TSTP Solution File: SEV153^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV153^5 : 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 : Thu Aug 31 19:32:46 EDT 2023
% Result : Theorem 34.44s 34.45s
% Output : Proof 34.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 191
% Syntax : Number of formulae : 233 ( 62 unt; 21 typ; 7 def)
% Number of atoms : 669 ( 7 equ; 0 cnn)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 2804 ( 749 ~; 74 |; 0 &;1169 @)
% ( 69 <=>; 743 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 109 ( 109 >; 0 *; 0 +; 0 <<)
% Number of symbols : 92 ( 90 usr; 85 con; 0-2 aty)
% Number of variables : 460 ( 7 ^; 453 !; 0 ?; 460 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__64,type,
eigen__64: a ).
thf(ty_eigen__44,type,
eigen__44: a ).
thf(ty_eigen__8,type,
eigen__8: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__45,type,
eigen__45: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__115,type,
eigen__115: a ).
thf(ty_eigen__65,type,
eigen__65: a ).
thf(ty_eigen__11,type,
eigen__11: a ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__103,type,
eigen__103: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__79,type,
eigen__79: a > $o ).
thf(ty_eigen__43,type,
eigen__43: a ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__77,type,
eigen__77: a ).
thf(ty_eigen__104,type,
eigen__104: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: a] :
~ ( ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) )
=> ( eigen__8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__115,definition,
( eigen__115
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__79 @ eigen__104 )
=> ~ ( eigen__0 @ eigen__104 @ X1 ) )
=> ( eigen__79 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__115])]) ).
thf(eigendef_eigen__77,definition,
( eigen__77
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__45 @ eigen__65 )
=> ~ ( eigen__1 @ eigen__65 @ X1 ) )
=> ( eigen__45 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__77])]) ).
thf(eigendef_eigen__64,definition,
( eigen__64
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__43 @ X1 )
=> ( eigen__45 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__64])]) ).
thf(eigendef_eigen__103,definition,
( eigen__103
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__43 @ X1 )
=> ( eigen__79 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__103])]) ).
thf(eigendef_eigen__104,definition,
( eigen__104
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__79 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__79 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__104])]) ).
thf(eigendef_eigen__65,definition,
( eigen__65
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__45 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__45 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__65])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__1 @ eigen__5 @ X1 ) )
=> ( eigen__8 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__8 @ X2 ) ) )
=> ( eigen__8 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__8 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ~ ( ( eigen__79 @ eigen__104 )
=> ~ ( ~ ( eigen__0 @ eigen__104 @ X1 )
=> ( eigen__1 @ eigen__104 @ X1 ) ) )
=> ( eigen__79 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: a] :
( ( eigen__0 @ eigen__43 @ X1 )
=> ( eigen__79 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__79 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__79 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( eigen__0 @ eigen__43 @ eigen__103 )
=> ( eigen__1 @ eigen__43 @ eigen__103 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ( eigen__8 @ eigen__6 )
=> ~ ( ~ ( eigen__0 @ eigen__6 @ eigen__11 )
=> ( eigen__1 @ eigen__6 @ eigen__11 ) ) )
=> ( eigen__8 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ~ ( ( eigen__45 @ eigen__65 )
=> ~ ( eigen__1 @ eigen__65 @ X1 ) )
=> ( eigen__45 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__43 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__44 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__43 @ eigen__103 )
=> ( eigen__79 @ eigen__103 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X2 )
=> ( eigen__1 @ eigen__2 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ( eigen__79 @ eigen__104 )
=> ~ ( eigen__0 @ eigen__104 @ eigen__115 ) )
=> ( eigen__79 @ eigen__115 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__43 @ X1 )
=> ( eigen__1 @ eigen__43 @ X1 ) )
=> ( eigen__45 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 @ eigen__65 @ eigen__77 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__45 @ eigen__64 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__8 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ~ ( ( eigen__79 @ eigen__104 )
=> ~ ( eigen__0 @ eigen__104 @ X1 ) )
=> ( eigen__79 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X2 )
=> ( eigen__1 @ eigen__5 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__79 @ eigen__104 )
=> ~ ( eigen__0 @ eigen__104 @ eigen__115 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__79 @ eigen__103 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( eigen__0 @ eigen__6 @ eigen__11 )
=> ( eigen__1 @ eigen__6 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP21
=> ( eigen__8 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__45 @ eigen__44 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__79 @ eigen__44 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__43 @ X1 )
=> ( eigen__1 @ eigen__43 @ X1 ) )
=> ( eigen__79 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ( eigen__0 @ eigen__43 @ eigen__64 )
=> ( eigen__1 @ eigen__43 @ eigen__64 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__1 @ eigen__5 @ X1 ) )
=> ( eigen__8 @ X1 ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__0 @ eigen__43 @ eigen__103 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( eigen__79 @ eigen__104 )
=> ~ ( ~ ( eigen__0 @ eigen__104 @ eigen__115 )
=> ( eigen__1 @ eigen__104 @ eigen__115 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) )
=> ( eigen__8 @ X1 ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP6
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP29
=> ( eigen__79 @ eigen__115 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) )
=> ( eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a] :
( ~ ( ( eigen__45 @ eigen__65 )
=> ~ ( ~ ( eigen__0 @ eigen__65 @ X1 )
=> ( eigen__1 @ eigen__65 @ X1 ) ) )
=> ( eigen__45 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ ( ! [X1: a] :
( ( eigen__1 @ eigen__43 @ X1 )
=> ( eigen__45 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__45 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__45 @ X2 ) ) )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a] :
( ~ ( sP16
=> ~ ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) ) )
=> ( eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( eigen__45 @ eigen__65 )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: a] :
( ( eigen__0 @ eigen__43 @ X1 )
=> ( eigen__79 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ ( eigen__0 @ eigen__104 @ eigen__115 )
=> ( eigen__1 @ eigen__104 @ eigen__115 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( eigen__1 @ eigen__43 @ eigen__64 )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ sP30
=> ( eigen__8 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP16
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP26
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__45 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__45 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( eigen__45 @ eigen__65 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( eigen__45 @ eigen__77 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( eigen__79 @ eigen__115 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( eigen__1 @ eigen__43 @ eigen__64 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__1 @ eigen__5 @ X1 ) )
=> ( eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__45 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__45 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ sP46
=> sP34 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( eigen__79 @ eigen__104 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( eigen__0 @ eigen__104 @ eigen__115 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( eigen__8 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__79 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__79 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: a] :
( ( eigen__1 @ eigen__43 @ X1 )
=> ( eigen__45 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ~ sP5
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( sP47
=> ~ ( ~ ( eigen__0 @ eigen__65 @ eigen__77 )
=> sP14 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP58
=> ~ sP52 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ~ sP60
=> sP48 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__79 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__79 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( ~ ( eigen__0 @ eigen__65 @ eigen__77 )
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__6 @ X2 )
=> ( eigen__1 @ eigen__6 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( ~ sP38
=> sP48 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__43 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__44 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( eigen__8 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(cTHM251H_pme,conjecture,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ~ ( ~ ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ~ ! [X5: a,X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( X1 @ X5 @ X8 )
=> ( X2 @ X5 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X6 ) )
=> ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X6 @ X9 )
=> ( X2 @ X6 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ~ ( ~ ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ~ ! [X5: a,X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( X1 @ X5 @ X8 )
=> ( X2 @ X5 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X6 ) )
=> ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X6 @ X9 )
=> ( X2 @ X6 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM251H_pme]) ).
thf(h2,assumption,
~ ! [X1: a > a > $o,X2: a,X3: a] :
( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ~ ( ~ ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a,X5: a] :
( ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( X1 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( X1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( ~ ( eigen__0 @ X4 @ X7 )
=> ( X1 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( ~ ( eigen__0 @ X7 @ X8 )
=> ( X1 @ X7 @ X8 ) ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( eigen__0 @ X4 @ X8 )
=> ( X1 @ X4 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X5 ) )
=> ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( eigen__0 @ X5 @ X8 )
=> ( X1 @ X5 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( eigen__0 @ X4 @ X8 )
=> ( X1 @ X4 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a,X2: a] :
( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ~ ( ~ ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a,X4: a] :
( ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( eigen__0 @ X3 @ X6 )
=> ( eigen__1 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( ~ ( eigen__0 @ X3 @ X7 )
=> ( eigen__1 @ X3 @ X7 ) )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X4 ) )
=> ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( ~ ( eigen__0 @ X4 @ X7 )
=> ( eigen__1 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( ~ ( eigen__0 @ X3 @ X7 )
=> ( eigen__1 @ X3 @ X7 ) )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X3 )
=> ( eigen__1 @ eigen__2 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ~ ( ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X3 )
=> ( eigen__1 @ eigen__2 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a,X3: a] :
( ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( eigen__1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( eigen__0 @ X2 @ X6 )
=> ( eigen__1 @ X2 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X3 ) )
=> ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( eigen__0 @ X3 @ X6 )
=> ( eigen__1 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( eigen__0 @ X2 @ X6 )
=> ( eigen__1 @ X2 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ sP11
=> ~ ( ~ ( ~ sP11
=> ~ ! [X1: a,X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( eigen__1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h7,assumption,
( ~ ( ~ sP11
=> ~ ! [X1: a,X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( eigen__1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP53,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP46,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP34,
introduced(assumption,[]) ).
thf(h11,assumption,
sP62,
introduced(assumption,[]) ).
thf(h12,assumption,
sP3,
introduced(assumption,[]) ).
thf(h13,assumption,
( ~ sP11
=> ~ ! [X1: a,X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( eigen__1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP11,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: a,X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP46
| ~ sP62
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP53
| sP46
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,h11,h12,h10,h15]) ).
thf(h17,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__43 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__43 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__43 @ X3 )
=> ( eigen__1 @ eigen__43 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ( ~ sP9
=> sP68 )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__43 @ X2 )
=> ( eigen__1 @ eigen__43 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__44 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
( ~ sP9
=> sP68 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__43 @ X2 )
=> ( eigen__1 @ eigen__43 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__44 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP9,
introduced(assumption,[]) ).
thf(h22,assumption,
sP68,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ~ ( sP25
=> ~ sP64 )
=> sP24 ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( sP25
=> ~ sP64 ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h26,assumption,
sP25,
introduced(assumption,[]) ).
thf(h27,assumption,
sP64,
introduced(assumption,[]) ).
thf(5,plain,
( sP40
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP29
| ~ sP54
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP32
| sP29
| sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP4
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP64
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP6
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP31
| ~ sP6
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP25
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP19
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP19
| sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP12
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP12
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP17
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__115]) ).
thf(18,plain,
( sP10
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP10
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP57
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__104]) ).
thf(21,plain,
( sP39
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__103]) ).
thf(22,plain,
( ~ sP5
| ~ sP39
| ~ sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP59
| sP5
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP9
| sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h27,h24,h25,h23,h21,h19,h20,h18,h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,h21,h26,h27,h25]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h23,h21,h19,h20,h18,h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h26,h27])],[h24,25,h26,h27]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h19,h20,h18,h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,26,h24,h25]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h19,h20,h18,h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__79)],[h20,27,h23]) ).
thf(h28,assumption,
~ ( ~ ( sP13
=> ~ sP45 )
=> sP23 ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( sP13
=> ~ sP45 ),
introduced(assumption,[]) ).
thf(h30,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(h31,assumption,
sP13,
introduced(assumption,[]) ).
thf(h32,assumption,
sP45,
introduced(assumption,[]) ).
thf(29,plain,
( sP65
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP60
| ~ sP47
| ~ sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP63
| sP60
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP35
| sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP45
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( sP26
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP44
| ~ sP26
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP13
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( sP38
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP38
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP67
| ~ sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP67
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP8
| ~ sP67 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__77]) ).
thf(42,plain,
( sP41
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP41
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP52
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__65]) ).
thf(45,plain,
( sP58
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__64]) ).
thf(46,plain,
( ~ sP61
| ~ sP58
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP36
| sP61
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP68
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h31,h32,h29,h30,h28,h22,h19,h20,h18,h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,h22,h31,h32,h30]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h30,h28,h22,h19,h20,h18,h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h29,49,h31,h32]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h22,h19,h20,h18,h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,50,h29,h30]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h19,h20,h18,h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__45)],[h20,51,h28]) ).
thf(53,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h19,h20,h18,h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h21]),tab_imp(discharge,[h22])],[h19,28,52,h21,h22]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,53,h19,h20]) ).
thf(55,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__44)],[h17,54,h18]) ).
thf(56,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__43)],[h16,55,h17]) ).
thf(57,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h13,4,56,h15,h16]) ).
thf(h33,assumption,
~ ! [X1: a,X2: a] :
( ~ ( ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X4 )
=> ( eigen__1 @ eigen__5 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X1 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X4 )
=> ( eigen__1 @ eigen__5 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ ! [X1: a] :
( ~ ( sP18
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__6 @ X3 )
=> ( eigen__1 @ eigen__6 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X3 )
=> ( eigen__1 @ eigen__5 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( ~ ( sP18
=> ~ sP66 )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X2 )
=> ( eigen__1 @ eigen__5 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(assumption,[]) ).
thf(h36,assumption,
~ ( sP18
=> ~ sP66 ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X2 )
=> ( eigen__1 @ eigen__5 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
sP18,
introduced(assumption,[]) ).
thf(h39,assumption,
sP66,
introduced(assumption,[]) ).
thf(h40,assumption,
~ ( ~ sP27
=> sP56 ),
introduced(assumption,[]) ).
thf(h41,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h42,assumption,
~ sP56,
introduced(assumption,[]) ).
thf(h43,assumption,
sP51,
introduced(assumption,[]) ).
thf(h44,assumption,
sP2,
introduced(assumption,[]) ).
thf(58,plain,
( ~ sP43
| ~ sP16
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP7
| sP43
| sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP37
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(61,plain,
( sP22
| ~ sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(62,plain,
( sP22
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( sP33
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(64,plain,
( ~ sP27
| ~ sP51
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP30
| ~ sP33
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP1
| sP27
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP42
| sP30
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP18
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP2
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP66
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(71,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h43,h44,h41,h42,h40,h38,h39,h36,h37,h35,h34,h33,h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[58,59,60,61,62,63,64,65,66,67,68,69,70,h38,h39,h43,h44,h42]) ).
thf(72,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h42,h40,h38,h39,h36,h37,h35,h34,h33,h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h43,h44])],[h41,71,h43,h44]) ).
thf(73,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h40,h38,h39,h36,h37,h35,h34,h33,h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h41,h42])],[h40,72,h41,h42]) ).
thf(74,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h38,h39,h36,h37,h35,h34,h33,h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h40]),tab_negall(eigenvar,eigen__8)],[h37,73,h40]) ).
thf(75,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h37,h35,h34,h33,h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h38,h39])],[h36,74,h38,h39]) ).
thf(76,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h34,h33,h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h36,h37])],[h35,75,h36,h37]) ).
thf(77,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h34,h33,h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h35]),tab_negall(eigenvar,eigen__7)],[h34,76,h35]) ).
thf(78,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h33,h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h34]),tab_negall(eigenvar,eigen__6)],[h33,77,h34]) ).
thf(79,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__5)],[h14,78,h33]) ).
thf(80,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[h7,57,79,h13,h14]) ).
thf(81,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,80,h11,h12]) ).
thf(82,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,81,h9,h10]) ).
thf(83,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__4)],[h6,82,h8]) ).
thf(84,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,83,h6,h7]) ).
thf(85,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,84,h5]) ).
thf(86,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,85,h4]) ).
thf(87,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,86,h3]) ).
thf(88,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,87,h2]) ).
thf(89,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[88,h0]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ~ ( ~ ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ~ ! [X5: a,X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( X1 @ X5 @ X8 )
=> ( X2 @ X5 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X6 ) )
=> ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X6 @ X9 )
=> ( X2 @ X6 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[88,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV153^5 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 03:34:27 EDT 2023
% 0.12/0.34 % CPUTime :
% 34.44/34.45 % SZS status Theorem
% 34.44/34.45 % Mode: cade22grackle2x798d
% 34.44/34.45 % Steps: 513587
% 34.44/34.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------