TSTP Solution File: SET023-3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET023-3 : TPTP v8.1.2. Released v1.0.0.
% 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 : n013.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 15:35:36 EDT 2023
% Result : Unsatisfiable 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 57
% Syntax : Number of formulae : 162 ( 15 unt; 0 def)
% Number of atoms : 531 ( 82 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 697 ( 328 ~; 335 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 39 ( 37 usr; 35 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 188 (; 188 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f470,plain,
$false,
inference(avatar_sat_refutation,[],[f266,f271,f275,f276,f280,f281,f285,f290,f294,f298,f306,f307,f315,f316,f325,f330,f334,f335,f339,f340,f345,f350,f355,f359,f363,f367,f371,f379,f389,f395,f405,f414,f416,f460,f469]) ).
fof(f469,plain,
( spl1_33
| spl1_34
| ~ spl1_2
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f459,f263,f259,f466,f462]) ).
fof(f462,plain,
( spl1_33
<=> member(f26(sF0),sF0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
fof(f466,plain,
( spl1_34
<=> empty_set = sF0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
fof(f259,plain,
( spl1_2
<=> little_set(f3(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f263,plain,
( spl1_3
<=> sF0 = f3(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f459,plain,
( empty_set = sF0
| member(f26(sF0),sF0)
| ~ spl1_2
| ~ spl1_3 ),
inference(resolution,[],[f427,f101]) ).
fof(f101,axiom,
! [X0] :
( ~ little_set(X0)
| empty_set = X0
| member(f26(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',choice2) ).
fof(f427,plain,
( little_set(sF0)
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_demodulation,[],[f260,f265]) ).
fof(f265,plain,
( sF0 = f3(a)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f260,plain,
( little_set(f3(a))
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f460,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f458,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(resolution,[],[f427,f198]) ).
fof(f198,plain,
~ little_set(sF0),
inference(definition_folding,[],[f150,f197]) ).
fof(f197,plain,
second(a) = sF0,
introduced(function_definition,[]) ).
fof(f150,axiom,
~ little_set(second(a)),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',prove_second_component_is_small) ).
fof(f416,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f415]) ).
fof(f415,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f406,f149]) ).
fof(f149,axiom,
ordered_pair_predicate(a),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',an_ordered_pair_predicate) ).
fof(f406,plain,
( ~ ordered_pair_predicate(a)
| spl1_2 ),
inference(resolution,[],[f261,f12]) ).
fof(f12,axiom,
! [X0] :
( little_set(f3(X0))
| ~ ordered_pair_predicate(X0) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',ordered_pair_predicate2) ).
fof(f261,plain,
( ~ little_set(f3(a))
| spl1_2 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f414,plain,
spl1_13,
inference(avatar_contradiction_clause,[],[f410]) ).
fof(f410,plain,
( $false
| spl1_13 ),
inference(resolution,[],[f311,f8]) ).
fof(f8,axiom,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',non_ordered_pair4) ).
fof(f311,plain,
( ~ little_set(non_ordered_pair(f2(a),f3(a)))
| spl1_13 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f309,plain,
( spl1_13
<=> little_set(non_ordered_pair(f2(a),f3(a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
fof(f405,plain,
( spl1_31
| spl1_32
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f396,f255,f402,f398]) ).
fof(f398,plain,
( spl1_31
<=> member(f26(f2(a)),f2(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
fof(f402,plain,
( spl1_32
<=> empty_set = f2(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
fof(f255,plain,
( spl1_1
<=> little_set(f2(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f396,plain,
( empty_set = f2(a)
| member(f26(f2(a)),f2(a))
| ~ spl1_1 ),
inference(resolution,[],[f256,f101]) ).
fof(f256,plain,
( little_set(f2(a))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f395,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f394]) ).
fof(f394,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f390,f149]) ).
fof(f390,plain,
( ~ ordered_pair_predicate(a)
| spl1_1 ),
inference(resolution,[],[f257,f11]) ).
fof(f11,axiom,
! [X0] :
( little_set(f2(X0))
| ~ ordered_pair_predicate(X0) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',ordered_pair_predicate1) ).
fof(f257,plain,
( ~ little_set(f2(a))
| spl1_1 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f389,plain,
( spl1_29
| spl1_30
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f380,f300,f386,f382]) ).
fof(f382,plain,
( spl1_29
<=> member(f26(a),a) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
fof(f386,plain,
( spl1_30
<=> empty_set = a ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
fof(f300,plain,
( spl1_11
<=> little_set(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f380,plain,
( empty_set = a
| member(f26(a),a)
| ~ spl1_11 ),
inference(resolution,[],[f301,f101]) ).
fof(f301,plain,
( little_set(a)
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f379,plain,
( ~ spl1_27
| ~ spl1_13
| ~ spl1_15
| spl1_28 ),
inference(avatar_split_clause,[],[f252,f377,f318,f309,f373]) ).
fof(f373,plain,
( spl1_27
<=> little_set(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
fof(f318,plain,
( spl1_15
<=> little_set(non_ordered_pair(f2(a),f2(a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
fof(f377,plain,
( spl1_28
<=> ! [X34,X36,X35] :
( member(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a),compose(X34,X35))
| ~ member(non_ordered_pair(non_ordered_pair(X36,X36),non_ordered_pair(X36,non_ordered_pair(f2(a),f3(a)))),X35)
| ~ little_set(X36)
| ~ member(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),non_ordered_pair(non_ordered_pair(f2(a),f2(a)),X36)),X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
fof(f252,plain,
! [X36,X34,X35] :
( member(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a),compose(X34,X35))
| ~ little_set(non_ordered_pair(f2(a),f2(a)))
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| ~ little_set(X36)
| ~ member(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),non_ordered_pair(non_ordered_pair(f2(a),f2(a)),X36)),X34)
| ~ member(non_ordered_pair(non_ordered_pair(X36,X36),non_ordered_pair(X36,non_ordered_pair(f2(a),f3(a)))),X35)
| ~ little_set(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a)) ),
inference(superposition,[],[f196,f203]) ).
fof(f203,plain,
a = non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f3(a))),
inference(resolution,[],[f149,f154]) ).
fof(f154,plain,
! [X0] :
( ~ ordered_pair_predicate(X0)
| non_ordered_pair(non_ordered_pair(f2(X0),f2(X0)),non_ordered_pair(f2(X0),f3(X0))) = X0 ),
inference(definition_unfolding,[],[f13,f152]) ).
fof(f152,plain,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),
inference(definition_unfolding,[],[f10,f9]) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',singleton_set) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',ordered_pair) ).
fof(f13,axiom,
! [X0] :
( ~ ordered_pair_predicate(X0)
| ordered_pair(f2(X0),f3(X0)) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',ordered_pair_predicate3) ).
fof(f196,plain,
! [X0,X1,X6,X9,X7] :
( member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),compose(X7,X9))
| ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X6)
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X6)),X7)
| ~ member(non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X1)),X9)
| ~ little_set(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))) ),
inference(equality_resolution,[],[f182]) ).
fof(f182,plain,
! [X3,X0,X1,X6,X9,X7] :
( ~ little_set(X3)
| ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X6)
| non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) != X3
| ~ member(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X6)),X7)
| ~ member(non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X1)),X9)
| member(X3,compose(X7,X9)) ),
inference(definition_unfolding,[],[f134,f152,f152,f152]) ).
fof(f134,axiom,
! [X3,X0,X1,X6,X9,X7] :
( ~ little_set(X3)
| ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X6)
| ordered_pair(X0,X1) != X3
| ~ member(ordered_pair(X0,X6),X7)
| ~ member(ordered_pair(X6,X1),X9)
| member(X3,compose(X7,X9)) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',compose7) ).
fof(f371,plain,
( ~ spl1_15
| ~ spl1_13
| spl1_26 ),
inference(avatar_split_clause,[],[f251,f369,f309,f318]) ).
fof(f369,plain,
( spl1_26
<=> ! [X32,X33] :
( member(non_ordered_pair(non_ordered_pair(X32,X32),non_ordered_pair(X32,non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))),flip_range_of(X33))
| ~ member(non_ordered_pair(non_ordered_pair(X32,X32),non_ordered_pair(X32,non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f3(a)),non_ordered_pair(f2(a),f3(a))),non_ordered_pair(non_ordered_pair(f2(a),f3(a)),non_ordered_pair(f2(a),f2(a)))))),X33)
| ~ little_set(non_ordered_pair(non_ordered_pair(X32,X32),non_ordered_pair(X32,non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))))
| ~ little_set(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
fof(f251,plain,
! [X32,X33] :
( member(non_ordered_pair(non_ordered_pair(X32,X32),non_ordered_pair(X32,non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))),flip_range_of(X33))
| ~ little_set(X32)
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| ~ little_set(non_ordered_pair(f2(a),f2(a)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X32,X32),non_ordered_pair(X32,non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))))
| ~ member(non_ordered_pair(non_ordered_pair(X32,X32),non_ordered_pair(X32,non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f3(a)),non_ordered_pair(f2(a),f3(a))),non_ordered_pair(non_ordered_pair(f2(a),f3(a)),non_ordered_pair(f2(a),f2(a)))))),X33) ),
inference(superposition,[],[f195,f203]) ).
fof(f195,plain,
! [X2,X0,X6,X4] :
( member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))),flip_range_of(X0))
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))))
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X4)))),X0) ),
inference(equality_resolution,[],[f181]) ).
fof(f181,plain,
! [X2,X3,X0,X6,X4] :
( ~ little_set(X3)
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(X3,flip_range_of(X0))
| non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))) != X3
| ~ member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X4)))),X0) ),
inference(definition_unfolding,[],[f56,f152,f152,f152,f152]) ).
fof(f56,axiom,
! [X2,X3,X0,X6,X4] :
( ~ little_set(X3)
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(X3,flip_range_of(X0))
| ordered_pair(X2,ordered_pair(X4,X6)) != X3
| ~ member(ordered_pair(X2,ordered_pair(X6,X4)),X0) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',flip_range6) ).
fof(f367,plain,
( ~ spl1_15
| ~ spl1_13
| spl1_25 ),
inference(avatar_split_clause,[],[f250,f365,f309,f318]) ).
fof(f365,plain,
( spl1_25
<=> ! [X30,X31] :
( member(non_ordered_pair(non_ordered_pair(X30,X30),non_ordered_pair(X30,non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))),rotate_right(X31))
| ~ member(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f3(a)),non_ordered_pair(f2(a),f3(a))),non_ordered_pair(non_ordered_pair(f2(a),f3(a)),X30)))),X31)
| ~ little_set(non_ordered_pair(non_ordered_pair(X30,X30),non_ordered_pair(X30,non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))))
| ~ little_set(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
fof(f250,plain,
! [X31,X30] :
( member(non_ordered_pair(non_ordered_pair(X30,X30),non_ordered_pair(X30,non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))),rotate_right(X31))
| ~ little_set(X30)
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| ~ little_set(non_ordered_pair(f2(a),f2(a)))
| ~ little_set(non_ordered_pair(non_ordered_pair(X30,X30),non_ordered_pair(X30,non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))))
| ~ member(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f3(a)),non_ordered_pair(f2(a),f3(a))),non_ordered_pair(non_ordered_pair(f2(a),f3(a)),X30)))),X31) ),
inference(superposition,[],[f194,f203]) ).
fof(f194,plain,
! [X2,X0,X6,X4] :
( member(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))),rotate_right(X0))
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| ~ little_set(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))))
| ~ member(non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X2)))),X0) ),
inference(equality_resolution,[],[f180]) ).
fof(f180,plain,
! [X2,X3,X0,X6,X4] :
( ~ little_set(X3)
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(X3,rotate_right(X0))
| non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X6)))) != X3
| ~ member(non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X2)))),X0) ),
inference(definition_unfolding,[],[f50,f152,f152,f152,f152]) ).
fof(f50,axiom,
! [X2,X3,X0,X6,X4] :
( ~ little_set(X3)
| ~ little_set(X2)
| ~ little_set(X6)
| ~ little_set(X4)
| member(X3,rotate_right(X0))
| ordered_pair(X2,ordered_pair(X4,X6)) != X3
| ~ member(ordered_pair(X4,ordered_pair(X6,X2)),X0) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',rotate_right6) ).
fof(f363,plain,
( ~ spl1_15
| ~ spl1_13
| spl1_24 ),
inference(avatar_split_clause,[],[f249,f361,f309,f318]) ).
fof(f361,plain,
( spl1_24
<=> ! [X29] :
( member(X29,second(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a)))
| ~ member(X29,non_ordered_pair(f2(a),f3(a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
fof(f249,plain,
! [X29] :
( member(X29,second(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a)))
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| ~ member(X29,non_ordered_pair(f2(a),f3(a)))
| ~ little_set(non_ordered_pair(f2(a),f2(a))) ),
inference(superposition,[],[f192,f203]) ).
fof(f192,plain,
! [X2,X3,X4] :
( member(X3,second(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4))))
| ~ little_set(X4)
| ~ member(X3,X4)
| ~ little_set(X2) ),
inference(equality_resolution,[],[f176]) ).
fof(f176,plain,
! [X2,X3,X0,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X4)
| member(X3,second(X0))
| non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)) != X0 ),
inference(definition_unfolding,[],[f24,f152]) ).
fof(f24,axiom,
! [X2,X3,X0,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X4)
| member(X3,second(X0))
| ordered_pair(X2,X4) != X0 ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',second5) ).
fof(f359,plain,
( ~ spl1_15
| ~ spl1_13
| spl1_23 ),
inference(avatar_split_clause,[],[f248,f357,f309,f318]) ).
fof(f357,plain,
( spl1_23
<=> ! [X28] :
( member(X28,first(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a)))
| ~ member(X28,non_ordered_pair(f2(a),f2(a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
fof(f248,plain,
! [X28] :
( member(X28,first(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a)))
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| ~ member(X28,non_ordered_pair(f2(a),f2(a)))
| ~ little_set(non_ordered_pair(f2(a),f2(a))) ),
inference(superposition,[],[f191,f203]) ).
fof(f191,plain,
! [X2,X3,X4] :
( member(X3,first(non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4))))
| ~ little_set(X4)
| ~ member(X3,X2)
| ~ little_set(X2) ),
inference(equality_resolution,[],[f175]) ).
fof(f175,plain,
! [X2,X3,X0,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X2)
| member(X3,first(X0))
| non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4)) != X0 ),
inference(definition_unfolding,[],[f19,f152]) ).
fof(f19,axiom,
! [X2,X3,X0,X4] :
( ~ little_set(X2)
| ~ little_set(X4)
| ~ member(X3,X2)
| member(X3,first(X0))
| ordered_pair(X2,X4) != X0 ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',first5) ).
fof(f355,plain,
( ~ spl1_15
| ~ spl1_13
| spl1_22 ),
inference(avatar_split_clause,[],[f247,f352,f309,f318]) ).
fof(f352,plain,
( spl1_22
<=> ordered_pair_predicate(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
fof(f247,plain,
( ordered_pair_predicate(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| ~ little_set(non_ordered_pair(f2(a),f2(a))) ),
inference(superposition,[],[f187,f203]) ).
fof(f187,plain,
! [X3,X1] :
( ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X3)))
| ~ little_set(X3)
| ~ little_set(X1) ),
inference(equality_resolution,[],[f172]) ).
fof(f172,plain,
! [X3,X0,X1] :
( ~ little_set(X1)
| ~ little_set(X3)
| ordered_pair_predicate(X0)
| non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X3)) != X0 ),
inference(definition_unfolding,[],[f14,f152]) ).
fof(f14,axiom,
! [X3,X0,X1] :
( ~ little_set(X1)
| ~ little_set(X3)
| ordered_pair_predicate(X0)
| ordered_pair(X1,X3) != X0 ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',ordered_pair_predicate4) ).
fof(f350,plain,
( ~ spl1_15
| spl1_21 ),
inference(avatar_split_clause,[],[f246,f347,f318]) ).
fof(f347,plain,
( spl1_21
<=> member(non_ordered_pair(f2(a),f2(a)),a) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
fof(f246,plain,
( member(non_ordered_pair(f2(a),f2(a)),a)
| ~ little_set(non_ordered_pair(f2(a),f2(a))) ),
inference(superposition,[],[f185,f203]) ).
fof(f185,plain,
! [X2,X1] :
( member(X2,non_ordered_pair(X2,X1))
| ~ little_set(X2) ),
inference(equality_resolution,[],[f6]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ little_set(X2)
| X0 != X2
| member(X2,non_ordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',non_ordered_pair2) ).
fof(f345,plain,
( ~ spl1_13
| spl1_20 ),
inference(avatar_split_clause,[],[f245,f342,f309]) ).
fof(f342,plain,
( spl1_20
<=> member(non_ordered_pair(f2(a),f3(a)),a) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
fof(f245,plain,
( member(non_ordered_pair(f2(a),f3(a)),a)
| ~ little_set(non_ordered_pair(f2(a),f3(a))) ),
inference(superposition,[],[f184,f203]) ).
fof(f184,plain,
! [X2,X0] :
( member(X2,non_ordered_pair(X0,X2))
| ~ little_set(X2) ),
inference(equality_resolution,[],[f7]) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ little_set(X2)
| X1 != X2
| member(X2,non_ordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',non_ordered_pair3) ).
fof(f340,plain,
( ~ spl1_15
| ~ spl1_13
| spl1_19 ),
inference(avatar_split_clause,[],[f244,f337,f309,f318]) ).
fof(f337,plain,
( spl1_19
<=> ! [X25,X24] :
( non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a) != non_ordered_pair(non_ordered_pair(X24,X24),non_ordered_pair(X24,X25))
| non_ordered_pair(f2(a),f3(a)) = X25
| ~ little_set(X24)
| ~ little_set(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
fof(f244,plain,
! [X26,X27] :
( non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a) != non_ordered_pair(non_ordered_pair(X26,X26),non_ordered_pair(X26,X27))
| ~ little_set(X27)
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| ~ little_set(non_ordered_pair(f2(a),f2(a)))
| non_ordered_pair(f2(a),f3(a)) = X27
| ~ little_set(X26) ),
inference(superposition,[],[f178,f203]) ).
fof(f178,plain,
! [X2,X0,X1,X4] :
( non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) != non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4))
| ~ little_set(X1)
| ~ little_set(X4)
| ~ little_set(X2)
| X1 = X4
| ~ little_set(X0) ),
inference(definition_unfolding,[],[f144,f152,f152]) ).
fof(f144,axiom,
! [X2,X0,X1,X4] :
( ~ little_set(X0)
| ~ little_set(X1)
| ~ little_set(X4)
| ~ little_set(X2)
| X1 = X4
| ordered_pair(X0,X1) != ordered_pair(X2,X4) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',second_components_are_equal) ).
fof(f339,plain,
( ~ spl1_15
| ~ spl1_13
| spl1_19 ),
inference(avatar_split_clause,[],[f243,f337,f309,f318]) ).
fof(f243,plain,
! [X24,X25] :
( non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a) != non_ordered_pair(non_ordered_pair(X24,X24),non_ordered_pair(X24,X25))
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| ~ little_set(X25)
| ~ little_set(X24)
| non_ordered_pair(f2(a),f3(a)) = X25
| ~ little_set(non_ordered_pair(f2(a),f2(a))) ),
inference(superposition,[],[f178,f203]) ).
fof(f335,plain,
( ~ spl1_15
| spl1_18 ),
inference(avatar_split_clause,[],[f242,f332,f318]) ).
fof(f332,plain,
( spl1_18
<=> ! [X20,X21] :
( non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a) != non_ordered_pair(non_ordered_pair(X20,X20),non_ordered_pair(X20,X21))
| ~ little_set(X20)
| non_ordered_pair(f2(a),f2(a)) = X20 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
fof(f242,plain,
! [X22,X23] :
( non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a) != non_ordered_pair(non_ordered_pair(X22,X22),non_ordered_pair(X22,X23))
| ~ little_set(X22)
| non_ordered_pair(f2(a),f2(a)) = X22
| ~ little_set(non_ordered_pair(f2(a),f2(a))) ),
inference(superposition,[],[f173,f203]) ).
fof(f173,plain,
! [X2,X0,X1,X4] :
( non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) != non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4))
| ~ little_set(X0)
| X0 = X2
| ~ little_set(X2) ),
inference(definition_unfolding,[],[f142,f152,f152]) ).
fof(f142,axiom,
! [X2,X0,X1,X4] :
( ~ little_set(X2)
| ~ little_set(X0)
| X0 = X2
| ordered_pair(X0,X1) != ordered_pair(X2,X4) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',first_components_are_equal) ).
fof(f334,plain,
( ~ spl1_15
| spl1_18 ),
inference(avatar_split_clause,[],[f241,f332,f318]) ).
fof(f241,plain,
! [X21,X20] :
( non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a) != non_ordered_pair(non_ordered_pair(X20,X20),non_ordered_pair(X20,X21))
| ~ little_set(non_ordered_pair(f2(a),f2(a)))
| non_ordered_pair(f2(a),f2(a)) = X20
| ~ little_set(X20) ),
inference(superposition,[],[f173,f203]) ).
fof(f330,plain,
( ~ spl1_15
| ~ spl1_13
| spl1_17 ),
inference(avatar_split_clause,[],[f240,f327,f309,f318]) ).
fof(f327,plain,
( spl1_17
<=> non_ordered_pair(f2(a),f2(a)) = first(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
fof(f240,plain,
( non_ordered_pair(f2(a),f2(a)) = first(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| ~ little_set(non_ordered_pair(f2(a),f2(a))) ),
inference(superposition,[],[f169,f203]) ).
fof(f169,plain,
! [X0,X1] :
( first(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))) = X0
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(definition_unfolding,[],[f146,f152]) ).
fof(f146,axiom,
! [X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| first(ordered_pair(X0,X1)) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',property_of_first) ).
fof(f325,plain,
( ~ spl1_15
| ~ spl1_13
| spl1_16 ),
inference(avatar_split_clause,[],[f239,f322,f309,f318]) ).
fof(f322,plain,
( spl1_16
<=> non_ordered_pair(f2(a),f3(a)) = second(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
fof(f239,plain,
( non_ordered_pair(f2(a),f3(a)) = second(non_ordered_pair(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),f2(a))),a))
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| ~ little_set(non_ordered_pair(f2(a),f2(a))) ),
inference(superposition,[],[f168,f203]) ).
fof(f168,plain,
! [X0,X1] :
( second(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))) = X1
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(definition_unfolding,[],[f147,f152]) ).
fof(f147,axiom,
! [X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| second(ordered_pair(X0,X1)) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',property_of_second) ).
fof(f316,plain,
( ~ spl1_13
| spl1_14 ),
inference(avatar_split_clause,[],[f238,f313,f309]) ).
fof(f313,plain,
( spl1_14
<=> ! [X18] :
( a != non_ordered_pair(non_ordered_pair(f2(a),f2(a)),X18)
| ~ little_set(X18)
| non_ordered_pair(f2(a),f3(a)) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
fof(f238,plain,
! [X19] :
( a != non_ordered_pair(non_ordered_pair(f2(a),f2(a)),X19)
| ~ little_set(X19)
| non_ordered_pair(f2(a),f3(a)) = X19
| ~ little_set(non_ordered_pair(f2(a),f3(a))) ),
inference(superposition,[],[f143,f203]) ).
fof(f143,axiom,
! [X3,X0,X1] :
( non_ordered_pair(X3,X0) != non_ordered_pair(X3,X1)
| ~ little_set(X0)
| X0 = X1
| ~ little_set(X1) ),
file('/export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024',left_cancellation) ).
fof(f315,plain,
( ~ spl1_13
| spl1_14 ),
inference(avatar_split_clause,[],[f237,f313,f309]) ).
fof(f237,plain,
! [X18] :
( a != non_ordered_pair(non_ordered_pair(f2(a),f2(a)),X18)
| ~ little_set(non_ordered_pair(f2(a),f3(a)))
| non_ordered_pair(f2(a),f3(a)) = X18
| ~ little_set(X18) ),
inference(superposition,[],[f143,f203]) ).
fof(f307,plain,
spl1_11,
inference(avatar_split_clause,[],[f236,f300]) ).
fof(f236,plain,
little_set(a),
inference(superposition,[],[f8,f203]) ).
fof(f306,plain,
( ~ spl1_11
| ~ spl1_2
| ~ spl1_1
| spl1_12 ),
inference(avatar_split_clause,[],[f234,f304,f255,f259,f300]) ).
fof(f304,plain,
( spl1_12
<=> ! [X16,X14,X15] :
( member(a,compose(X14,X15))
| ~ member(non_ordered_pair(non_ordered_pair(X16,X16),non_ordered_pair(X16,f3(a))),X15)
| ~ little_set(X16)
| ~ member(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),X16)),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f234,plain,
! [X16,X14,X15] :
( member(a,compose(X14,X15))
| ~ little_set(f2(a))
| ~ little_set(f3(a))
| ~ little_set(X16)
| ~ member(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),X16)),X14)
| ~ member(non_ordered_pair(non_ordered_pair(X16,X16),non_ordered_pair(X16,f3(a))),X15)
| ~ little_set(a) ),
inference(superposition,[],[f196,f203]) ).
fof(f298,plain,
( ~ spl1_1
| ~ spl1_2
| spl1_10 ),
inference(avatar_split_clause,[],[f233,f296,f259,f255]) ).
fof(f296,plain,
( spl1_10
<=> ! [X13,X12] :
( member(non_ordered_pair(non_ordered_pair(X12,X12),non_ordered_pair(X12,a)),flip_range_of(X13))
| ~ member(non_ordered_pair(non_ordered_pair(X12,X12),non_ordered_pair(X12,non_ordered_pair(non_ordered_pair(f3(a),f3(a)),non_ordered_pair(f3(a),f2(a))))),X13)
| ~ little_set(non_ordered_pair(non_ordered_pair(X12,X12),non_ordered_pair(X12,a)))
| ~ little_set(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f233,plain,
! [X12,X13] :
( member(non_ordered_pair(non_ordered_pair(X12,X12),non_ordered_pair(X12,a)),flip_range_of(X13))
| ~ little_set(X12)
| ~ little_set(f3(a))
| ~ little_set(f2(a))
| ~ little_set(non_ordered_pair(non_ordered_pair(X12,X12),non_ordered_pair(X12,a)))
| ~ member(non_ordered_pair(non_ordered_pair(X12,X12),non_ordered_pair(X12,non_ordered_pair(non_ordered_pair(f3(a),f3(a)),non_ordered_pair(f3(a),f2(a))))),X13) ),
inference(superposition,[],[f195,f203]) ).
fof(f294,plain,
( ~ spl1_1
| ~ spl1_2
| spl1_9 ),
inference(avatar_split_clause,[],[f232,f292,f259,f255]) ).
fof(f292,plain,
( spl1_9
<=> ! [X11,X10] :
( member(non_ordered_pair(non_ordered_pair(X10,X10),non_ordered_pair(X10,a)),rotate_right(X11))
| ~ member(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),non_ordered_pair(non_ordered_pair(f3(a),f3(a)),non_ordered_pair(f3(a),X10)))),X11)
| ~ little_set(non_ordered_pair(non_ordered_pair(X10,X10),non_ordered_pair(X10,a)))
| ~ little_set(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f232,plain,
! [X10,X11] :
( member(non_ordered_pair(non_ordered_pair(X10,X10),non_ordered_pair(X10,a)),rotate_right(X11))
| ~ little_set(X10)
| ~ little_set(f3(a))
| ~ little_set(f2(a))
| ~ little_set(non_ordered_pair(non_ordered_pair(X10,X10),non_ordered_pair(X10,a)))
| ~ member(non_ordered_pair(non_ordered_pair(f2(a),f2(a)),non_ordered_pair(f2(a),non_ordered_pair(non_ordered_pair(f3(a),f3(a)),non_ordered_pair(f3(a),X10)))),X11) ),
inference(superposition,[],[f194,f203]) ).
fof(f290,plain,
( ~ spl1_1
| ~ spl1_2
| spl1_8 ),
inference(avatar_split_clause,[],[f286,f288,f259,f255]) ).
fof(f288,plain,
( spl1_8
<=> ! [X9] :
( member(X9,sF0)
| ~ member(X9,f3(a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
fof(f286,plain,
! [X9] :
( member(X9,sF0)
| ~ little_set(f3(a))
| ~ member(X9,f3(a))
| ~ little_set(f2(a)) ),
inference(forward_demodulation,[],[f231,f197]) ).
fof(f231,plain,
! [X9] :
( member(X9,second(a))
| ~ little_set(f3(a))
| ~ member(X9,f3(a))
| ~ little_set(f2(a)) ),
inference(superposition,[],[f192,f203]) ).
fof(f285,plain,
( ~ spl1_1
| ~ spl1_2
| spl1_7 ),
inference(avatar_split_clause,[],[f230,f283,f259,f255]) ).
fof(f283,plain,
( spl1_7
<=> ! [X8] :
( member(X8,first(a))
| ~ member(X8,f2(a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
fof(f230,plain,
! [X8] :
( member(X8,first(a))
| ~ little_set(f3(a))
| ~ member(X8,f2(a))
| ~ little_set(f2(a)) ),
inference(superposition,[],[f191,f203]) ).
fof(f281,plain,
( ~ spl1_1
| ~ spl1_2
| spl1_6 ),
inference(avatar_split_clause,[],[f228,f278,f259,f255]) ).
fof(f278,plain,
( spl1_6
<=> ! [X4,X5] :
( a != non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X5))
| f3(a) = X5
| ~ little_set(X4)
| ~ little_set(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f228,plain,
! [X6,X7] :
( a != non_ordered_pair(non_ordered_pair(X6,X6),non_ordered_pair(X6,X7))
| ~ little_set(X7)
| ~ little_set(f3(a))
| ~ little_set(f2(a))
| f3(a) = X7
| ~ little_set(X6) ),
inference(superposition,[],[f178,f203]) ).
fof(f280,plain,
( ~ spl1_1
| ~ spl1_2
| spl1_6 ),
inference(avatar_split_clause,[],[f227,f278,f259,f255]) ).
fof(f227,plain,
! [X4,X5] :
( a != non_ordered_pair(non_ordered_pair(X4,X4),non_ordered_pair(X4,X5))
| ~ little_set(f3(a))
| ~ little_set(X5)
| ~ little_set(X4)
| f3(a) = X5
| ~ little_set(f2(a)) ),
inference(superposition,[],[f178,f203]) ).
fof(f276,plain,
( ~ spl1_1
| spl1_5 ),
inference(avatar_split_clause,[],[f226,f273,f255]) ).
fof(f273,plain,
( spl1_5
<=> ! [X0,X1] :
( a != non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))
| ~ little_set(X0)
| f2(a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f226,plain,
! [X2,X3] :
( a != non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X3))
| ~ little_set(X2)
| f2(a) = X2
| ~ little_set(f2(a)) ),
inference(superposition,[],[f173,f203]) ).
fof(f275,plain,
( ~ spl1_1
| spl1_5 ),
inference(avatar_split_clause,[],[f225,f273,f255]) ).
fof(f225,plain,
! [X0,X1] :
( a != non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))
| ~ little_set(f2(a))
| f2(a) = X0
| ~ little_set(X0) ),
inference(superposition,[],[f173,f203]) ).
fof(f271,plain,
( ~ spl1_1
| ~ spl1_2
| spl1_4 ),
inference(avatar_split_clause,[],[f224,f268,f259,f255]) ).
fof(f268,plain,
( spl1_4
<=> first(a) = f2(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f224,plain,
( first(a) = f2(a)
| ~ little_set(f3(a))
| ~ little_set(f2(a)) ),
inference(superposition,[],[f169,f203]) ).
fof(f266,plain,
( ~ spl1_1
| ~ spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f253,f263,f259,f255]) ).
fof(f253,plain,
( sF0 = f3(a)
| ~ little_set(f3(a))
| ~ little_set(f2(a)) ),
inference(forward_demodulation,[],[f223,f197]) ).
fof(f223,plain,
( second(a) = f3(a)
| ~ little_set(f3(a))
| ~ little_set(f2(a)) ),
inference(superposition,[],[f168,f203]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET023-3 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat Aug 26 14:48:32 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.16/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.wjM7ivux5o/Vampire---4.8_7024
% 0.16/0.37 % (7131)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (7135)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.22/0.43 % (7134)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.22/0.43 % (7136)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.22/0.43 % (7137)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.22/0.43 % (7133)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.22/0.43 % (7132)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.22/0.44 % (7138)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.22/0.44 % (7138)Refutation not found, incomplete strategy% (7138)------------------------------
% 0.22/0.44 % (7138)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.44 % (7138)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.44 % (7138)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44
% 0.22/0.44 % (7138)Memory used [KB]: 5628
% 0.22/0.44 % (7138)Time elapsed: 0.004 s
% 0.22/0.44 % (7138)------------------------------
% 0.22/0.44 % (7138)------------------------------
% 0.22/0.44 % (7132)First to succeed.
% 0.22/0.45 % (7136)Also succeeded, but the first one will report.
% 0.22/0.45 % (7132)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Unsatisfiable for Vampire---4
% 0.22/0.45 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.45 % (7132)------------------------------
% 0.22/0.45 % (7132)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45 % (7132)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45 % (7132)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (7132)Memory used [KB]: 6012
% 0.22/0.45 % (7132)Time elapsed: 0.015 s
% 0.22/0.45 % (7132)------------------------------
% 0.22/0.45 % (7132)------------------------------
% 0.22/0.45 % (7131)Success in time 0.078 s
% 0.22/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------