%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV122^5 : 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 : n002.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 02:56:18 PM UTC 2025
% Result : Theorem 0.15s 0.37s
% Output : Proof 0.15s
% Verified :
% SZS Type : Derivation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 5 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 143 ( 43 ~; 0 |; 0 &; 70 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 67 ( 20 ^; 47 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__1,type,
eigen__1: ( a > a > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: ( a > a > $o ) > $o ).
thf(cTHM530_pme,conjecture,
! [X1: ( a > a > $o ) > $o,X2: ( a > a > $o ) > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ~ ! [X8: a > a > $o] :
~ ( X8 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( X1 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ~ ! [X8: a > a > $o] :
~ ( X8 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( X1 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: ( a > a > $o ) > $o,X2: ( a > a > $o ) > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ~ ! [X8: a > a > $o] :
~ ( X8 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( X1 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ~ ! [X8: a > a > $o] :
~ ( X8 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( X1 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM530_pme]) ).
thf(h1,assumption,
~ ! [X1: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
~ ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ~ ! [X7: a > a > $o] :
~ ( X7 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ( eigen__0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
~ ( X6 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
!= ( ^ [X1: a,X2: a] :
! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ~ ! [X6: a > a > $o] :
~ ( X6 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_negrefl,[status(thm),assumptions([h2,h1,h0])],[h2]) ).
thf(2,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,1,h2]) ).
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: ( a > a > $o ) > $o,X2: ( a > a > $o ) > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ~ ! [X8: a > a > $o] :
~ ( X8 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( X1 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ~ ! [X8: a > a > $o] :
~ ( X8 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ( X1 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV122^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.35 % Computer : n002.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Oct 8 19:40:23 EDT 2025
% 0.15/0.35 % CPUTime :
% 0.15/0.37 % SZS status Theorem
% 0.15/0.37 % Mode: mode213
% 0.15/0.37 % Inferences: 0
% 0.15/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------