TSTP Solution File: SET686+3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET686+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:45:13 EDT 2023
% Result : Theorem 0.22s 0.53s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 26
% Syntax : Number of formulae : 140 ( 20 unt; 0 def)
% Number of atoms : 686 ( 14 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 882 ( 336 ~; 293 |; 189 &)
% ( 14 <=>; 48 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-4 aty)
% Number of variables : 347 (; 271 !; 76 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2229,plain,
$false,
inference(subsumption_resolution,[],[f2228,f220]) ).
fof(f220,plain,
ilf_type(sK7,sF35),
inference(definition_folding,[],[f124,f219]) ).
fof(f219,plain,
relation_type(sK4,sK6) = sF35,
introduced(function_definition,[]) ).
fof(f124,plain,
ilf_type(sK7,relation_type(sK4,sK6)),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(sK8,X5),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(sK8,inverse4(sK4,sK6,sK7,sK5)) )
& ( ( member(sK9,sK5)
& member(ordered_pair(sK8,sK9),sK7)
& ilf_type(sK9,member_type(sK6)) )
| member(sK8,inverse4(sK4,sK6,sK7,sK5)) )
& ilf_type(sK8,member_type(sK4))
& ilf_type(sK7,relation_type(sK4,sK6))
& ilf_type(sK6,set_type)
& ~ empty(sK6)
& ilf_type(sK5,set_type)
& ~ empty(sK5)
& ilf_type(sK4,set_type)
& ~ empty(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9])],[f72,f78,f77,f76,f75,f74,f73]) ).
fof(f73,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK4,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK4,X2,X3,X1)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(sK4,set_type)
& ~ empty(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK4,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK4,X2,X3,X1)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK4,X2,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK4,X2,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(sK5,set_type)
& ~ empty(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK4,X2,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK4,X2,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,inverse4(sK4,sK6,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(sK6)) )
| member(X4,inverse4(sK4,sK6,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,sK6)) )
& ilf_type(sK6,set_type)
& ~ empty(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,inverse4(sK4,sK6,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(sK6)) )
| member(X4,inverse4(sK4,sK6,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,sK6)) )
=> ( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,inverse4(sK4,sK6,sK7,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),sK7)
& ilf_type(X6,member_type(sK6)) )
| member(X4,inverse4(sK4,sK6,sK7,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(sK7,relation_type(sK4,sK6)) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,inverse4(sK4,sK6,sK7,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),sK7)
& ilf_type(X6,member_type(sK6)) )
| member(X4,inverse4(sK4,sK6,sK7,sK5)) )
& ilf_type(X4,member_type(sK4)) )
=> ( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(sK8,X5),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(sK8,inverse4(sK4,sK6,sK7,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(sK8,X6),sK7)
& ilf_type(X6,member_type(sK6)) )
| member(sK8,inverse4(sK4,sK6,sK7,sK5)) )
& ilf_type(sK8,member_type(sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(sK8,X6),sK7)
& ilf_type(X6,member_type(sK6)) )
=> ( member(sK9,sK5)
& member(ordered_pair(sK8,sK9),sK7)
& ilf_type(sK9,member_type(sK6)) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,inverse4(X0,X2,X3,X1))
<~> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,inverse4(X0,X2,X3,X1))
<~> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991',prove_relset_1_53) ).
fof(f2228,plain,
~ ilf_type(sK7,sF35),
inference(superposition,[],[f2227,f219]) ).
fof(f2227,plain,
! [X0] : ~ ilf_type(sK7,relation_type(X0,sK6)),
inference(resolution,[],[f2226,f237]) ).
fof(f237,plain,
! [X0,X1,X4] :
( ~ sP27(X4,X1)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f232,f223]) ).
fof(f223,plain,
! [X1] : ilf_type(X1,set_type),
inference(subsumption_resolution,[],[f192,f222]) ).
fof(f222,plain,
sP21,
inference(forward_literal_rewriting,[],[f123,f191]) ).
fof(f191,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| sP21 ),
inference(cnf_transformation,[],[f191_D]) ).
fof(f191_D,plain,
( ! [X0] : ~ ilf_type(X0,set_type)
<=> ~ sP21 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP21])]) ).
fof(f123,plain,
ilf_type(sK6,set_type),
inference(cnf_transformation,[],[f79]) ).
fof(f192,plain,
! [X1] :
( ilf_type(X1,set_type)
| ~ sP21 ),
inference(general_splitting,[],[f150,f191_D]) ).
fof(f150,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] : ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] : ilf_type(X1,set_type) ),
file('/export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991',p14) ).
fof(f232,plain,
! [X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X0,set_type)
| ~ sP27(X4,X1) ),
inference(subsumption_resolution,[],[f204,f223]) ).
fof(f204,plain,
! [X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ sP27(X4,X1) ),
inference(general_splitting,[],[f202,f203_D]) ).
fof(f203,plain,
! [X3,X1,X4] :
( member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP26(X4,X3)
| sP27(X4,X1) ),
inference(cnf_transformation,[],[f203_D]) ).
fof(f203_D,plain,
! [X1,X4] :
( ! [X3] :
( member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP26(X4,X3) )
<=> ~ sP27(X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP27])]) ).
fof(f202,plain,
! [X3,X0,X1,X4] :
( member(X3,X1)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ sP26(X4,X3) ),
inference(general_splitting,[],[f177,f201_D]) ).
fof(f201,plain,
! [X2,X3,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X2,set_type)
| sP26(X4,X3) ),
inference(cnf_transformation,[],[f201_D]) ).
fof(f201_D,plain,
! [X3,X4] :
( ! [X2] :
( ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X2,set_type) )
<=> ~ sP26(X4,X3) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP26])]) ).
fof(f177,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991',p2) ).
fof(f2226,plain,
sP27(sK7,sK6),
inference(subsumption_resolution,[],[f2225,f1286]) ).
fof(f1286,plain,
member(sK8,sF32),
inference(subsumption_resolution,[],[f1285,f215]) ).
fof(f215,plain,
( member(sF33,sK7)
| member(sK8,sF32) ),
inference(definition_folding,[],[f127,f211,f214]) ).
fof(f214,plain,
ordered_pair(sK8,sK9) = sF33,
introduced(function_definition,[]) ).
fof(f211,plain,
inverse4(sK4,sK6,sK7,sK5) = sF32,
introduced(function_definition,[]) ).
fof(f127,plain,
( member(ordered_pair(sK8,sK9),sK7)
| member(sK8,inverse4(sK4,sK6,sK7,sK5)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f1285,plain,
( member(sK8,sF32)
| ~ member(sF33,sK7) ),
inference(subsumption_resolution,[],[f1284,f213]) ).
fof(f213,plain,
( member(sK9,sK5)
| member(sK8,sF32) ),
inference(definition_folding,[],[f128,f211]) ).
fof(f128,plain,
( member(sK9,sK5)
| member(sK8,inverse4(sK4,sK6,sK7,sK5)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f1284,plain,
( member(sK8,sF32)
| ~ member(sF33,sK7)
| ~ member(sK9,sK5) ),
inference(subsumption_resolution,[],[f1282,f321]) ).
fof(f321,plain,
relation_like(sK7),
inference(resolution,[],[f320,f220]) ).
fof(f320,plain,
! [X0] :
( ~ ilf_type(X0,sF35)
| relation_like(X0) ),
inference(superposition,[],[f293,f219]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| relation_like(X2) ),
inference(forward_literal_rewriting,[],[f292,f255]) ).
fof(f255,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f254,f223]) ).
fof(f254,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f155,f223]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991',p5) ).
fof(f292,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f291,f223]) ).
fof(f291,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f180,f223]) ).
fof(f180,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991',p24) ).
fof(f1282,plain,
( member(sK8,sF32)
| ~ member(sF33,sK7)
| ~ member(sK9,sK5)
| ~ relation_like(sK7) ),
inference(superposition,[],[f906,f852]) ).
fof(f852,plain,
sF32 = inverse2(sK7,sK5),
inference(superposition,[],[f847,f211]) ).
fof(f847,plain,
! [X1] : inverse2(sK7,X1) = inverse4(sK4,sK6,sK7,X1),
inference(resolution,[],[f835,f220]) ).
fof(f835,plain,
! [X0,X1] :
( ~ ilf_type(X0,sF35)
| inverse2(X0,X1) = inverse4(sK4,sK6,X0,X1) ),
inference(superposition,[],[f290,f219]) ).
fof(f290,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ),
inference(subsumption_resolution,[],[f289,f223]) ).
fof(f289,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f288,f223]) ).
fof(f288,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f179,f223]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991',p25) ).
fof(f906,plain,
! [X0,X1] :
( member(sK8,inverse2(X0,X1))
| ~ member(sF33,X0)
| ~ member(sK9,X1)
| ~ relation_like(X0) ),
inference(superposition,[],[f278,f214]) ).
fof(f278,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X1,X3),X2)
| member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ relation_like(X2) ),
inference(forward_literal_rewriting,[],[f277,f252]) ).
fof(f252,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(subsumption_resolution,[],[f221,f223]) ).
fof(f221,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(duplicate_literal_removal,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991',p15) ).
fof(f277,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(subsumption_resolution,[],[f276,f223]) ).
fof(f276,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f275,f223]) ).
fof(f275,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f173,f223]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ( member(sK16(X0,X1,X2),X0)
& member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
& ilf_type(sK16(X0,X1,X2),set_type) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f105,f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X1,X4),X2)
& ilf_type(X4,set_type) )
=> ( member(sK16(X0,X1,X2),X0)
& member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
& ilf_type(sK16(X0,X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X1,X4),X2)
& ilf_type(X4,set_type) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991',p1) ).
fof(f2225,plain,
( ~ member(sK8,sF32)
| sP27(sK7,sK6) ),
inference(forward_demodulation,[],[f2224,f852]) ).
fof(f2224,plain,
( sP27(sK7,sK6)
| ~ member(sK8,inverse2(sK7,sK5)) ),
inference(subsumption_resolution,[],[f2223,f321]) ).
fof(f2223,plain,
( sP27(sK7,sK6)
| ~ relation_like(sK7)
| ~ member(sK8,inverse2(sK7,sK5)) ),
inference(resolution,[],[f2217,f281]) ).
fof(f281,plain,
! [X2,X0,X1] :
( member(sK16(X0,X1,X2),X0)
| ~ relation_like(X2)
| ~ member(X1,inverse2(X2,X0)) ),
inference(forward_literal_rewriting,[],[f280,f252]) ).
fof(f280,plain,
! [X2,X0,X1] :
( member(sK16(X0,X1,X2),X0)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(subsumption_resolution,[],[f279,f223]) ).
fof(f279,plain,
! [X2,X0,X1] :
( member(sK16(X0,X1,X2),X0)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f172,f223]) ).
fof(f172,plain,
! [X2,X0,X1] :
( member(sK16(X0,X1,X2),X0)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f2217,plain,
( ~ member(sK16(sK5,sK8,sK7),sK5)
| sP27(sK7,sK6) ),
inference(resolution,[],[f1905,f1921]) ).
fof(f1921,plain,
( ilf_type(sK16(sK5,sK8,sK7),sF31)
| sP27(sK7,sK6) ),
inference(resolution,[],[f1912,f309]) ).
fof(f309,plain,
! [X0] :
( ~ member(X0,sK6)
| ilf_type(X0,sF31) ),
inference(superposition,[],[f298,f210]) ).
fof(f210,plain,
member_type(sK6) = sF31,
introduced(function_definition,[]) ).
fof(f298,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(subsumption_resolution,[],[f297,f251]) ).
fof(f251,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ member(X2,X0) ),
inference(subsumption_resolution,[],[f250,f223]) ).
fof(f250,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f144,f223]) ).
fof(f144,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK13(X0),X0)
& ilf_type(sK13(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f88,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK13(X0),X0)
& ilf_type(sK13(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991',p9) ).
fof(f297,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1) ),
inference(subsumption_resolution,[],[f296,f223]) ).
fof(f296,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f183,f223]) ).
fof(f183,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991',p7) ).
fof(f1912,plain,
! [X0] :
( member(sK16(sK5,sK8,sK7),X0)
| sP27(sK7,X0) ),
inference(resolution,[],[f1907,f231]) ).
fof(f231,plain,
! [X3,X1,X4] :
( ~ sP26(X4,X3)
| member(X3,X1)
| sP27(X4,X1) ),
inference(subsumption_resolution,[],[f203,f223]) ).
fof(f1907,plain,
sP26(sK7,sK16(sK5,sK8,sK7)),
inference(resolution,[],[f1904,f396]) ).
fof(f396,plain,
! [X6,X7] :
( ~ member(sF30(X6),X7)
| sP26(X7,X6) ),
inference(superposition,[],[f230,f209]) ).
fof(f209,plain,
! [X5] : ordered_pair(sK8,X5) = sF30(X5),
introduced(function_definition,[]) ).
fof(f230,plain,
! [X2,X3,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| sP26(X4,X3) ),
inference(subsumption_resolution,[],[f201,f223]) ).
fof(f1904,plain,
member(sF30(sK16(sK5,sK8,sK7)),sK7),
inference(subsumption_resolution,[],[f1902,f1286]) ).
fof(f1902,plain,
( ~ member(sK8,sF32)
| member(sF30(sK16(sK5,sK8,sK7)),sK7) ),
inference(superposition,[],[f1625,f852]) ).
fof(f1625,plain,
! [X0] :
( ~ member(sK8,inverse2(sK7,X0))
| member(sF30(sK16(X0,sK8,sK7)),sK7) ),
inference(superposition,[],[f1077,f209]) ).
fof(f1077,plain,
! [X11,X12] :
( member(ordered_pair(X11,sK16(X12,X11,sK7)),sK7)
| ~ member(X11,inverse2(sK7,X12)) ),
inference(resolution,[],[f284,f321]) ).
fof(f284,plain,
! [X2,X0,X1] :
( ~ relation_like(X2)
| member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0)) ),
inference(forward_literal_rewriting,[],[f283,f252]) ).
fof(f283,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(subsumption_resolution,[],[f282,f223]) ).
fof(f282,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f171,f223]) ).
fof(f171,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f1905,plain,
( ~ ilf_type(sK16(sK5,sK8,sK7),sF31)
| ~ member(sK16(sK5,sK8,sK7),sK5) ),
inference(resolution,[],[f1904,f1287]) ).
fof(f1287,plain,
! [X5] :
( ~ member(sF30(X5),sK7)
| ~ ilf_type(X5,sF31)
| ~ member(X5,sK5) ),
inference(subsumption_resolution,[],[f212,f1286]) ).
fof(f212,plain,
! [X5] :
( ~ member(sK8,sF32)
| ~ member(sF30(X5),sK7)
| ~ ilf_type(X5,sF31)
| ~ member(X5,sK5) ),
inference(definition_folding,[],[f129,f211,f210,f209]) ).
fof(f129,plain,
! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(sK8,X5),sK7)
| ~ ilf_type(X5,member_type(sK6))
| ~ member(sK8,inverse4(sK4,sK6,sK7,sK5)) ),
inference(cnf_transformation,[],[f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET686+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 10:26:32 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.Jeucth8Hjo/Vampire---4.8_17991
% 0.15/0.37 % (18132)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (18140)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.22/0.43 % (18144)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.22/0.43 % (18146)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.43 % (18133)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.22/0.43 % (18137)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.22/0.43 % (18134)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.22/0.43 % (18150)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.22/0.53 % (18150)First to succeed.
% 0.22/0.53 % (18150)Refutation found. Thanks to Tanya!
% 0.22/0.53 % SZS status Theorem for Vampire---4
% 0.22/0.53 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.53 % (18150)------------------------------
% 0.22/0.53 % (18150)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.53 % (18150)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.53 % (18150)Termination reason: Refutation
% 0.22/0.53
% 0.22/0.53 % (18150)Memory used [KB]: 4605
% 0.22/0.53 % (18150)Time elapsed: 0.105 s
% 0.22/0.53 % (18150)------------------------------
% 0.22/0.53 % (18150)------------------------------
% 0.22/0.53 % (18132)Success in time 0.168 s
% 0.22/0.54 % Vampire---4.8 exiting
%------------------------------------------------------------------------------