TSTP Solution File: ALG267^1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG267^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.4SPPaKOaaW true
% Computer : n006.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 : 300s
% DateTime : Wed Aug 30 17:12:36 EDT 2023
% Result : Theorem 1.63s 0.90s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 137
% Syntax : Number of formulae : 149 ( 94 unt; 53 typ; 0 def)
% Number of atoms : 468 ( 244 equ; 0 cnn)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 1906 ( 29 ~; 0 |; 12 &;1481 @)
% ( 0 <=>; 384 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 115 ( 115 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 43 con; 0-4 aty)
% Number of variables : 590 ( 45 ^; 541 !; 4 ?; 590 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(axmap_type,type,
axmap: $o ).
thf(axclos_type,type,
axclos: $o ).
thf(lam_type,type,
lam: term > term ).
thf(lamnotap_type,type,
lamnotap: $o ).
thf(axvarcons_type,type,
axvarcons: $o ).
thf(substmonoid_type,type,
substmonoid: $o ).
thf(push_type,type,
push: term > subst > subst ).
thf(axshiftcons_type,type,
axshiftcons: $o ).
thf(hoasapinj1_type,type,
hoasapinj1: $o ).
thf(axapp_type,type,
axapp: $o ).
thf(shinj_type,type,
shinj: $o ).
thf(hoasap_type,type,
hoasap: subst > term > subst > term > term ).
thf(hoasinduction_lem3b_type,type,
hoasinduction_lem3b: $o ).
thf(hoaslaminj_type,type,
hoaslaminj: $o ).
thf(one_type,type,
one: term ).
thf(sk__171_type,type,
sk__171: term ).
thf(id_type,type,
id: subst ).
thf(comp_type,type,
comp: subst > subst > subst ).
thf(hoaslamnotap_type,type,
hoaslamnotap: $o ).
thf(induction2_type,type,
induction2: $o ).
thf(axvarid_type,type,
axvarid: $o ).
thf(axvarshift_type,type,
axvarshift: $o ).
thf(induction2lem_type,type,
induction2lem: $o ).
thf(sh_type,type,
sh: subst ).
thf(laminj_type,type,
laminj: $o ).
thf(ulamvarind_type,type,
ulamvarind: $o ).
thf(apinj2_type,type,
apinj2: $o ).
thf(ulamvarsh_type,type,
ulamvarsh: $o ).
thf(lamnotvar_type,type,
lamnotvar: $o ).
thf(apnotvar_type,type,
apnotvar: $o ).
thf(pushprop_type,type,
pushprop: $o ).
thf(sub_type,type,
sub: term > subst > term ).
thf(apinj1_type,type,
apinj1: $o ).
thf(axidl_type,type,
axidl: $o ).
thf(ap_type,type,
ap: term > term > term ).
thf(termmset_type,type,
termmset: $o ).
thf(hoasapinj2_type,type,
hoasapinj2: $o ).
thf(hoasinduction_lem1_type,type,
hoasinduction_lem1: $o ).
thf(hoasapnotvar_type,type,
hoasapnotvar: $o ).
thf(var_type,type,
var: term > $o ).
thf(axassoc_type,type,
axassoc: $o ).
thf(hoaslamnotvar_type,type,
hoaslamnotvar: $o ).
thf(hoaslam_type,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(hoasinduction_lem3b_gthm_type,type,
hoasinduction_lem3b_gthm: $o ).
thf(hoasinduction_lem2_type,type,
hoasinduction_lem2: $o ).
thf(axidr_type,type,
axidr: $o ).
thf(axabs_type,type,
axabs: $o ).
thf(hoasvar_type,type,
hoasvar: subst > term > subst > $o ).
thf(ulamvar1_type,type,
ulamvar1: $o ).
thf(induction_type,type,
induction: $o ).
thf(axscons_type,type,
axscons: $o ).
thf(hoasinduction_lem3b_gthm,axiom,
( hoasinduction_lem3b_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
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf('0',plain,
( hoasinduction_lem3b_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
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(hoasinduction_lem3b,axiom,
( hoasinduction_lem3b
= ( ! [B: term] :
? [F: subst > term > term] :
( ( sub @ B @ ( push @ one @ sh ) )
= ( F @ sh @ one ) ) ) ) ).
thf('1',plain,
( hoasinduction_lem3b
= ( ! [X4: term] :
? [X6: subst > term > term] :
( ( sub @ X4 @ ( push @ one @ sh ) )
= ( X6 @ sh @ one ) ) ) ),
define([status(thm)]) ).
thf(hoasinduction_lem2,axiom,
( hoasinduction_lem2
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ) ) ).
thf('2',plain,
( hoasinduction_lem2
= ( ! [X4: subst > term > subst > $o] :
( ! [X6: subst,X8: term,X10: subst,X12: subst] :
( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) )
=> ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) )
=> ( ! [X14: subst,X16: term,X18: subst,X20: subst] :
( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 )
=> ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) )
=> ( ! [X22: term,X24: term] :
( ( X4 @ id @ X22 @ id )
=> ( ( X4 @ id @ X24 @ id )
=> ( X4 @ id @ ( hoasap @ id @ X22 @ id @ X24 ) @ id ) ) )
=> ! [X26: term,X28: term] :
( ( X4 @ id @ X26 @ id )
=> ( ( X4 @ id @ X28 @ id )
=> ( X4 @ id @ ( ap @ X26 @ X28 ) @ id ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(hoasinduction_lem1,axiom,
( hoasinduction_lem1
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ id @ A @ id ) ) ) ) ) ) ) ).
thf('3',plain,
( hoasinduction_lem1
= ( ! [X4: subst > term > subst > $o] :
( ! [X6: subst,X8: term,X10: subst,X12: subst] :
( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) )
=> ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) )
=> ( ! [X14: subst,X16: term,X18: subst,X20: subst] :
( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 )
=> ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) )
=> ( ! [X22: term] :
( ( hoasvar @ id @ X22 @ id )
=> ( X4 @ id @ X22 @ id ) )
=> ! [X24: term] :
( ( var @ X24 )
=> ( X4 @ id @ X24 @ id ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(hoasapnotvar,axiom,
( hoasapnotvar
= ( ! [A: term,B: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ) ).
thf('4',plain,
( hoasapnotvar
= ( ! [X4: term,X6: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X4 @ id @ X6 ) @ id ) ) ),
define([status(thm)]) ).
thf(hoaslamnotvar,axiom,
( hoaslamnotvar
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) ) ) ).
thf('5',plain,
( hoaslamnotvar
= ( ! [X4: subst > term > term] :
( ! [X6: subst,X8: term,X10: subst] :
( ( sub @ ( X4 @ X6 @ X8 ) @ X10 )
= ( X4 @ ( comp @ X6 @ X10 ) @ ( sub @ X8 @ X10 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [V_1: subst,V_2: term] : ( X4 @ V_1 @ V_2 ) )
@ id ) ) ) ),
define([status(thm)]) ).
thf(hoaslamnotap,axiom,
( hoaslamnotap
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [A: term,B: term] :
( ( hoaslam @ id
@ ^ [M: subst,C: term] : ( F @ M @ C ) )
!= ( hoasap @ id @ A @ id @ B ) ) ) ) ) ).
thf('6',plain,
( hoaslamnotap
= ( ! [X4: subst > term > term] :
( ! [X6: subst,X8: term,X10: subst] :
( ( sub @ ( X4 @ X6 @ X8 ) @ X10 )
= ( X4 @ ( comp @ X6 @ X10 ) @ ( sub @ X8 @ X10 ) ) )
=> ! [X12: term,X14: term] :
( ( hoaslam @ id
@ ^ [V_1: subst,V_2: term] : ( X4 @ V_1 @ V_2 ) )
!= ( hoasap @ id @ X12 @ id @ X14 ) ) ) ) ),
define([status(thm)]) ).
thf(hoaslaminj,axiom,
( hoaslaminj
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [G: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( G @ M @ A ) @ N )
= ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
= ( hoaslam @ id
@ ^ [M: subst,A: term] : ( G @ M @ A ) ) )
=> ! [M: subst,A: term] :
( ( F @ M @ A )
= ( G @ M @ A ) ) ) ) ) ) ) ).
thf('7',plain,
( hoaslaminj
= ( ! [X4: subst > term > term] :
( ! [X6: subst,X8: term,X10: subst] :
( ( sub @ ( X4 @ X6 @ X8 ) @ X10 )
= ( X4 @ ( comp @ X6 @ X10 ) @ ( sub @ X8 @ X10 ) ) )
=> ! [X12: subst > term > term] :
( ! [X14: subst,X16: term,X18: subst] :
( ( sub @ ( X12 @ X14 @ X16 ) @ X18 )
= ( X12 @ ( comp @ X14 @ X18 ) @ ( sub @ X16 @ X18 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [V_1: subst,V_2: term] : ( X4 @ V_1 @ V_2 ) )
= ( hoaslam @ id
@ ^ [V_3: subst,V_4: term] : ( X12 @ V_3 @ V_4 ) ) )
=> ! [X20: subst,X22: term] :
( ( X4 @ X20 @ X22 )
= ( X12 @ X20 @ X22 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(hoasapinj2,axiom,
( hoasapinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( C = D ) ) ) ) ).
thf('8',plain,
( hoasapinj2
= ( ! [X4: term,X6: term,X8: term,X10: term] :
( ( ( hoasap @ id @ X4 @ id @ X8 )
= ( hoasap @ id @ X6 @ id @ X10 ) )
=> ( X8 = X10 ) ) ) ),
define([status(thm)]) ).
thf(hoasapinj1,axiom,
( hoasapinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( A = B ) ) ) ) ).
thf('9',plain,
( hoasapinj1
= ( ! [X4: term,X6: term,X8: term,X10: term] :
( ( ( hoasap @ id @ X4 @ id @ X8 )
= ( hoasap @ id @ X6 @ id @ X10 ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(hoasvar,axiom,
( hoasvar
= ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ) ).
thf('10',plain,
( hoasvar
= ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[hoasvar]) ).
thf('11',plain,
( hoasvar
= ( ^ [V_1: subst,V_2: term,V_3: subst] : ( var @ ( sub @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(hoaslam,axiom,
( hoaslam
= ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ) ).
thf('12',plain,
( hoaslam
= ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[hoaslam]) ).
thf('13',plain,
( hoaslam
= ( ^ [V_1: subst,V_2: subst > term > term] : ( lam @ ( V_2 @ sh @ one ) ) ) ),
define([status(thm)]) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ) ).
thf('14',plain,
( hoasap
= ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ),
inference(simplify_rw_rule,[status(thm)],[hoasap]) ).
thf('15',plain,
( hoasap
= ( ^ [V_1: subst,V_2: term,V_3: subst,V_4: term] : ( ap @ ( sub @ V_2 @ V_3 ) @ V_4 ) ) ),
define([status(thm)]) ).
thf(termmset,axiom,
( termmset
= ( ! [A: term] :
( ( sub @ A @ id )
= A )
& ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) ) ) ).
thf('16',plain,
( termmset
= ( ! [X4: term] :
( ( sub @ X4 @ id )
= X4 )
& ! [X6: term,X8: subst,X10: subst] :
( ( sub @ ( sub @ X6 @ X8 ) @ X10 )
= ( sub @ X6 @ ( comp @ X8 @ X10 ) ) ) ) ),
define([status(thm)]) ).
thf(substmonoid,axiom,
( substmonoid
= ( ! [M: subst] :
( ( comp @ M @ id )
= M )
& ! [M: subst] :
( ( comp @ id @ M )
= M )
& ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) ) ) ).
thf('17',plain,
( substmonoid
= ( ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 )
& ! [X6: subst] :
( ( comp @ id @ X6 )
= X6 )
& ! [X8: subst,X10: subst,X12: subst] :
( ( comp @ ( comp @ X8 @ X10 ) @ X12 )
= ( comp @ X8 @ ( comp @ X10 @ X12 ) ) ) ) ),
define([status(thm)]) ).
thf(induction2,axiom,
( induction2
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ) ).
thf('18',plain,
( induction2
= ( ! [X4: term > $o] :
( ! [X6: term] :
( ( var @ X6 )
=> ( X4 @ X6 ) )
=> ( ! [X8: term,X10: term] :
( ( X4 @ X8 )
=> ( ( X4 @ X10 )
=> ( X4 @ ( ap @ X8 @ X10 ) ) ) )
=> ( ! [X12: term] :
( ! [X14: term] :
( ( X4 @ X14 )
=> ( X4 @ ( sub @ X12 @ ( push @ X14 @ id ) ) ) )
=> ( X4 @ ( lam @ X12 ) ) )
=> ! [X16: term] : ( X4 @ X16 ) ) ) ) ) ),
define([status(thm)]) ).
thf(induction2lem,axiom,
( induction2lem
= ( ! [P: term > $o] :
( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( P @ ( sub @ A @ M ) ) ) ) ) ) ) ).
thf('19',plain,
( induction2lem
= ( ! [X4: term > $o] :
( ! [X6: term,X8: term] :
( ( X4 @ X6 )
=> ( ( X4 @ X8 )
=> ( X4 @ ( ap @ X6 @ X8 ) ) ) )
=> ( ! [X10: term] :
( ! [X12: term] :
( ( X4 @ X12 )
=> ( X4 @ ( sub @ X10 @ ( push @ X12 @ id ) ) ) )
=> ( X4 @ ( lam @ X10 ) ) )
=> ! [X14: term,X16: subst] :
( ! [X18: term] :
( ( var @ X18 )
=> ( X4 @ ( sub @ X18 @ X16 ) ) )
=> ( X4 @ ( sub @ X14 @ X16 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(pushprop,axiom,
( pushprop
= ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ) ).
thf('20',plain,
( pushprop
= ( ! [X4: term > $o,X6: term,X8: subst] :
( ! [X10: term] :
( ( var @ X10 )
=> ( X4 @ ( sub @ X10 @ X8 ) ) )
=> ( ( X4 @ X6 )
=> ! [X12: term] :
( ( var @ X12 )
=> ( X4 @ ( sub @ X12 @ ( push @ X6 @ X8 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(induction,axiom,
( induction
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ) ).
thf('21',plain,
( induction
= ( ! [X4: term > $o] :
( ! [X6: term] :
( ( var @ X6 )
=> ( X4 @ X6 ) )
=> ( ! [X8: term,X10: term] :
( ( X4 @ X8 )
=> ( ( X4 @ X10 )
=> ( X4 @ ( ap @ X8 @ X10 ) ) ) )
=> ( ! [X12: term] :
( ( X4 @ X12 )
=> ( X4 @ ( lam @ X12 ) ) )
=> ! [X14: term] : ( X4 @ X14 ) ) ) ) ) ),
define([status(thm)]) ).
thf(lamnotvar,axiom,
( lamnotvar
= ( ! [A: term] :
~ ( var @ ( lam @ A ) ) ) ) ).
thf('22',plain,
( lamnotvar
= ( ! [X4: term] :
~ ( var @ ( lam @ X4 ) ) ) ),
define([status(thm)]) ).
thf(apnotvar,axiom,
( apnotvar
= ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) ) ) ).
thf('23',plain,
( apnotvar
= ( ! [X4: term,X6: term] :
~ ( var @ ( ap @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(lamnotap,axiom,
( lamnotap
= ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) ) ) ).
thf('24',plain,
( lamnotap
= ( ! [X4: term,X6: term,X8: term] :
( ( lam @ X4 )
!= ( ap @ X6 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(shinj,axiom,
( shinj
= ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) ) ) ).
thf('25',plain,
( shinj
= ( ! [X4: term,X6: term] :
( ( ( sub @ X4 @ sh )
= ( sub @ X6 @ sh ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(laminj,axiom,
( laminj
= ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) ) ) ).
thf('26',plain,
( laminj
= ( ! [X4: term,X6: term] :
( ( ( lam @ X4 )
= ( lam @ X6 ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(apinj2,axiom,
( apinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) ) ) ).
thf('27',plain,
( apinj2
= ( ! [X4: term,X6: term,X8: term,X10: term] :
( ( ( ap @ X4 @ X8 )
= ( ap @ X6 @ X10 ) )
=> ( X8 = X10 ) ) ) ),
define([status(thm)]) ).
thf(apinj1,axiom,
( apinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) ) ) ).
thf('28',plain,
( apinj1
= ( ! [X4: term,X6: term,X8: term,X10: term] :
( ( ( ap @ X4 @ X8 )
= ( ap @ X6 @ X10 ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(ulamvarind,axiom,
( ulamvarind
= ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) ) ) ).
thf('29',plain,
( ulamvarind
= ( ! [X4: term > $o] :
( ( X4 @ one )
=> ( ! [X6: term] :
( ( var @ X6 )
=> ( ( X4 @ X6 )
=> ( X4 @ ( sub @ X6 @ sh ) ) ) )
=> ! [X8: term] :
( ( var @ X8 )
=> ( X4 @ X8 ) ) ) ) ) ),
define([status(thm)]) ).
thf(ulamvarsh,axiom,
( ulamvarsh
= ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) ) ) ).
thf('30',plain,
( ulamvarsh
= ( ! [X4: term] :
( ( var @ X4 )
=> ( var @ ( sub @ X4 @ sh ) ) ) ) ),
define([status(thm)]) ).
thf(ulamvar1,axiom,
( ulamvar1
= ( var @ one ) ) ).
thf('31',plain,
( ulamvar1
= ( var @ one ) ),
inference(simplify_rw_rule,[status(thm)],[ulamvar1]) ).
thf('32',plain,
( ulamvar1
= ( var @ one ) ),
define([status(thm)]) ).
thf(axscons,axiom,
( axscons
= ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) ) ) ).
thf('33',plain,
( axscons
= ( ! [X4: subst] :
( ( push @ ( sub @ one @ X4 ) @ ( comp @ sh @ X4 ) )
= X4 ) ) ),
define([status(thm)]) ).
thf(axvarshift,axiom,
( axvarshift
= ( ( push @ one @ sh )
= id ) ) ).
thf('34',plain,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
define([status(thm)]) ).
thf(axidr,axiom,
( axidr
= ( ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ) ).
thf('35',plain,
( axidr
= ( ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 ) ) ),
define([status(thm)]) ).
thf(axmap,axiom,
( axmap
= ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) ) ) ).
thf('36',plain,
( axmap
= ( ! [X4: term,X6: subst,X8: subst] :
( ( comp @ ( push @ X4 @ X6 ) @ X8 )
= ( push @ ( sub @ X4 @ X8 ) @ ( comp @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(axassoc,axiom,
( axassoc
= ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) ) ) ).
thf('37',plain,
( axassoc
= ( ! [X4: subst,X6: subst,X8: subst] :
( ( comp @ ( comp @ X4 @ X6 ) @ X8 )
= ( comp @ X4 @ ( comp @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(axshiftcons,axiom,
( axshiftcons
= ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) ) ) ).
thf('38',plain,
( axshiftcons
= ( ! [X4: term,X6: subst] :
( ( comp @ sh @ ( push @ X4 @ X6 ) )
= X6 ) ) ),
define([status(thm)]) ).
thf(axidl,axiom,
( axidl
= ( ! [M: subst] :
( ( comp @ id @ M )
= M ) ) ) ).
thf('39',plain,
( axidl
= ( ! [X4: subst] :
( ( comp @ id @ X4 )
= X4 ) ) ),
define([status(thm)]) ).
thf(axclos,axiom,
( axclos
= ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) ) ) ).
thf('40',plain,
( axclos
= ( ! [X4: term,X6: subst,X8: subst] :
( ( sub @ ( sub @ X4 @ X6 ) @ X8 )
= ( sub @ X4 @ ( comp @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(axabs,axiom,
( axabs
= ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) ) ).
thf('41',plain,
( axabs
= ( ! [X4: term,X6: subst] :
( ( sub @ ( lam @ X4 ) @ X6 )
= ( lam @ ( sub @ X4 @ ( push @ one @ ( comp @ X6 @ sh ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(axvarid,axiom,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf('42',plain,
( axvarid
= ( ! [X4: term] :
( ( sub @ X4 @ id )
= X4 ) ) ),
define([status(thm)]) ).
thf(axvarcons,axiom,
( axvarcons
= ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) ) ) ).
thf('43',plain,
( axvarcons
= ( ! [X4: term,X6: subst] :
( ( sub @ one @ ( push @ X4 @ X6 ) )
= X4 ) ) ),
define([status(thm)]) ).
thf(axapp,axiom,
( axapp
= ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) ) ) ).
thf('44',plain,
( axapp
= ( ! [X4: term,X6: term,X8: subst] :
( ( sub @ ( ap @ X4 @ X6 ) @ X8 )
= ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(thm,conjecture,
hoasinduction_lem3b_gthm ).
thf(zf_stmt_0,conjecture,
( ! [X4: term,X6: term,X8: subst] :
( ( sub @ ( ap @ X4 @ X6 ) @ X8 )
= ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) )
=> ( ! [X10: term,X12: subst] :
( ( sub @ one @ ( push @ X10 @ X12 ) )
= X10 )
=> ( ! [X14: term] :
( ( sub @ X14 @ id )
= X14 )
=> ( ! [X16: term,X18: subst] :
( ( sub @ ( lam @ X16 ) @ X18 )
= ( lam @ ( sub @ X16 @ ( push @ one @ ( comp @ X18 @ sh ) ) ) ) )
=> ( ! [X20: term,X22: subst,X24: subst] :
( ( sub @ ( sub @ X20 @ X22 ) @ X24 )
= ( sub @ X20 @ ( comp @ X22 @ X24 ) ) )
=> ( ! [X26: subst] :
( ( comp @ id @ X26 )
= X26 )
=> ( ! [X28: term,X30: subst] :
( ( comp @ sh @ ( push @ X28 @ X30 ) )
= X30 )
=> ( ! [X32: subst,X34: subst,X36: subst] :
( ( comp @ ( comp @ X32 @ X34 ) @ X36 )
= ( comp @ X32 @ ( comp @ X34 @ X36 ) ) )
=> ( ! [X38: term,X40: subst,X42: subst] :
( ( comp @ ( push @ X38 @ X40 ) @ X42 )
= ( push @ ( sub @ X38 @ X42 ) @ ( comp @ X40 @ X42 ) ) )
=> ( ! [X44: subst] :
( ( comp @ X44 @ id )
= X44 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X46: subst] :
( ( push @ ( sub @ one @ X46 ) @ ( comp @ sh @ X46 ) )
= X46 )
=> ( ( var @ one )
=> ( ! [X48: term] :
( ( var @ X48 )
=> ( var @ ( sub @ X48 @ sh ) ) )
=> ( ! [X50: term > $o] :
( ( X50 @ one )
=> ( ! [X52: term] :
( ( var @ X52 )
=> ( ( X50 @ X52 )
=> ( X50 @ ( sub @ X52 @ sh ) ) ) )
=> ! [X54: term] :
( ( var @ X54 )
=> ( X50 @ X54 ) ) ) )
=> ( ! [X56: term,X58: term,X60: term,X62: term] :
( ( ( ap @ X56 @ X60 )
= ( ap @ X58 @ X62 ) )
=> ( X56 = X58 ) )
=> ( ! [X64: term,X66: term,X68: term,X70: term] :
( ( ( ap @ X64 @ X68 )
= ( ap @ X66 @ X70 ) )
=> ( X68 = X70 ) )
=> ( ! [X72: term,X74: term] :
( ( ( lam @ X72 )
= ( lam @ X74 ) )
=> ( X72 = X74 ) )
=> ( ! [X76: term,X78: term] :
( ( ( sub @ X76 @ sh )
= ( sub @ X78 @ sh ) )
=> ( X76 = X78 ) )
=> ( ! [X80: term,X82: term,X84: term] :
( ( lam @ X80 )
!= ( ap @ X82 @ X84 ) )
=> ( ! [X86: term,X88: term] :
~ ( var @ ( ap @ X86 @ X88 ) )
=> ( ! [X90: term] :
~ ( var @ ( lam @ X90 ) )
=> ( ! [X92: term > $o] :
( ! [X94: term] :
( ( var @ X94 )
=> ( X92 @ X94 ) )
=> ( ! [X96: term,X98: term] :
( ( X92 @ X96 )
=> ( ( X92 @ X98 )
=> ( X92 @ ( ap @ X96 @ X98 ) ) ) )
=> ( ! [X100: term] :
( ( X92 @ X100 )
=> ( X92 @ ( lam @ X100 ) ) )
=> ! [X102: term] : ( X92 @ X102 ) ) ) )
=> ( ! [X104: term > $o,X106: term,X108: subst] :
( ! [X110: term] :
( ( var @ X110 )
=> ( X104 @ ( sub @ X110 @ X108 ) ) )
=> ( ( X104 @ X106 )
=> ! [X112: term] :
( ( var @ X112 )
=> ( X104 @ ( sub @ X112 @ ( push @ X106 @ X108 ) ) ) ) ) )
=> ( ! [X114: term > $o] :
( ! [X116: term,X118: term] :
( ( X114 @ X116 )
=> ( ( X114 @ X118 )
=> ( X114 @ ( ap @ X116 @ X118 ) ) ) )
=> ( ! [X120: term] :
( ! [X122: term] :
( ( X114 @ X122 )
=> ( X114 @ ( sub @ X120 @ ( push @ X122 @ id ) ) ) )
=> ( X114 @ ( lam @ X120 ) ) )
=> ! [X124: term,X126: subst] :
( ! [X128: term] :
( ( var @ X128 )
=> ( X114 @ ( sub @ X128 @ X126 ) ) )
=> ( X114 @ ( sub @ X124 @ X126 ) ) ) ) )
=> ( ! [X130: term > $o] :
( ! [X132: term] :
( ( var @ X132 )
=> ( X130 @ X132 ) )
=> ( ! [X134: term,X136: term] :
( ( X130 @ X134 )
=> ( ( X130 @ X136 )
=> ( X130 @ ( ap @ X134 @ X136 ) ) ) )
=> ( ! [X138: term] :
( ! [X140: term] :
( ( X130 @ X140 )
=> ( X130 @ ( sub @ X138 @ ( push @ X140 @ id ) ) ) )
=> ( X130 @ ( lam @ X138 ) ) )
=> ! [X142: term] : ( X130 @ X142 ) ) ) )
=> ( ( ! [X144: subst] :
( ( comp @ X144 @ id )
= X144 )
& ! [X146: subst] :
( ( comp @ id @ X146 )
= X146 )
& ! [X148: subst,X150: subst,X152: subst] :
( ( comp @ ( comp @ X148 @ X150 ) @ X152 )
= ( comp @ X148 @ ( comp @ X150 @ X152 ) ) ) )
=> ( ( ! [X154: term] :
( ( sub @ X154 @ id )
= X154 )
& ! [X156: term,X158: subst,X160: subst] :
( ( sub @ ( sub @ X156 @ X158 ) @ X160 )
= ( sub @ X156 @ ( comp @ X158 @ X160 ) ) ) )
=> ( ! [X162: term,X164: term,X166: term,X168: term] :
( ( ( ap @ ( sub @ X162 @ id ) @ X166 )
= ( ap @ ( sub @ X164 @ id ) @ X168 ) )
=> ( X162 = X164 ) )
=> ( ! [X170: term,X172: term,X174: term,X176: term] :
( ( ( ap @ ( sub @ X170 @ id ) @ X174 )
= ( ap @ ( sub @ X172 @ id ) @ X176 ) )
=> ( X174 = X176 ) )
=> ( ! [X178: subst > term > term] :
( ! [X180: subst,X182: term,X184: subst] :
( ( sub @ ( X178 @ X180 @ X182 ) @ X184 )
= ( X178 @ ( comp @ X180 @ X184 ) @ ( sub @ X182 @ X184 ) ) )
=> ! [X186: subst > term > term] :
( ! [X188: subst,X190: term,X192: subst] :
( ( sub @ ( X186 @ X188 @ X190 ) @ X192 )
= ( X186 @ ( comp @ X188 @ X192 ) @ ( sub @ X190 @ X192 ) ) )
=> ( ( ( lam @ ( X178 @ sh @ one ) )
= ( lam @ ( X186 @ sh @ one ) ) )
=> ! [X194: subst,X196: term] :
( ( X178 @ X194 @ X196 )
= ( X186 @ X194 @ X196 ) ) ) ) )
=> ( ! [X198: subst > term > term] :
( ! [X200: subst,X202: term,X204: subst] :
( ( sub @ ( X198 @ X200 @ X202 ) @ X204 )
= ( X198 @ ( comp @ X200 @ X204 ) @ ( sub @ X202 @ X204 ) ) )
=> ! [X206: term,X208: term] :
( ( lam @ ( X198 @ sh @ one ) )
!= ( ap @ ( sub @ X206 @ id ) @ X208 ) ) )
=> ( ! [X210: subst > term > term] :
( ! [X212: subst,X214: term,X216: subst] :
( ( sub @ ( X210 @ X212 @ X214 ) @ X216 )
= ( X210 @ ( comp @ X212 @ X216 ) @ ( sub @ X214 @ X216 ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( X210 @ sh @ one ) ) @ id ) ) )
=> ( ! [X218: term,X220: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ X218 @ id ) @ X220 ) @ id ) )
=> ( ! [X222: subst > term > subst > $o] :
( ! [X224: subst,X226: term,X228: subst,X230: subst] :
( ( X222 @ X224 @ X226 @ ( comp @ X230 @ X228 ) )
=> ( X222 @ ( comp @ X224 @ X230 ) @ ( sub @ X226 @ X230 ) @ X228 ) )
=> ( ! [X232: subst,X234: term,X236: subst,X238: subst] :
( ( X222 @ ( comp @ X232 @ X238 ) @ ( sub @ X234 @ X238 ) @ X236 )
=> ( X222 @ X232 @ X234 @ ( comp @ X238 @ X236 ) ) )
=> ( ! [X240: term] :
( ( var @ ( sub @ X240 @ id ) )
=> ( X222 @ id @ X240 @ id ) )
=> ! [X242: term] :
( ( var @ X242 )
=> ( X222 @ id @ X242 @ id ) ) ) ) )
=> ( ! [X244: subst > term > subst > $o] :
( ! [X246: subst,X248: term,X250: subst,X252: subst] :
( ( X244 @ X246 @ X248 @ ( comp @ X252 @ X250 ) )
=> ( X244 @ ( comp @ X246 @ X252 ) @ ( sub @ X248 @ X252 ) @ X250 ) )
=> ( ! [X254: subst,X256: term,X258: subst,X260: subst] :
( ( X244 @ ( comp @ X254 @ X260 ) @ ( sub @ X256 @ X260 ) @ X258 )
=> ( X244 @ X254 @ X256 @ ( comp @ X260 @ X258 ) ) )
=> ( ! [X262: term,X264: term] :
( ( X244 @ id @ X262 @ id )
=> ( ( X244 @ id @ X264 @ id )
=> ( X244 @ id @ ( ap @ ( sub @ X262 @ id ) @ X264 ) @ id ) ) )
=> ! [X266: term,X268: term] :
( ( X244 @ id @ X266 @ id )
=> ( ( X244 @ id @ X268 @ id )
=> ( X244 @ id @ ( ap @ X266 @ X268 ) @ id ) ) ) ) ) )
=> ! [X270: term] :
? [X272: subst > term > term] :
( ( sub @ X270 @ ( push @ one @ sh ) )
= ( X272 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: term,X6: term,X8: subst] :
( ( sub @ ( ap @ X4 @ X6 ) @ X8 )
= ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) )
=> ( ! [X10: term,X12: subst] :
( ( sub @ one @ ( push @ X10 @ X12 ) )
= X10 )
=> ( ! [X14: term] :
( ( sub @ X14 @ id )
= X14 )
=> ( ! [X16: term,X18: subst] :
( ( sub @ ( lam @ X16 ) @ X18 )
= ( lam @ ( sub @ X16 @ ( push @ one @ ( comp @ X18 @ sh ) ) ) ) )
=> ( ! [X20: term,X22: subst,X24: subst] :
( ( sub @ ( sub @ X20 @ X22 ) @ X24 )
= ( sub @ X20 @ ( comp @ X22 @ X24 ) ) )
=> ( ! [X26: subst] :
( ( comp @ id @ X26 )
= X26 )
=> ( ! [X28: term,X30: subst] :
( ( comp @ sh @ ( push @ X28 @ X30 ) )
= X30 )
=> ( ! [X32: subst,X34: subst,X36: subst] :
( ( comp @ ( comp @ X32 @ X34 ) @ X36 )
= ( comp @ X32 @ ( comp @ X34 @ X36 ) ) )
=> ( ! [X38: term,X40: subst,X42: subst] :
( ( comp @ ( push @ X38 @ X40 ) @ X42 )
= ( push @ ( sub @ X38 @ X42 ) @ ( comp @ X40 @ X42 ) ) )
=> ( ! [X44: subst] :
( ( comp @ X44 @ id )
= X44 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X46: subst] :
( ( push @ ( sub @ one @ X46 ) @ ( comp @ sh @ X46 ) )
= X46 )
=> ( ( var @ one )
=> ( ! [X48: term] :
( ( var @ X48 )
=> ( var @ ( sub @ X48 @ sh ) ) )
=> ( ! [X50: term > $o] :
( ( X50 @ one )
=> ( ! [X52: term] :
( ( var @ X52 )
=> ( ( X50 @ X52 )
=> ( X50 @ ( sub @ X52 @ sh ) ) ) )
=> ! [X54: term] :
( ( var @ X54 )
=> ( X50 @ X54 ) ) ) )
=> ( ! [X56: term,X58: term,X60: term,X62: term] :
( ( ( ap @ X56 @ X60 )
= ( ap @ X58 @ X62 ) )
=> ( X56 = X58 ) )
=> ( ! [X64: term,X66: term,X68: term,X70: term] :
( ( ( ap @ X64 @ X68 )
= ( ap @ X66 @ X70 ) )
=> ( X68 = X70 ) )
=> ( ! [X72: term,X74: term] :
( ( ( lam @ X72 )
= ( lam @ X74 ) )
=> ( X72 = X74 ) )
=> ( ! [X76: term,X78: term] :
( ( ( sub @ X76 @ sh )
= ( sub @ X78 @ sh ) )
=> ( X76 = X78 ) )
=> ( ! [X80: term,X82: term,X84: term] :
( ( lam @ X80 )
!= ( ap @ X82 @ X84 ) )
=> ( ! [X86: term,X88: term] :
~ ( var @ ( ap @ X86 @ X88 ) )
=> ( ! [X90: term] :
~ ( var @ ( lam @ X90 ) )
=> ( ! [X92: term > $o] :
( ! [X94: term] :
( ( var @ X94 )
=> ( X92 @ X94 ) )
=> ( ! [X96: term,X98: term] :
( ( X92 @ X96 )
=> ( ( X92 @ X98 )
=> ( X92 @ ( ap @ X96 @ X98 ) ) ) )
=> ( ! [X100: term] :
( ( X92 @ X100 )
=> ( X92 @ ( lam @ X100 ) ) )
=> ! [X102: term] : ( X92 @ X102 ) ) ) )
=> ( ! [X104: term > $o,X106: term,X108: subst] :
( ! [X110: term] :
( ( var @ X110 )
=> ( X104 @ ( sub @ X110 @ X108 ) ) )
=> ( ( X104 @ X106 )
=> ! [X112: term] :
( ( var @ X112 )
=> ( X104 @ ( sub @ X112 @ ( push @ X106 @ X108 ) ) ) ) ) )
=> ( ! [X114: term > $o] :
( ! [X116: term,X118: term] :
( ( X114 @ X116 )
=> ( ( X114 @ X118 )
=> ( X114 @ ( ap @ X116 @ X118 ) ) ) )
=> ( ! [X120: term] :
( ! [X122: term] :
( ( X114 @ X122 )
=> ( X114 @ ( sub @ X120 @ ( push @ X122 @ id ) ) ) )
=> ( X114 @ ( lam @ X120 ) ) )
=> ! [X124: term,X126: subst] :
( ! [X128: term] :
( ( var @ X128 )
=> ( X114 @ ( sub @ X128 @ X126 ) ) )
=> ( X114 @ ( sub @ X124 @ X126 ) ) ) ) )
=> ( ! [X130: term > $o] :
( ! [X132: term] :
( ( var @ X132 )
=> ( X130 @ X132 ) )
=> ( ! [X134: term,X136: term] :
( ( X130 @ X134 )
=> ( ( X130 @ X136 )
=> ( X130 @ ( ap @ X134 @ X136 ) ) ) )
=> ( ! [X138: term] :
( ! [X140: term] :
( ( X130 @ X140 )
=> ( X130 @ ( sub @ X138 @ ( push @ X140 @ id ) ) ) )
=> ( X130 @ ( lam @ X138 ) ) )
=> ! [X142: term] : ( X130 @ X142 ) ) ) )
=> ( ( ! [X144: subst] :
( ( comp @ X144 @ id )
= X144 )
& ! [X146: subst] :
( ( comp @ id @ X146 )
= X146 )
& ! [X148: subst,X150: subst,X152: subst] :
( ( comp @ ( comp @ X148 @ X150 ) @ X152 )
= ( comp @ X148 @ ( comp @ X150 @ X152 ) ) ) )
=> ( ( ! [X154: term] :
( ( sub @ X154 @ id )
= X154 )
& ! [X156: term,X158: subst,X160: subst] :
( ( sub @ ( sub @ X156 @ X158 ) @ X160 )
= ( sub @ X156 @ ( comp @ X158 @ X160 ) ) ) )
=> ( ! [X162: term,X164: term,X166: term,X168: term] :
( ( ( ap @ ( sub @ X162 @ id ) @ X166 )
= ( ap @ ( sub @ X164 @ id ) @ X168 ) )
=> ( X162 = X164 ) )
=> ( ! [X170: term,X172: term,X174: term,X176: term] :
( ( ( ap @ ( sub @ X170 @ id ) @ X174 )
= ( ap @ ( sub @ X172 @ id ) @ X176 ) )
=> ( X174 = X176 ) )
=> ( ! [X178: subst > term > term] :
( ! [X180: subst,X182: term,X184: subst] :
( ( sub @ ( X178 @ X180 @ X182 ) @ X184 )
= ( X178 @ ( comp @ X180 @ X184 ) @ ( sub @ X182 @ X184 ) ) )
=> ! [X186: subst > term > term] :
( ! [X188: subst,X190: term,X192: subst] :
( ( sub @ ( X186 @ X188 @ X190 ) @ X192 )
= ( X186 @ ( comp @ X188 @ X192 ) @ ( sub @ X190 @ X192 ) ) )
=> ( ( ( lam @ ( X178 @ sh @ one ) )
= ( lam @ ( X186 @ sh @ one ) ) )
=> ! [X194: subst,X196: term] :
( ( X178 @ X194 @ X196 )
= ( X186 @ X194 @ X196 ) ) ) ) )
=> ( ! [X198: subst > term > term] :
( ! [X200: subst,X202: term,X204: subst] :
( ( sub @ ( X198 @ X200 @ X202 ) @ X204 )
= ( X198 @ ( comp @ X200 @ X204 ) @ ( sub @ X202 @ X204 ) ) )
=> ! [X206: term,X208: term] :
( ( lam @ ( X198 @ sh @ one ) )
!= ( ap @ ( sub @ X206 @ id ) @ X208 ) ) )
=> ( ! [X210: subst > term > term] :
( ! [X212: subst,X214: term,X216: subst] :
( ( sub @ ( X210 @ X212 @ X214 ) @ X216 )
= ( X210 @ ( comp @ X212 @ X216 ) @ ( sub @ X214 @ X216 ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( X210 @ sh @ one ) ) @ id ) ) )
=> ( ! [X218: term,X220: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ X218 @ id ) @ X220 ) @ id ) )
=> ( ! [X222: subst > term > subst > $o] :
( ! [X224: subst,X226: term,X228: subst,X230: subst] :
( ( X222 @ X224 @ X226 @ ( comp @ X230 @ X228 ) )
=> ( X222 @ ( comp @ X224 @ X230 ) @ ( sub @ X226 @ X230 ) @ X228 ) )
=> ( ! [X232: subst,X234: term,X236: subst,X238: subst] :
( ( X222 @ ( comp @ X232 @ X238 ) @ ( sub @ X234 @ X238 ) @ X236 )
=> ( X222 @ X232 @ X234 @ ( comp @ X238 @ X236 ) ) )
=> ( ! [X240: term] :
( ( var @ ( sub @ X240 @ id ) )
=> ( X222 @ id @ X240 @ id ) )
=> ! [X242: term] :
( ( var @ X242 )
=> ( X222 @ id @ X242 @ id ) ) ) ) )
=> ( ! [X244: subst > term > subst > $o] :
( ! [X246: subst,X248: term,X250: subst,X252: subst] :
( ( X244 @ X246 @ X248 @ ( comp @ X252 @ X250 ) )
=> ( X244 @ ( comp @ X246 @ X252 ) @ ( sub @ X248 @ X252 ) @ X250 ) )
=> ( ! [X254: subst,X256: term,X258: subst,X260: subst] :
( ( X244 @ ( comp @ X254 @ X260 ) @ ( sub @ X256 @ X260 ) @ X258 )
=> ( X244 @ X254 @ X256 @ ( comp @ X260 @ X258 ) ) )
=> ( ! [X262: term,X264: term] :
( ( X244 @ id @ X262 @ id )
=> ( ( X244 @ id @ X264 @ id )
=> ( X244 @ id @ ( ap @ ( sub @ X262 @ id ) @ X264 ) @ id ) ) )
=> ! [X266: term,X268: term] :
( ( X244 @ id @ X266 @ id )
=> ( ( X244 @ id @ X268 @ id )
=> ( X244 @ id @ ( ap @ X266 @ X268 ) @ id ) ) ) ) ) )
=> ! [X270: term] :
? [X272: subst > term > term] :
( ( sub @ X270 @ ( push @ one @ sh ) )
= ( X272 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl51,plain,
! [X44: subst > term > term] :
( ( sub @ sk__171 @ ( push @ one @ sh ) )
!= ( X44 @ sh @ one ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl5,plain,
( ( push @ one @ sh )
= id ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
! [X3: term] :
( ( sub @ X3 @ id )
= X3 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl318,plain,
! [X44: subst > term > term] :
( sk__171
!= ( X44 @ sh @ one ) ),
inference(demod,[status(thm)],[zip_derived_cl51,zip_derived_cl5,zip_derived_cl1]) ).
thf(zip_derived_cl319,plain,
! [X44: term] :
( sk__171
!= ( ^ [Y0: subst,Y1: term] : X44
@ sh
@ one ) ),
inference(prune_arg_fun,[status(thm)],[zip_derived_cl318]) ).
thf(zip_derived_cl320,plain,
! [X44: term] : ( sk__171 != X44 ),
inference(ho_norm,[status(thm)],[zip_derived_cl319]) ).
thf(zip_derived_cl321,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG267^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.4SPPaKOaaW true
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 05:15:37 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.22/0.67 % Total configuration time : 828
% 0.22/0.67 % Estimated wc time : 1656
% 0.22/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.84/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.84/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.84/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.84/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.84/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.84/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.84/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.84/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.45/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.63/0.90 % Solved by lams/40_c.s.sh.
% 1.63/0.90 % done 46 iterations in 0.098s
% 1.63/0.90 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.63/0.90 % SZS output start Refutation
% See solution above
% 1.63/0.90
% 1.63/0.90
% 1.63/0.90 % Terminating...
% 1.63/1.00 % Runner terminated.
% 1.92/1.01 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------