TSTP Solution File: SYO300^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO300^5 : 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 : n026.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 1.96s 2.19s
% Output : Proof 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 20 ( 8 unt; 1 typ; 1 def)
% Number of atoms : 41 ( 1 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 82 ( 13 ~; 6 |; 0 &; 51 @)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 43 ( 25 ^ 12 !; 0 ?; 43 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o ).
thf(h0,assumption,
! [X1: ( ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o ) > $o,X2: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
~ ~ ! [X2: ( $i > $i ) > $i] :
~ ( ! [X3: ( $i > $i ) > $i] : ( X1 @ X3 @ X3 )
=> ( X1
@ ^ [X3: $i > $i] :
( X3
@ ( X2
@ ^ [X4: $i] : X4 ) )
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( $i > $i ) > $i] :
~ ( ! [X2: ( $i > $i ) > $i] : ( eigen__0 @ X2 @ X2 )
=> ( eigen__0
@ ^ [X2: $i > $i] :
( X2
@ ( X1
@ ^ [X3: $i] : X3 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: ( $i > $i ) > $i] : ( eigen__0 @ X1 @ X1 )
=> ( eigen__0
@ ^ [X1: $i > $i] :
( X1
@ @+[X2: $i] :
( eigen__0
@ ^ [X3: $i > $i] : X2
@ ^ [X3: $i > $i] : X2 ) )
@ ^ [X1: $i > $i] :
( X1
@ @+[X2: $i] :
( eigen__0
@ ^ [X3: $i > $i] : X2
@ ^ [X3: $i > $i] : X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0
@ ^ [X1: $i > $i] :
( X1
@ @+[X2: $i] :
( eigen__0
@ ^ [X3: $i > $i] : X2
@ ^ [X3: $i > $i] : X2 ) )
@ ^ [X1: $i > $i] :
( X1
@ @+[X2: $i] :
( eigen__0
@ ^ [X3: $i > $i] : X2
@ ^ [X3: $i > $i] : X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: ( $i > $i ) > $i] : ( eigen__0 @ X1 @ X1 )
=> ( eigen__0
@ ^ [X1: $i > $i] :
( X1
@ @+[X2: $i] :
( eigen__0
@ ^ [X3: $i > $i] : X2
@ ^ [X3: $i > $i] : X2 ) )
@ ^ [X1: $i > $i] :
@+[X2: $i] :
( eigen__0
@ ^ [X3: $i > $i] : X2
@ ^ [X3: $i > $i] : X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > $i ) > $o] :
~ ! [X2: ( $i > $i ) > $i] :
~ ( ! [X3: ( $i > $i ) > $i] : ( X1 @ X3 @ X3 )
=> ( X1
@ ^ [X3: $i > $i] :
( X3
@ ( X2
@ ^ [X4: $i] : X4 ) )
@ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: ( $i > $i ) > $i] : ( eigen__0 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(cUNIFTHM1,conjecture,
sP5 ).
thf(h1,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[cUNIFTHM1]) ).
thf(1,plain,
( sP2
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP4
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP5
| sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,h1]) ).
thf(8,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[7,h0]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO300^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n026.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 23:17:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.19 % SZS status Theorem
% 1.96/2.19 % Mode: mode506
% 1.96/2.19 % Inferences: 19399
% 1.96/2.19 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------