TSTP Solution File: SEV119^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV119^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 : 600s
% DateTime : Tue Jul 19 18:04:56 EDT 2022
% Result : Theorem 0.94s 1.14s
% Output : Proof 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 162
% Syntax : Number of formulae : 192 ( 50 unt; 18 typ; 10 def)
% Number of atoms : 492 ( 20 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1333 ( 277 ~; 72 |; 0 &; 630 @)
% ( 63 <=>; 291 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 172 ( 172 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 82 usr; 76 con; 0-2 aty)
% Number of variables : 281 ( 38 ^ 243 !; 0 ?; 281 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__12,type,
eigen__12: a > a > $o ).
thf(ty_eigen__2,type,
eigen__2: a > a > $o ).
thf(ty_eigen__16,type,
eigen__16: a > a > $o ).
thf(ty_eigen__30,type,
eigen__30: a ).
thf(ty_eigen__35,type,
eigen__35: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__47,type,
eigen__47: a ).
thf(ty_eigen__0,type,
eigen__0: ( a > a > $o ) > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__5,type,
eigen__5: a > a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__13,type,
eigen__13: a > a > $o ).
thf(ty_eigen__9,type,
eigen__9: a ).
thf(ty_eigen__28,type,
eigen__28: a ).
thf(ty_eigen__42,type,
eigen__42: a ).
thf(ty_eigen__22,type,
eigen__22: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__42,definition,
( eigen__42
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__30 @ X1 )
=> ( eigen__16 @ eigen__30 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__42])]) ).
thf(eigendef_eigen__47,definition,
( eigen__47
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__2 @ eigen__35 @ X1 )
=> ( eigen__16 @ eigen__35 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__47])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( ~ ( eigen__1 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ X2 ) )
=> ( eigen__5 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__1
@ ^ [X1: a > a > $o] :
~ ( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__6 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__22,definition,
( eigen__22
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__2 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ( eigen__16 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__22])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__1
@ ^ [X1: a > a > $o] :
~ ( ~ ( ! [X2: a,X3: a] :
( ( eigen__2 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__6 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: a] :
~ ( ( ~ ( eigen__1 @ eigen__6 @ X1 )
=> ( eigen__2 @ eigen__6 @ X1 ) )
=> ( eigen__5 @ eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__28,definition,
( eigen__28
= ( eps__0
@ ^ [X1: a] :
~ ( ( ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__22 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__2 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__22 @ X1 ) ) )
=> ( eigen__16 @ eigen__22 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__28])]) ).
thf(eigendef_eigen__30,definition,
( eigen__30
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__30])]) ).
thf(eigendef_eigen__35,definition,
( eigen__35
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__2 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__35])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( eigen__1 @ eigen__30 @ X1 )
=> ( eigen__16 @ eigen__30 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__1 @ eigen__30 @ eigen__42 )
=> ( eigen__16 @ eigen__30 @ eigen__42 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__6 @ eigen__9 ) )
=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__2 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__6 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__2 @ eigen__6 @ eigen__9 )
=> ( eigen__13 @ eigen__6 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( eigen__1 @ eigen__6 @ X1 )
=> ( eigen__12 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( ~ ( eigen__1 @ eigen__30 @ X1 )
=> ( eigen__2 @ eigen__30 @ X1 ) )
=> ( eigen__16 @ eigen__30 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) )
=> ~ ( eigen__0 @ eigen__16 ) )
=> ( eigen__16 @ eigen__22 @ eigen__28 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__1 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ X2 ) )
=> ( eigen__5 @ X1 @ X2 ) )
=> ~ sP2 )
=> ( eigen__5 @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__22 @ eigen__28 ) )
=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__2 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__22 @ eigen__28 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__1 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ X2 ) )
=> ( eigen__16 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ! [X1: a,X2: a] :
( ( eigen__2 @ X1 @ X2 )
=> ( eigen__13 @ X1 @ X2 ) )
=> ~ ( eigen__0 @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a,X2: a] :
( ( eigen__2 @ X1 @ X2 )
=> ( eigen__13 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__2 @ eigen__35 @ eigen__47 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__16 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__13 @ eigen__6 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__2 @ eigen__6 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__5 @ eigen__6 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__22 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__2 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__22 @ X1 ) ) )
=> ( eigen__16 @ eigen__22 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ( ~ ( eigen__1 @ eigen__35 @ X1 )
=> ( eigen__2 @ eigen__35 @ X1 ) )
=> ( eigen__16 @ eigen__35 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__2 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__22 @ eigen__28 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__1 @ eigen__6 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ ( eigen__1 @ eigen__30 @ eigen__42 )
=> ( eigen__2 @ eigen__30 @ eigen__42 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__16 @ eigen__22 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ( ! [X1: a,X2: a] :
( ( eigen__2 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) )
=> ~ sP10 )
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( eigen__1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( eigen__2 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( ( eigen__2 @ eigen__35 @ X1 )
=> ( eigen__16 @ eigen__35 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__2 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ( eigen__16 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__2 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__6 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a] :
( ( ~ ( eigen__1 @ eigen__6 @ X1 )
=> ( eigen__2 @ eigen__6 @ X1 ) )
=> ( eigen__5 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( eigen__12 @ eigen__6 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ! [X1: a,X2: a] :
( ( ~ ( eigen__1 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ X2 ) )
=> ( eigen__5 @ X1 @ X2 ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP15
=> ( eigen__16 @ eigen__35 @ eigen__47 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ sP13
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__16 @ eigen__30 @ eigen__42 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ ( sP29
=> ~ sP10 )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ sP23
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP39
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP11
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__2 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ( eigen__5 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__12 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( eigen__5 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: a,X2: a] :
( ( eigen__2 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__1 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ X2 ) )
=> ( eigen__5 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP45
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( eigen__1 @ eigen__30 @ eigen__42 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( eigen__16 @ eigen__35 @ eigen__47 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: a] :
( ( ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__6 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__2 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__6 @ X1 ) ) )
=> ( eigen__5 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ ( sP43
=> ~ ( eigen__0 @ eigen__12 ) )
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: a] :
( ( eigen__2 @ eigen__6 @ X1 )
=> ( eigen__13 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ ( eigen__1 @ eigen__35 @ eigen__47 )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP23
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP24
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP4
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP43
=> ~ ( eigen__0 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__1 @ X2 @ X3 )
=> ( eigen__2 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( sP53
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP29
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__6 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( X1 @ eigen__22 @ eigen__28 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(cTHM252_pme,conjecture,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o,X3: a > a > $o] :
( ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( X2 @ X7 @ X8 )
=> ( X3 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( X1 @ X6 ) )
=> ( X6 @ X4 @ X5 ) ) )
= ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X2 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ( X1 @ X9 ) )
=> ( X9 @ X7 @ X8 ) )
=> ! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X3 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ( X1 @ X9 ) )
=> ( X9 @ X7 @ X8 ) ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( X1 @ X6 ) )
=> ( X6 @ X4 @ X5 ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: ( a > a > $o ) > $o,X2: a > a > $o,X3: a > a > $o] :
( ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( X2 @ X7 @ X8 )
=> ( X3 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( X1 @ X6 ) )
=> ( X6 @ X4 @ X5 ) ) )
= ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X2 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ( X1 @ X9 ) )
=> ( X9 @ X7 @ X8 ) )
=> ! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X3 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ( X1 @ X9 ) )
=> ( X9 @ X7 @ X8 ) ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( X1 @ X6 ) )
=> ( X6 @ X4 @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM252_pme]) ).
thf(h3,assumption,
~ ! [X1: a > a > $o,X2: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( eigen__0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
=> ~ ( eigen__0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) )
=> ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
=> ~ ( eigen__0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( eigen__0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__1 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( eigen__1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ( eigen__0 @ X7 ) )
=> ( X7 @ X5 @ X6 ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ( eigen__0 @ X7 ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__1 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
!= ( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( eigen__1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( eigen__0 @ X6 ) )
=> ( X6 @ X4 @ X5 ) )
=> ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( eigen__2 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( eigen__0 @ X6 ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: a] :
( ( ^ [X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__1 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
= ( ^ [X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( eigen__1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( eigen__0 @ X6 ) )
=> ( X6 @ X4 @ X5 ) )
=> ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( eigen__2 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( eigen__0 @ X6 ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
( ^ [X1: a] :
! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__1 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__3 @ X1 ) ) )
!= ( ^ [X1: a] :
! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( eigen__0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( eigen__0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a] :
( ( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__1 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__3 @ X1 ) ) )
= ( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( eigen__0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( eigen__0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X2 @ eigen__3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP59 != sP27,
introduced(assumption,[]) ).
thf(h10,assumption,
sP59,
introduced(assumption,[]) ).
thf(h11,assumption,
sP27,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP59,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ( sP42
=> ~ sP2 )
=> sP44 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP42
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP44,
introduced(assumption,[]) ).
thf(h17,assumption,
sP42,
introduced(assumption,[]) ).
thf(h18,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP52
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP18
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP43
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP6
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP54
| ~ sP23
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP13
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP58
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP35
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP35
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP51
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP51
| ~ sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP30
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__13]) ).
thf(14,plain,
( sP62
| ~ sP51 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).
thf(15,plain,
( sP4
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP4
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP42
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP50
| sP57 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP57
| ~ sP4
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP39
| sP23
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP40
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP40
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP31
| ~ sP40 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(24,plain,
( sP46
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(25,plain,
( ~ sP59
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP9
| sP33
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP33
| ~ sP46
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h15,h16,h14,h10,h11,h9,h8,h7,h6,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,h10,h17,h18,h16]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,28,h17,h18]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,29,h15,h16]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h11,30,h14]) ).
thf(h19,assumption,
~ ( ~ ( sP12
=> ~ sP10 )
=> sP16 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP12
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h22,assumption,
sP12,
introduced(assumption,[]) ).
thf(h23,assumption,
sP10,
introduced(assumption,[]) ).
thf(32,plain,
( sP53
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP24
| ~ sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP12
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP21
| sP60 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP60
| ~ sP53
| sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP12
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP7
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP55
| ~ sP24
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP34
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP34
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP3
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP3
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP28
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__47]) ).
thf(45,plain,
( sP1
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__42]) ).
thf(46,plain,
( sP45
| ~ sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__35]) ).
thf(47,plain,
( sP56
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__30]) ).
thf(48,plain,
( ~ sP22
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP26
| sP47
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP63
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP8
| sP38
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP47
| ~ sP45
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP38
| ~ sP56
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP11
| sP63
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( sP41
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP41
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( sP20
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__28]) ).
thf(58,plain,
( sP29
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__22]) ).
thf(59,plain,
( ~ sP27
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP37
| sP61
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP61
| ~ sP29
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(62,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h23,h20,h21,h19,h12,h13,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[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,h22,h23,h21,h13]) ).
thf(63,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h19,h12,h13,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h20,62,h22,h23]) ).
thf(64,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h12,h13,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,63,h20,h21]) ).
thf(65,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__16)],[h12,64,h19]) ).
thf(66,plain,
$false,
inference(tab_be,[status(thm),assumptions([h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h10,h11]),tab_be(discharge,[h12,h13])],[h9,31,65,h10,h11,h12,h13]) ).
thf(67,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__4)],[h8,66,h9]) ).
thf(68,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h7,h6,h5,h4,h3,h2,h1,h0]),tab_fe(discharge,[h8])],[h7,67,h8]) ).
thf(69,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__3)],[h6,68,h7]) ).
thf(70,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_fe(discharge,[h6])],[h5,69,h6]) ).
thf(71,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,70,h5]) ).
thf(72,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,71,h4]) ).
thf(73,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,72,h3]) ).
thf(74,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[73,h1]) ).
thf(75,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[74,h0]) ).
thf(0,theorem,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o,X3: a > a > $o] :
( ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( X2 @ X7 @ X8 )
=> ( X3 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( X1 @ X6 ) )
=> ( X6 @ X4 @ X5 ) ) )
= ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X2 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ( X1 @ X9 ) )
=> ( X9 @ X7 @ X8 ) )
=> ! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X3 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ( X1 @ X9 ) )
=> ( X9 @ X7 @ X8 ) ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ( X1 @ X6 ) )
=> ( X6 @ X4 @ X5 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[73,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEV119^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 04:39:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.94/1.14 % SZS status Theorem
% 0.94/1.14 % Mode: mode213
% 0.94/1.14 % Inferences: 528
% 0.94/1.14 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------