TSTP Solution File: SEV239^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV239^5 : 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 : n007.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 19:33:04 EDT 2023
% Result : Theorem 60.26s 60.60s
% Output : Proof 60.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 39
% Syntax : Number of formulae : 47 ( 11 unt; 5 typ; 3 def)
% Number of atoms : 121 ( 33 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 128 ( 45 ~; 20 |; 0 &; 31 @)
% ( 15 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 20 con; 0-2 aty)
% Number of variables : 32 ( 15 ^; 17 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_y,type,
y: a > $o ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ! [X2: a] :
( ( y @ X2 )
=> ( X1
!= ( ^ [X3: a] : ( X2 = X3 ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a] :
( ( y @ X1 )
!= ( ~ ! [X2: a > $o] :
( ~ ! [X3: a] :
( ( y @ X3 )
=> ( X2
!= ( ^ [X4: a] : ( X3 = X4 ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a] :
~ ( ( y @ X1 )
=> ( eigen__1
!= ( ^ [X2: a] : ( X1 = X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( y @ X2 )
=> ( X1
!= ( ^ [X3: a] : ( X2 = X3 ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__1 @ eigen__0 )
= ( eigen__2 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( y @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
= ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( y @ eigen__2 )
=> ( eigen__1
!= ( ^ [X1: a] : ( eigen__2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( y @ X1 )
=> ( eigen__1
!= ( ^ [X2: a] : ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( y @ X1 )
= ( ~ ! [X2: a > $o] :
( ~ ! [X3: a] :
( ( y @ X3 )
=> ( X2
!= ( ^ [X4: a] : ( X3 = X4 ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( y
= ( ^ [X1: a] :
~ ! [X2: a > $o] :
( ~ ! [X3: a] :
( ( y @ X3 )
=> ( X2
!= ( ^ [X4: a] : ( X3 = X4 ) ) ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP7
=> ~ ( eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__1
= ( ^ [X1: a] : ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( y @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP3 = ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( y @ X1 )
=> ( ( ^ [X2: a] : ( eigen__0 = X2 ) )
!= ( ^ [X2: a] : ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cX5211_pme,conjecture,
sP9 ).
thf(h2,negated_conjecture,
~ sP9,
inference(assume_negation,[status(cth)],[cX5211_pme]) ).
thf(1,plain,
( ~ sP15
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| ~ sP11
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP13
| sP3
| ~ sP5 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP12
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP6
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP6
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP7
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(10,plain,
( sP10
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP10
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP1
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(13,plain,
( sP14
| ~ sP3
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP14
| sP3
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP8
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(16,plain,
( sP9
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h2]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[17,h1]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
sP9,
inference(contra,[status(thm),contra(discharge,[h2])],[17,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV239^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 03:06:40 EDT 2023
% 0.13/0.35 % CPUTime :
% 60.26/60.60 % SZS status Theorem
% 60.26/60.60 % Mode: cade22grackle2x34cb
% 60.26/60.60 % Steps: 356
% 60.26/60.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------