TSTP Solution File: SYO026^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO026^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 19:29:37 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 94
% Syntax : Number of formulae : 107 ( 19 unt; 6 typ; 4 def)
% Number of atoms : 294 ( 34 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 250 ( 93 ~; 60 |; 0 &; 30 @)
% ( 39 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 46 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 22 ( 12 ^ 10 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_p,type,
p: ( $o > $o ) > $o ).
thf(ty_eigen__2,type,
eigen__2: $o ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_eigen__0,type,
eigen__0: $o > $o ).
thf(ty_eigen__4,type,
eigen__4: $o ).
thf(ty_eigen__3,type,
eigen__3: $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $o] :
( ( ~ X1 )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $o] :
( ( ~ $false )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $o] :
( $false
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $o] :
( X1
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( p
@ ^ [X1: $o] : ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ^ [X1: $o] : $false )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
= ( eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__4 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( p
@ ^ [X1: $o] : X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__4 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ~ eigen__3 )
= ( eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__2 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $o] :
( ( eigen__4 = X1 )
=> ( X1 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( ^ [X1: $o] : ~ sP3 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__3 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( ~ sP3 )
= sP18 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( ^ [X1: $o] : X1 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $o] :
( ( ~ X1 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__2 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $o] :
( sP3
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $o] :
( ( ~ sP3 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( p
@ ^ [X1: $o] : sP3 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__4 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( p @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $o] :
( ( sP29 = X1 )
=> ( X1 = sP29 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> eigen__3 ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( ^ [X1: $o] : ~ X1 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $o] :
( X1
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__4 = sP20 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP9
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP10
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> eigen__4 ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( p
@ ^ [X1: $o] : ~ X1 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> eigen__2 ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(conj,conjecture,
( ~ ( ~ ( ~ ( sP7
=> ~ sP38 )
=> ~ sP26 )
=> ~ sP1 )
=> ( !! @ p ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( ~ ( sP7
=> ~ sP38 )
=> ~ sP26 )
=> ~ sP1 )
=> ( !! @ p ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( sP7
=> ~ sP38 )
=> ~ sP26 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( !! @ p ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP7
=> ~ sP38 )
=> ~ sP26 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP7
=> ~ sP38 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP26,
introduced(assumption,[]) ).
thf(h8,assumption,
sP7,
introduced(assumption,[]) ).
thf(h9,assumption,
sP38,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(1,plain,
( sP6
| sP37
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP10
| ~ sP37
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP36
| ~ sP10
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP14
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP27
| sP37
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP23
| sP39
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP17
| ~ sP31
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP9
| sP29
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP35
| ~ sP9
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP30
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP12
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP8
| sP20
| ~ sP13 ),
inference(mating_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP20
| sP18
| ~ sP6 ),
inference(mating_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP20
| sP16
| ~ sP27 ),
inference(mating_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP8
| sP16
| ~ sP23 ),
inference(mating_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| sP18
| ~ sP17 ),
inference(mating_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP8
| sP18
| ~ sP5 ),
inference(mating_rule,[status(thm)],]) ).
thf(18,plain,
~ sP3,
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP34
| ~ sP37
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP34
| sP37
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP12
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( sP33
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(23,plain,
( sP11
| sP31
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP11
| ~ sP31
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP22
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(26,plain,
( sP4
| sP3
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP24
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(28,plain,
( sP19
| sP3
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
sP12,
inference(eq_sym,[status(thm)],]) ).
thf(30,plain,
( sP25
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(31,plain,
( sP21
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP32
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP2
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP15
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP7
| sP28
| ~ sP21 ),
inference(mating_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP38
| sP28
| ~ sP32 ),
inference(mating_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP26
| sP28
| ~ sP2 ),
inference(mating_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP1
| sP28
| ~ sP15 ),
inference(mating_rule,[status(thm)],]) ).
thf(39,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,h8,h9,h7,h5,h10]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__0)],[h3,39,h10]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,40,h8,h9]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,41,h6,h7]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,42,h4,h5]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,43,h2,h3]) ).
thf(45,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[44,h0]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( sP7
=> ~ sP38 )
=> ~ sP26 )
=> ~ sP1 )
=> ( !! @ p ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[44,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO026^1 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 11:29:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % Mode: mode213
% 0.20/0.38 % Inferences: 58
% 0.20/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------