TSTP Solution File: SEV385^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV385^5 : 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 : n020.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 19:34:24 EDT 2023
% Result : Theorem 20.47s 20.69s
% Output : Proof 20.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 32
% Syntax : Number of formulae : 39 ( 10 unt; 6 typ; 2 def)
% Number of atoms : 93 ( 37 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 94 ( 42 ~; 15 |; 0 &; 10 @)
% ( 11 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 18 con; 0-2 aty)
% Number of variables : 25 ( 12 ^; 13 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_x,type,
x: b ).
thf(ty_eigen__3,type,
eigen__3: b ).
thf(ty_y,type,
y: a ).
thf(h0,assumption,
! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: b] :
( ( ~ ( ( x = X1 )
=> ( eigen__0 != y ) ) )
!= ( x = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
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: b] :
( ( ^ [X3: b] :
~ ( ( x = X3 )
=> ( X1 != y ) ) )
!= ( ^ [X3: b] : ( X2 = X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( y = X1 )
=> ~ ! [X2: b] :
( ( ^ [X3: b] :
~ ( ( x = X3 )
=> ( X1 != y ) ) )
!= ( ^ [X3: b] : ( X2 = X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 = y ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: b] :
( ( ^ [X2: b] :
~ ( ( x = X2 )
=> ~ sP2 ) )
!= ( ^ [X2: b] : ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( x = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP4
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( y = eigen__0 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: b > a] :
( ! [X2: b] :
( ( x = X2 )
=> ( y
= ( X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ( y = X2 )
=> ~ ! [X3: b] :
( ( ^ [X4: b] :
~ ( ( x = X4 )
=> ( X2
!= ( X1 @ X4 ) ) ) )
!= ( ^ [X4: b] : ( X3 = X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ^ [X1: b] :
~ ( ( x = X1 )
=> ~ sP2 ) )
= ( ^ [X1: b] : ( x = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: b] :
( ( ~ ( ( x = X1 )
=> ~ sP2 ) )
= ( x = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP5 = sP4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( y = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cX6004_pme,conjecture,
~ sP7 ).
thf(h2,negated_conjecture,
sP7,
inference(assume_negation,[status(cth)],[cX6004_pme]) ).
thf(1,plain,
( ~ sP5
| ~ sP4
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP5
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP10
| sP5
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP10
| ~ sP5
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP9
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(6,plain,
( sP8
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| sP2 ),
inference(symeq,[status(thm)],]) ).
thf(9,plain,
( sP6
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP6
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP1
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(12,plain,
( ~ sP7
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[13,h1]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[14,h0]) ).
thf(0,theorem,
~ sP7,
inference(contra,[status(thm),contra(discharge,[h2])],[13,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV385^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 02:05:00 EDT 2023
% 0.13/0.33 % CPUTime :
% 20.47/20.69 % SZS status Theorem
% 20.47/20.69 % Mode: cade22grackle2x798d
% 20.47/20.69 % Steps: 74
% 20.47/20.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------