TSTP Solution File: SYO108^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO108^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 : 600s
% DateTime : Thu Jul 21 19:30:20 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 36 ( 12 unt; 5 typ; 1 def)
% Number of atoms : 72 ( 1 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 107 ( 46 ~; 7 |; 0 &; 21 @)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 13 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 7 ( 1 ^ 6 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cG,type,
cG: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cM,type,
cM: $i > $o ).
thf(ty_cN,type,
cN: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cN @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ~ ( cM @ X1 )
=> ~ ! [X2: $i] :
~ ( cN @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
~ ( cN @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( cM @ eigen__0 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cN @ eigen__2 )
=> ~ ( !! @ cG ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( !! @ cG ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( cN @ X1 )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cN @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cM @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cTHM79,conjecture,
( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP5 )
=> ~ sP1 )
=> ~ sP6 ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP5 )
=> ~ sP1 )
=> ~ sP6 ),
inference(assume_negation,[status(cth)],[cTHM79]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( !! @ cM )
=> ~ sP5 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP6,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( !! @ cM )
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( !! @ cM ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP5,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| ~ sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP2
| sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(4,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP8
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,h8,h7,h5,h3]) ).
thf(7,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)],[h6,6,h8]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,7,h6,h7]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,8,h4,h5]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3]) ).
thf(11,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[10,h0]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( !! @ cM )
=> ~ sP5 )
=> ~ sP1 )
=> ~ sP6 ),
inference(contra,[status(thm),contra(discharge,[h1])],[10,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO108^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 04:39:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % Mode: mode213
% 0.19/0.37 % Inferences: 11
% 0.19/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------