TSTP Solution File: SET018+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET018+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n001.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 15:34:13 EDT 2023
% Result : Theorem 0.17s 0.62s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 31
% Syntax : Number of formulae : 196 ( 37 unt; 0 def)
% Number of atoms : 494 ( 161 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 503 ( 205 ~; 242 |; 33 &)
% ( 16 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-2 aty)
% Number of variables : 91 (; 75 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6102,plain,
$false,
inference(avatar_sat_refutation,[],[f370,f506,f533,f559,f567,f771,f795,f1114,f1644,f1672,f2225,f2796,f3767,f4026,f4867,f4891,f5114,f5488,f6100]) ).
fof(f6100,plain,
( spl18_27
| ~ spl18_45
| spl18_46 ),
inference(avatar_contradiction_clause,[],[f6099]) ).
fof(f6099,plain,
( $false
| spl18_27
| ~ spl18_45
| spl18_46 ),
inference(subsumption_resolution,[],[f6098,f765]) ).
fof(f765,plain,
( sF12 != sF16
| spl18_27 ),
inference(avatar_component_clause,[],[f764]) ).
fof(f764,plain,
( spl18_27
<=> sF12 = sF16 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_27])]) ).
fof(f6098,plain,
( sF12 = sF16
| ~ spl18_45
| spl18_46 ),
inference(subsumption_resolution,[],[f6092,f2223]) ).
fof(f2223,plain,
( sF10 != sF12
| spl18_46 ),
inference(avatar_component_clause,[],[f2222]) ).
fof(f2222,plain,
( spl18_46
<=> sF10 = sF12 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_46])]) ).
fof(f6092,plain,
( sF10 = sF12
| sF12 = sF16
| ~ spl18_45 ),
inference(resolution,[],[f5759,f305]) ).
fof(f305,plain,
member(sF12,sF13),
inference(subsumption_resolution,[],[f300,f283]) ).
fof(f283,plain,
member(sF12,universal_class),
inference(superposition,[],[f164,f273]) ).
fof(f273,plain,
unordered_pair(sK0,sF11) = sF12,
introduced(function_definition,[]) ).
fof(f164,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/tmp/tmp.66j9hncaj9/Vampire---4.8_17191',unordered_pair) ).
fof(f300,plain,
( member(sF12,sF13)
| ~ member(sF12,universal_class) ),
inference(superposition,[],[f269,f274]) ).
fof(f274,plain,
unordered_pair(sF10,sF12) = sF13,
introduced(function_definition,[]) ).
fof(f269,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f209]) ).
fof(f209,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( ( X1 = X2
| X0 = X2 )
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox/tmp/tmp.66j9hncaj9/Vampire---4.8_17191',unordered_pair_defn) ).
fof(f5759,plain,
( ! [X0] :
( ~ member(X0,sF13)
| sF10 = X0
| sF16 = X0 )
| ~ spl18_45 ),
inference(superposition,[],[f207,f5663]) ).
fof(f5663,plain,
( sF13 = unordered_pair(sF10,sF16)
| ~ spl18_45 ),
inference(backward_demodulation,[],[f288,f2220]) ).
fof(f2220,plain,
( sF10 = sF14
| ~ spl18_45 ),
inference(avatar_component_clause,[],[f2218]) ).
fof(f2218,plain,
( spl18_45
<=> sF10 = sF14 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_45])]) ).
fof(f288,plain,
sF13 = unordered_pair(sF14,sF16),
inference(forward_demodulation,[],[f278,f279]) ).
fof(f279,plain,
sF13 = sF17,
inference(definition_folding,[],[f232,f278,f277,f276,f275,f274,f273,f272,f271]) ).
fof(f271,plain,
unordered_pair(sK0,sK0) = sF10,
introduced(function_definition,[]) ).
fof(f272,plain,
unordered_pair(sK1,sK1) = sF11,
introduced(function_definition,[]) ).
fof(f275,plain,
unordered_pair(sK2,sK2) = sF14,
introduced(function_definition,[]) ).
fof(f276,plain,
unordered_pair(sK3,sK3) = sF15,
introduced(function_definition,[]) ).
fof(f277,plain,
unordered_pair(sK2,sF15) = sF16,
introduced(function_definition,[]) ).
fof(f232,plain,
unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),
inference(definition_unfolding,[],[f137,f230,f230]) ).
fof(f230,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f168,f145,f145]) ).
fof(f145,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.66j9hncaj9/Vampire---4.8_17191',singleton_set_defn) ).
fof(f168,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox/tmp/tmp.66j9hncaj9/Vampire---4.8_17191',ordered_pair_defn) ).
fof(f137,plain,
ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( sK1 != sK3
& member(sK1,universal_class)
& ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f73,f87]) ).
fof(f87,plain,
( ? [X0,X1,X2,X3] :
( X1 != X3
& member(X1,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) )
=> ( sK1 != sK3
& member(sK1,universal_class)
& ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
? [X0,X1,X2,X3] :
( X1 != X3
& member(X1,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
? [X0,X1,X2,X3] :
( X1 != X3
& member(X1,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
~ ! [X0,X1,X2,X3] :
( ( member(X1,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) )
=> X1 = X3 ),
inference(rectify,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X6,X0,X1,X4] :
( ( member(X0,universal_class)
& ordered_pair(X6,X0) = ordered_pair(X1,X4) )
=> X0 = X4 ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X6,X0,X1,X4] :
( ( member(X0,universal_class)
& ordered_pair(X6,X0) = ordered_pair(X1,X4) )
=> X0 = X4 ),
file('/export/starexec/sandbox/tmp/tmp.66j9hncaj9/Vampire---4.8_17191',ordered_pair_determines_components2) ).
fof(f278,plain,
unordered_pair(sF14,sF16) = sF17,
introduced(function_definition,[]) ).
fof(f207,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f124]) ).
fof(f5488,plain,
( ~ spl18_3
| spl18_45 ),
inference(avatar_contradiction_clause,[],[f5487]) ).
fof(f5487,plain,
( $false
| ~ spl18_3
| spl18_45 ),
inference(subsumption_resolution,[],[f5486,f2219]) ).
fof(f2219,plain,
( sF10 != sF14
| spl18_45 ),
inference(avatar_component_clause,[],[f2218]) ).
fof(f5486,plain,
( sF10 = sF14
| ~ spl18_3
| spl18_45 ),
inference(forward_demodulation,[],[f5480,f271]) ).
fof(f5480,plain,
( unordered_pair(sK0,sK0) = sF14
| ~ spl18_3
| spl18_45 ),
inference(backward_demodulation,[],[f275,f3180]) ).
fof(f3180,plain,
( sK0 = sK2
| ~ spl18_3
| spl18_45 ),
inference(resolution,[],[f3178,f484]) ).
fof(f484,plain,
! [X0] :
( ~ member(X0,sF10)
| sK0 = X0 ),
inference(duplicate_literal_removal,[],[f473]) ).
fof(f473,plain,
! [X0] :
( ~ member(X0,sF10)
| sK0 = X0
| sK0 = X0 ),
inference(superposition,[],[f207,f271]) ).
fof(f3178,plain,
( member(sK2,sF10)
| ~ spl18_3
| spl18_45 ),
inference(backward_demodulation,[],[f814,f3168]) ).
fof(f3168,plain,
( sF10 = sF16
| spl18_45 ),
inference(subsumption_resolution,[],[f3160,f2219]) ).
fof(f3160,plain,
( sF10 = sF14
| sF10 = sF16 ),
inference(resolution,[],[f480,f315]) ).
fof(f315,plain,
member(sF10,sF13),
inference(subsumption_resolution,[],[f313,f281]) ).
fof(f281,plain,
member(sF10,universal_class),
inference(superposition,[],[f164,f271]) ).
fof(f313,plain,
( member(sF10,sF13)
| ~ member(sF10,universal_class) ),
inference(superposition,[],[f270,f274]) ).
fof(f270,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f208]) ).
fof(f208,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f124]) ).
fof(f480,plain,
! [X7] :
( ~ member(X7,sF13)
| sF14 = X7
| sF16 = X7 ),
inference(superposition,[],[f207,f288]) ).
fof(f814,plain,
( member(sK2,sF16)
| ~ spl18_3 ),
inference(subsumption_resolution,[],[f311,f364]) ).
fof(f364,plain,
( member(sK2,universal_class)
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f363,plain,
( spl18_3
<=> member(sK2,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
fof(f311,plain,
( member(sK2,sF16)
| ~ member(sK2,universal_class) ),
inference(superposition,[],[f270,f277]) ).
fof(f5114,plain,
( ~ spl18_3
| ~ spl18_11
| ~ spl18_27
| ~ spl18_44
| ~ spl18_46 ),
inference(avatar_contradiction_clause,[],[f5113]) ).
fof(f5113,plain,
( $false
| ~ spl18_3
| ~ spl18_11
| ~ spl18_27
| ~ spl18_44
| ~ spl18_46 ),
inference(subsumption_resolution,[],[f5105,f142]) ).
fof(f142,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/tmp/tmp.66j9hncaj9/Vampire---4.8_17191',null_class_defn) ).
fof(f5105,plain,
( member(sK1,null_class)
| ~ spl18_3
| ~ spl18_11
| ~ spl18_27
| ~ spl18_44
| ~ spl18_46 ),
inference(backward_demodulation,[],[f2790,f5098]) ).
fof(f5098,plain,
( null_class = sK0
| ~ spl18_11
| ~ spl18_27
| ~ spl18_46 ),
inference(backward_demodulation,[],[f2668,f501]) ).
fof(f501,plain,
( null_class = sF15
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f499,plain,
( spl18_11
<=> null_class = sF15 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_11])]) ).
fof(f2668,plain,
( sK0 = sF15
| ~ spl18_27
| ~ spl18_46 ),
inference(resolution,[],[f2569,f484]) ).
fof(f2569,plain,
( member(sF15,sF10)
| ~ spl18_27
| ~ spl18_46 ),
inference(forward_demodulation,[],[f1148,f2224]) ).
fof(f2224,plain,
( sF10 = sF12
| ~ spl18_46 ),
inference(avatar_component_clause,[],[f2222]) ).
fof(f1148,plain,
( member(sF15,sF12)
| ~ spl18_27 ),
inference(backward_demodulation,[],[f304,f766]) ).
fof(f766,plain,
( sF12 = sF16
| ~ spl18_27 ),
inference(avatar_component_clause,[],[f764]) ).
fof(f304,plain,
member(sF15,sF16),
inference(subsumption_resolution,[],[f298,f286]) ).
fof(f286,plain,
member(sF15,universal_class),
inference(superposition,[],[f164,f276]) ).
fof(f298,plain,
( member(sF15,sF16)
| ~ member(sF15,universal_class) ),
inference(superposition,[],[f269,f277]) ).
fof(f2790,plain,
( member(sK1,sK0)
| ~ spl18_3
| ~ spl18_27
| ~ spl18_44
| ~ spl18_46 ),
inference(backward_demodulation,[],[f1685,f2669]) ).
fof(f2669,plain,
( sK0 = sK2
| ~ spl18_3
| ~ spl18_27
| ~ spl18_46 ),
inference(resolution,[],[f2575,f484]) ).
fof(f2575,plain,
( member(sK2,sF10)
| ~ spl18_3
| ~ spl18_27
| ~ spl18_46 ),
inference(forward_demodulation,[],[f1364,f2224]) ).
fof(f1364,plain,
( member(sK2,sF12)
| ~ spl18_3
| ~ spl18_27 ),
inference(forward_demodulation,[],[f814,f766]) ).
fof(f1685,plain,
( member(sK1,sK2)
| ~ spl18_44 ),
inference(backward_demodulation,[],[f303,f1643]) ).
fof(f1643,plain,
( sK2 = sF11
| ~ spl18_44 ),
inference(avatar_component_clause,[],[f1641]) ).
fof(f1641,plain,
( spl18_44
<=> sK2 = sF11 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_44])]) ).
fof(f303,plain,
member(sK1,sF11),
inference(subsumption_resolution,[],[f296,f138]) ).
fof(f138,plain,
member(sK1,universal_class),
inference(cnf_transformation,[],[f88]) ).
fof(f296,plain,
( member(sK1,sF11)
| ~ member(sK1,universal_class) ),
inference(superposition,[],[f269,f272]) ).
fof(f4891,plain,
( spl18_44
| ~ spl18_11
| spl18_15
| ~ spl18_27 ),
inference(avatar_split_clause,[],[f1046,f764,f552,f499,f1641]) ).
fof(f552,plain,
( spl18_15
<=> null_class = sF11 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_15])]) ).
fof(f1046,plain,
( sK2 = sF11
| ~ spl18_11
| spl18_15
| ~ spl18_27 ),
inference(subsumption_resolution,[],[f1041,f553]) ).
fof(f553,plain,
( null_class != sF11
| spl18_15 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f1041,plain,
( sK2 = sF11
| null_class = sF11
| ~ spl18_11
| ~ spl18_27 ),
inference(resolution,[],[f965,f302]) ).
fof(f302,plain,
member(sF11,sF12),
inference(subsumption_resolution,[],[f295,f282]) ).
fof(f282,plain,
member(sF11,universal_class),
inference(superposition,[],[f164,f272]) ).
fof(f295,plain,
( member(sF11,sF12)
| ~ member(sF11,universal_class) ),
inference(superposition,[],[f269,f273]) ).
fof(f965,plain,
( ! [X0] :
( ~ member(X0,sF12)
| sK2 = X0
| null_class = X0 )
| ~ spl18_11
| ~ spl18_27 ),
inference(superposition,[],[f207,f927]) ).
fof(f927,plain,
( sF12 = unordered_pair(sK2,null_class)
| ~ spl18_11
| ~ spl18_27 ),
inference(backward_demodulation,[],[f512,f766]) ).
fof(f512,plain,
( sF16 = unordered_pair(sK2,null_class)
| ~ spl18_11 ),
inference(backward_demodulation,[],[f277,f501]) ).
fof(f4867,plain,
( spl18_3
| ~ spl18_44 ),
inference(avatar_split_clause,[],[f4456,f1641,f363]) ).
fof(f4456,plain,
( member(sK2,universal_class)
| ~ spl18_44 ),
inference(superposition,[],[f164,f1681]) ).
fof(f1681,plain,
( sK2 = unordered_pair(sK1,sK1)
| ~ spl18_44 ),
inference(backward_demodulation,[],[f272,f1643]) ).
fof(f4026,plain,
( spl18_46
| ~ spl18_4
| ~ spl18_44
| ~ spl18_45 ),
inference(avatar_split_clause,[],[f3973,f2218,f1641,f367,f2222]) ).
fof(f367,plain,
( spl18_4
<=> member(sK2,sF14) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
fof(f3973,plain,
( sF10 = sF12
| ~ spl18_4
| ~ spl18_44
| ~ spl18_45 ),
inference(forward_demodulation,[],[f3964,f271]) ).
fof(f3964,plain,
( unordered_pair(sK0,sK0) = sF12
| ~ spl18_4
| ~ spl18_44
| ~ spl18_45 ),
inference(backward_demodulation,[],[f1682,f2331]) ).
fof(f2331,plain,
( sK0 = sK2
| ~ spl18_4
| ~ spl18_45 ),
inference(resolution,[],[f2229,f484]) ).
fof(f2229,plain,
( member(sK2,sF10)
| ~ spl18_4
| ~ spl18_45 ),
inference(backward_demodulation,[],[f369,f2220]) ).
fof(f369,plain,
( member(sK2,sF14)
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f1682,plain,
( sF12 = unordered_pair(sK0,sK2)
| ~ spl18_44 ),
inference(backward_demodulation,[],[f273,f1643]) ).
fof(f3767,plain,
( spl18_27
| ~ spl18_46 ),
inference(avatar_contradiction_clause,[],[f3766]) ).
fof(f3766,plain,
( $false
| spl18_27
| ~ spl18_46 ),
inference(subsumption_resolution,[],[f3761,f3441]) ).
fof(f3441,plain,
( sF10 != sF16
| spl18_27
| ~ spl18_46 ),
inference(backward_demodulation,[],[f765,f2224]) ).
fof(f3761,plain,
( sF10 = sF16
| ~ spl18_46 ),
inference(resolution,[],[f3504,f306]) ).
fof(f306,plain,
member(sF16,sF13),
inference(subsumption_resolution,[],[f301,f287]) ).
fof(f287,plain,
member(sF16,universal_class),
inference(superposition,[],[f164,f277]) ).
fof(f301,plain,
( member(sF16,sF13)
| ~ member(sF16,universal_class) ),
inference(superposition,[],[f269,f288]) ).
fof(f3504,plain,
( ! [X0] :
( ~ member(X0,sF13)
| sF10 = X0 )
| ~ spl18_46 ),
inference(duplicate_literal_removal,[],[f3459]) ).
fof(f3459,plain,
( ! [X0] :
( ~ member(X0,sF13)
| sF10 = X0
| sF10 = X0 )
| ~ spl18_46 ),
inference(superposition,[],[f207,f3440]) ).
fof(f3440,plain,
( sF13 = unordered_pair(sF10,sF10)
| ~ spl18_46 ),
inference(backward_demodulation,[],[f274,f2224]) ).
fof(f2796,plain,
( ~ spl18_3
| ~ spl18_27
| spl18_43
| ~ spl18_44
| ~ spl18_46 ),
inference(avatar_contradiction_clause,[],[f2795]) ).
fof(f2795,plain,
( $false
| ~ spl18_3
| ~ spl18_27
| spl18_43
| ~ spl18_44
| ~ spl18_46 ),
inference(subsumption_resolution,[],[f2776,f2669]) ).
fof(f2776,plain,
( sK0 != sK2
| ~ spl18_27
| spl18_43
| ~ spl18_44
| ~ spl18_46 ),
inference(backward_demodulation,[],[f1698,f2668]) ).
fof(f1698,plain,
( sK2 != sF15
| spl18_43
| ~ spl18_44 ),
inference(backward_demodulation,[],[f1638,f1643]) ).
fof(f1638,plain,
( sF11 != sF15
| spl18_43 ),
inference(avatar_component_clause,[],[f1637]) ).
fof(f1637,plain,
( spl18_43
<=> sF11 = sF15 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_43])]) ).
fof(f2225,plain,
( spl18_45
| spl18_46
| ~ spl18_27 ),
inference(avatar_split_clause,[],[f2116,f764,f2222,f2218]) ).
fof(f2116,plain,
( sF10 = sF12
| sF10 = sF14
| ~ spl18_27 ),
inference(resolution,[],[f315,f1705]) ).
fof(f1705,plain,
( ! [X0] :
( ~ member(X0,sF13)
| sF12 = X0
| sF14 = X0 )
| ~ spl18_27 ),
inference(forward_demodulation,[],[f773,f766]) ).
fof(f773,plain,
! [X0] :
( ~ member(X0,sF13)
| sF14 = X0
| sF16 = X0 ),
inference(superposition,[],[f207,f288]) ).
fof(f1672,plain,
( ~ spl18_12
| ~ spl18_16
| ~ spl18_43 ),
inference(avatar_contradiction_clause,[],[f1671]) ).
fof(f1671,plain,
( $false
| ~ spl18_12
| ~ spl18_16
| ~ spl18_43 ),
inference(subsumption_resolution,[],[f1670,f139]) ).
fof(f139,plain,
sK1 != sK3,
inference(cnf_transformation,[],[f88]) ).
fof(f1670,plain,
( sK1 = sK3
| ~ spl18_12
| ~ spl18_16
| ~ spl18_43 ),
inference(forward_demodulation,[],[f1656,f558]) ).
fof(f558,plain,
( sK1 = sK4(sF11)
| ~ spl18_16 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f556,plain,
( spl18_16
<=> sK1 = sK4(sF11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).
fof(f1656,plain,
( sK3 = sK4(sF11)
| ~ spl18_12
| ~ spl18_43 ),
inference(backward_demodulation,[],[f505,f1639]) ).
fof(f1639,plain,
( sF11 = sF15
| ~ spl18_43 ),
inference(avatar_component_clause,[],[f1637]) ).
fof(f505,plain,
( sK3 = sK4(sF15)
| ~ spl18_12 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f503,plain,
( spl18_12
<=> sK3 = sK4(sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).
fof(f1644,plain,
( spl18_43
| spl18_44
| ~ spl18_27 ),
inference(avatar_split_clause,[],[f1627,f764,f1641,f1637]) ).
fof(f1627,plain,
( sK2 = sF11
| sF11 = sF15
| ~ spl18_27 ),
inference(resolution,[],[f1152,f302]) ).
fof(f1152,plain,
( ! [X0] :
( ~ member(X0,sF12)
| sK2 = X0
| sF15 = X0 )
| ~ spl18_27 ),
inference(superposition,[],[f207,f1147]) ).
fof(f1147,plain,
( sF12 = unordered_pair(sK2,sF15)
| ~ spl18_27 ),
inference(backward_demodulation,[],[f277,f766]) ).
fof(f1114,plain,
~ spl18_28,
inference(avatar_contradiction_clause,[],[f1113]) ).
fof(f1113,plain,
( $false
| ~ spl18_28 ),
inference(subsumption_resolution,[],[f1109,f142]) ).
fof(f1109,plain,
( member(sF11,null_class)
| ~ spl18_28 ),
inference(backward_demodulation,[],[f302,f770]) ).
fof(f770,plain,
( null_class = sF12
| ~ spl18_28 ),
inference(avatar_component_clause,[],[f768]) ).
fof(f768,plain,
( spl18_28
<=> null_class = sF12 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_28])]) ).
fof(f795,plain,
( spl18_3
| spl18_13
| ~ spl18_14 ),
inference(avatar_contradiction_clause,[],[f794]) ).
fof(f794,plain,
( $false
| spl18_3
| spl18_13
| ~ spl18_14 ),
inference(subsumption_resolution,[],[f793,f527]) ).
fof(f527,plain,
( null_class != sF14
| spl18_13 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f526,plain,
( spl18_13
<=> null_class = sF14 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).
fof(f793,plain,
( null_class = sF14
| spl18_3
| ~ spl18_14 ),
inference(subsumption_resolution,[],[f788,f365]) ).
fof(f365,plain,
( ~ member(sK2,universal_class)
| spl18_3 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f788,plain,
( member(sK2,universal_class)
| null_class = sF14
| ~ spl18_14 ),
inference(superposition,[],[f150,f532]) ).
fof(f532,plain,
( sK2 = sK4(sF14)
| ~ spl18_14 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f530,plain,
( spl18_14
<=> sK2 = sK4(sF14) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).
fof(f150,plain,
! [X0] :
( member(sK4(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( disjoint(sK4(X0),X0)
& member(sK4(X0),X0)
& member(sK4(X0),universal_class) )
| null_class = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f74,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
=> ( disjoint(sK4(X0),X0)
& member(sK4(X0),X0)
& member(sK4(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
| null_class = X0 ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( null_class != X0
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( null_class != X0
=> ? [X2] :
( disjoint(X2,X0)
& member(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox/tmp/tmp.66j9hncaj9/Vampire---4.8_17191',regularity) ).
fof(f771,plain,
( spl18_27
| spl18_28
| ~ spl18_13 ),
inference(avatar_split_clause,[],[f758,f526,f768,f764]) ).
fof(f758,plain,
( null_class = sF12
| sF12 = sF16
| ~ spl18_13 ),
inference(resolution,[],[f540,f305]) ).
fof(f540,plain,
( ! [X0] :
( ~ member(X0,sF13)
| null_class = X0
| sF16 = X0 )
| ~ spl18_13 ),
inference(superposition,[],[f207,f537]) ).
fof(f537,plain,
( sF13 = unordered_pair(null_class,sF16)
| ~ spl18_13 ),
inference(backward_demodulation,[],[f288,f528]) ).
fof(f528,plain,
( null_class = sF14
| ~ spl18_13 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f567,plain,
~ spl18_15,
inference(avatar_contradiction_clause,[],[f566]) ).
fof(f566,plain,
( $false
| ~ spl18_15 ),
inference(subsumption_resolution,[],[f562,f142]) ).
fof(f562,plain,
( member(sK1,null_class)
| ~ spl18_15 ),
inference(backward_demodulation,[],[f303,f554]) ).
fof(f554,plain,
( null_class = sF11
| ~ spl18_15 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f559,plain,
( spl18_15
| spl18_16 ),
inference(avatar_split_clause,[],[f491,f556,f552]) ).
fof(f491,plain,
( sK1 = sK4(sF11)
| null_class = sF11 ),
inference(resolution,[],[f483,f151]) ).
fof(f151,plain,
! [X0] :
( member(sK4(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f483,plain,
! [X2] :
( ~ member(X2,sF11)
| sK1 = X2 ),
inference(duplicate_literal_removal,[],[f475]) ).
fof(f475,plain,
! [X2] :
( ~ member(X2,sF11)
| sK1 = X2
| sK1 = X2 ),
inference(superposition,[],[f207,f272]) ).
fof(f533,plain,
( spl18_13
| spl18_14 ),
inference(avatar_split_clause,[],[f487,f530,f526]) ).
fof(f487,plain,
( sK2 = sK4(sF14)
| null_class = sF14 ),
inference(resolution,[],[f482,f151]) ).
fof(f482,plain,
! [X3] :
( ~ member(X3,sF14)
| sK2 = X3 ),
inference(duplicate_literal_removal,[],[f476]) ).
fof(f476,plain,
! [X3] :
( ~ member(X3,sF14)
| sK2 = X3
| sK2 = X3 ),
inference(superposition,[],[f207,f275]) ).
fof(f506,plain,
( spl18_11
| spl18_12 ),
inference(avatar_split_clause,[],[f485,f503,f499]) ).
fof(f485,plain,
( sK3 = sK4(sF15)
| null_class = sF15 ),
inference(resolution,[],[f481,f151]) ).
fof(f481,plain,
! [X5] :
( ~ member(X5,sF15)
| sK3 = X5 ),
inference(duplicate_literal_removal,[],[f478]) ).
fof(f478,plain,
! [X5] :
( ~ member(X5,sF15)
| sK3 = X5
| sK3 = X5 ),
inference(superposition,[],[f207,f276]) ).
fof(f370,plain,
( ~ spl18_3
| spl18_4 ),
inference(avatar_split_clause,[],[f297,f367,f363]) ).
fof(f297,plain,
( member(sK2,sF14)
| ~ member(sK2,universal_class) ),
inference(superposition,[],[f269,f275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : SET018+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.11/0.17 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.37 % Computer : n001.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sat Aug 26 11:32:00 EDT 2023
% 0.13/0.37 % CPUTime :
% 0.13/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.66j9hncaj9/Vampire---4.8_17191
% 0.13/0.38 % (17321)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.43 % (17325)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)
% 0.17/0.43 % (17326)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)
% 0.17/0.43 % (17324)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)
% 0.17/0.43 % (17327)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.17/0.43 % (17323)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)
% 0.17/0.43 % (17322)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)
% 0.17/0.45 % (17328)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)
% 0.17/0.62 % (17327)First to succeed.
% 0.17/0.62 % (17327)Refutation found. Thanks to Tanya!
% 0.17/0.62 % SZS status Theorem for Vampire---4
% 0.17/0.62 % SZS output start Proof for Vampire---4
% See solution above
% 0.17/0.62 % (17327)------------------------------
% 0.17/0.62 % (17327)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.17/0.62 % (17327)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.17/0.62 % (17327)Termination reason: Refutation
% 0.17/0.62
% 0.17/0.62 % (17327)Memory used [KB]: 7547
% 0.17/0.62 % (17327)Time elapsed: 0.186 s
% 0.17/0.62 % (17327)------------------------------
% 0.17/0.62 % (17327)------------------------------
% 0.17/0.62 % (17321)Success in time 0.243 s
% 0.17/0.62 % Vampire---4.8 exiting
%------------------------------------------------------------------------------