TSTP Solution File: SEV128^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV128^5 : 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 : 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 : 300s
% DateTime : Thu Aug 31 19:32:41 EDT 2023
% Result : Theorem 54.07s 54.35s
% Output : Proof 54.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 87
% Syntax : Number of formulae : 105 ( 26 unt; 11 typ; 6 def)
% Number of atoms : 236 ( 27 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1113 ( 271 ~; 37 |; 0 &; 527 @)
% ( 33 <=>; 245 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 170 ( 170 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 42 con; 0-2 aty)
% Number of variables : 319 ( 42 ^; 277 !; 0 ?; 319 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: ( a > a > $o ) > $o ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_eigen__3,type,
eigen__3: a > a > $o ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__9,type,
eigen__9: a > a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__10,type,
eigen__10: a > a > $o ).
thf(ty_eigen__13,type,
eigen__13: a ).
thf(ty_eigen__12,type,
eigen__12: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(h0,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: a > a > $o] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__9
!= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__10 @ X1 @ X2 )
=> ( eigen__3 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: a] :
~ ( ~ ! [X2: a > a > $o] :
( ~ ! [X3: a > a > $o] :
( ( eigen__0 @ X3 )
=> ( X2
!= ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( X3 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) ) ) )
=> ~ ( X2 @ eigen__7 @ X1 ) )
=> ( eigen__3 @ eigen__7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__1
@ ^ [X1: a] :
~ ( ( eigen__10 @ eigen__12 @ X1 )
=> ( eigen__3 @ eigen__12 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: a > a > $o] :
~ ( ~ ! [X2: a > a > $o] :
( ( eigen__0 @ X2 )
=> ( X1
!= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ) )
=> ~ ( X1 @ eigen__7 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__3 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__10 @ eigen__12 @ eigen__13 )
=> ( eigen__3 @ eigen__12 @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > a > $o] :
( ( eigen__0 @ X1 )
=> ~ ( X1 @ eigen__12 @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__9
= ( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__10 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP3
=> ( eigen__3 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ( X3
!= ( ^ [X5: a,X6: a] :
! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X4 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) ) ) )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( eigen__9 @ X1 )
= ( ^ [X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__10 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__10 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__7 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ~ ! [X2: a > a > $o] :
( ( eigen__0 @ X2 )
=> ~ ( X2 @ eigen__12 @ X1 ) )
=> ( eigen__3 @ eigen__12 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__3 @ eigen__7 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__10 @ eigen__12 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__9 @ eigen__7 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ! [X1: a > a > $o] :
( ( eigen__0 @ X1 )
=> ( eigen__9
!= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) )
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > a > $o] :
( ( eigen__0 @ X1 )
=> ( eigen__9
!= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ~ ! [X2: a > a > $o] :
( ~ ! [X3: a > a > $o] :
( ( eigen__0 @ X3 )
=> ( X2
!= ( ^ [X4: a,X5: a] :
! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( X3 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) ) ) )
=> ~ ( X2 @ eigen__7 @ X1 ) )
=> ( eigen__3 @ eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ! [X1: a,X2: a] :
( ( eigen__10 @ X1 @ X2 )
=> ( eigen__3 @ X1 @ X2 ) )
=> ~ sP1 )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__3 @ eigen__12 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a > a > $o] :
( ~ ! [X2: a > a > $o] :
( ( eigen__0 @ X2 )
=> ( X1
!= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ) )
=> ~ ( X1 @ eigen__7 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ( eigen__9 @ eigen__7 @ X1 )
= ( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__10 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__7 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP17
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ( eigen__0 @ X3 )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__3 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a,X2: a] :
( ( eigen__10 @ X1 @ X2 )
=> ( eigen__3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ sP4
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP25
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP13 = sP9 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( eigen__9 @ eigen__7 )
= ( ^ [X1: a] :
! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__10 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__7 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP20
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a] :
( ( eigen__10 @ eigen__12 @ X1 )
=> ( eigen__3 @ eigen__12 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP17
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ~ ! [X5: a > a > $o] :
( ( eigen__0 @ X5 )
=> ( X4
!= ( ^ [X6: a,X7: a] :
! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( X5 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) ) ) )
=> ~ ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(cTHM253_B_pme,conjecture,
! [X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ~ ! [X8: a > a > $o] :
( ( X1 @ X8 )
=> ( X7
!= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ~ ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
=> ~ ! [X12: a,X13: a,X14: a] :
( ~ ( ( X11 @ X12 @ X13 )
=> ~ ( X11 @ X13 @ X14 ) )
=> ( X11 @ X12 @ X14 ) ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ( X1 @ X7 )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ~ ! [X8: a > a > $o] :
( ( X1 @ X8 )
=> ( X7
!= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ~ ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
=> ~ ! [X12: a,X13: a,X14: a] :
( ~ ( ( X11 @ X12 @ X13 )
=> ~ ( X11 @ X13 @ X14 ) )
=> ( X11 @ X12 @ X14 ) ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ( X1 @ X7 )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(assume_negation,[status(cth)],[cTHM253_B_pme]) ).
thf(h3,assumption,
~ ! [X1: a,X2: a] :
( ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
( ~ ! [X7: a > a > $o] :
( ( eigen__0 @ X7 )
=> ( X6
!= ( ^ [X8: a,X9: a] :
! [X10: a > a > $o] :
( ~ ( ! [X11: a,X12: a] :
( ( X7 @ X11 @ X12 )
=> ( X10 @ X11 @ X12 ) )
=> ~ ! [X11: a,X12: a,X13: a] :
( ~ ( ( X10 @ X11 @ X12 )
=> ~ ( X10 @ X12 @ X13 ) )
=> ( X10 @ X11 @ X13 ) ) )
=> ( X10 @ X8 @ X9 ) ) ) ) )
=> ~ ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
( ( eigen__0 @ X6 )
=> ~ ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ~ ! [X6: a > a > $o] :
( ( eigen__0 @ X6 )
=> ( X5
!= ( ^ [X7: a,X8: a] :
! [X9: a > a > $o] :
( ~ ( ! [X10: a,X11: a] :
( ( X6 @ X10 @ X11 )
=> ( X9 @ X10 @ X11 ) )
=> ~ ! [X10: a,X11: a,X12: a] :
( ~ ( ( X9 @ X10 @ X11 )
=> ~ ( X9 @ X11 @ X12 ) )
=> ( X9 @ X10 @ X12 ) ) )
=> ( X9 @ X7 @ X8 ) ) ) ) )
=> ~ ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__1 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ( eigen__0 @ X5 )
=> ~ ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP33
=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ~ ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP33,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ( eigen__0 @ X4 )
=> ~ ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( sP23
=> ~ sP1 )
=> sP24 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP23
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h11,assumption,
sP23,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP22
| ~ sP17
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP26
| sP4
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP23
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP18
| sP27
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP28
| ~ sP13
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP21
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP29
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP8
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( sP2
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP2
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP31
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__13]) ).
thf(15,plain,
( sP25
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).
thf(16,plain,
( ~ sP27
| ~ sP25
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP5
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP32
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP32
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP15
| ~ sP32 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(21,plain,
( sP14
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP14
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP20
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(24,plain,
( sP30
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP30
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP16
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(27,plain,
( sP7
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).
thf(28,plain,
( ~ sP3
| ~ sP7
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP6
| sP3
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP33
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,h6,h11,h12,h10]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,31,h11,h12]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,32,h9,h10]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,33,h8]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,34,h6,h7]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,35,h5]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,36,h4]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,37,h3]) ).
thf(39,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[38,h1]) ).
thf(40,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[39,h0]) ).
thf(0,theorem,
! [X1: ( a > a > $o ) > $o,X2: a,X3: a] :
( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ~ ! [X8: a > a > $o] :
( ( X1 @ X8 )
=> ( X7
!= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ~ ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
=> ~ ! [X12: a,X13: a,X14: a] :
( ~ ( ( X11 @ X12 @ X13 )
=> ~ ( X11 @ X13 @ X14 ) )
=> ( X11 @ X12 @ X14 ) ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
( ( X1 @ X7 )
=> ~ ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[38,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV128^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 01:53:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 54.07/54.35 % SZS status Theorem
% 54.07/54.35 % Mode: cade22grackle2x6987
% 54.07/54.35 % Steps: 158499
% 54.07/54.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------