TSTP Solution File: SEV148^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV148^5 : 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 19:32:45 EDT 2023
% Result : Theorem 0.60s 0.83s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 183
% Syntax : Number of formulae : 206 ( 26 unt; 17 typ; 11 def)
% Number of atoms : 575 ( 11 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1951 ( 510 ~; 97 |; 0 &; 762 @)
% ( 78 <=>; 504 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 97 ( 95 usr; 93 con; 0-2 aty)
% Number of variables : 342 ( 11 ^; 331 !; 0 ?; 342 :)
% 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__8,type,
eigen__8: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__15,type,
eigen__15: a ).
thf(ty_eigen__11,type,
eigen__11: a ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__9,type,
eigen__9: a ).
thf(ty_eigen__14,type,
eigen__14: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__10,type,
eigen__10: a ).
thf(ty_eigen__13,type,
eigen__13: a ).
thf(ty_eigen__12,type,
eigen__12: 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] :
~ ! [X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__6 @ X1 )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ! [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 ) ) ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__4 @ eigen__10 )
=> ~ ( eigen__0 @ eigen__10 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__4 @ eigen__11 )
=> ~ ( eigen__1 @ eigen__11 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__6 @ 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__6 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: a] :
~ ( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ 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__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__4 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( eigen__0 @ eigen__2 @ eigen__9 )
=> ( eigen__1 @ eigen__2 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__4 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ 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__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ( eigen__0 @ eigen__6 @ eigen__15 )
=> ( eigen__1 @ eigen__6 @ eigen__15 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__4 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ~ ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__6 @ 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__6 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ sP10
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__1 @ eigen__11 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP6
=> ~ ( eigen__0 @ eigen__10 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( ( eigen__4 @ eigen__11 )
=> ~ sP13 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( eigen__0 @ eigen__11 @ eigen__13 )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( eigen__0 @ eigen__6 @ eigen__15 )
=> ( eigen__1 @ eigen__6 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ~ ( ( eigen__4 @ eigen__11 )
=> ~ ( ~ ( eigen__0 @ eigen__11 @ X1 )
=> ( eigen__1 @ eigen__11 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ( eigen__0 @ eigen__6 @ eigen__14 )
=> ( eigen__1 @ eigen__6 @ eigen__14 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( sP7
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ! [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 ) ) ) )
=> ( eigen__4 @ X2 ) ) )
=> ( eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( eigen__0 @ eigen__6 @ eigen__14 )
=> ( eigen__4 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__1 @ eigen__2 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ( sP6
=> ~ ( ~ ( eigen__0 @ eigen__10 @ eigen__12 )
=> ( eigen__1 @ eigen__10 @ eigen__12 ) ) )
=> ( eigen__4 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( eigen__0 @ eigen__2 @ eigen__8 )
=> ( eigen__4 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( ! [X1: a] :
( ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__4 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__4 @ X2 ) ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__4 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__1 @ eigen__6 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( eigen__4 @ eigen__11 )
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( ~ ( eigen__0 @ eigen__2 @ eigen__8 )
=> ( eigen__1 @ eigen__2 @ eigen__8 ) )
=> ( eigen__4 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP24
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP7
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ! [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 ) ) ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__4 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a] :
( ~ ( sP6
=> ~ ( ~ ( eigen__0 @ eigen__10 @ X1 )
=> ( eigen__1 @ eigen__10 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__4 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( eigen__4 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__4 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X2 ) ) )
=> ( eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ ( eigen__0 @ eigen__10 @ eigen__12 )
=> ( eigen__1 @ eigen__10 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__4 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ sP14
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP6
=> ~ sP39 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ~ sP19
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ! [X1: a] :
( ( eigen__1 @ eigen__6 @ X1 )
=> ( eigen__4 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ sP12
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) )
=> ( eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP37
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP5
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP29
=> sP34 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( eigen__0 @ eigen__10 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ ( sP1
=> ~ sP53 )
=> ( eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( eigen__4 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( eigen__0 @ eigen__2 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ~ sP10
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( eigen__0 @ eigen__6 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( ~ sP57
=> ( eigen__1 @ eigen__2 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ! [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 ) ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: a] :
( ~ ( sP37
=> ~ ( eigen__1 @ eigen__11 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( ~ sP8
=> sP34 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: a] :
( ( eigen__1 @ eigen__6 @ X1 )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( ~ sP49
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ! [X1: a] :
( ~ ( sP21
=> ~ ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: a] :
( ~ ( sP6
=> ~ ( eigen__0 @ eigen__10 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ~ sP60
=> ( eigen__1 @ eigen__6 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ! [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 ) ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( ~ sP44
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ! [X1: a] :
( ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( sP75
=> ~ sP53 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( sP1
=> ~ sP53 ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(cTHM251C_pme,conjecture,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ 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 ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ 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 ) ) ),
inference(assume_negation,[status(cth)],[cTHM251C_pme]) ).
thf(h2,assumption,
~ ! [X1: a > a > $o,X2: a,X3: a] :
( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X2 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( X1 @ X2 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( X1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( eigen__0 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( eigen__0 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ 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 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a,X2: a] :
( ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ! [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] :
( ( eigen__1 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ 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(h4,assumption,
~ ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ! [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 ) ) ) )
=> ( 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 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP73
=> ! [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(assumption,[]) ).
thf(h6,assumption,
sP73,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [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(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( sP56
=> ~ sP2 )
=> sP58 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP56
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP58,
introduced(assumption,[]) ).
thf(h11,assumption,
sP56,
introduced(assumption,[]) ).
thf(h12,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( sP17
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP21
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP65
| sP8
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP70
| sP65 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP72
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP19
| ~ sP21
| ~ sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP43
| sP19
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP70
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP2
| sP70 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP16
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP49
| ~ sP37
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP68
| sP49
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP18
| sP68 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP2
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( sP39
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP42
| ~ sP6
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP25
| sP42
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP35
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP2
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( sP5
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP50
| ~ sP5
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP56
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( sP61
| ~ sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP31
| ~ sP61
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP56
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( sP51
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP51
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP66
| ~ sP51 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(29,plain,
( ~ sP44
| ~ sP66
| ~ sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP23
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP23
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP75
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).
thf(33,plain,
( ~ sP77
| ~ sP75
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP74
| sP44
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP27
| sP77
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP22
| sP74 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP10
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP59
| sP10
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP12
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP12
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP45
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP45
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP30
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP30
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP15
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP15
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP64
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(48,plain,
( sP14
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( sP14
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( sP41
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( sP41
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( sP71
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(53,plain,
( sP48
| ~ sP64 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(54,plain,
( sP53
| ~ sP71 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(55,plain,
( sP32
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP32
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( sP76
| ~ sP32 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(58,plain,
( ~ sP40
| ~ sP76
| ~ sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( sP26
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( sP26
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( sP1
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(62,plain,
( ~ sP78
| ~ sP1
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP38
| sP40
| sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP54
| sP78
| sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP67
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP69
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP47
| sP69
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( sP11
| ~ sP45 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(69,plain,
( sP46
| ~ sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( sP46
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( sP62
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(72,plain,
( sP7
| ~ sP46 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(73,plain,
( ~ sP33
| ~ sP7
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( ~ sP20
| sP33
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP73
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,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,h6,h11,h12,h10]) ).
thf(77,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,76,h11,h12]) ).
thf(78,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,77,h9,h10]) ).
thf(79,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)],[h7,78,h8]) ).
thf(80,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,79,h6,h7]) ).
thf(81,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,80,h5]) ).
thf(82,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,81,h4]) ).
thf(83,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,82,h3]) ).
thf(84,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,83,h2]) ).
thf(85,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[84,h0]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ 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 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[84,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV148^5 : 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 : n023.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 : Thu Aug 24 03:56:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.60/0.83 % SZS status Theorem
% 0.60/0.83 % Mode: cade22grackle2xfee4
% 0.60/0.83 % Steps: 5515
% 0.60/0.83 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------