TSTP Solution File: SEV136^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV136^5 : 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 : n018.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 18:05:01 EDT 2022
% Result : Theorem 37.40s 37.61s
% Output : Proof 37.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 71
% Syntax : Number of formulae : 83 ( 17 unt; 7 typ; 6 def)
% Number of atoms : 236 ( 6 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 550 ( 104 ~; 35 |; 0 &; 277 @)
% ( 30 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 38 con; 0-3 aty)
% Number of variables : 97 ( 6 ^ 91 !; 0 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__1,type,
eigen__1: ( a > a > $o ) > a > a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__28,type,
eigen__28: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
~ ( ! [X2: a > $o] :
( ! [X3: a,X4: a] :
( ~ ( ( eigen__0 @ X3 @ X4 )
=> ~ ( X2 @ X3 ) )
=> ( X2 @ X4 ) )
=> ( ( X2 @ eigen__2 )
=> ( X2 @ X1 ) ) )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( ( a > a > $o ) > a > a > $o ) > $o,X2: ( a > a > $o ) > a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: ( a > a > $o ) > a > a > $o] :
~ ( ~ ( ~ ( ! [X2: a] : ( X1 @ eigen__0 @ X2 @ X2 )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ eigen__0 @ X2 @ X3 )
=> ~ ( X1 @ eigen__0 @ X3 @ X4 ) )
=> ( X1 @ eigen__0 @ X2 @ X4 ) ) )
=> ~ ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ eigen__0 @ X2 @ X3 ) ) )
=> ! [X2: a,X3: a] :
( ! [X4: a > $o] :
( ! [X5: a,X6: a] :
( ~ ( ( eigen__0 @ X5 @ X6 )
=> ~ ( X4 @ X5 ) )
=> ( X4 @ X6 ) )
=> ( ( X4 @ X2 )
=> ( X4 @ X3 ) ) )
=> ( X1 @ eigen__0 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h2,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__2
@ ^ [X1: a > a > $o] :
~ ! [X2: ( a > a > $o ) > a > a > $o] :
( ~ ( ~ ( ! [X3: a] : ( X2 @ X1 @ X3 @ X3 )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X1 @ X3 @ X4 )
=> ~ ( X2 @ X1 @ X4 @ X5 ) )
=> ( X2 @ X1 @ X3 @ X5 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X1 @ X3 @ X4 ) ) )
=> ! [X3: a,X4: a] :
( ! [X5: a > $o] :
( ! [X6: a,X7: a] :
( ~ ( ( X1 @ X6 @ X7 )
=> ~ ( X5 @ X6 ) )
=> ( X5 @ X7 ) )
=> ( ( X5 @ X3 )
=> ( X5 @ X4 ) ) )
=> ( X2 @ X1 @ X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ! [X3: a > $o] :
( ! [X4: a,X5: a] :
( ~ ( ( eigen__0 @ X4 @ X5 )
=> ~ ( X3 @ X4 ) )
=> ( X3 @ X5 ) )
=> ( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
=> ( eigen__1 @ eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__0 @ eigen__2 @ X1 ) )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__28,definition,
( eigen__28
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__0 @ eigen__7 @ X1 )
=> ~ ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__7 ) )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__28])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( a > a > $o ) > a > a > $o] :
( ~ ( ~ ( ! [X2: a] : ( X1 @ eigen__0 @ X2 @ X2 )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ eigen__0 @ X2 @ X3 )
=> ~ ( X1 @ eigen__0 @ X3 @ X4 ) )
=> ( X1 @ eigen__0 @ X2 @ X4 ) ) )
=> ~ ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ eigen__0 @ X2 @ X3 ) ) )
=> ! [X2: a,X3: a] :
( ! [X4: a > $o] :
( ! [X5: a,X6: a] :
( ~ ( ( eigen__0 @ X5 @ X6 )
=> ~ ( X4 @ X5 ) )
=> ( X4 @ X6 ) )
=> ( ( X4 @ X2 )
=> ( X4 @ X3 ) ) )
=> ( X1 @ eigen__0 @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__0 @ eigen__2 @ X1 ) )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__7 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ~ ( ( eigen__0 @ eigen__7 @ X1 )
=> ~ ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__7 ) )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__1 @ eigen__0 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__0 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
=> ( eigen__1 @ eigen__0 @ eigen__7 @ eigen__28 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP2
=> ( ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__2 )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a,X2: a] :
( ! [X3: a > $o] :
( ! [X4: a,X5: a] :
( ~ ( ( eigen__0 @ X4 @ X5 )
=> ~ ( X3 @ X4 ) )
=> ( X3 @ X5 ) )
=> ( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
=> ( eigen__1 @ eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP6
=> ~ ( eigen__1 @ eigen__0 @ eigen__7 @ eigen__28 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP3
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__2 )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: a] : ( eigen__1 @ eigen__0 @ X1 @ X1 )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP12
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] : ( eigen__1 @ eigen__0 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ! [X1: a > $o] :
( ! [X2: a,X3: a] :
( ~ ( ( eigen__0 @ X2 @ X3 )
=> ~ ( X1 @ X2 ) )
=> ( X1 @ X3 ) )
=> ( ( X1 @ eigen__2 )
=> ( X1 @ eigen__3 ) ) )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__1 @ eigen__0 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ~ sP15
=> ~ sP4 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a] :
( ( eigen__0 @ eigen__7 @ X1 )
=> ( eigen__1 @ eigen__0 @ eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a > a > $o,X2: ( a > a > $o ) > a > a > $o] :
( ~ ( ~ ( ! [X3: a] : ( X2 @ X1 @ X3 @ X3 )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X1 @ X3 @ X4 )
=> ~ ( X2 @ X1 @ X4 @ X5 ) )
=> ( X2 @ X1 @ X3 @ X5 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X1 @ X3 @ X4 ) ) )
=> ! [X3: a,X4: a] :
( ! [X5: a > $o] :
( ! [X6: a,X7: a] :
( ~ ( ( X1 @ X6 @ X7 )
=> ~ ( X5 @ X6 ) )
=> ( X5 @ X7 ) )
=> ( ( X5 @ X3 )
=> ( X5 @ X4 ) ) )
=> ( X2 @ X1 @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a] :
( ~ ( sP6
=> ~ ( eigen__1 @ eigen__0 @ eigen__7 @ X1 ) )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ sP11
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__1 @ eigen__0 @ eigen__7 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ! [X3: a,X4: a] :
( ~ ( ( eigen__0 @ X3 @ X4 )
=> ~ ( X2 @ X3 ) )
=> ( X2 @ X4 ) )
=> ( ( X2 @ eigen__2 )
=> ( X2 @ X1 ) ) )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__1 @ eigen__0 @ eigen__2 @ X1 )
=> ~ ( eigen__1 @ eigen__0 @ X1 @ X2 ) )
=> ( eigen__1 @ eigen__0 @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a > $o] :
( ! [X2: a,X3: a] :
( ~ ( ( eigen__0 @ X2 @ X3 )
=> ~ ( X1 @ X2 ) )
=> ( X1 @ X3 ) )
=> ( ( X1 @ eigen__2 )
=> ( X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP15
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(cTHM203_pme,conjecture,
sP23 ).
thf(h3,negated_conjecture,
~ sP23,
inference(assume_negation,[status(cth)],[cTHM203_pme]) ).
thf(1,plain,
( ~ sP24
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP25
| sP11
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| ~ sP6
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP28
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP22
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| ~ sP3
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP12
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP12
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP17
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP17
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP5
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__28]) ).
thf(13,plain,
( ~ sP13
| ~ sP16
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP2
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(15,plain,
( ~ sP9
| ~ sP2
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP29
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP18
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP7
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( sP19
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP19
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP27
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(22,plain,
( sP15
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP15
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP10
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(25,plain,
( sP30
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP30
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP21
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP21
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP1
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(30,plain,
( sP23
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__0]) ).
thf(31,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h3]) ).
thf(32,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[31,h2]) ).
thf(33,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[32,h1]) ).
thf(34,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[33,h0]) ).
thf(0,theorem,
sP23,
inference(contra,[status(thm),contra(discharge,[h3])],[31,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV136^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 28 13:27:44 EDT 2022
% 0.12/0.32 % CPUTime :
% 37.40/37.61 % SZS status Theorem
% 37.40/37.61 % Mode: mode485
% 37.40/37.61 % Inferences: 2104
% 37.40/37.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------