%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET634^5 : 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 : n010.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 02:26:10 PM UTC 2025
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% 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 : 22 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 100 ( 40 ~; 0 |; 0 &; 36 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 24 ( 12 ^; 12 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(cBOOL_PROP_116_pme,conjecture,
! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ^ [X4: a] :
~ ( ~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) )
=> ( X3 @ X4 ) ) )
= ( ^ [X4: a] :
~ ( ~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) )
=> ( X3 @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ^ [X4: a] :
~ ( ~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) )
=> ( X3 @ X4 ) ) )
= ( ^ [X4: a] :
~ ( ~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) )
=> ( X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_116_pme]) ).
thf(h1,assumption,
~ ! [X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
~ ( ~ ( ( eigen__0 @ X3 )
=> ~ ( X1 @ X3 ) )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] :
~ ( ~ ( ( eigen__0 @ X3 )
=> ~ ( X1 @ X3 ) )
=> ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > $o] :
( ( ^ [X2: a] :
~ ( ~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__1 @ X2 ) )
=> ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
~ ( ~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__1 @ X2 ) )
=> ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ( ^ [X1: a] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) )
=> ( eigen__2 @ X1 ) ) )
!= ( ^ [X1: a] :
~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) )
=> ( eigen__2 @ X1 ) ) ) ),
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 > $o,X2: a > $o,X3: a > $o] :
( ( ^ [X4: a] :
~ ( ~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) )
=> ( X3 @ X4 ) ) )
= ( ^ [X4: a] :
~ ( ~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) )
=> ( X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET634^5 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 14:47:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 0
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------