TSTP Solution File: SEV400^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV400^5 : 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 : n021.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 18:06:13 EDT 2022
% Result : Theorem 64.13s 64.34s
% Output : Proof 64.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 57
% Syntax : Number of formulae : 66 ( 12 unt; 6 typ; 4 def)
% Number of atoms : 170 ( 4 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 288 ( 80 ~; 29 |; 0 &; 90 @)
% ( 24 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 30 con; 0-2 aty)
% Number of variables : 36 ( 4 ^ 32 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(ty_eigen__8,type,
eigen__8: $i > $o ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__8 @ X1 )
=> ~ ( ( cQ @ X1 )
=> ~ ( cP @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( cQ @ X1 )
=> ~ ( cP @ X1 ) )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(h1,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: $i > $o] :
~ ( ~ ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( cQ @ X2 ) ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( ( cQ @ X2 )
=> ~ ( cP @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( cQ @ X1 )
=> ~ ( cP @ X1 ) )
=> ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: $i] :
( ~ ( ( cQ @ X1 )
=> ~ ( cP @ X1 ) )
=> ( cP @ X1 ) )
=> ~ ! [X1: $i] :
( ~ ( ( cQ @ X1 )
=> ~ ( cP @ X1 ) )
=> ( cQ @ X1 ) ) )
=> ~ ! [X1: $i > $o] :
( ~ ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( cQ @ X2 ) ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( ( cQ @ X2 )
=> ~ ( cP @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__8 @ X1 )
=> ~ ( ( cQ @ X1 )
=> ~ ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cQ @ eigen__9 )
=> ~ ( cP @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( eigen__8 @ X1 )
=> ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cQ @ eigen__11 )
=> ~ ( cP @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $o] :
( ~ ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( cQ @ X2 ) ) )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( ( cQ @ X2 )
=> ~ ( cP @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cP @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cQ @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: $i] :
( ~ ( ( cQ @ X1 )
=> ~ ( cP @ X1 ) )
=> ( cP @ X1 ) )
=> ~ ! [X1: $i] :
( ~ ( ( cQ @ X1 )
=> ~ ( cP @ X1 ) )
=> ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP4
=> ~ ! [X1: $i] :
( ( eigen__8 @ X1 )
=> ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__8 @ eigen__11 )
=> ( cP @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ~ ( ( cQ @ X1 )
=> ~ ( cP @ X1 ) )
=> ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__8 @ eigen__11 )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ~ ( ( cQ @ X1 )
=> ~ ( cP @ X1 ) )
=> ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cQ @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( cQ @ eigen__10 )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i > $o] :
( ~ ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( cQ @ X2 ) ) )
=> ~ ! [X2: $i > $o] :
( ~ ( ! [X3: $i] :
( ( X2 @ X3 )
=> ( cP @ X3 ) )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( cQ @ X3 ) ) )
=> ! [X3: $i] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__8 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( eigen__8 @ X1 )
=> ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP16
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ sP10
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP3
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP18
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( cP @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(cTHM590_pme,conjecture,
~ sP17 ).
thf(h2,negated_conjecture,
sP17,
inference(assume_negation,[status(cth)],[cTHM590_pme]) ).
thf(1,plain,
( ~ sP11
| ~ sP18
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP23
| ~ sP18
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP19
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| ~ sP8
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP13
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP13
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP10
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP10
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP2
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(11,plain,
( sP21
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP21
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP3
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP22
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP22
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP16
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP20
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP20
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP14
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(20,plain,
( sP12
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(21,plain,
( ~ sP9
| ~ sP14
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP6
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(23,plain,
( ~ sP1
| sP9
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP17
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(25,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,h2]) ).
thf(26,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[25,h1]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[26,h0]) ).
thf(0,theorem,
~ sP17,
inference(contra,[status(thm),contra(discharge,[h2])],[25,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV400^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n021.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 : 600
% 0.13/0.34 % DateTime : Tue Jun 28 00:24:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 64.13/64.34 % SZS status Theorem
% 64.13/64.34 % Mode: mode453
% 64.13/64.34 % Inferences: 477
% 64.13/64.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------