%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV161^5 : 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 : n011.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 02:56:22 PM UTC 2025
% Result : Theorem 0.10s 0.33s
% Output : Proof 0.10s
% Verified :
% SZS Type : Derivation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 28 ( 4 ~; 0 |; 0 &; 24 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(cTHM183_pme,conjecture,
! [X1: a > a > $o,X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X2 @ X3 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > $o,X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X2 @ X3 ) ),
inference(assume_negation,[status(cth)],[cTHM183_pme]) ).
thf(h1,assumption,
~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a] :
( ( eigen__0 @ eigen__1 @ X1 )
= ( eigen__0 @ eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ( eigen__0 @ eigen__1 @ eigen__2 )
!= ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_negrefl,[status(thm),assumptions([h3,h2,h1,h0])],[h3]) ).
thf(2,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,1,h3]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,2,h2]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,3,h1]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X2 @ X3 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SEV161^5 : TPTP v9.2.0. Released v4.0.0.
% 0.08/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.32 % Computer : n011.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Wed Oct 8 18:58:38 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % SZS status Theorem
% 0.10/0.33 % Mode: mode213
% 0.10/0.33 % Inferences: 0
% 0.10/0.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------