TSTP Solution File: SYO064^4.004 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO064^4.004 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 : Fri Sep 1 04:45:00 EDT 2023
% Result : Theorem 0.60s 0.85s
% Output : Proof 0.70s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b3,type,
b3: $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_b2,type,
b2: $i > $o ).
thf(ty_a1,type,
a1: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_b1,type,
b1: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_b,type,
b: $i > $o ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_a,type,
a: $i > $o ).
thf(ty_a3,type,
a3: $i > $o ).
thf(ty_a2,type,
a2: $i > $o ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_a4,type,
a4: $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( irel @ X1 @ X2 )
=> ~ ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( irel @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( b3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( b3 @ X1 ) )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( b2 @ eigen__7 )
=> ~ ( a3 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( irel @ eigen__4 @ eigen__5 )
=> ( a2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b @ X1 ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__4 @ eigen__6 )
=> ~ ( irel @ eigen__6 @ X1 ) )
=> ( irel @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( irel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP17
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( a1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( a4 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( irel @ eigen__4 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ( ( irel @ eigen__2 @ eigen__4 )
=> ~ ( irel @ eigen__4 @ eigen__5 ) )
=> ( irel @ eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( irel @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( b2 @ X1 ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( irel @ eigen__0 @ eigen__2 )
=> ~ ( irel @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( b @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP25
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( irel @ eigen__6 @ eigen__8 )
=> ( b3 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( irel @ eigen__4 @ eigen__7 )
=> ( b2 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP24
=> ( b3 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( irel @ eigen__4 @ eigen__4 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ ( ( irel @ eigen__4 @ eigen__6 )
=> ~ ( irel @ eigen__6 @ eigen__8 ) )
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__2 @ eigen__4 )
=> ~ ( irel @ eigen__4 @ X1 ) )
=> ( irel @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( irel @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( a @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( b3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( irel @ eigen__4 @ eigen__6 )
=> ~ ( irel @ eigen__6 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( irel @ eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( irel @ eigen__4 @ eigen__4 )
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP44
=> ( b1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ( irel @ eigen__0 @ eigen__2 )
=> sP31 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( b1 @ eigen__5 )
=> ~ ( a2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( irel @ eigen__6 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( irel @ eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( irel @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( b2 @ X1 ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( a2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP2
=> sP41 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ sP21
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP27
=> sP30 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( b3 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP30
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( a3 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i] : ( a4 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ( irel @ eigen__4 @ eigen__6 )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( sP40
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( b2 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ( irel @ eigen__2 @ eigen__4 )
=> ( ~ sP12
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( b2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP51
=> sP59 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( sP57
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ~ sP12
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( b2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( b3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( irel @ eigen__4 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( b2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( irel @ eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__4 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( irel @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__0 @ eigen__2 )
=> ~ ( irel @ eigen__2 @ X1 ) )
=> ( irel @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( ~ sP29
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( ~ ( sP76
=> ~ sP51 )
=> sP50 ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( sP4
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( irel @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__2 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b3 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ( sP76
=> ~ sP51 ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( b1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( sP79
=> ~ sP85 ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( irel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( irel @ X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
( iand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
( ivalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(con,conjecture,
! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b @ X3 )
=> ~ ( a1 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( b1 @ X4 )
=> ~ ( a2 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( b2 @ X5 )
=> ~ ( a3 @ X5 ) ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( b3 @ X5 )
=> ~ ( a4 @ X5 ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b @ X3 )
=> ~ ( a1 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( b1 @ X4 )
=> ~ ( a2 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( b2 @ X5 )
=> ~ ( a3 @ X5 ) ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( b3 @ X5 )
=> ~ ( a4 @ X5 ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ ( ~ sP74
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b @ X2 )
=> ~ ( a1 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b1 @ X3 )
=> ~ ( a2 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( b2 @ X4 )
=> ~ ( a3 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( b3 @ X4 )
=> ~ ( a4 @ X4 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP74,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b @ X2 )
=> ~ ( a1 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b1 @ X3 )
=> ~ ( a2 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( b2 @ X4 )
=> ~ ( a3 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( b3 @ X4 )
=> ~ ( a4 @ X4 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP54,
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP41,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP92
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( b @ X1 )
=> ~ ( a1 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b1 @ X2 )
=> ~ ( a2 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b2 @ X3 )
=> ~ ( a3 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b3 @ X3 )
=> ~ ( a4 @ X3 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP92,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( b @ X1 )
=> ~ ( a1 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b1 @ X2 )
=> ~ ( a2 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b2 @ X3 )
=> ~ ( a3 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b3 @ X3 )
=> ~ ( a4 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( b @ X1 )
=> ~ ( a1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b1 @ X2 )
=> ~ ( a2 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b2 @ X3 )
=> ~ ( a3 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b3 @ X3 )
=> ~ ( a4 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP40
=> ~ sP58 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP40,
introduced(assumption,[]) ).
thf(h14,assumption,
sP58,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP79
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( b1 @ X1 )
=> ~ ( a2 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b2 @ X2 )
=> ~ ( a3 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b3 @ X2 )
=> ~ ( a4 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP79,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( b1 @ X1 )
=> ~ ( a2 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b2 @ X2 )
=> ~ ( a3 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b3 @ X2 )
=> ~ ( a4 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( b1 @ X1 )
=> ~ ( a2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b2 @ X2 )
=> ~ ( a3 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( b3 @ X2 )
=> ~ ( a4 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP85
=> ~ sP48 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP85,
introduced(assumption,[]) ).
thf(h22,assumption,
sP48,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP76
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( b2 @ X1 )
=> ~ ( a3 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( b3 @ X1 )
=> ~ ( a4 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP76,
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( b2 @ X1 )
=> ~ ( a3 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( b3 @ X1 )
=> ~ ( a4 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( b2 @ X1 )
=> ~ ( a3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( b3 @ X1 )
=> ~ ( a4 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ ( sP51
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h29,assumption,
sP51,
introduced(assumption,[]) ).
thf(h30,assumption,
sP10,
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( sP49
=> ~ sP69 ),
introduced(assumption,[]) ).
thf(h32,assumption,
sP49,
introduced(assumption,[]) ).
thf(h33,assumption,
sP69,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP54
| ~ sP2
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP74
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP47
| ~ sP92
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP13
| ~ sP84
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP29
| ~ sP92
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP81
| sP29
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP18
| ~ sP17
| sP71 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP80
| sP81 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP21
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP71
| sP84
| sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP68
| sP80 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP56
| ~ sP27
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP84
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP55
| sP21
| sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP65
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP1
| sP68 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP6
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP33
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP63
| ~ sP40
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP20
| sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP66
| ~ sP79
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP86
| sP66 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP38
| ~ sP77
| sP86 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP83
| ~ sP4
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP91
| ~ sP79
| ~ sP85 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP26
| sP91
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP25
| sP83 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP39
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP14
| sP77
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP46
| ~ sP44
| sP90 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP77
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP31
| sP25
| sP77 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP87
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP65
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP1
| sP87 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP19
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP11
| ~ sP85
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP15
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP36
| ~ sP73
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP3
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP52
| ~ sP75
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP45
| ~ sP73
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP62
| ~ sP76
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP43
| ~ sP76
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP37
| sP43
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP89
| ~ sP76
| ~ sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP82
| sP89
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP12
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP60
| sP62 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP16
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP16
| sP82 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP28
| sP75
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP34
| ~ sP50
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP75
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP70
| sP12
| sP75 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP35
| ~ sP24
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP42
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP5
| sP60
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP78
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP65
| sP73 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP1
| sP78 ),
inference(all_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP88
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP67
| ~ sP51
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP7
| sP67 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP32
| ~ sP49
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP72
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP8
| sP72
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP61
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP58
| ~ sP30
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP48
| ~ sP90
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( ~ sP10
| ~ sP64
| ~ sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( ~ sP69
| ~ sP57
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(axiom5,axiom,
sP6 ).
thf(axiom4,axiom,
sP33 ).
thf(axiom3,axiom,
sP19 ).
thf(axiom2,axiom,
sP88 ).
thf(axiom1,axiom,
sP61 ).
thf(trans_axiom,axiom,
sP1 ).
thf(refl_axiom,axiom,
sP65 ).
thf(74,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h32,h33,h31,h29,h30,h28,h26,h27,h24,h25,h23,h21,h22,h20,h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,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,h5,h6,h8,h13,h14,h16,h21,h22,h24,h29,h30,h32,h33,axiom5,axiom4,axiom3,axiom2,axiom1,trans_axiom,refl_axiom]) ).
thf(75,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h29,h30,h28,h26,h27,h24,h25,h23,h21,h22,h20,h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h32,h33])],[h31,74,h32,h33]) ).
thf(76,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h29,h30,h28,h26,h27,h24,h25,h23,h21,h22,h20,h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__8)],[h27,75,h31]) ).
thf(77,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h26,h27,h24,h25,h23,h21,h22,h20,h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,76,h29,h30]) ).
thf(78,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h27,h24,h25,h23,h21,h22,h20,h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__7)],[h26,77,h28]) ).
thf(79,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h23,h21,h22,h20,h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h26,h27])],[h25,78,h26,h27]) ).
thf(80,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h20,h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,79,h24,h25]) ).
thf(81,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__6)],[h19,80,h23]) ).
thf(82,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,81,h21,h22]) ).
thf(83,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h19,h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h18,82,h20]) ).
thf(84,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,83,h18,h19]) ).
thf(85,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,84,h16,h17]) ).
thf(86,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[h11,85,h15]) ).
thf(87,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,86,h13,h14]) ).
thf(88,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h10,87,h12]) ).
thf(89,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,88,h10,h11]) ).
thf(90,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,89,h8,h9]) ).
thf(91,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h3,90,h7]) ).
thf(92,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,91,h5,h6]) ).
thf(93,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,92,h4]) ).
thf(94,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,93,h2,h3]) ).
thf(95,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,94,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( b @ X3 )
=> ~ ( a1 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( b1 @ X4 )
=> ~ ( a2 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( b2 @ X5 )
=> ~ ( a3 @ X5 ) ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( b3 @ X5 )
=> ~ ( a4 @ X5 ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[95,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO064^4.004 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 03:43:41 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.60/0.85 % SZS status Theorem
% 0.60/0.85 % Mode: cade22grackle2xfee4
% 0.60/0.85 % Steps: 4585
% 0.60/0.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------