TSTP Solution File: ALG255^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG255^1 : 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 17:57:46 EDT 2022
% Result : Theorem 0.18s 0.45s
% Output : Proof 0.18s
% 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_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: term] :
~ ( var @ ( lam @ X1 ) )
=> ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) )
=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( ( X1 @ X2 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) )
=> ( ! [X1: term > $o] :
( ! [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 ) ) )
=> ! [X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ~ ( ~ ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) )
=> ~ ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) )
=> ~ ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: term > $o] :
( ( X1 @ one )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( ( X1 @ X2 )
=> ( X1 @ ( sub @ X2 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) ) ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) )
=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term,X3: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X3 ) )
=> ( ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) )
=> sP1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) )
=> ( ! [X1: term,X2: term,X3: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X3 ) )
=> ( ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) )
=> sP1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: term,X2: subst] :
( ( sub @ ( lam @ X1 ) @ X2 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
=> ( ! [X1: term,X2: subst] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 )
=> ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X1: subst] :
( ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) )
= X1 )
=> ( ( var @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) )
=> sP2 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: term,X2: term,X3: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X3 ) )
=> ( ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) )
=> sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ! [X1: term > $o,X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( ( X1 @ X2 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) )
=> ( ! [X1: term > $o] :
( ! [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 ) ) )
=> ! [X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ~ ( ~ ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) )
=> ~ ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) )
=> ~ ( sP6
=> ~ ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ~ ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) )
=> ~ ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) )
=> ~ ( sP6
=> ~ ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP6
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
=> ( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X1: subst] :
( ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) )
= X1 )
=> ( ( var @ one )
=> sP13 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X1: subst] :
( ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) )
= X1 )
=> ( ( var @ one )
=> sP13 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [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 ) ) ) )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ! [X1: term,X2: subst] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 )
=> ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> sP16 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP6
=> ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
=> sP19 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X1: subst] :
( ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) )
= X1 )
=> ( ( var @ one )
=> sP13 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ! [X1: term,X2: subst] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ! [X1: subst] :
( ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) )
= X1 )
=> ( ( var @ one )
=> sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ! [X1: term,X2: term,X3: subst] :
( ( sub @ ( ap @ X1 @ X2 ) @ X3 )
= ( ap @ ( sub @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ! [X1: term > $o] :
( ! [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 ) ) )
=> ! [X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) )
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( var @ one )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(def_axapp,definition,
( axapp
= ( ! [X1: term,X2: term,X3: subst] :
( ( sub @ ( ap @ X1 @ X2 ) @ X3 )
= ( ap @ ( sub @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ) ) ) ).
thf(def_axvarcons,definition,
( axvarcons
= ( ! [X1: term,X2: subst] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 ) ) ) ).
thf(def_axvarid,definition,
axvarid = sP14 ).
thf(def_axabs,definition,
( axabs
= ( ! [X1: term,X2: subst] :
( ( sub @ ( lam @ X1 ) @ X2 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) ) ) ) ).
thf(def_axclos,definition,
axclos = sP6 ).
thf(def_axidl,definition,
( axidl
= ( ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) ) ) ).
thf(def_axshiftcons,definition,
( axshiftcons
= ( ! [X1: term,X2: subst] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 ) ) ) ).
thf(def_axassoc,definition,
( axassoc
= ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) ) ) ) ).
thf(def_axmap,definition,
( axmap
= ( ! [X1: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X1 @ X2 ) @ X3 )
= ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) ) ) ) ).
thf(def_axidr,definition,
( axidr
= ( ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) ) ) ).
thf(def_axvarshift,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ) ).
thf(def_axscons,definition,
( axscons
= ( ! [X1: subst] :
( ( push @ ( sub @ one @ X1 ) @ ( comp @ sh @ X1 ) )
= X1 ) ) ) ).
thf(def_ulamvar1,definition,
( ulamvar1
= ( var @ one ) ) ).
thf(def_ulamvarsh,definition,
( ulamvarsh
= ( ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) ) ) ) ).
thf(def_ulamvarind,definition,
( ulamvarind
= ( ! [X1: term > $o] :
( ( X1 @ one )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( ( X1 @ X2 )
=> ( X1 @ ( sub @ X2 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_apinj1,definition,
( apinj1
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ) ) ).
thf(def_apinj2,definition,
( apinj2
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ).
thf(def_laminj,definition,
( laminj
= ( ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ) ) ).
thf(def_shinj,definition,
( shinj
= ( ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ) ) ).
thf(def_lamnotap,definition,
( lamnotap
= ( ! [X1: term,X2: term,X3: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X3 ) ) ) ) ).
thf(def_apnotvar,definition,
( apnotvar
= ( ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) ) ) ) ).
thf(def_lamnotvar,definition,
( lamnotvar
= ( ! [X1: term] :
~ ( var @ ( lam @ X1 ) ) ) ) ).
thf(def_induction,definition,
( induction
= ( ! [X1: term > $o] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X1 @ X2 ) )
=> ( ! [X2: term,X3: term] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X1 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( lam @ X2 ) ) )
=> ( !! @ X1 ) ) ) ) ) ) ).
thf(def_pushprop,definition,
( pushprop
= ( ! [X1: term > $o,X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( ( X1 @ X2 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) ) ) ) ).
thf(def_induction2lem,definition,
( induction2lem
= ( ! [X1: term > $o] :
( ! [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 ) ) )
=> ! [X2: term,X3: subst] :
( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ( X1 @ ( sub @ X2 @ X3 ) ) ) ) ) ) ) ).
thf(def_induction2,definition,
( induction2
= ( ! [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 ) ) ) ) ) ) ).
thf(def_substmonoid,definition,
( substmonoid
= ( ~ ( ~ ( ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
=> ~ ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) )
=> ~ ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) ) ) ) ).
thf(def_termmset,definition,
( termmset
= ( ~ sP15 ) ) ).
thf(def_termmset_gthm,definition,
( termmset_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm,conjecture,
sP25 ).
thf(h0,negated_conjecture,
~ sP25,
inference(assume_negation,[status(cth)],[thm]) ).
thf(1,plain,
( ~ sP15
| ~ sP6
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP12
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP18
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP29
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP11
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP26
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP1
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP7
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP5
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP9
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP3
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP8
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP27
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP2
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP13
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP30
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP24
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP22
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP17
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP16
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP28
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP19
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP21
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP20
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP20
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP4
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP10
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP10
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP23
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP25
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,h0]) ).
thf(0,theorem,
sP25,
inference(contra,[status(thm),contra(discharge,[h0])],[31,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : ALG255^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.09/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Wed Jun 8 14:02:36 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.18/0.45 % SZS status Theorem
% 0.18/0.45 % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 0.18/0.45 % Inferences: 28
% 0.18/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------