%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO066^4.002 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 : Thu Oct 9 03:22:39 PM UTC 2025
% Result : Theorem 0.71s 0.89s
% Output : Proof 0.71s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_o12,type,
o12: $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_o32,type,
o32: $i > $o ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(ty_o11,type,
o11: $i > $o ).
thf(ty_o22,type,
o22: $i > $o ).
thf(ty_o21,type,
o21: $i > $o ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_o31,type,
o31: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( ( o11 @ eigen__1 )
=> ~ ( o21 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( irel @ X1 @ X2 )
=> ~ ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__4 @ eigen__6 )
=> ~ ( irel @ eigen__6 @ X1 ) )
=> ( irel @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__2 @ eigen__6 )
=> ~ ( irel @ eigen__6 @ X1 ) )
=> ( irel @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( o31 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( irel @ eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( irel @ eigen__8 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__2 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( irel @ eigen__2 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( o31 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( irel @ eigen__4 @ eigen__7 )
=> ( o22 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( irel @ eigen__6 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__2 @ eigen__4 )
=> ~ ( irel @ eigen__4 @ X1 ) )
=> ( irel @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( irel @ eigen__6 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( irel @ eigen__0 @ eigen__9 )
=> ( o12 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( o21 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ( irel @ eigen__2 @ eigen__4 )
=> ~ ( irel @ eigen__4 @ eigen__7 ) )
=> ( irel @ eigen__2 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( irel @ eigen__2 @ eigen__4 )
=> ~ ( irel @ eigen__4 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> ( o11 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o31 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o32 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP12
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( o21 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( sP12
=> ~ ( irel @ eigen__8 @ eigen__9 ) )
=> ( irel @ eigen__6 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( irel @ eigen__4 @ eigen__6 )
=> ~ ( irel @ eigen__6 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( o22 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o21 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o22 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( irel @ eigen__0 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( irel @ eigen__4 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP6
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP29
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( irel @ eigen__2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( o22 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( o22 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP25
=> ~ ( o32 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( irel @ eigen__6 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ ( sP31
=> ~ sP14 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( o31 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( irel @ eigen__4 @ eigen__5 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( o21 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( o11 @ eigen__3 )
=> ~ ( o31 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i] :
( ~ ( sP6
=> ~ ( irel @ eigen__4 @ X1 ) )
=> ( irel @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( irel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( o11 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ~ ( ( irel @ eigen__2 @ eigen__4 )
=> ~ ( irel @ eigen__4 @ eigen__6 ) )
=> sP31 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( irel @ eigen__2 @ eigen__3 )
=> ( o31 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__4 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o22 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ~ sP21
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ sP37
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( o32 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( irel @ eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( irel @ eigen__8 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP9
=> ( o32 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ( o12 @ eigen__7 )
=> ~ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP50
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP28
=> ( o32 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( o12 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ( irel @ eigen__4 @ eigen__10 )
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o11 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o12 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o21 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( irel @ eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ~ ( sP6
=> ~ ( irel @ eigen__4 @ eigen__10 ) )
=> ( irel @ eigen__0 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( o11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( o12 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( irel @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o11 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o12 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( irel @ eigen__4 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ( irel @ eigen__0 @ eigen__10 )
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: $i] :
( ~ ( sP12
=> ~ ( irel @ eigen__8 @ X1 ) )
=> ( irel @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( o32 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( ~ sP55
=> sP69 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( ~ sP24
=> sP62 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( sP31
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( ~ sP10
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( o32 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( sP66
=> ~ ( o32 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ~ sP39
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( irel @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( ( irel @ eigen__2 @ eigen__7 )
=> sP57 ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( o31 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( ~ ( sP50
=> ~ sP35 )
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( ~ sP65
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( o12 @ 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 )
=> ( o32 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( irel @ eigen__0 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( sP22
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__6 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__6 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( sP50
=> ~ sP35 ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( o11 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( sP69
=> sP72 ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( o12 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o12 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ( ~ ( sP42
=> ~ sP67 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o21 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o22 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( sP85
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( irel @ eigen__2 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( o32 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( sP12
=> ~ sP52 ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ! [X1: $i] :
( ~ ( sP42
=> ~ ( irel @ eigen__2 @ X1 ) )
=> ( irel @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( ( irel @ eigen__2 @ eigen__3 )
=> sP91 ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ( sP67
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( irel @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( o32 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( sP42
=> ~ sP67 ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ( sP6
=> ~ sP69 ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
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 )
=> ~ ( ( o11 @ X2 )
=> ~ ( o21 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o11 @ X3 )
=> ~ ( o31 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o21 @ X4 )
=> ~ ( o31 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( o12 @ X5 )
=> ~ ( o22 @ X5 ) ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( ~ ! [X6: $i] :
( ( irel @ X5 @ X6 )
=> ~ ( ( o12 @ X6 )
=> ~ ( o32 @ X6 ) ) )
=> ! [X6: $i] :
( ( irel @ X5 @ X6 )
=> ~ ( ( o22 @ X6 )
=> ~ ( o32 @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o11 @ X2 )
=> ~ ( o21 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o11 @ X3 )
=> ~ ( o31 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o21 @ X4 )
=> ~ ( o31 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( o12 @ X5 )
=> ~ ( o22 @ X5 ) ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( ~ ! [X6: $i] :
( ( irel @ X5 @ X6 )
=> ~ ( ( o12 @ X6 )
=> ~ ( o32 @ X6 ) ) )
=> ! [X6: $i] :
( ( irel @ X5 @ X6 )
=> ~ ( ( o22 @ X6 )
=> ~ ( o32 @ X6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( o11 @ X1 )
=> ~ ( o21 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o11 @ X2 )
=> ~ ( o31 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o21 @ X3 )
=> ~ ( o31 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o12 @ X4 )
=> ~ ( o22 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( o12 @ X5 )
=> ~ ( o32 @ X5 ) ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( o22 @ X5 )
=> ~ ( o32 @ X5 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( o11 @ X1 )
=> ~ ( o21 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o11 @ X2 )
=> ~ ( o31 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o21 @ X3 )
=> ~ ( o31 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o12 @ X4 )
=> ~ ( o22 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( o12 @ X5 )
=> ~ ( o32 @ X5 ) ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( o22 @ X5 )
=> ~ ( o32 @ X5 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP64
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP64,
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP42
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( o11 @ X1 )
=> ~ ( o31 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o21 @ X2 )
=> ~ ( o31 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o12 @ X3 )
=> ~ ( o22 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o12 @ X4 )
=> ~ ( o32 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o22 @ X4 )
=> ~ ( o32 @ X4 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP42,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( o11 @ X1 )
=> ~ ( o31 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o21 @ X2 )
=> ~ ( o31 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o12 @ X3 )
=> ~ ( o22 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o12 @ X4 )
=> ~ ( o32 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o22 @ X4 )
=> ~ ( o32 @ X4 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( o11 @ X1 )
=> ~ ( o31 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o21 @ X2 )
=> ~ ( o31 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o12 @ X3 )
=> ~ ( o22 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o12 @ X4 )
=> ~ ( o32 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o22 @ X4 )
=> ~ ( o32 @ X4 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP104
=> ~ sP40 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP104,
introduced(assumption,[]) ).
thf(h14,assumption,
sP40,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP67
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( o21 @ X1 )
=> ~ ( o31 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o12 @ X2 )
=> ~ ( o22 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o12 @ X3 )
=> ~ ( o32 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o22 @ X3 )
=> ~ ( o32 @ X3 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP67,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( o21 @ X1 )
=> ~ ( o31 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o12 @ X2 )
=> ~ ( o22 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o12 @ X3 )
=> ~ ( o32 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o22 @ X3 )
=> ~ ( o32 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( o21 @ X1 )
=> ~ ( o31 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o12 @ X2 )
=> ~ ( o22 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o12 @ X3 )
=> ~ ( o32 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o22 @ X3 )
=> ~ ( o32 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP85
=> ~ sP88 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP85,
introduced(assumption,[]) ).
thf(h22,assumption,
sP88,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP50
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( o12 @ X1 )
=> ~ ( o22 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o12 @ X2 )
=> ~ ( o32 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o22 @ X2 )
=> ~ ( o32 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP50,
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( o12 @ X1 )
=> ~ ( o22 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o12 @ X2 )
=> ~ ( o32 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o22 @ X2 )
=> ~ ( o32 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( o12 @ X1 )
=> ~ ( o22 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o12 @ X2 )
=> ~ ( o32 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o22 @ X2 )
=> ~ ( o32 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ ( sP80
=> ~ sP54 ),
introduced(assumption,[]) ).
thf(h29,assumption,
sP80,
introduced(assumption,[]) ).
thf(h30,assumption,
sP54,
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( sP12
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( o12 @ X1 )
=> ~ ( o32 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( o22 @ X1 )
=> ~ ( o32 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h32,assumption,
sP12,
introduced(assumption,[]) ).
thf(h33,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( o12 @ X1 )
=> ~ ( o32 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( o22 @ X1 )
=> ~ ( o32 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( o12 @ X1 )
=> ~ ( o32 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( o22 @ X1 )
=> ~ ( o32 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h36,assumption,
~ ( sP52
=> ~ sP77 ),
introduced(assumption,[]) ).
thf(h37,assumption,
sP52,
introduced(assumption,[]) ).
thf(h38,assumption,
sP77,
introduced(assumption,[]) ).
thf(h39,assumption,
~ ( sP7
=> ~ sP34 ),
introduced(assumption,[]) ).
thf(h40,assumption,
sP7,
introduced(assumption,[]) ).
thf(h41,assumption,
sP34,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP59
| ~ sP64
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP19
| ~ sP64
| sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP61
| sP59 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP78
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP107
| ~ sP6
| ~ sP69 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP63
| sP107
| sP87 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP29
| ~ sP6
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP30
| sP29
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP106
| ~ sP42
| ~ sP67 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP95
| sP106
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP41
| sP63 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP41
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP101
| sP95 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP51
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP51
| sP101 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP15
| ~ sP27
| sP66 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP94
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP60
| sP78
| sP94 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP70
| ~ sP87
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP47
| sP70 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP26
| sP61
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP2
| sP51 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP68
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP96
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP45
| ~ sP104
| sP82 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP102
| ~ sP104
| sP91 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP37
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP65
| sP102 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP75
| ~ sP31
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP36
| sP75
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP103
| ~ sP67
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP44
| sP103
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP18
| ~ sP67
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP17
| sP18
| sP98 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP4
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP13
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP13
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP8
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP81
| ~ sP98
| sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP93
| sP81 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP84
| sP65
| sP93 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP53
| ~ sP9
| sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP86
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP49
| sP37
| sP86 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP68
| sP84 ),
inference(all_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP20
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP38
| ~ sP85
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP97
| ~ sP85
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP10
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP39
| sP97 ),
inference(all_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP55
| ~ sP50
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP73
| sP55
| sP69 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP90
| ~ sP50
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP83
| sP90
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP24
| ~ sP50
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP74
| sP24
| sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP3
| sP73 ),
inference(all_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP3
| sP83 ),
inference(all_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP3
| sP74 ),
inference(all_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP46
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP58
| ~ sP69
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP11
| ~ sP62
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP32
| sP58 ),
inference(all_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP32
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP79
| sP39
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP92
| ~ sP69
| sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP56
| ~ sP28
| sP99 ),
inference(prop_rule,[status(thm)],[]) ).
thf(70,plain,
( ~ sP105
| sP92 ),
inference(all_rule,[status(thm)],[]) ).
thf(71,plain,
( ~ sP105
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(72,plain,
( ~ sP76
| sP10
| sP105 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( ~ sP2
| sP46 ),
inference(all_rule,[status(thm)],[]) ).
thf(74,plain,
( ~ sP96
| sP79 ),
inference(all_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP20
| sP76 ),
inference(all_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP21
| ~ sP12
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(77,plain,
( ~ sP48
| sP21
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(78,plain,
( ~ sP100
| ~ sP12
| ~ sP52 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP23
| sP100
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(80,plain,
( ~ sP71
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(81,plain,
( ~ sP71
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(82,plain,
( ~ sP89
| sP71 ),
inference(all_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP2
| sP89 ),
inference(all_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP1
| ~ sP43
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(85,plain,
( ~ sP40
| ~ sP91
| ~ sP82 ),
inference(prop_rule,[status(thm)],[]) ).
thf(86,plain,
( ~ sP88
| ~ sP22
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(87,plain,
( ~ sP54
| ~ sP57
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(88,plain,
( ~ sP77
| ~ sP66
| ~ sP99 ),
inference(prop_rule,[status(thm)],[]) ).
thf(89,plain,
( ~ sP34
| ~ sP25
| ~ sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(axiom3,axiom,
sP20 ).
thf(axiom2,axiom,
sP96 ).
thf(axiom1,axiom,
sP68 ).
thf(trans_axiom,axiom,
sP2 ).
thf(90,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h40,h41,h39,h37,h38,h36,h34,h35,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])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,h5,h6,h8,h13,h14,h16,h21,h22,h24,h29,h30,h32,h37,h38,h40,h41,axiom3,axiom2,axiom1,trans_axiom]) ).
thf(91,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h39,h37,h38,h36,h34,h35,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]),tab_negimp(discharge,[h40,h41])],[h39,90,h40,h41]) ).
thf(92,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h37,h38,h36,h34,h35,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]),tab_negall(discharge,[h39]),tab_negall(eigenvar,eigen__10)],[h35,91,h39]) ).
thf(93,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h34,h35,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]),tab_negimp(discharge,[h37,h38])],[h36,92,h37,h38]) ).
thf(94,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h34,h35,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]),tab_negall(discharge,[h36]),tab_negall(eigenvar,eigen__9)],[h34,93,h36]) ).
thf(95,plain,
$false,
inference(tab_negimp,[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]),tab_negimp(discharge,[h34,h35])],[h33,94,h34,h35]) ).
thf(96,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])],[h31,95,h32,h33]) ).
thf(97,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)],[h27,96,h31]) ).
thf(98,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])],[h28,97,h29,h30]) ).
thf(99,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)],[h26,98,h28]) ).
thf(100,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])],[h25,99,h26,h27]) ).
thf(101,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])],[h23,100,h24,h25]) ).
thf(102,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)],[h19,101,h23]) ).
thf(103,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])],[h20,102,h21,h22]) ).
thf(104,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)],[h18,103,h20]) ).
thf(105,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])],[h17,104,h18,h19]) ).
thf(106,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])],[h15,105,h16,h17]) ).
thf(107,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)],[h11,106,h15]) ).
thf(108,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])],[h12,107,h13,h14]) ).
thf(109,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)],[h10,108,h12]) ).
thf(110,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,109,h10,h11]) ).
thf(111,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,110,h8,h9]) ).
thf(112,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h3,111,h7]) ).
thf(113,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,112,h5,h6]) ).
thf(114,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,113,h4]) ).
thf(115,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,114,h2,h3]) ).
thf(116,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,115,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( o11 @ X2 )
=> ~ ( o21 @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( o11 @ X3 )
=> ~ ( o31 @ X3 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( o21 @ X4 )
=> ~ ( o31 @ X4 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ~ ( ( o12 @ X5 )
=> ~ ( o22 @ X5 ) ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( ~ ! [X6: $i] :
( ( irel @ X5 @ X6 )
=> ~ ( ( o12 @ X6 )
=> ~ ( o32 @ X6 ) ) )
=> ! [X6: $i] :
( ( irel @ X5 @ X6 )
=> ~ ( ( o22 @ X6 )
=> ~ ( o32 @ X6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[116,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO066^4.002 : TPTP v9.2.0. Released v4.0.0.
% 0.12/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Oct 9 01:22:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.71/0.89 % SZS status Theorem
% 0.71/0.89 % Mode: cade22grackle2xfee4
% 0.71/0.89 % Steps: 4116
% 0.71/0.89 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------