%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET604^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 02:26:02 PM UTC 2025
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : Derivation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 13 ~; 0 |; 0 &; 10 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 8 ^; 4 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(cBOOL_PROP_75_pme,conjecture,
! [X1: a > $o] :
( ( ^ [X2: a] :
~ ( $false
=> ( X1 @ X2 ) ) )
= ( ^ [X2: a] : $false ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o] :
( ( ^ [X2: a] :
~ ( $false
=> ( X1 @ X2 ) ) )
= ( ^ [X2: a] : $false ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_75_pme]) ).
thf(h1,assumption,
( ( ^ [X1: a] :
~ ( $false
=> ( eigen__0 @ X1 ) ) )
!= ( ^ [X1: a] : $false ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a] :
( ( ~ ( $false
=> ( eigen__0 @ X1 ) ) )
= $false ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ( ~ ( $false
=> ( eigen__0 @ eigen__1 ) ) )
!= $false ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( $false
=> ( eigen__0 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
$false,
introduced(assumption,[]) ).
thf(h6,assumption,
( $false
=> ( eigen__0 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ $false,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( eigen__0 @ eigen__1 ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_false,[status(thm),assumptions([h5,h8,h4,h5,h3,h2,h1,h0])],[h5]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h8])],[h4,1,h5,h8]) ).
thf(h9,assumption,
eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(3,plain,
$false,
inference(tab_false,[status(thm),assumptions([h7,h6,h7,h3,h2,h1,h0])],[h7]) ).
thf(4,plain,
$false,
inference(tab_false,[status(thm),assumptions([h9,h6,h7,h3,h2,h1,h0])],[h7]) ).
thf(5,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h3,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h9])],[h6,3,4,h7,h9]) ).
thf(6,plain,
$false,
inference(tab_be,[status(thm),assumptions([h3,h2,h1,h0]),tab_be(discharge,[h4,h5]),tab_be(discharge,[h6,h7])],[h3,2,5,h4,h5,h6,h7]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,6,h3]) ).
thf(8,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h1,h0]),tab_fe(discharge,[h2])],[h1,7,h2]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,8,h1]) ).
thf(0,theorem,
! [X1: a > $o] :
( ( ^ [X2: a] :
~ ( $false
=> ( X1 @ X2 ) ) )
= ( ^ [X2: a] : $false ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET604^5 : TPTP v9.2.0. Released v4.0.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n027.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 : 300
% 0.13/0.34 % DateTime : Wed Oct 8 14:29:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 0
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------