%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU059+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:47:09 PM UTC 2026
% Result : Theorem 4.52s 1.53s
% Output : Refutation 5.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 132 ( 19 unt; 13 def)
% Number of atoms : 489 ( 36 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 624 ( 267 ~; 280 |; 53 &)
% ( 21 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 149 ( 0 sgn 137 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> relation_inverse_image(X2,set_difference(X0,X1)) = set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> relation_inverse_image(X2,set_difference(X0,X1)) = set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f50,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f50]) ).
fof(f58,plain,
? [X0,X1,X2] :
( relation_inverse_image(X2,set_difference(X0,X1)) != set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f59,plain,
? [X0,X1,X2] :
( relation_inverse_image(X2,set_difference(X0,X1)) != set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f58]) ).
fof(f71,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f72,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK0(X0,X1,X2)),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(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_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X0)
& ~ in(sK1(X0,X1,X2),X1) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f77]) ).
fof(f90,plain,
( relation_inverse_image(sK15,set_difference(sK13,sK14)) != set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))
& relation(sK15)
& function(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f59]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f99,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f100,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f101,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| in(apply(X0,sK0(X0,X1,X2)),X1)
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f102,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| in(sK0(X0,X1,X2),relation_dom(X0))
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f103,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ in(sK0(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),X2)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f104,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f78]) ).
fof(f105,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f78]) ).
fof(f106,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f78]) ).
fof(f140,plain,
function(sK15),
inference(cnf_transformation,[],[f90]) ).
fof(f141,plain,
relation(sK15),
inference(cnf_transformation,[],[f90]) ).
fof(f142,plain,
relation_inverse_image(sK15,set_difference(sK13,sK14)) != set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)),
inference(cnf_transformation,[],[f90]) ).
fof(f155,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| ~ relation(X0)
| in(X4,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f100]) ).
fof(f156,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ relation(X0)
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f99]) ).
fof(f157,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ relation(X0)
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f98]) ).
fof(f158,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f106]) ).
fof(f159,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f105]) ).
fof(f160,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f104]) ).
fof(f161,definition,
! [X0,X1] :
( sQ17_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ17_eqProxy])],[equality_proxy_definition]) ).
fof(f162,plain,
! [X2,X0,X1] :
( sQ17_eqProxy(relation_inverse_image(X0,X1),X2)
| ~ in(sK0(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),X2)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_proxy_replacement,[],[f103,f161]) ).
fof(f163,plain,
! [X2,X0,X1] :
( sQ17_eqProxy(relation_inverse_image(X0,X1),X2)
| in(sK0(X0,X1,X2),relation_dom(X0))
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_proxy_replacement,[],[f102,f161]) ).
fof(f164,plain,
! [X2,X0,X1] :
( sQ17_eqProxy(relation_inverse_image(X0,X1),X2)
| in(apply(X0,sK0(X0,X1,X2)),X1)
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_proxy_replacement,[],[f101,f161]) ).
fof(f168,plain,
~ sQ17_eqProxy(relation_inverse_image(sK15,set_difference(sK13,sK14)),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),
inference(equality_proxy_replacement,[],[f142,f161]) ).
fof(f315,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK15,X1))
| ~ relation(sK15)
| in(X0,relation_dom(sK15)) ),
inference(resolution,[],[f156,f140]) ).
fof(f317,definition,
( spl18_13
<=> relation(sK15) ),
introduced(definition,[new_symbols(definition,[spl18_13])],[avatar_definition]) ).
fof(f318,plain,
( ~ relation(sK15)
| spl18_13 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f320,definition,
( spl18_14
<=> ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK15,X1))
| in(X0,relation_dom(sK15)) ) ),
introduced(definition,[new_symbols(definition,[spl18_14])],[avatar_definition]) ).
fof(f321,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK15,X1))
| in(X0,relation_dom(sK15)) )
| ~ spl18_14 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f322,plain,
( ~ spl18_13
| spl18_14 ),
inference(avatar_split_clause,[],[f315,f320,f317]) ).
fof(f344,plain,
( $false
| spl18_13 ),
inference(resolution,[],[f318,f141]) ).
fof(f346,plain,
spl18_13,
inference(avatar_contradiction_clause,[],[f344]) ).
fof(f423,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK15,X1))
| ~ relation(sK15)
| in(apply(sK15,X0),X1) ),
inference(resolution,[],[f157,f140]) ).
fof(f425,definition,
( spl18_29
<=> ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK15,X1))
| in(apply(sK15,X0),X1) ) ),
introduced(definition,[new_symbols(definition,[spl18_29])],[avatar_definition]) ).
fof(f426,plain,
( ! [X0,X1] :
( in(apply(sK15,X0),X1)
| ~ in(X0,relation_inverse_image(sK15,X1)) )
| ~ spl18_29 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f427,plain,
( ~ spl18_13
| spl18_29 ),
inference(avatar_split_clause,[],[f423,f425,f317]) ).
fof(f866,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(sK15))
| ~ in(apply(sK15,X0),X1)
| ~ relation(sK15)
| in(X0,relation_inverse_image(sK15,X1)) ),
inference(resolution,[],[f155,f140]) ).
fof(f868,definition,
( spl18_35
<=> ! [X0,X1] :
( ~ in(X0,relation_dom(sK15))
| in(X0,relation_inverse_image(sK15,X1))
| ~ in(apply(sK15,X0),X1) ) ),
introduced(definition,[new_symbols(definition,[spl18_35])],[avatar_definition]) ).
fof(f869,plain,
( ! [X0,X1] :
( ~ in(apply(sK15,X0),X1)
| in(X0,relation_inverse_image(sK15,X1))
| ~ in(X0,relation_dom(sK15)) )
| ~ spl18_35 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f870,plain,
( ~ spl18_13
| spl18_35 ),
inference(avatar_split_clause,[],[f866,f868,f317]) ).
fof(f880,plain,
( ! [X2,X0,X1] :
( in(X0,relation_inverse_image(sK15,set_difference(X1,X2)))
| ~ in(X0,relation_dom(sK15))
| ~ in(apply(sK15,X0),X1)
| in(apply(sK15,X0),X2) )
| ~ spl18_35 ),
inference(resolution,[],[f869,f158]) ).
fof(f1014,plain,
( in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(resolution,[],[f163,f168]) ).
fof(f1016,definition,
( spl18_38
<=> function(sK15) ),
introduced(definition,[new_symbols(definition,[spl18_38])],[avatar_definition]) ).
fof(f1017,plain,
( ~ function(sK15)
| spl18_38 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f1019,definition,
( spl18_39
<=> in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))) ),
introduced(definition,[new_symbols(definition,[spl18_39])],[avatar_definition]) ).
fof(f1020,plain,
( in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))
| ~ spl18_39 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1022,definition,
( spl18_40
<=> in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15)) ),
introduced(definition,[new_symbols(definition,[spl18_40])],[avatar_definition]) ).
fof(f1024,plain,
( ~ spl18_38
| ~ spl18_13
| spl18_39
| spl18_40 ),
inference(avatar_split_clause,[],[f1014,f1022,f1019,f317,f1016]) ).
fof(f1025,plain,
( $false
| spl18_38 ),
inference(resolution,[],[f1017,f140]) ).
fof(f1027,plain,
spl18_38,
inference(avatar_contradiction_clause,[],[f1025]) ).
fof(f1032,plain,
( ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14))
| ~ spl18_39 ),
inference(resolution,[],[f1020,f160]) ).
fof(f1033,plain,
( in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK13))
| ~ spl18_39 ),
inference(resolution,[],[f1020,f159]) ).
fof(f1045,plain,
( in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| ~ spl18_14
| ~ spl18_39 ),
inference(resolution,[],[f1033,f321]) ).
fof(f1048,plain,
( spl18_40
| ~ spl18_14
| ~ spl18_39 ),
inference(avatar_split_clause,[],[f1045,f1019,f320,f1022]) ).
fof(f1147,plain,
( in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),set_difference(sK13,sK14))
| in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(resolution,[],[f164,f168]) ).
fof(f1446,plain,
( ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| ~ in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),set_difference(sK13,sK14))
| ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(resolution,[],[f162,f168]) ).
fof(f1447,plain,
( ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))
| spl18_39 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1449,definition,
( spl18_43
<=> in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),set_difference(sK13,sK14)) ),
introduced(definition,[new_symbols(definition,[spl18_43])],[avatar_definition]) ).
fof(f1450,plain,
( ~ in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),set_difference(sK13,sK14))
| spl18_43 ),
inference(avatar_component_clause,[],[f1449]) ).
fof(f1452,plain,
( ~ spl18_38
| ~ spl18_13
| ~ spl18_39
| ~ spl18_43
| ~ spl18_40 ),
inference(avatar_split_clause,[],[f1446,f1022,f1449,f1019,f317,f1016]) ).
fof(f1453,plain,
( ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,set_difference(sK13,sK14)))
| ~ spl18_29
| spl18_43 ),
inference(resolution,[],[f1450,f426]) ).
fof(f1456,definition,
( spl18_44
<=> in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK14) ),
introduced(definition,[new_symbols(definition,[spl18_44])],[avatar_definition]) ).
fof(f1457,plain,
( in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK14)
| ~ spl18_44 ),
inference(avatar_component_clause,[],[f1456]) ).
fof(f1459,definition,
( spl18_45
<=> in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK13) ),
introduced(definition,[new_symbols(definition,[spl18_45])],[avatar_definition]) ).
fof(f1460,plain,
( ~ in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK13)
| spl18_45 ),
inference(avatar_component_clause,[],[f1459]) ).
fof(f1466,plain,
( ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK13))
| ~ spl18_29
| spl18_45 ),
inference(resolution,[],[f1460,f426]) ).
fof(f1471,plain,
( ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| ~ in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK13)
| in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK14)
| ~ spl18_29
| ~ spl18_35
| spl18_43 ),
inference(resolution,[],[f1453,f880]) ).
fof(f1548,plain,
( $false
| ~ spl18_29
| ~ spl18_39
| spl18_45 ),
inference(resolution,[],[f1466,f1033]) ).
fof(f1549,plain,
( ~ spl18_29
| ~ spl18_39
| spl18_45 ),
inference(avatar_contradiction_clause,[],[f1548]) ).
fof(f1550,plain,
( spl18_44
| ~ spl18_45
| ~ spl18_40
| ~ spl18_29
| ~ spl18_35
| spl18_43 ),
inference(avatar_split_clause,[],[f1471,f1449,f868,f425,f1022,f1459,f1456]) ).
fof(f1555,plain,
( in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14))
| ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| ~ spl18_35
| ~ spl18_44 ),
inference(resolution,[],[f1457,f869]) ).
fof(f1559,definition,
( spl18_46
<=> in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14)) ),
introduced(definition,[new_symbols(definition,[spl18_46])],[avatar_definition]) ).
fof(f1560,plain,
( in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14))
| ~ spl18_46 ),
inference(avatar_component_clause,[],[f1559]) ).
fof(f1561,plain,
( ~ spl18_40
| spl18_46
| ~ spl18_35
| ~ spl18_44 ),
inference(avatar_split_clause,[],[f1555,f1456,f868,f1559,f1022]) ).
fof(f1578,plain,
( $false
| ~ spl18_39
| ~ spl18_46 ),
inference(resolution,[],[f1560,f1032]) ).
fof(f1583,plain,
( ~ spl18_39
| ~ spl18_46 ),
inference(avatar_contradiction_clause,[],[f1578]) ).
fof(f1584,plain,
( in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),set_difference(sK13,sK14))
| ~ spl18_43 ),
inference(avatar_component_clause,[],[f1449]) ).
fof(f1585,plain,
( ~ spl18_38
| ~ spl18_13
| spl18_39
| spl18_43 ),
inference(avatar_split_clause,[],[f1147,f1449,f1019,f317,f1016]) ).
fof(f1591,plain,
( ~ in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK14)
| ~ spl18_43 ),
inference(resolution,[],[f1584,f160]) ).
fof(f1592,plain,
( in(apply(sK15,sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK13)
| ~ spl18_43 ),
inference(resolution,[],[f1584,f159]) ).
fof(f1603,plain,
( ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK13))
| in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14))
| spl18_39 ),
inference(resolution,[],[f1447,f158]) ).
fof(f1609,plain,
( ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14))
| ~ spl18_29
| ~ spl18_43 ),
inference(resolution,[],[f1591,f426]) ).
fof(f1615,plain,
( in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK13))
| ~ in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| ~ spl18_35
| ~ spl18_43 ),
inference(resolution,[],[f1592,f869]) ).
fof(f1619,definition,
( spl18_48
<=> in(sK0(sK15,set_difference(sK13,sK14),set_difference(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK13)) ),
introduced(definition,[new_symbols(definition,[spl18_48])],[avatar_definition]) ).
fof(f1621,plain,
( ~ spl18_40
| spl18_48
| ~ spl18_35
| ~ spl18_43 ),
inference(avatar_split_clause,[],[f1615,f1449,f868,f1619,f1022]) ).
fof(f1646,plain,
( $false
| ~ spl18_29
| ~ spl18_43
| ~ spl18_46 ),
inference(resolution,[],[f1609,f1560]) ).
fof(f1647,plain,
( ~ spl18_29
| ~ spl18_43
| ~ spl18_46 ),
inference(avatar_contradiction_clause,[],[f1646]) ).
fof(f1649,plain,
( spl18_46
| ~ spl18_48
| spl18_39 ),
inference(avatar_split_clause,[],[f1603,f1019,f1619,f1559]) ).
cnf(s8,plain,
( ~ spl18_13
| spl18_14 ),
inference(sat_conversion,[],[f322]) ).
cnf(s12,plain,
spl18_13,
inference(sat_conversion,[],[f346]) ).
cnf(s23,plain,
( ~ spl18_13
| spl18_29 ),
inference(sat_conversion,[],[f427]) ).
cnf(s28,plain,
( ~ spl18_13
| spl18_35 ),
inference(sat_conversion,[],[f870]) ).
cnf(s31,plain,
( ~ spl18_13
| ~ spl18_38
| spl18_39
| spl18_40 ),
inference(sat_conversion,[],[f1024]) ).
cnf(s32,plain,
spl18_38,
inference(sat_conversion,[],[f1027]) ).
cnf(s33,plain,
( ~ spl18_14
| ~ spl18_39
| spl18_40 ),
inference(sat_conversion,[],[f1048]) ).
cnf(s36,plain,
( ~ spl18_13
| ~ spl18_38
| ~ spl18_39
| ~ spl18_40
| ~ spl18_43 ),
inference(sat_conversion,[],[f1452]) ).
cnf(s38,plain,
( ~ spl18_29
| ~ spl18_39
| spl18_45 ),
inference(sat_conversion,[],[f1549]) ).
cnf(s39,plain,
( ~ spl18_29
| ~ spl18_35
| ~ spl18_40
| spl18_43
| spl18_44
| ~ spl18_45 ),
inference(sat_conversion,[],[f1550]) ).
cnf(s40,plain,
( ~ spl18_35
| ~ spl18_40
| ~ spl18_44
| spl18_46 ),
inference(sat_conversion,[],[f1561]) ).
cnf(s41,plain,
( ~ spl18_39
| ~ spl18_46 ),
inference(sat_conversion,[],[f1583]) ).
cnf(s42,plain,
( ~ spl18_13
| ~ spl18_38
| spl18_39
| spl18_43 ),
inference(sat_conversion,[],[f1585]) ).
cnf(s45,plain,
( ~ spl18_35
| ~ spl18_40
| ~ spl18_43
| spl18_48 ),
inference(sat_conversion,[],[f1621]) ).
cnf(s46,plain,
( ~ spl18_29
| ~ spl18_43
| ~ spl18_46 ),
inference(sat_conversion,[],[f1647]) ).
cnf(s47,plain,
( spl18_39
| spl18_46
| ~ spl18_48 ),
inference(sat_conversion,[],[f1649]) ).
cnf(s48,plain,
( ~ spl18_13
| spl18_39
| spl18_40 ),
inference(rat,[],[s31,s32]) ).
cnf(s54,plain,
spl18_35,
inference(rat,[],[s28,s12]) ).
cnf(s55,plain,
spl18_29,
inference(rat,[],[s23,s12]) ).
cnf(s59,plain,
spl18_14,
inference(rat,[],[s8,s12]) ).
cnf(s60,plain,
spl18_39,
inference(rat,[],[s47,s45,s46,s48,s42,s54,s55,s12,s32]) ).
cnf(s61,plain,
~ spl18_46,
inference(rat,[],[s41,s60]) ).
cnf(s62,plain,
spl18_45,
inference(rat,[],[s38,s55,s60]) ).
cnf(s63,plain,
spl18_40,
inference(rat,[],[s33,s59,s60]) ).
cnf(s64,plain,
~ spl18_44,
inference(rat,[],[s40,s61,s54,s63]) ).
cnf(s65,plain,
~ spl18_43,
inference(rat,[],[s36,s60,s12,s32,s63]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s39,s62,s65,s55,s54,s64,s63]) ).
fof(f1650,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU059+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:29:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 4.52/1.53 % (3635010)Detected formulas, will run a generic FOF schedule.
% 4.52/1.53 % (3635031)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=2864762539:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.52/1.53 % (3635036)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=983286521:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.52/1.53 % (3635037)dis-21_1_sil=8000:lcm=predicate:random_seed=3811494933: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)
% 4.52/1.53 % (3635035)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2482075101:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.52/1.53 % (3635034)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1777504485:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.52/1.53 % (3635032)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=823285112:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.52/1.53 % (3635033)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=942472184:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.52/1.53 % (3635034)Refutation not found, incomplete strategy
% 4.52/1.53 % (3635034)------------------------------
% 4.52/1.53 % (3635034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.52/1.53 % (3635034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.52/1.53 % (3635034)CaDiCaL version: 2.1.3
% 4.52/1.53 % (3635034)Termination reason: Refutation not found, incomplete strategy
% 4.52/1.53 % (3635034)Time elapsed: 0.002 s
% 4.52/1.53 % (3635034)Peak memory usage: 88 MB
% 4.52/1.53 % (3635034)Instructions burned: 1 (million)
% 4.52/1.53 % (3635037)First to succeed.
% 4.52/1.53 % (3635037)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3635010"
% 4.52/1.53 % (3635036)Instruction limit reached!
% 4.52/1.53 % (3635036)------------------------------
% 4.52/1.53 % (3635036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.52/1.53 % (3635036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.52/1.53 % (3635036)CaDiCaL version: 2.1.3
% 4.52/1.53 % (3635036)Termination reason: Instruction limit
% 4.52/1.53 % (3635036)Termination phase: Saturation
% 4.52/1.53 % (3635036)Time elapsed: 0.127 s
% 4.52/1.53 % (3635036)Peak memory usage: 89 MB
% 4.52/1.53 % (3635036)Instructions burned: 139 (million)
% 4.52/1.53 % (3635035)Instruction limit reached!
% 4.52/1.53 % (3635035)------------------------------
% 4.52/1.53 % (3635035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.52/1.53 % (3635035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.52/1.53 % (3635035)CaDiCaL version: 2.1.3
% 4.52/1.53 % (3635035)Termination reason: Instruction limit
% 4.52/1.53 % (3635035)Termination phase: Saturation
% 4.52/1.53 % (3635035)Time elapsed: 0.075 s
% 4.52/1.53 % (3635035)Peak memory usage: 88 MB
% 4.52/1.53 % (3635035)Instructions burned: 120 (million)
% 4.52/1.53 % (3635052)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1651704245:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.52/1.53 % (3635050)lrs+10_1_sil=8000:sp=occurrence:random_seed=1778671411:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.52/1.53 % (3635052)Instruction limit reached!
% 4.52/1.53 % (3635052)------------------------------
% 4.52/1.53 % (3635052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.52/1.53 % (3635052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.52/1.53 % (3635052)CaDiCaL version: 2.1.3
% 4.52/1.53 % (3635052)Termination reason: Instruction limit
% 4.52/1.53 % (3635052)Termination phase: Saturation
% 4.52/1.53 % (3635052)Time elapsed: 0.117 s
% 4.52/1.53 % (3635052)Peak memory usage: 91 MB
% 4.52/1.53 % (3635052)Instructions burned: 157 (million)
% 4.52/1.53 % (3635034)------------------------------
% 4.52/1.53 % (3635034)------------------------------
% 4.52/1.53 % (3635031)Also succeeded, but the first one will report.
% 4.52/1.53 % (3635037)Refutation found. Thanks to Tanya!
% 4.52/1.53 % SZS status Theorem for theBenchmark
% 4.52/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.35/1.75 % (3635037)------------------------------
% 5.35/1.75 % (3635037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.35/1.75 % (3635037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.75 % (3635037)CaDiCaL version: 2.1.3
% 5.35/1.75 % (3635037)Termination reason: Refutation
% 5.35/1.75 % (3635037)Time elapsed: 0.046 s
% 5.35/1.75 % (3635037)Peak memory usage: 90 MB
% 5.35/1.75 % (3635037)Instructions burned: 44 (million)
% 5.35/1.75 % (3635037)------------------------------
% 5.35/1.75 % (3635037)------------------------------
% 5.35/1.75 % (3635010)Success in time 0.663 s
% 5.35/1.75 % Vampire exiting
%------------------------------------------------------------------------------