TSTP Solution File: SEV221^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV221^5 : 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 18:05:25 EDT 2022
% Result : Theorem 26.12s 26.30s
% Output : Proof 26.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 63
% Syntax : Number of formulae : 72 ( 13 unt; 7 typ; 4 def)
% Number of atoms : 194 ( 21 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 306 ( 112 ~; 35 |; 0 &; 85 @)
% ( 25 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 29 con; 0-2 aty)
% Number of variables : 41 ( 18 ^ 23 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_cZ,type,
cZ: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a > $o ).
thf(ty_cW,type,
cW: ( a > $o ) > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ( cW @ X1 )
=> ( eigen__1
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ! [X2: a > $o] :
( ( cW @ X2 )
=> ( X1
!= ( ^ [X3: a] :
~ ( ( cZ @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a] :
( ( ~ ( ~ ! [X2: a > $o] :
( ( cW @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( cZ @ X1 ) ) )
!= ( ~ ! [X2: a > $o] :
( ~ ! [X3: a > $o] :
( ( cW @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ( ( cZ @ X4 )
=> ~ ( X3 @ X4 ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ( cW @ X1 )
=> ~ ( X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ( ~ ( ~ ! [X1: a > $o] :
( ( cW @ X1 )
=> ~ ( X1 @ eigen__0 ) )
=> ~ ( cZ @ eigen__0 ) ) )
= ( ~ ! [X1: a > $o] :
( ~ ! [X2: a > $o] :
( ( cW @ X2 )
=> ( X1
!= ( ^ [X3: a] :
~ ( ( cZ @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cW @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cZ @ eigen__0 )
=> ~ ( eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ~ ! [X2: a > $o] :
( ( cW @ X2 )
=> ( X1
!= ( ^ [X3: a] :
~ ( ( cZ @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cZ @ eigen__0 )
=> ~ ( eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
= ( ~ ( ( cZ @ X1 )
=> ~ ( eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > $o] :
( ( cW @ X1 )
=> ( ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( eigen__2 @ X2 ) ) )
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__1 @ eigen__0 )
= ( ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ^ [X1: a] :
~ ( ( cZ @ X1 )
=> ~ ( eigen__2 @ X1 ) ) )
= ( ^ [X1: a] :
~ ( ( cZ @ X1 )
=> ~ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cW @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP2
=> ( eigen__1
!= ( ^ [X1: a] :
~ ( ( cZ @ X1 )
=> ~ ( eigen__3 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ! [X1: a > $o] :
( ( cW @ X1 )
=> ( eigen__1
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) )
=> ~ ( eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ! [X1: a > $o] :
( ( cW @ X1 )
=> ~ ( X1 @ eigen__0 ) )
=> ~ ( cZ @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a > $o] :
( ( cW @ X1 )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__1
= ( ^ [X1: a] :
~ ( ( cZ @ X1 )
=> ~ ( eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ( ~ ( ~ ! [X2: a > $o] :
( ( cW @ X2 )
=> ~ ( X2 @ X1 ) )
=> ~ ( cZ @ X1 ) ) )
= ( ~ ! [X2: a > $o] :
( ~ ! [X3: a > $o] :
( ( cW @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ( ( cZ @ X4 )
=> ~ ( X3 @ X4 ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cZ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP2
=> ~ ( eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a > $o] :
( ( cW @ X1 )
=> ( eigen__1
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP10
=> ~ ( eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP10
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP7
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(cTHM61_pme,conjecture,
sP17 ).
thf(h2,negated_conjecture,
~ sP17,
inference(assume_negation,[status(cth)],[cTHM61_pme]) ).
thf(1,plain,
sP9,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP23
| ~ sP10
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| ~ sP18
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP24
| sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP5
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP5
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP8
| ~ sP16
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP14
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP19
| ~ sP2
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP15
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP11
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP11
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP20
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(17,plain,
( sP21
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP21
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP12
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP12
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP14
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(22,plain,
( ~ sP13
| sP14
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP4
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(24,plain,
( sP13
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP13
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP1
| sP13
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP1
| ~ sP13
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP17
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,h2]) ).
thf(30,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[29,h1]) ).
thf(31,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[30,h0]) ).
thf(0,theorem,
sP17,
inference(contra,[status(thm),contra(discharge,[h2])],[29,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV221^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % 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 11:46:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 26.12/26.30 % SZS status Theorem
% 26.12/26.30 % Mode: mode454
% 26.12/26.30 % Inferences: 423
% 26.12/26.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------