TSTP Solution File: SEV228^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV228^5 : 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 : n032.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 18:05:27 EDT 2022
% Result : Theorem 1.92s 2.13s
% Output : Proof 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 28 ( 8 unt; 4 typ; 2 def)
% Number of atoms : 53 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 83 ( 18 ~; 9 |; 0 &; 31 @)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 15 ( 2 ^ 13 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cS,type,
cS: a > $o ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: a] :
~ ( ( cS @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cS @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ( ( cS @ X1 )
=> ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ( cS @ eigen__0 )
=> ~ ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cS @ X2 ) )
=> ~ ( X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cS @ eigen__2 )
=> ( cS @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: a] :
( ( cS @ X1 )
=> ( cS @ X1 ) )
=> ~ ( cS @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( cS @ X1 )
=> ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cS @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cS @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( cS @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cS @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cS @ X2 ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(cTHM91A_pme,conjecture,
sP7 ).
thf(h1,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[cTHM91A_pme]) ).
thf(1,plain,
( sP2
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP2
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP4
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(4,plain,
( ~ sP3
| ~ sP4
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP1
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP1
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP7
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
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
% 0.02/0.08 % Problem : SEV228^5 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.09 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Tue Jun 28 17:09:12 EDT 2022
% 0.07/0.27 % CPUTime :
% 1.92/2.13 % SZS status Theorem
% 1.92/2.13 % Mode: mode506
% 1.92/2.13 % Inferences: 38897
% 1.92/2.13 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------