TSTP Solution File: SYO301^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO301^5 : 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 : n013.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 19:31:20 EDT 2022
% Result : Theorem 1.97s 2.19s
% Output : Proof 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 27 ( 7 unt; 4 typ; 1 def)
% Number of atoms : 47 ( 1 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 61 ( 13 ~; 9 |; 0 &; 21 @)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 9 ( 1 ^ 8 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_b,type,
b: $i ).
thf(ty_f,type,
f: $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( cP @ X1 )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( cP @ ( f @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cP @ X2 ) )
=> ~ ( X1 @ ( f @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cP @ eigen__1 )
=> ( cP @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( cP @ X1 )
=> ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( cP @ X3 ) )
=> ~ ( X2 @ ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP1
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP5
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cBLEDSOE5,conjecture,
sP7 ).
thf(h1,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[cBLEDSOE5]) ).
thf(1,plain,
( sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP3
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP5
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(4,plain,
( ~ sP8
| ~ sP5
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP7
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP7
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,h1]) ).
thf(10,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[9,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h1])],[9,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYO301^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n013.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 14:16:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.97/2.19 % SZS status Theorem
% 1.97/2.19 % Mode: mode506
% 1.97/2.19 % Inferences: 19454
% 1.97/2.19 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------