TSTP Solution File: SYN049^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN049^5 : 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 03:19:38 EDT 2023
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 41
% Syntax : Number of formulae : 51 ( 12 unt; 9 typ; 6 def)
% Number of atoms : 129 ( 6 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 166 ( 26 ~; 16 |; 0 &; 64 @)
% ( 15 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 24 con; 0-2 aty)
% Number of variables : 23 ( 6 ^; 17 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( ( cP @ X1 )
=> ( cQ @ X2 ) )
=> ( ( cP @ eigen__2 )
=> ( cQ @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( ( cP @ X1 )
=> ( cQ @ X2 ) )
=> ( ( cP @ eigen__0 )
=> ( cQ @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ( ( cP @ eigen__5 )
=> ( cQ @ X1 ) )
=> ( ( cP @ eigen__1 )
=> ( cQ @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( ( cP @ eigen__1 )
=> ( cQ @ X1 ) )
=> ( ( cP @ eigen__0 )
=> ( cQ @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( ( cP @ eigen__3 )
=> ( cQ @ X1 ) )
=> ( ( cP @ eigen__2 )
=> ( cQ @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( ( cP @ X1 )
=> ( cQ @ X2 ) )
=> ( ( cP @ eigen__1 )
=> ( cQ @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( ( cP @ X1 )
=> ( cQ @ X2 ) )
=> ( ( cP @ eigen__0 )
=> ( cQ @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
=> ( cQ @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ( cQ @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cP @ eigen__2 )
=> ( cQ @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ( ( cP @ X1 )
=> ( cQ @ X2 ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( ( cP @ eigen__5 )
=> ( cQ @ X1 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( sP2
=> ( cQ @ X1 ) )
=> ( ( cP @ eigen__0 )
=> ( cQ @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( ( cP @ X1 )
=> ( cQ @ X2 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ( ( cP @ X2 )
=> ( cQ @ X3 ) )
=> ( ( cP @ X1 )
=> ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cQ @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( cP @ eigen__3 )
=> ( cQ @ eigen__4 ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( ( cP @ eigen__3 )
=> ( cQ @ X1 ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP3
=> ( ( cP @ eigen__0 )
=> ( cQ @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( ( cP @ eigen__5 )
=> ( cQ @ eigen__6 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cPELL19,conjecture,
~ sP10 ).
thf(h1,negated_conjecture,
sP10,
inference(assume_negation,[status(cth)],[cPELL19]) ).
thf(1,plain,
( sP4
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP15
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP7
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(4,plain,
( sP9
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(5,plain,
( ~ sP10
| ~ sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP5
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP12
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP13
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(9,plain,
( sP6
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(10,plain,
( ~ sP10
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| ~ sP2
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP14
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP8
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(14,plain,
( sP1
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(15,plain,
( ~ sP10
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h1]) ).
thf(17,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[16,h0]) ).
thf(0,theorem,
~ sP10,
inference(contra,[status(thm),contra(discharge,[h1])],[16,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN049^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n016.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 : Sat Aug 26 18:10:57 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 % Mode: cade22grackle2xfee4
% 0.18/0.41 % Steps: 42
% 0.18/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------