TSTP Solution File: ITP115^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP115^2 : 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 : n010.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 22:52:22 EDT 2024
% Result : Theorem 1.31s 0.56s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 147
% Syntax : Number of formulae : 191 ( 11 unt; 135 typ; 0 def)
% Number of atoms : 593 ( 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 : 4 ( 3 usr)
% Number of type conns : 207 ( 206 >; 1 *; 0 +; 0 <<)
% Number of symbols : 140 ( 137 usr; 14 con; 0-6 aty)
% Number of variables : 157 ( 0 ^ 14 !; 14 ?; 157 :)
% ( 129 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set: $tType > $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
filter: $tType > $tType ).
thf(type_def_8,type,
b: $tType ).
thf(type_def_9,type,
a: $tType ).
thf(type_def_10,type,
nat: $tType ).
thf(func_def_0,type,
filter: $tType > $tType ).
thf(func_def_1,type,
set: $tType > $tType ).
thf(func_def_2,type,
nat: $tType ).
thf(func_def_3,type,
b: $tType ).
thf(func_def_4,type,
a: $tType ).
thf(func_def_5,type,
topolo2117631714pology:
!>[X0: $tType] : $o ).
thf(func_def_6,type,
comple1035589618norder:
!>[X0: $tType] : $o ).
thf(func_def_7,type,
finite_finite:
!>[X0: $tType] : $o ).
thf(func_def_8,type,
bounded_lattice:
!>[X0: $tType] : $o ).
thf(func_def_9,type,
type:
!>[X0: $tType] : $o ).
thf(func_def_10,type,
countable:
!>[X0: $tType] : $o ).
thf(func_def_11,type,
minus:
!>[X0: $tType] : $o ).
thf(func_def_12,type,
bot:
!>[X0: $tType] : $o ).
thf(func_def_13,type,
ord:
!>[X0: $tType] : $o ).
thf(func_def_14,type,
top:
!>[X0: $tType] : $o ).
thf(func_def_15,type,
order:
!>[X0: $tType] : $o ).
thf(func_def_16,type,
group_add:
!>[X0: $tType] : $o ).
thf(func_def_17,type,
lattice:
!>[X0: $tType] : $o ).
thf(func_def_18,type,
linorder:
!>[X0: $tType] : $o ).
thf(func_def_19,type,
preorder:
!>[X0: $tType] : $o ).
thf(func_def_20,type,
order_bot:
!>[X0: $tType] : $o ).
thf(func_def_21,type,
semilattice_inf:
!>[X0: $tType] : $o ).
thf(func_def_22,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
thf(func_def_23,type,
topological_t0_space:
!>[X0: $tType] : $o ).
thf(func_def_24,type,
topological_t1_space:
!>[X0: $tType] : $o ).
thf(func_def_25,type,
topological_t2_space:
!>[X0: $tType] : $o ).
thf(func_def_26,type,
bounded_lattice_bot:
!>[X0: $tType] : $o ).
thf(func_def_27,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
thf(func_def_28,type,
topolo890362671_space:
!>[X0: $tType] : $o ).
thf(func_def_29,type,
topolo47006728_space:
!>[X0: $tType] : $o ).
thf(func_def_30,type,
topolo2133971006pology:
!>[X0: $tType] : $o ).
thf(func_def_31,type,
topolo503727757_space:
!>[X0: $tType] : $o ).
thf(func_def_32,type,
topolo2135403230pology:
!>[X0: $tType] : $o ).
thf(func_def_33,type,
elementary_closure:
!>[X0: $tType] : ( set(X0) > set(X0) ) ).
thf(func_def_34,type,
minus_minus:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_35,type,
inf_inf:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_36,type,
lower_582600101lsc_at:
!>[X0: $tType,X1: $tType] : ( X0 > ( X0 > X1 ) > $o ) ).
thf(func_def_37,type,
bot_bot:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
ord_less_eq:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
top_top:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_41,type,
insert:
!>[X0: $tType] : ( X0 > set(X0) > set(X0) ) ).
thf(func_def_42,type,
is_empty:
!>[X0: $tType] : ( set(X0) > $o ) ).
thf(func_def_43,type,
is_singleton:
!>[X0: $tType] : ( set(X0) > $o ) ).
thf(func_def_44,type,
remove:
!>[X0: $tType] : ( X0 > set(X0) > set(X0) ) ).
thf(func_def_45,type,
the_elem:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_46,type,
topolo1751647064n_open:
!>[X0: $tType] : ( set(X0) > $o ) ).
thf(func_def_47,type,
topolo507301023within:
!>[X0: $tType] : ( X0 > set(X0) > filter(X0) ) ).
thf(func_def_48,type,
topolo406746546ounded:
!>[X0: $tType] : ( set(X0) > $o ) ).
thf(func_def_49,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_50,type,
a2: b ).
thf(func_def_51,type,
f: a > b ).
thf(func_def_52,type,
thesis: $o ).
thf(func_def_53,type,
x0: a ).
thf(func_def_57,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_58,type,
vAND: $o > $o > $o ).
thf(func_def_59,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_60,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_61,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_62,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_63,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_64,type,
vIMP: $o > $o > $o ).
thf(func_def_65,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_66,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_67,type,
vNOT: $o > $o ).
thf(func_def_68,type,
vOR: $o > $o > $o ).
thf(func_def_69,type,
sP0: $o ).
thf(func_def_70,type,
sP1:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_71,type,
sP2:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_72,type,
sP3:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_73,type,
sP4:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_74,type,
sP5:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_75,type,
sK6: set(b) ).
thf(func_def_76,type,
sK7: set(b) ).
thf(func_def_77,type,
sK8: set(b) > set(a) ).
thf(func_def_78,type,
sK9: set(b) > set(a) ).
thf(func_def_79,type,
sK10:
!>[X0: $tType] : ( X0 > X0 > set(X0) ) ).
thf(func_def_80,type,
sK11:
!>[X0: $tType] : ( X0 > X0 > set(X0) ) ).
thf(func_def_81,type,
sK12:
!>[X0: $tType] : ( X0 > X0 > set(X0) ) ).
thf(func_def_82,type,
sK13:
!>[X0: $tType] : ( X0 > X0 > set(X0) ) ).
thf(func_def_83,type,
sK14:
!>[X0: $tType] : ( X0 > nat > set(X0) ) ).
thf(func_def_84,type,
sK15:
!>[X0: $tType] : ( set(X0) > X0 > nat ) ).
thf(func_def_85,type,
sK16:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_86,type,
sK17:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_87,type,
sK18:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_88,type,
sK19:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_89,type,
sK20:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_90,type,
sK21:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_91,type,
sK22:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_92,type,
sK23:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_93,type,
sK24:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_94,type,
sK25:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_95,type,
sK26:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_96,type,
sK27:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_97,type,
sK28:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_98,type,
sK29:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_99,type,
sK30:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_100,type,
sK31:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_101,type,
sK32:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_102,type,
sK33:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_103,type,
sK34:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_104,type,
sK35:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_105,type,
sK36:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_106,type,
sK37:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_107,type,
sK38:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_108,type,
sK39:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_109,type,
sK40:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_110,type,
sK41:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_111,type,
sK42:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_112,type,
sK43:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_113,type,
sK44:
!>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).
thf(func_def_114,type,
sK45:
!>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).
thf(func_def_115,type,
sK46:
!>[X0: $tType] : ( set(X0) > X0 > set(X0) ) ).
thf(func_def_116,type,
sK47:
!>[X0: $tType] : ( set(X0) > X0 > set(X0) ) ).
thf(func_def_117,type,
sK48:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_118,type,
sK49:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_120,type,
sK51:
!>[X0: $tType] : ( X0 > set(X0) > X0 > set(X0) > set(X0) ) ).
thf(func_def_121,type,
sK52:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > set(X0) > X0 ) ).
thf(func_def_122,type,
sK53:
!>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_123,type,
sK54:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_124,type,
sK55:
!>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).
thf(func_def_125,type,
sK56:
!>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).
thf(func_def_126,type,
sK57:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_127,type,
sK58:
!>[X0: $tType] : ( set(X0) > X0 ) ).
thf(func_def_128,type,
sK59:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_129,type,
sK60:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_130,type,
sK61:
!>[X0: $tType] : ( X0 > X0 > set(X0) ) ).
thf(func_def_131,type,
sK62:
!>[X0: $tType] : ( X0 > X0 > set(X0) ) ).
thf(func_def_132,type,
sK63:
!>[X0: $tType] : ( X0 > X0 > set(X0) ) ).
thf(f3019,plain,
$false,
inference(avatar_sat_refutation,[],[f2187,f2192,f2197,f2202,f2207,f2209,f3018]) ).
thf(f3018,plain,
( ~ spl50_2
| ~ spl50_3
| ~ spl50_4
| ~ spl50_5
| ~ spl50_6 ),
inference(avatar_contradiction_clause,[],[f3017]) ).
thf(f3017,plain,
( $false
| ~ spl50_2
| ~ spl50_3
| ~ spl50_4
| ~ spl50_5
| ~ spl50_6 ),
inference(subsumption_resolution,[],[f3016,f2206]) ).
thf(f2206,plain,
( ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
| ~ spl50_6 ),
inference(avatar_component_clause,[],[f2204]) ).
thf(f2204,plain,
( spl50_6
<=> ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_6])]) ).
thf(f3016,plain,
( ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
| ~ spl50_2
| ~ spl50_3
| ~ spl50_4
| ~ spl50_5 ),
inference(subsumption_resolution,[],[f3015,f2201]) ).
thf(f2201,plain,
( ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
| ~ spl50_5 ),
inference(avatar_component_clause,[],[f2199]) ).
thf(f2199,plain,
( spl50_5
<=> ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_5])]) ).
thf(f3015,plain,
( ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
| ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
| ~ spl50_2
| ~ spl50_3
| ~ spl50_4 ),
inference(subsumption_resolution,[],[f3014,f2196]) ).
thf(f2196,plain,
( ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),sK6) )
| ~ spl50_4 ),
inference(avatar_component_clause,[],[f2194]) ).
thf(f2194,plain,
( spl50_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,[spl50_4])]) ).
thf(f3014,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,topolo1751647064n_open(b),sK7) )
| ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
| ~ spl50_2
| ~ spl50_3 ),
inference(subsumption_resolution,[],[f3013,f2191]) ).
thf(f2191,plain,
( ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),sK7) )
| ~ spl50_3 ),
inference(avatar_component_clause,[],[f2189]) ).
thf(f2189,plain,
( spl50_3
<=> ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_3])]) ).
thf(f3013,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,topolo1751647064n_open(b),sK7) )
| ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
| ~ spl50_2 ),
inference(trivial_inequality_removal,[],[f3012]) ).
thf(f3012,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,topolo1751647064n_open(b),sK7) )
| ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
| ~ spl50_2 ),
inference(superposition,[],[f2178,f2186]) ).
thf(f2186,plain,
( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),sK6),sK7) )
| ~ spl50_2 ),
inference(avatar_component_clause,[],[f2184]) ).
thf(f2184,plain,
( spl50_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,[spl50_2])]) ).
thf(f2178,plain,
! [X0: set(b),X1: set(b)] :
( ( bot_bot(set(b)) != vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
| ( $true != vAPP(set(b),$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,topolo1751647064n_open(b),X1) )
| ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ),
inference(subsumption_resolution,[],[f1421,f1420]) ).
thf(f1420,plain,
thesis != $true,
inference(cnf_transformation,[],[f1014]) ).
thf(f1014,plain,
thesis != $true,
inference(flattening,[],[f363]) ).
thf(f363,plain,
thesis != $true,
inference(fool_elimination,[],[f362]) ).
thf(f362,plain,
~ thesis,
inference(rectify,[],[f359]) ).
thf(f359,negated_conjecture,
~ thesis,
inference(negated_conjecture,[],[f358]) ).
thf(f358,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(f1421,plain,
! [X0: set(b),X1: set(b)] :
( ( thesis = $true )
| ( bot_bot(set(b)) != vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
| ( $true != vAPP(set(b),$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,topolo1751647064n_open(b),X1) )
| ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ),
inference(cnf_transformation,[],[f1075]) ).
thf(f1075,plain,
! [X0: set(b),X1: set(b)] :
( ( thesis = $true )
| ( bot_bot(set(b)) != vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
| ( $true != vAPP(set(b),$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,topolo1751647064n_open(b),X1) )
| ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ),
inference(flattening,[],[f1074]) ).
thf(f1074,plain,
! [X0: set(b),X1: set(b)] :
( ( thesis = $true )
| ( bot_bot(set(b)) != vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
| ( $true != vAPP(set(b),$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,topolo1751647064n_open(b),X1) )
| ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ),
inference(ennf_transformation,[],[f365]) ).
thf(f365,plain,
! [X0: set(b),X1: set(b)] :
( ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
& ( $true = vAPP(set(b),$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,topolo1751647064n_open(b),X1) )
& ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) )
=> ( thesis = $true ) ),
inference(fool_elimination,[],[f364]) ).
thf(f364,plain,
! [X0: set(b),X1: set(b)] :
( ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
& vAPP(set(b),$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,topolo1751647064n_open(b),X1)
& vAPP(set(b),$o,topolo1751647064n_open(b),X0) )
=> thesis ),
inference(rectify,[],[f357]) ).
thf(f357,axiom,
! [X19: set(b),X59: set(b)] :
( ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X19),X59) )
& vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X59)
& vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X19)
& vAPP(set(b),$o,topolo1751647064n_open(b),X59)
& vAPP(set(b),$o,topolo1751647064n_open(b),X19) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f2209,plain,
spl50_1,
inference(avatar_split_clause,[],[f2208,f2180]) ).
thf(f2180,plain,
( spl50_1
<=> ( $true = sP0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl50_1])]) ).
thf(f2208,plain,
$true = sP0,
inference(subsumption_resolution,[],[f1431,f1425]) ).
thf(f1425,plain,
a2 != vAPP(a,b,f,x0),
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
a2 != vAPP(a,b,f,x0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062) ).
thf(f1431,plain,
( ( $true = sP0 )
| ( a2 = vAPP(a,b,f,x0) ) ),
inference(cnf_transformation,[],[f1341]) ).
thf(f1341,plain,
( ( $true = sP0 )
| ( a2 = vAPP(a,b,f,x0) ) ),
inference(definition_folding,[],[f1076,f1340]) ).
thf(f1340,plain,
( ? [X0: set(b),X1: set(b)] :
( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
& ( $true = vAPP(set(b),$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,topolo1751647064n_open(b),X1) )
& ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) )
| ( $true != sP0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1076,plain,
( ? [X0: set(b),X1: set(b)] :
( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
& ( $true = vAPP(set(b),$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,topolo1751647064n_open(b),X1) )
& ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) )
| ( a2 = vAPP(a,b,f,x0) ) ),
inference(ennf_transformation,[],[f373]) ).
thf(f373,plain,
( ( a2 != vAPP(a,b,f,x0) )
=> ? [X0: set(b),X1: set(b)] :
( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
& ( $true = vAPP(set(b),$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,topolo1751647064n_open(b),X1) )
& ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ) ),
inference(fool_elimination,[],[f372]) ).
thf(f372,plain,
( ( a2 != vAPP(a,b,f,x0) )
=> ? [X0: set(b),X1: set(b)] :
( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
& 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),$o,topolo1751647064n_open(b),X1)
& vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( ( a2 != vAPP(a,b,f,x0) )
=> ? [X2: set(b),X3: set(b)] :
( ( vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X2),X3) = bot_bot(set(b)) )
& vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X3)
& vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X2)
& vAPP(set(b),$o,topolo1751647064n_open(b),X3)
& vAPP(set(b),$o,topolo1751647064n_open(b),X2) ) ),
file('/export/starexec/sandbox/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(f2207,plain,
( ~ spl50_1
| spl50_6 ),
inference(avatar_split_clause,[],[f1426,f2204,f2180]) ).
thf(f1426,plain,
( ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f1351]) ).
thf(f1351,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,topolo1751647064n_open(b),sK7) )
& ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK6) ) )
| ( $true != sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f1349,f1350]) ).
thf(f1350,plain,
( ? [X0: set(b),X1: set(b)] :
( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
& ( $true = vAPP(set(b),$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,topolo1751647064n_open(b),X1) )
& ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) )
=> ( ( 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,topolo1751647064n_open(b),sK7) )
& ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK6) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1349,plain,
( ? [X0: set(b),X1: set(b)] :
( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
& ( $true = vAPP(set(b),$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,topolo1751647064n_open(b),X1) )
& ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) )
| ( $true != sP0 ) ),
inference(nnf_transformation,[],[f1340]) ).
thf(f2202,plain,
( ~ spl50_1
| spl50_5 ),
inference(avatar_split_clause,[],[f1427,f2199,f2180]) ).
thf(f1427,plain,
( ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f1351]) ).
thf(f2197,plain,
( ~ spl50_1
| spl50_4 ),
inference(avatar_split_clause,[],[f1428,f2194,f2180]) ).
thf(f1428,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,[],[f1351]) ).
thf(f2192,plain,
( ~ spl50_1
| spl50_3 ),
inference(avatar_split_clause,[],[f1429,f2189,f2180]) ).
thf(f1429,plain,
( ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),sK7) )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f1351]) ).
thf(f2187,plain,
( ~ spl50_1
| spl50_2 ),
inference(avatar_split_clause,[],[f1430,f2184,f2180]) ).
thf(f1430,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,[],[f1351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ITP115^2 : TPTP v8.2.0. Released v7.5.0.
% 0.05/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n010.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat May 18 17:00:22 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (9762)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.35 % (9767)WARNING: value z3 for option sas not known
% 0.10/0.35 % (9771)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)
% 0.10/0.35 % (9765)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.35 % (9770)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)
% 0.10/0.35 % (9769)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)
% 0.10/0.35 % (9766)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.35 % (9768)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.35 % (9767)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)
% 0.10/0.38 % (9771)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.39 % Exception at run slice level
% 0.16/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.39 % Exception at run slice level
% 0.16/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.39 % Exception at run slice level
% 0.16/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.40 % (9774)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.16/0.44 % (9775)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)
% 0.16/0.44 % (9776)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)
% 0.16/0.45 % (9774)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.45 % Exception at run slice level
% 0.16/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.47 % (9777)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)
% 0.16/0.49 % (9775)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.31/0.55 % (9776)First to succeed.
% 1.31/0.56 % (9776)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9762"
% 1.31/0.56 % (9776)Refutation found. Thanks to Tanya!
% 1.31/0.56 % SZS status Theorem for theBenchmark
% 1.31/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.31/0.56 % (9776)------------------------------
% 1.31/0.56 % (9776)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.31/0.56 % (9776)Termination reason: Refutation
% 1.31/0.56
% 1.31/0.56 % (9776)Memory used [KB]: 2578
% 1.31/0.56 % (9776)Time elapsed: 0.156 s
% 1.31/0.56 % (9776)Instructions burned: 258 (million)
% 1.31/0.56 % (9762)Success in time 0.235 s
%------------------------------------------------------------------------------