TSTP Solution File: SEV245^6 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV245^6 : TPTP v8.1.2. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n009.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 19:33:06 EDT 2023
% Result : Theorem 20.97s 21.25s
% Output : Proof 20.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 42
% Syntax : Number of formulae : 52 ( 14 unt; 5 typ; 1 def)
% Number of atoms : 114 ( 1 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 259 ( 56 ~; 16 |; 0 &; 112 @)
% ( 15 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 19 con; 0-2 aty)
% Number of variables : 59 ( 8 ^; 51 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cK,type,
cK: ( a > $o ) > a > $o ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cK @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__1 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( cK @ eigen__1 @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ~ ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( cK @ eigen__1 @ X1 ) )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP2
=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( cK @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cK
@ ^ [X1: a] :
~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK @ eigen__1 @ X2 )
=> ( cK @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: a] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP8
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cTHM116_2S,conjecture,
( sP14
=> ! [X1: a] :
( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP14
=> ! [X1: a] :
( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
inference(assume_negation,[status(cth)],[cTHM116_2S]) ).
thf(h2,assumption,
sP14,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a] :
( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__0 ) )
=> sP12 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cK @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP11
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP11,
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| ~ sP11
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| ~ sP2
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP6
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP6
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP8
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(8,plain,
( ~ sP15
| ~ sP8
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP13
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP5
| ~ sP1
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP14
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP11
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2,h8,h9,h6]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,13,h8,h9]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h5,14,h7]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,15,h5,h6]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,16,h4]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,17,h2,h3]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
( sP14
=> ! [X1: a] :
( ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cK @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cK @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SEV245^6 : TPTP v8.1.2. Released v5.1.0.
% 0.08/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 02:59:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 20.97/21.25 % SZS status Theorem
% 20.97/21.25 % Mode: cade22grackle2x798d
% 20.97/21.25 % Steps: 228
% 20.97/21.25 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------