TSTP Solution File: SEV009^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV009^5 : 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 : n007.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 19:32:18 EDT 2023
% Result : Theorem 10.27s 10.34s
% Output : Proof 10.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 122
% Syntax : Number of formulae : 140 ( 23 unt; 13 typ; 11 def)
% Number of atoms : 356 ( 29 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1017 ( 401 ~; 62 |; 0 &; 275 @)
% ( 52 <=>; 227 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 66 usr; 61 con; 0-2 aty)
% Number of variables : 134 ( 11 ^; 123 !; 0 ?; 134 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: ( a > $o ) > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__37,type,
eigen__37: a > $o ).
thf(ty_eigen__8,type,
eigen__8: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__9,type,
eigen__9: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__29,type,
eigen__29: a > $o ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__2 ) )
=> ~ ( X2 @ X1 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( X2 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ eigen__5 ) )
=> ~ ( X3 @ X1 ) )
=> ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ~ ( X3 @ X2 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ eigen__5 ) )
=> ~ ( X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__5 ) )
=> ~ ( X1 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__2 ) )
=> ~ ( X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__6 ) )
=> ~ ( X1 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__37,definition,
( eigen__37
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__1 ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__37])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__5 ) )
=> ~ ( X2 @ eigen__6 ) )
=> ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__6 ) )
=> ~ ( X2 @ X1 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__5 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a,X3: a] :
( ~ ( ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X2 ) )
=> ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(eigendef_eigen__29,definition,
( eigen__29
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__6 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__6 ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__29])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__5 ) )
=> ~ ( X1 @ eigen__6 ) )
=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__6 ) )
=> ~ ( X1 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ( X3 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( eigen__0 @ eigen__9 )
=> ~ ( eigen__9 @ eigen__6 ) )
=> ~ ( eigen__9 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__2 ) )
=> ~ ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( eigen__8 @ X1 )
= ( eigen__29 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ( eigen__0 @ eigen__37 )
=> ~ ( eigen__37 @ eigen__1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ( X1 = eigen__37 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__5 ) )
=> ~ ( X1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( eigen__0 @ eigen__29 )
=> ~ ( eigen__29 @ eigen__6 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__6 ) )
=> ( X1 = eigen__29 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ( eigen__0 @ eigen__37 )
=> ~ ( eigen__37 @ eigen__1 ) )
=> ~ ( eigen__37 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__6 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__6 ) )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a,X2: a] :
( ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__8 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a,X2: a] :
( ~ ( ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ eigen__5 ) )
=> ~ ( X3 @ X1 ) )
=> ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 ) )
=> ~ ( X3 @ X2 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( eigen__0 @ X3 )
=> ~ ( X3 @ eigen__5 ) )
=> ~ ( X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP1
=> ~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__5 ) )
=> ~ ( X1 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__6 ) )
=> ( X1 = eigen__29 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__0 @ eigen__4 )
=> ~ ( eigen__4 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP5
=> ~ ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__3 ) )
=> ~ ( X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( eigen__0 @ eigen__4 )
=> ~ ( eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__3 ) )
=> ~ ( X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__8 = eigen__29 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__8 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( eigen__0 @ eigen__37 )
=> ~ ( eigen__37 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__1 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__1 ) )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__5 ) )
=> ~ ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP11
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ ( sP11
=> ~ ( eigen__8 @ eigen__5 ) )
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__4 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP8
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: a > $o] :
( ~ ( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__6 ) )
=> ~ ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ sP31
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X2 ) )
=> ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: a] :
( ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__2 ) )
=> ~ ( X2 @ X1 ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( X2 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ ( sP11
=> ~ ( eigen__8 @ eigen__5 ) )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ sP19
=> ~ ( eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( eigen__9 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( eigen__37 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( eigen__29 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ sP21
=> ~ sP30 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ ( ( eigen__0 @ eigen__9 )
=> ~ ( eigen__9 @ eigen__6 ) )
=> ( eigen__9 = eigen__29 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( eigen__9 = eigen__29 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ~ sP28
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( eigen__0 @ eigen__9 )
=> ~ ( eigen__9 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: a] :
( ( eigen__9 @ X1 )
= ( eigen__29 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP15 = sP39 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X2 ) )
=> ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( eigen__0 @ X4 )
=> ~ ( X4 @ X1 ) )
=> ~ ( X4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP11
=> ~ ( eigen__8 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: a] :
( ~ ( ~ sP9
=> ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__6 ) )
=> ~ ( X2 @ X1 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__5 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP37 = sP39 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(cTHM261_B_pme,conjecture,
! [X1: ( a > $o ) > $o] :
( ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ( X4 = X3 ) ) )
=> ~ ( ~ ( ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) )
=> ~ ( X4 @ X2 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X3 ) )
=> ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X3 ) )
=> ~ ( X5 @ X4 ) ) )
=> ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X4 ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: ( a > $o ) > $o] :
( ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ( X4 = X3 ) ) )
=> ~ ( ~ ( ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) )
=> ~ ( X4 @ X2 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X3 ) )
=> ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X3 ) )
=> ~ ( X5 @ X4 ) ) )
=> ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM261_B_pme]) ).
thf(h3,assumption,
~ ( sP2
=> ~ sP33 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP2,
introduced(assumption,[]) ).
thf(h5,assumption,
sP33,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP12
| sP25
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP25
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP7
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP26
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__37]) ).
thf(6,plain,
( ~ sP2
| ~ sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP48
| sP15
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP52
| ~ sP37
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP6
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP47
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP28
| ~ sP11
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP43
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP41
| sP46
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP23
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP44
| sP28
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP18
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP18
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( sP10
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP13
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__29]) ).
thf(20,plain,
( ~ sP2
| ~ sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP21
| ~ sP42
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP40
| sP21
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP22
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP35
| sP50
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP27
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( sP3
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP3
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP32
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9]) ).
thf(29,plain,
( sP50
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP29
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP29
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP9
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(33,plain,
( sP1
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP1
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP17
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP17
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP51
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(38,plain,
( sP16
| ~ sP51 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(39,plain,
( sP49
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(40,plain,
( sP19
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP19
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP36
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP36
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP5
| ~ sP36 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(45,plain,
( sP20
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP20
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP34
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(48,plain,
( sP14
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(49,plain,
( sP8
| sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(50,plain,
( ~ sP31
| ~ sP8
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP33
| sP31
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,h4,h5]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,52,h4,h5]) ).
thf(54,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,53,h3]) ).
thf(55,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[54,h1]) ).
thf(56,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[55,h0]) ).
thf(0,theorem,
! [X1: ( a > $o ) > $o] :
( ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ( X4 = X3 ) ) )
=> ~ ( ~ ( ! [X2: a] :
~ ! [X3: a > $o] :
( ~ ( ( X1 @ X3 )
=> ~ ( X3 @ X2 ) )
=> ~ ( X3 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X2 ) )
=> ~ ( X4 @ X3 ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) )
=> ~ ( X4 @ X2 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X3 ) )
=> ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X3 ) )
=> ~ ( X5 @ X4 ) ) )
=> ~ ! [X5: a > $o] :
( ~ ( ( X1 @ X5 )
=> ~ ( X5 @ X2 ) )
=> ~ ( X5 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[54,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SEV009^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 03:34:10 EDT 2023
% 0.21/0.36 % CPUTime :
% 10.27/10.34 % SZS status Theorem
% 10.27/10.34 % Mode: cade22grackle2xfee4
% 10.27/10.34 % Steps: 142951
% 10.27/10.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------