TSTP Solution File: SEU967^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU967^5 : 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 : n025.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 : Tue Jul 19 14:11:04 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 21 ( 8 unt; 4 typ; 1 def)
% Number of atoms : 38 ( 1 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 109 ( 48 ~; 4 |; 0 &; 42 @)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 32 ( 12 ^ 20 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP_0,type,
cP_0: $i > $o ).
thf(ty_cY_0,type,
cY_0: ( ( $i > $i ) > $o ) > $i ).
thf(ty_cH_0,type,
cH_0: ( ( $i > $i ) > $o ) > $i > $i ).
thf(ty_cG_0,type,
cG_0: ( ( $i > $i ) > $o ) > $i > $i ).
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 ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ! [X1: $i] : ~ $false
=> ! [X1: $i] : ~ $false )
=> ~ ( ~ ! [X1: $i] : ~ $false
=> ~ ( ( cP_0
@ ( cY_0
@ ^ [X1: $i > $i] :
~ ! [X2: $i] : ~ $false ) )
=> ( cP_0
@ ( cG_0
@ ^ [X1: $i > $i] :
~ ! [X2: $i] : ~ $false
@ ( cY_0
@ ^ [X1: $i > $i] :
~ ! [X2: $i] : ~ $false ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] : ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ sP3
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: ( $i > $i ) > $i > $o] :
~ ( ~ ( ~ ! [X2: $i] :
~ ( X1
@ ( cG_0
@ ^ [X3: $i > $i] :
~ ! [X4: $i] :
~ ( X1 @ X3 @ X4 ) )
@ X2 )
=> ! [X2: $i] :
~ ( X1
@ ( cH_0
@ ^ [X3: $i > $i] :
~ ! [X4: $i] :
~ ( X1 @ X3 @ X4 ) )
@ X2 ) )
=> ~ ( ~ ! [X2: $i] :
~ ( X1
@ ^ [X3: $i] :
( cG_0
@ ^ [X4: $i > $i] :
~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 )
@ ( cH_0
@ ^ [X4: $i > $i] :
~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 )
@ X3 ) )
@ X2 )
=> ~ ( ( cP_0
@ ( cY_0
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) )
=> ( cP_0
@ ( cG_0
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 )
@ ( cY_0
@ ^ [X2: $i > $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(cBUGWFFA_pme,conjecture,
~ sP5 ).
thf(h1,negated_conjecture,
sP5,
inference(assume_negation,[status(cth)],[cBUGWFFA_pme]) ).
thf(1,plain,
~ sP2,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP3
| sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(3,plain,
( sP4
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP1
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,h1]) ).
thf(7,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[6,h0]) ).
thf(0,theorem,
~ sP5,
inference(contra,[status(thm),contra(discharge,[h1])],[6,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU967^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n025.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 : Mon Jun 20 00:56:29 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: 53
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------