TSTP Solution File: SYO107^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO107^5 : 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 : n005.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 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 45
% Syntax : Number of formulae : 58 ( 22 unt; 7 typ; 3 def)
% Number of atoms : 108 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 112 ( 32 ~; 15 |; 0 &; 34 @)
% ( 14 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 23 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 10 ( 3 ^ 7 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ( cP @ eigen__3 )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ( ( cP @ eigen__3 )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( cP @ eigen__0 )
=> ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cP @ eigen__3 )
=> ( cP @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cP @ eigen__0 )
=> ( cP @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cP @ eigen__3 )
=> ( cP @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cP @ eigen__1 )
=> ( !! @ cP ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cP @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ X1 )
=> ( cP @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( cP @ eigen__3 )
=> ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cP @ eigen__0 )
=> ( !! @ cP ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cP @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cP @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
~ ( ( cP @ X1 )
=> ( !! @ cP ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( !! @ cP ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(cTHM66,conjecture,
( ( ~ sP7 )
= ( ~ sP13 ) ) ).
thf(h1,negated_conjecture,
( ~ sP7 )
!= ( ~ sP13 ),
inference(assume_negation,[status(cth)],[cTHM66]) ).
thf(h2,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h4,assumption,
sP7,
introduced(assumption,[]) ).
thf(h5,assumption,
sP13,
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( sP9
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP13
| ~ sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| ~ sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP14
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(6,plain,
( sP5
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP13
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h2,h3,h1,h0])],[1,2,3,4,5,6,7,h6,h3]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h2,8,h6]) ).
thf(h7,assumption,
( sP11
=> sP14 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h9,assumption,
sP14,
introduced(assumption,[]) ).
thf(10,plain,
( sP4
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP8
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(12,plain,
( ~ sP7
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h7,h4,h5,h1,h0])],[10,11,12,h4,h8]) ).
thf(14,plain,
( ~ sP14
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( sP2
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP8
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(17,plain,
( ~ sP7
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h7,h4,h5,h1,h0])],[14,15,16,17,h4,h9]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h4,h5,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h7,13,18,h8,h9]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__3)],[h5,19,h7]) ).
thf(21,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,9,20,h2,h3,h4,h5]) ).
thf(22,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[21,h0]) ).
thf(0,theorem,
( ( ~ sP7 )
= ( ~ sP13 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[21,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO107^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n005.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 : 600
% 0.12/0.33 % DateTime : Sat Jul 9 11:27:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 74
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------