TSTP Solution File: SEV167^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV167^5 : 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 : n026.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 18:05:11 EDT 2022
% Result : Theorem 26.25s 26.46s
% Output : Proof 26.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 73
% Syntax : Number of formulae : 83 ( 18 unt; 6 typ; 5 def)
% Number of atoms : 193 ( 58 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 326 ( 64 ~; 36 |; 0 &; 151 @)
% ( 32 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 39 con; 0-4 aty)
% Number of variables : 112 ( 61 ^ 51 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: a > a > a > a > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__3,type,
eigen__3: 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] :
( ( eigen__0 @ eigen__1 @ eigen__2 @ X1 @ X2 )
=> ~ ( ( eigen__1 = X1 )
=> ( eigen__2 != X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a,X3: a,X4: a] :
( ( eigen__0 @ X1 @ X2 @ X3 @ X4 )
=> ~ ( ( X1 = X3 )
=> ( X2 != X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: ( a > a > a > a > $o ) > $o,X2: a > a > a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a > a > a > a > $o] :
~ ( ! [X2: ( a > a > a ) > a,X3: ( a > a > a ) > a] :
( ( X1
@ ( X2
@ ^ [X4: a,X5: a] : X4 )
@ ( X2
@ ^ [X4: a,X5: a] : X5 )
@ ( X3
@ ^ [X4: a,X5: a] : X4 )
@ ( X3
@ ^ [X4: a,X5: a] : X5 ) )
=> ( X2 = X3 ) )
=> ! [X2: a,X3: a,X4: a,X5: a] :
( ( X1 @ X2 @ X3 @ X4 @ X5 )
=> ~ ( ( X2 = X4 )
=> ( X3 != X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a,X3: a] :
( ( eigen__0 @ eigen__1 @ X1 @ X2 @ X3 )
=> ~ ( ( eigen__1 = X2 )
=> ( X1 != X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 @ X1 )
=> ~ ( ( eigen__1 = eigen__3 )
=> ( eigen__2 != X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: ( a > a > a ) > a,X2: ( a > a > a ) > a] :
( ( eigen__0
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 )
@ ( X2
@ ^ [X3: a,X4: a] : X3 )
@ ( X2
@ ^ [X3: a,X4: a] : X4 ) )
=> ( X1 = X2 ) )
=> ! [X1: a,X2: a,X3: a,X4: a] :
( ( eigen__0 @ X1 @ X2 @ X3 @ X4 )
=> ~ ( ( X1 = X3 )
=> ( X2 != X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 @ X1 )
=> ~ ( ( eigen__1 = eigen__3 )
=> ( eigen__2 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__1 = eigen__3 )
=> ( eigen__2 != eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ eigen__1 @ X1 @ X2 @ X3 )
=> ~ ( ( eigen__1 = X2 )
=> ( X1 != X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( eigen__4 = X1 )
=> ( X1 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__3 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 @ eigen__4 )
=> ( ( ^ [X1: a > a > a] : ( X1 @ eigen__1 @ eigen__2 ) )
= ( ^ [X1: a > a > a] : ( X1 @ eigen__3 @ eigen__4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ eigen__1 @ eigen__2 @ X1 @ X2 )
=> ~ ( ( eigen__1 = X1 )
=> ( eigen__2 != X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > a > a] :
( ( X1 @ eigen__1 @ eigen__4 )
= ( X1 @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__4 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ^ [X1: a > a > a] : ( X1 @ eigen__3 @ eigen__4 ) )
= ( ^ [X1: a > a > a] : ( X1 @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > a > a] :
( ( X1 @ eigen__3 @ eigen__4 )
= ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: ( a > a > a ) > a] :
( ( eigen__0 @ eigen__1 @ eigen__2
@ ( X1
@ ^ [X2: a,X3: a] : X2 )
@ ( X1
@ ^ [X2: a,X3: a] : X3 ) )
=> ( ( ^ [X2: a > a > a] : ( X2 @ eigen__1 @ eigen__2 ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: ( a > a > a ) > a] :
( ( eigen__0 @ eigen__1 @ eigen__4
@ ( X1
@ ^ [X2: a,X3: a] : X2 )
@ ( X1
@ ^ [X2: a,X3: a] : X3 ) )
=> ( ( ^ [X2: a > a > a] : ( X2 @ eigen__1 @ eigen__4 ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ eigen__1 @ eigen__4 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP17
=> ( ( ^ [X1: a > a > a] : ( X1 @ eigen__1 @ eigen__4 ) )
= ( ^ [X1: a > a > a] : ( X1 @ eigen__3 @ eigen__4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: ( a > a > a ) > a,X2: ( a > a > a ) > a] :
( ( eigen__0
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 )
@ ( X2
@ ^ [X3: a,X4: a] : X3 )
@ ( X2
@ ^ [X3: a,X4: a] : X4 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP10
=> ( eigen__2 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a > a > a > a > $o] :
( ! [X2: ( a > a > a ) > a,X3: ( a > a > a ) > a] :
( ( X1
@ ( X2
@ ^ [X4: a,X5: a] : X4 )
@ ( X2
@ ^ [X4: a,X5: a] : X5 )
@ ( X3
@ ^ [X4: a,X5: a] : X4 )
@ ( X3
@ ^ [X4: a,X5: a] : X5 ) )
=> ( X2 = X3 ) )
=> ! [X2: a,X3: a,X4: a,X5: a] :
( ( X1 @ X2 @ X3 @ X4 @ X5 )
=> ~ ( ( X2 = X4 )
=> ( X3 != X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP13
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( ( ^ [X1: a > a > a] : ( X1 @ eigen__1 @ eigen__2 ) )
= ( ^ [X1: a > a > a] : ( X1 @ eigen__3 @ eigen__4 ) ) )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__2 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( ^ [X1: a > a > a] : ( X1 @ eigen__1 @ eigen__2 ) )
= ( ^ [X1: a > a > a] : ( X1 @ eigen__3 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( ^ [X1: a > a > a] : ( X1 @ eigen__1 @ eigen__4 ) )
= ( ^ [X1: a > a > a] : ( X1 @ eigen__3 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a,X2: a] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__4 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: a,X2: a,X3: a,X4: a] :
( ( eigen__0 @ X1 @ X2 @ X3 @ X4 )
=> ~ ( ( X1 = X3 )
=> ( X2 != X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: ( a > a > a ) > a] :
( ( ( ^ [X2: a > a > a] : ( X2 @ eigen__1 @ eigen__2 ) )
= X1 )
=> ( X1
= ( ^ [X2: a > a > a] : ( X2 @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: ( a > a > a ) > a,X2: ( a > a > a ) > a] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(cTHM189_pme,conjecture,
sP21 ).
thf(h2,negated_conjecture,
~ sP21,
inference(assume_negation,[status(cth)],[cTHM189_pme]) ).
thf(1,plain,
( ~ sP12
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP11
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP24
| ~ sP26
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP31
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP32
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| ~ sP13
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP15
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP19
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP27
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP13
| sP17
| ~ sP22
| ~ sP25
| ~ sP6
| ~ sP29 ),
inference(mating_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP18
| ~ sP17
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP16
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP19
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
sP22,
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
sP6,
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
sP32,
inference(eq_sym,[status(thm)],]) ).
thf(18,plain,
sP29,
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP20
| ~ sP10
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP5
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP28
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
sP28,
inference(eq_sym,[status(thm)],]) ).
thf(23,plain,
( ~ sP3
| ~ sP14
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP23
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP23
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP2
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(27,plain,
( sP8
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(28,plain,
( sP4
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(29,plain,
( sP30
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(30,plain,
( sP1
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP1
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP21
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(33,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,h2]) ).
thf(34,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[33,h1]) ).
thf(35,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[34,h0]) ).
thf(0,theorem,
sP21,
inference(contra,[status(thm),contra(discharge,[h2])],[33,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV167^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n026.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 : Tue Jun 28 16:04:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 26.25/26.46 % SZS status Theorem
% 26.25/26.46 % Mode: mode454
% 26.25/26.46 % Inferences: 4968
% 26.25/26.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------