TSTP Solution File: SEU610^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU610^2 : 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 : n002.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 17:19:41 EDT 2023
% Result : Theorem 1.54s 1.72s
% Output : Proof 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 61
% Syntax : Number of formulae : 73 ( 22 unt; 7 typ; 5 def)
% Number of atoms : 188 ( 31 equ; 1 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 295 ( 33 ~; 21 |; 0 &; 157 @)
% ( 21 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 31 con; 0-2 aty)
% Number of variables : 79 ( 15 ^; 64 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_setminus,type,
setminus: $i > $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ( setminus @ eigen__0 @ eigen__1 )
= emptyset ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( in @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__2 @ eigen__0 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__2 @ emptyset )
=> ! [X1: $o] : X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP2
=> ( subset @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $o] : X2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ eigen__2 @ ( setminus @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $o] : X1 ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP3
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( subset @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP15
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> $false ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( in @ eigen__2 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(def_emptysetE,definition,
( emptysetE
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( in @ X1 @ emptyset )
@ sP9 ) ) ) ).
thf(def_in__Cong,definition,
( in__Cong
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( X1 = X2 )
@ ! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X3 = X4 )
@ ( ( in @ X3 @ X1 )
<=> ( in @ X4 @ X2 ) ) ) ) ) ) ).
thf(def_subsetI2,definition,
( subsetI2
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) )
@ ( subset @ X1 @ X2 ) ) ) ) ).
thf(def_setminusI,definition,
( setminusI
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( (~) @ ( in @ X3 @ X2 ) )
@ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ).
thf(setminusSubset1,conjecture,
( sP7
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP19
=> ( sP11
=> ! [X1: $i,X2: $i] :
( ( ( setminus @ X1 @ X2 )
= emptyset )
=> ( subset @ X1 @ X2 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP7
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP19
=> ( sP11
=> ! [X1: $i,X2: $i] :
( ( ( setminus @ X1 @ X2 )
= emptyset )
=> ( subset @ X1 @ X2 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setminusSubset1]) ).
thf(h2,assumption,
sP7,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP19
=> ( sP11
=> ! [X1: $i,X2: $i] :
( ( ( setminus @ X1 @ X2 )
= emptyset )
=> ( subset @ X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP19
=> ( sP11
=> ! [X1: $i,X2: $i] :
( ( ( setminus @ X1 @ X2 )
= emptyset )
=> ( subset @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP19,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP11
=> ! [X1: $i,X2: $i] :
( ( ( setminus @ X1 @ X2 )
= emptyset )
=> ( subset @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP11,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i,X2: $i] :
( ( ( setminus @ X1 @ X2 )
= emptyset )
=> ( subset @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( ( setminus @ eigen__0 @ X1 )
= emptyset )
=> ( subset @ eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP1
=> sP14 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| sP20
| ~ sP1
| sP18 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| sP3
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP17
| ~ sP15
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| ~ sP20
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP13
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP4
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP4
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP2
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(10,plain,
( ~ sP6
| ~ sP2
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP16
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
~ sP18,
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP9
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP11
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP19
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h2,h6,h8,h12,h13]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,17,h12,h13]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__1)],[h10,18,h11]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__0)],[h9,19,h10]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,20,h8,h9]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,21,h6,h7]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,22,h4,h5]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,23,h2,h3]) ).
thf(25,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[24,h0]) ).
thf(0,theorem,
( sP7
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP19
=> ( sP11
=> ! [X1: $i,X2: $i] :
( ( ( setminus @ X1 @ X2 )
= emptyset )
=> ( subset @ X1 @ X2 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[24,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU610^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 22:25:16 EDT 2023
% 0.14/0.35 % CPUTime :
% 1.54/1.72 % SZS status Theorem
% 1.54/1.72 % Mode: cade22grackle2xfee4
% 1.54/1.72 % Steps: 45131
% 1.54/1.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------