TSTP Solution File: SEV021^7 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV021^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 19:32:21 EDT 2023
% Result : Theorem 123.43s 123.64s
% Output : Proof 123.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 199
% Syntax : Number of formulae : 229 ( 57 unt; 11 typ; 5 def)
% Number of atoms : 634 ( 55 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 1028 ( 391 ~; 110 |; 0 &; 255 @)
% ( 78 <=>; 194 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 92 ( 90 usr; 85 con; 0-2 aty)
% Number of variables : 102 ( 13 ^; 89 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cP,type,
cP: ( a > $o ) > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__128,type,
eigen__128: a ).
thf(ty_eigen__127,type,
eigen__127: a ).
thf(ty_eigen__12,type,
eigen__12: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__129,type,
eigen__129: a > $o ).
thf(ty_eigen__10,type,
eigen__10: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ( cP @ X1 )
=> ~ ( X1 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ( cP @ X1 )
=> ( ( X1 @ eigen__1 )
= ( X1 @ eigen__4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ( cP @ X1 )
=> ~ ( X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: a] :
( ( eigen__2 @ X1 )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ! [X2: a] :
( ( eigen__0 @ X2 )
= ( ! [X3: a > $o] :
( ( cP @ X3 )
=> ( ( X3 @ X1 )
= ( X3 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ~ ( ~ ( ~ ( ( cP @ eigen__0 )
=> ~ ( cP @ eigen__129 ) )
=> ~ ( eigen__0 @ eigen__127 ) )
=> ~ ( eigen__129 @ eigen__127 ) )
=> ~ ( eigen__0 @ eigen__128 ) )
=> ( eigen__129 @ eigen__128 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o,X2: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ~ ( X1 @ eigen__127 ) )
=> ~ ( X2 @ eigen__127 ) )
=> ~ ( X1 @ eigen__128 ) )
=> ( X2 @ eigen__128 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ~ ( ~ ( ~ ( ( cP @ eigen__2 )
=> ~ ( cP @ eigen__10 ) )
=> ~ ( eigen__2 @ eigen__4 ) )
=> ~ ( eigen__10 @ eigen__4 ) )
=> ~ ( eigen__2 @ eigen__1 ) )
=> ( eigen__10 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > $o] :
( ( cP @ X1 )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a > $o,X2: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ( X2 @ eigen__1 ) )
=> ~ ( X1 @ eigen__4 ) )
=> ( X2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cP @ eigen__12 )
=> ( ( eigen__12 @ eigen__1 )
= ( eigen__12 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ~ ( ( cP @ eigen__2 )
=> ~ ( cP @ eigen__10 ) )
=> ~ ( eigen__2 @ eigen__4 ) )
=> ~ ( eigen__10 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ~ ( ( cP @ eigen__10 )
=> ~ ( cP @ eigen__12 ) )
=> ~ ( eigen__10 @ eigen__4 ) )
=> ~ ( eigen__12 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__129 @ eigen__127 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP4
= ( ! [X1: a > $o] :
( ( cP @ X1 )
=> ( ( X1 @ eigen__1 )
= ( X1 @ eigen__4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eigen__12 @ eigen__1 )
= ( eigen__12 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
~ ( eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ~ ( ~ ( ~ ( ( cP @ eigen__0 )
=> ~ ( cP @ eigen__129 ) )
=> ~ ( eigen__0 @ eigen__128 ) )
=> ~ ( eigen__129 @ eigen__128 ) )
=> ~ ( eigen__0 @ eigen__127 ) )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ( cP @ eigen__2 )
=> ~ ( cP @ eigen__10 ) )
=> ~ ( eigen__2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( cP @ eigen__0 )
=> ~ ( cP @ eigen__129 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__127 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__129 @ eigen__128 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( eigen__2 @ eigen__1 )
= sP21 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__12 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ~ ( X2 @ eigen__128 ) )
=> ~ ( X3 @ eigen__128 ) )
=> ~ ( X2 @ X1 ) )
=> ( X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( cP @ eigen__10 )
=> ~ ( eigen__10 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a > $o] :
( ( cP @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( cP @ eigen__2 )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ eigen__0 )
=> ~ ( cP @ X1 ) )
=> ~ ( eigen__0 @ eigen__128 ) )
=> ~ ( X1 @ eigen__128 ) )
=> ~ sP20 )
=> ( X1 @ eigen__127 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__10 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ~ ( X2 @ eigen__4 ) )
=> ~ ( X3 @ eigen__4 ) )
=> ~ ( X2 @ X1 ) )
=> ( X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( ( cP @ eigen__10 )
=> ~ ( cP @ eigen__12 ) )
=> ~ sP30 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ eigen__2 )
=> ~ ( cP @ X1 ) )
=> ~ sP21 )
=> ~ ( X1 @ eigen__4 ) )
=> ~ ( eigen__2 @ eigen__1 ) )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( cP @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP21 = sP4 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( cP @ eigen__0 )
=> ( sP20
= ( eigen__0 @ eigen__128 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ ( ~ sP19
=> ~ sP20 )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( ~ ( ( cP @ eigen__10 )
=> ~ sP34 )
=> ~ ( eigen__10 @ eigen__1 ) )
=> ~ ( eigen__12 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ sP10
=> ~ sP39 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: a,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ~ ( X2 @ eigen__127 ) )
=> ~ ( X3 @ eigen__127 ) )
=> ~ ( X2 @ X1 ) )
=> ( X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ( eigen__0 @ eigen__1 )
=> ! [X1: a] :
( ( eigen__0 @ X1 )
= ( ! [X2: a > $o] :
( ( cP @ X2 )
=> ( ( X2 @ eigen__1 )
= ( X2 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( cP @ eigen__2 )
=> ~ sP39 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ eigen__10 )
=> ~ ( cP @ X1 ) )
=> ~ ( eigen__10 @ eigen__1 ) )
=> ~ ( X1 @ eigen__1 ) )
=> ~ sP30 )
=> ( X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ ( ( cP @ eigen__10 )
=> ~ sP34 )
=> ~ ( eigen__10 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: a > $o] :
( ( cP @ X1 )
=> ( ( X1 @ eigen__1 )
= ( X1 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ sP38
=> ~ sP30 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( cP @ eigen__0 )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( eigen__0 @ eigen__128 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ sP37
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( eigen__10 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ ( ~ ( ~ sP19
=> ~ sP49 )
=> ~ sP22 )
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ ( ~ sP19
=> ~ sP49 )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( cP @ eigen__129 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ eigen__10 )
=> ~ ( cP @ X1 ) )
=> ~ sP30 )
=> ~ ( X1 @ eigen__4 ) )
=> ~ sP52 )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: a,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ~ ( X2 @ eigen__1 ) )
=> ~ ( X3 @ eigen__1 ) )
=> ~ ( X2 @ X1 ) )
=> ( X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ~ ( ~ sP11
=> ~ sP52 )
=> ( eigen__12 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ sP11
=> ~ sP52 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: a > $o] :
( ( cP @ X1 )
=> ~ ( X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( cP @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ! [X1: a] :
( ( eigen__2 @ X1 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( cP @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP20 = sP49 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( sP62
=> ~ sP64 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
= ( ! [X2: a > $o] :
( ( cP @ X2 )
=> ( ( X2 @ eigen__1 )
= ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ( ~ ( sP54
=> ~ ( cP @ X1 ) )
=> ~ sP20 )
=> ~ ( X1 @ eigen__127 ) )
=> ~ sP49 )
=> ( X1 @ eigen__128 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ~ sP47
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ~ sP19
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ~ sP19
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( sP64
=> ~ sP34 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ! [X1: a > $o,X2: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ~ ( X1 @ eigen__4 ) )
=> ~ ( X2 @ eigen__4 ) )
=> ~ ( X1 @ eigen__1 ) )
=> ( X2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ! [X1: a > $o,X2: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ~ ( X1 @ eigen__128 ) )
=> ~ ( X2 @ eigen__128 ) )
=> ~ ( X1 @ eigen__127 ) )
=> ( X2 @ eigen__127 ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ! [X1: a,X2: a,X3: a > $o,X4: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ~ ( X3 @ X1 ) )
=> ~ ( X4 @ X1 ) )
=> ~ ( X3 @ X2 ) )
=> ( X4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ! [X1: a > $o] :
( ( cP @ X1 )
=> ( ( X1 @ eigen__127 )
= ( X1 @ eigen__128 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( eigen__12 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(def_cQ,definition,
( cQ
= ( ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( cP @ X3 )
@ ( ( X3 @ X1 )
<=> ( X3 @ X2 ) ) ) ) ) ).
thf(cTHM262_D_EXT2_pme,conjecture,
( ! [X1: a > $o,X2: a > $o] :
( ~ ( ( X1 = X2 )
=> ~ ( cP @ X1 ) )
=> ( cP @ X2 ) )
=> ( ~ ( ~ ( sP27
=> ~ sP13 )
=> ~ sP75 )
=> ( ( ^ [X1: a > $o] :
~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( ! [X4: a > $o] :
( ( cP @ X4 )
=> ( ( X4 @ X2 )
= ( X4 @ X3 ) ) ) ) ) ) ) )
= cP ) ) ) ).
thf(h2,negated_conjecture,
~ ( ! [X1: a > $o,X2: a > $o] :
( ~ ( ( X1 = X2 )
=> ~ ( cP @ X1 ) )
=> ( cP @ X2 ) )
=> ( ~ ( ~ ( sP27
=> ~ sP13 )
=> ~ sP75 )
=> ( ( ^ [X1: a > $o] :
~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( ! [X4: a > $o] :
( ( cP @ X4 )
=> ( ( X4 @ X2 )
= ( X4 @ X3 ) ) ) ) ) ) ) )
= cP ) ) ),
inference(assume_negation,[status(cth)],[cTHM262_D_EXT2_pme]) ).
thf(h3,assumption,
! [X1: a > $o,X2: a > $o] :
( ~ ( ( X1 = X2 )
=> ~ ( cP @ X1 ) )
=> ( cP @ X2 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ( sP27
=> ~ sP13 )
=> ~ sP75 )
=> ( ( ^ [X1: a > $o] :
~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( ! [X4: a > $o] :
( ( cP @ X4 )
=> ( ( X4 @ X2 )
= ( X4 @ X3 ) ) ) ) ) ) ) )
= cP ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( sP27
=> ~ sP13 )
=> ~ sP75 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ( ^ [X1: a > $o] :
~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( ! [X4: a > $o] :
( ( cP @ X4 )
=> ( ( X4 @ X2 )
= ( X4 @ X3 ) ) ) ) ) ) ) )
!= cP ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP27
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP75,
introduced(assumption,[]) ).
thf(h9,assumption,
sP27,
introduced(assumption,[]) ).
thf(h10,assumption,
sP13,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: a > $o] :
( ( ~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( ! [X4: a > $o] :
( ( cP @ X4 )
=> ( ( X4 @ X2 )
= ( X4 @ X3 ) ) ) ) ) ) ) )
= ( cP @ X1 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
( ( ~ ( ~ sP16
=> ~ sP1 ) )
!= sP54 ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ sP16
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP54,
introduced(assumption,[]) ).
thf(h15,assumption,
( ~ sP16
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP54,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
sP50,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP32
| sP72
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP11
| sP32
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP72
| ~ sP64
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP45
| sP72
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP38
| sP45
| ~ sP77 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP60
| sP11
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP47
| sP38
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP59
| sP60
| sP77 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP69
| sP47
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP57
| sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP44
| sP69 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP18
| sP66
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP10
| sP18
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP66
| ~ sP62
| ~ sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP40
| sP10
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP6
| sP40
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP8
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP73
| sP57 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP33
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP73
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP31
| sP73 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( sP15
| ~ sP77
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP15
| sP77
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP23
| ~ sP39
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP9
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP9
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP28
| ~ sP62
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP26
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP26
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP46
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(31,plain,
( ~ sP46
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( sP61
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(33,plain,
( ~ sP14
| ~ sP4
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP14
| sP4
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP13
| ~ sP61 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP75
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP58
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP67
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( sP35
| ~ sP21
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP35
| sP21
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP63
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(42,plain,
( sP2
| ~ sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP62
| sP54
| ~ sP2 ),
inference(mating_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP42
| ~ sP50
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP43
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP43
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP7
| ~ sP43 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(48,plain,
( ~ sP13
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP1
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP75
| sP58 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h17,h18,h13,h14,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,h10,h8,h19,h18,h14]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h18,h13,h14,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__1)],[h17,51,h19]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h13,52,h17,h18]) ).
thf(h20,assumption,
sP16,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(54,plain,
( ~ sP48
| ~ sP54
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP27
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],[54,55,h9,h20,h16]) ).
thf(h22,assumption,
~ ( sP20
=> ! [X1: a] :
( ( eigen__0 @ X1 )
= ( ! [X2: a > $o] :
( ( cP @ X2 )
=> ( ( X2 @ eigen__127 )
= ( X2 @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
sP20,
introduced(assumption,[]) ).
thf(h24,assumption,
~ ! [X1: a] :
( ( eigen__0 @ X1 )
= ( ! [X2: a > $o] :
( ( cP @ X2 )
=> ( ( X2 @ eigen__127 )
= ( X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
sP49 != sP76,
introduced(assumption,[]) ).
thf(h26,assumption,
sP49,
introduced(assumption,[]) ).
thf(h27,assumption,
sP76,
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP49,
introduced(assumption,[]) ).
thf(h29,assumption,
~ sP76,
introduced(assumption,[]) ).
thf(h30,assumption,
~ ( sP56
=> ( sP12 = sP22 ) ),
introduced(assumption,[]) ).
thf(h31,assumption,
sP56,
introduced(assumption,[]) ).
thf(h32,assumption,
sP12 != sP22,
introduced(assumption,[]) ).
thf(h33,assumption,
sP12,
introduced(assumption,[]) ).
thf(h34,assumption,
sP22,
introduced(assumption,[]) ).
thf(h35,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h36,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(57,plain,
( ~ sP19
| ~ sP54
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP71
| sP19
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP37
| sP71
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP51
| sP37
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP3
| sP51
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP68
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP5
| sP68 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP41
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP75
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h33,h34,h31,h32,h30,h26,h27,h25,h23,h24,h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],[57,58,59,60,61,62,63,64,65,h8,h23,h26,h31,h33,h34,h16]) ).
thf(67,plain,
( ~ sP19
| ~ sP54
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP70
| sP19
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP55
| sP70
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP53
| sP55
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP17
| sP53
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( ~ sP29
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(73,plain,
( ~ sP74
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(74,plain,
( ~ sP25
| sP74 ),
inference(all_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP75
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h35,h36,h31,h32,h30,h26,h27,h25,h23,h24,h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],[67,68,69,70,71,72,73,74,75,h8,h23,h26,h31,h35,h36,h16]) ).
thf(77,plain,
$false,
inference(tab_be,[status(thm),assumptions([h31,h32,h30,h26,h27,h25,h23,h24,h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_be(discharge,[h33,h34]),tab_be(discharge,[h35,h36])],[h32,66,76,h33,h34,h35,h36]) ).
thf(78,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h26,h27,h25,h23,h24,h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h30,77,h31,h32]) ).
thf(79,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h27,h25,h23,h24,h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__129)],[h27,78,h30]) ).
thf(80,plain,
( ~ sP65
| ~ sP20
| sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP36
| ~ sP54
| sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(82,plain,
( ~ sP76
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(83,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h28,h29,h25,h23,h24,h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],[80,81,82,h23,h28,h29,h16]) ).
thf(84,plain,
$false,
inference(tab_be,[status(thm),assumptions([h25,h23,h24,h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_be(discharge,[h26,h27]),tab_be(discharge,[h28,h29])],[h25,79,83,h26,h27,h28,h29]) ).
thf(85,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h24,h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__128)],[h24,84,h25]) ).
thf(86,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h22,85,h23,h24]) ).
thf(87,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__127)],[h21,86,h22]) ).
thf(88,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h20]),tab_imp(discharge,[h21])],[h15,56,87,h20,h21]) ).
thf(89,plain,
$false,
inference(tab_be,[status(thm),assumptions([h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_be(discharge,[h13,h14]),tab_be(discharge,[h15,h16])],[h12,53,88,h13,h14,h15,h16]) ).
thf(90,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__0)],[h11,89,h12]) ).
thf(91,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_fe(discharge,[h11])],[h6,90,h11]) ).
thf(92,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,91,h9,h10]) ).
thf(93,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,92,h7,h8]) ).
thf(94,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,93,h5,h6]) ).
thf(95,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,94,h3,h4]) ).
thf(96,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[95,h1]) ).
thf(97,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[96,h0]) ).
thf(0,theorem,
( ! [X1: a > $o,X2: a > $o] :
( ~ ( ( X1 = X2 )
=> ~ ( cP @ X1 ) )
=> ( cP @ X2 ) )
=> ( ~ ( ~ ( sP27
=> ~ sP13 )
=> ~ sP75 )
=> ( ( ^ [X1: a > $o] :
~ ( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
= ( ! [X4: a > $o] :
( ( cP @ X4 )
=> ( ( X4 @ X2 )
= ( X4 @ X3 ) ) ) ) ) ) ) )
= cP ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[95,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV021^7 : TPTP v8.1.2. Released v5.5.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n003.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
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Aug 24 04:08:22 EDT 2023
% 0.12/0.35 % CPUTime :
% 123.43/123.64 % SZS status Theorem
% 123.43/123.64 % Mode: cade22grackle2xb9cd
% 123.43/123.64 % Steps: 41013
% 123.43/123.64 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------