TSTP Solution File: SEV386^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV386^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 : 300s
% DateTime : Thu Aug 31 19:34:25 EDT 2023
% Result : Theorem 0.19s 0.67s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 56
% Syntax : Number of formulae : 67 ( 21 unt; 6 typ; 2 def)
% Number of atoms : 147 ( 32 equ; 1 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 119 ( 41 ~; 25 |; 0 &; 21 @)
% ( 21 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 28 con; 0-2 aty)
% Number of variables : 15 ( 5 ^; 10 !; 0 ?; 15 :)
% 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__0,type,
eigen__0: a ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__1,type,
eigen__1: 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 )
=> ( eigen__0 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
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
= ( ^ [X1: a] : ( eigen__0 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( p @ eigen__5 )
= ( eigen__2 = eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( p @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( p
= ( ^ [X1: a] : ( eigen__2 = 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
<=> ( ( p @ eigen__0 )
=> ~ ! [X1: a] :
( ( p @ X1 )
=> ( eigen__0 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( p @ X1 )
= ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( p @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( p
!= ( ^ [X2: a] : ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP4
= ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP4
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( p @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( p @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ( p @ X1 )
= ( eigen__0 = X1 ) ) ),
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: a] :
( ( p @ X1 )
=> ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP14
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( p @ X1 )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP9 = ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(cTTTP5306A_pme,conjecture,
( ~ sP10 = ~ sP17 ) ).
thf(h1,negated_conjecture,
( ~ sP10 != ~ sP17 ),
inference(assume_negation,[status(cth)],[cTTTP5306A_pme]) ).
thf(h2,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h4,assumption,
sP10,
introduced(assumption,[]) ).
thf(h5,assumption,
sP17,
introduced(assumption,[]) ).
thf(h6,assumption,
( p
= ( (=) @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP11
| ~ sP4
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP16
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP12
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP12
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP18
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(6,plain,
( ~ sP7
| ~ sP9
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
~ sP3,
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP21
| sP9
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP16
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h6,h3]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h2,12,h6]) ).
thf(h7,assumption,
~ ( sP15
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP15,
introduced(assumption,[]) ).
thf(h9,assumption,
sP20,
introduced(assumption,[]) ).
thf(14,plain,
( ~ sP19
| ~ sP14
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP20
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP15
| sP14
| ~ sP6 ),
inference(mating_rule,[status(thm)],]) ).
thf(17,plain,
( sP2
| ~ sP14
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP2
| sP14
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP8
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(20,plain,
( sP5
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP10
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h4,h5,h1,h0])],[14,15,16,17,18,19,20,21,h4,h8,h9]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h4,h5,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,22,h8,h9]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h5,23,h7]) ).
thf(25,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,13,24,h2,h3,h4,h5]) ).
thf(26,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[25,h0]) ).
thf(0,theorem,
( ~ sP10 = ~ sP17 ),
inference(contra,[status(thm),contra(discharge,[h1])],[25,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV386^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 02:09:57 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.67 % SZS status Theorem
% 0.19/0.67 % Mode: cade22grackle2xfee4
% 0.19/0.67 % Steps: 10312
% 0.19/0.67 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------