%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL950^17 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:27:57 PM UTC 2026
% Result : Theorem 1.15s 1.44s
% Output : Proof 1.15s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_eigen__2,type,
eigen__2: mworld ).
thf(ty_eigen__4,type,
eigen__4: mworld ).
thf(ty_eigen__7,type,
eigen__7: mworld ).
thf(ty_member,type,
member: $i > $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eigen__6,type,
eigen__6: mworld ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_intersect,type,
intersect: $i > $i > mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: mworld,X2: mworld,X3: mworld] :
( ~ ( ( mrel @ X1 @ X3 )
=> ~ ( mrel @ X1 @ X2 ) )
=> ( mrel @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( mrel @ eigen__0 @ mactual )
=> ~ ( mrel @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( mrel @ eigen__4 @ eigen__2 )
=> ~ ( mrel @ eigen__4 @ eigen__7 ) )
=> ( mrel @ eigen__2 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: mworld] :
( ~ ( ( mrel @ eigen__6 @ X1 )
=> ~ ( mrel @ eigen__6 @ eigen__6 ) )
=> ( mrel @ X1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( mrel @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: mworld,X2: mworld] :
( ~ ( ( mrel @ eigen__4 @ X2 )
=> ~ ( mrel @ eigen__4 @ X1 ) )
=> ( mrel @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( intersect @ eigen__3 @ eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eiw_di @ eigen__5 @ eigen__6 )
=> ~ ( mrel @ eigen__6 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eiw_di @ eigen__3 @ eigen__2 )
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( intersect @ eigen__3 @ X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ( ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( member @ X4 @ eigen__3 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( member @ X4 @ X2 @ X5 ) ) ) ) ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ~ ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ( ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( member @ X4 @ eigen__3 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( member @ X4 @ X2 @ X5 ) ) ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( intersect @ eigen__3 @ X2 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( eiw_di @ eigen__5 @ eigen__4 )
=> ~ ( mrel @ eigen__4 @ eigen__6 ) )
=> ( eiw_di @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( member @ eigen__1 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( mrel @ eigen__4 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( mrel @ eigen__6 @ eigen__7 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ( mrel @ mactual @ eigen__0 )
=> ~ ( mrel @ mactual @ mactual ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eiw_di @ eigen__1 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( mrel @ eigen__2 @ eigen__7 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__7 )
=> ~ ( ! [X2: mworld] :
( ( mrel @ eigen__7 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( intersect @ eigen__3 @ X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ( ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( member @ X3 @ eigen__3 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( member @ X3 @ X1 @ X4 ) ) ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__7 @ X2 )
=> ( ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ( ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( member @ X3 @ eigen__3 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( member @ X3 @ X1 @ X4 ) ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( intersect @ eigen__3 @ X1 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ( mrel @ eigen__4 @ eigen__6 )
=> ~ sP12 )
=> ( mrel @ eigen__6 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ( eiw_di @ eigen__1 @ eigen__2 )
=> ~ ( mrel @ eigen__2 @ eigen__4 ) )
=> ( eiw_di @ eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: mworld,X2: mworld] :
( ~ ( ( mrel @ eigen__0 @ X2 )
=> ~ ( mrel @ eigen__0 @ X1 ) )
=> ( mrel @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ( mrel @ eigen__2 @ eigen__4 )
=> ~ ( mrel @ eigen__2 @ eigen__2 ) )
=> ( mrel @ eigen__4 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ~ ( ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( intersect @ X2 @ X4 @ X6 ) )
=> ~ ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ( ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( member @ X6 @ X2 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( member @ X6 @ X4 @ X7 ) ) ) ) ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ~ ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ( ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( member @ X6 @ X2 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( member @ X6 @ X4 @ X7 ) ) ) )
=> ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( intersect @ X2 @ X4 @ X6 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: mworld] :
( ( mrel @ eigen__7 @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( member @ X2 @ eigen__3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( member @ X2 @ eigen__5 @ X3 ) ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( intersect @ eigen__3 @ eigen__5 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( mrel @ eigen__6 @ eigen__4 )
=> ~ ( mrel @ eigen__6 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: mworld] :
( ~ ( ( mrel @ eigen__2 @ X1 )
=> ~ ( mrel @ eigen__2 @ eigen__2 ) )
=> ( mrel @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ eigen__0 )
=> ~ ( mrel @ eigen__0 @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ eigen__2 )
=> ~ ( mrel @ eigen__2 @ eigen__4 ) )
=> ( eiw_di @ X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( mrel @ eigen__4 @ eigen__6 )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( mrel @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP11
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( member @ eigen__1 @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ ( ( mrel @ eigen__6 @ eigen__7 )
=> ~ ( mrel @ eigen__6 @ eigen__6 ) )
=> ( mrel @ eigen__7 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__7 )
=> ~ ( ! [X2: mworld] :
( ( mrel @ eigen__7 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( intersect @ eigen__3 @ X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ( ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( member @ X3 @ eigen__3 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( member @ X3 @ X1 @ X4 ) ) ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__7 @ X2 )
=> ( ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ( ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( member @ X3 @ eigen__3 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( member @ X3 @ X1 @ X4 ) ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( intersect @ eigen__3 @ X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP2
=> ( mrel @ mactual @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( mrel @ eigen__4 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ eigen__4 )
=> ~ ( mrel @ eigen__4 @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: mworld] :
( ~ ( ( mrel @ eigen__4 @ X1 )
=> ~ ( mrel @ eigen__4 @ eigen__7 ) )
=> ( mrel @ X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( mrel @ mactual @ eigen__2 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( intersect @ X1 @ X3 @ X5 ) )
=> ~ ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ( ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( member @ X5 @ X1 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( member @ X5 @ X3 @ X6 ) ) ) ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ~ ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ( ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( member @ X5 @ X1 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( member @ X5 @ X3 @ X6 ) ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( intersect @ X1 @ X3 @ X5 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ eigen__2 )
=> ~ ( mrel @ eigen__2 @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( mrel @ mactual @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( mrel @ eigen__6 @ eigen__7 )
=> ~ ( mrel @ eigen__6 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP33
=> ~ ( mrel @ eigen__4 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__6 )
=> ( ! [X2: mworld] :
( ( mrel @ eigen__6 @ X2 )
=> ( member @ X1 @ eigen__3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__6 @ X2 )
=> ( member @ X1 @ eigen__5 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP38
=> ~ ( mrel @ mactual @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( eiw_di @ eigen__1 @ eigen__4 )
=> ~ ( mrel @ eigen__4 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( mrel @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ eigen__6 )
=> ~ ( mrel @ eigen__6 @ eigen__7 ) )
=> ( eiw_di @ X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( member @ eigen__1 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( mrel @ eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( mrel @ eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( intersect @ eigen__3 @ X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ( ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( member @ X4 @ eigen__3 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( member @ X4 @ X2 @ X5 ) ) ) ) ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ~ ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ( ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( member @ X4 @ eigen__3 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( member @ X4 @ X2 @ X5 ) ) ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( intersect @ eigen__3 @ X2 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ eigen__0 )
=> ~ ( mrel @ eigen__0 @ eigen__2 ) )
=> ( eiw_di @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ( mrel @ eigen__7 @ eigen__6 )
=> ( ~ sP41
=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( intersect @ eigen__3 @ eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( intersect @ X1 @ X3 @ X5 ) )
=> ~ ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ( ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( member @ X5 @ X1 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( member @ X5 @ X3 @ X6 ) ) ) ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ~ ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ( ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( member @ X5 @ X1 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( member @ X5 @ X3 @ X6 ) ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( intersect @ X1 @ X3 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( eiw_di @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ sP43
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP15
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ eigen__4 )
=> ~ sP48 )
=> ( eiw_di @ X1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: mworld,X2: mworld] :
( ~ ( ( mrel @ mactual @ X2 )
=> ~ ( mrel @ mactual @ X1 ) )
=> ( mrel @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( eiw_di @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( eiw_di @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( mrel @ mactual @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: mworld] : ( mrel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: mworld,X2: mworld] :
( ~ ( ( mrel @ eigen__2 @ X2 )
=> ~ ( mrel @ eigen__2 @ X1 ) )
=> ( mrel @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ! [X1: mworld] :
( ~ ( ( mrel @ eigen__6 @ X1 )
=> ~ ( mrel @ eigen__6 @ eigen__7 ) )
=> ( mrel @ X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: mworld] :
( ~ ( ( mrel @ eigen__4 @ X1 )
=> ~ sP12 )
=> ( mrel @ X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( mrel @ eigen__7 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( sP44
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP58
=> ~ ( mrel @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: mworld] :
( ~ ( ( mrel @ eigen__0 @ X1 )
=> ~ ( mrel @ eigen__0 @ eigen__2 ) )
=> ( mrel @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ~ sP67
=> sP59 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ! [X1: mworld,X2: mworld] :
( ~ ( ( mrel @ eigen__6 @ X2 )
=> ~ ( mrel @ eigen__6 @ X1 ) )
=> ( mrel @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( mrel @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( eiw_di @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( eiw_di @ eigen__5 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( sP73
=> ~ sP48 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ! [X1: mworld] :
( ~ ( ( mrel @ mactual @ X1 )
=> ~ ( mrel @ mactual @ mactual ) )
=> ( mrel @ X1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( ( eiw_di @ eigen__5 @ eigen__7 )
=> ~ ( ! [X1: mworld] :
( ( mrel @ eigen__7 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( intersect @ eigen__3 @ eigen__5 @ X2 ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( member @ X2 @ eigen__3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( member @ X2 @ eigen__5 @ X3 ) ) ) ) ) )
=> ~ sP22 ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__7 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( intersect @ eigen__3 @ eigen__5 @ X2 ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( member @ X2 @ eigen__3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( member @ X2 @ eigen__5 @ X3 ) ) ) ) ) )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ eigen__6 )
=> ~ ( mrel @ eigen__6 @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( mrel @ eigen__2 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( mrel @ eigen__6 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( mrel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( ~ sP23
=> sP47 ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( ~ sP8
=> ( eiw_di @ eigen__5 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( mrel @ eigen__6 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( eiw_di @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( ~ sP41
=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( intersect @ eigen__3 @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ! [X1: mworld] :
( ( mrel @ eigen__6 @ X1 )
=> ( intersect @ eigen__3 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ! [X1: mworld,X2: mworld,X3: $i] :
( ~ ( ( eiw_di @ X3 @ X1 )
=> ~ ( mrel @ X1 @ X2 ) )
=> ( eiw_di @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ( sP59
=> ~ sP44 ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( mrel @ mactual @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( eiw_di @ eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(def_mlocal,definition,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( mrel @ X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: mworld > $o,X2: mworld] :
? [X3: mworld] :
( ( mrel @ X2 @ X3 )
& ( X1 @ X3 ) ) ) ) ).
thf(def_mforall_di,definition,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( eiw_di @ X3 @ X2 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X3: $i] :
( ( eiw_di @ X3 @ X2 )
& ( X1 @ X3 @ X2 ) ) ) ) ).
thf(prove_th13,conjecture,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( member @ X2 @ X4 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( member @ X2 @ X6 @ X8 ) ) )
=> ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( intersect @ X4 @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( member @ X2 @ X4 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( member @ X2 @ X6 @ X8 ) ) )
=> ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( intersect @ X4 @ X6 @ X8 ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_th13]) ).
thf(h1,assumption,
~ ( sP38
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( ~ ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( member @ X1 @ X3 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( member @ X1 @ X5 @ X7 ) ) )
=> ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( intersect @ X3 @ X5 @ X7 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP38,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ! [X5: $i] :
( ( eiw_di @ X5 @ X4 )
=> ! [X6: mworld] :
( ( mrel @ X4 @ X6 )
=> ( ~ ( ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( member @ X1 @ X3 @ X7 ) )
=> ~ ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( member @ X1 @ X5 @ X7 ) ) )
=> ! [X7: mworld] :
( ( mrel @ X6 @ X7 )
=> ( intersect @ X3 @ X5 @ X7 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP58
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ~ ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( member @ eigen__1 @ X2 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( member @ eigen__1 @ X4 @ X6 ) ) )
=> ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( intersect @ X2 @ X4 @ X6 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP58,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( ~ ( ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( member @ eigen__1 @ X2 @ X6 ) )
=> ~ ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( member @ eigen__1 @ X4 @ X6 ) ) )
=> ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( intersect @ X2 @ X4 @ X6 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP81
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ~ ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( member @ eigen__1 @ X1 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( member @ eigen__1 @ X3 @ X5 ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( intersect @ X1 @ X3 @ X5 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP81,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__2 )
=> ! [X2: mworld] :
( ( mrel @ eigen__2 @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( ~ ( ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( member @ eigen__1 @ X1 @ X5 ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( member @ eigen__1 @ X3 @ X5 ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( intersect @ X1 @ X3 @ X5 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP85
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ~ ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( member @ eigen__1 @ eigen__3 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( member @ eigen__1 @ X2 @ X4 ) ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( intersect @ eigen__3 @ X2 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP85,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ~ ( ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( member @ eigen__1 @ eigen__3 @ X4 ) )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( member @ eigen__1 @ X2 @ X4 ) ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( intersect @ eigen__3 @ X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP44
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__4 )
=> ! [X2: mworld] :
( ( mrel @ eigen__4 @ X2 )
=> ( ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( member @ eigen__1 @ eigen__3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( member @ eigen__1 @ X1 @ X3 ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( intersect @ eigen__3 @ X1 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP44,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__4 )
=> ! [X2: mworld] :
( ( mrel @ eigen__4 @ X2 )
=> ( ~ ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( member @ eigen__1 @ eigen__3 @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( member @ eigen__1 @ X1 @ X3 ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( intersect @ eigen__3 @ X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP73
=> ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( member @ eigen__1 @ eigen__3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( member @ eigen__1 @ eigen__5 @ X2 ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( intersect @ eigen__3 @ eigen__5 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP73,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__4 @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( member @ eigen__1 @ eigen__3 @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( member @ eigen__1 @ eigen__5 @ X2 ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( intersect @ eigen__3 @ eigen__5 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP48
=> ( ~ sP29
=> sP87 ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP48,
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ sP29
=> sP87 ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP29,
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP87,
introduced(assumption,[]) ).
thf(h24,assumption,
sP11,
introduced(assumption,[]) ).
thf(h25,assumption,
sP46,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h27,assumption,
sP71,
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP5
| ~ sP81 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP32
| sP2
| sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP67
| ~ sP58
| ~ sP81 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP69
| sP67
| sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP68
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP50
| sP69 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP19
| sP68 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP25
| sP50 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP42
| ~ sP38
| ~ sP90 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP14
| sP42
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP1
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP88
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP75
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP16
| ~ sP79
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP49
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP9
| ~ sP85
| sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP52
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP36
| ~ sP60
| sP52 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP66
| ~ sP44
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP20
| sP66
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP89
| ~ sP59
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP18
| sP89
| sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP24
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP26
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP62
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP37
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP40
| ~ sP33
| ~ sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP3
| sP40
| sP79 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP61
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP1
| sP62 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP88
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP21
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP35
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP27
| ~ sP48
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP17
| sP27
| sP84 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP74
| ~ sP73
| ~ sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP10
| sP74
| sP53 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP43
| ~ sP72
| ~ sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP54
| sP43
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP64
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP56
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP56
| sP54 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP6
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP6
| sP64 ),
inference(all_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP34
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP23
| ~ sP84
| ~ sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP82
| sP23
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP61
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP88
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP63
| sP82 ),
inference(all_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP29
| ~ sP11
| ~ sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP55
| ~ sP15
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP41
| sP55 ),
inference(all_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP86
| sP41
| sP87 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP51
| ~ sP65
| sP86 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP39
| ~ sP71
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP30
| sP39
| sP65 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP8
| ~ sP53
| ~ sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP83
| sP8
| sP91 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP4
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP45
| sP83 ),
inference(all_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP13
| ~ sP71
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP87
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP70
| sP63 ),
inference(all_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP70
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP78
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP61
| sP80 ),
inference(all_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP1
| sP70 ),
inference(all_rule,[status(thm)],[]) ).
thf(70,plain,
( ~ sP88
| sP78 ),
inference(all_rule,[status(thm)],[]) ).
thf(71,plain,
( ~ sP22
| sP51 ),
inference(all_rule,[status(thm)],[]) ).
thf(72,plain,
( sP77
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( ~ sP76
| ~ sP91
| ~ sP77 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( ~ sP31
| sP76 ),
inference(all_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP57
| sP75 ),
inference(all_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP61
| sP90 ),
inference(all_rule,[status(thm)],[]) ).
thf(77,plain,
( ~ sP1
| sP57 ),
inference(all_rule,[status(thm)],[]) ).
thf(intersect_defn,axiom,
sP21 ).
thf(eiw_di_cumul,axiom,
sP88 ).
thf(mrel_euclidean,axiom,
sP1 ).
thf(mrel_reflexive,axiom,
sP61 ).
thf(78,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h27,h28,h26,h24,h25,h22,h23,h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,h2,h5,h8,h11,h14,h17,h20,h24,h25,h27,h28,intersect_defn,eiw_di_cumul,mrel_euclidean,mrel_reflexive]) ).
thf(79,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h24,h25,h22,h23,h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,78,h27,h28]) ).
thf(80,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h25,h22,h23,h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__7)],[h23,79,h26]) ).
thf(81,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h22,80,h24,h25]) ).
thf(82,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,81,h22,h23]) ).
thf(83,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,82,h20,h21]) ).
thf(84,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__6)],[h18,83,h19]) ).
thf(85,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,84,h17,h18]) ).
thf(86,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__5)],[h15,85,h16]) ).
thf(87,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,86,h14,h15]) ).
thf(88,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,87,h13]) ).
thf(89,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,88,h11,h12]) ).
thf(90,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,89,h10]) ).
thf(91,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,90,h8,h9]) ).
thf(92,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,91,h7]) ).
thf(93,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,92,h5,h6]) ).
thf(94,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,93,h4]) ).
thf(95,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,94,h2,h3]) ).
thf(96,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,95,h1]) ).
thf(0,theorem,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ! [X4: $i] :
( ( eiw_di @ X4 @ X3 )
=> ! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ X5 )
=> ! [X7: mworld] :
( ( mrel @ X5 @ X7 )
=> ( ~ ( ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( member @ X2 @ X4 @ X8 ) )
=> ~ ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( member @ X2 @ X6 @ X8 ) ) )
=> ! [X8: mworld] :
( ( mrel @ X7 @ X8 )
=> ( intersect @ X4 @ X6 @ X8 ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[96,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL950^17 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 13:55:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 1.15/1.44 % SZS status Theorem
% 1.15/1.44 % Mode: cade22grackle2xfee4
% 1.15/1.44 % Steps: 12892
% 1.15/1.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------