TSTP Solution File: SYN058^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN058^5 : 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 : n016.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 : Fri Sep 1 03:19:42 EDT 2023
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 51
% Syntax : Number of formulae : 63 ( 17 unt; 9 typ; 2 def)
% Number of atoms : 127 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 172 ( 62 ~; 16 |; 0 &; 40 @)
% ( 17 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 22 con; 0-2 aty)
% Number of variables : 15 ( 2 ^; 13 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cF,type,
cF: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(ty_cR,type,
cR: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_cG,type,
cG: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cS,type,
cS: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( cQ @ X1 )
=> ( cR @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( cQ @ X1 )
=> ~ ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( cF @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( cQ @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
~ ( cS @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( cQ @ X1 )
=> ~ ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i] :
( ~ ( cQ @ X1 )
=> ( cR @ X1 ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( cP @ X1 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP1
=> ( cG @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cQ @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ~ ( cQ @ X1 )
=> ( cR @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP8
=> ( cR @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cS @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cG @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( cF @ X1 )
=> ( cG @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( cQ @ eigen__2 )
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP3
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP12
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cPELL28,conjecture,
( ~ ( ~ ( sP6
=> ~ sP5 )
=> ~ sP16 )
=> ! [X1: $i] :
( ~ ( ( cP @ X1 )
=> ~ ( cF @ X1 ) )
=> ( cG @ X1 ) ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( sP6
=> ~ sP5 )
=> ~ sP16 )
=> ! [X1: $i] :
( ~ ( ( cP @ X1 )
=> ~ ( cF @ X1 ) )
=> ( cG @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cPELL28]) ).
thf(h2,assumption,
~ ( ~ ( sP6
=> ~ sP5 )
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ~ ( ( cP @ X1 )
=> ~ ( cF @ X1 ) )
=> ( cG @ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP6
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP16,
introduced(assumption,[]) ).
thf(h6,assumption,
sP6,
introduced(assumption,[]) ).
thf(h7,assumption,
sP5,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( sP12
=> ~ sP1 )
=> sP13 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP12
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h11,assumption,
sP12,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP17
| ~ sP12
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| ~ sP1
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP6
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP14
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP15
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP10
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP4
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(10,plain,
( sP9
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(11,plain,
( ~ sP5
| ~ sP9
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| sP3
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h6,h7,h5,h11,h12,h10]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,13,h11,h12]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,14,h9,h10]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h3,15,h8]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,16,h6,h7]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,17,h4,h5]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,18,h2,h3]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[19,h0]) ).
thf(0,theorem,
( ~ ( ~ ( sP6
=> ~ sP5 )
=> ~ sP16 )
=> ! [X1: $i] :
( ~ ( ( cP @ X1 )
=> ~ ( cF @ X1 ) )
=> ( cG @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[19,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN058^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 22:10:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % Mode: cade22grackle2xfee4
% 0.20/0.40 % Steps: 58
% 0.20/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------