TSTP Solution File: SYO362^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO362^5 : 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 : n017.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 : Fri Sep 1 04:46:25 EDT 2023
% Result : Theorem 0.19s 0.65s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 50
% Syntax : Number of formulae : 61 ( 15 unt; 5 typ; 1 def)
% Number of atoms : 164 ( 10 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 226 ( 44 ~; 22 |; 0 &; 100 @)
% ( 18 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 22 con; 0-2 aty)
% Number of variables : 40 ( 11 ^; 29 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__24,type,
eigen__24: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_cK,type,
cK: ( $i > $o ) > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__24,definition,
( eigen__24
= ( eps__0
@ ^ [X1: $i] :
( ( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__24])]) ).
thf(sP1,plain,
( sP1
<=> ( cK @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cK
@ ^ [X1: $i] :
( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= ( ^ [X1: $i] :
( ~ ( cK @ eigen__0 @ X1 )
=> ( cK @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ~ ( eigen__0 @ eigen__24 )
=> ( eigen__1 @ eigen__24 ) )
= ( eigen__1 @ eigen__24 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( cK
@ ^ [X2: $i] :
( ~ ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
@ X1 )
= ( ~ ( cK @ eigen__0 @ X1 )
=> ( cK @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 @ eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cK
@ ^ [X1: $i] :
( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
@ eigen__2 )
= ( ~ sP1
=> ( cK @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ^ [X1: $i] :
( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $o] :
( ( cK
@ ^ [X2: $i] :
( ~ ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) )
= ( ^ [X2: $i] :
( ~ ( cK @ eigen__0 @ X2 )
=> ( cK @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> $false ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cK
@ ^ [X1: $i] :
( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP12
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cK @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( cK
@ ^ [X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: $i] :
( ~ ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP1
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP12
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cTHM631A_pme,conjecture,
( sP16
=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP16
=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM631A_pme]) ).
thf(h2,assumption,
sP16,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( cK @ eigen__0 @ X2 )
=> ( cK @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP13
=> ! [X1: $i] :
( ( cK @ eigen__0 @ X1 )
=> ( cK @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP13,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( cK @ eigen__0 @ X1 )
=> ( cK @ eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP1
=> sP15 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| ~ sP12
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP13
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP15
| sP10
| ~ sP8 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( sP18
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP18
| sP12
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP3
| ~ sP18
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP3
| sP18
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP4
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__24]) ).
thf(9,plain,
( sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP17
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP7
| sP11
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP5
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP2
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP16
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
~ sP10,
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h2,h6,h9,h10]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,17,h9,h10]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h7,18,h8]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,19,h6,h7]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,20,h5]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,21,h4]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,22,h2,h3]) ).
thf(24,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[23,h0]) ).
thf(0,theorem,
( sP16
=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[23,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO362^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 01:33:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.65 % SZS status Theorem
% 0.19/0.65 % Mode: cade22grackle2xfee4
% 0.19/0.65 % Steps: 2122
% 0.19/0.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------