TSTP Solution File: SYO307^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO307^5 : 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 : n007.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 19:31:22 EDT 2022
% Result : Theorem 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 32 ( 10 unt; 7 typ; 3 def)
% Number of atoms : 91 ( 3 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 165 ( 60 ~; 8 |; 0 &; 41 @)
% ( 8 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 18 ( 3 ^ 15 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_p,type,
p: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_q,type,
q: $i > $o ).
thf(ty_cT,type,
cT: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cR,type,
cR: $i > $o ).
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] :
~ ! [X2: $i] :
( ( ~ $false
=> ~ ( $false
=> ~ $false ) )
=> ( ( ( p @ eigen__0 )
=> ~ ( cR @ X1 ) )
=> ~ ( ( q @ eigen__0 )
=> ~ ( cT @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ( ~ $false
=> ~ ( $false
=> ~ $false ) )
=> ( ( ( p @ X1 )
=> ~ ( cR @ X2 ) )
=> ~ ( ( q @ X1 )
=> ~ ( cT @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( ~ $false
=> ~ ( $false
=> ~ $false ) )
=> ( ( ( p @ eigen__0 )
=> ~ ( cR @ eigen__1 ) )
=> ~ ( ( q @ eigen__0 )
=> ~ ( cT @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( ~ $false
=> ~ ( $false
=> ~ $false ) )
=> ( ( ( p @ X1 )
=> ~ ( cR @ X2 ) )
=> ~ ( ( q @ X1 )
=> ~ ( cT @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ~ $false
=> ~ ( $false
=> ~ $false ) )
=> ( ( ( p @ eigen__0 )
=> ~ ( cR @ eigen__1 ) )
=> ~ ( ( q @ eigen__0 )
=> ~ ( cT @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ $false
=> ~ ( $false
=> ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( $false
=> ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( sP3
=> ( ( ( p @ eigen__0 )
=> ~ ( cR @ X1 ) )
=> ~ ( ( q @ eigen__0 )
=> ~ ( cT @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $o] :
~ ! [X2: $i,X3: $i,X4: $i] :
( ( ~ ( X1 @ X2 )
=> ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) ) )
=> ( ( ( p @ X2 )
=> ~ ( cR @ X3 ) )
=> ~ ( ( q @ X2 )
=> ~ ( cT @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> $false ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( sP3
=> ( ( ( p @ eigen__0 )
=> ~ ( cR @ eigen__1 ) )
=> ~ ( ( q @ eigen__0 )
=> ~ ( cT @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cBLEDSOE5F,conjecture,
~ sP6 ).
thf(h1,negated_conjecture,
sP6,
inference(assume_negation,[status(cth)],[cBLEDSOE5F]) ).
thf(1,plain,
( sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
~ sP7,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP7
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP2
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP8
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(6,plain,
( sP5
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(7,plain,
( sP1
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(8,plain,
( ~ sP6
| ~ sP1 ),
inference(all_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,
~ sP6,
inference(contra,[status(thm),contra(discharge,[h1])],[9,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SYO307^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jul 8 23:52:45 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % Mode: mode213
% 0.21/0.38 % Inferences: 52
% 0.21/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------