TSTP Solution File: SEV223^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV223^5 : 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 18:05:26 EDT 2022
% Result : Theorem 26.68s 26.97s
% Output : Proof 26.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 80
% Syntax : Number of formulae : 93 ( 19 unt; 10 typ; 6 def)
% Number of atoms : 239 ( 53 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 381 ( 137 ~; 40 |; 0 &; 109 @)
% ( 32 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 40 con; 0-2 aty)
% Number of variables : 76 ( 22 ^ 54 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__1,type,
eigen__1: b ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__4,type,
eigen__4: b > $o ).
thf(ty_eigen__5,type,
eigen__5: b ).
thf(ty_eigen__3,type,
eigen__3: b > $o ).
thf(ty_w,type,
w: ( b > $o ) > $o ).
thf(ty_f,type,
f: b > a ).
thf(h0,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: b > $o] :
~ ( ( w @ X1 )
=> ~ ( X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: b] :
~ ( ~ ! [X2: b > $o] :
( ( w @ X2 )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
!= ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h2,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__2
@ ^ [X1: a] :
( ( ~ ! [X2: b] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ~ ( X3 @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
!= ( ~ ! [X2: a > $o] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ! [X5: b] :
( ( X3 @ X5 )
=> ( X4
!= ( f @ X5 ) ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h3,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__3
@ ^ [X1: a > $o] :
~ ( ~ ! [X2: b > $o] :
( ( w @ X2 )
=> ( X1
!= ( ^ [X3: a] :
~ ! [X4: b] :
( ( X2 @ X4 )
=> ( X3
!= ( f @ X4 ) ) ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: b > $o] :
~ ( ( w @ X1 )
=> ( eigen__2
!= ( ^ [X2: a] :
~ ! [X3: b] :
( ( X1 @ X3 )
=> ( X2
!= ( f @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: b] :
~ ( ( eigen__4 @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( eigen__2 @ X1 )
= ( ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ! [X1: b > $o] :
( ( w @ X1 )
=> ~ ( X1 @ eigen__5 ) )
=> ( eigen__0
!= ( f @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: b > $o] :
( ( w @ X1 )
=> ( ( ^ [X2: a] :
~ ! [X3: b] :
( ( eigen__3 @ X3 )
=> ( X2
!= ( f @ X3 ) ) ) )
!= ( ^ [X2: a] :
~ ! [X3: b] :
( ( X1 @ X3 )
=> ( X2
!= ( f @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__2 @ eigen__0 )
= ( ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( w @ eigen__4 )
=> ( eigen__2
!= ( ^ [X1: a] :
~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2
= ( ^ [X1: a] :
~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: b > $o] :
( ( w @ X1 )
=> ~ ( X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: b] :
( ( eigen__3 @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: b > $o] :
( ( w @ X1 )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP2
=> ( eigen__0
!= ( f @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( w @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__0
= ( f @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > $o] :
( ~ ! [X2: b > $o] :
( ( w @ X2 )
=> ( X1
!= ( ^ [X3: a] :
~ ! [X4: b] :
( ( X2 @ X4 )
=> ( X3
!= ( f @ X4 ) ) ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ! [X1: b > $o] :
( ( w @ X1 )
=> ( eigen__2
!= ( ^ [X2: a] :
~ ! [X3: b] :
( ( X1 @ X3 )
=> ( X2
!= ( f @ X3 ) ) ) ) ) )
=> ~ ( eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ^ [X1: a] :
~ ! [X2: b] :
( ( eigen__3 @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ^ [X1: a] :
~ ! [X2: b] :
( ( eigen__3 @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( ~ ! [X1: b] :
( ~ ! [X2: b > $o] :
( ( w @ X2 )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
!= ( f @ X1 ) ) ) )
= ( ~ sP15 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP12
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP4
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP13
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( w @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: b > $o] :
( ( w @ X1 )
=> ( eigen__2
!= ( ^ [X2: a] :
~ ! [X3: b] :
( ( X1 @ X3 )
=> ( X2
!= ( f @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: b] :
( ~ ! [X2: b > $o] :
( ( w @ X2 )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
!= ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__0
= ( f @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( ^ [X1: a] :
~ ! [X2: b] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ~ ( X3 @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ^ [X1: a] :
~ ! [X2: a > $o] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ! [X5: b] :
( ( X3 @ X5 )
=> ( X4
!= ( f @ X5 ) ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a] :
( ( ~ ! [X2: b] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ~ ( X3 @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ~ ! [X2: a > $o] :
( ~ ! [X3: b > $o] :
( ( w @ X3 )
=> ( X2
!= ( ^ [X4: a] :
~ ! [X5: b] :
( ( X3 @ X5 )
=> ( X4
!= ( f @ X5 ) ) ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP22
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP12
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP10
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(cX5204_pme,conjecture,
sP26 ).
thf(h4,negated_conjecture,
~ sP26,
inference(assume_negation,[status(cth)],[cX5204_pme]) ).
thf(1,plain,
sP17,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| ~ sP2
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP30
| ~ sP12
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP20
| sP4
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP15
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP8
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP29
| ~ sP22
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP24
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| sP8
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP21
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP21
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP28
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(15,plain,
( ~ sP5
| ~ sP31
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP7
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP6
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP6
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP19
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP19
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP23
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(23,plain,
( sP10
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(24,plain,
( sP16
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP16
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP32
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP32
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP15
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h3])],[h3,eigendef_eigen__2]) ).
thf(29,plain,
( sP24
| ~ sP32 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(30,plain,
( sP18
| sP24
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP18
| ~ sP24
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP27
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__0]) ).
thf(33,plain,
( sP26
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h3,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,h4]) ).
thf(35,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h4,h2,h1,h0]),eigenvar_choice(discharge,[h3])],[34,h3]) ).
thf(36,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h4,h1,h0]),eigenvar_choice(discharge,[h2])],[35,h2]) ).
thf(37,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h4,h0]),eigenvar_choice(discharge,[h1])],[36,h1]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h4]),eigenvar_choice(discharge,[h0])],[37,h0]) ).
thf(0,theorem,
sP26,
inference(contra,[status(thm),contra(discharge,[h4])],[34,h4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV223^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % 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 : Mon Jun 27 18:05:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 26.68/26.97 % SZS status Theorem
% 26.68/26.97 % Mode: mode454
% 26.68/26.97 % Inferences: 2319
% 26.68/26.97 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------