TSTP Solution File: SYO064^4.003 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO064^4.003 : 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 : n002.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 04:44:59 EDT 2023
% Result : Theorem 0.56s 0.76s
% Output : Proof 0.56s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_a1,type,
a1: $i > $o ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_b2,type,
b2: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_b1,type,
b1: $i > $o ).
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__3,type,
eigen__3: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_b,type,
b: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( a2 @ eigen__5 ) ),
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
<=> ( ( b2 @ eigen__6 )
=> ~ ( a3 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( irel @ eigen__0 @ eigen__2 )
=> ~ ( irel @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( irel @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( irel @ eigen__2 @ eigen__3 )
=> ( a1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [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,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( irel @ eigen__2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ( irel @ eigen__2 @ eigen__4 )
=> ~ ( irel @ eigen__4 @ eigen__6 ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( irel @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( a1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ( irel @ eigen__2 @ eigen__4 )
=> ~ sP5 )
=> ( irel @ eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( irel @ eigen__0 @ eigen__3 )
=> ( b @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__0 @ eigen__2 )
=> ~ ( irel @ eigen__2 @ X1 ) )
=> ( irel @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [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,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( irel @ eigen__0 @ eigen__2 )
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP5
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [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,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( b2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP16
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( irel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ sP21
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( b1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b1 @ X1 ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [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,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP9
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP4
=> ( irel @ eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> ( a @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( irel @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP26
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ sP28
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( irel @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [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
<=> ( sP37
=> ~ ( irel @ eigen__4 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( b @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] : ( a3 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( irel @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( b2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [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,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP37
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ( irel @ eigen__2 @ eigen__5 )
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ~ ( sP37
=> ~ ( irel @ eigen__4 @ X1 ) )
=> ( irel @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( b2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP24
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( irel @ eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP37
=> ( ~ sP45
=> sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP40
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP53
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( irel @ eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sP12
=> sP30 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( a @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__2 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( irel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [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,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP12
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( sP16
=> sP46 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( ~ sP45
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP35
=> sP38 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( a3 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
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 )
=> ~ ( ( b2 @ X4 )
=> ~ ( a3 @ X4 ) ) ) ) ) ) ) ) ).
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 )
=> ~ ( ( b2 @ X4 )
=> ~ ( a3 @ X4 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ ( ~ sP48
=> ! [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 )
=> ~ ( ( b2 @ X3 )
=> ~ ( a3 @ X3 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP48,
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 )
=> ~ ( ( b2 @ X3 )
=> ~ ( a3 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP32,
introduced(assumption,[]) ).
thf(h5,assumption,
sP41,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP60,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP62
=> ( ~ ! [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 )
=> ~ ( ( b2 @ X2 )
=> ~ ( a3 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP62,
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 )
=> ~ ( ( b2 @ X2 )
=> ~ ( a3 @ X2 ) ) ) ) ) ),
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 )
=> ~ ( ( b2 @ X2 )
=> ~ ( a3 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP33
=> ~ sP55 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP33,
introduced(assumption,[]) ).
thf(h14,assumption,
sP55,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP37
=> ( ~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( b1 @ X1 )
=> ~ ( a2 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( b2 @ X1 )
=> ~ ( a3 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP37,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( b1 @ X1 )
=> ~ ( a2 @ X1 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( b2 @ X1 )
=> ~ ( a3 @ X1 ) ) ) ),
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 )
=> ~ ( ( b2 @ X1 )
=> ~ ( a3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP5
=> ~ sP34 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP5,
introduced(assumption,[]) ).
thf(h22,assumption,
sP34,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP53
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP53,
introduced(assumption,[]) ).
thf(h25,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP32
| ~ sP41
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP48
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP19
| ~ sP62
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP46
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP66
| ~ sP16
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| ~ sP62
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP31
| sP4
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP52
| ~ sP24
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP28
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP23
| sP16
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP63
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP15
| ~ sP43
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP16
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP36
| sP28
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP44
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP2
| sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP18
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP8
| sP66 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP7
| ~ sP33
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP10
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP59
| ~ sP12
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP38
| sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP68
| ~ sP35
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP65
| ~ sP12
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP54
| ~ sP37
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP39
| ~ sP37
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP11
| sP39
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP47
| ~ sP37
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP14
| sP47
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP21
| sP65 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP57
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP50
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP50
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP27
| sP35
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP49
| ~ sP58
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP35
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP25
| sP21
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP29
| ~ sP9
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP51
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP30
| sP57
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP61
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP44
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP2
| sP61 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP64
| sP68 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP20
| ~ sP5
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP6
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP56
| ~ sP53
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP45
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP67
| sP45
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP42
| sP69 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP55
| ~ sP40
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP34
| ~ sP26
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP3
| ~ sP22
| ~ sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(axiom4,axiom,
sP18 ).
thf(axiom3,axiom,
sP8 ).
thf(axiom2,axiom,
sP64 ).
thf(axiom1,axiom,
sP42 ).
thf(trans_axiom,axiom,
sP2 ).
thf(refl_axiom,axiom,
sP44 ).
thf(55,plain,
$false,
inference(prop_unsat,[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])],[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,h5,h6,h8,h13,h14,h16,h21,h22,h24,h25,axiom4,axiom3,axiom2,axiom1,trans_axiom,refl_axiom]) ).
thf(56,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])],[h23,55,h24,h25]) ).
thf(57,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)],[h19,56,h23]) ).
thf(58,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])],[h20,57,h21,h22]) ).
thf(59,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)],[h18,58,h20]) ).
thf(60,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])],[h17,59,h18,h19]) ).
thf(61,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])],[h15,60,h16,h17]) ).
thf(62,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)],[h11,61,h15]) ).
thf(63,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])],[h12,62,h13,h14]) ).
thf(64,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)],[h10,63,h12]) ).
thf(65,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,64,h10,h11]) ).
thf(66,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,65,h8,h9]) ).
thf(67,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h3,66,h7]) ).
thf(68,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,67,h5,h6]) ).
thf(69,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,68,h4]) ).
thf(70,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,69,h2,h3]) ).
thf(71,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,70,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 )
=> ~ ( ( b2 @ X4 )
=> ~ ( a3 @ X4 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[71,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO064^4.003 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 07:12:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.56/0.76 % SZS status Theorem
% 0.56/0.76 % Mode: cade22grackle2xfee4
% 0.56/0.76 % Steps: 4855
% 0.56/0.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------