TSTP Solution File: SET980+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : n024.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 : Sat Sep 2 00:05:56 EDT 2023
% Result : Theorem 0.18s 0.53s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 55
% Syntax : Number of formulae : 301 ( 53 unt; 0 def)
% Number of atoms : 779 ( 197 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 870 ( 392 ~; 393 |; 33 &)
% ( 42 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 42 ( 40 usr; 39 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 254 (; 232 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f632,plain,
$false,
inference(avatar_smt_refutation,[],[f60,f65,f70,f75,f80,f89,f94,f107,f120,f121,f141,f143,f210,f225,f235,f242,f254,f263,f275,f283,f295,f307,f314,f342,f349,f350,f351,f358,f382,f394,f402,f403,f410,f466,f498,f500,f502,f504,f506,f508,f539,f544,f545,f546,f551,f552,f555,f560,f561,f562,f568,f576,f625,f631]) ).
fof(f631,plain,
( spl8_6
| ~ spl8_17
| ~ spl8_38 ),
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f630,plain,
( $false
| spl8_6
| ~ spl8_17
| ~ spl8_38 ),
inference(subsumption_resolution,[],[f629,f624]) ).
fof(f624,plain,
( in(sK5(sK0,sK2),sK0)
| ~ spl8_38 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f622,plain,
( spl8_38
<=> in(sK5(sK0,sK2),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
fof(f629,plain,
( ~ in(sK5(sK0,sK2),sK0)
| spl8_6
| ~ spl8_17
| ~ spl8_38 ),
inference(subsumption_resolution,[],[f626,f84]) ).
fof(f84,plain,
( sK0 != sK2
| spl8_6 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f82,plain,
( spl8_6
<=> sK0 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
fof(f626,plain,
( sK0 = sK2
| ~ in(sK5(sK0,sK2),sK0)
| ~ spl8_17
| ~ spl8_38 ),
inference(resolution,[],[f624,f366]) ).
fof(f366,plain,
( ! [X2] :
( ~ in(sK5(X2,sK2),sK0)
| sK2 = X2
| ~ in(sK5(X2,sK2),X2) )
| ~ spl8_17 ),
inference(resolution,[],[f238,f47]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| X0 = X1
| ~ in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) )
& ( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f24,f25]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) )
& ( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',t2_tarski) ).
fof(f238,plain,
( ! [X11] :
( in(X11,sK2)
| ~ in(X11,sK0) )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f237,plain,
( spl8_17
<=> ! [X11] :
( ~ in(X11,sK0)
| in(X11,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
fof(f625,plain,
( spl8_38
| spl8_6
| ~ spl8_26 ),
inference(avatar_split_clause,[],[f620,f377,f82,f622]) ).
fof(f377,plain,
( spl8_26
<=> ! [X7] :
( ~ in(X7,sK2)
| in(X7,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
fof(f620,plain,
( in(sK5(sK0,sK2),sK0)
| spl8_6
| ~ spl8_26 ),
inference(subsumption_resolution,[],[f612,f84]) ).
fof(f612,plain,
( in(sK5(sK0,sK2),sK0)
| sK0 = sK2
| ~ spl8_26 ),
inference(factoring,[],[f414]) ).
fof(f414,plain,
( ! [X2] :
( in(sK5(X2,sK2),sK0)
| in(sK5(X2,sK2),X2)
| sK2 = X2 )
| ~ spl8_26 ),
inference(resolution,[],[f378,f46]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f378,plain,
( ! [X7] :
( ~ in(X7,sK2)
| in(X7,sK0) )
| ~ spl8_26 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f576,plain,
( ~ spl8_37
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f570,f565,f573]) ).
fof(f573,plain,
( spl8_37
<=> in(sK1,sK5(sK1,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).
fof(f565,plain,
( spl8_36
<=> in(sK5(sK1,sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).
fof(f570,plain,
( ~ in(sK1,sK5(sK1,sK1))
| ~ spl8_36 ),
inference(resolution,[],[f567,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',antisymmetry_r2_hidden) ).
fof(f567,plain,
( in(sK5(sK1,sK1),sK1)
| ~ spl8_36 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f568,plain,
( spl8_36
| ~ spl8_7
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f563,f463,f86,f565]) ).
fof(f86,plain,
( spl8_7
<=> sK1 = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
fof(f463,plain,
( spl8_30
<=> in(sK5(sK1,sK3),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).
fof(f563,plain,
( in(sK5(sK1,sK1),sK1)
| ~ spl8_7
| ~ spl8_30 ),
inference(forward_demodulation,[],[f465,f87]) ).
fof(f87,plain,
( sK1 = sK3
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f465,plain,
( in(sK5(sK1,sK3),sK1)
| ~ spl8_30 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f562,plain,
( ~ spl8_35
| ~ spl8_34 ),
inference(avatar_split_clause,[],[f553,f548,f557]) ).
fof(f557,plain,
( spl8_35
<=> in(sK1,sK4(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).
fof(f548,plain,
( spl8_34
<=> in(sK4(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).
fof(f553,plain,
( ~ in(sK1,sK4(sK1))
| ~ spl8_34 ),
inference(resolution,[],[f550,f45]) ).
fof(f550,plain,
( in(sK4(sK1),sK1)
| ~ spl8_34 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f561,plain,
( ~ spl8_35
| ~ spl8_7
| spl8_25 ),
inference(avatar_split_clause,[],[f518,f355,f86,f557]) ).
fof(f355,plain,
( spl8_25
<=> in(sK1,sK4(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
fof(f518,plain,
( ~ in(sK1,sK4(sK1))
| ~ spl8_7
| spl8_25 ),
inference(superposition,[],[f357,f87]) ).
fof(f357,plain,
( ~ in(sK1,sK4(sK3))
| spl8_25 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f560,plain,
( ~ spl8_35
| ~ spl8_7
| spl8_25 ),
inference(avatar_split_clause,[],[f477,f355,f86,f557]) ).
fof(f477,plain,
( ~ in(sK1,sK4(sK1))
| ~ spl8_7
| spl8_25 ),
inference(superposition,[],[f357,f87]) ).
fof(f555,plain,
( spl8_31
| ~ spl8_7
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f468,f91,f86,f495]) ).
fof(f495,plain,
( spl8_31
<=> cartesian_product2(sK0,sK1) = cartesian_product2(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
fof(f91,plain,
( spl8_8
<=> cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
fof(f468,plain,
( cartesian_product2(sK0,sK1) = cartesian_product2(sK2,sK1)
| ~ spl8_7
| ~ spl8_8 ),
inference(superposition,[],[f93,f87]) ).
fof(f93,plain,
( cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1)
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f552,plain,
( spl8_34
| ~ spl8_7
| ~ spl8_24 ),
inference(avatar_split_clause,[],[f517,f292,f86,f548]) ).
fof(f292,plain,
( spl8_24
<=> in(sK4(sK3),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
fof(f517,plain,
( in(sK4(sK1),sK1)
| ~ spl8_7
| ~ spl8_24 ),
inference(superposition,[],[f294,f87]) ).
fof(f294,plain,
( in(sK4(sK3),sK1)
| ~ spl8_24 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f551,plain,
( spl8_34
| ~ spl8_7
| ~ spl8_24 ),
inference(avatar_split_clause,[],[f476,f292,f86,f548]) ).
fof(f476,plain,
( in(sK4(sK1),sK1)
| ~ spl8_7
| ~ spl8_24 ),
inference(superposition,[],[f294,f87]) ).
fof(f546,plain,
( ~ spl8_33
| ~ spl8_7
| spl8_21 ),
inference(avatar_split_clause,[],[f515,f260,f86,f541]) ).
fof(f541,plain,
( spl8_33
<=> in(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).
fof(f260,plain,
( spl8_21
<=> in(sK3,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
fof(f515,plain,
( ~ in(sK1,sK0)
| ~ spl8_7
| spl8_21 ),
inference(superposition,[],[f262,f87]) ).
fof(f262,plain,
( ~ in(sK3,sK0)
| spl8_21 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f545,plain,
( ~ spl8_32
| ~ spl8_7
| spl8_16 ),
inference(avatar_split_clause,[],[f514,f232,f86,f536]) ).
fof(f536,plain,
( spl8_32
<=> in(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).
fof(f232,plain,
( spl8_16
<=> in(sK3,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
fof(f514,plain,
( ~ in(sK1,sK1)
| ~ spl8_7
| spl8_16 ),
inference(superposition,[],[f234,f87]) ).
fof(f234,plain,
( ~ in(sK3,sK1)
| spl8_16 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f544,plain,
( ~ spl8_33
| ~ spl8_7
| spl8_21 ),
inference(avatar_split_clause,[],[f474,f260,f86,f541]) ).
fof(f474,plain,
( ~ in(sK1,sK0)
| ~ spl8_7
| spl8_21 ),
inference(superposition,[],[f262,f87]) ).
fof(f539,plain,
( ~ spl8_32
| ~ spl8_7
| spl8_16 ),
inference(avatar_split_clause,[],[f473,f232,f86,f536]) ).
fof(f473,plain,
( ~ in(sK1,sK1)
| ~ spl8_7
| spl8_16 ),
inference(superposition,[],[f234,f87]) ).
fof(f508,plain,
( spl8_7
| ~ spl8_15
| ~ spl8_23 ),
inference(avatar_contradiction_clause,[],[f507]) ).
fof(f507,plain,
( $false
| spl8_7
| ~ spl8_15
| ~ spl8_23 ),
inference(global_subsumption,[],[f39,f54,f55,f36,f37,f42,f38,f35,f40,f45,f41,f43,f95,f49,f50,f44,f123,f124,f126,f127,f128,f51,f130,f132,f52,f48,f122,f154,f155,f157,f158,f159,f160,f125,f161,f162,f163,f164,f165,f166,f167,f156,f170,f171,f172,f173,f174,f175,f176,f46,f178,f183,f180,f182,f185,f47,f53,f199,f209,f226,f230,f200,f286,f287,f288,f289,f285,f227,f274,f372,f177,f369,f371,f179,f417,f420,f228,f370,f448,f452,f467,f461,f88]) ).
fof(f88,plain,
( sK1 != sK3
| spl8_7 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f461,plain,
( in(sK5(sK1,sK3),sK1)
| spl8_7
| ~ spl8_23 ),
inference(subsumption_resolution,[],[f456,f88]) ).
fof(f456,plain,
( in(sK5(sK1,sK3),sK1)
| sK1 = sK3
| ~ spl8_23 ),
inference(factoring,[],[f370]) ).
fof(f467,plain,
( sK1 = sK3
| ~ spl8_15
| ~ spl8_23 ),
inference(subsumption_resolution,[],[f456,f228]) ).
fof(f452,plain,
( ! [X0] :
( in(sK5(X0,sK3),sK1)
| sK3 = X0
| ~ in(X0,sK5(X0,sK3)) )
| ~ spl8_23 ),
inference(resolution,[],[f370,f45]) ).
fof(f448,plain,
( ! [X1] :
( in(sK5(X1,sK3),X1)
| sK3 = X1
| ~ in(sK1,sK5(X1,sK3)) )
| ~ spl8_23 ),
inference(resolution,[],[f370,f45]) ).
fof(f370,plain,
( ! [X2] :
( in(sK5(X2,sK3),sK1)
| in(sK5(X2,sK3),X2)
| sK3 = X2 )
| ~ spl8_23 ),
inference(resolution,[],[f274,f46]) ).
fof(f228,plain,
( ! [X2] :
( ~ in(sK5(X2,sK3),sK1)
| sK3 = X2
| ~ in(sK5(X2,sK3),X2) )
| ~ spl8_15 ),
inference(resolution,[],[f209,f47]) ).
fof(f420,plain,
( ! [X0] :
( ~ in(sK1,sK5(sK3,X0))
| empty_set != X0
| sK3 = X0 )
| ~ spl8_23 ),
inference(resolution,[],[f371,f45]) ).
fof(f417,plain,
( ! [X0] :
( ~ in(sK1,sK5(X0,sK3))
| empty_set != X0
| sK3 = X0 )
| ~ spl8_23 ),
inference(resolution,[],[f369,f45]) ).
fof(f179,plain,
! [X0,X1] :
( ~ in(X0,sK5(X0,X1))
| X0 = X1
| in(sK5(X0,X1),X1) ),
inference(resolution,[],[f46,f45]) ).
fof(f371,plain,
( ! [X3] :
( in(sK5(sK3,X3),sK1)
| sK3 = X3
| empty_set != X3 )
| ~ spl8_23 ),
inference(resolution,[],[f274,f178]) ).
fof(f369,plain,
( ! [X1] :
( in(sK5(X1,sK3),sK1)
| sK3 = X1
| empty_set != X1 )
| ~ spl8_23 ),
inference(resolution,[],[f274,f180]) ).
fof(f177,plain,
! [X0,X1] :
( ~ in(X1,sK5(X0,X1))
| X0 = X1
| in(sK5(X0,X1),X0) ),
inference(resolution,[],[f46,f45]) ).
fof(f372,plain,
( ! [X4] :
( in(sK5(sK3,X4),sK1)
| in(sK5(sK3,X4),X4)
| sK3 = X4 )
| ~ spl8_23 ),
inference(resolution,[],[f274,f46]) ).
fof(f274,plain,
( ! [X4] :
( ~ in(X4,sK3)
| in(X4,sK1) )
| ~ spl8_23 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f273,plain,
( spl8_23
<=> ! [X4] :
( ~ in(X4,sK3)
| in(X4,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
fof(f227,plain,
( ! [X1] :
( ~ in(X1,sK1)
| empty_set != sK3 )
| ~ spl8_15 ),
inference(resolution,[],[f209,f40]) ).
fof(f285,plain,
( in(sK4(sK3),sK1)
| empty_set = sK3
| ~ spl8_23 ),
inference(resolution,[],[f274,f41]) ).
fof(f289,plain,
( ! [X4] :
( in(sK5(sK3,X4),sK1)
| in(sK5(sK3,X4),X4)
| sK3 = X4 )
| ~ spl8_23 ),
inference(resolution,[],[f274,f46]) ).
fof(f288,plain,
( ! [X3] :
( in(sK5(sK3,X3),sK1)
| sK3 = X3
| empty_set != X3 )
| ~ spl8_23 ),
inference(resolution,[],[f274,f178]) ).
fof(f287,plain,
( ! [X2] :
( in(sK5(X2,sK3),sK1)
| in(sK5(X2,sK3),X2)
| sK3 = X2 )
| ~ spl8_23 ),
inference(resolution,[],[f274,f46]) ).
fof(f286,plain,
( ! [X1] :
( in(sK5(X1,sK3),sK1)
| sK3 = X1
| empty_set != X1 )
| ~ spl8_23 ),
inference(resolution,[],[f274,f180]) ).
fof(f200,plain,
! [X18,X19,X16,X17] :
( empty_set != cartesian_product2(X19,X17)
| ~ in(X18,X19)
| ~ in(X16,X17) ),
inference(resolution,[],[f53,f40]) ).
fof(f230,plain,
( ~ in(sK3,sK1)
| ~ spl8_15 ),
inference(duplicate_literal_removal,[],[f229]) ).
fof(f229,plain,
( ~ in(sK3,sK1)
| ~ in(sK3,sK1)
| ~ spl8_15 ),
inference(resolution,[],[f226,f209]) ).
fof(f226,plain,
( ! [X0] :
( ~ in(sK3,X0)
| ~ in(X0,sK1) )
| ~ spl8_15 ),
inference(resolution,[],[f209,f45]) ).
fof(f209,plain,
( ! [X8] :
( in(X8,sK3)
| ~ in(X8,sK1) )
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f208,plain,
( spl8_15
<=> ! [X8] :
( ~ in(X8,sK1)
| in(X8,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
fof(f199,plain,
! [X14,X15,X12,X13] :
( ~ in(cartesian_product2(X15,X13),ordered_pair(X14,X12))
| ~ in(X14,X15)
| ~ in(X12,X13) ),
inference(resolution,[],[f53,f45]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',l55_zfmisc_1) ).
fof(f185,plain,
! [X0,X1] :
( ~ in(X1,sK5(X0,X1))
| empty_set != X0
| X0 = X1 ),
inference(resolution,[],[f180,f45]) ).
fof(f182,plain,
! [X0,X1] :
( ~ in(X0,sK5(X0,X1))
| empty_set != X1
| X0 = X1 ),
inference(resolution,[],[f178,f45]) ).
fof(f180,plain,
! [X2,X3] :
( in(sK5(X2,X3),X3)
| X2 = X3
| empty_set != X2 ),
inference(resolution,[],[f46,f40]) ).
fof(f183,plain,
! [X2,X3] :
( empty_set != X3
| X2 = X3
| empty_set != X2 ),
inference(resolution,[],[f178,f40]) ).
fof(f178,plain,
! [X2,X3] :
( in(sK5(X2,X3),X2)
| X2 = X3
| empty_set != X3 ),
inference(resolution,[],[f46,f40]) ).
fof(f176,plain,
! [X6,X5] : ordered_pair(singleton(X5),unordered_pair(X6,X5)) = unordered_pair(ordered_pair(X5,X6),singleton(singleton(X5))),
inference(superposition,[],[f44,f156]) ).
fof(f175,plain,
! [X3,X4] : ordered_pair(unordered_pair(X4,X3),singleton(X3)) = unordered_pair(ordered_pair(X3,X4),singleton(unordered_pair(X4,X3))),
inference(superposition,[],[f122,f156]) ).
fof(f174,plain,
! [X2,X1] : ordered_pair(singleton(X1),unordered_pair(X2,X1)) = unordered_pair(singleton(singleton(X1)),ordered_pair(X1,X2)),
inference(superposition,[],[f125,f156]) ).
fof(f173,plain,
! [X10,X11] : ordered_pair(unordered_pair(X11,X10),singleton(X10)) = unordered_pair(singleton(unordered_pair(X11,X10)),ordered_pair(X10,X11)),
inference(superposition,[],[f156,f156]) ).
fof(f172,plain,
! [X8,X9] : ordered_pair(unordered_pair(X8,X9),singleton(X8)) = unordered_pair(singleton(unordered_pair(X8,X9)),ordered_pair(X8,X9)),
inference(superposition,[],[f156,f125]) ).
fof(f171,plain,
! [X6,X7] : ordered_pair(singleton(X7),unordered_pair(X6,X7)) = unordered_pair(singleton(singleton(X7)),ordered_pair(X7,X6)),
inference(superposition,[],[f156,f122]) ).
fof(f170,plain,
! [X4,X5] : ordered_pair(singleton(X4),unordered_pair(X4,X5)) = unordered_pair(singleton(singleton(X4)),ordered_pair(X4,X5)),
inference(superposition,[],[f156,f44]) ).
fof(f156,plain,
! [X3,X4] : unordered_pair(singleton(X4),unordered_pair(X3,X4)) = ordered_pair(X4,X3),
inference(superposition,[],[f122,f43]) ).
fof(f167,plain,
! [X2,X3] : ordered_pair(singleton(X2),unordered_pair(X2,X3)) = unordered_pair(ordered_pair(X2,X3),singleton(singleton(X2))),
inference(superposition,[],[f44,f125]) ).
fof(f166,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f122,f125]) ).
fof(f165,plain,
! [X8,X9] : ordered_pair(singleton(X8),unordered_pair(X8,X9)) = unordered_pair(singleton(singleton(X8)),ordered_pair(X8,X9)),
inference(superposition,[],[f125,f125]) ).
fof(f164,plain,
! [X6,X7] : ordered_pair(unordered_pair(X6,X7),singleton(X7)) = unordered_pair(singleton(unordered_pair(X6,X7)),ordered_pair(X7,X6)),
inference(superposition,[],[f125,f122]) ).
fof(f163,plain,
! [X4,X5] : ordered_pair(unordered_pair(X4,X5),singleton(X4)) = unordered_pair(singleton(unordered_pair(X4,X5)),ordered_pair(X4,X5)),
inference(superposition,[],[f125,f44]) ).
fof(f162,plain,
! [X2,X3] : ordered_pair(X2,X3) = unordered_pair(singleton(X2),unordered_pair(X3,X2)),
inference(superposition,[],[f125,f43]) ).
fof(f161,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f125,f43]) ).
fof(f125,plain,
! [X2,X3] : ordered_pair(X2,X3) = unordered_pair(singleton(X2),unordered_pair(X2,X3)),
inference(superposition,[],[f44,f43]) ).
fof(f160,plain,
! [X6,X5] : unordered_pair(singleton(X6),unordered_pair(X5,X6)) = ordered_pair(X6,X5),
inference(superposition,[],[f43,f122]) ).
fof(f159,plain,
! [X3,X4] : unordered_pair(singleton(X4),unordered_pair(X3,X4)) = ordered_pair(X4,X3),
inference(superposition,[],[f43,f122]) ).
fof(f158,plain,
! [X2,X1] : ordered_pair(unordered_pair(X1,X2),singleton(X2)) = unordered_pair(ordered_pair(X2,X1),singleton(unordered_pair(X1,X2))),
inference(superposition,[],[f44,f122]) ).
fof(f157,plain,
! [X6,X5] : unordered_pair(singleton(X6),unordered_pair(X5,X6)) = ordered_pair(X6,X5),
inference(superposition,[],[f122,f43]) ).
fof(f155,plain,
! [X6,X7] : ordered_pair(singleton(X7),unordered_pair(X6,X7)) = unordered_pair(ordered_pair(X7,X6),singleton(singleton(X7))),
inference(superposition,[],[f122,f122]) ).
fof(f154,plain,
! [X4,X5] : ordered_pair(singleton(X4),unordered_pair(X4,X5)) = unordered_pair(ordered_pair(X4,X5),singleton(singleton(X4))),
inference(superposition,[],[f122,f44]) ).
fof(f122,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f44,f43]) ).
fof(f48,plain,
! [X0,X1] :
( empty_set != cartesian_product2(X0,X1)
| empty_set = X0
| empty_set = X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) )
& ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) )
& ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
<=> ( empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',t113_zfmisc_1) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f30]) ).
fof(f132,plain,
! [X8,X6,X9] :
( ~ in(ordered_pair(X8,X9),empty_set)
| empty_set != X6 ),
inference(subsumption_resolution,[],[f131,f40]) ).
fof(f131,plain,
! [X8,X6,X9] :
( ~ in(ordered_pair(X8,X9),empty_set)
| in(X8,X6)
| empty_set != X6 ),
inference(superposition,[],[f51,f49]) ).
fof(f130,plain,
! [X2,X3,X4,X5] :
( ~ in(ordered_pair(X4,X5),empty_set)
| in(X4,X2)
| empty_set != X3 ),
inference(superposition,[],[f51,f50]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f128,plain,
! [X2,X3] : ordered_pair(X2,X3) = unordered_pair(singleton(X2),unordered_pair(X2,X3)),
inference(superposition,[],[f43,f44]) ).
fof(f127,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f43,f44]) ).
fof(f126,plain,
! [X4,X5] : ordered_pair(X4,X5) = unordered_pair(singleton(X4),unordered_pair(X4,X5)),
inference(superposition,[],[f44,f43]) ).
fof(f124,plain,
! [X4,X5] : ordered_pair(unordered_pair(X4,X5),singleton(X4)) = unordered_pair(ordered_pair(X4,X5),singleton(unordered_pair(X4,X5))),
inference(superposition,[],[f44,f44]) ).
fof(f123,plain,
! [X2,X3] : ordered_pair(X2,X3) = unordered_pair(unordered_pair(X3,X2),singleton(X2)),
inference(superposition,[],[f44,f43]) ).
fof(f44,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',d5_tarski) ).
fof(f50,plain,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
| empty_set != X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
| empty_set != X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f95,plain,
! [X0] :
( ~ in(X0,sK4(X0))
| empty_set = X0 ),
inference(resolution,[],[f41,f45]) ).
fof(f43,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',commutativity_k2_tarski) ).
fof(f41,plain,
! [X0] :
( in(sK4(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( ( empty_set = X0
| in(sK4(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f21,f22]) ).
fof(f22,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',d1_xboole_0) ).
fof(f40,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f35,plain,
cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ( sK1 != sK3
| sK0 != sK2 )
& empty_set != sK1
& empty_set != sK0
& cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f18]) ).
fof(f18,plain,
( ? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0
& cartesian_product2(X2,X3) = cartesian_product2(X0,X1) )
=> ( ( sK1 != sK3
| sK0 != sK2 )
& empty_set != sK1
& empty_set != sK0
& cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0
& cartesian_product2(X2,X3) = cartesian_product2(X0,X1) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0
& cartesian_product2(X2,X3) = cartesian_product2(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
=> ( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0 ) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
( cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
=> ( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',t134_zfmisc_1) ).
fof(f38,plain,
( sK1 != sK3
| sK0 != sK2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',fc1_zfmisc_1) ).
fof(f37,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f19]) ).
fof(f55,plain,
empty(sK7),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f8,f33]) ).
fof(f33,plain,
( ? [X0] : empty(X0)
=> empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f8,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',rc1_xboole_0) ).
fof(f54,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
~ empty(sK6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f9,f31]) ).
fof(f31,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK6) ),
introduced(choice_axiom,[]) ).
fof(f9,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',rc2_xboole_0) ).
fof(f39,plain,
empty(empty_set),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
empty(empty_set),
file('/export/starexec/sandbox/tmp/tmp.BInfNSvYUJ/Vampire---4.8_27675',fc1_xboole_0) ).
fof(f506,plain,
( spl8_7
| ~ spl8_15
| ~ spl8_23 ),
inference(avatar_contradiction_clause,[],[f505]) ).
fof(f505,plain,
( $false
| spl8_7
| ~ spl8_15
| ~ spl8_23 ),
inference(global_subsumption,[],[f39,f54,f55,f36,f37,f42,f38,f88,f35,f40,f45,f41,f43,f95,f49,f50,f44,f123,f124,f126,f127,f128,f51,f130,f132,f52,f48,f122,f154,f155,f157,f158,f159,f160,f125,f161,f162,f163,f164,f165,f166,f167,f156,f170,f171,f172,f173,f174,f175,f176,f46,f178,f183,f180,f182,f185,f47,f53,f199,f209,f226,f230,f200,f286,f287,f288,f289,f285,f227,f274,f372,f177,f369,f371,f179,f417,f420,f228,f370,f448,f452,f467,f461]) ).
fof(f504,plain,
( spl8_7
| ~ spl8_15
| ~ spl8_23
| ~ spl8_30 ),
inference(avatar_contradiction_clause,[],[f503]) ).
fof(f503,plain,
( $false
| spl8_7
| ~ spl8_15
| ~ spl8_23
| ~ spl8_30 ),
inference(global_subsumption,[],[f465,f39,f54,f55,f36,f37,f42,f38,f88,f35,f40,f45,f41,f43,f95,f49,f50,f44,f123,f124,f126,f127,f128,f51,f130,f132,f52,f48,f122,f154,f155,f157,f158,f159,f160,f125,f161,f162,f163,f164,f165,f166,f167,f156,f170,f171,f172,f173,f174,f175,f176,f46,f178,f183,f180,f182,f185,f47,f53,f199,f209,f226,f230,f200,f286,f287,f288,f289,f285,f227,f274,f372,f177,f369,f371,f179,f417,f420,f228,f370,f448,f452,f461,f467]) ).
fof(f502,plain,
( spl8_7
| ~ spl8_15
| ~ spl8_23
| spl8_31 ),
inference(avatar_contradiction_clause,[],[f501]) ).
fof(f501,plain,
( $false
| spl8_7
| ~ spl8_15
| ~ spl8_23
| spl8_31 ),
inference(global_subsumption,[],[f496,f39,f54,f55,f36,f37,f42,f38,f88,f35,f40,f45,f41,f43,f95,f49,f50,f44,f123,f124,f126,f127,f128,f51,f130,f132,f52,f48,f122,f154,f155,f157,f158,f159,f160,f125,f161,f162,f163,f164,f165,f166,f167,f156,f170,f171,f172,f173,f174,f175,f176,f46,f178,f183,f180,f182,f185,f47,f53,f199,f209,f226,f230,f200,f286,f287,f288,f289,f285,f227,f274,f372,f177,f369,f371,f179,f417,f420,f228,f370,f448,f452,f461,f467]) ).
fof(f496,plain,
( cartesian_product2(sK0,sK1) != cartesian_product2(sK2,sK1)
| spl8_31 ),
inference(avatar_component_clause,[],[f495]) ).
fof(f500,plain,
( spl8_7
| ~ spl8_15
| ~ spl8_23 ),
inference(avatar_contradiction_clause,[],[f499]) ).
fof(f499,plain,
( $false
| spl8_7
| ~ spl8_15
| ~ spl8_23 ),
inference(global_subsumption,[],[f39,f54,f55,f36,f37,f42,f38,f88,f35,f40,f45,f41,f43,f95,f49,f50,f44,f123,f124,f126,f127,f128,f51,f130,f132,f52,f48,f122,f154,f155,f157,f158,f159,f160,f125,f161,f162,f163,f164,f165,f166,f167,f156,f170,f171,f172,f173,f174,f175,f176,f46,f178,f183,f180,f182,f185,f47,f53,f199,f209,f226,f230,f200,f286,f287,f288,f289,f285,f227,f274,f372,f177,f369,f371,f179,f417,f420,f228,f370,f448,f452,f461,f467]) ).
fof(f498,plain,
( spl8_31
| ~ spl8_7
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f468,f91,f86,f495]) ).
fof(f466,plain,
( spl8_30
| spl8_7
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f461,f273,f86,f463]) ).
fof(f410,plain,
( ~ spl8_29
| ~ spl8_28 ),
inference(avatar_split_clause,[],[f404,f391,f407]) ).
fof(f407,plain,
( spl8_29
<=> in(sK0,sK4(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).
fof(f391,plain,
( spl8_28
<=> in(sK4(sK2),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).
fof(f404,plain,
( ~ in(sK0,sK4(sK2))
| ~ spl8_28 ),
inference(resolution,[],[f393,f45]) ).
fof(f393,plain,
( in(sK4(sK2),sK0)
| ~ spl8_28 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f403,plain,
( spl8_28
| spl8_9
| ~ spl8_26 ),
inference(avatar_split_clause,[],[f389,f377,f100,f391]) ).
fof(f100,plain,
( spl8_9
<=> empty_set = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
fof(f389,plain,
( in(sK4(sK2),sK0)
| spl8_9
| ~ spl8_26 ),
inference(subsumption_resolution,[],[f384,f102]) ).
fof(f102,plain,
( empty_set != sK2
| spl8_9 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f384,plain,
( in(sK4(sK2),sK0)
| empty_set = sK2
| ~ spl8_26 ),
inference(resolution,[],[f378,f41]) ).
fof(f402,plain,
( spl8_11
| ~ spl8_27 ),
inference(avatar_contradiction_clause,[],[f401]) ).
fof(f401,plain,
( $false
| spl8_11
| ~ spl8_27 ),
inference(subsumption_resolution,[],[f396,f119]) ).
fof(f119,plain,
( empty_set != sK3
| spl8_11 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f117,plain,
( spl8_11
<=> empty_set = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
fof(f396,plain,
( empty_set = sK3
| ~ spl8_27 ),
inference(resolution,[],[f381,f41]) ).
fof(f381,plain,
( ! [X6] : ~ in(X6,sK3)
| ~ spl8_27 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f380,plain,
( spl8_27
<=> ! [X6] : ~ in(X6,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
fof(f394,plain,
( spl8_28
| spl8_9
| ~ spl8_26 ),
inference(avatar_split_clause,[],[f389,f377,f100,f391]) ).
fof(f382,plain,
( spl8_26
| spl8_27
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f214,f91,f380,f377]) ).
fof(f214,plain,
( ! [X6,X7] :
( ~ in(X6,sK3)
| ~ in(X7,sK2)
| in(X7,sK0) )
| ~ spl8_8 ),
inference(resolution,[],[f201,f51]) ).
fof(f201,plain,
( ! [X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| ~ in(X1,sK3)
| ~ in(X0,sK2) )
| ~ spl8_8 ),
inference(superposition,[],[f53,f93]) ).
fof(f358,plain,
( ~ spl8_25
| ~ spl8_24 ),
inference(avatar_split_clause,[],[f352,f292,f355]) ).
fof(f352,plain,
( ~ in(sK1,sK4(sK3))
| ~ spl8_24 ),
inference(resolution,[],[f294,f45]) ).
fof(f351,plain,
( spl8_24
| spl8_11
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f290,f273,f117,f292]) ).
fof(f290,plain,
( in(sK4(sK3),sK1)
| spl8_11
| ~ spl8_23 ),
inference(subsumption_resolution,[],[f285,f119]) ).
fof(f350,plain,
( ~ spl8_11
| ~ spl8_8
| spl8_10 ),
inference(avatar_split_clause,[],[f115,f104,f91,f117]) ).
fof(f104,plain,
( spl8_10
<=> empty_set = cartesian_product2(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
fof(f115,plain,
( empty_set != sK3
| ~ spl8_8
| spl8_10 ),
inference(subsumption_resolution,[],[f111,f105]) ).
fof(f105,plain,
( empty_set != cartesian_product2(sK0,sK1)
| spl8_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f111,plain,
( empty_set = cartesian_product2(sK0,sK1)
| empty_set != sK3
| ~ spl8_8 ),
inference(superposition,[],[f93,f50]) ).
fof(f349,plain,
( ~ spl8_11
| ~ spl8_8
| spl8_10 ),
inference(avatar_split_clause,[],[f114,f104,f91,f117]) ).
fof(f114,plain,
( empty_set != sK3
| ~ spl8_8
| spl8_10 ),
inference(subsumption_resolution,[],[f110,f105]) ).
fof(f110,plain,
( empty_set = cartesian_product2(sK0,sK1)
| empty_set != sK3
| ~ spl8_8 ),
inference(superposition,[],[f50,f93]) ).
fof(f342,plain,
( spl8_4
| spl8_5
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f341]) ).
fof(f341,plain,
( $false
| spl8_4
| spl8_5
| ~ spl8_10 ),
inference(subsumption_resolution,[],[f340,f79]) ).
fof(f79,plain,
( empty_set != sK1
| spl8_5 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f77,plain,
( spl8_5
<=> empty_set = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f340,plain,
( empty_set = sK1
| spl8_4
| ~ spl8_10 ),
inference(subsumption_resolution,[],[f336,f74]) ).
fof(f74,plain,
( empty_set != sK0
| spl8_4 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f72,plain,
( spl8_4
<=> empty_set = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f336,plain,
( empty_set = sK0
| empty_set = sK1
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f330]) ).
fof(f330,plain,
( empty_set != empty_set
| empty_set = sK0
| empty_set = sK1
| ~ spl8_10 ),
inference(superposition,[],[f48,f106]) ).
fof(f106,plain,
( empty_set = cartesian_product2(sK0,sK1)
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f314,plain,
( spl8_5
| ~ spl8_18 ),
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f313,plain,
( $false
| spl8_5
| ~ spl8_18 ),
inference(subsumption_resolution,[],[f308,f79]) ).
fof(f308,plain,
( empty_set = sK1
| ~ spl8_18 ),
inference(resolution,[],[f241,f41]) ).
fof(f241,plain,
( ! [X10] : ~ in(X10,sK1)
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f240,plain,
( spl8_18
<=> ! [X10] : ~ in(X10,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
fof(f307,plain,
( spl8_18
| ~ spl8_11
| ~ spl8_15
| ~ spl8_23
| spl8_24 ),
inference(avatar_split_clause,[],[f304,f292,f273,f208,f117,f240]) ).
fof(f304,plain,
( ! [X0] : ~ in(X0,sK1)
| ~ spl8_11
| ~ spl8_15
| ~ spl8_23
| spl8_24 ),
inference(global_subsumption,[],[f299,f39,f54,f55,f36,f37,f42,f38,f35,f40,f45,f41,f43,f95,f49,f50,f44,f123,f124,f126,f127,f128,f51,f130,f132,f52,f48,f122,f154,f155,f157,f158,f159,f160,f125,f161,f162,f163,f164,f165,f166,f167,f156,f170,f171,f172,f173,f174,f175,f176,f46,f177,f179,f178,f183,f180,f182,f185,f47,f53,f199,f209,f228,f226,f230,f200,f274,f286,f287,f288,f289,f285,f227,f293]) ).
fof(f293,plain,
( ~ in(sK4(sK3),sK1)
| spl8_24 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f299,plain,
( ! [X0] :
( in(X0,empty_set)
| ~ in(X0,sK1) )
| ~ spl8_11
| ~ spl8_15 ),
inference(superposition,[],[f209,f118]) ).
fof(f118,plain,
( empty_set = sK3
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f295,plain,
( spl8_24
| spl8_11
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f290,f273,f117,f292]) ).
fof(f283,plain,
( spl8_9
| ~ spl8_22 ),
inference(avatar_contradiction_clause,[],[f282]) ).
fof(f282,plain,
( $false
| spl8_9
| ~ spl8_22 ),
inference(subsumption_resolution,[],[f277,f102]) ).
fof(f277,plain,
( empty_set = sK2
| ~ spl8_22 ),
inference(resolution,[],[f271,f41]) ).
fof(f271,plain,
( ! [X5] : ~ in(X5,sK2)
| ~ spl8_22 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f270,plain,
( spl8_22
<=> ! [X5] : ~ in(X5,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
fof(f275,plain,
( spl8_22
| spl8_23
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f213,f91,f273,f270]) ).
fof(f213,plain,
( ! [X4,X5] :
( ~ in(X4,sK3)
| ~ in(X5,sK2)
| in(X4,sK1) )
| ~ spl8_8 ),
inference(resolution,[],[f201,f52]) ).
fof(f263,plain,
( ~ spl8_20
| ~ spl8_21
| ~ spl8_15
| ~ spl8_17 ),
inference(avatar_split_clause,[],[f245,f237,f208,f260,f256]) ).
fof(f256,plain,
( spl8_20
<=> in(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
fof(f245,plain,
( ~ in(sK3,sK0)
| ~ in(sK2,sK1)
| ~ spl8_15
| ~ spl8_17 ),
inference(resolution,[],[f238,f226]) ).
fof(f254,plain,
( ~ spl8_19
| ~ spl8_17 ),
inference(avatar_split_clause,[],[f249,f237,f251]) ).
fof(f251,plain,
( spl8_19
<=> in(sK2,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
fof(f249,plain,
( ~ in(sK2,sK0)
| ~ spl8_17 ),
inference(duplicate_literal_removal,[],[f248]) ).
fof(f248,plain,
( ~ in(sK2,sK0)
| ~ in(sK2,sK0)
| ~ spl8_17 ),
inference(resolution,[],[f243,f238]) ).
fof(f243,plain,
( ! [X0] :
( ~ in(sK2,X0)
| ~ in(X0,sK0) )
| ~ spl8_17 ),
inference(resolution,[],[f238,f45]) ).
fof(f242,plain,
( spl8_17
| spl8_18
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f198,f91,f240,f237]) ).
fof(f198,plain,
( ! [X10,X11] :
( ~ in(X10,sK1)
| ~ in(X11,sK0)
| in(X11,sK2) )
| ~ spl8_8 ),
inference(resolution,[],[f53,f129]) ).
fof(f129,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| in(X0,sK2) )
| ~ spl8_8 ),
inference(superposition,[],[f51,f93]) ).
fof(f235,plain,
( ~ spl8_16
| ~ spl8_15 ),
inference(avatar_split_clause,[],[f230,f208,f232]) ).
fof(f225,plain,
( spl8_4
| ~ spl8_14 ),
inference(avatar_contradiction_clause,[],[f224]) ).
fof(f224,plain,
( $false
| spl8_4
| ~ spl8_14 ),
inference(subsumption_resolution,[],[f219,f74]) ).
fof(f219,plain,
( empty_set = sK0
| ~ spl8_14 ),
inference(resolution,[],[f206,f41]) ).
fof(f206,plain,
( ! [X9] : ~ in(X9,sK0)
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f205,plain,
( spl8_14
<=> ! [X9] : ~ in(X9,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
fof(f210,plain,
( spl8_14
| spl8_15
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f197,f91,f208,f205]) ).
fof(f197,plain,
( ! [X8,X9] :
( ~ in(X8,sK1)
| ~ in(X9,sK0)
| in(X8,sK3) )
| ~ spl8_8 ),
inference(resolution,[],[f53,f144]) ).
fof(f144,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| in(X1,sK3) )
| ~ spl8_8 ),
inference(superposition,[],[f52,f93]) ).
fof(f143,plain,
~ spl8_12,
inference(avatar_contradiction_clause,[],[f142]) ).
fof(f142,plain,
( $false
| ~ spl8_12 ),
inference(equality_resolution,[],[f137]) ).
fof(f137,plain,
( ! [X6] : empty_set != X6
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f136,plain,
( spl8_12
<=> ! [X6] : empty_set != X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
fof(f141,plain,
( spl8_12
| spl8_13 ),
inference(avatar_split_clause,[],[f132,f139,f136]) ).
fof(f139,plain,
( spl8_13
<=> ! [X9,X8] : ~ in(ordered_pair(X8,X9),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
fof(f121,plain,
( ~ spl8_11
| ~ spl8_8
| spl8_10 ),
inference(avatar_split_clause,[],[f115,f104,f91,f117]) ).
fof(f120,plain,
( ~ spl8_11
| ~ spl8_8
| spl8_10 ),
inference(avatar_split_clause,[],[f114,f104,f91,f117]) ).
fof(f107,plain,
( ~ spl8_9
| spl8_10
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f97,f91,f104,f100]) ).
fof(f97,plain,
( empty_set = cartesian_product2(sK0,sK1)
| empty_set != sK2
| ~ spl8_8 ),
inference(superposition,[],[f49,f93]) ).
fof(f94,plain,
spl8_8,
inference(avatar_split_clause,[],[f35,f91]) ).
fof(f89,plain,
( ~ spl8_6
| ~ spl8_7 ),
inference(avatar_split_clause,[],[f38,f86,f82]) ).
fof(f80,plain,
~ spl8_5,
inference(avatar_split_clause,[],[f37,f77]) ).
fof(f75,plain,
~ spl8_4,
inference(avatar_split_clause,[],[f36,f72]) ).
fof(f70,plain,
spl8_3,
inference(avatar_split_clause,[],[f55,f67]) ).
fof(f67,plain,
( spl8_3
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f65,plain,
~ spl8_2,
inference(avatar_split_clause,[],[f54,f62]) ).
fof(f62,plain,
( spl8_2
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f60,plain,
spl8_1,
inference(avatar_split_clause,[],[f39,f57]) ).
fof(f57,plain,
( spl8_1
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.15 % Problem : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : n024.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 : Wed Aug 30 15:45:52 EDT 2023
% 0.13/0.37 % CPUTime :
% 0.18/0.43 % (27783)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.43 % (27784)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.18/0.43 % (27786)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.18/0.43 % (27785)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.18/0.43 % (27787)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.18/0.43 % (27789)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.18/0.43 % (27790)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.18/0.44 TRYING [1]
% 0.18/0.44 TRYING [2]
% 0.18/0.44 TRYING [3]
% 0.18/0.44 % (27788)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.18/0.44 TRYING [4]
% 0.18/0.44 TRYING [1]
% 0.18/0.44 TRYING [2]
% 0.18/0.45 TRYING [5]
% 0.18/0.45 TRYING [3]
% 0.18/0.46 TRYING [4]
% 0.18/0.52 TRYING [6]
% 0.18/0.52 % (27786)First to succeed.
% 0.18/0.53 % (27786)Refutation found. Thanks to Tanya!
% 0.18/0.53 % SZS status Theorem for Vampire---4
% 0.18/0.53 % SZS output start Proof for Vampire---4
% See solution above
% 0.18/0.53 % (27786)------------------------------
% 0.18/0.53 % (27786)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.53 % (27786)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.53 % (27786)Termination reason: Refutation
% 0.18/0.53
% 0.18/0.53 % (27786)Memory used [KB]: 5756
% 0.18/0.53 % (27786)Time elapsed: 0.091 s
% 0.18/0.53 % (27786)------------------------------
% 0.18/0.53 % (27786)------------------------------
% 0.18/0.53 % (27783)Success in time 0.145 s
% 0.18/0.53 % Vampire---4.8 exiting
%------------------------------------------------------------------------------