TSTP Solution File: SYO145^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO145^5 : 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 : n028.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 19:30:31 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 24
% Syntax : Number of formulae : 32 ( 9 unt; 4 typ; 2 def)
% Number of atoms : 58 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 102 ( 30 ~; 8 |; 0 &; 45 @)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 13 con; 0-2 aty)
% Number of variables : 23 ( 2 ^ 21 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__5,type,
eigen__5: $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__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cP @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cP @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ( cP @ eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( cP @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( cP @ eigen__3 @ X1 )
=> ~ ( cP @ eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cP @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cP @ eigen__3 @ eigen__5 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
=> ~ ( cP @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cP @ eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
~ ( cP @ eigen__3 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cEXPVAR_BUG,conjecture,
( sP2
=> ! [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ( cP @ X2 @ X3 )
=> ~ ( cP @ X1 @ X2 ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP2
=> ! [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ( cP @ X2 @ X3 )
=> ~ ( cP @ X1 @ X2 ) ) ),
inference(assume_negation,[status(cth)],[cEXPVAR_BUG]) ).
thf(h2,assumption,
sP2,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ( cP @ X2 @ X3 )
=> ~ ( cP @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| ~ sP7
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP8
| sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(4,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP1
| sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(7,plain,
( ~ sP2
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,h2,h4]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,8,h4]) ).
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,
( sP2
=> ! [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ( cP @ X2 @ X3 )
=> ~ ( cP @ X1 @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[10,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO145^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n028.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 : Fri Jul 8 22:55:55 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: 104
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------