TSTP Solution File: SEV152^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV152^5 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:32:46 EDT 2023
% Result : Theorem 124.07s 124.28s
% Output : Proof 124.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 209
% Syntax : Number of formulae : 260 ( 74 unt; 24 typ; 7 def)
% Number of atoms : 763 ( 7 equ; 0 cnn)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 3080 ( 800 ~; 74 |; 0 &;1312 @)
% ( 69 <=>; 825 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 115 ( 115 >; 0 *; 0 +; 0 <<)
% Number of symbols : 95 ( 93 usr; 85 con; 0-2 aty)
% Number of variables : 503 ( 7 ^; 496 !; 0 ?; 503 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__41,type,
eigen__41: a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__8,type,
eigen__8: a > $o ).
thf(ty_eigen__40,type,
eigen__40: a ).
thf(ty_eigen__39,type,
eigen__39: a ).
thf(ty_eigen__62,type,
eigen__62: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__42,type,
eigen__42: a > $o ).
thf(ty_eigen__63,type,
eigen__63: a ).
thf(ty_eigen__25,type,
eigen__25: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__38,type,
eigen__38: a ).
thf(ty_eigen__61,type,
eigen__61: a ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__9,type,
eigen__9: a > $o ).
thf(ty_eigen__24,type,
eigen__24: a > $o ).
thf(ty_eigen__22,type,
eigen__22: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__21,type,
eigen__21: a ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__23,type,
eigen__23: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__39,definition,
( eigen__39
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__24 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__24 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__39])]) ).
thf(eigendef_eigen__62,definition,
( eigen__62
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__41 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__41 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__62])]) ).
thf(eigendef_eigen__21,definition,
( eigen__21
= ( eps__0
@ ^ [X1: a] :
~ ( ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) )
=> ( eigen__8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__21])]) ).
thf(eigendef_eigen__63,definition,
( eigen__63
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__41 @ eigen__62 )
=> ~ ( eigen__0 @ eigen__62 @ X1 ) )
=> ( eigen__41 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__63])]) ).
thf(eigendef_eigen__40,definition,
( eigen__40
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__24 @ eigen__39 )
=> ~ ( eigen__1 @ eigen__39 @ X1 ) )
=> ( eigen__24 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__40])]) ).
thf(eigendef_eigen__61,definition,
( eigen__61
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__22 @ X1 )
=> ( eigen__41 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__61])]) ).
thf(eigendef_eigen__38,definition,
( eigen__38
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__22 @ X1 )
=> ( eigen__24 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__38])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 @ eigen__22 @ eigen__38 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__8 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X2 )
=> ( eigen__1 @ eigen__5 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( eigen__0 @ eigen__22 @ X1 )
=> ( eigen__41 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( sP5
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__41 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__41 @ X2 ) ) )
=> ( eigen__41 @ eigen__23 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ( eigen__41 @ eigen__62 )
=> ~ ( eigen__0 @ eigen__62 @ eigen__63 ) )
=> ( eigen__41 @ eigen__63 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__24 @ eigen__39 )
=> ~ ( ~ ( eigen__0 @ eigen__39 @ eigen__40 )
=> ( eigen__1 @ eigen__39 @ eigen__40 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__41 @ eigen__63 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__1 @ eigen__5 @ X1 ) )
=> ( eigen__8 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__8 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__24 @ eigen__39 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__24 @ eigen__40 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__22 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__23 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__1 @ eigen__5 @ X1 ) )
=> ( eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) )
=> ( eigen__8 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__8 @ X2 ) ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__41 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__41 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ~ ( eigen__0 @ eigen__22 @ eigen__61 )
=> ( eigen__1 @ eigen__22 @ eigen__61 ) )
=> ( eigen__41 @ eigen__61 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) )
=> ( eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__8 @ eigen__6 )
=> ~ ( ~ ( eigen__0 @ eigen__6 @ eigen__21 )
=> ( eigen__1 @ eigen__6 @ eigen__21 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ( eigen__41 @ eigen__62 )
=> ~ ( ~ ( eigen__0 @ eigen__62 @ eigen__63 )
=> ( eigen__1 @ eigen__62 @ eigen__63 ) ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ sP10
=> ( eigen__8 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( eigen__41 @ eigen__62 )
=> ~ ( ~ ( eigen__0 @ eigen__62 @ eigen__63 )
=> ( eigen__1 @ eigen__62 @ eigen__63 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__24 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__24 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__1 @ eigen__39 @ eigen__40 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__41 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__41 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__6 @ X2 )
=> ( eigen__1 @ eigen__6 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( eigen__0 @ eigen__6 @ eigen__21 )
=> ( eigen__1 @ eigen__6 @ eigen__21 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( ~ ( ( eigen__8 @ eigen__6 )
=> ~ ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) ) )
=> ( eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( eigen__41 @ eigen__62 )
=> ~ ( eigen__0 @ eigen__62 @ eigen__63 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: a] :
( ~ ( ( eigen__41 @ eigen__62 )
=> ~ ( ~ ( eigen__0 @ eigen__62 @ X1 )
=> ( eigen__1 @ eigen__62 @ X1 ) ) )
=> ( eigen__41 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP5
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( eigen__41 @ eigen__62 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( eigen__0 @ eigen__22 @ eigen__61 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP11
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP33
=> ( eigen__41 @ eigen__61 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__24 @ eigen__23 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP18
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__8 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ sP19
=> ( eigen__8 @ eigen__21 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP27
=> ( eigen__8 @ eigen__21 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( ~ ( eigen__0 @ eigen__22 @ eigen__38 )
=> sP2 )
=> ( eigen__24 @ eigen__38 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__8 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP2
=> ( eigen__24 @ eigen__38 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( eigen__24 @ eigen__38 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ~ ( ! [X1: a] :
( ( eigen__1 @ eigen__22 @ X1 )
=> ( eigen__24 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__24 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__24 @ X2 ) ) )
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eigen__0 @ eigen__62 @ eigen__63 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ sP8
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__22 @ X1 )
=> ( eigen__1 @ eigen__22 @ X1 ) )
=> ( eigen__41 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( eigen__41 @ eigen__61 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( eigen__8 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__22 @ X1 )
=> ( eigen__1 @ eigen__22 @ X1 ) )
=> ( eigen__24 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP46
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ ( eigen__0 @ eigen__39 @ eigen__40 )
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ sP45
=> ( eigen__1 @ eigen__62 @ eigen__63 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: a] :
( ~ ( sP11
=> ~ ( eigen__1 @ eigen__39 @ X1 ) )
=> ( eigen__24 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ ( eigen__0 @ eigen__22 @ eigen__38 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: a] :
( ~ ( sP32
=> ~ ( eigen__0 @ eigen__62 @ X1 ) )
=> ( eigen__41 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__24 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__24 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: a] :
( ~ ( sP11
=> ~ ( ~ ( eigen__0 @ eigen__39 @ X1 )
=> ( eigen__1 @ eigen__39 @ X1 ) ) )
=> ( eigen__24 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( ~ sP33
=> ( eigen__1 @ eigen__22 @ eigen__61 ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ~ sP53
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ! [X1: a] :
( ( eigen__1 @ eigen__22 @ X1 )
=> ( eigen__24 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( eigen__41 @ eigen__23 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X2 )
=> ( eigen__1 @ eigen__2 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ~ sP34
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP63
=> ~ sP59 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( eigen__8 @ eigen__21 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__22 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__23 ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(cTHM251D_pme,conjecture,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( X1 @ X5 @ X8 )
=> ( X2 @ X5 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X6 ) )
=> ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X6 @ X9 )
=> ( X2 @ X6 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( X1 @ X5 @ X8 )
=> ( X2 @ X5 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X6 ) )
=> ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X6 @ X9 )
=> ( X2 @ X6 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ),
inference(assume_negation,[status(cth)],[cTHM251D_pme]) ).
thf(h2,assumption,
~ ! [X1: a > a > $o,X2: a,X3: a] :
( ( ~ ( ! [X4: a,X5: a] :
( ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( X1 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( X1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( ~ ( eigen__0 @ X4 @ X7 )
=> ( X1 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( ~ ( eigen__0 @ X7 @ X8 )
=> ( X1 @ X7 @ X8 ) ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( eigen__0 @ X4 @ X8 )
=> ( X1 @ X4 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X5 ) )
=> ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( eigen__0 @ X5 @ X8 )
=> ( X1 @ X5 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( eigen__0 @ X4 @ X8 )
=> ( X1 @ X4 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a,X2: a] :
( ( ~ ( ! [X3: a,X4: a] :
( ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( eigen__0 @ X3 @ X6 )
=> ( eigen__1 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( ~ ( eigen__0 @ X3 @ X7 )
=> ( eigen__1 @ X3 @ X7 ) )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X4 ) )
=> ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( ~ ( eigen__0 @ X4 @ X7 )
=> ( eigen__1 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( ~ ( eigen__0 @ X3 @ X7 )
=> ( eigen__1 @ X3 @ X7 ) )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ( ~ ( ! [X2: a,X3: a] :
( ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( eigen__1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( eigen__0 @ X2 @ X6 )
=> ( eigen__1 @ X2 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X3 ) )
=> ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( eigen__0 @ X3 @ X6 )
=> ( eigen__1 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( eigen__0 @ X2 @ X6 )
=> ( eigen__1 @ X2 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X3 )
=> ( eigen__1 @ eigen__2 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X3 )
=> ( eigen__1 @ eigen__2 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ( ~ ( ! [X1: a,X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( eigen__1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) )
=> sP65 )
=> sP65 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ ( ! [X1: a,X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( eigen__1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) )
=> sP65 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP65,
introduced(assumption,[]) ).
thf(h8,assumption,
( ! [X1: a,X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( eigen__1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP65,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: a,X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( eigen__1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X1 @ X5 )
=> ( eigen__1 @ X1 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__22 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__22 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__22 @ X3 )
=> ( eigen__1 @ eigen__22 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ( ~ sP69
=> sP13 )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__22 @ X2 )
=> ( eigen__1 @ eigen__22 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__23 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
( ~ sP69
=> sP13 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__22 @ X2 )
=> ( eigen__1 @ eigen__22 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__23 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP69,
introduced(assumption,[]) ).
thf(h17,assumption,
sP13,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ~ ( sP48
=> ~ sP25 )
=> sP64 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP48
=> ~ sP25 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP64,
introduced(assumption,[]) ).
thf(h21,assumption,
sP48,
introduced(assumption,[]) ).
thf(h22,assumption,
sP25,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ~ ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__42 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__42 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__42 @ X2 ) ) )
=> ( eigen__42 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__42 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__42 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__42 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( eigen__42 @ eigen__3 ),
introduced(assumption,[]) ).
thf(h26,assumption,
! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__42 @ X1 ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
! [X1: a,X2: a] :
( ~ ( ( eigen__42 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__42 @ X2 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP22
| ~ sP32
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP20
| sP22
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP55
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP30
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP25
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP61
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP17
| ~ sP61
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP48
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP29
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP29
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP7
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP7
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP58
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__63]) ).
thf(14,plain,
( sP16
| ~ sP58 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__62]) ).
thf(15,plain,
( sP35
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP35
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP5
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__61]) ).
thf(18,plain,
( ~ sP31
| ~ sP5
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP6
| sP31
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP69
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h27,h24,h25,h23,h21,h22,h19,h20,h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h16,h21,h22,h20]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h23,h21,h22,h19,h20,h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h26,h27])],[h24,21,h26,h27]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h19,h20,h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,22,h24,h25]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h19,h20,h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__42)],[h7,23,h23]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h19,24,h21,h22]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,25,h19,h20]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__41)],[h15,26,h18]) ).
thf(h28,assumption,
~ ( ~ ( sP52
=> ~ sP23 )
=> sP36 ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( sP52
=> ~ sP23 ),
introduced(assumption,[]) ).
thf(h30,assumption,
~ sP36,
introduced(assumption,[]) ).
thf(h31,assumption,
sP52,
introduced(assumption,[]) ).
thf(h32,assumption,
sP23,
introduced(assumption,[]) ).
thf(h33,assumption,
~ ( ~ ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__25 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__25 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__25 @ X2 ) ) )
=> ( eigen__25 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__25 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__25 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__25 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( eigen__25 @ eigen__3 ),
introduced(assumption,[]) ).
thf(h36,assumption,
! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__25 @ X1 ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
! [X1: a,X2: a] :
( ~ ( ( eigen__25 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__25 @ X2 ) ),
introduced(assumption,[]) ).
thf(28,plain,
( ~ sP8
| ~ sP11
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP47
| sP8
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP54
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP60
| sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP23
| sP60 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( sP57
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP40
| ~ sP57
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP52
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( sP34
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP34
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP66
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP66
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP56
| ~ sP66 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__40]) ).
thf(41,plain,
( sP59
| ~ sP56 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__39]) ).
thf(42,plain,
( sP42
| ~ sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP42
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP63
| ~ sP42 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__38]) ).
thf(45,plain,
( ~ sP67
| ~ sP63
| ~ sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP44
| sP67
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP13
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h36,h37,h34,h35,h33,h31,h32,h29,h30,h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,h17,h31,h32,h30]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h35,h33,h31,h32,h29,h30,h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h36,h37])],[h34,48,h36,h37]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h31,h32,h29,h30,h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h34,h35])],[h33,49,h34,h35]) ).
thf(51,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h31,h32,h29,h30,h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__25)],[h7,50,h33]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h30,h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h29,51,h31,h32]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,52,h29,h30]) ).
thf(54,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__24)],[h15,53,h28]) ).
thf(55,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h15,h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h17])],[h14,27,54,h16,h17]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,55,h14,h15]) ).
thf(57,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__23)],[h12,56,h13]) ).
thf(58,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__22)],[h10,57,h12]) ).
thf(h38,assumption,
~ ! [X1: a,X2: a] :
( ~ ( ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X4 )
=> ( eigen__1 @ eigen__5 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X1 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X4 )
=> ( eigen__1 @ eigen__5 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h39,assumption,
~ ! [X1: a] :
( ~ ( sP4
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__6 @ X3 )
=> ( eigen__1 @ eigen__6 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X3 )
=> ( eigen__1 @ eigen__5 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h40,assumption,
~ ( ~ ( sP4
=> ~ sP26 )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X2 )
=> ( eigen__1 @ eigen__5 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(assumption,[]) ).
thf(h41,assumption,
~ ( sP4
=> ~ sP26 ),
introduced(assumption,[]) ).
thf(h42,assumption,
~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__5 @ X2 )
=> ( eigen__1 @ eigen__5 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ),
introduced(assumption,[]) ).
thf(h43,assumption,
sP4,
introduced(assumption,[]) ).
thf(h44,assumption,
sP26,
introduced(assumption,[]) ).
thf(h45,assumption,
~ ( ~ sP10
=> sP3 ),
introduced(assumption,[]) ).
thf(h46,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h47,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h48,assumption,
sP14,
introduced(assumption,[]) ).
thf(h49,assumption,
sP41,
introduced(assumption,[]) ).
thf(h50,assumption,
~ ( ~ ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__9 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__9 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__9 @ X2 ) ) )
=> ( eigen__9 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h51,assumption,
~ ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__9 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__9 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__9 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h52,assumption,
~ ( eigen__9 @ eigen__3 ),
introduced(assumption,[]) ).
thf(h53,assumption,
! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__9 @ X1 ) ),
introduced(assumption,[]) ).
thf(h54,assumption,
! [X1: a,X2: a] :
( ~ ( ( eigen__9 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__9 @ X2 ) ),
introduced(assumption,[]) ).
thf(59,plain,
( ~ sP19
| ~ sP51
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP38
| sP19
| sP68 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP28
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( sP39
| ~ sP68 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( sP39
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(64,plain,
( sP18
| ~ sP39 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__21]) ).
thf(65,plain,
( ~ sP37
| ~ sP18
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP15
| sP37
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP10
| ~ sP14
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP21
| sP10
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP26
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP4
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP41
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(72,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h53,h54,h51,h52,h50,h48,h49,h46,h47,h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[59,60,61,62,63,64,65,66,67,68,69,70,71,h43,h44,h48,h49,h47]) ).
thf(73,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h51,h52,h50,h48,h49,h46,h47,h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h53,h54])],[h51,72,h53,h54]) ).
thf(74,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h50,h48,h49,h46,h47,h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h51,h52])],[h50,73,h51,h52]) ).
thf(75,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h48,h49,h46,h47,h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h50]),tab_negall(eigenvar,eigen__9)],[h7,74,h50]) ).
thf(76,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h46,h47,h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h48,h49])],[h46,75,h48,h49]) ).
thf(77,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h46,h47])],[h45,76,h46,h47]) ).
thf(78,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h43,h44,h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h45]),tab_negall(eigenvar,eigen__8)],[h42,77,h45]) ).
thf(79,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h42,h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h43,h44])],[h41,78,h43,h44]) ).
thf(80,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h40,h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h41,h42])],[h40,79,h41,h42]) ).
thf(81,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h39,h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h40]),tab_negall(eigenvar,eigen__7)],[h39,80,h40]) ).
thf(82,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h38,h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h39]),tab_negall(eigenvar,eigen__6)],[h38,81,h39]) ).
thf(83,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h38]),tab_negall(eigenvar,eigen__5)],[h11,82,h38]) ).
thf(84,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h8,58,83,h10,h11]) ).
thf(h55,assumption,
~ sP62,
introduced(assumption,[]) ).
thf(h56,assumption,
~ sP53,
introduced(assumption,[]) ).
thf(h57,assumption,
~ sP49,
introduced(assumption,[]) ).
thf(h58,assumption,
sP46,
introduced(assumption,[]) ).
thf(h59,assumption,
sP1,
introduced(assumption,[]) ).
thf(85,plain,
( ~ sP53
| ~ sP46
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(86,plain,
( ~ sP62
| sP53
| sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(87,plain,
( ~ sP65
| sP62 ),
inference(all_rule,[status(thm)],]) ).
thf(88,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h58,h59,h56,h57,h55,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[85,86,87,h9,h58,h59,h57]) ).
thf(89,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h56,h57,h55,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h58,h59])],[h56,88,h58,h59]) ).
thf(90,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h55,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h56,h57])],[h55,89,h56,h57]) ).
thf(91,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h55]),tab_negall(eigenvar,eigen__4)],[h7,90,h55]) ).
thf(92,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h6,84,91,h8,h9]) ).
thf(93,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,92,h6,h7]) ).
thf(94,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,93,h5]) ).
thf(95,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,94,h4]) ).
thf(96,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,95,h3]) ).
thf(97,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,96,h2]) ).
thf(98,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[97,h0]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( ~ ( X1 @ X5 @ X8 )
=> ( X2 @ X5 @ X8 ) )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X6 ) )
=> ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X6 @ X9 )
=> ( X2 @ X6 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( ~ ( X1 @ X5 @ X9 )
=> ( X2 @ X5 @ X9 ) )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[97,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV152^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 02:27:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 124.07/124.28 % SZS status Theorem
% 124.07/124.28 % Mode: cade22grackle2xb9cd
% 124.07/124.28 % Steps: 74694
% 124.07/124.28 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------