TSTP Solution File: SEU686^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU686^2 : 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 : n027.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 13:56:36 EDT 2022
% Result : Theorem 1.07s 1.28s
% Output : Proof 1.07s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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_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_ap,type,
ap: $i > $i > $i > $i > $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ ( kpair @ X1 @ ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ X1 ) ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ X1 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( kpair @ X4 @ ( ap @ X1 @ X2 @ X3 @ X4 ) ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ( in @ ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ~ ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in @ ( ap @ eigen__0 @ eigen__1 @ X1 @ X2 ) @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__1
@ ^ [X3: $i] : ( in @ ( kpair @ X1 @ X3 ) @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X3: $i] : ( in @ ( kpair @ X1 @ X3 ) @ eigen__2 ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 )
=> ( ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 )
=> ( X1 = X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 ) ) @ eigen__2 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 )
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 )
= X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ sP7 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) )
!= ( setadjoin @ X1 @ emptyset ) ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ~ ( ( subset @ X2 @ ( cartprod @ eigen__0 @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( in @ ( ap @ eigen__0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ~ ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( in @ ( kpair @ eigen__3 @ ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 ) ) @ eigen__2 )
=> ( sP2
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 )
= eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( ap @ X1 @ X2 @ X3 @ X4 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ( in @ ( kpair @ eigen__3 @ ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 ) ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( sP13
=> ~ sP7 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP13
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i] :
( ~ ( ( subset @ X2 @ ( cartprod @ eigen__0 @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( in @ ( kpair @ X3 @ ( ap @ eigen__0 @ X1 @ X2 @ X3 ) ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X2: $i] : ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__2 ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( in @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ~ ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in @ ( kpair @ X2 @ ( ap @ eigen__0 @ eigen__1 @ X1 @ X2 ) ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 )
= eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( in @ ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 ) @ eigen__1 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i > $o] :
( ~ ! [X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( ( dsetconstr @ X1 @ X2 )
!= ( setadjoin @ X3 @ emptyset ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( in @ ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__1 @ X1 ) )
=> ( ( dsetconstr @ eigen__1 @ X1 )
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP22
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( in @ ( kpair @ eigen__3 @ ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 ) ) @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP2
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
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_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
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(def_app,definition,
( app
= ( ! [X1: $i,X2: $i,X3: $i] :
( ( func @ X1 @ X2 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( ap @ X1 @ X2 @ X3 @ X4 ) @ X2 ) ) ) ) ) ).
thf(def_ex1E2,definition,
( ex1E2
= ( ! [X1: $i,X2: $i > $o] :
( ( ex1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ) ).
thf(def_funcGraphProp1,definition,
( funcGraphProp1
= ( ! [X1: $i,X2: $i,X3: $i] :
( ( func @ X1 @ X2 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( kpair @ X4 @ ( ap @ X1 @ X2 @ X3 @ X4 ) ) @ X3 ) ) ) ) ) ).
thf(funcGraphProp2,conjecture,
( sP16
=> ( sP26
=> ( sP4
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP16
=> ( sP26
=> ( sP4
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcGraphProp2]) ).
thf(h1,assumption,
sP16,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP26
=> ( sP4
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP26,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP4
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( subset @ X2 @ ( cartprod @ eigen__0 @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] : ( in @ ( kpair @ X3 @ X5 ) @ X2 ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ eigen__0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ~ ( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) ) )
=> ( ( dsetconstr @ eigen__1
@ ^ [X4: $i] : ( in @ ( kpair @ X2 @ X4 ) @ X1 ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( ( ap @ eigen__0 @ eigen__1 @ X1 @ X2 )
= X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ sP19
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 )
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ X1 )
= X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 )
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ X1 )
= X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP13,
introduced(assumption,[]) ).
thf(h13,assumption,
sP7,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP28
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 )
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 )
= X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP28,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__2 )
=> ( ( ap @ eigen__0 @ eigen__1 @ eigen__2 @ eigen__3 )
= X1 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP22
=> sP32 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP22,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP32,
introduced(assumption,[]) ).
thf(h20,assumption,
sP2,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP25
| ~ sP27
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP30
| ~ sP22
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP15
| ~ sP31
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP32
| ~ sP2
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP26
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP29
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP21
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP5
| ~ sP28
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP12
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP6
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP18
| sP19
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP1
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP17
| ~ sP28
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP4
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP20
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP23
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP10
| sP19
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP19
| ~ sP13
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP7
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP14
| ~ sP28
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h21,h18,h19,h17,h15,h16,h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,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,h1,h3,h5,h12,h13,h15,h18,h20,h21]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h20,h21])],[h19,25,h20,h21]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,26,h18,h19]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h16,27,h17]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,28,h15,h16]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h11,29,h14]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h10,30,h12,h13]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,31,h10,h11]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,32,h9]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,33,h8]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,34,h7]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,35,h5,h6]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,36,h3,h4]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,37,h1,h2]) ).
thf(0,theorem,
( sP16
=> ( sP26
=> ( sP4
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) ) )
=> ( ( dsetconstr @ X2
@ ^ [X6: $i] : ( in @ ( kpair @ X4 @ X6 ) @ X3 ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[38,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU686^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 03:48:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.07/1.28 % SZS status Theorem
% 1.07/1.28 % Mode: mode213
% 1.07/1.28 % Inferences: 11
% 1.07/1.28 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------