%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU883^5 : 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 : n024.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 02:52:53 PM UTC 2025
% Result : Theorem 0.12s 0.34s
% Output : Proof 0.12s
% 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 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 31 ( 13 ~; 0 |; 0 &; 12 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 12 ( 6 ^; 6 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_g,type,
g: b > $o ).
thf(ty_f,type,
f: b > a ).
thf(cX5212_pme,conjecture,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ( g @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ^ [X1: a] :
~ ! [X2: b] :
( ( g @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ( g @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) )
!= ( ^ [X1: a] :
~ ! [X2: b] :
( ( g @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cX5212_pme]) ).
thf(1,plain,
$false,
inference(tab_negrefl,[status(thm),assumptions([h0])],[h0]) ).
thf(0,theorem,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ( g @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ^ [X1: a] :
~ ! [X2: b] :
( ( g @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU883^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Oct 8 21:47:23 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.34 % SZS status Theorem
% 0.12/0.34 % Mode: mode213
% 0.12/0.34 % Inferences: 0
% 0.12/0.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------