TSTP Solution File: SEV179^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV179^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n009.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 18:05:14 EDT 2022
% Result : Theorem 1.99s 2.17s
% Output : Proof 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 17 ( 9 unt; 1 typ; 2 def)
% Number of atoms : 36 ( 15 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 104 ( 39 ~; 4 |; 0 &; 44 @)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 10 ^ 14 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i ).
thf(h0,assumption,
! [X1: ( ( $i > $o ) > $i ) > $o,X2: ( $i > $o ) > $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: ( $i > $o ) > $i] :
~ ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
=> ( X3
!= ( X1 @ X4 ) ) ) )
!= ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ( ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
!= ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: ( $i > $o ) > $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
=> ( X3
!= ( X1 @ X4 ) ) ) )
!= ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(def_cD_FOR_X5309,definition,
( cD_FOR_X5309
= ( ^ [X1: ( $i > $o ) > $i,X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( X1 @ X3 ) )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ) ).
thf(cTHM144C_pme,conjecture,
sP3 ).
thf(h1,negated_conjecture,
~ sP3,
inference(assume_negation,[status(cth)],[cTHM144C_pme]) ).
thf(1,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP1
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP3
| sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,h1]) ).
thf(6,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[5,h0]) ).
thf(0,theorem,
sP3,
inference(contra,[status(thm),contra(discharge,[h1])],[5,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV179^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n009.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 : Tue Jun 28 07:01:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.99/2.17 % SZS status Theorem
% 1.99/2.17 % Mode: mode506
% 1.99/2.17 % Inferences: 5
% 1.99/2.17 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------