TSTP Solution File: SYO109^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO109^5 : 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 : n022.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 19:30:21 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 51
% Syntax : Number of formulae : 60 ( 12 unt; 5 typ; 1 def)
% Number of atoms : 147 ( 1 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 256 ( 72 ~; 22 |; 0 &; 93 @)
% ( 20 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 25 con; 0-2 aty)
% ( 9 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 12 ( 1 ^ 11 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_cM,type,
cM: $i > $i > $o ).
thf(ty_cN,type,
cN: $i > $i > $o ).
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] :
~ ~ ( ~ ( !! @ ( cM @ X1 ) )
=> ( cN @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( ~ ( cM @ X1 @ X2 )
=> ( cN @ X1 @ X2 ) )
=> ( ~ ( ~ ( ~ ( cM @ X2 @ X1 )
=> ( cN @ X2 @ X1 ) )
=> ( cM @ X2 @ X2 ) )
=> ( cN @ X2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ~ ( cM @ eigen__0 @ eigen__3 )
=> ( cN @ eigen__0 @ eigen__3 ) )
=> ( cM @ eigen__0 @ eigen__0 ) )
=> ( cN @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
~ ( ~ ( cM @ eigen__0 @ X1 )
=> ( cN @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( cM @ eigen__0 @ eigen__0 )
=> ( cN @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ~ ( cM @ eigen__0 @ eigen__3 )
=> ( cN @ eigen__0 @ eigen__3 ) )
=> ( cM @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( ~ ( cM @ eigen__3 @ X1 )
=> ( cN @ eigen__3 @ X1 ) )
=> ( ~ ( ~ ( ~ ( cM @ X1 @ eigen__3 )
=> ( cN @ X1 @ eigen__3 ) )
=> ( cM @ X1 @ X1 ) )
=> ( cN @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( cM @ eigen__3 @ eigen__0 )
=> ( cN @ eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP3
=> ( cP @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP7
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cN @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cN @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( ~ ( !! @ ( cM @ X2 ) )
=> ( cN @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( cM @ eigen__0 @ eigen__3 )
=> ( cN @ eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
~ ( ~ ( !! @ ( cM @ X1 ) )
=> ( cN @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cM @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( ~ ( cM @ X1 @ X2 )
=> ( cN @ X1 @ X2 ) )
=> ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( !! @ ( cM @ eigen__3 ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( cM @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( !! @ ( cM @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cTHM271,conjecture,
( ~ ( ~ ( sP17
=> ~ sP12 )
=> ~ sP1 )
=> ( !! @ cP ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( sP17
=> ~ sP12 )
=> ~ sP1 )
=> ( !! @ cP ) ),
inference(assume_negation,[status(cth)],[cTHM271]) ).
thf(h2,assumption,
~ ( ~ ( sP17
=> ~ sP12 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( !! @ cP ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP17
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
sP17,
introduced(assumption,[]) ).
thf(h7,assumption,
sP12,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(1,plain,
( sP7
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP7
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| ~ sP7
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP5
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP14
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| ~ sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP20
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP18
| sP20
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP15
| sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(12,plain,
( sP4
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP4
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP12
| ~ sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP3
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP17
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP8
| sP3
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h6,h7,h5,h8]) ).
thf(19,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)],[h3,18,h8]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,19,h6,h7]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,20,h4,h5]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,21,h2,h3]) ).
thf(23,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[22,h0]) ).
thf(0,theorem,
( ~ ( ~ ( sP17
=> ~ sP12 )
=> ~ sP1 )
=> ( !! @ cP ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[22,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO109^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 01:49:56 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % Mode: mode213
% 0.21/0.41 % Inferences: 972
% 0.21/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------