TSTP Solution File: ALG263^3 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG263^3 : 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.fdfGB3kPzf true
% Computer : n011.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 17:12:34 EDT 2023
% Result : Theorem 1.51s 1.02s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 128
% Syntax : Number of formulae : 143 ( 84 unt; 54 typ; 0 def)
% Number of atoms : 429 ( 198 equ; 0 cnn)
% Maximal formula atoms : 50 ( 4 avg)
% Number of connectives : 1584 ( 31 ~; 3 |; 12 &;1201 @)
% ( 5 <=>; 332 =>; 0 <=; 0 <~>)
% Maximal formula depth : 50 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 117 ( 117 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 41 con; 0-4 aty)
% Number of variables : 490 ( 49 ^; 441 !; 0 ?; 490 :)
% Comments :
%------------------------------------------------------------------------------
thf(subst_type,type,
subst: $tType ).
thf(term_type,type,
term: $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(hoasinduction_lem1v2_type,type,
hoasinduction_lem1v2: $o ).
thf(hoasapinj1_type,type,
hoasapinj1: $o ).
thf(hoasinduction_p_and_p_prime_type,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(axapp_type,type,
axapp: $o ).
thf(shinj_type,type,
shinj: $o ).
thf(hoasap_type,type,
hoasap: subst > term > subst > term > term ).
thf(hoaslaminj_type,type,
hoaslaminj: $o ).
thf(one_type,type,
one: term ).
thf(sk__187_type,type,
sk__187: subst > term > subst > $o ).
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(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(axidr_type,type,
axidr: $o ).
thf(axabs_type,type,
axabs: $o ).
thf(sk__188_type,type,
sk__188: term > $o ).
thf(hoasvar_type,type,
hoasvar: subst > term > subst > $o ).
thf(ulamvar1_type,type,
ulamvar1: $o ).
thf(hoasinduction_lem1v2_gthm_type,type,
hoasinduction_lem1v2_gthm: $o ).
thf(induction_type,type,
induction: $o ).
thf(axscons_type,type,
axscons: $o ).
thf(sk__189_type,type,
sk__189: term ).
thf(hoasinduction_lem1v2_gthm,axiom,
( hoasinduction_lem1v2_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_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf('0',plain,
( hoasinduction_lem1v2_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_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(hoasinduction_lem1v2,axiom,
( hoasinduction_lem1v2
= ( ! [P: subst > term > subst > $o,Q: term > $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 ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ( var @ A )
=> ( Q @ A ) ) ) ) ) ) ) ) ).
thf('1',plain,
( hoasinduction_lem1v2
= ( ! [X4: subst > term > subst > $o,X6: term > $o] :
( ! [X8: subst,X10: term,X12: subst,X14: subst] :
( ( X4 @ X8 @ X10 @ ( comp @ X14 @ X12 ) )
=> ( X4 @ ( comp @ X8 @ X14 ) @ ( sub @ X10 @ X14 ) @ X12 ) )
=> ( ! [X16: subst,X18: term,X20: subst,X22: subst] :
( ( X4 @ ( comp @ X16 @ X22 ) @ ( sub @ X18 @ X22 ) @ X20 )
=> ( X4 @ X16 @ X18 @ ( comp @ X22 @ X20 ) ) )
=> ( ! [X24: term] :
( ( hoasvar @ id @ X24 @ id )
=> ( X4 @ id @ X24 @ id ) )
=> ( ( hoasinduction_p_and_p_prime @ X4 @ X6 )
=> ! [X26: term] :
( ( var @ X26 )
=> ( X6 @ X26 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(hoasinduction_p_and_p_prime,axiom,
( hoasinduction_p_and_p_prime
= ( ^ [P: subst > term > subst > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ id @ X @ id ) ) ) ) ).
thf('2',plain,
( hoasinduction_p_and_p_prime
= ( ^ [P: subst > term > subst > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ id @ X @ id ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[hoasinduction_p_and_p_prime]) ).
thf('3',plain,
( hoasinduction_p_and_p_prime
= ( ^ [V_1: subst > term > subst > $o,V_2: term > $o] :
! [X4: term] :
( ( V_2 @ X4 )
<=> ( V_1 @ id @ X4 @ 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(laminj,axiom,
( laminj
= ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) ) ) ).
thf('25',plain,
( laminj
= ( ! [X4: term,X6: term] :
( ( ( lam @ X4 )
= ( lam @ X6 ) )
=> ( 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('26',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('27',plain,
( ulamvarsh
= ( ! [X4: term] :
( ( var @ X4 )
=> ( var @ ( sub @ X4 @ sh ) ) ) ) ),
define([status(thm)]) ).
thf(ulamvar1,axiom,
( ulamvar1
= ( var @ one ) ) ).
thf('28',plain,
( ulamvar1
= ( var @ one ) ),
inference(simplify_rw_rule,[status(thm)],[ulamvar1]) ).
thf('29',plain,
( ulamvar1
= ( var @ one ) ),
define([status(thm)]) ).
thf(axscons,axiom,
( axscons
= ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) ) ) ).
thf('30',plain,
( axscons
= ( ! [X4: subst] :
( ( push @ ( sub @ one @ X4 ) @ ( comp @ sh @ X4 ) )
= X4 ) ) ),
define([status(thm)]) ).
thf(axvarshift,axiom,
( axvarshift
= ( ( push @ one @ sh )
= id ) ) ).
thf('31',plain,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
define([status(thm)]) ).
thf(axidr,axiom,
( axidr
= ( ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ) ).
thf('32',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('33',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('34',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('35',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('36',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('37',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('38',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('39',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('40',plain,
( axvarcons
= ( ! [X4: term,X6: subst] :
( ( sub @ one @ ( push @ X4 @ X6 ) )
= X4 ) ) ),
define([status(thm)]) ).
thf(thm,conjecture,
hoasinduction_lem1v2_gthm ).
thf(zf_stmt_0,conjecture,
( axapp
=> ( ! [X4: term,X6: subst] :
( ( sub @ one @ ( push @ X4 @ X6 ) )
= X4 )
=> ( ! [X8: term] :
( ( sub @ X8 @ id )
= X8 )
=> ( ! [X10: term,X12: subst] :
( ( sub @ ( lam @ X10 ) @ X12 )
= ( lam @ ( sub @ X10 @ ( push @ one @ ( comp @ X12 @ sh ) ) ) ) )
=> ( ! [X14: term,X16: subst,X18: subst] :
( ( sub @ ( sub @ X14 @ X16 ) @ X18 )
= ( sub @ X14 @ ( comp @ X16 @ X18 ) ) )
=> ( ! [X20: subst] :
( ( comp @ id @ X20 )
= X20 )
=> ( ! [X22: term,X24: subst] :
( ( comp @ sh @ ( push @ X22 @ X24 ) )
= X24 )
=> ( ! [X26: subst,X28: subst,X30: subst] :
( ( comp @ ( comp @ X26 @ X28 ) @ X30 )
= ( comp @ X26 @ ( comp @ X28 @ X30 ) ) )
=> ( ! [X32: term,X34: subst,X36: subst] :
( ( comp @ ( push @ X32 @ X34 ) @ X36 )
= ( push @ ( sub @ X32 @ X36 ) @ ( comp @ X34 @ X36 ) ) )
=> ( ! [X38: subst] :
( ( comp @ X38 @ id )
= X38 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X40: subst] :
( ( push @ ( sub @ one @ X40 ) @ ( comp @ sh @ X40 ) )
= X40 )
=> ( ( var @ one )
=> ( ! [X42: term] :
( ( var @ X42 )
=> ( var @ ( sub @ X42 @ sh ) ) )
=> ( ! [X44: term > $o] :
( ( X44 @ one )
=> ( ! [X46: term] :
( ( var @ X46 )
=> ( ( X44 @ X46 )
=> ( X44 @ ( sub @ X46 @ sh ) ) ) )
=> ! [X48: term] :
( ( var @ X48 )
=> ( X44 @ X48 ) ) ) )
=> ( apinj1
=> ( apinj2
=> ( ! [X50: term,X52: term] :
( ( ( lam @ X50 )
= ( lam @ X52 ) )
=> ( X50 = X52 ) )
=> ( shinj
=> ( ! [X54: term,X56: term,X58: term] :
( ( lam @ X54 )
!= ( ap @ X56 @ X58 ) )
=> ( ! [X60: term,X62: term] :
~ ( var @ ( ap @ X60 @ X62 ) )
=> ( ! [X64: term] :
~ ( var @ ( lam @ X64 ) )
=> ( ! [X66: term > $o] :
( ! [X68: term] :
( ( var @ X68 )
=> ( X66 @ X68 ) )
=> ( ! [X70: term,X72: term] :
( ( X66 @ X70 )
=> ( ( X66 @ X72 )
=> ( X66 @ ( ap @ X70 @ X72 ) ) ) )
=> ( ! [X74: term] :
( ( X66 @ X74 )
=> ( X66 @ ( lam @ X74 ) ) )
=> ! [X76: term] : ( X66 @ X76 ) ) ) )
=> ( ! [X78: term > $o,X80: term,X82: subst] :
( ! [X84: term] :
( ( var @ X84 )
=> ( X78 @ ( sub @ X84 @ X82 ) ) )
=> ( ( X78 @ X80 )
=> ! [X86: term] :
( ( var @ X86 )
=> ( X78 @ ( sub @ X86 @ ( push @ X80 @ X82 ) ) ) ) ) )
=> ( ! [X88: term > $o] :
( ! [X90: term,X92: term] :
( ( X88 @ X90 )
=> ( ( X88 @ X92 )
=> ( X88 @ ( ap @ X90 @ X92 ) ) ) )
=> ( ! [X94: term] :
( ! [X96: term] :
( ( X88 @ X96 )
=> ( X88 @ ( sub @ X94 @ ( push @ X96 @ id ) ) ) )
=> ( X88 @ ( lam @ X94 ) ) )
=> ! [X98: term,X100: subst] :
( ! [X102: term] :
( ( var @ X102 )
=> ( X88 @ ( sub @ X102 @ X100 ) ) )
=> ( X88 @ ( sub @ X98 @ X100 ) ) ) ) )
=> ( ! [X104: term > $o] :
( ! [X106: term] :
( ( var @ X106 )
=> ( X104 @ X106 ) )
=> ( ! [X108: term,X110: term] :
( ( X104 @ X108 )
=> ( ( X104 @ X110 )
=> ( X104 @ ( ap @ X108 @ X110 ) ) ) )
=> ( ! [X112: term] :
( ! [X114: term] :
( ( X104 @ X114 )
=> ( X104 @ ( sub @ X112 @ ( push @ X114 @ id ) ) ) )
=> ( X104 @ ( lam @ X112 ) ) )
=> ! [X116: term] : ( X104 @ X116 ) ) ) )
=> ( ( ! [X118: subst] :
( ( comp @ X118 @ id )
= X118 )
& ! [X120: subst] :
( ( comp @ id @ X120 )
= X120 )
& ! [X122: subst,X124: subst,X126: subst] :
( ( comp @ ( comp @ X122 @ X124 ) @ X126 )
= ( comp @ X122 @ ( comp @ X124 @ X126 ) ) ) )
=> ( ( ! [X128: term] :
( ( sub @ X128 @ id )
= X128 )
& ! [X130: term,X132: subst,X134: subst] :
( ( sub @ ( sub @ X130 @ X132 ) @ X134 )
= ( sub @ X130 @ ( comp @ X132 @ X134 ) ) ) )
=> ( ! [X136: term,X138: term,X140: term,X142: term] :
( ( ( ap @ ( sub @ X136 @ id ) @ X140 )
= ( ap @ ( sub @ X138 @ id ) @ X142 ) )
=> ( X136 = X138 ) )
=> ( ! [X144: term,X146: term,X148: term,X150: term] :
( ( ( ap @ ( sub @ X144 @ id ) @ X148 )
= ( ap @ ( sub @ X146 @ id ) @ X150 ) )
=> ( X148 = X150 ) )
=> ( ! [X152: subst > term > term] :
( ! [X154: subst,X156: term,X158: subst] :
( ( sub @ ( X152 @ X154 @ X156 ) @ X158 )
= ( X152 @ ( comp @ X154 @ X158 ) @ ( sub @ X156 @ X158 ) ) )
=> ! [X160: subst > term > term] :
( ! [X162: subst,X164: term,X166: subst] :
( ( sub @ ( X160 @ X162 @ X164 ) @ X166 )
= ( X160 @ ( comp @ X162 @ X166 ) @ ( sub @ X164 @ X166 ) ) )
=> ( ( ( lam @ ( X152 @ sh @ one ) )
= ( lam @ ( X160 @ sh @ one ) ) )
=> ! [X168: subst,X170: term] :
( ( X152 @ X168 @ X170 )
= ( X160 @ X168 @ X170 ) ) ) ) )
=> ( ! [X172: subst > term > term] :
( ! [X174: subst,X176: term,X178: subst] :
( ( sub @ ( X172 @ X174 @ X176 ) @ X178 )
= ( X172 @ ( comp @ X174 @ X178 ) @ ( sub @ X176 @ X178 ) ) )
=> ! [X180: term,X182: term] :
( ( lam @ ( X172 @ sh @ one ) )
!= ( ap @ ( sub @ X180 @ id ) @ X182 ) ) )
=> ( ! [X184: subst > term > term] :
( ! [X186: subst,X188: term,X190: subst] :
( ( sub @ ( X184 @ X186 @ X188 ) @ X190 )
= ( X184 @ ( comp @ X186 @ X190 ) @ ( sub @ X188 @ X190 ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( X184 @ sh @ one ) ) @ id ) ) )
=> ( ! [X192: term,X194: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ X192 @ id ) @ X194 ) @ id ) )
=> ! [X196: subst > term > subst > $o,X198: term > $o] :
( ! [X200: subst,X202: term,X204: subst,X206: subst] :
( ( X196 @ X200 @ X202 @ ( comp @ X206 @ X204 ) )
=> ( X196 @ ( comp @ X200 @ X206 ) @ ( sub @ X202 @ X206 ) @ X204 ) )
=> ( ! [X208: subst,X210: term,X212: subst,X214: subst] :
( ( X196 @ ( comp @ X208 @ X214 ) @ ( sub @ X210 @ X214 ) @ X212 )
=> ( X196 @ X208 @ X210 @ ( comp @ X214 @ X212 ) ) )
=> ( ! [X216: term] :
( ( var @ ( sub @ X216 @ id ) )
=> ( X196 @ id @ X216 @ id ) )
=> ( ! [X218: term] :
( ( X198 @ X218 )
<=> ( X196 @ id @ X218 @ id ) )
=> ! [X220: term] :
( ( var @ X220 )
=> ( X198 @ X220 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( axapp
=> ( ! [X4: term,X6: subst] :
( ( sub @ one @ ( push @ X4 @ X6 ) )
= X4 )
=> ( ! [X8: term] :
( ( sub @ X8 @ id )
= X8 )
=> ( ! [X10: term,X12: subst] :
( ( sub @ ( lam @ X10 ) @ X12 )
= ( lam @ ( sub @ X10 @ ( push @ one @ ( comp @ X12 @ sh ) ) ) ) )
=> ( ! [X14: term,X16: subst,X18: subst] :
( ( sub @ ( sub @ X14 @ X16 ) @ X18 )
= ( sub @ X14 @ ( comp @ X16 @ X18 ) ) )
=> ( ! [X20: subst] :
( ( comp @ id @ X20 )
= X20 )
=> ( ! [X22: term,X24: subst] :
( ( comp @ sh @ ( push @ X22 @ X24 ) )
= X24 )
=> ( ! [X26: subst,X28: subst,X30: subst] :
( ( comp @ ( comp @ X26 @ X28 ) @ X30 )
= ( comp @ X26 @ ( comp @ X28 @ X30 ) ) )
=> ( ! [X32: term,X34: subst,X36: subst] :
( ( comp @ ( push @ X32 @ X34 ) @ X36 )
= ( push @ ( sub @ X32 @ X36 ) @ ( comp @ X34 @ X36 ) ) )
=> ( ! [X38: subst] :
( ( comp @ X38 @ id )
= X38 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X40: subst] :
( ( push @ ( sub @ one @ X40 ) @ ( comp @ sh @ X40 ) )
= X40 )
=> ( ( var @ one )
=> ( ! [X42: term] :
( ( var @ X42 )
=> ( var @ ( sub @ X42 @ sh ) ) )
=> ( ! [X44: term > $o] :
( ( X44 @ one )
=> ( ! [X46: term] :
( ( var @ X46 )
=> ( ( X44 @ X46 )
=> ( X44 @ ( sub @ X46 @ sh ) ) ) )
=> ! [X48: term] :
( ( var @ X48 )
=> ( X44 @ X48 ) ) ) )
=> ( apinj1
=> ( apinj2
=> ( ! [X50: term,X52: term] :
( ( ( lam @ X50 )
= ( lam @ X52 ) )
=> ( X50 = X52 ) )
=> ( shinj
=> ( ! [X54: term,X56: term,X58: term] :
( ( lam @ X54 )
!= ( ap @ X56 @ X58 ) )
=> ( ! [X60: term,X62: term] :
~ ( var @ ( ap @ X60 @ X62 ) )
=> ( ! [X64: term] :
~ ( var @ ( lam @ X64 ) )
=> ( ! [X66: term > $o] :
( ! [X68: term] :
( ( var @ X68 )
=> ( X66 @ X68 ) )
=> ( ! [X70: term,X72: term] :
( ( X66 @ X70 )
=> ( ( X66 @ X72 )
=> ( X66 @ ( ap @ X70 @ X72 ) ) ) )
=> ( ! [X74: term] :
( ( X66 @ X74 )
=> ( X66 @ ( lam @ X74 ) ) )
=> ! [X76: term] : ( X66 @ X76 ) ) ) )
=> ( ! [X78: term > $o,X80: term,X82: subst] :
( ! [X84: term] :
( ( var @ X84 )
=> ( X78 @ ( sub @ X84 @ X82 ) ) )
=> ( ( X78 @ X80 )
=> ! [X86: term] :
( ( var @ X86 )
=> ( X78 @ ( sub @ X86 @ ( push @ X80 @ X82 ) ) ) ) ) )
=> ( ! [X88: term > $o] :
( ! [X90: term,X92: term] :
( ( X88 @ X90 )
=> ( ( X88 @ X92 )
=> ( X88 @ ( ap @ X90 @ X92 ) ) ) )
=> ( ! [X94: term] :
( ! [X96: term] :
( ( X88 @ X96 )
=> ( X88 @ ( sub @ X94 @ ( push @ X96 @ id ) ) ) )
=> ( X88 @ ( lam @ X94 ) ) )
=> ! [X98: term,X100: subst] :
( ! [X102: term] :
( ( var @ X102 )
=> ( X88 @ ( sub @ X102 @ X100 ) ) )
=> ( X88 @ ( sub @ X98 @ X100 ) ) ) ) )
=> ( ! [X104: term > $o] :
( ! [X106: term] :
( ( var @ X106 )
=> ( X104 @ X106 ) )
=> ( ! [X108: term,X110: term] :
( ( X104 @ X108 )
=> ( ( X104 @ X110 )
=> ( X104 @ ( ap @ X108 @ X110 ) ) ) )
=> ( ! [X112: term] :
( ! [X114: term] :
( ( X104 @ X114 )
=> ( X104 @ ( sub @ X112 @ ( push @ X114 @ id ) ) ) )
=> ( X104 @ ( lam @ X112 ) ) )
=> ! [X116: term] : ( X104 @ X116 ) ) ) )
=> ( ( ! [X118: subst] :
( ( comp @ X118 @ id )
= X118 )
& ! [X120: subst] :
( ( comp @ id @ X120 )
= X120 )
& ! [X122: subst,X124: subst,X126: subst] :
( ( comp @ ( comp @ X122 @ X124 ) @ X126 )
= ( comp @ X122 @ ( comp @ X124 @ X126 ) ) ) )
=> ( ( ! [X128: term] :
( ( sub @ X128 @ id )
= X128 )
& ! [X130: term,X132: subst,X134: subst] :
( ( sub @ ( sub @ X130 @ X132 ) @ X134 )
= ( sub @ X130 @ ( comp @ X132 @ X134 ) ) ) )
=> ( ! [X136: term,X138: term,X140: term,X142: term] :
( ( ( ap @ ( sub @ X136 @ id ) @ X140 )
= ( ap @ ( sub @ X138 @ id ) @ X142 ) )
=> ( X136 = X138 ) )
=> ( ! [X144: term,X146: term,X148: term,X150: term] :
( ( ( ap @ ( sub @ X144 @ id ) @ X148 )
= ( ap @ ( sub @ X146 @ id ) @ X150 ) )
=> ( X148 = X150 ) )
=> ( ! [X152: subst > term > term] :
( ! [X154: subst,X156: term,X158: subst] :
( ( sub @ ( X152 @ X154 @ X156 ) @ X158 )
= ( X152 @ ( comp @ X154 @ X158 ) @ ( sub @ X156 @ X158 ) ) )
=> ! [X160: subst > term > term] :
( ! [X162: subst,X164: term,X166: subst] :
( ( sub @ ( X160 @ X162 @ X164 ) @ X166 )
= ( X160 @ ( comp @ X162 @ X166 ) @ ( sub @ X164 @ X166 ) ) )
=> ( ( ( lam @ ( X152 @ sh @ one ) )
= ( lam @ ( X160 @ sh @ one ) ) )
=> ! [X168: subst,X170: term] :
( ( X152 @ X168 @ X170 )
= ( X160 @ X168 @ X170 ) ) ) ) )
=> ( ! [X172: subst > term > term] :
( ! [X174: subst,X176: term,X178: subst] :
( ( sub @ ( X172 @ X174 @ X176 ) @ X178 )
= ( X172 @ ( comp @ X174 @ X178 ) @ ( sub @ X176 @ X178 ) ) )
=> ! [X180: term,X182: term] :
( ( lam @ ( X172 @ sh @ one ) )
!= ( ap @ ( sub @ X180 @ id ) @ X182 ) ) )
=> ( ! [X184: subst > term > term] :
( ! [X186: subst,X188: term,X190: subst] :
( ( sub @ ( X184 @ X186 @ X188 ) @ X190 )
= ( X184 @ ( comp @ X186 @ X190 ) @ ( sub @ X188 @ X190 ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( X184 @ sh @ one ) ) @ id ) ) )
=> ( ! [X192: term,X194: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ X192 @ id ) @ X194 ) @ id ) )
=> ! [X196: subst > term > subst > $o,X198: term > $o] :
( ! [X200: subst,X202: term,X204: subst,X206: subst] :
( ( X196 @ X200 @ X202 @ ( comp @ X206 @ X204 ) )
=> ( X196 @ ( comp @ X200 @ X206 ) @ ( sub @ X202 @ X206 ) @ X204 ) )
=> ( ! [X208: subst,X210: term,X212: subst,X214: subst] :
( ( X196 @ ( comp @ X208 @ X214 ) @ ( sub @ X210 @ X214 ) @ X212 )
=> ( X196 @ X208 @ X210 @ ( comp @ X214 @ X212 ) ) )
=> ( ! [X216: term] :
( ( var @ ( sub @ X216 @ id ) )
=> ( X196 @ id @ X216 @ id ) )
=> ( ! [X218: term] :
( ( X198 @ X218 )
<=> ( X196 @ id @ X218 @ id ) )
=> ! [X220: term] :
( ( var @ X220 )
=> ( X198 @ X220 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl44,plain,
! [X37: term] :
( ( sk__187 @ id @ X37 @ id )
| ~ ( var @ ( sub @ X37 @ id ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
! [X0: term] :
( ( sub @ X0 @ id )
= X0 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl720,plain,
! [X37: term] :
( ( sk__187 @ id @ X37 @ id )
| ~ ( var @ X37 ) ),
inference(demod,[status(thm)],[zip_derived_cl44,zip_derived_cl1]) ).
thf(zip_derived_cl48,plain,
! [X42: term] :
( ( sk__188 @ X42 )
| ~ ( sk__187 @ id @ X42 @ id ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl46,plain,
~ ( sk__188 @ sk__189 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl80,plain,
~ ( sk__187 @ id @ sk__189 @ id ),
inference('sup-',[status(thm)],[zip_derived_cl48,zip_derived_cl46]) ).
thf(zip_derived_cl721,plain,
~ ( var @ sk__189 ),
inference('sup-',[status(thm)],[zip_derived_cl720,zip_derived_cl80]) ).
thf(zip_derived_cl47,plain,
var @ sk__189,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl803,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl721,zip_derived_cl47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG263^3 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fdfGB3kPzf true
% 0.13/0.34 % Computer : n011.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 : 300
% 0.13/0.34 % DateTime : Mon Aug 28 05:41:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.20/0.60 % Total configuration time : 828
% 0.20/0.60 % Estimated wc time : 1656
% 0.20/0.60 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.70 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.70 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.74 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.38/0.88 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.51/1.02 % Solved by lams/40_c.s.sh.
% 1.51/1.02 % done 67 iterations in 0.268s
% 1.51/1.02 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.51/1.02 % SZS output start Refutation
% See solution above
% 1.51/1.02
% 1.51/1.02
% 1.51/1.02 % Terminating...
% 1.78/1.20 % Runner terminated.
% 1.78/1.21 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------