%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV232^5 : 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 : n009.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 02:56:30 PM UTC 2025
% Result : Theorem 0.21s 0.37s
% Output : Proof 0.21s
% Verified :
% SZS Type : Derivation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 3 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 61 ( 13 ~; 0 |; 0 &; 30 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 18 ( 6 ^; 12 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cS,type,
cS: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(ty_c0,type,
c0: ( $i > $o ) > $o ).
thf(cX6007_pme,conjecture,
( ( ^ [X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ c0 )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) ) )
=> ( X2 @ X1 ) ) )
= ( ^ [X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ c0 )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) ) )
=> ( X2 @ X1 ) ) ) ) ).
thf(h0,negated_conjecture,
( ( ^ [X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ c0 )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) ) )
=> ( X2 @ X1 ) ) )
!= ( ^ [X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ c0 )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[cX6007_pme]) ).
thf(1,plain,
$false,
inference(tab_negrefl,[status(thm),assumptions([h0])],[h0]) ).
thf(0,theorem,
( ( ^ [X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ c0 )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) ) )
=> ( X2 @ X1 ) ) )
= ( ^ [X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ c0 )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEV232^5 : TPTP v9.2.0. Released v4.0.0.
% 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 19:46:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.21/0.37 % SZS status Theorem
% 0.21/0.37 % Mode: mode213
% 0.21/0.37 % Inferences: 0
% 0.21/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------