TSTP Solution File: SEV141^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV141^5 : 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 : n010.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 19:32:44 EDT 2023
% Result : Theorem 45.50s 45.67s
% Output : Proof 45.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 160
% Syntax : Number of formulae : 189 ( 48 unt; 17 typ; 10 def)
% Number of atoms : 451 ( 19 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1936 ( 407 ~; 72 |; 0 &; 974 @)
% ( 63 <=>; 420 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 152 ( 152 >; 0 *; 0 +; 0 <<)
% Number of symbols : 83 ( 81 usr; 76 con; 0-2 aty)
% Number of variables : 470 ( 34 ^; 436 !; 0 ?; 470 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__64,type,
eigen__64: a ).
thf(ty_eigen__40,type,
eigen__40: a > a > $o ).
thf(ty_eigen__39,type,
eigen__39: a > a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__71,type,
eigen__71: a ).
thf(ty_eigen__72,type,
eigen__72: a ).
thf(ty_eigen__4,type,
eigen__4: a > a > $o ).
thf(ty_eigen__65,type,
eigen__65: a ).
thf(ty_eigen__38,type,
eigen__38: a > a > $o ).
thf(ty_eigen__15,type,
eigen__15: a ).
thf(ty_eigen__66,type,
eigen__66: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__67,type,
eigen__67: a ).
thf(ty_eigen__13,type,
eigen__13: 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__71,definition,
( eigen__71
= ( eps__0
@ ^ [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__40 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__71])]) ).
thf(h1,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__39,definition,
( eigen__39
= ( eps__1
@ ^ [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__13 @ eigen__15 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__39])]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: a] :
~ ( ( ~ ( eigen__0 @ eigen__13 @ X1 )
=> ( eigen__1 @ eigen__13 @ X1 ) )
=> ( eigen__4 @ eigen__13 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__64,definition,
( eigen__64
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__40 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__64])]) ).
thf(eigendef_eigen__66,definition,
( eigen__66
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__40 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__66])]) ).
thf(eigendef_eigen__67,definition,
( eigen__67
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__66 @ X1 )
=> ( eigen__40 @ eigen__66 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__67])]) ).
thf(eigendef_eigen__72,definition,
( eigen__72
= ( eps__0
@ ^ [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__71 @ 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__71 @ X1 ) ) )
=> ( eigen__40 @ eigen__71 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__72])]) ).
thf(eigendef_eigen__65,definition,
( eigen__65
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__64 @ X1 )
=> ( eigen__40 @ eigen__64 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__65])]) ).
thf(eigendef_eigen__38,definition,
( eigen__38
= ( eps__1
@ ^ [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__13 @ eigen__15 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__38])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [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__40 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__40 @ X1 @ X2 )
=> ~ ( eigen__40 @ X2 @ X3 ) )
=> ( eigen__40 @ X1 @ X3 ) ) )
=> ( eigen__40 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__40 @ eigen__64 @ eigen__65 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__4 @ X1 @ X2 )
=> ~ ( eigen__4 @ X2 @ X3 ) )
=> ( eigen__4 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__40 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__40 @ X1 @ X2 )
=> ~ ( eigen__40 @ X2 @ X3 ) )
=> ( eigen__40 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( eigen__0 @ eigen__13 @ X1 )
=> ( eigen__38 @ eigen__13 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ~ ! [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__71 @ eigen__72 ) )
=> ! [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__71 @ eigen__72 ) ) )
=> ( eigen__40 @ eigen__71 @ eigen__72 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [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__71 @ 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__71 @ X1 ) ) )
=> ( eigen__40 @ eigen__71 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP4
=> ( eigen__40 @ eigen__71 @ eigen__72 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__38 @ eigen__13 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [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__71 @ eigen__72 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__64 @ X1 )
=> ( eigen__1 @ eigen__64 @ X1 ) )
=> ( eigen__40 @ eigen__64 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ~ ( eigen__0 @ eigen__64 @ eigen__65 )
=> ( eigen__1 @ eigen__64 @ eigen__65 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [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__13 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ( eigen__1 @ eigen__64 @ X1 )
=> ( eigen__40 @ eigen__64 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__66 @ X1 )
=> ( eigen__1 @ eigen__66 @ X1 ) )
=> ( eigen__40 @ eigen__66 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP10
=> ! [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__71 @ eigen__72 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP13
=> ! [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__13 @ eigen__15 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__39 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__39 @ X1 @ X2 )
=> ~ ( eigen__39 @ X2 @ X3 ) )
=> ( eigen__39 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [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,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__39 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__0 @ eigen__13 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP18
=> ( eigen__39 @ eigen__13 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__40 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( ~ sP21
=> ( eigen__1 @ eigen__13 @ eigen__15 ) )
=> ( eigen__4 @ eigen__13 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ( sP24
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__40 @ X1 @ X2 )
=> ~ ( eigen__40 @ X2 @ X3 ) )
=> ( eigen__40 @ X1 @ X3 ) ) )
=> ( eigen__40 @ eigen__71 @ eigen__72 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [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__40 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP21
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( eigen__1 @ eigen__13 @ eigen__15 )
=> ( eigen__39 @ eigen__13 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__13 @ X1 )
=> ( eigen__1 @ eigen__13 @ X1 ) )
=> ( eigen__4 @ eigen__13 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP22
=> ( eigen__4 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__38 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__38 @ X1 @ X2 )
=> ~ ( eigen__38 @ X2 @ X3 ) )
=> ( eigen__38 @ X1 @ X3 ) ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ ( eigen__0 @ eigen__66 @ eigen__67 )
=> ( eigen__1 @ eigen__66 @ eigen__67 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: a] :
( ( eigen__1 @ eigen__13 @ X1 )
=> ( eigen__39 @ eigen__13 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__38 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__38 @ X1 @ X2 )
=> ~ ( eigen__38 @ X2 @ X3 ) )
=> ( eigen__38 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP33
=> ( eigen__40 @ eigen__66 @ eigen__67 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( eigen__40 @ eigen__71 @ eigen__72 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( eigen__40 @ eigen__66 @ eigen__67 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: a] :
( ( eigen__0 @ eigen__66 @ X1 )
=> ( eigen__40 @ eigen__66 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ sP21
=> ( eigen__1 @ eigen__13 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( eigen__0 @ eigen__66 @ eigen__67 )
=> sP38 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__40 @ X1 @ X2 )
=> ~ ( eigen__40 @ X2 @ X3 ) )
=> ( eigen__40 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [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,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( eigen__4 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP24
=> ~ sP42 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [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__13 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__38 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ ( eigen__0 @ eigen__64 @ eigen__65 )
=> ( eigen__1 @ eigen__64 @ eigen__65 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( eigen__40 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP17
=> ( eigen__4 @ eigen__13 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( eigen__1 @ eigen__64 @ eigen__65 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [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__13 @ 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__13 @ X1 ) ) )
=> ( eigen__4 @ eigen__13 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__40 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( eigen__39 @ eigen__13 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__40 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [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,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP52
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sP27
=> ~ sP42 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [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__71 @ eigen__72 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( eigen__1 @ eigen__13 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( eigen__0 @ eigen__66 @ eigen__67 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( eigen__4 @ eigen__13 @ eigen__15 ) ),
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,
sP57 != sP19,
introduced(assumption,[]) ).
thf(h9,assumption,
sP57,
introduced(assumption,[]) ).
thf(h10,assumption,
sP19,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP57,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( sP43
=> ~ sP3 )
=> sP44 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP43
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP44,
introduced(assumption,[]) ).
thf(h16,assumption,
sP43,
introduced(assumption,[]) ).
thf(h17,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP29
| ~ sP61
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP34
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP20
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP18
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP28
| ~ sP21
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP48
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP35
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP23
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP23
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP32
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP32
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP46
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__39]) ).
thf(14,plain,
( sP13
| ~ sP32 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__38]) ).
thf(15,plain,
( sP17
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP17
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP51
| ~ sP17
| sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP53
| sP51 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP43
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP40
| sP21
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP25
| ~ sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP25
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP30
| ~ sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(24,plain,
( sP47
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(25,plain,
( ~ sP22
| ~ sP47
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP31
| sP22
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP57
| sP31 ),
inference(all_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,
~ ( ~ ( sP54
=> ~ sP42 )
=> sP50 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP54
=> ~ sP42 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP50,
introduced(assumption,[]) ).
thf(h21,assumption,
sP54,
introduced(assumption,[]) ).
thf(h22,assumption,
sP42,
introduced(assumption,[]) ).
thf(32,plain,
( sP33
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP36
| ~ sP33
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP15
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP54
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( sP49
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP12
| ~ sP49
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP11
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP54
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP8
| sP4
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP26
| sP45
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP60
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP10
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP16
| sP10
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP6
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP6
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP7
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__72]) ).
thf(48,plain,
( sP27
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__71]) ).
thf(49,plain,
( ~ sP59
| ~ sP27
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP1
| sP59
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( sP41
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( sP41
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( sP39
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__67]) ).
thf(54,plain,
( sP24
| ~ sP39 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__66]) ).
thf(55,plain,
( ~ sP45
| ~ sP24
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP58
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( sP58
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( sP14
| ~ sP58 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__65]) ).
thf(59,plain,
( sP56
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__64]) ).
thf(60,plain,
( ~ sP4
| ~ sP56
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP19
| sP1 ),
inference(all_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__40)],[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
% 0.00/0.12 % Problem : SEV141^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n010.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 02:05:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 45.50/45.67 % SZS status Theorem
% 45.50/45.67 % Mode: cade22grackle2x6987
% 45.50/45.67 % Steps: 100958
% 45.50/45.67 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------