%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV141^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 02:56:20 PM UTC 2025
% Result : Theorem 6.65s 6.99s
% Output : Proof 6.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 143
% Syntax : Number of formulae : 172 ( 48 unt; 0 typ; 10 def)
% Number of atoms : 455 ( 19 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1974 ( 414 ~; 72 |; 0 &; 996 @)
% ( 63 <=>; 429 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 142 ( 142 >; 0 *; 0 +; 0 <<)
% Number of symbols : 83 ( 81 usr; 76 con; 0-2 aty)
% Number of variables : 481 ( 34 ^; 447 !; 0 ?; 481 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__12,type,
eigen__12: a > a > $o ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__16,type,
eigen__16: a > a > $o ).
thf(ty_eigen__35,type,
eigen__35: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__59,type,
eigen__59: a ).
thf(ty_eigen__11,type,
eigen__11: a > a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_eigen__41,type,
eigen__41: a ).
thf(ty_eigen__53,type,
eigen__53: a ).
thf(ty_eigen__23,type,
eigen__23: a ).
thf(ty_eigen__31,type,
eigen__31: a ).
thf(h0,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: a > a > $o] :
~ ( ~ ( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: a > a > $o] :
~ ( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: a] :
~ ( ( ~ ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__1 @ eigen__5 @ X1 ) )
=> ( eigen__4 @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__23,definition,
( eigen__23
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ( eigen__16 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__23])]) ).
thf(eigendef_eigen__41,definition,
( eigen__41
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__41])]) ).
thf(eigendef_eigen__31,definition,
( eigen__31
= ( eps__1
@ ^ [X1: a] :
~ ( ( ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__23 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__23 @ X1 ) ) )
=> ( eigen__16 @ eigen__23 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__31])]) ).
thf(eigendef_eigen__53,definition,
( eigen__53
= ( eps__1
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__35 @ X1 )
=> ( eigen__16 @ eigen__35 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__53])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(eigendef_eigen__35,definition,
( eigen__35
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__35])]) ).
thf(eigendef_eigen__59,definition,
( eigen__59
= ( eps__1
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__41 @ X1 )
=> ( eigen__16 @ eigen__41 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__59])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__4 @ X1 @ X2 )
=> ~ ( eigen__4 @ X2 @ X3 ) )
=> ( eigen__4 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__8 ) )
=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( eigen__0 @ eigen__5 @ eigen__8 )
=> ( eigen__1 @ eigen__5 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0 @ eigen__5 @ eigen__8 )
=> ( eigen__11 @ eigen__5 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__35 @ eigen__53 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) )
=> ~ sP1 )
=> ( eigen__4 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 @ eigen__5 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__16 @ X1 @ X2 )
=> ~ ( eigen__16 @ X2 @ X3 ) )
=> ( eigen__16 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ~ ( eigen__0 @ eigen__41 @ eigen__59 )
=> ( eigen__1 @ eigen__41 @ eigen__59 ) )
=> ( eigen__16 @ eigen__41 @ eigen__59 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ eigen__5 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ~ ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__23 @ eigen__31 ) )
=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__23 @ eigen__31 ) ) )
=> ( eigen__16 @ eigen__23 @ eigen__31 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__1 @ eigen__41 @ eigen__59 )
=> ( eigen__16 @ eigen__41 @ eigen__59 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__11 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ( eigen__0 @ eigen__35 @ X1 )
=> ( eigen__16 @ eigen__35 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ( eigen__16 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__16 @ X1 @ X2 )
=> ~ ( eigen__16 @ X2 @ X3 ) )
=> ( eigen__16 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP2
=> ( eigen__4 @ eigen__5 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__12 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__12 @ X1 @ X2 )
=> ~ ( eigen__12 @ X2 @ X3 ) )
=> ( eigen__12 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__16 @ X1 @ X2 )
=> ~ ( eigen__16 @ X2 @ X3 ) )
=> ( eigen__16 @ X1 @ X3 ) ) )
=> ( eigen__16 @ eigen__23 @ eigen__31 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__23 @ eigen__31 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__16 @ eigen__41 @ eigen__59 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__12 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__12 @ eigen__5 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__16 @ eigen__23 @ eigen__31 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( ~ sP5
=> ( eigen__1 @ eigen__35 @ eigen__53 ) )
=> ( eigen__16 @ eigen__35 @ eigen__53 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP17
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__11 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__4 @ eigen__5 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__16 @ eigen__35 @ eigen__53 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__1 @ eigen__5 @ X1 ) )
=> ( eigen__4 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( eigen__11 @ eigen__5 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ sP15
=> ( eigen__16 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ sP8
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ sP5
=> ( eigen__1 @ eigen__35 @ eigen__53 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__41 @ X1 )
=> ( eigen__1 @ eigen__41 @ X1 ) )
=> ( eigen__16 @ eigen__41 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP3
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__16 @ X1 @ X2 )
=> ~ ( eigen__16 @ X2 @ X3 ) )
=> ( eigen__16 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP5
=> sP30 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__35 @ X1 )
=> ( eigen__1 @ eigen__35 @ X1 ) )
=> ( eigen__16 @ eigen__35 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP7
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__16 @ X1 @ X2 )
=> ~ ( eigen__16 @ X2 @ X3 ) )
=> ( eigen__16 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eigen__4 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: a] :
( ( eigen__1 @ eigen__5 @ X1 )
=> ( eigen__12 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: a] :
( ( ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__5 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__5 @ X1 ) ) )
=> ( eigen__4 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ~ ( sP13
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__11 @ X1 @ X2 )
=> ~ ( eigen__11 @ X2 @ X3 ) )
=> ( eigen__11 @ X1 @ X3 ) ) )
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ sP21
=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__23 @ eigen__31 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ( eigen__16 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: a] :
( ( eigen__1 @ eigen__41 @ X1 )
=> ( eigen__16 @ eigen__41 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ ( eigen__0 @ eigen__41 @ eigen__59 )
=> ( eigen__1 @ eigen__41 @ eigen__59 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( eigen__1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__16 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: a] :
( ( ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__23 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__23 @ X1 ) ) )
=> ( eigen__16 @ eigen__23 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( eigen__1 @ eigen__41 @ eigen__59 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sP13
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__11 @ X1 @ X2 )
=> ~ ( eigen__11 @ X2 @ X3 ) )
=> ( eigen__11 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( eigen__16 @ eigen__2 @ eigen__3 ) ),
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 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__23 @ eigen__31 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(cTHM250_pme,conjecture,
! [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 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( 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 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) )
=> ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [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 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( 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 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) )
=> ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM250_pme]) ).
thf(h3,assumption,
~ ! [X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( eigen__0 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
!= ( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( eigen__0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( eigen__1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a] :
( ( ^ [X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
= ( ^ [X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( eigen__0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( eigen__1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ( ^ [X1: a] :
! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) )
!= ( ^ [X1: a] :
! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a] :
( ( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) )
= ( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP60 != sP54,
introduced(assumption,[]) ).
thf(h9,assumption,
sP60,
introduced(assumption,[]) ).
thf(h10,assumption,
sP54,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP60,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP54,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( sP40
=> ~ sP1 )
=> sP45 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP40
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP45,
introduced(assumption,[]) ).
thf(h16,assumption,
sP40,
introduced(assumption,[]) ).
thf(h17,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP23
| sP46 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP46
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP43
| ~ sP7
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP17
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP27
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP27
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP13
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP28
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP4
| ~ sP10
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP59
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP48
| ~ sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP48
| ~ sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP19
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(14,plain,
( sP61
| ~ sP48 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(15,plain,
( sP2
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP2
| ~ sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP40
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP47
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP16
| ~ sP2
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP3
| sP10
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP38
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP38
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP31
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(24,plain,
( sP51
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(25,plain,
( ~ sP60
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP6
| sP33
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP33
| ~ sP51
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h14,h15,h13,h9,h10,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,h9,h16,h17,h15]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,28,h16,h17]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,29,h14,h15]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h10,30,h13]) ).
thf(h18,assumption,
~ ( ~ ( sP56
=> ~ sP44 )
=> sP62 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP56
=> ~ sP44 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP62,
introduced(assumption,[]) ).
thf(h21,assumption,
sP56,
introduced(assumption,[]) ).
thf(h22,assumption,
sP44,
introduced(assumption,[]) ).
thf(32,plain,
( sP53
| ~ sP58 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP56
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP37
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP9
| ~ sP53
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( sP12
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( sP12
| sP58 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP36
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP56
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP42
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP26
| ~ sP36
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( sP41
| ~ sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( sP41
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( sP52
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__59]) ).
thf(45,plain,
( sP14
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__53]) ).
thf(46,plain,
( ~ sP63
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP35
| sP8
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP21
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP20
| sP39
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP49
| sP21
| sP63 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( sP11
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( sP11
| sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( sP18
| ~ sP52 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__41]) ).
thf(54,plain,
( sP55
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__35]) ).
thf(55,plain,
( ~ sP8
| ~ sP18
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP39
| ~ sP55
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( sP57
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__31]) ).
thf(58,plain,
( sP50
| ~ sP57 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__23]) ).
thf(59,plain,
( ~ sP54
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP34
| sP15
| sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP15
| ~ sP50
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h19,h20,h18,h11,h12,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,h21,h22,h20,h12]) ).
thf(63,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h19,62,h21,h22]) ).
thf(64,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,63,h19,h20]) ).
thf(65,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__16)],[h11,64,h18]) ).
thf(66,plain,
$false,
inference(tab_be,[status(thm),assumptions([h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h9,h10]),tab_be(discharge,[h11,h12])],[h8,31,65,h9,h10,h11,h12]) ).
thf(67,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,66,h8]) ).
thf(68,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_fe(discharge,[h7])],[h6,67,h7]) ).
thf(69,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,68,h6]) ).
thf(70,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_fe(discharge,[h5])],[h4,69,h5]) ).
thf(71,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,70,h4]) ).
thf(72,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,71,h3]) ).
thf(73,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[72,h1]) ).
thf(74,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[73,h0]) ).
thf(0,theorem,
! [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 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( 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 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) )
=> ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[72,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEV141^5 : TPTP v9.2.0. Released v4.0.0.
% 0.12/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 19:38:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 6.65/6.99 % SZS status Theorem
% 6.65/6.99 % Mode: mode515
% 6.65/6.99 % Inferences: 665
% 6.65/6.99 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------