f119]) ).
fof(f129,plain,
ordinal(sK0),
inference(cnf_transformation,[],[f101]) ).
fof(f130,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f101]) ).
fof(f131,plain,
( ordinal_subset(sK0,sK1)
| in(sK0,succ(sK1)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f132,plain,
( ~ ordinal_subset(sK0,sK1)
| ~ in(sK0,succ(sK1)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f142,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f144,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f145,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f150,plain,
! [X0,X1] :
( in(X1,X0)
| in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f175,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f181,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f111]) ).
fof(f182,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f111]) ).
fof(f183,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f111]) ).
fof(f188,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f114]) ).
fof(f189,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f114]) ).
fof(f195,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f198,plain,
! [X0,X1] :
( subset(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f120]) ).
fof(f200,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f120]) ).
fof(f230,plain,
( ~ ordinal_subset(sK0,sK1)
| ~ in(sK0,set_union2(sK1,singleton(sK1))) ),
inference(definition_unfolding,[],[f132,f142]) ).
fof(f231,plain,
( ordinal_subset(sK0,sK1)
| in(sK0,set_union2(sK1,singleton(sK1))) ),
inference(definition_unfolding,[],[f131,f142]) ).
fof(f239,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f183]) ).
fof(f240,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f182]) ).
fof(f241,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f181]) ).
fof(f242,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f189]) ).
fof(f243,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f242]) ).
fof(f244,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f188]) ).
fof(f246,plain,
! [X1] : subset(X1,X1),
inference(equality_resolution,[],[f198]) ).
fof(f255,definition,
( spl18_3
<=> in(sK0,set_union2(sK1,singleton(sK1))) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
fof(f256,plain,
( ~ in(sK0,set_union2(sK1,singleton(sK1)))
| spl18_3 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( in(sK0,set_union2(sK1,singleton(sK1)))
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f259,definition,
( spl18_4
<=> ordinal_subset(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
fof(f260,plain,
( ~ ordinal_subset(sK0,sK1)
| spl18_4 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f261,plain,
( ordinal_subset(sK0,sK1)
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f262,plain,
( spl18_3
| spl18_4 ),
inference(avatar_split_clause,[],[f231,f259,f255]) ).
fof(f263,plain,
( ~ spl18_3
| ~ spl18_4 ),
inference(avatar_split_clause,[],[f230,f259,f255]) ).
fof(f289,plain,
epsilon_transitive(sK1),
inference(resolution,[],[f175,f130]) ).
fof(f437,plain,
( ~ in(sK0,sK1)
| spl18_3 ),
inference(resolution,[],[f239,f256]) ).
fof(f469,plain,
( subset(sK0,sK1)
| ~ ordinal(sK0)
| ~ ordinal(sK1)
| ~ spl18_4 ),
inference(resolution,[],[f144,f261]) ).
fof(f471,plain,
( subset(sK0,sK1)
| ~ ordinal(sK1)
| ~ spl18_4 ),
inference(forward_subsumption_resolution,[],[f469,f129]) ).
fof(f472,plain,
( subset(sK0,sK1)
| ~ spl18_4 ),
inference(forward_subsumption_resolution,[],[f471,f130]) ).
fof(f473,plain,
( ~ subset(sK1,sK0)
| sK0 = sK1
| ~ spl18_4 ),
inference(resolution,[],[f472,f200]) ).
fof(f475,definition,
( spl18_7
<=> sK0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
fof(f477,plain,
( sK0 = sK1
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f479,definition,
( spl18_8
<=> subset(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
fof(f480,plain,
( subset(sK1,sK0)
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f481,plain,
( ~ subset(sK1,sK0)
| spl18_8 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f482,plain,
( spl18_7
| ~ spl18_8
| ~ spl18_4 ),
inference(avatar_split_clause,[],[f473,f259,f479,f475]) ).
fof(f526,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0)
| subset(X0,X1)
| ~ epsilon_transitive(X1) ),
inference(resolution,[],[f150,f195]) ).
fof(f540,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0)
| in(X1,X0) ),
inference(forward_subsumption_resolution,[],[f526,f175]) ).
fof(f733,plain,
( in(sK0,singleton(sK1))
| in(sK0,sK1)
| ~ spl18_3 ),
inference(resolution,[],[f257,f241]) ).
fof(f739,definition,
( spl18_15
<=> in(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl18_15])],[avatar_definition]) ).
fof(f740,plain,
( ~ in(sK0,sK1)
| spl18_15 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f741,plain,
( in(sK0,sK1)
| ~ spl18_15 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f743,definition,
( spl18_16
<=> in(sK0,singleton(sK1)) ),
introduced(definition,[new_symbols(definition,[spl18_16])],[avatar_definition]) ).
fof(f745,plain,
( in(sK0,singleton(sK1))
| ~ spl18_16 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f746,plain,
( spl18_15
| spl18_16
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f733,f255,f743,f739]) ).
fof(f747,plain,
( ~ spl18_15
| spl18_3 ),
inference(avatar_split_clause,[],[f437,f255,f739]) ).
fof(f760,plain,
( ~ in(sK0,singleton(sK1))
| spl18_3 ),
inference(resolution,[],[f256,f240]) ).
fof(f970,plain,
( sK0 = sK1
| ~ ordinal(sK0)
| ~ ordinal(sK1)
| in(sK0,sK1)
| spl18_8 ),
inference(resolution,[],[f540,f481]) ).
fof(f973,plain,
( sK0 = sK1
| ~ ordinal(sK1)
| in(sK0,sK1)
| spl18_8 ),
inference(forward_subsumption_resolution,[],[f970,f129]) ).
fof(f974,plain,
( sK0 = sK1
| in(sK0,sK1)
| spl18_8 ),
inference(forward_subsumption_resolution,[],[f973,f130]) ).
fof(f975,plain,
( sK0 = sK1
| spl18_8
| spl18_15 ),
inference(forward_subsumption_resolution,[],[f974,f740]) ).
fof(f976,plain,
( spl18_7
| spl18_8
| spl18_15 ),
inference(avatar_split_clause,[],[f975,f739,f479,f475]) ).
fof(f982,plain,
( subset(sK0,sK1)
| ~ epsilon_transitive(sK1)
| ~ spl18_15 ),
inference(resolution,[],[f741,f195]) ).
fof(f986,plain,
( subset(sK0,sK1)
| ~ spl18_15 ),
inference(forward_subsumption_resolution,[],[f982,f289]) ).
fof(f1002,plain,
( ordinal_subset(sK0,sK1)
| ~ ordinal(sK0)
| ~ ordinal(sK1)
| ~ spl18_15 ),
inference(resolution,[],[f986,f145]) ).
fof(f1005,plain,
( ~ ordinal(sK0)
| ~ ordinal(sK1)
| spl18_4
| ~ spl18_15 ),
inference(forward_subsumption_resolution,[],[f1002,f260]) ).
fof(f1006,plain,
( ~ ordinal(sK1)
| spl18_4
| ~ spl18_15 ),
inference(forward_subsumption_resolution,[],[f1005,f129]) ).
fof(f1007,plain,
( $false
| spl18_4
| ~ spl18_15 ),
inference(forward_subsumption_resolution,[],[f1006,f130]) ).
fof(f1008,plain,
( spl18_4
| ~ spl18_15 ),
inference(avatar_contradiction_clause,[],[f1007]) ).
fof(f1012,plain,
( ordinal_subset(sK1,sK0)
| ~ ordinal(sK1)
| ~ ordinal(sK0)
| ~ spl18_8 ),
inference(resolution,[],[f480,f145]) ).
fof(f1019,plain,
( ordinal_subset(sK1,sK0)
| ~ ordinal(sK0)
| ~ spl18_8 ),
inference(forward_subsumption_resolution,[],[f1012,f130]) ).
fof(f1020,plain,
( ordinal_subset(sK1,sK0)
| ~ spl18_8 ),
inference(forward_subsumption_resolution,[],[f1019,f129]) ).
fof(f1021,plain,
( sK0 = sK1
| ~ spl18_16 ),
inference(resolution,[],[f745,f244]) ).
fof(f1035,plain,
( spl18_7
| ~ spl18_16 ),
inference(avatar_split_clause,[],[f1021,f743,f475]) ).
fof(f1039,plain,
( ~ ordinal_subset(sK0,sK0)
| spl18_4
| ~ spl18_7 ),
inference(superposition,[],[f260,f477]) ).
fof(f1134,plain,
( ordinal_subset(sK0,sK0)
| ~ spl18_7
| ~ spl18_8 ),
inference(superposition,[],[f1020,f477]) ).
fof(f1135,plain,
( $false
| spl18_4
| ~ spl18_7
| ~ spl18_8 ),
inference(forward_subsumption_resolution,[],[f1134,f1039]) ).
fof(f1136,plain,
( spl18_4
| ~ spl18_7
| ~ spl18_8 ),
inference(avatar_contradiction_clause,[],[f1135]) ).
fof(f1139,plain,
( ~ in(sK0,singleton(sK0))
| spl18_3
| ~ spl18_7 ),
inference(forward_demodulation,[],[f760,f477]) ).
fof(f1147,plain,
( $false
| spl18_3
| ~ spl18_7 ),
inference(forward_subsumption_resolution,[],[f1139,f243]) ).
fof(f1148,plain,
( spl18_3
| ~ spl18_7 ),
inference(avatar_contradiction_clause,[],[f1147]) ).
fof(f1155,plain,
( ~ subset(sK0,sK0)
| ~ spl18_7
| spl18_8 ),
inference(forward_demodulation,[],[f481,f477]) ).
fof(f1159,plain,
( $false
| ~ spl18_7
| spl18_8 ),
inference(forward_subsumption_resolution,[],[f1155,f246]) ).
fof(f1160,plain,
( ~ spl18_7
| spl18_8 ),
inference(avatar_contradiction_clause,[],[f1159]) ).
cnf(s2,plain,
( spl18_3
| spl18_4 ),
inference(sat_conversion,[],[f262]) ).
cnf(s3,plain,
( ~ spl18_3
| ~ spl18_4 ),
inference(sat_conversion,[],[f263]) ).
cnf(s6,plain,
( ~ spl18_4
| spl18_7
| ~ spl18_8 ),
inference(sat_conversion,[],[f482]) ).
cnf(s10,plain,
( ~ spl18_3
| spl18_15
| spl18_16 ),
inference(sat_conversion,[],[f746]) ).
cnf(s11,plain,
( spl18_3
| ~ spl18_15 ),
inference(sat_conversion,[],[f747]) ).
cnf(s20,plain,
( spl18_7
| spl18_8
| spl18_15 ),
inference(sat_conversion,[],[f976]) ).
cnf(s22,plain,
( spl18_4
| ~ spl18_15 ),
inference(sat_conversion,[],[f1008]) ).
cnf(s25,plain,
( spl18_7
| ~ spl18_16 ),
inference(sat_conversion,[],[f1035]) ).
cnf(s27,plain,
( spl18_4
| ~ spl18_7
| ~ spl18_8 ),
inference(sat_conversion,[],[f1136]) ).
cnf(s30,plain,
( spl18_3
| ~ spl18_7 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s32,plain,
( ~ spl18_7
| spl18_8 ),
inference(sat_conversion,[],[f1160]) ).
cnf(s34,plain,
spl18_3,
inference(rat,[],[s6,s20,s2,s11,s30]) ).
cnf(s36,plain,
~ spl18_4,
inference(rat,[],[s3,s34]) ).
cnf(s37,plain,
~ spl18_15,
inference(rat,[],[s22,s36]) ).
cnf(s38,plain,
spl18_16,
inference(rat,[],[s10,s34,s37]) ).
cnf(s39,plain,
spl18_7,
inference(rat,[],[s25,s38]) ).
cnf(s40,plain,
spl18_8,
inference(rat,[],[s32,s39]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s27,s36,s40,s39]) ).
fof(f1161,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM401+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 19:47:25 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.99/1.53 % (1554342)Detected formulas, will run a generic FOF schedule.
% 3.99/1.53 % (1554351)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=54452825:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.99/1.53 % (1554351)Refutation not found, incomplete strategy
% 3.99/1.53 % (1554351)------------------------------
% 3.99/1.53 % (1554351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1554351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1554351)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1554351)Termination reason: Refutation not found, incomplete strategy
% 3.99/1.53 % (1554351)Time elapsed: 0.002 s
% 3.99/1.53 % (1554351)Peak memory usage: 88 MB
% 3.99/1.53 % (1554351)Instructions burned: 4 (million)
% 3.99/1.53 % (1554350)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=322537618:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.99/1.53 % (1554350)Refutation not found, incomplete strategy
% 3.99/1.53 % (1554350)------------------------------
% 3.99/1.53 % (1554350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1554350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1554350)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1554350)Termination reason: Refutation not found, incomplete strategy
% 3.99/1.53 % (1554350)Time elapsed: 0.001 s
% 3.99/1.53 % (1554350)Peak memory usage: 88 MB
% 3.99/1.53 % (1554349)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=3169253234:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.99/1.53 % (1554348)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=1508998917:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.99/1.53 % (1554347)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=3294986109:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.99/1.53 % (1554353)dis-21_1_sil=8000:lcm=predicate:random_seed=3723301041:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.99/1.53 % (1554352)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3955893937:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.99/1.53 % (1554353)Instruction limit reached!
% 3.99/1.53 % (1554353)------------------------------
% 3.99/1.53 % (1554353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1554353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1554353)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1554353)Termination reason: Instruction limit
% 3.99/1.53 % (1554353)Termination phase: Saturation
% 3.99/1.53 % (1554353)Time elapsed: 0.074 s
% 3.99/1.53 % (1554353)Peak memory usage: 90 MB
% 3.99/1.53 % (1554353)Instructions burned: 129 (million)
% 3.99/1.53 % (1554352)Instruction limit reached!
% 3.99/1.53 % (1554352)------------------------------
% 3.99/1.53 % (1554352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1554352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1554352)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1554352)Termination reason: Instruction limit
% 3.99/1.53 % (1554352)Termination phase: Saturation
% 3.99/1.53 % (1554352)Time elapsed: 0.097 s
% 3.99/1.53 % (1554352)Peak memory usage: 90 MB
% 3.99/1.53 % (1554352)Instructions burned: 140 (million)
% 3.99/1.53 % (1554351)------------------------------
% 3.99/1.53 % (1554351)------------------------------
% 3.99/1.53 % (1554361)lrs+10_1_sil=8000:sp=occurrence:random_seed=3451365825:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.99/1.53 % (1554363)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1026873080:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.99/1.53 % (1554350)------------------------------
% 3.99/1.53 % (1554350)------------------------------
% 3.99/1.53 % (1554362)lrs+10_1_sil=32000:urr=on:br=off:random_seed=167863088:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.99/1.53 % (1554361)First to succeed.
% 3.99/1.53 % (1554361)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1554342"
% 3.99/1.53 % (1554362)Instruction limit reached!
% 3.99/1.53 % (1554362)------------------------------
% 3.99/1.53 % (1554362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1554362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1554362)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1554362)Termination reason: Instruction limit
% 3.99/1.53 % (1554362)Termination phase: Saturation
% 3.99/1.53 % (1554362)Time elapsed: 0.077 s
% 3.99/1.53 % (1554362)Peak memory usage: 93 MB
% 3.99/1.53 % (1554362)Instructions burned: 158 (million)
% 3.99/1.53 % (1554363)Instruction limit reached!
% 3.99/1.53 % (1554363)------------------------------
% 3.99/1.53 % (1554363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1554363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1554363)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1554363)Termination reason: Instruction limit
% 3.99/1.53 % (1554363)Termination phase: Saturation
% 3.99/1.53 % (1554363)Time elapsed: 0.111 s
% 3.99/1.53 % (1554363)Peak memory usage: 91 MB
% 3.99/1.53 % (1554363)Instructions burned: 327 (million)
% 3.99/1.53 % (1554367)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=2249161211:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 3.99/1.53 % (1554369)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2509440489:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 3.99/1.53 % (1554368)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=299704750:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 3.99/1.53 % (1554368)Refutation not found, incomplete strategy
% 3.99/1.53 % (1554368)------------------------------
% 3.99/1.53 % (1554368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1554368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.53 % (1554368)CaDiCaL version: 2.1.3
% 3.99/1.53 % (1554368)Termination reason: Refutation not found, incomplete strategy
% 3.99/1.53 % (1554368)Time elapsed: 0.004 s
% 3.99/1.53 % (1554368)Peak memory usage: 89 MB
% 3.99/1.53 % (1554368)Instructions burned: 5 (million)
% 3.99/1.53 % (1554367)Instruction limit reached!
% 3.99/1.53 % (1554367)------------------------------
% 3.99/1.53 % (1554367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.53 % (1554361)Refutation found. Thanks to Tanya!
% 3.99/1.53 % SZS status Theorem for theBenchmark
% 3.99/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.22/1.63 % (1554361)------------------------------
% 5.22/1.63 % (1554361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.22/1.63 % (1554361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.63 % (1554361)CaDiCaL version: 2.1.3
% 5.22/1.63 % (1554361)Termination reason: Refutation
% 5.22/1.63 % (1554361)Time elapsed: 0.024 s
% 5.22/1.63 % (1554361)Peak memory usage: 90 MB
% 5.22/1.63 % (1554361)Instructions burned: 34 (million)
% 5.22/1.63 % (1554361)------------------------------
% 5.22/1.63 % (1554361)------------------------------
% 5.22/1.63 % (1554342)Success in time 0.664 s
% 5.22/1.63 % Vampire exiting
%------------------------------------------------------------------------------