TSTP Solution File: ITP115^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP115^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.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 : Mon May 20 22:52:21 EDT 2024
% Result : Theorem 1.08s 0.54s
% Output : Refutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 143
% Syntax : Number of formulae : 187 ( 11 unt; 131 typ; 0 def)
% Number of atoms : 574 ( 121 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 215 ( 84 ~; 70 |; 48 &; 0 @)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 245 ( 244 >; 1 *; 0 +; 0 <<)
% Number of symbols : 133 ( 130 usr; 17 con; 0-6 aty)
% Number of variables : 43 ( 0 ^ 14 !; 14 ?; 43 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
set_b: $tType ).
thf(type_def_8,type,
b: $tType ).
thf(type_def_9,type,
a: $tType ).
thf(func_def_0,type,
set_b: $tType ).
thf(func_def_1,type,
set_a: $tType ).
thf(func_def_2,type,
b: $tType ).
thf(func_def_3,type,
a: $tType ).
thf(func_def_4,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(func_def_5,type,
minus_minus_set_b: set_b > set_b > set_b ).
thf(func_def_6,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(func_def_7,type,
inf_inf_set_b: set_b > set_b > set_b ).
thf(func_def_8,type,
inf_inf_b: b > b > b ).
thf(func_def_9,type,
lower_464587817at_a_b: a > ( a > b ) > $o ).
thf(func_def_10,type,
bot_bot_a_o: a > $o ).
thf(func_def_11,type,
bot_bot_b_o: b > $o ).
thf(func_def_12,type,
bot_bot_set_a: set_a ).
thf(func_def_13,type,
bot_bot_set_b: set_b ).
thf(func_def_14,type,
bot_bot_b: b ).
thf(func_def_15,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_16,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(func_def_17,type,
ord_less_eq_b: b > b > $o ).
thf(func_def_18,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_19,type,
collect_b: ( b > $o ) > set_b ).
thf(func_def_20,type,
insert_a: a > set_a > set_a ).
thf(func_def_21,type,
insert_b: b > set_b > set_b ).
thf(func_def_22,type,
is_empty_a: set_a > $o ).
thf(func_def_23,type,
is_empty_b: set_b > $o ).
thf(func_def_24,type,
is_singleton_a: set_a > $o ).
thf(func_def_25,type,
is_singleton_b: set_b > $o ).
thf(func_def_26,type,
the_elem_a: set_a > a ).
thf(func_def_27,type,
the_elem_b: set_b > b ).
thf(func_def_28,type,
topolo1276428101open_a: set_a > $o ).
thf(func_def_29,type,
topolo1276428102open_b: set_b > $o ).
thf(func_def_30,type,
member_a: a > set_a > $o ).
thf(func_def_31,type,
member_b: b > set_b > $o ).
thf(func_def_32,type,
a2: b ).
thf(func_def_33,type,
f: a > b ).
thf(func_def_34,type,
thesis: $o ).
thf(func_def_35,type,
x0: a ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_42,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_43,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_44,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
sP0: $o ).
thf(func_def_51,type,
sP1: b > b > $o ).
thf(func_def_52,type,
sP2: b > b > b > $o ).
thf(func_def_53,type,
sP3: b > b > b > $o ).
thf(func_def_54,type,
sP4: b > b > b > $o ).
thf(func_def_55,type,
sP5: b > b > b > $o ).
thf(func_def_56,type,
sK6: set_b ).
thf(func_def_57,type,
sK7: set_b ).
thf(func_def_58,type,
sK8: set_b > set_a ).
thf(func_def_59,type,
sK9: set_a > a ).
thf(func_def_60,type,
sK10: set_a > a ).
thf(func_def_61,type,
sK11: set_b > b ).
thf(func_def_62,type,
sK12: set_b > b ).
thf(func_def_63,type,
sK13: set_b > set_a ).
thf(func_def_64,type,
sK14: set_a > a ).
thf(func_def_65,type,
sK15: set_b > b ).
thf(func_def_66,type,
sK16: set_a > a ).
thf(func_def_67,type,
sK17: set_b > b ).
thf(func_def_68,type,
sK18: b > b > set_b ).
thf(func_def_69,type,
sK19: b > b > set_b ).
thf(func_def_70,type,
sK20: b > b > set_b ).
thf(func_def_71,type,
sK21: b > b > set_b ).
thf(func_def_72,type,
sK22: set_a > set_a > a ).
thf(func_def_73,type,
sK23: set_b > set_b > b ).
thf(func_def_74,type,
sK24: set_a > a > set_a ).
thf(func_def_75,type,
sK25: set_a > a > set_a ).
thf(func_def_76,type,
sK26: set_b > b > set_b ).
thf(func_def_77,type,
sK27: set_b > b > set_b ).
thf(func_def_78,type,
sK28: ( b > b > $o ) > b ).
thf(func_def_79,type,
sK29: ( b > b > $o ) > b ).
thf(func_def_80,type,
sK30: ( b > b > $o ) > b ).
thf(func_def_81,type,
sK31: ( b > b > $o ) > b ).
thf(func_def_82,type,
sK32: ( b > b > b ) > b ).
thf(func_def_83,type,
sK33: ( b > b > b ) > b ).
thf(func_def_84,type,
sK34: ( b > b > b ) > b ).
thf(func_def_85,type,
sK35: ( b > b > b ) > b ).
thf(func_def_86,type,
sK36: ( b > b > b ) > b ).
thf(func_def_87,type,
sK37: ( b > b > b ) > b ).
thf(func_def_88,type,
sK38: ( b > b > b ) > b ).
thf(func_def_89,type,
sK39: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_90,type,
sK40: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_91,type,
sK41: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_92,type,
sK42: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_93,type,
sK43: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_94,type,
sK44: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_95,type,
sK45: ( set_a > set_a > set_a ) > set_a ).
thf(func_def_96,type,
sK46: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_97,type,
sK47: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_98,type,
sK48: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_99,type,
sK49: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_100,type,
sK50: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_101,type,
sK51: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_102,type,
sK52: ( set_b > set_b > set_b ) > set_b ).
thf(func_def_103,type,
sK53: ( b > b ) > b ).
thf(func_def_104,type,
sK54: ( b > b ) > b ).
thf(func_def_105,type,
sK55: ( b > b ) > b ).
thf(func_def_106,type,
sK56: ( b > b ) > b ).
thf(func_def_107,type,
sK57: ( b > b ) > b ).
thf(func_def_108,type,
sK58: ( b > b ) > b ).
thf(func_def_109,type,
sK59: ( b > b ) > b ).
thf(func_def_110,type,
sK60: ( b > b ) > b ).
thf(func_def_112,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_113,type,
sK62: set_b > b > set_b > b > set_b ).
thf(func_def_114,type,
sK63: set_a > a > set_a > a > set_a ).
thf(func_def_115,type,
sK64: set_b > set_b > b ).
thf(func_def_116,type,
sK65: set_b > set_b > b ).
thf(func_def_117,type,
sK66: set_a > set_a > a ).
thf(func_def_118,type,
sK67: set_a > set_a > a ).
thf(func_def_119,type,
sK68: b > b > set_b ).
thf(func_def_120,type,
sK69: b > b > set_b ).
thf(func_def_121,type,
sK70: b > b > set_b ).
thf(func_def_122,type,
sK71: set_b > b ).
thf(func_def_123,type,
sK72: set_a > a ).
thf(func_def_124,type,
sK73: set_b > b ).
thf(func_def_125,type,
sK74: set_a > a ).
thf(func_def_126,type,
sK75: ( b > $o ) > b ).
thf(func_def_127,type,
sK76: ( b > $o ) > b ).
thf(func_def_128,type,
sK77: ( a > $o ) > a ).
thf(func_def_129,type,
sK78: ( a > $o ) > a ).
thf(f2343,plain,
$false,
inference(avatar_sat_refutation,[],[f2221,f2226,f2231,f2236,f2241,f2243,f2342]) ).
thf(f2342,plain,
( ~ spl61_2
| ~ spl61_3
| ~ spl61_4
| ~ spl61_5
| ~ spl61_6 ),
inference(avatar_contradiction_clause,[],[f2341]) ).
thf(f2341,plain,
( $false
| ~ spl61_2
| ~ spl61_3
| ~ spl61_4
| ~ spl61_5
| ~ spl61_6 ),
inference(subsumption_resolution,[],[f2340,f2240]) ).
thf(f2240,plain,
( ( $true = vAPP(set_b,$o,topolo1276428102open_b,sK6) )
| ~ spl61_6 ),
inference(avatar_component_clause,[],[f2238]) ).
thf(f2238,plain,
( spl61_6
<=> ( $true = vAPP(set_b,$o,topolo1276428102open_b,sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_6])]) ).
thf(f2340,plain,
( ( $true != vAPP(set_b,$o,topolo1276428102open_b,sK6) )
| ~ spl61_2
| ~ spl61_3
| ~ spl61_4
| ~ spl61_5 ),
inference(subsumption_resolution,[],[f2339,f2235]) ).
thf(f2235,plain,
( ( $true = vAPP(set_b,$o,topolo1276428102open_b,sK7) )
| ~ spl61_5 ),
inference(avatar_component_clause,[],[f2233]) ).
thf(f2233,plain,
( spl61_5
<=> ( $true = vAPP(set_b,$o,topolo1276428102open_b,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_5])]) ).
thf(f2339,plain,
( ( $true != vAPP(set_b,$o,topolo1276428102open_b,sK7) )
| ( $true != vAPP(set_b,$o,topolo1276428102open_b,sK6) )
| ~ spl61_2
| ~ spl61_3
| ~ spl61_4 ),
inference(subsumption_resolution,[],[f2338,f2230]) ).
thf(f2230,plain,
( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),sK6) )
| ~ spl61_4 ),
inference(avatar_component_clause,[],[f2228]) ).
thf(f2228,plain,
( spl61_4
<=> ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_4])]) ).
thf(f2338,plain,
( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),sK6) )
| ( $true != vAPP(set_b,$o,topolo1276428102open_b,sK7) )
| ( $true != vAPP(set_b,$o,topolo1276428102open_b,sK6) )
| ~ spl61_2
| ~ spl61_3 ),
inference(subsumption_resolution,[],[f2337,f2225]) ).
thf(f2225,plain,
( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),sK7) )
| ~ spl61_3 ),
inference(avatar_component_clause,[],[f2223]) ).
thf(f2223,plain,
( spl61_3
<=> ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_3])]) ).
thf(f2337,plain,
( ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),sK7) )
| ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),sK6) )
| ( $true != vAPP(set_b,$o,topolo1276428102open_b,sK7) )
| ( $true != vAPP(set_b,$o,topolo1276428102open_b,sK6) )
| ~ spl61_2 ),
inference(trivial_inequality_removal,[],[f2336]) ).
thf(f2336,plain,
( ( bot_bot_set_b != bot_bot_set_b )
| ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),sK7) )
| ( $true != vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),sK6) )
| ( $true != vAPP(set_b,$o,topolo1276428102open_b,sK7) )
| ( $true != vAPP(set_b,$o,topolo1276428102open_b,sK6) )
| ~ spl61_2 ),
inference(superposition,[],[f2210,f2220]) ).
thf(f2220,plain,
( ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,sK6),sK7) )
| ~ spl61_2 ),
inference(avatar_component_clause,[],[f2218]) ).
thf(f2218,plain,
( spl61_2
<=> ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,sK6),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_2])]) ).
thf(f2210,plain,
! [X0: set_b,X1: set_b] :
( ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) != bot_bot_set_b )
| ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1) != $true )
| ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0) != $true )
| ( vAPP(set_b,$o,topolo1276428102open_b,X1) != $true )
| ( vAPP(set_b,$o,topolo1276428102open_b,X0) != $true ) ),
inference(subsumption_resolution,[],[f1318,f1317]) ).
thf(f1317,plain,
thesis != $true,
inference(cnf_transformation,[],[f901]) ).
thf(f901,plain,
thesis != $true,
inference(flattening,[],[f362]) ).
thf(f362,plain,
thesis != $true,
inference(fool_elimination,[],[f361]) ).
thf(f361,plain,
~ thesis,
inference(rectify,[],[f358]) ).
thf(f358,negated_conjecture,
~ thesis,
inference(negated_conjecture,[],[f357]) ).
thf(f357,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(f1318,plain,
! [X0: set_b,X1: set_b] :
( ( thesis = $true )
| ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) != bot_bot_set_b )
| ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1) != $true )
| ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0) != $true )
| ( vAPP(set_b,$o,topolo1276428102open_b,X1) != $true )
| ( vAPP(set_b,$o,topolo1276428102open_b,X0) != $true ) ),
inference(cnf_transformation,[],[f1035]) ).
thf(f1035,plain,
! [X0: set_b,X1: set_b] :
( ( thesis = $true )
| ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) != bot_bot_set_b )
| ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1) != $true )
| ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0) != $true )
| ( vAPP(set_b,$o,topolo1276428102open_b,X1) != $true )
| ( vAPP(set_b,$o,topolo1276428102open_b,X0) != $true ) ),
inference(flattening,[],[f1034]) ).
thf(f1034,plain,
! [X0: set_b,X1: set_b] :
( ( thesis = $true )
| ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) != bot_bot_set_b )
| ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1) != $true )
| ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0) != $true )
| ( vAPP(set_b,$o,topolo1276428102open_b,X1) != $true )
| ( vAPP(set_b,$o,topolo1276428102open_b,X0) != $true ) ),
inference(ennf_transformation,[],[f364]) ).
thf(f364,plain,
! [X0: set_b,X1: set_b] :
( ( ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) = bot_bot_set_b )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1) = $true )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X1) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X0) = $true ) )
=> ( thesis = $true ) ),
inference(fool_elimination,[],[f363]) ).
thf(f363,plain,
! [X0: set_b,X1: set_b] :
( ( ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) = bot_bot_set_b )
& vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1)
& vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0)
& vAPP(set_b,$o,topolo1276428102open_b,X1)
& vAPP(set_b,$o,topolo1276428102open_b,X0) )
=> thesis ),
inference(rectify,[],[f356]) ).
thf(f356,axiom,
! [X15: set_b,X38: set_b] :
( ( ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X15),X38) )
& vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X38)
& vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X15)
& vAPP(set_b,$o,topolo1276428102open_b,X38)
& vAPP(set_b,$o,topolo1276428102open_b,X15) )
=> thesis ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f2243,plain,
spl61_1,
inference(avatar_split_clause,[],[f2242,f2214]) ).
thf(f2214,plain,
( spl61_1
<=> ( $true = sP0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_1])]) ).
thf(f2242,plain,
$true = sP0,
inference(subsumption_resolution,[],[f1358,f1319]) ).
thf(f1319,plain,
a2 != vAPP(a,b,f,x0),
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
a2 != vAPP(a,b,f,x0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062) ).
thf(f1358,plain,
( ( $true = sP0 )
| ( a2 = vAPP(a,b,f,x0) ) ),
inference(cnf_transformation,[],[f1236]) ).
thf(f1236,plain,
( ( $true = sP0 )
| ( a2 = vAPP(a,b,f,x0) ) ),
inference(definition_folding,[],[f1036,f1235]) ).
thf(f1235,plain,
( ? [X0: set_b,X1: set_b] :
( ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) = bot_bot_set_b )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1) = $true )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X1) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X0) = $true ) )
| ( $true != sP0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1036,plain,
( ? [X0: set_b,X1: set_b] :
( ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) = bot_bot_set_b )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1) = $true )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X1) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X0) = $true ) )
| ( a2 = vAPP(a,b,f,x0) ) ),
inference(ennf_transformation,[],[f428]) ).
thf(f428,plain,
( ( a2 != vAPP(a,b,f,x0) )
=> ? [X0: set_b,X1: set_b] :
( ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) = bot_bot_set_b )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1) = $true )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X1) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X0) = $true ) ) ),
inference(fool_elimination,[],[f427]) ).
thf(f427,plain,
( ( a2 != vAPP(a,b,f,x0) )
=> ? [X0: set_b,X1: set_b] :
( ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) = bot_bot_set_b )
& vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1)
& vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0)
& vAPP(set_b,$o,topolo1276428102open_b,X1)
& vAPP(set_b,$o,topolo1276428102open_b,X0) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( ( a2 != vAPP(a,b,f,x0) )
=> ? [X0: set_b,X1: set_b] :
( ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) = bot_bot_set_b )
& vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1)
& vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0)
& vAPP(set_b,$o,topolo1276428102open_b,X1)
& vAPP(set_b,$o,topolo1276428102open_b,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062) ).
thf(f2241,plain,
( ~ spl61_1
| spl61_6 ),
inference(avatar_split_clause,[],[f1353,f2238,f2214]) ).
thf(f1353,plain,
( ( $true = vAPP(set_b,$o,topolo1276428102open_b,sK6) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f1246]) ).
thf(f1246,plain,
( ( ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,sK6),sK7) )
& ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),sK7) )
& ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),sK6) )
& ( $true = vAPP(set_b,$o,topolo1276428102open_b,sK7) )
& ( $true = vAPP(set_b,$o,topolo1276428102open_b,sK6) ) )
| ( $true != sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f1244,f1245]) ).
thf(f1245,plain,
( ? [X0: set_b,X1: set_b] :
( ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) = bot_bot_set_b )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1) = $true )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X1) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X0) = $true ) )
=> ( ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,sK6),sK7) )
& ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),sK7) )
& ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),sK6) )
& ( $true = vAPP(set_b,$o,topolo1276428102open_b,sK7) )
& ( $true = vAPP(set_b,$o,topolo1276428102open_b,sK6) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1244,plain,
( ? [X0: set_b,X1: set_b] :
( ( vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,X0),X1) = bot_bot_set_b )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),X1) = $true )
& ( vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),X0) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X1) = $true )
& ( vAPP(set_b,$o,topolo1276428102open_b,X0) = $true ) )
| ( $true != sP0 ) ),
inference(nnf_transformation,[],[f1235]) ).
thf(f2236,plain,
( ~ spl61_1
| spl61_5 ),
inference(avatar_split_clause,[],[f1354,f2233,f2214]) ).
thf(f1354,plain,
( ( $true = vAPP(set_b,$o,topolo1276428102open_b,sK7) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f1246]) ).
thf(f2231,plain,
( ~ spl61_1
| spl61_4 ),
inference(avatar_split_clause,[],[f1355,f2228,f2214]) ).
thf(f1355,plain,
( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,vAPP(a,b,f,x0)),sK6) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f1246]) ).
thf(f2226,plain,
( ~ spl61_1
| spl61_3 ),
inference(avatar_split_clause,[],[f1356,f2223,f2214]) ).
thf(f1356,plain,
( ( $true = vAPP(set_b,$o,vAPP(b,sTfun(set_b,$o),member_b,a2),sK7) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f1246]) ).
thf(f2221,plain,
( ~ spl61_1
| spl61_2 ),
inference(avatar_split_clause,[],[f1357,f2218,f2214]) ).
thf(f1357,plain,
( ( bot_bot_set_b = vAPP(set_b,set_b,vAPP(set_b,sTfun(set_b,set_b),inf_inf_set_b,sK6),sK7) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f1246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ITP115^1 : TPTP v8.2.0. Released v7.5.0.
% 0.08/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.37 % Computer : n012.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Sat May 18 16:01:08 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.16/0.38 % (5041)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.41 % (5044)WARNING: value z3 for option sas not known
% 0.23/0.42 % (5048)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 theBenchmark for (497ds/0Mi)
% 0.23/0.42 % (5043)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.42 % (5042)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.42 % (5045)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.42 % (5046)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 theBenchmark for (531ds/0Mi)
% 0.23/0.42 % (5044)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 theBenchmark for (569ds/0Mi)
% 0.23/0.42 % (5047)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 theBenchmark for (522ds/0Mi)
% 0.23/0.45 % (5048)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.45 % Exception at run slice level
% 0.23/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.45 % Exception at run slice level
% 0.23/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.46 % Exception at run slice level
% 0.23/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.47 % (5050)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.23/0.47 % (5051)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.23/0.47 % (5049)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.23/0.49 % (5049)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.49 % Exception at run slice level
% 0.23/0.49 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.50 % (5050)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.50 % (5052)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.08/0.54 % (5051)First to succeed.
% 1.08/0.54 % (5051)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5041"
% 1.08/0.54 % (5051)Refutation found. Thanks to Tanya!
% 1.08/0.54 % SZS status Theorem for theBenchmark
% 1.08/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 1.08/0.54 % (5051)------------------------------
% 1.08/0.54 % (5051)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.08/0.54 % (5051)Termination reason: Refutation
% 1.08/0.54
% 1.08/0.54 % (5051)Memory used [KB]: 2286
% 1.08/0.54 % (5051)Time elapsed: 0.068 s
% 1.08/0.54 % (5051)Instructions burned: 205 (million)
% 1.08/0.54 % (5041)Success in time 0.144 s
%------------------------------------------------------------------------------