TSTP Solution File: SEV095^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV095^5 : 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 : 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 : Tue Jul 19 18:04:49 EDT 2022
% Result : Theorem 45.26s 45.50s
% Output : Proof 45.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 82
% Syntax : Number of formulae : 96 ( 20 unt; 9 typ; 9 def)
% Number of atoms : 298 ( 50 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 460 ( 124 ~; 42 |; 0 &; 165 @)
% ( 35 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 41 con; 0-2 aty)
% Number of variables : 93 ( 9 ^ 84 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__14,type,
eigen__14: $i ).
thf(ty_eigen__12,type,
eigen__12: $i > $o ).
thf(ty_eigen__16,type,
eigen__16: $i > $o ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_eigen__11,type,
eigen__11: $i > $o ).
thf(ty_eigen__17,type,
eigen__17: $i > $o ).
thf(ty_eigen__10,type,
eigen__10: $i > $o ).
thf(ty_eigen__13,type,
eigen__13: $i > $o ).
thf(ty_eigen__18,type,
eigen__18: $i ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( ( X1 @ X2 )
!= $false )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__1
@ ^ [X1: $i] :
~ ( ( ( eigen__11 @ X1 )
!= $false )
=> ( eigen__11 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ! [X2: $i] :
( ( ( eigen__10 @ X2 )
!= $false )
=> ( eigen__16 @ X2 ) )
=> ~ ! [X2: $i] :
( ( ( eigen__16 @ X2 )
!= $false )
=> ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( ( eigen__10 @ X2 )
!= $false )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eigen__12 @ X1 )
=> ( eigen__13 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] :
( ( ( X1 @ X4 )
!= $false )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
!= $false )
=> ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( ( X1 @ X4 )
!= $false )
=> ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
!= $false )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__18,definition,
( eigen__18
= ( eps__1
@ ^ [X1: $i] :
~ ( ( ( eigen__10 @ X1 )
!= $false )
=> ( eigen__17 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__18])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ! [X2: $i] :
( ( ( eigen__12 @ X2 )
!= $false )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__12 @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ! [X3: $i] :
( ( ( eigen__10 @ X3 )
!= $false )
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( ( X1 @ X3 )
!= $false )
=> ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( ( eigen__10 @ X3 )
!= $false )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( ( eigen__12 @ X2 )
!= $false )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__12 @ X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__16 @ eigen__18 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( ( eigen__12 @ X1 )
!= $false )
=> ( eigen__13 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
!= $false )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP2
=> ( eigen__17 @ eigen__18 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ~ ( X1 @ X2 @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ! [X2: $i > $o,X3: $i] :
( ~ ( X1 @ X2 @ X2 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ! [X5: $i] :
( ~ ( X1 @ X2 @ X3 @ X5 )
=> ( X3 @ X5 ) )
=> ~ ! [X5: $i] :
( ~ ( X1 @ X3 @ X4 @ X5 )
=> ( X4 @ X5 ) ) )
=> ! [X5: $i] :
( ~ ( X1 @ X2 @ X4 @ X5 )
=> ( X4 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__11 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__13 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP7 = $false ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__17 @ eigen__18 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP9
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= $false )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP3
=> ! [X1: $i] :
( ( eigen__12 @ X1 )
=> ( eigen__13 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( ( eigen__10 @ eigen__18 )
!= $false )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( ( eigen__10 @ X1 )
!= $false )
=> ( eigen__17 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i > $o] :
( ~ ( ! [X2: $i] :
( ( ( eigen__10 @ X2 )
!= $false )
=> ( eigen__16 @ X2 ) )
=> ~ ! [X2: $i] :
( ( ( eigen__16 @ X2 )
!= $false )
=> ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( ( eigen__10 @ X2 )
!= $false )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__12 @ eigen__14 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ! [X1: $i] :
( ( ( eigen__10 @ X1 )
!= $false )
=> ( eigen__16 @ X1 ) )
=> ~ ! [X1: $i] :
( ( ( eigen__16 @ X1 )
!= $false )
=> ( eigen__17 @ X1 ) ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__16 @ eigen__18 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( eigen__12 @ eigen__14 )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( ( eigen__10 @ eigen__18 )
!= $false )
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP17
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( ( eigen__11 @ X1 )
!= $false )
=> ( eigen__11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ! [X1: $i] :
( ( ( eigen__10 @ X1 )
!= $false )
=> ( eigen__16 @ X1 ) )
=> ~ ! [X1: $i] :
( ( ( eigen__16 @ X1 )
!= $false )
=> ( eigen__17 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( ( eigen__10 @ X1 )
!= $false )
=> ( eigen__16 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ! [X3: $i > $o,X4: $i > $o] :
( ! [X5: $i] :
( ~ ( X2 @ X3 @ X4 @ X5 )
=> ( X1 @ X3 @ X4 @ X5 ) )
=> ! [X5: $i] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ! [X3: $i > $o,X4: $i] :
( ~ ( X2 @ X3 @ X3 @ X4 )
=> ( X1 @ X3 @ X3 @ X4 ) ) )
=> ~ ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ~ ( ! [X6: $i] :
( ~ ( X2 @ X3 @ X4 @ X6 )
=> ( X1 @ X3 @ X4 @ X6 ) )
=> ~ ! [X6: $i] :
( ~ ( X2 @ X4 @ X5 @ X6 )
=> ( X1 @ X4 @ X5 @ X6 ) ) )
=> ! [X6: $i] :
( ~ ( X2 @ X3 @ X5 @ X6 )
=> ( X1 @ X3 @ X5 @ X6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] :
( ( ( X1 @ X4 )
!= $false )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( ( X2 @ X4 )
!= $false )
=> ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( ( X1 @ X4 )
!= $false )
=> ( X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__12 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ( ( eigen__16 @ X1 )
!= $false )
=> ( eigen__17 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( eigen__12 @ X1 )
=> ( eigen__13 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( eigen__10 @ eigen__18 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ! [X3: $i] :
( ( ( eigen__10 @ X3 )
!= $false )
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( ( X1 @ X3 )
!= $false )
=> ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( ( eigen__10 @ X3 )
!= $false )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> $false ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP4
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ sP34
=> ~ sP27 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(cTHM122C_pme,conjecture,
~ sP26 ).
thf(h2,negated_conjecture,
sP26,
inference(assume_negation,[status(cth)],[cTHM122C_pme]) ).
thf(1,plain,
( ~ sP21
| sP31
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP19
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP2
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP29
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP25
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP14
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP14
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP24
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP24
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP15
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__18]) ).
thf(11,plain,
( sP18
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP18
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP16
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__17]) ).
thf(14,plain,
( sP32
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).
thf(15,plain,
( sP9
| sP7
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP11
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP11
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP23
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__15]) ).
thf(19,plain,
( ~ sP17
| ~ sP28
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP22
| sP17
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP3
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( sP20
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP20
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
~ sP33,
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP30
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__14]) ).
thf(26,plain,
( sP13
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP13
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP1
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(29,plain,
( sP4
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(30,plain,
( sP12
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(31,plain,
( ~ sP34
| ~ sP4
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP27
| ~ sP32 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(33,plain,
( ~ sP35
| sP34
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP6
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP26
| sP6 ),
inference(all_rule,[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(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[36,h1]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[37,h0]) ).
thf(0,theorem,
~ sP26,
inference(contra,[status(thm),contra(discharge,[h2])],[36,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV095^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n004.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 16:28:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 45.26/45.50 % SZS status Theorem
% 45.26/45.50 % Mode: mode456
% 45.26/45.50 % Inferences: 368
% 45.26/45.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------