TSTP Solution File: SEV189^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV189^5 : 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 : n014.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 19:32:56 EDT 2023
% Result : Theorem 0.19s 0.76s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 52
% Syntax : Number of formulae : 62 ( 13 unt; 6 typ; 2 def)
% Number of atoms : 154 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 237 ( 58 ~; 22 |; 0 &; 80 @)
% ( 20 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 22 con; 0-2 aty)
% Number of variables : 44 ( 14 ^; 30 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_cQ,type,
cQ: ( b > $o ) > $o ).
thf(ty_eigen__5,type,
eigen__5: b > $o ).
thf(ty_cP,type,
cP: ( b > $o ) > $o ).
thf(ty_eigen__4,type,
eigen__4: b > $o ).
thf(ty_eigen__0,type,
eigen__0: ( b > $o ) > $o ).
thf(h0,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: b > $o] :
~ ( ( eigen__0 @ X1 )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: b > $o] :
~ ( ( eigen__0 @ X1 )
=> ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b > $o] :
( ( eigen__0 @ X1 )
=> ~ ( ( cP @ X1 )
=> ~ ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ eigen__5 )
=> ( cQ @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cP
@ ^ [X1: b] :
! [X2: b > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: b > $o] :
( ( eigen__0 @ X1 )
=> ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: b > $o] :
( ( eigen__0 @ X1 )
=> ( cP @ X1 ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cP @ eigen__5 )
=> ~ ( cQ @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cP @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cQ
@ ^ [X1: b] :
! [X2: b > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__5 )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: b > $o] :
( ( eigen__0 @ X1 )
=> ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ( cQ @ X2 ) )
=> ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP7
=> ~ ( cQ @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP4
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP3
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cQ @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP9
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP9
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cTHM567_pme,conjecture,
( ~ ( sP19
=> ~ sP12 )
=> ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ~ ( ( cP @ X2 )
=> ~ ( cQ @ X2 ) ) )
=> ~ ( ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) )
=> ~ ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( sP19
=> ~ sP12 )
=> ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ~ ( ( cP @ X2 )
=> ~ ( cQ @ X2 ) ) )
=> ~ ( ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) )
=> ~ ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM567_pme]) ).
thf(h2,assumption,
~ ( sP19
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ~ ( ( cP @ X2 )
=> ~ ( cQ @ X2 ) ) )
=> ~ ( ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) )
=> ~ ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP19,
introduced(assumption,[]) ).
thf(h5,assumption,
sP12,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
sP15,
introduced(assumption,[]) ).
thf(1,plain,
( sP6
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| ~ sP18
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP13
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP17
| ~ sP9
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP1
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP2
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP2
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP4
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(10,plain,
( ~ sP14
| ~ sP4
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP20
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP20
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP11
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(14,plain,
( ~ sP5
| ~ sP11
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP12
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP19
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP15
| ~ sP3
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h4,h5,h7,h8]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,18,h7,h8]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,19,h6]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,20,h4,h5]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,21,h2,h3]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[22,h0]) ).
thf(0,theorem,
( ~ ( sP19
=> ~ sP12 )
=> ! [X1: ( b > $o ) > $o] :
( ! [X2: b > $o] :
( ( X1 @ X2 )
=> ~ ( ( cP @ X2 )
=> ~ ( cQ @ X2 ) ) )
=> ~ ( ( cP
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) )
=> ~ ( cQ
@ ^ [X2: b] :
! [X3: b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[22,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV189^5 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n014.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 : 300
% 0.12/0.34 % DateTime : Thu Aug 24 03:36:19 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.76 % SZS status Theorem
% 0.19/0.76 % Mode: cade22grackle2xfee4
% 0.19/0.76 % Steps: 10421
% 0.19/0.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------