%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU058+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 3.30s 1.33s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 125 ( 18 unt; 13 def)
% Number of atoms : 462 ( 36 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 579 ( 242 ~; 260 |; 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 : 146 ( 0 sgn 134 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f28,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> relation_inverse_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_funct_1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> relation_inverse_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f52,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,[],[f6]) ).
fof(f53,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,[],[f52]) ).
fof(f60,plain,
? [X0,X1,X2] :
( relation_inverse_image(X2,set_intersection2(X0,X1)) != set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f29]) ).
fof(f61,plain,
? [X0,X1,X2] :
( relation_inverse_image(X2,set_intersection2(X0,X1)) != set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f60]) ).
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) ) ) )
& ( ! [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,[],[f53]) ).
fof(f74,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,[],[f73]) ).
fof(f75,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,[],[f74]) ).
fof(f76,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))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f79]) ).
fof(f92,plain,
( relation_inverse_image(sK15,set_intersection2(sK13,sK14)) != set_intersection2(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)],[f61]) ).
fof(f101,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,[],[f76]) ).
fof(f102,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,[],[f76]) ).
fof(f103,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,[],[f76]) ).
fof(f104,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,[],[f76]) ).
fof(f105,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,[],[f76]) ).
fof(f106,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,[],[f76]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f108,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f144,plain,
function(sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f145,plain,
relation(sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f146,plain,
relation_inverse_image(sK15,set_intersection2(sK13,sK14)) != set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)),
inference(cnf_transformation,[],[f92]) ).
fof(f158,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,[],[f103]) ).
fof(f159,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ relation(X0)
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f102]) ).
fof(f160,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ relation(X0)
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f101]) ).
fof(f161,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f109]) ).
fof(f162,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f108]) ).
fof(f163,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f107]) ).
fof(f164,definition,
! [X0,X1] :
( sQ17_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ17_eqProxy])],[equality_proxy_definition]) ).
fof(f166,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,[],[f106,f164]) ).
fof(f167,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,[],[f105,f164]) ).
fof(f168,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,[],[f104,f164]) ).
fof(f173,plain,
~ sQ17_eqProxy(relation_inverse_image(sK15,set_intersection2(sK13,sK14)),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),
inference(equality_proxy_replacement,[],[f146,f164]) ).
fof(f319,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK15,X1))
| ~ relation(sK15)
| in(X0,relation_dom(sK15)) ),
inference(resolution,[],[f159,f144]) ).
fof(f321,definition,
( spl18_13
<=> relation(sK15) ),
introduced(definition,[new_symbols(definition,[spl18_13])],[avatar_definition]) ).
fof(f322,plain,
( ~ relation(sK15)
| spl18_13 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f324,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(f325,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK15,X1))
| in(X0,relation_dom(sK15)) )
| ~ spl18_14 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f326,plain,
( ~ spl18_13
| spl18_14 ),
inference(avatar_split_clause,[],[f319,f324,f321]) ).
fof(f348,plain,
( $false
| spl18_13 ),
inference(resolution,[],[f322,f145]) ).
fof(f350,plain,
spl18_13,
inference(avatar_contradiction_clause,[],[f348]) ).
fof(f429,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK15,X1))
| ~ relation(sK15)
| in(apply(sK15,X0),X1) ),
inference(resolution,[],[f160,f144]) ).
fof(f431,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(f432,plain,
( ! [X0,X1] :
( in(apply(sK15,X0),X1)
| ~ in(X0,relation_inverse_image(sK15,X1)) )
| ~ spl18_29 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f433,plain,
( ~ spl18_13
| spl18_29 ),
inference(avatar_split_clause,[],[f429,f431,f321]) ).
fof(f873,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(sK15))
| ~ in(apply(sK15,X0),X1)
| ~ relation(sK15)
| in(X0,relation_inverse_image(sK15,X1)) ),
inference(resolution,[],[f158,f144]) ).
fof(f875,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(f876,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,[],[f875]) ).
fof(f877,plain,
( ~ spl18_13
| spl18_35 ),
inference(avatar_split_clause,[],[f873,f875,f321]) ).
fof(f1018,plain,
( in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(resolution,[],[f167,f173]) ).
fof(f1020,definition,
( spl18_38
<=> function(sK15) ),
introduced(definition,[new_symbols(definition,[spl18_38])],[avatar_definition]) ).
fof(f1021,plain,
( ~ function(sK15)
| spl18_38 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f1023,definition,
( spl18_39
<=> in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))) ),
introduced(definition,[new_symbols(definition,[spl18_39])],[avatar_definition]) ).
fof(f1024,plain,
( in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))
| ~ spl18_39 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f1026,definition,
( spl18_40
<=> in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15)) ),
introduced(definition,[new_symbols(definition,[spl18_40])],[avatar_definition]) ).
fof(f1028,plain,
( ~ spl18_38
| ~ spl18_13
| spl18_39
| spl18_40 ),
inference(avatar_split_clause,[],[f1018,f1026,f1023,f321,f1020]) ).
fof(f1029,plain,
( $false
| spl18_38 ),
inference(resolution,[],[f1021,f144]) ).
fof(f1031,plain,
spl18_38,
inference(avatar_contradiction_clause,[],[f1029]) ).
fof(f1036,plain,
( in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14))
| ~ spl18_39 ),
inference(resolution,[],[f1024,f163]) ).
fof(f1037,plain,
( in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK13))
| ~ spl18_39 ),
inference(resolution,[],[f1024,f162]) ).
fof(f1045,plain,
( in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| ~ spl18_14
| ~ spl18_39 ),
inference(resolution,[],[f1036,f325]) ).
fof(f1048,plain,
( spl18_40
| ~ spl18_14
| ~ spl18_39 ),
inference(avatar_split_clause,[],[f1045,f1023,f324,f1026]) ).
fof(f1155,plain,
( in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),set_intersection2(sK13,sK14))
| in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(resolution,[],[f168,f173]) ).
fof(f1457,plain,
( ~ in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| ~ in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),set_intersection2(sK13,sK14))
| ~ in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))
| ~ relation(sK15)
| ~ function(sK15) ),
inference(resolution,[],[f166,f173]) ).
fof(f1458,plain,
( ~ in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))
| spl18_39 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f1460,definition,
( spl18_43
<=> in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),set_intersection2(sK13,sK14)) ),
introduced(definition,[new_symbols(definition,[spl18_43])],[avatar_definition]) ).
fof(f1461,plain,
( ~ in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),set_intersection2(sK13,sK14))
| spl18_43 ),
inference(avatar_component_clause,[],[f1460]) ).
fof(f1463,plain,
( ~ spl18_38
| ~ spl18_13
| ~ spl18_39
| ~ spl18_43
| ~ spl18_40 ),
inference(avatar_split_clause,[],[f1457,f1026,f1460,f1023,f321,f1020]) ).
fof(f1465,plain,
( ~ in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK13)
| ~ in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK14)
| spl18_43 ),
inference(resolution,[],[f1461,f161]) ).
fof(f1467,definition,
( spl18_44
<=> in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK14) ),
introduced(definition,[new_symbols(definition,[spl18_44])],[avatar_definition]) ).
fof(f1468,plain,
( ~ in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK14)
| spl18_44 ),
inference(avatar_component_clause,[],[f1467]) ).
fof(f1470,definition,
( spl18_45
<=> in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK13) ),
introduced(definition,[new_symbols(definition,[spl18_45])],[avatar_definition]) ).
fof(f1471,plain,
( ~ in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK13)
| spl18_45 ),
inference(avatar_component_clause,[],[f1470]) ).
fof(f1472,plain,
( ~ spl18_44
| ~ spl18_45
| spl18_43 ),
inference(avatar_split_clause,[],[f1465,f1460,f1470,f1467]) ).
fof(f1477,plain,
( ~ in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14))
| ~ spl18_29
| spl18_44 ),
inference(resolution,[],[f1468,f432]) ).
fof(f1584,plain,
( $false
| ~ spl18_29
| ~ spl18_39
| spl18_44 ),
inference(resolution,[],[f1477,f1036]) ).
fof(f1585,plain,
( ~ spl18_29
| ~ spl18_39
| spl18_44 ),
inference(avatar_contradiction_clause,[],[f1584]) ).
fof(f1591,plain,
( ~ in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK13))
| ~ spl18_29
| spl18_45 ),
inference(resolution,[],[f1471,f432]) ).
fof(f1596,plain,
( $false
| ~ spl18_29
| ~ spl18_39
| spl18_45 ),
inference(resolution,[],[f1591,f1037]) ).
fof(f1597,plain,
( ~ spl18_29
| ~ spl18_39
| spl18_45 ),
inference(avatar_contradiction_clause,[],[f1596]) ).
fof(f1598,plain,
( in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),set_intersection2(sK13,sK14))
| ~ spl18_43 ),
inference(avatar_component_clause,[],[f1460]) ).
fof(f1599,plain,
( ~ spl18_38
| ~ spl18_13
| spl18_39
| spl18_43 ),
inference(avatar_split_clause,[],[f1155,f1460,f1023,f321,f1020]) ).
fof(f1605,plain,
( in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK14)
| ~ spl18_43 ),
inference(resolution,[],[f1598,f163]) ).
fof(f1606,plain,
( in(apply(sK15,sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14)))),sK13)
| ~ spl18_43 ),
inference(resolution,[],[f1598,f162]) ).
fof(f1617,plain,
( ~ in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK13))
| ~ in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14))
| spl18_39 ),
inference(resolution,[],[f1458,f161]) ).
fof(f1622,plain,
( in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14))
| ~ in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| ~ spl18_35
| ~ spl18_43 ),
inference(resolution,[],[f1605,f876]) ).
fof(f1626,definition,
( spl18_47
<=> in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK14)) ),
introduced(definition,[new_symbols(definition,[spl18_47])],[avatar_definition]) ).
fof(f1628,plain,
( ~ spl18_40
| spl18_47
| ~ spl18_35
| ~ spl18_43 ),
inference(avatar_split_clause,[],[f1622,f1460,f875,f1626,f1026]) ).
fof(f1634,plain,
( in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_inverse_image(sK15,sK13))
| ~ in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(relation_inverse_image(sK15,sK13),relation_inverse_image(sK15,sK14))),relation_dom(sK15))
| ~ spl18_35
| ~ spl18_43 ),
inference(resolution,[],[f1606,f876]) ).
fof(f1639,definition,
( spl18_48
<=> in(sK0(sK15,set_intersection2(sK13,sK14),set_intersection2(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(f1641,plain,
( ~ spl18_40
| spl18_48
| ~ spl18_35
| ~ spl18_43 ),
inference(avatar_split_clause,[],[f1634,f1460,f875,f1639,f1026]) ).
fof(f1644,plain,
( ~ spl18_47
| ~ spl18_48
| spl18_39 ),
inference(avatar_split_clause,[],[f1617,f1023,f1639,f1626]) ).
cnf(s8,plain,
( ~ spl18_13
| spl18_14 ),
inference(sat_conversion,[],[f326]) ).
cnf(s12,plain,
spl18_13,
inference(sat_conversion,[],[f350]) ).
cnf(s23,plain,
( ~ spl18_13
| spl18_29 ),
inference(sat_conversion,[],[f433]) ).
cnf(s28,plain,
( ~ spl18_13
| spl18_35 ),
inference(sat_conversion,[],[f877]) ).
cnf(s31,plain,
( ~ spl18_13
| ~ spl18_38
| spl18_39
| spl18_40 ),
inference(sat_conversion,[],[f1028]) ).
cnf(s32,plain,
spl18_38,
inference(sat_conversion,[],[f1031]) ).
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,[],[f1463]) ).
cnf(s37,plain,
( spl18_43
| ~ spl18_44
| ~ spl18_45 ),
inference(sat_conversion,[],[f1472]) ).
cnf(s39,plain,
( ~ spl18_29
| ~ spl18_39
| spl18_44 ),
inference(sat_conversion,[],[f1585]) ).
cnf(s41,plain,
( ~ spl18_29
| ~ spl18_39
| spl18_45 ),
inference(sat_conversion,[],[f1597]) ).
cnf(s42,plain,
( ~ spl18_13
| ~ spl18_38
| spl18_39
| spl18_43 ),
inference(sat_conversion,[],[f1599]) ).
cnf(s44,plain,
( ~ spl18_35
| ~ spl18_40
| ~ spl18_43
| spl18_47 ),
inference(sat_conversion,[],[f1628]) ).
cnf(s46,plain,
( ~ spl18_35
| ~ spl18_40
| ~ spl18_43
| spl18_48 ),
inference(sat_conversion,[],[f1641]) ).
cnf(s47,plain,
( spl18_39
| ~ spl18_47
| ~ spl18_48 ),
inference(sat_conversion,[],[f1644]) ).
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,s44,s46,s48,s42,s54,s12,s32]) ).
cnf(s61,plain,
spl18_45,
inference(rat,[],[s41,s55,s60]) ).
cnf(s62,plain,
spl18_44,
inference(rat,[],[s39,s55,s60]) ).
cnf(s63,plain,
spl18_40,
inference(rat,[],[s33,s59,s60]) ).
cnf(s64,plain,
spl18_43,
inference(rat,[],[s37,s61,s62]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s36,s60,s12,s32,s64,s63]) ).
fof(f1645,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU058+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:28:15 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.30/1.33 % (2987869)Detected formulas, will run a generic FOF schedule.
% 3.30/1.33 % (2987878)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2973057354:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.30/1.33 % (2987878)Instruction limit reached!
% 3.30/1.33 % (2987878)------------------------------
% 3.30/1.33 % (2987878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.33 % (2987878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.33 % (2987878)CaDiCaL version: 2.1.3
% 3.30/1.33 % (2987878)Termination reason: Instruction limit
% 3.30/1.33 % (2987878)Termination phase: Saturation
% 3.30/1.33 % (2987878)Time elapsed: 0.036 s
% 3.30/1.33 % (2987878)Peak memory usage: 88 MB
% 3.30/1.33 % (2987878)Instructions burned: 120 (million)
% 3.30/1.33 % (2987877)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3689141957:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.30/1.33 % (2987879)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2475023190:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.30/1.33 % (2987875)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=418671530:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.30/1.33 % (2987874)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=2585722302:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.30/1.33 % (2987876)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=3136027288:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.30/1.33 % (2987877)Refutation not found, incomplete strategy
% 3.30/1.33 % (2987877)------------------------------
% 3.30/1.33 % (2987877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.33 % (2987877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.33 % (2987877)CaDiCaL version: 2.1.3
% 3.30/1.33 % (2987877)Termination reason: Refutation not found, incomplete strategy
% 3.30/1.33 % (2987877)Time elapsed: 0.002 s
% 3.30/1.33 % (2987877)Peak memory usage: 88 MB
% 3.30/1.33 % (2987877)Instructions burned: 1 (million)
% 3.30/1.33 % (2987880)dis-21_1_sil=8000:lcm=predicate:random_seed=3261897446: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)
% 3.30/1.33 % (2987880)First to succeed.
% 3.30/1.33 % (2987880)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2987869"
% 3.30/1.33 % (2987879)Instruction limit reached!
% 3.30/1.33 % (2987879)------------------------------
% 3.30/1.33 % (2987879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.33 % (2987879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.33 % (2987879)CaDiCaL version: 2.1.3
% 3.30/1.33 % (2987879)Termination reason: Instruction limit
% 3.30/1.33 % (2987879)Termination phase: Saturation
% 3.30/1.33 % (2987879)Time elapsed: 0.092 s
% 3.30/1.33 % (2987879)Peak memory usage: 89 MB
% 3.30/1.33 % (2987879)Instructions burned: 139 (million)
% 3.30/1.33 % (2987887)lrs+10_1_sil=8000:sp=occurrence:random_seed=1866093824:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.30/1.33 % (2987887)Instruction limit reached!
% 3.30/1.33 % (2987887)------------------------------
% 3.30/1.33 % (2987887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.33 % (2987887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.33 % (2987887)CaDiCaL version: 2.1.3
% 3.30/1.33 % (2987887)Termination reason: Instruction limit
% 3.30/1.33 % (2987887)Termination phase: Saturation
% 3.30/1.33 % (2987887)Time elapsed: 0.091 s
% 3.30/1.33 % (2987887)Peak memory usage: 91 MB
% 3.30/1.33 % (2987887)Instructions burned: 288 (million)
% 3.30/1.33 % (2987877)------------------------------
% 3.30/1.33 % (2987877)------------------------------
% 3.30/1.33 % (2987889)lrs+10_1_sil=32000:urr=on:br=off:random_seed=160106175:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.30/1.33 % (2987880)Refutation found. Thanks to Tanya!
% 3.30/1.33 % SZS status Theorem for theBenchmark
% 3.30/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.87/1.42 % (2987880)------------------------------
% 3.87/1.42 % (2987880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.42 % (2987880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.42 % (2987880)CaDiCaL version: 2.1.3
% 3.87/1.42 % (2987880)Termination reason: Refutation
% 3.87/1.42 % (2987880)Time elapsed: 0.028 s
% 3.87/1.42 % (2987880)Peak memory usage: 90 MB
% 3.87/1.42 % (2987880)Instructions burned: 44 (million)
% 3.87/1.42 % (2987880)------------------------------
% 3.87/1.42 % (2987880)------------------------------
% 3.87/1.42 % (2987869)Success in time 0.468 s
% 3.87/1.42 % Vampire exiting
%------------------------------------------------------------------------------