TSTP Solution File: SEU903^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU903^5 : 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 : n031.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 17:37:49 EDT 2023
% Result : Theorem 20.05s 20.16s
% Output : Proof 20.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 90
% Syntax : Number of formulae : 112 ( 29 unt; 13 typ; 2 def)
% Number of atoms : 314 ( 42 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1253 ( 321 ~; 34 |; 0 &; 577 @)
% ( 29 <=>; 292 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 33 con; 0-2 aty)
% Number of variables : 188 ( 2 ^; 186 !; 0 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_g,type,
g: $tType ).
thf(ty_eigen__3,type,
eigen__3: g > g ).
thf(ty_eigen__6,type,
eigen__6: a > $o ).
thf(ty_eigen__1,type,
eigen__1: b > a ).
thf(ty_eigen__2,type,
eigen__2: g > $o ).
thf(ty_eigen__9,type,
eigen__9: g ).
thf(ty_eigen__5,type,
eigen__5: b > b ).
thf(ty_eigen__7,type,
eigen__7: a > a ).
thf(ty_eigen__4,type,
eigen__4: b > $o ).
thf(ty_eigen__8,type,
eigen__8: g ).
thf(ty_eigen__0,type,
eigen__0: g > b ).
thf(h0,assumption,
! [X1: g > $o,X2: g] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: g] :
~ ( ( eigen__2 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: g] :
~ ( ( eigen__2 @ X1 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( ( eigen__1 @ ( eigen__5 @ X1 ) )
= ( eigen__7 @ ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__4 @ ( eigen__0 @ eigen__8 ) )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__4 @ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__2 @ eigen__9 )
=> ( eigen__4 @ ( eigen__0 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__2 @ eigen__8 )
=> ( eigen__4 @ ( eigen__0 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__9 ) ) )
= ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__2 @ eigen__9 )
=> ( ( eigen__0 @ ( eigen__3 @ eigen__9 ) )
= ( eigen__5 @ ( eigen__0 @ eigen__9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( ( eigen__0 @ ( eigen__3 @ X1 ) )
= ( eigen__5 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__4 @ ( eigen__0 @ eigen__9 ) )
=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__9 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__9 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> $false ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__4 @ ( eigen__0 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__2 @ eigen__8 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: a] :
( ( eigen__6 @ X1 )
=> ( eigen__6 @ ( eigen__7 @ X1 ) ) ) )
=> ~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__9 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: a] :
( ( eigen__6 @ X1 )
=> ( eigen__6 @ ( eigen__7 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__5 @ ( eigen__0 @ eigen__9 ) )
= ( eigen__0 @ ( eigen__3 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__2 @ eigen__9 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__9 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__9 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__9 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__2 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP14
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__2 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a] :
( ( eigen__6 @ X1 )
=> ( eigen__6 @ ( eigen__7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__4 @ ( eigen__0 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( eigen__0 @ ( eigen__3 @ eigen__9 ) )
= ( eigen__5 @ ( eigen__0 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(cTHM131_pme,conjecture,
! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g,X5: b > $o,X6: b > b,X7: a > $o,X8: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X1 @ ( X4 @ X9 ) )
= ( X6 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( ( X2 @ ( X6 @ X9 ) )
= ( X8 @ ( X2 @ X9 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X7 @ ( X2 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g,X5: b > $o,X6: b > b,X7: a > $o,X8: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X1 @ ( X4 @ X9 ) )
= ( X6 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( ( X2 @ ( X6 @ X9 ) )
= ( X8 @ ( X2 @ X9 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X7 @ ( X2 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM131_pme]) ).
thf(h2,assumption,
~ ! [X1: b > a,X2: g > $o,X3: g > g,X4: b > $o,X5: b > b,X6: a > $o,X7: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__0 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( ( eigen__0 @ ( X3 @ X8 ) )
= ( X5 @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) ) )
=> ~ ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( ( X1 @ ( X5 @ X8 ) )
= ( X7 @ ( X1 @ X8 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
=> ~ ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X1 @ ( eigen__0 @ ( X3 @ X8 ) ) )
= ( X7 @ ( X1 @ ( eigen__0 @ X8 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: g > $o,X2: g > g,X3: b > $o,X4: b > b,X5: a > $o,X6: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X7: g] :
( ( X1 @ X7 )
=> ( X1 @ ( X2 @ X7 ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X3 @ ( X4 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__0 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( ( eigen__0 @ ( X2 @ X7 ) )
= ( X4 @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X3 @ ( X4 @ X7 ) ) ) )
=> ~ ! [X7: a] :
( ( X5 @ X7 )
=> ( X5 @ ( X6 @ X7 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X5 @ ( eigen__1 @ X7 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( ( eigen__1 @ ( X4 @ X7 ) )
= ( X6 @ ( eigen__1 @ X7 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X7: g] :
( ( X1 @ X7 )
=> ( X1 @ ( X2 @ X7 ) ) )
=> ~ ! [X7: a] :
( ( X5 @ X7 )
=> ( X5 @ ( X6 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X5 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( ( eigen__1 @ ( eigen__0 @ ( X2 @ X7 ) ) )
= ( X6 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: g > g,X2: b > $o,X3: b > b,X4: a > $o,X5: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( eigen__2 @ ( X1 @ X6 ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X2 @ ( X3 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X2 @ ( eigen__0 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( ( eigen__0 @ ( X1 @ X6 ) )
= ( X3 @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X2 @ ( X3 @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X4 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X4 @ ( eigen__1 @ X6 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( ( eigen__1 @ ( X3 @ X6 ) )
= ( X5 @ ( eigen__1 @ X6 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( eigen__2 @ ( X1 @ X6 ) ) )
=> ~ ! [X6: a] :
( ( X4 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X4 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( ( eigen__1 @ ( eigen__0 @ ( X1 @ X6 ) ) )
= ( X5 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: b > $o,X2: b > b,X3: a > $o,X4: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP23
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X1 @ ( X2 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X1 @ ( eigen__0 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( ( eigen__0 @ ( eigen__3 @ X5 ) )
= ( X2 @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X1 @ ( X2 @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X3 @ ( eigen__1 @ X5 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( ( eigen__1 @ ( X2 @ X5 ) )
= ( X4 @ ( eigen__1 @ X5 ) ) ) ) )
=> ~ ( ~ ( ~ ( sP23
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X3 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X5 ) ) )
= ( X4 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: b > b,X2: a > $o,X3: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP23
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( eigen__4 @ ( X1 @ X4 ) ) ) )
=> ~ sP3 )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( ( eigen__0 @ ( eigen__3 @ X4 ) )
= ( X1 @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( eigen__4 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( X2 @ ( eigen__1 @ X4 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( ( eigen__1 @ ( X1 @ X4 ) )
= ( X3 @ ( eigen__1 @ X4 ) ) ) ) )
=> ~ ( ~ ( ~ ( sP23
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( X2 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X4 ) ) )
= ( X3 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a > $o,X2: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP23
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( eigen__4 @ ( eigen__5 @ X3 ) ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( eigen__4 @ ( eigen__5 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( X1 @ ( eigen__1 @ X3 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( ( eigen__1 @ ( eigen__5 @ X3 ) )
= ( X2 @ ( eigen__1 @ X3 ) ) ) ) )
=> ~ ( ~ ( ~ ( sP23
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X3 ) ) )
= ( X2 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP23
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( eigen__4 @ ( eigen__5 @ X2 ) ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( eigen__4 @ ( eigen__5 @ X2 ) ) ) )
=> ~ ! [X2: a] :
( ( eigen__6 @ X2 )
=> ( eigen__6 @ ( X1 @ X2 ) ) ) )
=> ~ sP20 )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( ( eigen__1 @ ( eigen__5 @ X2 ) )
= ( X1 @ ( eigen__1 @ X2 ) ) ) ) )
=> ~ ( ~ ( ~ ( sP23
=> ~ ! [X2: a] :
( ( eigen__6 @ X2 )
=> ( eigen__6 @ ( X1 @ X2 ) ) ) )
=> ~ sP24 )
=> ~ ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X2 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP23
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP27 )
=> ~ sP20 )
=> ~ sP1 )
=> ~ sP22 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP23
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP27 )
=> ~ sP20 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP22,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP23
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP27 )
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( sP23
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP27 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP20,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( ~ ( ~ ( ~ ( sP23
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP27,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ~ ( ~ ( sP23
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP3 )
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h19,assumption,
! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ~ ( sP23
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP9,
introduced(assumption,[]) ).
thf(h22,assumption,
~ ( sP23
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
sP3,
introduced(assumption,[]) ).
thf(h24,assumption,
sP23,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP29
| sP17
| ~ sP29
| sP11 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP15
| sP19
| ~ sP7
| ~ sP15 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
~ sP11,
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP7
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| ~ sP12
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP20
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP10
| ~ sP28
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP8
| ~ sP21
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP4
| ~ sP21
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP9
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP6
| ~ sP26
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( sP18
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP18
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP16
| ~ sP23
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP5
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(19,plain,
( sP13
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP13
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP24
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(22,plain,
( ~ sP14
| sP16
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP22
| sP14
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h19,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,h24,h23,h21,h17,h15,h13,h11]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h24,h19])],[h22,24,h24,h19]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h20,25,h22,h23]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h18,26,h20,h21]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h16,27,h18,h19]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,28,h16,h17]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,29,h14,h15]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,30,h12,h13]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,31,h10,h11]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__7)],[h8,32,h9]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__6)],[h7,33,h8]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__5)],[h6,34,h7]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__4)],[h5,35,h6]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,36,h5]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,37,h4]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,38,h3]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,39,h2]) ).
thf(41,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[40,h0]) ).
thf(0,theorem,
! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g,X5: b > $o,X6: b > b,X7: a > $o,X8: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X1 @ ( X4 @ X9 ) )
= ( X6 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( ( X2 @ ( X6 @ X9 ) )
= ( X8 @ ( X2 @ X9 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X7 @ ( X2 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[40,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SEU903^5 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 18:02:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 20.05/20.16 % SZS status Theorem
% 20.05/20.16 % Mode: cade22grackle2xfee4
% 20.05/20.16 % Steps: 214325
% 20.05/20.16 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------