TSTP Solution File: SYO362^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO362^5 : 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 : n016.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 : Thu Jul 21 19:31:38 EDT 2022
% Result : Theorem 2.65s 2.91s
% Output : Proof 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 57
% Syntax : Number of formulae : 66 ( 13 unt; 5 typ; 4 def)
% Number of atoms : 192 ( 14 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 244 ( 47 ~; 31 |; 0 &; 103 @)
% ( 24 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 29 con; 0-2 aty)
% Number of variables : 38 ( 14 ^ 24 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(ty_cK,type,
cK: ( $i > $o ) > $i > $o ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( cK @ eigen__0 @ X2 )
=> ( cK @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__1
@ ^ [X1: $i] :
( ( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: $i] :
~ ( ( cK @ eigen__0 @ X1 )
=> ( cK @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [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,[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
<=> ! [X1: $i] :
( ( cK @ eigen__0 @ X1 )
=> ( cK @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ^ [X1: $i] :
( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cK @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ~ sP7
=> ( eigen__1 @ eigen__10 ) )
= ( eigen__1 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP7
=> ( eigen__1 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [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,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP7
=> ( eigen__1 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( cK
@ ^ [X1: $i] :
( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
@ eigen__2 )
= ( ~ ( cK @ eigen__0 @ eigen__2 )
=> sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cK @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP1
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( cK
@ ^ [X1: $i] :
( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP14
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP14
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__1 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [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,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( cK @ eigen__0 @ X2 )
=> ( cK @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(cTHM631A_pme,conjecture,
sP16 ).
thf(h2,negated_conjecture,
~ sP16,
inference(assume_negation,[status(cth)],[cTHM631A_pme]) ).
thf(1,plain,
( ~ sP12
| sP7
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| ~ sP7
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP12
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP8
| ~ sP12
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP8
| sP12
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP18
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__10]) ).
thf(8,plain,
( sP4
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP20
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP17
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP17
| sP5
| ~ sP4
| ~ sP21 ),
inference(mating_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP11
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP2
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP23
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP1
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
sP21,
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP19
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP19
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP3
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(20,plain,
( sP6
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP6
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP24
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(23,plain,
( sP15
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(24,plain,
( sP16
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP16
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h2]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[26,h1]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
sP16,
inference(contra,[status(thm),contra(discharge,[h2])],[26,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO362^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 20:54:23 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.65/2.91 % SZS status Theorem
% 2.65/2.91 % Mode: mode506
% 2.65/2.91 % Inferences: 80300
% 2.65/2.91 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------