TSTP Solution File: ALG269^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG269^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 : Thu Jul 14 17:57:52 EDT 2022
% Result : Theorem 65.92s 66.41s
% Output : Proof 65.92s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subst,type,
subst: $tType ).
thf(ty_term,type,
term: $tType ).
thf(ty_push,type,
push: term > subst > subst ).
thf(ty_eigen__1,type,
eigen__1: term ).
thf(ty_eigen__0,type,
eigen__0: subst > term > subst > $o ).
thf(ty_ap,type,
ap: term > term > term ).
thf(ty_id,type,
id: subst ).
thf(ty_one,type,
one: term ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(ty_lam,type,
lam: term > term ).
thf(ty_sh,type,
sh: subst ).
thf(ty_var,type,
var: term > $o ).
thf(ty_comp,type,
comp: subst > subst > subst ).
thf(sP1,plain,
( sP1
<=> ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ( ! [X2: term] :
( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( X1 @ id @ X2 ) @ id ) )
=> ( eigen__0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__0 @ id @ X1 @ id ) )
=> ! [X1: term] :
( ( var @ X1 )
=> ( eigen__0 @ id @ X1 @ id ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__0 @ id @ X1 @ id ) )
=> ! [X1: term] :
( ( var @ X1 )
=> ( eigen__0 @ id @ X1 @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ! [X3: term] :
( ( X1 @ X3 )
=> ( X1 @ ( sub @ X2 @ ( push @ X3 @ id ) ) ) )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: term] :
( ! [X2: term] :
( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( eigen__0 @ id @ ( lam @ X1 ) @ id ) )
=> ! [X1: term] : ( eigen__0 @ id @ X1 @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: term] :
( ! [X2: term] :
( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( eigen__0 @ id @ ( lam @ X1 ) @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: term] :
( ( var @ X1 )
=> ( eigen__0 @ id @ X1 @ id ) )
=> ( ! [X1: term,X2: term] :
( ( eigen__0 @ id @ X1 @ id )
=> ( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( ap @ X1 @ X2 ) @ id ) ) )
=> sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP8
=> ( ! [X1: term,X2: term] :
( ( eigen__0 @ id @ X1 @ id )
=> ( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) )
=> ! [X1: term,X2: term] :
( ( eigen__0 @ id @ X1 @ id )
=> ( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( ap @ X1 @ X2 ) @ id ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: term] :
( ( var @ X1 )
=> ( eigen__0 @ id @ X1 @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ! [X1: term,X2: term] :
( ( eigen__0 @ id @ X1 @ id )
=> ( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( ap @ X1 @ X2 ) @ id ) ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP12
=> ( sP8
=> ( sP1
=> sP7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP1
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( X1 @ id @ X2 @ id ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP12
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP8
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: term,X2: term] :
( ( eigen__0 @ id @ X1 @ id )
=> ( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ id @ eigen__1 @ id ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: term,X2: term] :
( ( eigen__0 @ id @ X1 @ id )
=> ( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( ap @ X1 @ X2 ) @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP19
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: term] : ( eigen__0 @ id @ X1 @ id ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP12
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( eigen__0 @ id @ X1 @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(def_induction2,definition,
induction2 = sP5 ).
thf(def_hoasap,definition,
( hoasap
= ( ^ [X1: subst,X2: term,X3: subst] : ( ap @ ( sub @ X2 @ X3 ) ) ) ) ).
thf(def_hoaslam,definition,
( hoaslam
= ( ^ [X1: subst,X2: subst > term > term] : ( lam @ ( X2 @ sh @ one ) ) ) ) ).
thf(def_hoasvar,definition,
( hoasvar
= ( ^ [X1: subst,X2: term,X3: subst] : ( var @ ( sub @ X2 @ X3 ) ) ) ) ).
thf(def_hoasinduction_lem1,definition,
( hoasinduction_lem1
= ( ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term] :
( ( hoasvar @ id @ X2 @ id )
=> ( X1 @ id @ X2 @ id ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) ).
thf(def_hoasinduction_lem2,definition,
( hoasinduction_lem2
= ( ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( hoasap @ id @ X2 @ id @ X3 ) @ id ) ) )
=> ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( ap @ X2 @ X3 ) @ id ) ) ) ) ) ) ) ) ).
thf(def_hoasinduction_lem3,definition,
( hoasinduction_lem3
= ( ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( hoaslam @ id @ X2 ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) ) ) ).
thf(def_hoasinduction,definition,
( hoasinduction
= ( ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term] :
( ( hoasvar @ id @ X2 @ id )
=> ( X1 @ id @ X2 @ id ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( hoasap @ id @ X2 @ id @ X3 ) @ id ) ) )
=> ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( hoaslam @ id @ X2 ) @ id ) ) )
=> ! [X2: term] : ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) ) ).
thf(def_hoasinduction_lthm,definition,
( hoasinduction_lthm
= ( induction2
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ) ).
thf(thm,conjecture,
( sP5
=> ( sP16
=> ( sP23
=> ( sP4
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( X1 @ id @ X2 @ id ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] : ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP5
=> ( sP16
=> ( sP23
=> ( sP4
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( X1 @ id @ X2 @ id ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] : ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP16
=> ( sP23
=> ( sP4
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( X1 @ id @ X2 @ id ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] : ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP16,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP23
=> ( sP4
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( X1 @ id @ X2 @ id ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] : ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP23,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP4
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( X1 @ id @ X2 @ id ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] : ( X1 @ id @ X2 @ id ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP4,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( X1 @ id @ X2 @ id ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] : ( X1 @ id @ X2 @ id ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP12
=> ( sP8
=> ( sP26
=> ( sP19
=> ( sP1
=> sP24 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP12,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP8
=> ( sP26
=> ( sP19
=> ( sP1
=> sP24 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP8,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP26
=> ( sP19
=> ( sP1
=> sP24 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP26,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP19
=> ( sP1
=> sP24 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP19,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP1
=> sP24 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP8
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| ~ sP8
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP18
| ~ sP8
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| ~ sP26
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP22
| ~ sP19
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP15
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| ~ sP12
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP25
| ~ sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| ~ sP12
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP24
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| ~ sP7
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP13
| ~ sP21
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| ~ sP11
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP5
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP16
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP23
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP4
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h1,h3,h5,h7,h10,h12,h14,h16,h18,h20]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__1)],[h19,18,h20]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,19,h18,h19]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,20,h16,h17]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,21,h14,h15]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,22,h12,h13]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,23,h10,h11]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h8,24,h9]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,25,h7,h8]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,26,h5,h6]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,27,h3,h4]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,28,h1,h2]) ).
thf(0,theorem,
( sP5
=> ( sP16
=> ( sP23
=> ( sP4
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( X1 @ id @ X2 @ id ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ id @ X2 @ id )
=> ( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( ap @ ( sub @ X2 @ id ) @ X3 ) @ id ) ) )
=> ( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] : ( X1 @ id @ X2 @ id ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[29,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG269^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.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 : Wed Jun 8 00:19:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.64/0.94 slave returned with unknown status
% 65.92/66.41 % SZS status Theorem
% 65.92/66.41 % Mode: mode438:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 65.92/66.41 % Inferences: 1250
% 65.92/66.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------