TSTP Solution File: SEV021^6 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV021^6 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 18:04:29 EDT 2022
% Result : Theorem 265.56s 265.61s
% Output : Proof 265.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 168
% Syntax : Number of formulae : 197 ( 53 unt; 11 typ; 5 def)
% Number of atoms : 489 ( 32 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 863 ( 354 ~; 83 |; 0 &; 198 @)
% ( 64 <=>; 164 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 77 usr; 72 con; 0-2 aty)
% Number of variables : 86 ( 11 ^ 75 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__16,type,
eigen__16: a > $o ).
thf(ty_cP,type,
cP: ( a > $o ) > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__3,type,
eigen__3: a > $o ).
thf(ty_eigen__132,type,
eigen__132: a ).
thf(ty_eigen__133,type,
eigen__133: a > $o ).
thf(ty_eigen__131,type,
eigen__131: a ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ( cP @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ( X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
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(eigendef_eigen__16,definition,
( eigen__16
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ( cP @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ( X1 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
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
<=> ( ~ ( ~ ( ( cP @ eigen__133 )
=> ~ ( cP @ eigen__0 ) )
=> ~ ( eigen__133 @ eigen__131 ) )
=> ~ ( eigen__0 @ eigen__131 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cP @ eigen__16 )
=> ~ ( eigen__16 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cP @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [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,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( cP @ eigen__3 )
=> ~ ( eigen__3 @ eigen__1 ) )
=> ~ ( eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ eigen__132 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a > $o] :
( ~ ( ( cP @ X1 )
=> ~ ( X1 @ eigen__131 ) )
=> ~ ( X1 @ eigen__132 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ~ ( ~ ( sP4
=> ~ ( cP @ eigen__3 ) )
=> ~ ( eigen__16 @ eigen__1 ) )
=> ~ ( eigen__3 @ eigen__1 ) )
=> ~ ( eigen__16 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
~ ( eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a > $o] :
( ~ ( ( cP @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__133 @ eigen__132 ) ),
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
<=> ( eigen__16 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eigen__2 @ eigen__4 )
= ( eigen__0 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ( eigen__2 @ X1 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP3
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a > $o,X2: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ~ ( X1 @ eigen__131 ) )
=> ~ ( X2 @ eigen__131 ) )
=> ~ ( X1 @ eigen__132 ) )
=> ( X2 @ eigen__132 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( cP @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP4
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP2
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__0 @ eigen__131 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( cP @ eigen__0 )
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ( ~ sP21
=> ~ ( eigen__16 @ eigen__1 ) )
=> ~ ( eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ( sP20
=> ~ ( cP @ eigen__2 ) )
=> ~ ( eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( ( cP @ eigen__2 )
=> ~ ( eigen__2 @ eigen__1 ) )
=> ~ ( eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a > $o] :
( ( cP @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ eigen__133 )
=> ~ ( cP @ X1 ) )
=> ~ ( eigen__133 @ eigen__131 ) )
=> ~ ( X1 @ eigen__131 ) )
=> ~ sP12 )
=> ( X1 @ eigen__132 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP24
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( cP @ eigen__133 )
=> ~ ( cP @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ sP9
=> ( eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ( ~ ( sP4
=> ~ ( cP @ X1 ) )
=> ~ ( eigen__16 @ eigen__1 ) )
=> ~ ( X1 @ eigen__1 ) )
=> ~ sP14 )
=> ( X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ ( ~ ( ~ sP26
=> ~ ( eigen__2 @ eigen__1 ) )
=> ~ ( eigen__3 @ eigen__4 ) )
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
= ( ~ ! [X2: a > $o] :
( ~ ( ( cP @ X2 )
=> ~ ( X2 @ eigen__1 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ sP33
=> ~ ( eigen__133 @ eigen__131 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: a > $o] :
( ( cP @ X1 )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ sP26
=> ~ ( eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( eigen__16 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( cP @ eigen__0 )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( cP @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eigen__133 @ eigen__131 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ ( sP44
=> ~ ( eigen__2 @ eigen__1 ) )
=> ~ sP27 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP44
=> ~ ( eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [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,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( cP @ eigen__133 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: a,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ~ ( X2 @ eigen__131 ) )
=> ~ ( X3 @ eigen__131 ) )
=> ~ ( X2 @ X1 ) )
=> ( X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ sP22
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP20
=> ~ sP44 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP46
=> sP37 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP20
=> ~ sP41 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP30
= ( ~ ! [X1: a > $o] :
( ~ ( ( cP @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ( X1 @ eigen__4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: a > $o] :
( ~ ( ( cP @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ( X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ( ~ ( sP20
=> ~ ( cP @ X1 ) )
=> ~ sP41 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ sP57 )
=> ( X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( ~ sP21
=> ~ sP42 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [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,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ~ sP40
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(def_cQ,definition,
( cQ
= ( ^ [X1: a,X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( cP @ X3 )
=> ~ ( X3 @ X1 ) )
=> ~ ( X3 @ X2 ) ) ) ) ).
thf(cTHM262_D_EXT2_pme,conjecture,
( ! [X1: a > $o,X2: a > $o] :
( ~ ( ( X1 = X2 )
=> ~ ( cP @ X1 ) )
=> ( cP @ X2 ) )
=> ( ~ ( ~ ( sP29
=> ~ sP13 )
=> ~ sP62 )
=> ( ( ^ [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 ) )
=> ( ~ ( ~ ( sP29
=> ~ sP13 )
=> ~ sP62 )
=> ( ( ^ [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,
~ ( ~ ( ~ ( sP29
=> ~ sP13 )
=> ~ sP62 )
=> ( ( ^ [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,
~ ( ~ ( sP29
=> ~ sP13 )
=> ~ sP62 ),
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,
~ ( sP29
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP62,
introduced(assumption,[]) ).
thf(h9,assumption,
sP29,
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,
( ~ ( ~ sP10
=> ~ sP1 ) )
!= sP49,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ sP10
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP49,
introduced(assumption,[]) ).
thf(h15,assumption,
( ~ sP10
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP49,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
sP46,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP35
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP34
| sP9
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| sP25
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP25
| sP61
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP61
| sP21
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP21
| ~ sP4
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP50
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP60
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP36
| sP64
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP64
| sP40
| ~ sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP40
| sP26
| ~ sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP26
| sP54
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP3
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP3
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP50
| sP60 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( sP18
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP18
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP59
| sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP47
| sP48
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP59
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).
thf(21,plain,
( ~ sP58
| ~ sP30
| ~ sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP58
| sP30
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP5
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP37
| sP58 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP54
| ~ sP20
| ~ sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP16
| ~ sP27
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP16
| sP27
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP17
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(29,plain,
( sP15
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP56
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP6
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP6
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP11
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP28
| sP48
| ~ sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP11
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(36,plain,
( ~ sP44
| sP49
| ~ sP15 ),
inference(mating_rule,[status(thm)],]) ).
thf(37,plain,
( sP48
| sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP48
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP39
| ~ sP48 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(40,plain,
( ~ sP13
| ~ sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP62
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP55
| ~ sP46
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP1
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(44,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,h10,h8,h19,h18,h14]) ).
thf(45,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)],[h17,44,h19]) ).
thf(46,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])],[h13,45,h17,h18]) ).
thf(h20,assumption,
sP10,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(47,plain,
( ~ sP29
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP43
| ~ sP49
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],[47,48,h9,h20,h16]) ).
thf(h22,assumption,
~ ( sP23
=> ! [X1: a] :
( ( eigen__0 @ X1 )
= ( ~ ! [X2: a > $o] :
( ~ ( ( cP @ X2 )
=> ~ ( X2 @ eigen__131 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
sP23,
introduced(assumption,[]) ).
thf(h24,assumption,
~ ! [X1: a] :
( ( eigen__0 @ X1 )
= ( ~ ! [X2: a > $o] :
( ~ ( ( cP @ X2 )
=> ~ ( X2 @ eigen__131 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
sP7
!= ( ~ sP8 ),
introduced(assumption,[]) ).
thf(h26,assumption,
sP7,
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h29,assumption,
sP8,
introduced(assumption,[]) ).
thf(50,plain,
( ~ sP8
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP32
| sP24
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP24
| ~ sP49
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
$false,
inference(prop_unsat,[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])],[50,51,52,h23,h26,h27,h16]) ).
thf(h30,assumption,
~ ( ~ ( sP51
=> ~ sP45 )
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( sP51
=> ~ sP45 ),
introduced(assumption,[]) ).
thf(h32,assumption,
sP12,
introduced(assumption,[]) ).
thf(h33,assumption,
sP51,
introduced(assumption,[]) ).
thf(h34,assumption,
sP45,
introduced(assumption,[]) ).
thf(54,plain,
( ~ sP31
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP53
| sP22
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP22
| sP2
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP2
| sP38
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP38
| sP33
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP33
| ~ sP51
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP19
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP52
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP62
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(63,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h33,h34,h31,h32,h30,h28,h29,h25,h23,h24,h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],[54,55,56,57,58,59,60,61,62,h8,h23,h28,h33,h34,h32,h16]) ).
thf(64,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h32,h30,h28,h29,h25,h23,h24,h22,h21,h15,h16,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h33,h34])],[h31,63,h33,h34]) ).
thf(65,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h28,h29,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])],[h30,64,h31,h32]) ).
thf(66,plain,
$false,
inference(tab_negall,[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]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__133)],[h29,65,h30]) ).
thf(67,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])],[h25,53,66,h26,h27,h28,h29]) ).
thf(68,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__132)],[h24,67,h25]) ).
thf(69,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])],[h22,68,h23,h24]) ).
thf(70,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__131)],[h21,69,h22]) ).
thf(71,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])],[h15,49,70,h20,h21]) ).
thf(72,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])],[h12,46,71,h13,h14,h15,h16]) ).
thf(73,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)],[h11,72,h12]) ).
thf(74,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_fe(discharge,[h11])],[h6,73,h11]) ).
thf(75,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,74,h9,h10]) ).
thf(76,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,75,h7,h8]) ).
thf(77,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,76,h5,h6]) ).
thf(78,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,77,h3,h4]) ).
thf(79,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[78,h1]) ).
thf(80,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[79,h0]) ).
thf(0,theorem,
( ! [X1: a > $o,X2: a > $o] :
( ~ ( ( X1 = X2 )
=> ~ ( cP @ X1 ) )
=> ( cP @ X2 ) )
=> ( ~ ( ~ ( sP29
=> ~ sP13 )
=> ~ sP62 )
=> ( ( ^ [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])],[78,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEV021^6 : TPTP v8.1.0. Released v5.5.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 14:08:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 265.56/265.61 % SZS status Theorem
% 265.56/265.61 % Mode: mode493
% 265.56/265.61 % Inferences: 3178
% 265.56/265.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------