TSTP Solution File: SEU364+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU364+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n017.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 : Sun May 5 09:22:45 EDT 2024
% Result : Theorem 0.57s 0.72s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 35
% Syntax : Number of formulae : 149 ( 13 unt; 0 def)
% Number of atoms : 1003 ( 132 equ)
% Maximal formula atoms : 36 ( 6 avg)
% Number of connectives : 1269 ( 415 ~; 478 |; 327 &)
% ( 26 <=>; 21 =>; 0 <=; 2 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 20 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-4 aty)
% Number of variables : 380 ( 220 !; 160 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f451,plain,
$false,
inference(avatar_sat_refutation,[],[f161,f163,f173,f180,f199,f251,f253,f270,f272,f287,f359,f364,f369,f374,f405,f429,f434,f444,f447,f450]) ).
fof(f450,plain,
( ~ spl27_18
| spl27_39 ),
inference(avatar_contradiction_clause,[],[f448]) ).
fof(f448,plain,
( $false
| ~ spl27_18
| spl27_39 ),
inference(resolution,[],[f439,f333]) ).
fof(f333,plain,
( in(sK4(sK23(sK1,sK2,sK3)),sK23(sK1,sK2,sK3))
| ~ spl27_18 ),
inference(factoring,[],[f326]) ).
fof(f326,plain,
( ! [X0] :
( in(sK4(X0),sK23(sK1,sK2,sK3))
| in(sK4(X0),X0) )
| ~ spl27_18 ),
inference(duplicate_literal_removal,[],[f325]) ).
fof(f325,plain,
( ! [X0] :
( in(sK4(X0),X0)
| in(sK4(X0),sK23(sK1,sK2,sK3))
| in(sK4(X0),X0)
| in(sK4(X0),X0) )
| ~ spl27_18 ),
inference(resolution,[],[f324,f141]) ).
fof(f141,plain,
! [X0] :
( relstr_set_smaller(sK1,sK4(X0),sK6(X0))
| in(sK4(X0),X0) ),
inference(duplicate_literal_removal,[],[f140]) ).
fof(f140,plain,
! [X0] :
( relstr_set_smaller(sK1,sK4(X0),sK6(X0))
| in(sK4(X0),X0)
| in(sK4(X0),X0) ),
inference(superposition,[],[f92,f89]) ).
fof(f89,plain,
! [X3] :
( sK4(X3) = sK5(X3)
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
( ! [X3] :
( ( ! [X5] :
( ! [X6] :
( ~ relstr_set_smaller(sK1,X5,X6)
| ~ in(X6,sK2)
| ~ element(X6,the_carrier(sK1)) )
| sK4(X3) != X5 )
| ~ in(sK4(X3),powerset(sK3))
| ~ in(sK4(X3),X3) )
& ( ( relstr_set_smaller(sK1,sK5(X3),sK6(X3))
& in(sK6(X3),sK2)
& element(sK6(X3),the_carrier(sK1))
& sK4(X3) = sK5(X3)
& in(sK4(X3),powerset(sK3)) )
| in(sK4(X3),X3) ) )
& element(sK3,powerset(sK2))
& finite(sK3)
& element(sK2,powerset(the_carrier(sK1)))
& rel_str(sK1)
& transitive_relstr(sK1)
& ~ empty_carrier(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6])],[f43,f47,f46,f45,f44]) ).
fof(f44,plain,
( ? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ! [X5] :
( ! [X6] :
( ~ relstr_set_smaller(X0,X5,X6)
| ~ in(X6,X1)
| ~ element(X6,the_carrier(X0)) )
| X4 != X5 )
| ~ in(X4,powerset(X2))
| ~ in(X4,X3) )
& ( ( ? [X7] :
( ? [X8] :
( relstr_set_smaller(X0,X7,X8)
& in(X8,X1)
& element(X8,the_carrier(X0)) )
& X4 = X7 )
& in(X4,powerset(X2)) )
| in(X4,X3) ) )
& element(X2,powerset(X1))
& finite(X2)
& element(X1,powerset(the_carrier(X0)))
& rel_str(X0)
& transitive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( ! [X3] :
? [X4] :
( ( ! [X5] :
( ! [X6] :
( ~ relstr_set_smaller(sK1,X5,X6)
| ~ in(X6,sK2)
| ~ element(X6,the_carrier(sK1)) )
| X4 != X5 )
| ~ in(X4,powerset(sK3))
| ~ in(X4,X3) )
& ( ( ? [X7] :
( ? [X8] :
( relstr_set_smaller(sK1,X7,X8)
& in(X8,sK2)
& element(X8,the_carrier(sK1)) )
& X4 = X7 )
& in(X4,powerset(sK3)) )
| in(X4,X3) ) )
& element(sK3,powerset(sK2))
& finite(sK3)
& element(sK2,powerset(the_carrier(sK1)))
& rel_str(sK1)
& transitive_relstr(sK1)
& ~ empty_carrier(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X3] :
( ? [X4] :
( ( ! [X5] :
( ! [X6] :
( ~ relstr_set_smaller(sK1,X5,X6)
| ~ in(X6,sK2)
| ~ element(X6,the_carrier(sK1)) )
| X4 != X5 )
| ~ in(X4,powerset(sK3))
| ~ in(X4,X3) )
& ( ( ? [X7] :
( ? [X8] :
( relstr_set_smaller(sK1,X7,X8)
& in(X8,sK2)
& element(X8,the_carrier(sK1)) )
& X4 = X7 )
& in(X4,powerset(sK3)) )
| in(X4,X3) ) )
=> ( ( ! [X5] :
( ! [X6] :
( ~ relstr_set_smaller(sK1,X5,X6)
| ~ in(X6,sK2)
| ~ element(X6,the_carrier(sK1)) )
| sK4(X3) != X5 )
| ~ in(sK4(X3),powerset(sK3))
| ~ in(sK4(X3),X3) )
& ( ( ? [X7] :
( ? [X8] :
( relstr_set_smaller(sK1,X7,X8)
& in(X8,sK2)
& element(X8,the_carrier(sK1)) )
& sK4(X3) = X7 )
& in(sK4(X3),powerset(sK3)) )
| in(sK4(X3),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X3] :
( ? [X7] :
( ? [X8] :
( relstr_set_smaller(sK1,X7,X8)
& in(X8,sK2)
& element(X8,the_carrier(sK1)) )
& sK4(X3) = X7 )
=> ( ? [X8] :
( relstr_set_smaller(sK1,sK5(X3),X8)
& in(X8,sK2)
& element(X8,the_carrier(sK1)) )
& sK4(X3) = sK5(X3) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X3] :
( ? [X8] :
( relstr_set_smaller(sK1,sK5(X3),X8)
& in(X8,sK2)
& element(X8,the_carrier(sK1)) )
=> ( relstr_set_smaller(sK1,sK5(X3),sK6(X3))
& in(sK6(X3),sK2)
& element(sK6(X3),the_carrier(sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ! [X5] :
( ! [X6] :
( ~ relstr_set_smaller(X0,X5,X6)
| ~ in(X6,X1)
| ~ element(X6,the_carrier(X0)) )
| X4 != X5 )
| ~ in(X4,powerset(X2))
| ~ in(X4,X3) )
& ( ( ? [X7] :
( ? [X8] :
( relstr_set_smaller(X0,X7,X8)
& in(X8,X1)
& element(X8,the_carrier(X0)) )
& X4 = X7 )
& in(X4,powerset(X2)) )
| in(X4,X3) ) )
& element(X2,powerset(X1))
& finite(X2)
& element(X1,powerset(the_carrier(X0)))
& rel_str(X0)
& transitive_relstr(X0)
& ~ empty_carrier(X0) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ! [X5] :
( ! [X6] :
( ~ relstr_set_smaller(X0,X5,X6)
| ~ in(X6,X1)
| ~ element(X6,the_carrier(X0)) )
| X4 != X5 )
| ~ in(X4,powerset(X2))
| ~ in(X4,X3) )
& ( ( ? [X5] :
( ? [X6] :
( relstr_set_smaller(X0,X5,X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& X4 = X5 )
& in(X4,powerset(X2)) )
| in(X4,X3) ) )
& element(X2,powerset(X1))
& finite(X2)
& element(X1,powerset(the_carrier(X0)))
& rel_str(X0)
& transitive_relstr(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ! [X5] :
( ! [X6] :
( ~ relstr_set_smaller(X0,X5,X6)
| ~ in(X6,X1)
| ~ element(X6,the_carrier(X0)) )
| X4 != X5 )
| ~ in(X4,powerset(X2))
| ~ in(X4,X3) )
& ( ( ? [X5] :
( ? [X6] :
( relstr_set_smaller(X0,X5,X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& X4 = X5 )
& in(X4,powerset(X2)) )
| in(X4,X3) ) )
& element(X2,powerset(X1))
& finite(X2)
& element(X1,powerset(the_carrier(X0)))
& rel_str(X0)
& transitive_relstr(X0)
& ~ empty_carrier(X0) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( ? [X5] :
( ? [X6] :
( relstr_set_smaller(X0,X5,X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& X4 = X5 )
& in(X4,powerset(X2)) ) )
& element(X2,powerset(X1))
& finite(X2)
& element(X1,powerset(the_carrier(X0)))
& rel_str(X0)
& transitive_relstr(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( ? [X5] :
( ? [X6] :
( relstr_set_smaller(X0,X5,X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& X4 = X5 )
& in(X4,powerset(X2)) ) )
& element(X2,powerset(X1))
& finite(X2)
& element(X1,powerset(the_carrier(X0)))
& rel_str(X0)
& transitive_relstr(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( element(X2,powerset(X1))
& finite(X2)
& element(X1,powerset(the_carrier(X0)))
& rel_str(X0)
& transitive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5] :
( ? [X6] :
( relstr_set_smaller(X0,X5,X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& X4 = X5 )
& in(X4,powerset(X2)) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1,X2] :
( ( element(X2,powerset(X1))
& finite(X2)
& element(X1,powerset(the_carrier(X0)))
& rel_str(X0)
& transitive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5] :
( ? [X6] :
( relstr_set_smaller(X0,X5,X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& X4 = X5 )
& in(X4,powerset(X2)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zhbxcUtS29/Vampire---4.8_10179',s1_xboole_0__e11_2_1__waybel_0__1) ).
fof(f92,plain,
! [X3] :
( relstr_set_smaller(sK1,sK5(X3),sK6(X3))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f324,plain,
( ! [X0,X1] :
( ~ relstr_set_smaller(sK1,sK4(X0),sK6(X1))
| in(sK4(X0),X0)
| in(sK4(X0),sK23(sK1,sK2,sK3))
| in(sK4(X1),X1) )
| ~ spl27_18 ),
inference(duplicate_literal_removal,[],[f323]) ).
fof(f323,plain,
( ! [X0,X1] :
( ~ relstr_set_smaller(sK1,sK4(X0),sK6(X1))
| in(sK4(X0),X0)
| in(sK4(X0),sK23(sK1,sK2,sK3))
| in(sK4(X1),X1)
| in(sK4(X1),X1) )
| ~ spl27_18 ),
inference(resolution,[],[f322,f90]) ).
fof(f90,plain,
! [X3] :
( element(sK6(X3),the_carrier(sK1))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f322,plain,
( ! [X0,X1] :
( ~ element(sK6(X1),the_carrier(sK1))
| ~ relstr_set_smaller(sK1,sK4(X0),sK6(X1))
| in(sK4(X0),X0)
| in(sK4(X0),sK23(sK1,sK2,sK3))
| in(sK4(X1),X1) )
| ~ spl27_18 ),
inference(resolution,[],[f250,f91]) ).
fof(f91,plain,
! [X3] :
( in(sK6(X3),sK2)
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f250,plain,
( ! [X0,X1] :
( ~ in(X1,sK2)
| in(sK4(X0),sK23(sK1,sK2,sK3))
| ~ relstr_set_smaller(sK1,sK4(X0),X1)
| in(sK4(X0),X0)
| ~ element(X1,the_carrier(sK1)) )
| ~ spl27_18 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f249,plain,
( spl27_18
<=> ! [X0,X1] :
( in(sK4(X0),X0)
| in(sK4(X0),sK23(sK1,sK2,sK3))
| ~ relstr_set_smaller(sK1,sK4(X0),X1)
| ~ in(X1,sK2)
| ~ element(X1,the_carrier(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_18])]) ).
fof(f439,plain,
( ~ in(sK4(sK23(sK1,sK2,sK3)),sK23(sK1,sK2,sK3))
| spl27_39 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f437,plain,
( spl27_39
<=> in(sK4(sK23(sK1,sK2,sK3)),sK23(sK1,sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_39])]) ).
fof(f447,plain,
( ~ spl27_28
| ~ spl27_29
| spl27_40 ),
inference(avatar_contradiction_clause,[],[f445]) ).
fof(f445,plain,
( $false
| ~ spl27_28
| ~ spl27_29
| spl27_40 ),
inference(resolution,[],[f443,f375]) ).
fof(f375,plain,
( in(sK4(sK23(sK1,sK2,sK3)),powerset(sK3))
| ~ spl27_28
| ~ spl27_29 ),
inference(forward_demodulation,[],[f358,f363]) ).
fof(f363,plain,
( sK4(sK23(sK1,sK2,sK3)) = sK24(sK1,sK2,sK3,sK4(sK23(sK1,sK2,sK3)))
| ~ spl27_29 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f361,plain,
( spl27_29
<=> sK4(sK23(sK1,sK2,sK3)) = sK24(sK1,sK2,sK3,sK4(sK23(sK1,sK2,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_29])]) ).
fof(f358,plain,
( in(sK24(sK1,sK2,sK3,sK4(sK23(sK1,sK2,sK3))),powerset(sK3))
| ~ spl27_28 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f356,plain,
( spl27_28
<=> in(sK24(sK1,sK2,sK3,sK4(sK23(sK1,sK2,sK3))),powerset(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_28])]) ).
fof(f443,plain,
( ~ in(sK4(sK23(sK1,sK2,sK3)),powerset(sK3))
| spl27_40 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f441,plain,
( spl27_40
<=> in(sK4(sK23(sK1,sK2,sK3)),powerset(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_40])]) ).
fof(f444,plain,
( ~ spl27_39
| ~ spl27_40
| ~ spl27_34
| ~ spl27_30
| ~ spl27_38 ),
inference(avatar_split_clause,[],[f435,f431,f366,f392,f441,f437]) ).
fof(f392,plain,
( spl27_34
<=> element(sK26(sK1,sK2,sK4(sK23(sK1,sK2,sK3))),the_carrier(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_34])]) ).
fof(f366,plain,
( spl27_30
<=> in(sK26(sK1,sK2,sK4(sK23(sK1,sK2,sK3))),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_30])]) ).
fof(f431,plain,
( spl27_38
<=> relstr_set_smaller(sK1,sK4(sK23(sK1,sK2,sK3)),sK26(sK1,sK2,sK4(sK23(sK1,sK2,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_38])]) ).
fof(f435,plain,
( ~ in(sK26(sK1,sK2,sK4(sK23(sK1,sK2,sK3))),sK2)
| ~ element(sK26(sK1,sK2,sK4(sK23(sK1,sK2,sK3))),the_carrier(sK1))
| ~ in(sK4(sK23(sK1,sK2,sK3)),powerset(sK3))
| ~ in(sK4(sK23(sK1,sK2,sK3)),sK23(sK1,sK2,sK3))
| ~ spl27_38 ),
inference(resolution,[],[f433,f136]) ).
fof(f136,plain,
! [X3,X6] :
( ~ relstr_set_smaller(sK1,sK4(X3),X6)
| ~ in(X6,sK2)
| ~ element(X6,the_carrier(sK1))
| ~ in(sK4(X3),powerset(sK3))
| ~ in(sK4(X3),X3) ),
inference(equality_resolution,[],[f93]) ).
fof(f93,plain,
! [X3,X6,X5] :
( ~ relstr_set_smaller(sK1,X5,X6)
| ~ in(X6,sK2)
| ~ element(X6,the_carrier(sK1))
| sK4(X3) != X5
| ~ in(sK4(X3),powerset(sK3))
| ~ in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f433,plain,
( relstr_set_smaller(sK1,sK4(sK23(sK1,sK2,sK3)),sK26(sK1,sK2,sK4(sK23(sK1,sK2,sK3))))
| ~ spl27_38 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f434,plain,
( spl27_1
| ~ spl27_2
| ~ spl27_11
| ~ spl27_7
| spl27_9
| spl27_35
| spl27_38
| ~ spl27_31 ),
inference(avatar_split_clause,[],[f424,f371,f431,f403,f191,f183,f206,f155,f151]) ).
fof(f151,plain,
( spl27_1
<=> empty_carrier(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_1])]) ).
fof(f155,plain,
( spl27_2
<=> transitive_relstr(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_2])]) ).
fof(f206,plain,
( spl27_11
<=> rel_str(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_11])]) ).
fof(f183,plain,
( spl27_7
<=> element(sK2,powerset(the_carrier(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_7])]) ).
fof(f191,plain,
( spl27_9
<=> sP0(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_9])]) ).
fof(f403,plain,
( spl27_35
<=> ! [X0] :
( ~ in(sK4(sK23(sK1,sK2,sK3)),sK23(sK1,sK2,X0))
| ~ finite(X0)
| ~ element(X0,powerset(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_35])]) ).
fof(f371,plain,
( spl27_31
<=> sK4(sK23(sK1,sK2,sK3)) = sK25(sK1,sK2,sK4(sK23(sK1,sK2,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_31])]) ).
fof(f424,plain,
( ! [X0] :
( relstr_set_smaller(sK1,sK4(sK23(sK1,sK2,sK3)),sK26(sK1,sK2,sK4(sK23(sK1,sK2,sK3))))
| ~ in(sK4(sK23(sK1,sK2,sK3)),sK23(sK1,sK2,X0))
| sP0(sK1,sK2)
| ~ element(X0,powerset(sK2))
| ~ finite(X0)
| ~ element(sK2,powerset(the_carrier(sK1)))
| ~ rel_str(sK1)
| ~ transitive_relstr(sK1)
| empty_carrier(sK1) )
| ~ spl27_31 ),
inference(superposition,[],[f134,f373]) ).
fof(f373,plain,
( sK4(sK23(sK1,sK2,sK3)) = sK25(sK1,sK2,sK4(sK23(sK1,sK2,sK3)))
| ~ spl27_31 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f134,plain,
! [X2,X0,X1,X4] :
( relstr_set_smaller(X0,sK25(X0,X1,X4),sK26(X0,X1,X4))
| ~ in(X4,sK23(X0,X1,X2))
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK23(X0,X1,X2))
| ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ relstr_set_smaller(X0,X6,X7)
| ~ in(X7,X1)
| ~ element(X7,the_carrier(X0)) )
| X4 != X6 )
| X4 != X5
| ~ in(X5,powerset(X2)) ) )
& ( ( relstr_set_smaller(X0,sK25(X0,X1,X4),sK26(X0,X1,X4))
& in(sK26(X0,X1,X4),X1)
& element(sK26(X0,X1,X4),the_carrier(X0))
& sK25(X0,X1,X4) = X4
& sK24(X0,X1,X2,X4) = X4
& in(sK24(X0,X1,X2,X4),powerset(X2)) )
| ~ in(X4,sK23(X0,X1,X2)) ) )
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24,sK25,sK26])],[f76,f80,f79,f78,f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ relstr_set_smaller(X0,X6,X7)
| ~ in(X7,X1)
| ~ element(X7,the_carrier(X0)) )
| X4 != X6 )
| X4 != X5
| ~ in(X5,powerset(X2)) ) )
& ( ? [X8] :
( ? [X9] :
( ? [X10] :
( relstr_set_smaller(X0,X9,X10)
& in(X10,X1)
& element(X10,the_carrier(X0)) )
& X4 = X9 )
& X4 = X8
& in(X8,powerset(X2)) )
| ~ in(X4,X3) ) )
=> ! [X4] :
( ( in(X4,sK23(X0,X1,X2))
| ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ relstr_set_smaller(X0,X6,X7)
| ~ in(X7,X1)
| ~ element(X7,the_carrier(X0)) )
| X4 != X6 )
| X4 != X5
| ~ in(X5,powerset(X2)) ) )
& ( ? [X8] :
( ? [X9] :
( ? [X10] :
( relstr_set_smaller(X0,X9,X10)
& in(X10,X1)
& element(X10,the_carrier(X0)) )
& X4 = X9 )
& X4 = X8
& in(X8,powerset(X2)) )
| ~ in(X4,sK23(X0,X1,X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1,X2,X4] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( relstr_set_smaller(X0,X9,X10)
& in(X10,X1)
& element(X10,the_carrier(X0)) )
& X4 = X9 )
& X4 = X8
& in(X8,powerset(X2)) )
=> ( ? [X9] :
( ? [X10] :
( relstr_set_smaller(X0,X9,X10)
& in(X10,X1)
& element(X10,the_carrier(X0)) )
& X4 = X9 )
& sK24(X0,X1,X2,X4) = X4
& in(sK24(X0,X1,X2,X4),powerset(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1,X4] :
( ? [X9] :
( ? [X10] :
( relstr_set_smaller(X0,X9,X10)
& in(X10,X1)
& element(X10,the_carrier(X0)) )
& X4 = X9 )
=> ( ? [X10] :
( relstr_set_smaller(X0,sK25(X0,X1,X4),X10)
& in(X10,X1)
& element(X10,the_carrier(X0)) )
& sK25(X0,X1,X4) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1,X4] :
( ? [X10] :
( relstr_set_smaller(X0,sK25(X0,X1,X4),X10)
& in(X10,X1)
& element(X10,the_carrier(X0)) )
=> ( relstr_set_smaller(X0,sK25(X0,X1,X4),sK26(X0,X1,X4))
& in(sK26(X0,X1,X4),X1)
& element(sK26(X0,X1,X4),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ relstr_set_smaller(X0,X6,X7)
| ~ in(X7,X1)
| ~ element(X7,the_carrier(X0)) )
| X4 != X6 )
| X4 != X5
| ~ in(X5,powerset(X2)) ) )
& ( ? [X8] :
( ? [X9] :
( ? [X10] :
( relstr_set_smaller(X0,X9,X10)
& in(X10,X1)
& element(X10,the_carrier(X0)) )
& X4 = X9 )
& X4 = X8
& in(X8,powerset(X2)) )
| ~ in(X4,X3) ) )
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( ( in(X11,X10)
| ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ relstr_set_smaller(X0,X13,X14)
| ~ in(X14,X1)
| ~ element(X14,the_carrier(X0)) )
| X11 != X13 )
| X11 != X12
| ~ in(X12,powerset(X2)) ) )
& ( ? [X12] :
( ? [X13] :
( ? [X14] :
( relstr_set_smaller(X0,X13,X14)
& in(X14,X1)
& element(X14,the_carrier(X0)) )
& X11 = X13 )
& X11 = X12
& in(X12,powerset(X2)) )
| ~ in(X11,X10) ) )
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13] :
( ? [X14] :
( relstr_set_smaller(X0,X13,X14)
& in(X14,X1)
& element(X14,the_carrier(X0)) )
& X11 = X13 )
& X11 = X12
& in(X12,powerset(X2)) ) )
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f38,f39]) ).
fof(f39,plain,
! [X0,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& ? [X6] :
( ? [X7] :
( relstr_set_smaller(X0,X6,X7)
& in(X7,X1)
& element(X7,the_carrier(X0)) )
& X5 = X6 )
& X3 = X5
& ? [X8] :
( ? [X9] :
( relstr_set_smaller(X0,X8,X9)
& in(X9,X1)
& element(X9,the_carrier(X0)) )
& X4 = X8 )
& X3 = X4 )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13] :
( ? [X14] :
( relstr_set_smaller(X0,X13,X14)
& in(X14,X1)
& element(X14,the_carrier(X0)) )
& X11 = X13 )
& X11 = X12
& in(X12,powerset(X2)) ) )
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6] :
( ? [X7] :
( relstr_set_smaller(X0,X6,X7)
& in(X7,X1)
& element(X7,the_carrier(X0)) )
& X5 = X6 )
& X3 = X5
& ? [X8] :
( ? [X9] :
( relstr_set_smaller(X0,X8,X9)
& in(X9,X1)
& element(X9,the_carrier(X0)) )
& X4 = X8 )
& X3 = X4 )
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13] :
( ? [X14] :
( relstr_set_smaller(X0,X13,X14)
& in(X14,X1)
& element(X14,the_carrier(X0)) )
& X11 = X13 )
& X11 = X12
& in(X12,powerset(X2)) ) )
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6] :
( ? [X7] :
( relstr_set_smaller(X0,X6,X7)
& in(X7,X1)
& element(X7,the_carrier(X0)) )
& X5 = X6 )
& X3 = X5
& ? [X8] :
( ? [X9] :
( relstr_set_smaller(X0,X8,X9)
& in(X9,X1)
& element(X9,the_carrier(X0)) )
& X4 = X8 )
& X3 = X4 )
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( element(X2,powerset(X1))
& finite(X2)
& element(X1,powerset(the_carrier(X0)))
& rel_str(X0)
& transitive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( ! [X3,X4,X5] :
( ( ? [X6] :
( ? [X7] :
( relstr_set_smaller(X0,X6,X7)
& in(X7,X1)
& element(X7,the_carrier(X0)) )
& X5 = X6 )
& X3 = X5
& ? [X8] :
( ? [X9] :
( relstr_set_smaller(X0,X8,X9)
& in(X9,X1)
& element(X9,the_carrier(X0)) )
& X4 = X8 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13] :
( ? [X14] :
( relstr_set_smaller(X0,X13,X14)
& in(X14,X1)
& element(X14,the_carrier(X0)) )
& X11 = X13 )
& X11 = X12
& in(X12,powerset(X2)) ) ) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X1))
& finite(X2)
& element(X1,powerset(the_carrier(X0)))
& rel_str(X0)
& transitive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( ! [X3,X4,X5] :
( ( ? [X8] :
( ? [X9] :
( relstr_set_smaller(X0,X8,X9)
& in(X9,X1)
& element(X9,the_carrier(X0)) )
& X5 = X8 )
& X3 = X5
& ? [X6] :
( ? [X7] :
( relstr_set_smaller(X0,X6,X7)
& in(X7,X1)
& element(X7,the_carrier(X0)) )
& X4 = X6 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( ? [X10] :
( ? [X11] :
( relstr_set_smaller(X0,X10,X11)
& in(X11,X1)
& element(X11,the_carrier(X0)) )
& X4 = X10 )
& X4 = X5
& in(X5,powerset(X2)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zhbxcUtS29/Vampire---4.8_10179',s1_tarski__e11_2_1__waybel_0__1) ).
fof(f429,plain,
( ~ spl27_12
| ~ spl27_4
| ~ spl27_18
| ~ spl27_35 ),
inference(avatar_split_clause,[],[f427,f403,f249,f167,f210]) ).
fof(f210,plain,
( spl27_12
<=> element(sK3,powerset(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_12])]) ).
fof(f167,plain,
( spl27_4
<=> finite(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_4])]) ).
fof(f427,plain,
( ~ finite(sK3)
| ~ element(sK3,powerset(sK2))
| ~ spl27_18
| ~ spl27_35 ),
inference(resolution,[],[f404,f333]) ).
fof(f404,plain,
( ! [X0] :
( ~ in(sK4(sK23(sK1,sK2,sK3)),sK23(sK1,sK2,X0))
| ~ finite(X0)
| ~ element(X0,powerset(sK2)) )
| ~ spl27_35 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f405,plain,
( spl27_1
| ~ spl27_2
| ~ spl27_11
| ~ spl27_7
| spl27_9
| spl27_35
| spl27_34 ),
inference(avatar_split_clause,[],[f401,f392,f403,f191,f183,f206,f155,f151]) ).
fof(f401,plain,
( ! [X0] :
( ~ in(sK4(sK23(sK1,sK2,sK3)),sK23(sK1,sK2,X0))
| sP0(sK1,sK2)
| ~ element(X0,powerset(sK2))
| ~ finite(X0)
| ~ element(sK2,powerset(the_carrier(sK1)))
| ~ rel_str(sK1)
| ~ transitive_relstr(sK1)
| empty_carrier(sK1) )
| spl27_34 ),
inference(resolution,[],[f394,f132]) ).
fof(f132,plain,
! [X2,X0,X1,X4] :
( element(sK26(X0,X1,X4),the_carrier(X0))
| ~ in(X4,sK23(X0,X1,X2))
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f394,plain,
( ~ element(sK26(sK1,sK2,sK4(sK23(sK1,sK2,sK3))),the_carrier(sK1))
| spl27_34 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f374,plain,
( spl27_1
| ~ spl27_2
| ~ spl27_11
| ~ spl27_7
| ~ spl27_4
| ~ spl27_12
| spl27_9
| spl27_31
| ~ spl27_18 ),
inference(avatar_split_clause,[],[f353,f249,f371,f191,f210,f167,f183,f206,f155,f151]) ).
fof(f353,plain,
( sK4(sK23(sK1,sK2,sK3)) = sK25(sK1,sK2,sK4(sK23(sK1,sK2,sK3)))
| sP0(sK1,sK2)
| ~ element(sK3,powerset(sK2))
| ~ finite(sK3)
| ~ element(sK2,powerset(the_carrier(sK1)))
| ~ rel_str(sK1)
| ~ transitive_relstr(sK1)
| empty_carrier(sK1)
| ~ spl27_18 ),
inference(resolution,[],[f333,f131]) ).
fof(f131,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK23(X0,X1,X2))
| sK25(X0,X1,X4) = X4
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f369,plain,
( spl27_1
| ~ spl27_2
| ~ spl27_11
| ~ spl27_7
| ~ spl27_4
| ~ spl27_12
| spl27_9
| spl27_30
| ~ spl27_18 ),
inference(avatar_split_clause,[],[f352,f249,f366,f191,f210,f167,f183,f206,f155,f151]) ).
fof(f352,plain,
( in(sK26(sK1,sK2,sK4(sK23(sK1,sK2,sK3))),sK2)
| sP0(sK1,sK2)
| ~ element(sK3,powerset(sK2))
| ~ finite(sK3)
| ~ element(sK2,powerset(the_carrier(sK1)))
| ~ rel_str(sK1)
| ~ transitive_relstr(sK1)
| empty_carrier(sK1)
| ~ spl27_18 ),
inference(resolution,[],[f333,f133]) ).
fof(f133,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK23(X0,X1,X2))
| in(sK26(X0,X1,X4),X1)
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f364,plain,
( spl27_1
| ~ spl27_2
| ~ spl27_11
| ~ spl27_7
| ~ spl27_4
| ~ spl27_12
| spl27_9
| spl27_29
| ~ spl27_18 ),
inference(avatar_split_clause,[],[f351,f249,f361,f191,f210,f167,f183,f206,f155,f151]) ).
fof(f351,plain,
( sK4(sK23(sK1,sK2,sK3)) = sK24(sK1,sK2,sK3,sK4(sK23(sK1,sK2,sK3)))
| sP0(sK1,sK2)
| ~ element(sK3,powerset(sK2))
| ~ finite(sK3)
| ~ element(sK2,powerset(the_carrier(sK1)))
| ~ rel_str(sK1)
| ~ transitive_relstr(sK1)
| empty_carrier(sK1)
| ~ spl27_18 ),
inference(resolution,[],[f333,f130]) ).
fof(f130,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK23(X0,X1,X2))
| sK24(X0,X1,X2,X4) = X4
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f359,plain,
( spl27_1
| ~ spl27_2
| ~ spl27_11
| ~ spl27_7
| ~ spl27_4
| ~ spl27_12
| spl27_9
| spl27_28
| ~ spl27_18 ),
inference(avatar_split_clause,[],[f350,f249,f356,f191,f210,f167,f183,f206,f155,f151]) ).
fof(f350,plain,
( in(sK24(sK1,sK2,sK3,sK4(sK23(sK1,sK2,sK3))),powerset(sK3))
| sP0(sK1,sK2)
| ~ element(sK3,powerset(sK2))
| ~ finite(sK3)
| ~ element(sK2,powerset(the_carrier(sK1)))
| ~ rel_str(sK1)
| ~ transitive_relstr(sK1)
| empty_carrier(sK1)
| ~ spl27_18 ),
inference(resolution,[],[f333,f129]) ).
fof(f129,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK23(X0,X1,X2))
| in(sK24(X0,X1,X2,X4),powerset(X2))
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f287,plain,
( ~ spl27_9
| ~ spl27_9 ),
inference(avatar_split_clause,[],[f286,f191,f191]) ).
fof(f286,plain,
( ~ sP0(sK1,sK2)
| ~ spl27_9 ),
inference(trivial_inequality_removal,[],[f285]) ).
fof(f285,plain,
( sK17(sK1,sK2) != sK17(sK1,sK2)
| ~ sP0(sK1,sK2)
| ~ spl27_9 ),
inference(superposition,[],[f128,f283]) ).
fof(f283,plain,
( sK18(sK1,sK2) = sK17(sK1,sK2)
| ~ spl27_9 ),
inference(superposition,[],[f276,f274]) ).
fof(f274,plain,
( sK18(sK1,sK2) = sK16(sK1,sK2)
| ~ spl27_9 ),
inference(resolution,[],[f193,f123]) ).
fof(f123,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK16(X0,X1) = sK18(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ( sK17(X0,X1) != sK18(X0,X1)
& relstr_set_smaller(X0,sK19(X0,X1),sK20(X0,X1))
& in(sK20(X0,X1),X1)
& element(sK20(X0,X1),the_carrier(X0))
& sK18(X0,X1) = sK19(X0,X1)
& sK16(X0,X1) = sK18(X0,X1)
& relstr_set_smaller(X0,sK21(X0,X1),sK22(X0,X1))
& in(sK22(X0,X1),X1)
& element(sK22(X0,X1),the_carrier(X0))
& sK17(X0,X1) = sK21(X0,X1)
& sK16(X0,X1) = sK17(X0,X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19,sK20,sK21,sK22])],[f68,f73,f72,f71,f70,f69]) ).
fof(f69,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( ? [X6] :
( relstr_set_smaller(X0,X5,X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& X4 = X5 )
& X2 = X4
& ? [X7] :
( ? [X8] :
( relstr_set_smaller(X0,X7,X8)
& in(X8,X1)
& element(X8,the_carrier(X0)) )
& X3 = X7 )
& X2 = X3 )
=> ( sK17(X0,X1) != sK18(X0,X1)
& ? [X5] :
( ? [X6] :
( relstr_set_smaller(X0,X5,X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& sK18(X0,X1) = X5 )
& sK16(X0,X1) = sK18(X0,X1)
& ? [X7] :
( ? [X8] :
( relstr_set_smaller(X0,X7,X8)
& in(X8,X1)
& element(X8,the_carrier(X0)) )
& sK17(X0,X1) = X7 )
& sK16(X0,X1) = sK17(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0,X1] :
( ? [X5] :
( ? [X6] :
( relstr_set_smaller(X0,X5,X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& sK18(X0,X1) = X5 )
=> ( ? [X6] :
( relstr_set_smaller(X0,sK19(X0,X1),X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& sK18(X0,X1) = sK19(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X6] :
( relstr_set_smaller(X0,sK19(X0,X1),X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
=> ( relstr_set_smaller(X0,sK19(X0,X1),sK20(X0,X1))
& in(sK20(X0,X1),X1)
& element(sK20(X0,X1),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X7] :
( ? [X8] :
( relstr_set_smaller(X0,X7,X8)
& in(X8,X1)
& element(X8,the_carrier(X0)) )
& sK17(X0,X1) = X7 )
=> ( ? [X8] :
( relstr_set_smaller(X0,sK21(X0,X1),X8)
& in(X8,X1)
& element(X8,the_carrier(X0)) )
& sK17(X0,X1) = sK21(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X8] :
( relstr_set_smaller(X0,sK21(X0,X1),X8)
& in(X8,X1)
& element(X8,the_carrier(X0)) )
=> ( relstr_set_smaller(X0,sK21(X0,X1),sK22(X0,X1))
& in(sK22(X0,X1),X1)
& element(sK22(X0,X1),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( ? [X6] :
( relstr_set_smaller(X0,X5,X6)
& in(X6,X1)
& element(X6,the_carrier(X0)) )
& X4 = X5 )
& X2 = X4
& ? [X7] :
( ? [X8] :
( relstr_set_smaller(X0,X7,X8)
& in(X8,X1)
& element(X8,the_carrier(X0)) )
& X3 = X7 )
& X2 = X3 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& ? [X6] :
( ? [X7] :
( relstr_set_smaller(X0,X6,X7)
& in(X7,X1)
& element(X7,the_carrier(X0)) )
& X5 = X6 )
& X3 = X5
& ? [X8] :
( ? [X9] :
( relstr_set_smaller(X0,X8,X9)
& in(X9,X1)
& element(X9,the_carrier(X0)) )
& X4 = X8 )
& X3 = X4 )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f39]) ).
fof(f193,plain,
( sP0(sK1,sK2)
| ~ spl27_9 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f276,plain,
( sK16(sK1,sK2) = sK17(sK1,sK2)
| ~ spl27_9 ),
inference(resolution,[],[f193,f118]) ).
fof(f118,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK16(X0,X1) = sK17(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f128,plain,
! [X0,X1] :
( sK17(X0,X1) != sK18(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f272,plain,
spl27_12,
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f271,plain,
( $false
| spl27_12 ),
inference(resolution,[],[f212,f87]) ).
fof(f87,plain,
element(sK3,powerset(sK2)),
inference(cnf_transformation,[],[f48]) ).
fof(f212,plain,
( ~ element(sK3,powerset(sK2))
| spl27_12 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f270,plain,
spl27_11,
inference(avatar_contradiction_clause,[],[f269]) ).
fof(f269,plain,
( $false
| spl27_11 ),
inference(resolution,[],[f208,f84]) ).
fof(f84,plain,
rel_str(sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f208,plain,
( ~ rel_str(sK1)
| spl27_11 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f253,plain,
~ spl27_1,
inference(avatar_contradiction_clause,[],[f252]) ).
fof(f252,plain,
( $false
| ~ spl27_1 ),
inference(resolution,[],[f153,f82]) ).
fof(f82,plain,
~ empty_carrier(sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f153,plain,
( empty_carrier(sK1)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f251,plain,
( ~ spl27_7
| spl27_9
| spl27_18
| ~ spl27_5 ),
inference(avatar_split_clause,[],[f239,f171,f249,f191,f183]) ).
fof(f171,plain,
( spl27_5
<=> ! [X2,X0,X1] :
( in(sK4(X0),sK23(sK1,X1,sK3))
| in(sK4(X0),X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(sK1))
| ~ relstr_set_smaller(sK1,sK4(X0),X2)
| sP0(sK1,X1)
| ~ element(sK3,powerset(X1))
| ~ element(X1,powerset(the_carrier(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_5])]) ).
fof(f239,plain,
( ! [X0,X1] :
( in(sK4(X0),X0)
| ~ in(X1,sK2)
| ~ element(X1,the_carrier(sK1))
| ~ relstr_set_smaller(sK1,sK4(X0),X1)
| sP0(sK1,sK2)
| in(sK4(X0),sK23(sK1,sK2,sK3))
| ~ element(sK2,powerset(the_carrier(sK1))) )
| ~ spl27_5 ),
inference(resolution,[],[f172,f87]) ).
fof(f172,plain,
( ! [X2,X0,X1] :
( ~ element(sK3,powerset(X1))
| in(sK4(X0),X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(sK1))
| ~ relstr_set_smaller(sK1,sK4(X0),X2)
| sP0(sK1,X1)
| in(sK4(X0),sK23(sK1,X1,sK3))
| ~ element(X1,powerset(the_carrier(sK1))) )
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f199,plain,
spl27_7,
inference(avatar_contradiction_clause,[],[f198]) ).
fof(f198,plain,
( $false
| spl27_7 ),
inference(resolution,[],[f185,f85]) ).
fof(f85,plain,
element(sK2,powerset(the_carrier(sK1))),
inference(cnf_transformation,[],[f48]) ).
fof(f185,plain,
( ~ element(sK2,powerset(the_carrier(sK1)))
| spl27_7 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f180,plain,
spl27_4,
inference(avatar_contradiction_clause,[],[f178]) ).
fof(f178,plain,
( $false
| spl27_4 ),
inference(resolution,[],[f169,f86]) ).
fof(f86,plain,
finite(sK3),
inference(cnf_transformation,[],[f48]) ).
fof(f169,plain,
( ~ finite(sK3)
| spl27_4 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f173,plain,
( ~ spl27_4
| spl27_5
| ~ spl27_3 ),
inference(avatar_split_clause,[],[f164,f159,f171,f167]) ).
fof(f159,plain,
( spl27_3
<=> ! [X0,X3,X2,X1] :
( ~ relstr_set_smaller(sK1,X0,X1)
| in(X0,sK23(sK1,X2,X3))
| ~ element(X2,powerset(the_carrier(sK1)))
| ~ finite(X3)
| ~ element(X3,powerset(X2))
| sP0(sK1,X2)
| ~ in(X0,powerset(X3))
| ~ element(X1,the_carrier(sK1))
| ~ in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_3])]) ).
fof(f164,plain,
( ! [X2,X0,X1] :
( in(sK4(X0),sK23(sK1,X1,sK3))
| ~ element(X1,powerset(the_carrier(sK1)))
| ~ finite(sK3)
| ~ element(sK3,powerset(X1))
| sP0(sK1,X1)
| ~ relstr_set_smaller(sK1,sK4(X0),X2)
| ~ element(X2,the_carrier(sK1))
| ~ in(X2,X1)
| in(sK4(X0),X0) )
| ~ spl27_3 ),
inference(resolution,[],[f160,f88]) ).
fof(f88,plain,
! [X3] :
( in(sK4(X3),powerset(sK3))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f160,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,powerset(X3))
| in(X0,sK23(sK1,X2,X3))
| ~ element(X2,powerset(the_carrier(sK1)))
| ~ finite(X3)
| ~ element(X3,powerset(X2))
| sP0(sK1,X2)
| ~ relstr_set_smaller(sK1,X0,X1)
| ~ element(X1,the_carrier(sK1))
| ~ in(X1,X2) )
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f163,plain,
spl27_2,
inference(avatar_contradiction_clause,[],[f162]) ).
fof(f162,plain,
( $false
| spl27_2 ),
inference(resolution,[],[f157,f83]) ).
fof(f83,plain,
transitive_relstr(sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f157,plain,
( ~ transitive_relstr(sK1)
| spl27_2 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f161,plain,
( spl27_1
| ~ spl27_2
| spl27_3 ),
inference(avatar_split_clause,[],[f149,f159,f155,f151]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( ~ relstr_set_smaller(sK1,X0,X1)
| ~ in(X1,X2)
| ~ element(X1,the_carrier(sK1))
| ~ in(X0,powerset(X3))
| sP0(sK1,X2)
| ~ element(X3,powerset(X2))
| ~ finite(X3)
| ~ element(X2,powerset(the_carrier(sK1)))
| in(X0,sK23(sK1,X2,X3))
| ~ transitive_relstr(sK1)
| empty_carrier(sK1) ),
inference(resolution,[],[f138,f84]) ).
fof(f138,plain,
! [X2,X0,X1,X6,X7] :
( ~ rel_str(X0)
| ~ relstr_set_smaller(X0,X6,X7)
| ~ in(X7,X1)
| ~ element(X7,the_carrier(X0))
| ~ in(X6,powerset(X2))
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| in(X6,sK23(X0,X1,X2))
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(equality_resolution,[],[f137]) ).
fof(f137,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(X6,sK23(X0,X1,X2))
| ~ relstr_set_smaller(X0,X6,X7)
| ~ in(X7,X1)
| ~ element(X7,the_carrier(X0))
| X5 != X6
| ~ in(X5,powerset(X2))
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(equality_resolution,[],[f135]) ).
fof(f135,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK23(X0,X1,X2))
| ~ relstr_set_smaller(X0,X6,X7)
| ~ in(X7,X1)
| ~ element(X7,the_carrier(X0))
| X4 != X6
| X4 != X5
| ~ in(X5,powerset(X2))
| sP0(X0,X1)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU364+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.12/0.31 % Computer : n017.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Fri May 3 10:35:21 EDT 2024
% 0.12/0.31 % CPUTime :
% 0.12/0.31 This is a FOF_THM_RFO_SEQ problem
% 0.17/0.31 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.zhbxcUtS29/Vampire---4.8_10179
% 0.48/0.70 % (10537)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.48/0.70 % (10530)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.48/0.70 % (10532)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.48/0.70 % (10531)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.48/0.70 % (10533)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.48/0.70 % (10535)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.48/0.70 % (10534)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.48/0.70 % (10536)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.48/0.71 % (10535)Refutation not found, incomplete strategy% (10535)------------------------------
% 0.48/0.71 % (10535)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.48/0.71 % (10535)Termination reason: Refutation not found, incomplete strategy
% 0.48/0.71
% 0.48/0.71 % (10535)Memory used [KB]: 1146
% 0.48/0.71 % (10535)Time elapsed: 0.006 s
% 0.48/0.71 % (10535)Instructions burned: 7 (million)
% 0.48/0.71 % (10535)------------------------------
% 0.48/0.71 % (10535)------------------------------
% 0.48/0.71 % (10530)Refutation not found, incomplete strategy% (10530)------------------------------
% 0.48/0.71 % (10530)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.48/0.71 % (10530)Termination reason: Refutation not found, incomplete strategy
% 0.48/0.71
% 0.48/0.71 % (10530)Memory used [KB]: 1160
% 0.48/0.71 % (10530)Time elapsed: 0.008 s
% 0.48/0.71 % (10530)Instructions burned: 12 (million)
% 0.48/0.71 % (10530)------------------------------
% 0.48/0.71 % (10530)------------------------------
% 0.48/0.71 % (10538)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.48/0.72 % (10532)Refutation not found, incomplete strategy% (10532)------------------------------
% 0.48/0.72 % (10532)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.48/0.72 % (10532)Termination reason: Refutation not found, incomplete strategy
% 0.48/0.72
% 0.48/0.72 % (10532)Memory used [KB]: 1208
% 0.48/0.72 % (10532)Time elapsed: 0.013 s
% 0.48/0.72 % (10532)Instructions burned: 18 (million)
% 0.48/0.72 % (10539)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.48/0.72 % (10531)First to succeed.
% 0.48/0.72 % (10532)------------------------------
% 0.48/0.72 % (10532)------------------------------
% 0.57/0.72 % (10537)Instruction limit reached!
% 0.57/0.72 % (10537)------------------------------
% 0.57/0.72 % (10537)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.72 % (10537)Termination reason: Unknown
% 0.57/0.72 % (10537)Termination phase: Saturation
% 0.57/0.72
% 0.57/0.72 % (10537)Memory used [KB]: 1343
% 0.57/0.72 % (10537)Time elapsed: 0.017 s
% 0.57/0.72 % (10537)Instructions burned: 56 (million)
% 0.57/0.72 % (10537)------------------------------
% 0.57/0.72 % (10537)------------------------------
% 0.57/0.72 % (10531)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10377"
% 0.57/0.72 % (10540)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.57/0.72 % (10531)Refutation found. Thanks to Tanya!
% 0.57/0.72 % SZS status Theorem for Vampire---4
% 0.57/0.72 % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.72 % (10531)------------------------------
% 0.57/0.72 % (10531)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.72 % (10531)Termination reason: Refutation
% 0.57/0.72
% 0.57/0.72 % (10531)Memory used [KB]: 1251
% 0.57/0.72 % (10531)Time elapsed: 0.017 s
% 0.57/0.72 % (10531)Instructions burned: 25 (million)
% 0.57/0.72 % (10377)Success in time 0.393 s
% 0.57/0.72 % Vampire---4.8 exiting
%------------------------------------------------------------------------------