TSTP Solution File: SEV310^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV310^5 : 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 : n024.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 19:33:17 EDT 2023
% Result : Theorem 182.65s 182.88s
% Output : Proof 182.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 62
% Syntax : Number of formulae : 73 ( 14 unt; 6 typ; 3 def)
% Number of atoms : 188 ( 3 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 419 ( 33 ~; 29 |; 0 &; 223 @)
% ( 25 <=>; 109 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 31 con; 0-2 aty)
% Number of variables : 118 ( 22 ^; 96 !; 0 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cK,type,
cK: ( a > $o ) > a > $o ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__13,type,
eigen__13: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ( ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ! [X2: a] :
( ( cK @ X1 @ X2 )
=> ( X1 @ X2 ) )
=> ( X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: a] :
~ ( ! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
=> ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( cK @ X1 @ X2 )
=> ( X1 @ X2 ) )
=> ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( cK
@ ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) ) )
@ X1 )
=> ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( cK
@ ^ [X3: a] :
! [X4: a > $o] :
( ! [X5: a] :
( ( cK @ X4 @ X5 )
=> ( X4 @ X5 ) )
=> ( X4 @ X3 ) )
@ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK
@ ( cK
@ ^ [X3: a] :
! [X4: a > $o] :
( ! [X5: a] :
( ( cK @ X4 @ X5 )
=> ( X4 @ X5 ) )
=> ( X4 @ X3 ) ) )
@ X2 )
=> ( cK @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: a > $o] :
( ! [X2: a] :
( ( cK @ X1 @ X2 )
=> ( X1 @ X2 ) )
=> ( X1 @ eigen__13 ) )
=> ( eigen__2 @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: a] :
( ! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
=> ( eigen__2 @ X1 ) )
=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ( cK @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( cK @ X1 @ X2 )
=> ( X1 @ X2 ) )
=> ( X1 @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP2
=> ( cK
@ ^ [X1: a] :
! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
@ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( cK @ eigen__2 @ eigen__1 )
=> ( eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cK @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
=> ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK
@ ^ [X3: a] :
! [X4: a > $o] :
( ! [X5: a] :
( ( cK @ X4 @ X5 )
=> ( X4 @ X5 ) )
=> ( X4 @ X3 ) )
@ X2 )
=> ( cK @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( cK @ X1 @ X2 )
=> ( X1 @ X2 ) )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( cK
@ ^ [X1: a] :
! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
@ eigen__1 )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( cK
@ ^ [X1: a] :
! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
@ eigen__1 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: a] :
( ( cK @ eigen__2 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ( eigen__2 @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: a] :
( ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: a] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( cK
@ ^ [X1: a] :
! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
@ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ( cK @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( cK
@ ^ [X1: a] :
! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__2 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a] :
( ( cK @ eigen__2 @ X1 )
=> ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP24
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(cTHM90A_pme,conjecture,
( sP18
=> ! [X1: a] :
( ! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 ) ) ) ).
thf(h2,negated_conjecture,
~ ( sP18
=> ! [X1: a] :
( ! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 ) ) ),
inference(assume_negation,[status(cth)],[cTHM90A_pme]) ).
thf(h3,assumption,
sP18,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP1
=> sP19 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| ~ sP22
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP15
| ~ sP24
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP4
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP20
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP10
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(8,plain,
( ~ sP5
| ~ sP10
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| ~ sP9
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP24
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| ~ sP21
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP3
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP7
| ~ sP2
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP25
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP25
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP12
| ~ sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(18,plain,
( sP13
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP13
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP21
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(21,plain,
( ~ sP18
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP18
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,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,h3,h6,h7]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,24,h6,h7]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,25,h5]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,26,h3,h4]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[27,h1]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[28,h0]) ).
thf(0,theorem,
( sP18
=> ! [X1: a] :
( ! [X2: a > $o] :
( ! [X3: a] :
( ( cK @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cK @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[27,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV310^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 04:08:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 182.65/182.88 % SZS status Theorem
% 182.65/182.88 % Mode: cade22grackle2x2d0b
% 182.65/182.88 % Steps: 188
% 182.65/182.88 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------