%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET062^6 : TPTP v9.2.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 : 300s
% DateTime : Thu Oct 9 02:25:13 PM UTC 2025
% Result : Theorem 0.14s 0.35s
% Output : Proof 0.14s
% Verified :
% SZS Type : Derivation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 3 ~; 0 |; 0 &; 5 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 2 usr; 2 con; 0-1 aty)
% Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cA,type,
cA: $i > $o ).
thf(cSET76_pme,conjecture,
! [X1: $i] :
( $false
=> ( cA @ X1 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( $false
=> ( cA @ X1 ) ),
inference(assume_negation,[status(cth)],[cSET76_pme]) ).
thf(h1,assumption,
~ ( $false
=> ( cA @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
$false,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( cA @ eigen__0 ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_false,[status(thm),assumptions([h2,h3,h1,h0])],[h2]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,1,h2,h3]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,2,h1]) ).
thf(0,theorem,
! [X1: $i] :
( $false
=> ( cA @ X1 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET062^6 : TPTP v9.2.0. Released v5.1.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 14:37:53 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % SZS status Theorem
% 0.14/0.35 % Mode: mode213
% 0.14/0.35 % Inferences: 0
% 0.14/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------