TSTP Solution File: SEV254^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV254^5 : TPTP v8.1.0. Released v4.0.0.
% 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 18:05:35 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 110
% Syntax : Number of formulae : 136 ( 46 unt; 10 typ; 3 def)
% Number of atoms : 299 ( 10 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 901 ( 211 ~; 48 |; 0 &; 405 @)
% ( 34 <=>; 203 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 42 con; 0-2 aty)
% Number of variables : 215 ( 38 ^ 177 !; 0 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__12,type,
eigen__12: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__9,type,
eigen__9: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__2 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__9 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__2 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__2 @ eigen__6 )
=> ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__9 @ eigen__12 )
=> ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__12 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__2 @ eigen__1 )
=> ( eigen__0 @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__9 @ eigen__8 )
=> ( eigen__0 @ eigen__9 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__0 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__0 @ eigen__9 @ eigen__8 )
=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__9 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__9 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( eigen__9 @ X1 )
=> ( eigen__0 @ eigen__9 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 @ eigen__9 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__9 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__9 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP16
=> ! [X1: $i] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP10
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP13
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP17
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP7
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP7
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP21
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(cTHM2C_pme,conjecture,
! [X1: ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 ) ) )
=> ~ ( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( X1
@ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
@ X2 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 ) ) )
=> ~ ( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( X1
@ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
@ X2 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM2C_pme]) ).
thf(h2,assumption,
~ ( ~ ( sP12
=> ~ ( ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> sP30 ) )
=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP12
=> ~ ( ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> sP30 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP12,
introduced(assumption,[]) ).
thf(h6,assumption,
( ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) )
=> sP30 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP30,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) )
=> sP23 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP7
=> ~ sP29 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP7,
introduced(assumption,[]) ).
thf(h14,assumption,
sP29,
introduced(assumption,[]) ).
thf(h15,assumption,
( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__3 )
!= ( ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__3 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__3 ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__3 ),
introduced(assumption,[]) ).
thf(h19,assumption,
! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP32
| ~ sP7
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP34
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP34
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP16
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(6,plain,
( ~ sP12
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP22
| ~ sP16
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP27
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP28
| ~ sP17
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP4
| ~ sP29
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h5,h13,h14,h11]) ).
thf(h20,assumption,
~ ( ! [X1: $i] :
( ( eigen__5 @ X1 )
=> ( eigen__0 @ eigen__5 @ X1 ) )
=> ~ ( eigen__5 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
! [X1: $i] :
( ( eigen__5 @ X1 )
=> ( eigen__0 @ eigen__5 @ X1 ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
eigen__5 @ eigen__3,
introduced(assumption,[]) ).
thf(13,plain,
( ~ sP3
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP31
| ~ sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP1
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP1
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP16
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(18,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP4
| ~ sP29
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP12
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP22
| ~ sP16
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP27
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP28
| ~ sP17
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h20,h18,h19,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[13,14,15,16,17,18,19,20,21,22,23,h5,h13,h14,h11]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,24,h21,h22]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h19,h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h19,25,h20]) ).
thf(27,plain,
$false,
inference(tab_be,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_be(discharge,[h16,h17]),tab_be(discharge,[h18,h19])],[h15,12,26,h16,h17,h18,h19]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__3)],[h4,27,h15]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,28,h13,h14]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h10,29,h12]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,30,h10,h11]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h7,31,h9]) ).
thf(h23,assumption,
sP14
!= ( ~ sP33 ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP14,
introduced(assumption,[]) ).
thf(h25,assumption,
~ sP33,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h27,assumption,
sP33,
introduced(assumption,[]) ).
thf(33,plain,
( ~ sP33
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP19
| ~ sP30
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h25,h23,h8,h5,h6,h3,h4,h2,h1,h0])],[33,34,h8,h24,h25]) ).
thf(h28,assumption,
~ ( sP13
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h29,assumption,
sP13,
introduced(assumption,[]) ).
thf(h30,assumption,
sP11,
introduced(assumption,[]) ).
thf(36,plain,
( ~ sP26
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP25
| ~ sP13
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP2
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP2
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP10
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(41,plain,
( ~ sP12
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP24
| ~ sP10
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP20
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP9
| ~ sP15
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP13
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP6
| ~ sP11
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h29,h30,h28,h26,h27,h23,h8,h5,h6,h3,h4,h2,h1,h0])],[36,37,38,39,40,41,42,43,44,45,46,h5,h26,h29,h30]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h26,h27,h23,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,47,h29,h30]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h27,h23,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__9)],[h27,48,h28]) ).
thf(50,plain,
$false,
inference(tab_be,[status(thm),assumptions([h23,h8,h5,h6,h3,h4,h2,h1,h0]),tab_be(discharge,[h24,h25]),tab_be(discharge,[h26,h27])],[h23,35,49,h24,h25,h26,h27]) ).
thf(51,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__8)],[h4,50,h23]) ).
thf(52,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,32,51,h7,h8]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,52,h5,h6]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,53,h3,h4]) ).
thf(55,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,54,h2]) ).
thf(56,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[55,h0]) ).
thf(0,theorem,
! [X1: ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ~ ( X5 @ X4 ) )
@ X3 ) ) )
=> ~ ( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( X1
@ ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) ) )
@ X2 ) ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[55,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV254^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % 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 : Mon Jun 27 18:04:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 % Mode: mode213
% 0.18/0.41 % Inferences: 190
% 0.18/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------