TSTP Solution File: SEU678^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU678^2 : 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 : n010.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 13:56:22 EDT 2022
% Result : Theorem 0.56s 0.78s
% Output : Proof 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 121
% Syntax : Number of formulae : 138 ( 34 unt; 13 typ; 9 def)
% Number of atoms : 463 ( 104 equ; 54 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1273 ( 117 ~; 46 |; 0 &; 906 @)
% ( 43 <=>; 161 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 65 usr; 59 con; 0-3 aty)
% Number of variables : 219 ( 93 ^ 126 !; 0 ?; 219 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cartprod,type,
cartprod: $i > $i > $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( eigen__2 @ X2 ) ) ) )
=> ( X1
= ( eigen__2 @ eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ ( eigen__2 @ X1 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__2 @ eigen__3 )
= ( eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $i > $o] : ( subset @ ( dpsetconstr @ eigen__0 @ eigen__1 @ X1 ) @ ( cartprod @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( in @ ( kpair @ eigen__3 @ eigen__4 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5
=> ( eigen__4
= ( eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $i > $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ eigen__0 @ eigen__1 @ X1 ) )
=> ( X1 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( X3 @ X4 @ X5 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X1 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( dpsetconstr @ eigen__0 @ X1 @ X2 ) )
=> ( X2 @ X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( in @ eigen__4 @ eigen__1 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( in @ ( eigen__2 @ eigen__3 ) @ eigen__1 )
=> ( sP2
=> ( in @ ( kpair @ eigen__3 @ ( eigen__2 @ eigen__3 ) )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( eigen__2 @ X2 ) ) ) )
=> ( ( eigen__2 @ eigen__3 )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( dpsetconstr @ eigen__0 @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X4 )
=> ( X4 = X3 ) ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
=> ( ( dsetconstr @ X1 @ X2 )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP5
=> ( ( eigen__2 @ eigen__3 )
= eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( in @ eigen__4 @ eigen__1 )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( in @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( in @ ( eigen__2 @ eigen__3 ) @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ ( eigen__2 @ eigen__3 ) )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( eigen__2 @ X2 ) ) ) )
=> ( X1
= ( eigen__2 @ eigen__3 ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( in @ ( kpair @ eigen__3 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X3: $i] : ( (=) @ ( eigen__2 @ X3 ) ) ) ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( in @ ( kpair @ eigen__3 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X3: $i] : ( (=) @ ( eigen__2 @ X3 ) ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ ( dsetconstr @ eigen__1 @ X1 ) )
=> ( ( dsetconstr @ eigen__1 @ X1 )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__4
= ( eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( in @ ( kpair @ eigen__3 @ ( eigen__2 @ eigen__3 ) )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X3: $i] : ( (=) @ ( eigen__2 @ X3 ) ) ) )
=> ( ( eigen__2 @ X1 )
= X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( in @ ( kpair @ eigen__3 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X3: $i] : ( (=) @ ( eigen__2 @ X3 ) ) ) ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X2: $i] :
( in @ ( kpair @ eigen__3 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X3: $i] : ( (=) @ ( eigen__2 @ X3 ) ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( in @ ( eigen__2 @ eigen__3 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i > $i > $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( ( X1 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ eigen__0 @ eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP2
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP22
=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( eigen__2 @ X2 ) ) ) )
=> ( X1
= ( eigen__2 @ eigen__3 ) ) ) )
=> ~ sP24 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP6
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( ( eigen__2 @ eigen__3 )
= X1 )
=> ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( eigen__2 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X1 @ X2 @ X3 ) )
=> ( X3 @ X4 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( ( eigen__2 @ eigen__3 )
= eigen__4 )
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( ( eigen__2 @ eigen__3 )
= X1 )
=> ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( eigen__2 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( subset
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) )
@ ( cartprod @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i,X2: $i > $i > $o] : ( subset @ ( dpsetconstr @ eigen__0 @ X1 @ X2 ) @ ( cartprod @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( ( eigen__2 @ eigen__3 )
= X1 )
=> ( X1
= ( eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP6
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( eigen__2 @ X2 ) ) ) )
=> ( X1
= ( eigen__2 @ eigen__3 ) ) ) )
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( eigen__2 @ X2 ) ) ) )
=> ( X1
= ( eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP6
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i,X2: $i,X3: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1 @ X2 @ X3 ) @ ( cartprod @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( eigen__2 @ eigen__3 )
= eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( ( eigen__2 @ X1 )
= X2 )
=> ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X3: $i] : ( (=) @ ( eigen__2 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( eigen__2 @ X2 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X3: $i] : ( (=) @ ( eigen__2 @ X3 ) ) ) )
=> ( X2 = X1 ) ) )
=> ~ sP24 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).
thf(def_ex1,definition,
( ex1
= ( ^ [X1: $i,X2: $i > $o] : ( singleton @ ( dsetconstr @ X1 @ X2 ) ) ) ) ).
thf(def_ex1I,definition,
( ex1I
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X4 )
=> ( X4 = X3 ) ) )
=> ( ex1 @ X1 @ X2 ) ) ) ) ) ) ).
thf(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_dpsetconstrI,definition,
dpsetconstrI = sP9 ).
thf(def_setOfPairsIsBReln,definition,
( setOfPairsIsBReln
= ( ! [X1: $i,X2: $i,X3: $i > $i > $o] : ( breln @ X1 @ X2 @ ( dpsetconstr @ X1 @ X2 @ X3 ) ) ) ) ).
thf(def_dpsetconstrERa,definition,
dpsetconstrERa = sP30 ).
thf(def_func,definition,
( func
= ( ^ [X1: $i,X2: $i,X3: $i] :
~ ( ( breln @ X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ex1 @ X2
@ ^ [X5: $i] : ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) ) ) ).
thf(lamProp,conjecture,
( sP15
=> ( sP9
=> ( sP40
=> ( sP30
=> ! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ~ ( ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
@ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP15
=> ( sP9
=> ( sP40
=> ( sP30
=> ! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ~ ( ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
@ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[lamProp]) ).
thf(h2,assumption,
sP15,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP9
=> ( sP40
=> ( sP30
=> ! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ~ ( ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
@ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP9,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP40
=> ( sP30
=> ! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ~ ( ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
@ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP40,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP30
=> ! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ~ ( ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
@ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP30,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ~ ( ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
@ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ~ ( ( subset
@ ( dpsetconstr @ eigen__0 @ X1
@ ^ [X3: $i] : ( (=) @ ( X2 @ X3 ) ) )
@ ( cartprod @ eigen__0 @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( in @ ( kpair @ X3 @ X5 )
@ ( dpsetconstr @ eigen__0 @ X1
@ ^ [X6: $i] : ( (=) @ ( X2 @ X6 ) ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( in @ ( kpair @ X3 @ X5 )
@ ( dpsetconstr @ eigen__0 @ X1
@ ^ [X6: $i] : ( (=) @ ( X2 @ X6 ) ) ) ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in @ ( X1 @ X2 ) @ eigen__1 ) )
=> ~ ( ( subset
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( X1 @ X2 ) ) )
@ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__1
@ ^ [X4: $i] :
( in @ ( kpair @ X2 @ X4 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X5: $i] : ( (=) @ ( X1 @ X5 ) ) ) ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X4: $i] :
( in @ ( kpair @ X2 @ X4 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X5: $i] : ( (=) @ ( X1 @ X5 ) ) ) ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP1
=> ~ ( sP33
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( in @ ( kpair @ X1 @ X3 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X4: $i] : ( (=) @ ( eigen__2 @ X4 ) ) ) ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( in @ ( kpair @ X1 @ X3 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X4: $i] : ( (=) @ ( eigen__2 @ X4 ) ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
( sP33
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( in @ ( kpair @ X1 @ X3 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X4: $i] : ( (=) @ ( eigen__2 @ X4 ) ) ) ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( in @ ( kpair @ X1 @ X3 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X4: $i] : ( (=) @ ( eigen__2 @ X4 ) ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP33,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( in @ ( kpair @ X1 @ X3 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X4: $i] : ( (=) @ ( eigen__2 @ X4 ) ) ) ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X3: $i] :
( in @ ( kpair @ X1 @ X3 )
@ ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X4: $i] : ( (=) @ ( eigen__2 @ X4 ) ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP40
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP34
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h13,h14,h12,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,h6,h15]) ).
thf(h17,assumption,
~ ( sP6
=> ~ sP24 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP6,
introduced(assumption,[]) ).
thf(h19,assumption,
sP24,
introduced(assumption,[]) ).
thf(5,plain,
( ~ sP31
| ~ sP41
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP35
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP4
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
sP4,
inference(eq_sym,[status(thm)],]) ).
thf(9,plain,
( ~ sP30
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP8
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP23
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP39
| ~ sP6
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP13
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP17
| ~ sP18
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| ~ sP5
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP7
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP7
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP11
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP11
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
sP2,
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP38
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(23,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP14
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP26
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP42
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP29
| ~ sP6
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP32
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP12
| ~ sP25
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP27
| ~ sP2
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP15
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP20
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP43
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP19
| ~ sP25
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP28
| ~ sP22
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP37
| ~ sP38
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP1
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP36
| ~ sP6
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h17,h16,h13,h14,h12,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,h2,h4,h8,h13,h18,h19]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h16,h13,h14,h12,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,39,h18,h19]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h13,h14,h12,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__3)],[h16,40,h17]) ).
thf(42,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h12,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h14,4,41,h15,h16]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,42,h13,h14]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h11,43,h12]) ).
thf(45,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)],[h10,44,h11]) ).
thf(46,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)],[h9,45,h10]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,46,h8,h9]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,47,h6,h7]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,48,h4,h5]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,49,h2,h3]) ).
thf(51,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[50,h0]) ).
thf(0,theorem,
( sP15
=> ( sP9
=> ( sP40
=> ( sP30
=> ! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ~ ( ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
@ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] :
( in @ ( kpair @ X4 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i] : ( (=) @ ( X3 @ X7 ) ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[50,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU678^2 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 08:39:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.56/0.78 % SZS status Theorem
% 0.56/0.78 % Mode: mode213
% 0.56/0.78 % Inferences: 50
% 0.56/0.78 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------