TSTP Solution File: SYO556^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO556^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 19:33:24 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 77
% Syntax : Number of formulae : 86 ( 18 unt; 4 typ; 4 def)
% Number of atoms : 285 ( 66 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 353 ( 133 ~; 37 |; 0 &; 93 @)
% ( 34 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 40 con; 0-2 aty)
% Number of variables : 82 ( 43 ^ 39 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eps,type,
eps: ( $i > $o ) > $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
( ( eigen__0 @ X1 )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i] : ( $false != $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
( ( eigen__0 @ X1 )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ( eps
@ ^ [X1: $i] :
( ( ~ ! [X2: $i] :
~ ( eigen__0 @ X2 )
=> ( X1
!= ( eps @ eigen__0 ) ) )
=> ~ ( ! [X2: $i] :
~ ( eigen__0 @ X2 )
=> ( X1
!= ( eps
@ ^ [X2: $i] : $false ) ) ) ) )
= ( eps @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eps
@ ^ [X1: $i] :
( ( ~ ! [X2: $i] :
~ ( eigen__0 @ X2 )
=> ( X1
!= ( eps @ eigen__0 ) ) )
=> ~ ( ! [X2: $i] :
~ ( eigen__0 @ X2 )
=> ( X1
!= ( eps
@ ^ [X2: $i] : $false ) ) ) ) )
= ( eps
@ ^ [X1: $i] :
( ( ~ ! [X2: $i] :
~ ( eigen__0 @ X2 )
=> ( X1
!= ( eps @ eigen__0 ) ) )
=> ~ ( ! [X2: $i] :
~ ( eigen__0 @ X2 )
=> ( X1
!= ( eps
@ ^ [X2: $i] : $false ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ( ( eps @ eigen__0 )
= ( eps
@ ^ [X1: $i] :
( ( ~ ! [X2: $i] :
~ ( eigen__0 @ X2 )
=> ( X1
!= ( eps @ eigen__0 ) ) )
=> ~ ( ! [X2: $i] :
~ ( eigen__0 @ X2 )
=> ( X1
!= ( eps
@ ^ [X2: $i] : $false ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eps @ eigen__0 )
= ( eps @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eps
@ ^ [X1: $i] : $false )
= ( eps @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ! [X1: $i] :
~ ( eigen__0 @ X1 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: $i] :
~ ( eigen__0 @ X1 )
=> ( ( eps
@ ^ [X1: $i] : $false )
!= ( eps
@ ^ [X1: $i] : $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ! [X1: $i] :
~ ( eigen__0 @ X1 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eps
@ ^ [X1: $i] : $false )
= ( eps
@ ^ [X1: $i] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> $false ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__0 @ eigen__5 )
= ( eigen__0 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( ( eps
@ ^ [X2: $i] :
( ( ~ ! [X3: $i] :
~ ( eigen__0 @ X3 )
=> ( X2
!= ( eps @ eigen__0 ) ) )
=> ~ ( ! [X3: $i] :
~ ( eigen__0 @ X3 )
=> ( X2
!= ( eps
@ ^ [X3: $i] : sP13 ) ) ) ) )
= X1 )
=> ( X1
= ( eps
@ ^ [X2: $i] :
( ( ~ ! [X3: $i] :
~ ( eigen__0 @ X3 )
=> ( X2
!= ( eps @ eigen__0 ) ) )
=> ~ ( ! [X3: $i] :
~ ( eigen__0 @ X3 )
=> ( X2
!= ( eps
@ ^ [X3: $i] : sP13 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
~ ( eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
~ ( ( ~ sP16
=> ( X1
!= ( eps @ eigen__0 ) ) )
=> ~ ( sP16
=> ( X1
!= ( eps
@ ^ [X2: $i] : sP13 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] : ( sP13 = sP13 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP8
=> ~ ( sP16
=> ( ( eps @ eigen__0 )
!= ( eps
@ ^ [X1: $i] : sP13 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( eps
@ ^ [X1: $i] :
( ( ~ sP16
=> ( X1
!= ( eps @ eigen__0 ) ) )
=> ~ ( sP16
=> ( X1
!= ( eps
@ ^ [X2: $i] : sP13 ) ) ) ) )
= ( eps
@ ^ [X1: $i] : sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP16
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( eps @ eigen__0 )
= ( eps
@ ^ [X1: $i] :
( ( ~ sP16
=> ( X1
!= ( eps @ eigen__0 ) ) )
=> ~ ( sP16
=> ( X1
!= ( eps
@ ^ [X2: $i] : sP13 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( eigen__0
= ( ^ [X1: $i] : sP13 ) )
=> ( ( ^ [X1: $i] : sP13 )
= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP12 = sP13 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__0
= ( ^ [X1: $i] : sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP10
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i > $o] :
( ( eigen__0 = X1 )
=> ( X1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( ~ sP16
=> ~ sP6 )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( ^ [X1: $i] : sP13 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP13 = sP13 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( ^ [X1: $i] : sP13 )
= ( ^ [X1: $i] : sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(def_if,definition,
( if
= ( ^ [X1: $o,X2: $i,X3: $i] :
( eps
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ).
thf(conj,conjecture,
! [X1: $i > $o] :
( ( eps @ X1 )
= ( eps
@ ^ [X2: $i] :
( ( ~ ! [X3: $i] :
~ ( X1 @ X3 )
=> ( X2
!= ( eps @ X1 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
~ ( X1 @ X3 )
=> ( X2
!= ( eps
@ ^ [X3: $i] : sP13 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $o] :
( ( eps @ X1 )
= ( eps
@ ^ [X2: $i] :
( ( ~ ! [X3: $i] :
~ ( X1 @ X3 )
=> ( X2
!= ( eps @ X1 ) ) )
=> ~ ( ! [X3: $i] :
~ ( X1 @ X3 )
=> ( X2
!= ( eps
@ ^ [X3: $i] : sP13 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP16
| ~ sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
sP2,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
sP32,
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP18
| ~ sP32 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(5,plain,
( sP25
| sP12
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP5
| ~ sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(7,plain,
sP14,
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP34
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(9,plain,
( ~ sP20
| sP1
| ~ sP2
| ~ sP6 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(10,plain,
( sP33
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP26
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP24
| ~ sP26
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP28
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP7
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
~ sP13,
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP22
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP22
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP10
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP27
| ~ sP10
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP11
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP6
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP9
| ~ sP16
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP30
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP4
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP8
| sP16
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP19
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP17
| ~ sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP17
| ~ sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP29
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
sP29,
inference(eq_sym,[status(thm)],]) ).
thf(choiceax,axiom,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( eps @ X1 ) ) ) ).
thf(31,plain,
( sP27
| sP17 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(32,plain,
( ~ sP3
| ~ sP1
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP15
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP21
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
sP21,
inference(eq_sym,[status(thm)],]) ).
thf(36,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,h2]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,36,h2]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[37,h0]) ).
thf(0,theorem,
! [X1: $i > $o] :
( ( eps @ X1 )
= ( eps
@ ^ [X2: $i] :
( ( ~ ! [X3: $i] :
~ ( X1 @ X3 )
=> ( X2
!= ( eps @ X1 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
~ ( X1 @ X3 )
=> ( X2
!= ( eps
@ ^ [X3: $i] : sP13 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[37,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO556^1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.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 : Sat Jul 9 12:44:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % Mode: mode213
% 0.19/0.41 % Inferences: 349
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------