TSTP Solution File: SEV086^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV086^5 : 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 18:04:47 EDT 2022
% Result : Theorem 9.78s 10.01s
% Output : Proof 9.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 68
% Syntax : Number of formulae : 80 ( 16 unt; 7 typ; 7 def)
% Number of atoms : 248 ( 69 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 248 ( 84 ~; 37 |; 0 &; 57 @)
% ( 28 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 32 con; 0-2 aty)
% Number of variables : 52 ( 7 ^ 45 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i > $o ).
thf(ty_eigen__8,type,
eigen__8: $i > $o ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ( X1 = eigen__0 )
=> ( eigen__0 != X1 ) )
=> ! [X2: $i] :
( ( eigen__0 @ X2 )
= ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ( eigen__5 = eigen__4 )
=> ( X1 != eigen__5 ) )
=> ( X1 = eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X1 != X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i > $o] : ( X1 != X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__1
@ ^ [X1: $i] :
( ( eigen__6 @ X1 )
!= ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ( X1 = eigen__4 )
=> ( X2 != X1 ) )
=> ( X2 = eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: $i > $o] : ( X1 = X1 )
=> ~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) )
=> ~ ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X1 != X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X1 != X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ( X1 = eigen__4 )
=> ( X2 != X1 ) )
=> ( X2 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 = eigen__0 )
=> ( eigen__0 != eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $o] : ( X1 = X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $o] :
( ~ ( ( eigen__5 = eigen__4 )
=> ( X1 != eigen__5 ) )
=> ( X1 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ( eigen__5 = eigen__4 )
=> ( eigen__6 != eigen__5 ) )
=> ( eigen__6 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__6 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP5
=> ~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__6 @ eigen__7 )
= ( eigen__5 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eigen__5 @ X1 )
= ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( eigen__6 @ X1 )
= ( eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP4
=> ! [X1: $i] :
( ( eigen__0 @ X1 )
= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__5 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__8 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( ! [X2: $i > $o] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
= ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( X2 = X1 )
=> ( X3 != X2 ) )
=> ( X3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( eigen__6 @ eigen__7 )
= ( eigen__4 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i > $o] :
( ~ ( ( X1 = eigen__0 )
=> ( eigen__0 != X1 ) )
=> ! [X2: $i] :
( ( eigen__0 @ X2 )
= ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( eigen__6 @ X1 )
= ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP19
= ( eigen__4 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP16
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__6 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(cTHM120I_pme,conjecture,
~ sP18 ).
thf(h2,negated_conjecture,
sP18,
inference(assume_negation,[status(cth)],[cTHM120I_pme]) ).
thf(1,plain,
sP17,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP5
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(3,plain,
( ~ sP11
| ~ sP25
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP11
| sP25
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP24
| ~ sP19
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP24
| sP19
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP12
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP13
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP21
| ~ sP25
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP21
| sP25
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP23
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).
thf(12,plain,
( ~ sP16
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP27
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP27
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP28
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP8
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP8
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP6
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(20,plain,
( sP3
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(21,plain,
( sP20
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(22,plain,
( ~ sP10
| ~ sP5
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP7
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP14
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP14
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP22
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(28,plain,
( sP2
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(29,plain,
( ~ sP1
| sP10
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP18
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(31,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,h2]) ).
thf(32,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[31,h1]) ).
thf(33,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[32,h0]) ).
thf(0,theorem,
~ sP18,
inference(contra,[status(thm),contra(discharge,[h2])],[31,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV086^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n021.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 03:07:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 9.78/10.01 % SZS status Theorem
% 9.78/10.01 % Mode: mode495
% 9.78/10.01 % Inferences: 159
% 9.78/10.01 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------