TSTP Solution File: SEV246^6 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV246^6 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -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 : 600s
% DateTime : Tue Jul 19 18:05:33 EDT 2022
% Result : Theorem 77.22s 77.59s
% Output : Proof 77.22s
% 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 : 179 ( 3 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 405 ( 87 ~; 29 |; 0 &; 176 @)
% ( 25 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 31 con; 0-2 aty)
% Number of variables : 91 ( 16 ^ 75 !; 0 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__21,type,
eigen__21: a ).
thf(ty_eigen__10,type,
eigen__10: a > $o ).
thf(ty_cK,type,
cK: ( a > $o ) > a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__2 ) ) ) ),
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__21,definition,
( eigen__21
= ( eps__1
@ ^ [X1: a] :
~ ( ( eigen__10 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__21])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a] :
~ ( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK
@ ^ [X3: a] :
~ ! [X4: a > $o] :
( ! [X5: a] :
( ( X4 @ X5 )
=> ( cK @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( cK @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__10 @ eigen__2 )
=> ( cK @ eigen__10 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( cK @ eigen__10 @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__21 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cK @ eigen__10 @ eigen__2 )
=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: a] :
( ( eigen__10 @ X1 )
=> ( cK @ eigen__10 @ X1 ) )
=> ~ ( eigen__10 @ eigen__21 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ( eigen__10 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( eigen__10 @ X1 )
=> ( cK @ eigen__10 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP10
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( eigen__10 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK @ eigen__10 @ X2 )
=> ( cK @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cK @ eigen__10 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP11
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__10 @ eigen__21 )
=> ~ sP5 ) ),
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
<=> ( eigen__10 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( cK
@ ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP6
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP12
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP21
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__10 @ eigen__21 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(cTHM116_1S,conjecture,
( sP18
=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ).
thf(h2,negated_conjecture,
~ ( sP18
=> ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM116_1S]) ).
thf(h3,assumption,
sP18,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP1
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
sP20,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| ~ sP12
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP17
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP17
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| ~ sP15
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP10
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__21]) ).
thf(8,plain,
( ~ sP13
| ~ sP10
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP18
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| ~ sP19
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP12
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP23
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP23
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP11
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(16,plain,
( sP16
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP16
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP22
| ~ sP6
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP2
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( sP6
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(21,plain,
( ~ sP24
| ~ sP21
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP18
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP20
| sP24 ),
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] :
( ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[27,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEV246^6 : TPTP v8.1.0. Released v5.1.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Tue Jun 28 12:01:57 EDT 2022
% 0.11/0.32 % CPUTime :
% 77.22/77.59 % SZS status Theorem
% 77.22/77.59 % Mode: mode484
% 77.22/77.59 % Inferences: 20397
% 77.22/77.59 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------