TSTP Solution File: SEU920^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU920^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n025.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 Aug 31 17:37:53 EDT 2023
% Result : Theorem 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 30 ( 11 unt; 7 typ; 1 def)
% Number of atoms : 37 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 73 ( 33 ~; 3 |; 0 &; 27 @)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 34 ( 1 ^; 33 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_c,type,
c: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__1,type,
eigen__1: b > c ).
thf(ty_eigen__2,type,
eigen__2: c ).
thf(ty_eigen__0,type,
eigen__0: a > b ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
( ( eigen__1 @ ( eigen__0 @ X1 ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: c] :
~ ! [X2: a] :
( ( eigen__1 @ ( eigen__0 @ X2 ) )
!= X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( eigen__1 @ ( eigen__0 @ X1 ) )
!= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: b] :
( ( eigen__1 @ X1 )
!= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 @ ( eigen__0 @ eigen__3 ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(cFN_THM_4_pme,conjecture,
! [X1: a > b,X2: b > c] :
( ! [X3: c] :
~ ! [X4: a] :
( ( X2 @ ( X1 @ X4 ) )
!= X3 )
=> ! [X3: c] :
~ ! [X4: b] :
( ( X2 @ X4 )
!= X3 ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: a > b,X2: b > c] :
( ! [X3: c] :
~ ! [X4: a] :
( ( X2 @ ( X1 @ X4 ) )
!= X3 )
=> ! [X3: c] :
~ ! [X4: b] :
( ( X2 @ X4 )
!= X3 ) ),
inference(assume_negation,[status(cth)],[cFN_THM_4_pme]) ).
thf(h2,assumption,
~ ! [X1: b > c] :
( ! [X2: c] :
~ ! [X3: a] :
( ( X1 @ ( eigen__0 @ X3 ) )
!= X2 )
=> ! [X2: c] :
~ ! [X3: b] :
( ( X1 @ X3 )
!= X2 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP1
=> ! [X1: c] :
~ ! [X2: b] :
( ( eigen__1 @ X2 )
!= X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: c] :
~ ! [X2: b] :
( ( eigen__1 @ X2 )
!= X1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( sP2
| sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(3,plain,
( ~ sP1
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0])],[1,2,3,h4,h6]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,4,h6]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,5,h4,h5]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,6,h3]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,7,h2]) ).
thf(9,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[8,h0]) ).
thf(0,theorem,
! [X1: a > b,X2: b > c] :
( ! [X3: c] :
~ ! [X4: a] :
( ( X2 @ ( X1 @ X4 ) )
!= X3 )
=> ! [X3: c] :
~ ! [X4: b] :
( ( X2 @ X4 )
!= X3 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[8,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU920^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 18:53:05 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.42 % SZS status Theorem
% 0.22/0.42 % Mode: cade22grackle2xfee4
% 0.22/0.42 % Steps: 22
% 0.22/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------