TSTP Solution File: SEU610^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU610^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 : 600s
% DateTime : Tue Jul 19 13:54:15 EDT 2022
% Result : Theorem 26.14s 26.27s
% Output : Proof 26.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 69
% Syntax : Number of formulae : 76 ( 16 unt; 7 typ; 7 def)
% Number of atoms : 178 ( 19 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 235 ( 36 ~; 32 |; 0 &; 104 @)
% ( 28 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 38 con; 0-2 aty)
% Number of variables : 36 ( 3 ^ 33 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_setminus,type,
setminus: $i > $i > $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__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( ( setminus @ eigen__0 @ X1 )
= emptyset )
=> ( subset @ eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( ( setminus @ X1 @ X2 )
= emptyset )
=> ( subset @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
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
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $o] : X2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( ( setminus @ X1 @ X2 )
= emptyset )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in @ eigen__2 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( in @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> ! [X1: $o] : X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> $false ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP2
=> ( ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
=> sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP5
=> ( in @ eigen__2 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ eigen__2 @ ( setminus @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( setminus @ eigen__0 @ eigen__1 )
= emptyset ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( ( setminus @ eigen__0 @ X1 )
= emptyset )
=> ( subset @ eigen__0 @ X1 ) ) ),
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
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP1
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP14
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP13
=> ( subset @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP11
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( subset @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $o] : X1 ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP11
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP17
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(def_emptysetE,definition,
emptysetE = sP1 ).
thf(def_in__Cong,definition,
( in__Cong
= ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ) ) ).
thf(def_subsetI2,definition,
subsetI2 = sP2 ).
thf(def_setminusI,definition,
setminusI = sP14 ).
thf(setminusSubset1,conjecture,
sP19 ).
thf(h1,negated_conjecture,
~ sP19,
inference(assume_negation,[status(cth)],[setminusSubset1]) ).
thf(1,plain,
( ~ sP12
| sP4
| ~ sP7
| ~ sP13 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP26
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP25
| ~ sP11
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP5
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP6
| ~ sP4
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
sP7,
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP14
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP28
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
~ sP8,
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP22
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP22
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP17
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(14,plain,
( ~ sP24
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP2
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP27
| ~ sP17
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP21
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP21
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP15
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(21,plain,
( sP3
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(22,plain,
( sP20
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP20
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP9
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP9
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP18
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP19
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP19
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,h1]) ).
thf(30,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[29,h0]) ).
thf(0,theorem,
sP19,
inference(contra,[status(thm),contra(discharge,[h1])],[29,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU610^2 : TPTP v8.1.0. Released v3.7.0.
% 0.13/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n014.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 : 600
% 0.13/0.34 % DateTime : Mon Jun 20 07:29:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 26.14/26.27 % SZS status Theorem
% 26.14/26.27 % Mode: mode454
% 26.14/26.27 % Inferences: 682
% 26.14/26.27 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------