TSTP Solution File: SYO258^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO258^5 : 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 : n023.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 19:31:07 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 19
% Syntax : Number of formulae : 26 ( 9 unt; 5 typ; 1 def)
% Number of atoms : 55 ( 1 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 108 ( 34 ~; 3 |; 0 &; 42 @)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 10 con; 0-2 aty)
% ( 5 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 13 ( 4 ^ 9 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $i ).
thf(ty_cP,type,
cP: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_b,type,
b: $i ).
thf(ty_cQ,type,
cQ: $i > ( $i > $o ) > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ( $false
=> ~ ( ~ ! [X2: $i] :
( ( cP @ X1 @ X2 )
=> ~ ( cQ @ X2
@ ^ [X3: $i] : $false ) )
=> ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( sP1
=> ~ ( ~ ! [X2: $i] :
( ( cP @ X1 @ X2 )
=> ~ ( cQ @ X2
@ ^ [X3: $i] : sP1 ) )
=> ~ sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ~ ( ~ ! [X1: $i] :
( ( cP @ eigen__0 @ X1 )
=> ~ ( cQ @ X1
@ ^ [X2: $i] : sP1 ) )
=> ~ sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( ~ ! [X3: $i] :
( ( cP @ X2 @ X3 )
=> ~ ( cQ @ X3 @ X1 ) )
=> ~ ( X1 @ a ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(cBLEDSOE_FENG_6,conjecture,
( ~ ( ( cP @ a @ b )
=> ~ ( !! @ ( cQ @ b ) ) )
=> ~ sP4 ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ( cP @ a @ b )
=> ~ ( !! @ ( cQ @ b ) ) )
=> ~ sP4 ),
inference(assume_negation,[status(cth)],[cBLEDSOE_FENG_6]) ).
thf(h2,assumption,
~ ( ( cP @ a @ b )
=> ~ ( !! @ ( cQ @ b ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP4,
introduced(assumption,[]) ).
thf(h4,assumption,
cP @ a @ b,
introduced(assumption,[]) ).
thf(h5,assumption,
!! @ ( cQ @ b ),
introduced(assumption,[]) ).
thf(1,plain,
~ sP1,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP3
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP2
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(4,plain,
( ~ sP4
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h2,h3,h1,h0])],[1,2,3,4,h3]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,5,h4,h5]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,6,h2,h3]) ).
thf(8,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[7,h0]) ).
thf(0,theorem,
( ~ ( ( cP @ a @ b )
=> ~ ( !! @ ( cQ @ b ) ) )
=> ~ sP4 ),
inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYO258^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n023.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 18:00:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 51
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------