TSTP Solution File: SEU633^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU633^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 17:20:11 EDT 2023
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 34
% Syntax : Number of formulae : 43 ( 12 unt; 5 typ; 2 def)
% Number of atoms : 91 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 185 ( 32 ~; 11 |; 0 &; 95 @)
% ( 11 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 17 con; 0-2 aty)
% Number of variables : 40 ( 9 ^; 31 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_setunion,type,
setunion: $i > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ eigen__1 @ X1 )
=> ~ ( in @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__1 @ ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $o] :
( ! [X2: $i] :
( ( in @ eigen__1 @ X2 )
=> ( ( in @ X2 @ eigen__0 )
=> X1 ) )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__1 @ eigen__3 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ! [X3: $o] :
( ! [X4: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X4 @ X1 )
=> X3 ) )
=> X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ eigen__1 @ X1 )
=> ~ ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ( in @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
=> ~ ( in @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ eigen__0 )
=> X2 ) )
=> X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( in @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP1
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(def_setunionE,definition,
( setunionE
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( setunion @ X1 ) )
@ ! [X3: $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X2 @ X4 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ X3 ) )
@ X3 ) ) ) ) ).
thf(setunionE2,conjecture,
( sP5
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ~ ( in @ X2 @ X3 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP5
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ~ ( in @ X2 @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[setunionE2]) ).
thf(h2,assumption,
sP5,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ~ ( in @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( setunion @ eigen__0 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ( in @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP1
=> ~ sP7 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| ~ sP3
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP4
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP4
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP6
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(6,plain,
( ~ sP2
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP11
| ~ sP1
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP5
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,h2,h6,h7]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,10,h6,h7]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,11,h5]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,12,h4]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[14,h0]) ).
thf(0,theorem,
( sP5
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ~ ( in @ X2 @ X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[14,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU633^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 17:52:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % Mode: cade22grackle2xfee4
% 0.19/0.42 % Steps: 175
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------