TSTP Solution File: SEV044^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV044^5 : 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 : n028.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 19:32:25 EDT 2023
% Result : Theorem 2.27s 2.48s
% Output : Proof 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 95
% Syntax : Number of formulae : 110 ( 17 unt; 11 typ; 7 def)
% Number of atoms : 291 ( 7 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 909 ( 122 ~; 47 |; 0 &; 549 @)
% ( 39 <=>; 152 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 50 usr; 44 con; 0-3 aty)
% Number of variables : 156 ( 7 ^; 149 !; 0 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__4,type,
eigen__4: b ).
thf(ty_eigen__7,type,
eigen__7: b > a ).
thf(ty_eigen__2,type,
eigen__2: b > a ).
thf(ty_eigen__3,type,
eigen__3: b > a ).
thf(ty_eigen__6,type,
eigen__6: b > a ).
thf(ty_eigen__8,type,
eigen__8: b ).
thf(ty_eigen__0,type,
eigen__0: b > $o ).
thf(ty_eigen__5,type,
eigen__5: b > a ).
thf(ty_eigen__1,type,
eigen__1: b > a > a > $o ).
thf(h0,assumption,
! [X1: ( b > a ) > $o,X2: b > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: b > a] :
~ ( ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__2 @ X2 ) @ ( X1 @ X2 ) ) )
=> ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( X1 @ X2 ) @ ( eigen__2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: b > a] :
~ ! [X2: b > a] :
( ~ ( ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( eigen__5 @ X3 ) @ ( X1 @ X3 ) ) )
=> ~ ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) )
=> ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( eigen__5 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: b] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__5 @ X1 ) @ ( eigen__7 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: b > a] :
~ ! [X2: b > a] :
( ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) )
=> ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: b] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__3 @ X1 ) @ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: b > a] :
~ ( ~ ( ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__5 @ X2 ) @ ( eigen__6 @ X2 ) ) )
=> ~ ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__6 @ X2 ) @ ( X1 @ X2 ) ) ) )
=> ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__5 @ X2 ) @ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: b > a] :
~ ! [X2: b > a,X3: b > a] :
( ~ ( ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
=> ~ ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) ) )
=> ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__5 @ X1 ) @ ( eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X1 @ X2 @ X3 )
=> ( eigen__1 @ X1 @ X3 @ X2 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( eigen__1 @ X1 @ X2 @ X3 )
=> ~ ( eigen__1 @ X1 @ X3 @ X4 ) )
=> ( eigen__1 @ X1 @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: b > a] :
( ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__2 @ X2 ) @ ( X1 @ X2 ) ) )
=> ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( X1 @ X2 ) @ ( eigen__2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 @ eigen__8 @ ( eigen__6 @ eigen__8 ) @ ( eigen__7 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__1 @ eigen__8 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__8 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__8 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ X1 )
=> ~ ( eigen__1 @ eigen__8 @ X1 @ X2 ) )
=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP3
=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__3 @ X1 ) @ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ ( eigen__6 @ eigen__8 ) )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ! [X1: a,X2: a] :
( ( eigen__1 @ eigen__4 @ X1 @ X2 )
=> ( eigen__1 @ eigen__4 @ X2 @ X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__1 @ eigen__4 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__4 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__4 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__0 @ eigen__8 )
=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ ( eigen__7 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ ( eigen__7 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eigen__0 @ eigen__8 )
=> ~ ( ! [X1: a,X2: a] :
( ( eigen__1 @ eigen__8 @ X1 @ X2 )
=> ( eigen__1 @ eigen__8 @ X2 @ X1 ) )
=> ~ sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: b > a] :
( ~ ( sP1
=> ~ ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__6 @ X2 ) @ ( X1 @ X2 ) ) ) )
=> ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__5 @ X2 ) @ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP5
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP5
=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__2 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ eigen__4 @ X1 @ X2 )
=> ( eigen__1 @ eigen__4 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ~ ( ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ ( eigen__6 @ eigen__8 ) )
=> ~ ( eigen__1 @ eigen__8 @ ( eigen__6 @ eigen__8 ) @ X1 ) )
=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__6 @ X1 ) @ ( eigen__7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__5 @ X1 ) @ ( eigen__7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: b > a,X2: b > a] :
( ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) )
=> ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP24
=> ~ ! [X1: b > a,X2: b > a,X3: b > a] :
( ~ ( ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
=> ~ ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) ) )
=> ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ ( eigen__6 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__3 @ X1 ) @ ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP11
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: b > a,X2: b > a] :
( ~ ( ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( eigen__5 @ X3 ) @ ( X1 @ X3 ) ) )
=> ~ ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) )
=> ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( eigen__5 @ X3 ) @ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ! [X1: a,X2: a] :
( ( eigen__1 @ eigen__8 @ X1 @ X2 )
=> ( eigen__1 @ eigen__8 @ X2 @ X1 ) )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP1
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: a] :
( ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ X1 )
=> ( eigen__1 @ eigen__4 @ X1 @ ( eigen__2 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ sP31
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP5
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: b > a,X2: b > a,X3: b > a] :
( ~ ( ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
=> ~ ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) ) )
=> ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( eigen__0 @ eigen__8 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( eigen__0 @ eigen__8 )
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP4
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( eigen__0 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(cTHM506_pme,conjecture,
! [X1: b > $o,X2: b > a > a > $o] :
( ! [X3: b] :
( ( X1 @ X3 )
=> ~ ( ! [X4: a,X5: a] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ! [X3: b > a,X4: b > a] :
( ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) )
=> ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X4 @ X5 ) @ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: b > a,X4: b > a,X5: b > a] :
( ~ ( ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) )
=> ~ ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X6 ) ) ) )
=> ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X5 @ X6 ) ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: b > $o,X2: b > a > a > $o] :
( ! [X3: b] :
( ( X1 @ X3 )
=> ~ ( ! [X4: a,X5: a] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ! [X3: b > a,X4: b > a] :
( ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) )
=> ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X4 @ X5 ) @ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: b > a,X4: b > a,X5: b > a] :
( ~ ( ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) )
=> ~ ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X6 ) ) ) )
=> ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X5 @ X6 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM506_pme]) ).
thf(h3,assumption,
~ ! [X1: b > a > a > $o] :
( ! [X2: b] :
( ( eigen__0 @ X2 )
=> ~ ( ! [X3: a,X4: a] :
( ( X1 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 @ X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X1 @ X2 @ X3 @ X4 )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X2 @ X3 @ X5 ) ) ) )
=> ~ ( ! [X2: b > a,X3: b > a] :
( ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) )
=> ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( X1 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: b > a,X3: b > a,X4: b > a] :
( ~ ( ! [X5: b] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X5 ) ) )
=> ~ ! [X5: b] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) ) )
=> ! [X5: b] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X4 @ X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP2
=> ~ sP25 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
sP25,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP11
| ~ sP26
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP28
| sP11
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP21
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP38
| ~ sP4
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP32
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP20
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP12
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP34
| ~ sP5
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP17
| ~ sP5
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP3
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP2
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP30
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP15
| ~ sP39
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP37
| ~ sP39
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP36
| ~ sP39
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP2
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP1
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP22
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP31
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP31
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP13
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP13
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP23
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(26,plain,
( sP33
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP33
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP16
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(29,plain,
( sP29
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(30,plain,
( sP35
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(31,plain,
( sP18
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP18
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP27
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(34,plain,
( sP10
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP10
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP6
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(37,plain,
( sP24
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(38,plain,
( ~ sP25
| ~ sP24
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,h5,h6]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,39,h5,h6]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,40,h4]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,41,h3]) ).
thf(43,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[42,h1]) ).
thf(44,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[43,h0]) ).
thf(0,theorem,
! [X1: b > $o,X2: b > a > a > $o] :
( ! [X3: b] :
( ( X1 @ X3 )
=> ~ ( ! [X4: a,X5: a] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ! [X3: b > a,X4: b > a] :
( ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) )
=> ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X4 @ X5 ) @ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: b > a,X4: b > a,X5: b > a] :
( ~ ( ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) )
=> ~ ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X6 ) ) ) )
=> ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X5 @ X6 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[42,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEV044^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.37 % Computer : n028.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Aug 24 02:11:49 EDT 2023
% 0.14/0.37 % CPUTime :
% 2.27/2.48 % SZS status Theorem
% 2.27/2.48 % Mode: cade22grackle2xfee4
% 2.27/2.48 % Steps: 8697
% 2.27/2.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------