TSTP Solution File: SEV386^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV386^5 : 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 18:06:09 EDT 2022
% Result : Theorem 2.62s 2.85s
% Output : Proof 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 76
% Syntax : Number of formulae : 84 ( 13 unt; 6 typ; 4 def)
% Number of atoms : 212 ( 41 equ; 5 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 213 ( 59 ~; 43 |; 0 &; 45 @)
% ( 33 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 40 con; 0-2 aty)
% Number of variables : 29 ( 4 ^ 25 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_p,type,
p: a > $o ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ( ( p @ X1 )
=> ~ ! [X2: a] :
( ( p @ X2 )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ( ( p
!= ( (=) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: a] :
( ( p @ X1 )
!= ( eigen__1 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: a] :
~ ( ( p @ X1 )
=> ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ( p @ eigen__2 )
= ( eigen__2 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( p @ X1 )
=> ( eigen__1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__1 = eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( p @ X1 )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( p @ eigen__7 )
=> ! [X1: a] :
( ( X1 = eigen__7 )
=> ~ ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__2 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( p @ eigen__5 )
= sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( p @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP8
=> ~ ( sP6
=> sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ( p @ eigen__5 )
=> sP6 )
=> ! [X1: $o] :
( ( ( p @ eigen__5 )
= X1 )
=> ~ ( X1
=> sP6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( p @ eigen__7 )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a,X2: a > $o] :
( ( X2 @ X1 )
=> ! [X3: a] :
( ( X3 = X1 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( p @ X1 )
= ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( p @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ( p @ X1 )
=> ~ ! [X2: a] :
( ( p @ X2 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $o > $o] :
( ( X1 @ ( p @ eigen__5 ) )
=> ! [X2: $o] :
( ( ( p @ eigen__5 )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $o] :
( ( ( p @ eigen__5 )
= X1 )
=> ~ ( X1
=> sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP6
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP16
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( p @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a > $o] :
( ( X1 @ eigen__7 )
=> ! [X2: a] :
( ( X2 = eigen__7 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP9
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( ~ ! [X1: a] :
( p
!= ( (=) @ X1 ) ) )
= ( ~ sP17 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( p @ eigen__5 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP3
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( p
!= ( (=) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a] :
( ( p @ X1 )
= ( eigen__1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( p
= ( (=) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP22
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( p
= ( (=) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a] :
( ( X1 = eigen__7 )
=> ~ ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(cTTTP5306A_pme,conjecture,
sP25 ).
thf(h1,negated_conjecture,
~ sP25,
inference(assume_negation,[status(cth)],[cTTTP5306A_pme]) ).
thf(1,plain,
( ~ sP27
| ~ sP3
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP33
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP22
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP23
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP13
| ~ sP22
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP13
| sP22
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP31
| ~ sP22
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP20
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP20
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP15
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP10
| ~ sP8
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP19
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP12
| sP26
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP18
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP11
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( sP29
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(19,plain,
( sP32
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
sP7,
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP28
| ~ sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
sP14,
inference(eq_ind_sym,[status(thm)],]) ).
thf(23,plain,
( sP21
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP21
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP4
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(26,plain,
( ~ sP24
| ~ sP9
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP1
| sP9
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
sP11,
inference(eq_ind,[status(thm)],]) ).
thf(29,plain,
( ~ sP17
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP15
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP30
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP28
| sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(33,plain,
( sP17
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(34,plain,
( sP25
| sP28
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP25
| ~ sP28
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h1]) ).
thf(37,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[36,h0]) ).
thf(0,theorem,
sP25,
inference(contra,[status(thm),contra(discharge,[h1])],[36,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV386^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 27 18:10:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.62/2.85 % SZS status Theorem
% 2.62/2.85 % Mode: mode506
% 2.62/2.85 % Inferences: 23229
% 2.62/2.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------