TSTP Solution File: LCL738^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL738^5 : 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 : n006.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 08:04:47 EDT 2023
% Result : Theorem 20.17s 20.42s
% Output : Proof 20.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 35
% Syntax : Number of formulae : 48 ( 18 unt; 7 typ; 2 def)
% Number of atoms : 75 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 274 ( 86 ~; 10 |; 0 &; 138 @)
% ( 8 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 10 con; 0-3 aty)
% Number of variables : 75 ( 2 ^; 67 !; 0 ?; 75 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__18,type,
eigen__18: b > $o ).
thf(ty_eigen__0,type,
eigen__0: ( b > $o ) > b > b > $o ).
thf(ty_eigen__20,type,
eigen__20: b > $o ).
thf(ty_eigen__1,type,
eigen__1: ( b > $o ) > b > b > $o ).
thf(ty_eigen__28,type,
eigen__28: b > $o ).
thf(ty_eigen__2,type,
eigen__2: ( b > $o ) > b ).
thf(h0,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__18,definition,
( eigen__18
= ( eps__0
@ ^ [X1: b > $o] :
~ ( ~ ! [X2: b] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: b] : ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__18])]) ).
thf(eigendef_eigen__28,definition,
( eigen__28
= ( eps__0
@ ^ [X1: b > $o] :
~ ( ~ ! [X2: b] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: b] : ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__28])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ! [X1: b] :
~ ( eigen__18 @ X1 )
=> ( eigen__18
@ @+[X1: b] : ( eigen__18 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: b] :
~ ( eigen__28 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: b] :
~ ( eigen__18 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__28
@ @+[X1: b] : ( eigen__28 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: b > $o] :
( ~ ! [X2: b] :
~ ( X1 @ X2 )
=> ( X1
@ @+[X2: b] : ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__18
@ @+[X1: b] : ( eigen__18 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: ( b > $o ) > b] :
~ ! [X2: b > $o] :
( ~ ! [X3: b] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP2
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cX5310_SUB,conjecture,
( ~ ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
~ ( ! [X3: b > $o] :
~ ! [X4: b] :
~ ! [X5: b] :
( ~ ( X2 @ X3 @ X4 @ X5 )
=> ( X1 @ X3 @ X4 @ X5 ) )
=> ~ ! [X3: ( b > $o ) > b] :
~ ! [X4: b > $o,X5: b] :
( ~ ( X2 @ X4 @ ( X3 @ X4 ) @ X5 )
=> ( X1 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
=> ~ sP7 ) ).
thf(h1,negated_conjecture,
~ ( ~ ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
~ ( ! [X3: b > $o] :
~ ! [X4: b] :
~ ! [X5: b] :
( ~ ( X2 @ X3 @ X4 @ X5 )
=> ( X1 @ X3 @ X4 @ X5 ) )
=> ~ ! [X3: ( b > $o ) > b] :
~ ! [X4: b > $o,X5: b] :
( ~ ( X2 @ X4 @ ( X3 @ X4 ) @ X5 )
=> ( X1 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
=> ~ sP7 ),
inference(assume_negation,[status(cth)],[cX5310_SUB]) ).
thf(h2,assumption,
~ ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
~ ( ! [X3: b > $o] :
~ ! [X4: b] :
~ ! [X5: b] :
( ~ ( X2 @ X3 @ X4 @ X5 )
=> ( X1 @ X3 @ X4 @ X5 ) )
=> ~ ! [X3: ( b > $o ) > b] :
~ ! [X4: b > $o,X5: b] :
( ~ ( X2 @ X4 @ ( X3 @ X4 ) @ X5 )
=> ( X1 @ X4 @ ( X3 @ X4 ) @ X5 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP7,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: ( b > $o ) > b > b > $o] :
~ ( ! [X2: b > $o] :
~ ! [X3: b] :
~ ! [X4: b] :
( ~ ( X1 @ X2 @ X3 @ X4 )
=> ( eigen__0 @ X2 @ X3 @ X4 ) )
=> ~ ! [X2: ( b > $o ) > b] :
~ ! [X3: b > $o,X4: b] :
( ~ ( X1 @ X3 @ ( X2 @ X3 ) @ X4 )
=> ( eigen__0 @ X3 @ ( X2 @ X3 ) @ X4 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ! [X1: b > $o] :
~ ! [X2: b] :
~ ! [X3: b] :
( ~ ( eigen__1 @ X1 @ X2 @ X3 )
=> ( eigen__0 @ X1 @ X2 @ X3 ) )
=> ~ ! [X1: ( b > $o ) > b] :
~ ! [X2: b > $o,X3: b] :
( ~ ( eigen__1 @ X2 @ ( X1 @ X2 ) @ X3 )
=> ( eigen__0 @ X2 @ ( X1 @ X2 ) @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: b > $o] :
~ ! [X2: b] :
~ ! [X3: b] :
( ~ ( eigen__1 @ X1 @ X2 @ X3 )
=> ( eigen__0 @ X1 @ X2 @ X3 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: ( b > $o ) > b] :
~ ! [X2: b > $o,X3: b] :
( ~ ( eigen__1 @ X2 @ ( X1 @ X2 ) @ X3 )
=> ( eigen__0 @ X2 @ ( X1 @ X2 ) @ X3 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: b] :
~ ! [X2: b] :
( ~ ( eigen__1 @ eigen__20 @ X1 @ X2 )
=> ( eigen__0 @ eigen__20 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( sP4
| sP2 ),
inference(choice_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP8
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP5
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__28]) ).
thf(5,plain,
( ~ sP7
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h6,h5,h4,h2,h3,h1,h0])],[1,2,3,4,5,h3]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__20)],[h6,6,h8]) ).
thf(h9,assumption,
! [X1: b > $o,X2: b] :
( ~ ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ X2 )
=> ( eigen__0 @ X1 @ ( eigen__2 @ X1 ) @ X2 ) ),
introduced(assumption,[]) ).
thf(8,plain,
( sP6
| sP3 ),
inference(choice_rule,[status(thm)],]) ).
thf(9,plain,
( sP1
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP1
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP5
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__18]) ).
thf(12,plain,
( ~ sP7
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h7,h5,h4,h2,h3,h1,h0])],[8,9,10,11,12,h3]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h7,13,h9]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h5,7,14,h6,h7]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,15,h5]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h2,16,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,
( ~ ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
~ ( ! [X3: b > $o] :
~ ! [X4: b] :
~ ! [X5: b] :
( ~ ( X2 @ X3 @ X4 @ X5 )
=> ( X1 @ X3 @ X4 @ X5 ) )
=> ~ ! [X3: ( b > $o ) > b] :
~ ! [X4: b > $o,X5: b] :
( ~ ( X2 @ X4 @ ( X3 @ X4 ) @ X5 )
=> ( X1 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
=> ~ sP7 ),
inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL738^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n006.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 : 300
% 0.12/0.33 % DateTime : Thu Aug 24 22:37:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 20.17/20.42 % SZS status Theorem
% 20.17/20.42 % Mode: cade22grackle2x798d
% 20.17/20.42 % Steps: 1001
% 20.17/20.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------