TSTP Solution File: SEV260^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV260^5 : 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 : n006.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 18:05:37 EDT 2022
% Result : Theorem 159.46s 159.44s
% Output : Proof 159.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 87
% Syntax : Number of formulae : 112 ( 31 unt; 10 typ; 2 def)
% Number of atoms : 500 ( 151 equ; 0 cnn)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 1351 ( 502 ~; 29 |; 0 &; 414 @)
% ( 23 <=>; 383 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 316 ( 316 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 28 con; 0-2 aty)
% Number of variables : 429 ( 146 ^ 283 !; 0 ?; 429 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__6,type,
eigen__6: b ).
thf(ty_eigen__14,type,
eigen__14: a ).
thf(ty_eigen__2,type,
eigen__2: a > b ).
thf(ty_eigen__1,type,
eigen__1: ( b > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: ( a > $o ) > $o ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__5,type,
eigen__5: a > $o ).
thf(ty_eigen__3,type,
eigen__3: b > $o ).
thf(h0,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: b] :
( ( ~ ( eigen__3 @ X1 ) )
!= ( ~ ( eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__1
@ ^ [X1: a] :
( ( eigen__5 @ X1 )
!= ( ~ ( eigen__3 @ ( eigen__2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__5
= ( ^ [X1: a] :
~ ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__5 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__5
= ( ^ [X1: a] :
~ ( eigen__3 @ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: b > $o] :
( ( eigen__1 @ X1 )
=> ! [X2: a > $o] :
( ( X2
= ( ^ [X3: a] : ( X1 @ ( eigen__2 @ X3 ) ) ) )
=> ( eigen__0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] :
~ ( eigen__3 @ ( eigen__2 @ X2 ) ) ) )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ( eigen__0 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__1
@ ^ [X1: b] :
~ ( eigen__3 @ X1 ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( eigen__5 @ X1 )
= ( ~ ( eigen__3 @ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP2
= ( ~ ( eigen__3 @ ( eigen__2 @ eigen__14 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__4 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ( ^ [X1: b] :
~ ( eigen__3 @ X1 ) )
= ( ^ [X1: b] :
~ ( eigen__3 @ X1 ) ) )
=> ( eigen__1
@ ^ [X1: b] :
~ ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( eigen__5 @ X1 )
= ( ~ ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__4
= ( ^ [X1: a] : ( eigen__3 @ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__3 @ ( eigen__2 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( eigen__4 @ X1 )
= ( eigen__3 @ ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( ^ [X1: b] :
~ ( eigen__3 @ X1 ) )
= ( ^ [X1: b] :
~ ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__1
@ ^ [X1: b] :
~ ( eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP2
= ( ~ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: b] :
( ( ~ ( eigen__3 @ X1 ) )
= ( ~ ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] :
~ ( eigen__3 @ X2 ) ) )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( ~ ( eigen__3 @ eigen__6 ) )
= ( ~ ( eigen__3 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP10 = sP14 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(cCLOSED_THM1_pme,conjecture,
! [X1: ( a > $o ) > $o,X2: ( b > $o ) > $o,X3: a > b] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X4: a > $o] :
( ( X4
= ( ^ [X5: a] : $false ) )
=> ( X1 @ X4 ) )
=> ~ ! [X4: a > $o] :
( ( X4
= ( ^ [X5: a] : ~ $false ) )
=> ( X1 @ X4 ) ) )
=> ~ ! [X4: ( a > $o ) > $o,X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ( X4 @ X6 )
=> ( X1 @ X6 ) )
=> ( X5
!= ( ^ [X6: a] :
~ ! [X7: a > $o] :
( ( X4 @ X7 )
=> ~ ( X7 @ X6 ) ) ) ) )
=> ( X1 @ X5 ) ) )
=> ~ ! [X4: a > $o,X5: a > $o,X6: a > $o] :
( ~ ( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X6
!= ( ^ [X7: a] :
~ ( ( X4 @ X7 )
=> ~ ( X5 @ X7 ) ) ) ) )
=> ( X1 @ X6 ) ) )
=> ~ ! [X4: b > $o] :
( ( X4
= ( ^ [X5: b] : $false ) )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: b > $o] :
( ( X4
= ( ^ [X5: b] : ~ $false ) )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: ( b > $o ) > $o,X5: b > $o] :
( ~ ( ! [X6: b > $o] :
( ( X4 @ X6 )
=> ( X2 @ X6 ) )
=> ( X5
!= ( ^ [X6: b] :
~ ! [X7: b > $o] :
( ( X4 @ X7 )
=> ~ ( X7 @ X6 ) ) ) ) )
=> ( X2 @ X5 ) ) )
=> ~ ! [X4: b > $o,X5: b > $o,X6: b > $o] :
( ~ ( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X6
!= ( ^ [X7: b] :
~ ( ( X4 @ X7 )
=> ~ ( X5 @ X7 ) ) ) ) )
=> ( X2 @ X6 ) ) )
=> ~ ! [X4: b > $o] :
( ( X2 @ X4 )
=> ! [X5: a > $o] :
( ( X5
= ( ^ [X6: a] : ( X4 @ ( X3 @ X6 ) ) ) )
=> ( X1 @ X5 ) ) ) )
=> ! [X4: b > $o] :
( ! [X5: b > $o] :
( ( X5
= ( ^ [X6: b] :
~ ( X4 @ X6 ) ) )
=> ( X2 @ X5 ) )
=> ! [X5: a > $o] :
( ( X5
= ( ^ [X6: a] : ( X4 @ ( X3 @ X6 ) ) ) )
=> ! [X6: a > $o] :
( ( X6
= ( ^ [X7: a] :
~ ( X5 @ X7 ) ) )
=> ( X1 @ X6 ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: ( a > $o ) > $o,X2: ( b > $o ) > $o,X3: a > b] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X4: a > $o] :
( ( X4
= ( ^ [X5: a] : $false ) )
=> ( X1 @ X4 ) )
=> ~ ! [X4: a > $o] :
( ( X4
= ( ^ [X5: a] : ~ $false ) )
=> ( X1 @ X4 ) ) )
=> ~ ! [X4: ( a > $o ) > $o,X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ( X4 @ X6 )
=> ( X1 @ X6 ) )
=> ( X5
!= ( ^ [X6: a] :
~ ! [X7: a > $o] :
( ( X4 @ X7 )
=> ~ ( X7 @ X6 ) ) ) ) )
=> ( X1 @ X5 ) ) )
=> ~ ! [X4: a > $o,X5: a > $o,X6: a > $o] :
( ~ ( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X6
!= ( ^ [X7: a] :
~ ( ( X4 @ X7 )
=> ~ ( X5 @ X7 ) ) ) ) )
=> ( X1 @ X6 ) ) )
=> ~ ! [X4: b > $o] :
( ( X4
= ( ^ [X5: b] : $false ) )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: b > $o] :
( ( X4
= ( ^ [X5: b] : ~ $false ) )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: ( b > $o ) > $o,X5: b > $o] :
( ~ ( ! [X6: b > $o] :
( ( X4 @ X6 )
=> ( X2 @ X6 ) )
=> ( X5
!= ( ^ [X6: b] :
~ ! [X7: b > $o] :
( ( X4 @ X7 )
=> ~ ( X7 @ X6 ) ) ) ) )
=> ( X2 @ X5 ) ) )
=> ~ ! [X4: b > $o,X5: b > $o,X6: b > $o] :
( ~ ( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X6
!= ( ^ [X7: b] :
~ ( ( X4 @ X7 )
=> ~ ( X5 @ X7 ) ) ) ) )
=> ( X2 @ X6 ) ) )
=> ~ ! [X4: b > $o] :
( ( X2 @ X4 )
=> ! [X5: a > $o] :
( ( X5
= ( ^ [X6: a] : ( X4 @ ( X3 @ X6 ) ) ) )
=> ( X1 @ X5 ) ) ) )
=> ! [X4: b > $o] :
( ! [X5: b > $o] :
( ( X5
= ( ^ [X6: b] :
~ ( X4 @ X6 ) ) )
=> ( X2 @ X5 ) )
=> ! [X5: a > $o] :
( ( X5
= ( ^ [X6: a] : ( X4 @ ( X3 @ X6 ) ) ) )
=> ! [X6: a > $o] :
( ( X6
= ( ^ [X7: a] :
~ ( X5 @ X7 ) ) )
=> ( X1 @ X6 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cCLOSED_THM1_pme]) ).
thf(h3,assumption,
~ ! [X1: ( b > $o ) > $o,X2: a > b] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a > $o] :
( ( X3
= ( ^ [X4: a] : $false ) )
=> ( eigen__0 @ X3 ) )
=> ~ ! [X3: a > $o] :
( ( X3
= ( ^ [X4: a] : ~ $false ) )
=> ( eigen__0 @ X3 ) ) )
=> ~ ! [X3: ( a > $o ) > $o,X4: a > $o] :
( ~ ( ! [X5: a > $o] :
( ( X3 @ X5 )
=> ( eigen__0 @ X5 ) )
=> ( X4
!= ( ^ [X5: a] :
~ ! [X6: a > $o] :
( ( X3 @ X6 )
=> ~ ( X6 @ X5 ) ) ) ) )
=> ( eigen__0 @ X4 ) ) )
=> ~ ! [X3: a > $o,X4: a > $o,X5: a > $o] :
( ~ ( ~ ( ( eigen__0 @ X3 )
=> ~ ( eigen__0 @ X4 ) )
=> ( X5
!= ( ^ [X6: a] :
~ ( ( X3 @ X6 )
=> ~ ( X4 @ X6 ) ) ) ) )
=> ( eigen__0 @ X5 ) ) )
=> ~ ! [X3: b > $o] :
( ( X3
= ( ^ [X4: b] : $false ) )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: b > $o] :
( ( X3
= ( ^ [X4: b] : ~ $false ) )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: ( b > $o ) > $o,X4: b > $o] :
( ~ ( ! [X5: b > $o] :
( ( X3 @ X5 )
=> ( X1 @ X5 ) )
=> ( X4
!= ( ^ [X5: b] :
~ ! [X6: b > $o] :
( ( X3 @ X6 )
=> ~ ( X6 @ X5 ) ) ) ) )
=> ( X1 @ X4 ) ) )
=> ~ ! [X3: b > $o,X4: b > $o,X5: b > $o] :
( ~ ( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X5
!= ( ^ [X6: b] :
~ ( ( X3 @ X6 )
=> ~ ( X4 @ X6 ) ) ) ) )
=> ( X1 @ X5 ) ) )
=> ~ ! [X3: b > $o] :
( ( X1 @ X3 )
=> ! [X4: a > $o] :
( ( X4
= ( ^ [X5: a] : ( X3 @ ( X2 @ X5 ) ) ) )
=> ( eigen__0 @ X4 ) ) ) )
=> ! [X3: b > $o] :
( ! [X4: b > $o] :
( ( X4
= ( ^ [X5: b] :
~ ( X3 @ X5 ) ) )
=> ( X1 @ X4 ) )
=> ! [X4: a > $o] :
( ( X4
= ( ^ [X5: a] : ( X3 @ ( X2 @ X5 ) ) ) )
=> ! [X5: a > $o] :
( ( X5
= ( ^ [X6: a] :
~ ( X4 @ X6 ) ) )
=> ( eigen__0 @ X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a > b] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X2: a > $o] :
( ( X2
= ( ^ [X3: a] : $false ) )
=> ( eigen__0 @ X2 ) )
=> ~ ! [X2: a > $o] :
( ( X2
= ( ^ [X3: a] : ~ $false ) )
=> ( eigen__0 @ X2 ) ) )
=> ~ ! [X2: ( a > $o ) > $o,X3: a > $o] :
( ~ ( ! [X4: a > $o] :
( ( X2 @ X4 )
=> ( eigen__0 @ X4 ) )
=> ( X3
!= ( ^ [X4: a] :
~ ! [X5: a > $o] :
( ( X2 @ X5 )
=> ~ ( X5 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ) )
=> ~ ! [X2: a > $o,X3: a > $o,X4: a > $o] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__0 @ X3 ) )
=> ( X4
!= ( ^ [X5: a] :
~ ( ( X2 @ X5 )
=> ~ ( X3 @ X5 ) ) ) ) )
=> ( eigen__0 @ X4 ) ) )
=> ~ ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] : $false ) )
=> ( eigen__1 @ X2 ) ) )
=> ~ ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] : ~ $false ) )
=> ( eigen__1 @ X2 ) ) )
=> ~ ! [X2: ( b > $o ) > $o,X3: b > $o] :
( ~ ( ! [X4: b > $o] :
( ( X2 @ X4 )
=> ( eigen__1 @ X4 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ! [X5: b > $o] :
( ( X2 @ X5 )
=> ~ ( X5 @ X4 ) ) ) ) )
=> ( eigen__1 @ X3 ) ) )
=> ~ ! [X2: b > $o,X3: b > $o,X4: b > $o] :
( ~ ( ~ ( ( eigen__1 @ X2 )
=> ~ ( eigen__1 @ X3 ) )
=> ( X4
!= ( ^ [X5: b] :
~ ( ( X2 @ X5 )
=> ~ ( X3 @ X5 ) ) ) ) )
=> ( eigen__1 @ X4 ) ) )
=> ~ ! [X2: b > $o] :
( ( eigen__1 @ X2 )
=> ! [X3: a > $o] :
( ( X3
= ( ^ [X4: a] : ( X2 @ ( X1 @ X4 ) ) ) )
=> ( eigen__0 @ X3 ) ) ) )
=> ! [X2: b > $o] :
( ! [X3: b > $o] :
( ( X3
= ( ^ [X4: b] :
~ ( X2 @ X4 ) ) )
=> ( eigen__1 @ X3 ) )
=> ! [X3: a > $o] :
( ( X3
= ( ^ [X4: a] : ( X2 @ ( X1 @ X4 ) ) ) )
=> ! [X4: a > $o] :
( ( X4
= ( ^ [X5: a] :
~ ( X3 @ X5 ) ) )
=> ( eigen__0 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: ( b > $o ) > $o,X2: b > $o] :
( ~ ( ! [X3: b > $o] :
( ( X1 @ X3 )
=> ( eigen__1 @ X3 ) )
=> ( X2
!= ( ^ [X3: b] :
~ ! [X4: b > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__1 @ X2 ) ) )
=> ~ ! [X1: b > $o,X2: b > $o,X3: b > $o] :
( ~ ( ~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__1 @ X2 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__1 @ X3 ) ) )
=> ~ sP4 )
=> ! [X1: b > $o] :
( ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] :
~ ( X1 @ X3 ) ) )
=> ( eigen__1 @ X2 ) )
=> ! [X2: a > $o] :
( ( X2
= ( ^ [X3: a] : ( X1 @ ( eigen__2 @ X3 ) ) ) )
=> ! [X3: a > $o] :
( ( X3
= ( ^ [X4: a] :
~ ( X2 @ X4 ) ) )
=> ( eigen__0 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: ( b > $o ) > $o,X2: b > $o] :
( ~ ( ! [X3: b > $o] :
( ( X1 @ X3 )
=> ( eigen__1 @ X3 ) )
=> ( X2
!= ( ^ [X3: b] :
~ ! [X4: b > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__1 @ X2 ) ) )
=> ~ ! [X1: b > $o,X2: b > $o,X3: b > $o] :
( ~ ( ~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__1 @ X2 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__1 @ X3 ) ) )
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: b > $o] :
( ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] :
~ ( X1 @ X3 ) ) )
=> ( eigen__1 @ X2 ) )
=> ! [X2: a > $o] :
( ( X2
= ( ^ [X3: a] : ( X1 @ ( eigen__2 @ X3 ) ) ) )
=> ! [X3: a > $o] :
( ( X3
= ( ^ [X4: a] :
~ ( X2 @ X4 ) ) )
=> ( eigen__0 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: ( b > $o ) > $o,X2: b > $o] :
( ~ ( ! [X3: b > $o] :
( ( X1 @ X3 )
=> ( eigen__1 @ X3 ) )
=> ( X2
!= ( ^ [X3: b] :
~ ! [X4: b > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__1 @ X2 ) ) )
=> ~ ! [X1: b > $o,X2: b > $o,X3: b > $o] :
( ~ ( ~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__1 @ X2 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP4,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: ( b > $o ) > $o,X2: b > $o] :
( ~ ( ! [X3: b > $o] :
( ( X1 @ X3 )
=> ( eigen__1 @ X3 ) )
=> ( X2
!= ( ^ [X3: b] :
~ ! [X4: b > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: b > $o,X2: b > $o,X3: b > $o] :
( ~ ( ~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__1 @ X2 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__1 @ X1 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ~ ( ! [X3: b > $o] :
( ( X1 @ X3 )
=> ( eigen__1 @ X3 ) )
=> ( X2
!= ( ^ [X3: b] :
~ ! [X4: b > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( ~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ( eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ( eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( sP21
=> ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ( eigen__3 @ ( eigen__2 @ X2 ) ) ) )
=> ! [X2: a > $o] :
( ( X2
= ( ^ [X3: a] :
~ ( X1 @ X3 ) ) )
=> ( eigen__0 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
sP21,
introduced(assumption,[]) ).
thf(h26,assumption,
~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ( eigen__3 @ ( eigen__2 @ X2 ) ) ) )
=> ! [X2: a > $o] :
( ( X2
= ( ^ [X3: a] :
~ ( X1 @ X3 ) ) )
=> ( eigen__0 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( sP13
=> ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] :
~ ( eigen__4 @ X2 ) ) )
=> ( eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
sP13,
introduced(assumption,[]) ).
thf(h29,assumption,
~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] :
~ ( eigen__4 @ X2 ) ) )
=> ( eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
~ ( sP1
=> sP17 ),
introduced(assumption,[]) ).
thf(h31,assumption,
sP1,
introduced(assumption,[]) ).
thf(h32,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP19
| ~ sP2
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP19
| sP2
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP23
| ~ sP10
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP23
| sP10
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP15
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP12
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP9
| ~ sP2
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP9
| sP2
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP8
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__14]) ).
thf(10,plain,
( sP3
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| ~ sP3
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP7
| ~ sP18
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
sP22,
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP20
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(16,plain,
( sP16
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP11
| ~ sP16
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP1
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP13
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP21
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP4
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h31,h32,h30,h28,h29,h27,h25,h26,h24,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,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,h9,h25,h28,h31,h32]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h28,h29,h27,h25,h26,h24,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h30,22,h31,h32]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h28,h29,h27,h25,h26,h24,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__5)],[h29,23,h30]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h25,h26,h24,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,24,h28,h29]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h26,h24,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__4)],[h26,25,h27]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h24,26,h25,h26]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__3)],[h7,27,h24]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h20,28,h22,h23]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h18,29,h20,h21]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h16,30,h18,h19]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,31,h16,h17]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,32,h14,h15]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,33,h12,h13]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,34,h10,h11]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,35,h8,h9]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,36,h6,h7]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,37,h5]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,38,h4]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,39,h3]) ).
thf(41,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[40,h1]) ).
thf(42,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[41,h0]) ).
thf(0,theorem,
! [X1: ( a > $o ) > $o,X2: ( b > $o ) > $o,X3: a > b] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X4: a > $o] :
( ( X4
= ( ^ [X5: a] : $false ) )
=> ( X1 @ X4 ) )
=> ~ ! [X4: a > $o] :
( ( X4
= ( ^ [X5: a] : ~ $false ) )
=> ( X1 @ X4 ) ) )
=> ~ ! [X4: ( a > $o ) > $o,X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ( X4 @ X6 )
=> ( X1 @ X6 ) )
=> ( X5
!= ( ^ [X6: a] :
~ ! [X7: a > $o] :
( ( X4 @ X7 )
=> ~ ( X7 @ X6 ) ) ) ) )
=> ( X1 @ X5 ) ) )
=> ~ ! [X4: a > $o,X5: a > $o,X6: a > $o] :
( ~ ( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( X6
!= ( ^ [X7: a] :
~ ( ( X4 @ X7 )
=> ~ ( X5 @ X7 ) ) ) ) )
=> ( X1 @ X6 ) ) )
=> ~ ! [X4: b > $o] :
( ( X4
= ( ^ [X5: b] : $false ) )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: b > $o] :
( ( X4
= ( ^ [X5: b] : ~ $false ) )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: ( b > $o ) > $o,X5: b > $o] :
( ~ ( ! [X6: b > $o] :
( ( X4 @ X6 )
=> ( X2 @ X6 ) )
=> ( X5
!= ( ^ [X6: b] :
~ ! [X7: b > $o] :
( ( X4 @ X7 )
=> ~ ( X7 @ X6 ) ) ) ) )
=> ( X2 @ X5 ) ) )
=> ~ ! [X4: b > $o,X5: b > $o,X6: b > $o] :
( ~ ( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X6
!= ( ^ [X7: b] :
~ ( ( X4 @ X7 )
=> ~ ( X5 @ X7 ) ) ) ) )
=> ( X2 @ X6 ) ) )
=> ~ ! [X4: b > $o] :
( ( X2 @ X4 )
=> ! [X5: a > $o] :
( ( X5
= ( ^ [X6: a] : ( X4 @ ( X3 @ X6 ) ) ) )
=> ( X1 @ X5 ) ) ) )
=> ! [X4: b > $o] :
( ! [X5: b > $o] :
( ( X5
= ( ^ [X6: b] :
~ ( X4 @ X6 ) ) )
=> ( X2 @ X5 ) )
=> ! [X5: a > $o] :
( ( X5
= ( ^ [X6: a] : ( X4 @ ( X3 @ X6 ) ) ) )
=> ! [X6: a > $o] :
( ( X6
= ( ^ [X7: a] :
~ ( X5 @ X7 ) ) )
=> ( X1 @ X6 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[40,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEV260^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n006.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 09:55:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 159.46/159.44 % SZS status Theorem
% 159.46/159.44 % Mode: mode460
% 159.46/159.44 % Inferences: 398
% 159.46/159.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------