%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG267^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:05 AM UTC 2026
% Result : Theorem 12.36s 3.71s
% Output : Refutation 14.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 88
% Syntax : Number of formulae : 99 ( 96 unt; 0 typ; 87 def)
% Number of atoms : 460 ( 258 equ; 0 cnn)
% Maximal formula atoms : 106 ( 4 avg)
% Number of connectives : 3014 ( 172 ~; 126 |; 82 &;2306 @)
% ( 0 <=>; 328 =>; 0 <=; 0 <~>)
% Maximal formula depth : 163 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 197 ( 197 >; 0 *; 0 +; 0 <<)
% Number of symbols : 105 ( 103 usr; 43 con; 0-4 aty)
% Number of variables : 647 ( 60 ^; 523 !; 18 ?; 647 :)
% ( 0 !>; 0 ?*; 0 @-; 46 @+)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(one_decl,type,
one: term ).
thf(ap_decl,type,
ap: term > term > term ).
thf(lam_decl,type,
lam: term > term ).
thf(sub_decl,type,
sub: term > subst > term ).
thf(id_decl,type,
id: subst ).
thf(sh_decl,type,
sh: subst ).
thf(push_decl,type,
push: term > subst > subst ).
thf(comp_decl,type,
comp: subst > subst > subst ).
thf(var_decl,type,
var: term > $o ).
thf(axmap_decl,type,
axmap: $o ).
thf(shinj_decl,type,
shinj: $o ).
thf(hoasap_decl,type,
hoasap: subst > term > subst > term > term ).
thf(induction2lem_decl,type,
induction2lem: $o ).
thf(axvarshift_decl,type,
axvarshift: $o ).
thf(hoasapinj2_decl,type,
hoasapinj2: $o ).
thf(hoasapinj1_decl,type,
hoasapinj1: $o ).
thf(ulamvar1_decl,type,
ulamvar1: $o ).
thf(apnotvar_decl,type,
apnotvar: $o ).
thf(hoaslaminj_decl,type,
hoaslaminj: $o ).
thf(hoasinduction_lem2_decl,type,
hoasinduction_lem2: $o ).
thf(hoasinduction_lem1_decl,type,
hoasinduction_lem1: $o ).
thf(hoasapnotvar_decl,type,
hoasapnotvar: $o ).
thf(axapp_decl,type,
axapp: $o ).
thf(ulamvarind_decl,type,
ulamvarind: $o ).
thf(induction_decl,type,
induction: $o ).
thf(hoasinduction_lem3b_gthm_decl,type,
hoasinduction_lem3b_gthm: $o ).
thf(axclos_decl,type,
axclos: $o ).
thf(axassoc_decl,type,
axassoc: $o ).
thf(apinj2_decl,type,
apinj2: $o ).
thf(apinj1_decl,type,
apinj1: $o ).
thf(axvarcons_decl,type,
axvarcons: $o ).
thf(hoaslam_decl,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(axscons_decl,type,
axscons: $o ).
thf(axidr_decl,type,
axidr: $o ).
thf(laminj_decl,type,
laminj: $o ).
thf(axabs_decl,type,
axabs: $o ).
thf(lamnotap_decl,type,
lamnotap: $o ).
thf(hoaslamnotvar_decl,type,
hoaslamnotvar: $o ).
thf(axidl_decl,type,
axidl: $o ).
thf(pushprop_decl,type,
pushprop: $o ).
thf(hoasinduction_lem3b_decl,type,
hoasinduction_lem3b: $o ).
thf(substmonoid_decl,type,
substmonoid: $o ).
thf(lamnotvar_decl,type,
lamnotvar: $o ).
thf(hoasvar_decl,type,
hoasvar: subst > term > subst > $o ).
thf(hoaslamnotap_decl,type,
hoaslamnotap: $o ).
thf(ulamvarsh_decl,type,
ulamvarsh: $o ).
thf(induction2_decl,type,
induction2: $o ).
thf(axshiftcons_decl,type,
axshiftcons: $o ).
thf(termmset_decl,type,
termmset: $o ).
thf(axvarid_decl,type,
axvarid: $o ).
thf(sk1_decl,type,
sk1: ( term > $o ) > term ).
thf(sk2_decl,type,
sk2: ( term > $o ) > $o ).
thf(sk3_decl,type,
sk3: ( term > $o ) > term ).
thf(sk4_decl,type,
sk4: ( term > $o ) > term ).
thf(sk5_decl,type,
sk5: ( term > $o ) > term ).
thf(sk6_decl,type,
sk6: ( term > $o ) > term ).
thf(sk7_decl,type,
sk7: subst > term > ( term > $o ) > term ).
thf(sk8_decl,type,
sk8: ( term > $o ) > $o ).
thf(sk9_decl,type,
sk9: ( term > $o ) > term ).
thf(sk10_decl,type,
sk10: ( term > $o ) > term ).
thf(sk11_decl,type,
sk11: ( term > $o ) > $o ).
thf(sk12_decl,type,
sk12: ( term > $o ) > term ).
thf(sk13_decl,type,
sk13: subst > term > ( term > $o ) > term ).
thf(sk14_decl,type,
sk14: ( term > $o ) > $o ).
thf(sk15_decl,type,
sk15: ( term > $o ) > term ).
thf(sk16_decl,type,
sk16: ( term > $o ) > $o ).
thf(sk17_decl,type,
sk17: ( term > $o ) > term ).
thf(sk18_decl,type,
sk18: ( term > $o ) > term ).
thf(sk19_decl,type,
sk19: ( term > $o ) > term ).
thf(sk20_decl,type,
sk20: ( subst > term > term ) > subst ).
thf(sk21_decl,type,
sk21: ( subst > term > term ) > term ).
thf(sk22_decl,type,
sk22: ( subst > term > term ) > subst ).
thf(sk23_decl,type,
sk23: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(sk24_decl,type,
sk24: ( subst > term > term ) > ( subst > term > term ) > term ).
thf(sk25_decl,type,
sk25: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(sk26_decl,type,
sk26: ( subst > term > term ) > subst ).
thf(sk27_decl,type,
sk27: ( subst > term > term ) > term ).
thf(sk28_decl,type,
sk28: ( subst > term > term ) > subst ).
thf(sk29_decl,type,
sk29: ( subst > term > term ) > subst ).
thf(sk30_decl,type,
sk30: ( subst > term > term ) > term ).
thf(sk31_decl,type,
sk31: ( subst > term > term ) > subst ).
thf(sk32_decl,type,
sk32: ( subst > term > subst > $o ) > $o ).
thf(sk33_decl,type,
sk33: ( subst > term > subst > $o ) > subst ).
thf(sk34_decl,type,
sk34: ( subst > term > subst > $o ) > term ).
thf(sk35_decl,type,
sk35: ( subst > term > subst > $o ) > subst ).
thf(sk36_decl,type,
sk36: ( subst > term > subst > $o ) > subst ).
thf(sk37_decl,type,
sk37: ( subst > term > subst > $o ) > subst ).
thf(sk38_decl,type,
sk38: ( subst > term > subst > $o ) > term ).
thf(sk39_decl,type,
sk39: ( subst > term > subst > $o ) > subst ).
thf(sk40_decl,type,
sk40: ( subst > term > subst > $o ) > subst ).
thf(sk41_decl,type,
sk41: ( subst > term > subst > $o ) > term ).
thf(sk42_decl,type,
sk42: ( subst > term > subst > $o ) > $o ).
thf(sk43_decl,type,
sk43: ( subst > term > subst > $o ) > subst ).
thf(sk44_decl,type,
sk44: ( subst > term > subst > $o ) > term ).
thf(sk45_decl,type,
sk45: ( subst > term > subst > $o ) > subst ).
thf(sk46_decl,type,
sk46: ( subst > term > subst > $o ) > subst ).
thf(sk47_decl,type,
sk47: ( subst > term > subst > $o ) > subst ).
thf(sk48_decl,type,
sk48: ( subst > term > subst > $o ) > term ).
thf(sk49_decl,type,
sk49: ( subst > term > subst > $o ) > subst ).
thf(sk50_decl,type,
sk50: ( subst > term > subst > $o ) > subst ).
thf(sk51_decl,type,
sk51: ( subst > term > subst > $o ) > term ).
thf(sk52_decl,type,
sk52: ( subst > term > subst > $o ) > term ).
thf(sk53_decl,type,
sk53: term ).
thf(axmap_def,definition,
( axmap
= ( ! [A: term,B: subst,C: subst] :
( ( comp @ ( push @ A @ B ) @ C )
= ( push @ ( sub @ A @ C ) @ ( comp @ B @ C ) ) ) ) ) ).
thf(shinj_def,definition,
( shinj
= ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) ) ) ).
thf(hoasap_def,definition,
( hoasap
= ( ^ [A: subst,B: term,C: subst] : ( ap @ ( sub @ B @ C ) ) ) ) ).
thf(induction2lem_def,definition,
( induction2lem
= ( ! [A: term > $o] :
( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( A @ ( sub @ B @ C ) ) ) ) ) ) ) ).
thf(axvarshift_def,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ) ).
thf(hoasapinj2_def,definition,
( hoasapinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( C = D ) ) ) ) ).
thf(hoasapinj1_def,definition,
( hoasapinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( A = B ) ) ) ) ).
thf(ulamvar1_def,definition,
( ulamvar1
= ( var @ one ) ) ).
thf(apnotvar_def,definition,
( apnotvar
= ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) ) ) ).
thf(hoaslaminj_def,definition,
( hoaslaminj
= ( ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ! [B: subst > term > term] :
( ! [C: subst,D: term,E: subst] :
( ( sub @ ( B @ C @ D ) @ E )
= ( B @ ( comp @ C @ E ) @ ( sub @ D @ E ) ) )
=> ( ( ( hoaslam @ id @ A )
= ( hoaslam @ id @ B ) )
=> ! [C: subst,D: term] :
( ( A @ C @ D )
= ( B @ C @ D ) ) ) ) ) ) ) ).
thf(hoasinduction_lem2_def,definition,
( hoasinduction_lem2
= ( ! [A: subst > term > subst > $o] :
( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ B @ C @ ( comp @ E @ D ) )
=> ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D ) )
=> ( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D )
=> ( A @ B @ C @ ( comp @ E @ D ) ) )
=> ( ! [B: term,C: term] :
( ( A @ id @ B @ id )
=> ( ( A @ id @ C @ id )
=> ( A @ id @ ( hoasap @ id @ B @ id @ C ) @ id ) ) )
=> ! [B: term,C: term] :
( ( A @ id @ B @ id )
=> ( ( A @ id @ C @ id )
=> ( A @ id @ ( ap @ B @ C ) @ id ) ) ) ) ) ) ) ) ).
thf(hoasinduction_lem1_def,definition,
( hoasinduction_lem1
= ( ! [A: subst > term > subst > $o] :
( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ B @ C @ ( comp @ E @ D ) )
=> ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D ) )
=> ( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D )
=> ( A @ B @ C @ ( comp @ E @ D ) ) )
=> ( ! [B: term] :
( ( hoasvar @ id @ B @ id )
=> ( A @ id @ B @ id ) )
=> ! [B: term] :
( ( var @ B )
=> ( A @ id @ B @ id ) ) ) ) ) ) ) ).
thf(hoasapnotvar_def,definition,
( hoasapnotvar
= ( ! [A: term,B: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ) ).
thf(axapp_def,definition,
( axapp
= ( ! [A: term,B: term,C: subst] :
( ( sub @ ( ap @ A @ B ) @ C )
= ( ap @ ( sub @ A @ C ) @ ( sub @ B @ C ) ) ) ) ) ).
thf(ulamvarind_def,definition,
( ulamvarind
= ( ! [A: term > $o] :
( ( A @ one )
=> ( ! [B: term] :
( ( var @ B )
=> ( ( A @ B )
=> ( A @ ( sub @ B @ sh ) ) ) )
=> ! [B: term] :
( ( var @ B )
=> ( A @ B ) ) ) ) ) ) ).
thf(induction_def,definition,
( induction
= ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ( A @ B )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) ) ) ) ).
thf(hoasinduction_lem3b_gthm_def,definition,
( 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(axclos_def,definition,
( axclos
= ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) ) ) ) ).
thf(axassoc_def,definition,
( axassoc
= ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) ) ) ) ).
thf(apinj2_def,definition,
( apinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) ) ) ).
thf(apinj1_def,definition,
( apinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) ) ) ).
thf(axvarcons_def,definition,
( axvarcons
= ( ! [A: term,B: subst] :
( ( sub @ one @ ( push @ A @ B ) )
= A ) ) ) ).
thf(hoaslam_def,definition,
( hoaslam
= ( ^ [A: subst,B: subst > term > term] : ( lam @ ( B @ sh @ one ) ) ) ) ).
thf(axscons_def,definition,
( axscons
= ( ! [A: subst] :
( ( push @ ( sub @ one @ A ) @ ( comp @ sh @ A ) )
= A ) ) ) ).
thf(axidr_def,definition,
( axidr
= ( ! [A: subst] :
( ( comp @ A @ id )
= A ) ) ) ).
thf(laminj_def,definition,
( laminj
= ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) ) ) ).
thf(axabs_def,definition,
( axabs
= ( ! [A: term,B: subst] :
( ( sub @ ( lam @ A ) @ B )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ B @ sh ) ) ) ) ) ) ) ).
thf(lamnotap_def,definition,
( lamnotap
= ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) ) ) ).
thf(hoaslamnotvar_def,definition,
( hoaslamnotvar
= ( ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ~ ( hoasvar @ id @ ( hoaslam @ id @ A ) @ id ) ) ) ) ).
thf(axidl_def,definition,
( axidl
= ( ! [A: subst] :
( ( comp @ id @ A )
= A ) ) ) ).
thf(pushprop_def,definition,
( pushprop
= ( ! [A: term > $o,B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( ( A @ B )
=> ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ ( push @ B @ C ) ) ) ) ) ) ) ) ).
thf(hoasinduction_lem3b_def,definition,
( hoasinduction_lem3b
= ( ! [A: term] :
? [B: subst > term > term] :
( ( sub @ A @ ( push @ one @ sh ) )
= ( B @ sh @ one ) ) ) ) ).
thf(substmonoid_def,definition,
( substmonoid
= ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
& ! [A: subst] :
( ( comp @ id @ A )
= A )
& ! [A: subst] :
( ( comp @ A @ id )
= A ) ) ) ).
thf(lamnotvar_def,definition,
( lamnotvar
= ( ! [A: term] :
~ ( var @ ( lam @ A ) ) ) ) ).
thf(hoasvar_def,definition,
( hoasvar
= ( ^ [A: subst,B: term,C: subst] : ( var @ ( sub @ B @ C ) ) ) ) ).
thf(hoaslamnotap_def,definition,
( hoaslamnotap
= ( ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ! [B: term,C: term] :
( ( hoaslam @ id @ A )
!= ( hoasap @ id @ B @ id @ C ) ) ) ) ) ).
thf(ulamvarsh_def,definition,
( ulamvarsh
= ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) ) ) ).
thf(induction2_def,definition,
( induction2
= ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) ) ) ) ).
thf(axshiftcons_def,definition,
( axshiftcons
= ( ! [A: term,B: subst] :
( ( comp @ sh @ ( push @ A @ B ) )
= B ) ) ) ).
thf(termmset_def,definition,
( termmset
= ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf(axvarid_def,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ( var @ B )
=> ( ( A @ B )
=> ( A @ ( sub @ B @ sh ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ( var @ B )
=> ( A @ B ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ( A @ B )
=> ! [C: term] :
( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ( A @ B )
=> ( A @ ( ap @ ( sk4 @ A ) @ B ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ( A @ B )
=> ( A @ ( lam @ B ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: subst,B: term,C: term > $o] :
@+[D: term] :
~ ( ( var @ D )
=> ( C @ ( sub @ D @ A ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ( A @ B )
=> ! [C: term] :
( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ( A @ B )
=> ( A @ ( ap @ ( sk9 @ A ) @ B ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: subst,B: term,C: term > $o] :
@+[D: term] :
~ ( ( var @ D )
=> ( C @ ( sub @ D @ A ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ( var @ B )
=> ( A @ B ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ( A @ B )
=> ! [C: term] :
( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ( A @ B )
=> ( A @ ( ap @ ( sk17 @ A ) @ B ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: term > $o] :
@+[B: term] :
~ ( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: subst > term > term] :
@+[B: subst] :
~ ! [C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: subst > term > term] :
@+[B: term] :
~ ! [C: subst] :
( ( sub @ ( A @ ( sk20 @ A ) @ B ) @ C )
= ( A @ ( comp @ ( sk20 @ A ) @ C ) @ ( sub @ B @ C ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: subst > term > term] :
@+[B: subst] :
( ( sub @ ( A @ ( sk20 @ A ) @ ( sk21 @ A ) ) @ B )
!= ( A @ ( comp @ ( sk20 @ A ) @ B ) @ ( sub @ ( sk21 @ A ) @ B ) ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( ^ [A: subst > term > term,B: subst > term > term] :
@+[C: subst] :
~ ! [D: term,E: subst] :
( ( sub @ ( A @ C @ D ) @ E )
= ( A @ ( comp @ C @ E ) @ ( sub @ D @ E ) ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: subst > term > term,B: subst > term > term] :
@+[C: term] :
~ ! [D: subst] :
( ( sub @ ( A @ ( sk23 @ A @ B ) @ C ) @ D )
= ( A @ ( comp @ ( sk23 @ A @ B ) @ D ) @ ( sub @ C @ D ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: subst > term > term,B: subst > term > term] :
@+[C: subst] :
( ( sub @ ( A @ ( sk23 @ A @ B ) @ ( sk24 @ A @ B ) ) @ C )
!= ( A @ ( comp @ ( sk23 @ A @ B ) @ C ) @ ( sub @ ( sk24 @ A @ B ) @ C ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: subst > term > term] :
@+[B: subst] :
~ ! [C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: subst > term > term] :
@+[B: term] :
~ ! [C: subst] :
( ( sub @ ( A @ ( sk26 @ A ) @ B ) @ C )
= ( A @ ( comp @ ( sk26 @ A ) @ C ) @ ( sub @ B @ C ) ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: subst > term > term] :
@+[B: subst] :
( ( sub @ ( A @ ( sk26 @ A ) @ ( sk27 @ A ) ) @ B )
!= ( A @ ( comp @ ( sk26 @ A ) @ B ) @ ( sub @ ( sk27 @ A ) @ B ) ) ) ) ) ).
thf(sk29_def,definition,
( sk29
= ( ^ [A: subst > term > term] :
@+[B: subst] :
~ ! [C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( ^ [A: subst > term > term] :
@+[B: term] :
~ ! [C: subst] :
( ( sub @ ( A @ ( sk29 @ A ) @ B ) @ C )
= ( A @ ( comp @ ( sk29 @ A ) @ C ) @ ( sub @ B @ C ) ) ) ) ) ).
thf(sk31_def,definition,
( sk31
= ( ^ [A: subst > term > term] :
@+[B: subst] :
( ( sub @ ( A @ ( sk29 @ A ) @ ( sk30 @ A ) ) @ B )
!= ( A @ ( comp @ ( sk29 @ A ) @ B ) @ ( sub @ ( sk30 @ A ) @ B ) ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ! [C: term,D: subst,E: subst] :
( ( A @ B @ C @ ( comp @ E @ D ) )
=> ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D ) ) ) ) ).
thf(sk34_def,definition,
( sk34
= ( ^ [A: subst > term > subst > $o] :
@+[B: term] :
~ ! [C: subst,D: subst] :
( ( A @ ( sk33 @ A ) @ B @ ( comp @ D @ C ) )
=> ( A @ ( comp @ ( sk33 @ A ) @ D ) @ ( sub @ B @ D ) @ C ) ) ) ) ).
thf(sk35_def,definition,
( sk35
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ! [C: subst] :
( ( A @ ( sk33 @ A ) @ ( sk34 @ A ) @ ( comp @ C @ B ) )
=> ( A @ ( comp @ ( sk33 @ A ) @ C ) @ ( sub @ ( sk34 @ A ) @ C ) @ B ) ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ( ( A @ ( sk33 @ A ) @ ( sk34 @ A ) @ ( comp @ B @ ( sk35 @ A ) ) )
=> ( A @ ( comp @ ( sk33 @ A ) @ B ) @ ( sub @ ( sk34 @ A ) @ B ) @ ( sk35 @ A ) ) ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ! [C: term,D: subst,E: subst] :
( ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D )
=> ( A @ B @ C @ ( comp @ E @ D ) ) ) ) ) ).
thf(sk38_def,definition,
( sk38
= ( ^ [A: subst > term > subst > $o] :
@+[B: term] :
~ ! [C: subst,D: subst] :
( ( A @ ( comp @ ( sk37 @ A ) @ D ) @ ( sub @ B @ D ) @ C )
=> ( A @ ( sk37 @ A ) @ B @ ( comp @ D @ C ) ) ) ) ) ).
thf(sk39_def,definition,
( sk39
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ! [C: subst] :
( ( A @ ( comp @ ( sk37 @ A ) @ C ) @ ( sub @ ( sk38 @ A ) @ C ) @ B )
=> ( A @ ( sk37 @ A ) @ ( sk38 @ A ) @ ( comp @ C @ B ) ) ) ) ) ).
thf(sk40_def,definition,
( sk40
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ( ( A @ ( comp @ ( sk37 @ A ) @ B ) @ ( sub @ ( sk38 @ A ) @ B ) @ ( sk39 @ A ) )
=> ( A @ ( sk37 @ A ) @ ( sk38 @ A ) @ ( comp @ B @ ( sk39 @ A ) ) ) ) ) ) ).
thf(sk41_def,definition,
( sk41
= ( ^ [A: subst > term > subst > $o] :
@+[B: term] :
~ ( ( var @ ( sub @ B @ id ) )
=> ( A @ id @ B @ id ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ! [C: term,D: subst,E: subst] :
( ( A @ B @ C @ ( comp @ E @ D ) )
=> ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D ) ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( ^ [A: subst > term > subst > $o] :
@+[B: term] :
~ ! [C: subst,D: subst] :
( ( A @ ( sk43 @ A ) @ B @ ( comp @ D @ C ) )
=> ( A @ ( comp @ ( sk43 @ A ) @ D ) @ ( sub @ B @ D ) @ C ) ) ) ) ).
thf(sk45_def,definition,
( sk45
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ! [C: subst] :
( ( A @ ( sk43 @ A ) @ ( sk44 @ A ) @ ( comp @ C @ B ) )
=> ( A @ ( comp @ ( sk43 @ A ) @ C ) @ ( sub @ ( sk44 @ A ) @ C ) @ B ) ) ) ) ).
thf(sk46_def,definition,
( sk46
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ( ( A @ ( sk43 @ A ) @ ( sk44 @ A ) @ ( comp @ B @ ( sk45 @ A ) ) )
=> ( A @ ( comp @ ( sk43 @ A ) @ B ) @ ( sub @ ( sk44 @ A ) @ B ) @ ( sk45 @ A ) ) ) ) ) ).
thf(sk47_def,definition,
( sk47
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ! [C: term,D: subst,E: subst] :
( ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D )
=> ( A @ B @ C @ ( comp @ E @ D ) ) ) ) ) ).
thf(sk48_def,definition,
( sk48
= ( ^ [A: subst > term > subst > $o] :
@+[B: term] :
~ ! [C: subst,D: subst] :
( ( A @ ( comp @ ( sk47 @ A ) @ D ) @ ( sub @ B @ D ) @ C )
=> ( A @ ( sk47 @ A ) @ B @ ( comp @ D @ C ) ) ) ) ) ).
thf(sk49_def,definition,
( sk49
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ! [C: subst] :
( ( A @ ( comp @ ( sk47 @ A ) @ C ) @ ( sub @ ( sk48 @ A ) @ C ) @ B )
=> ( A @ ( sk47 @ A ) @ ( sk48 @ A ) @ ( comp @ C @ B ) ) ) ) ) ).
thf(sk50_def,definition,
( sk50
= ( ^ [A: subst > term > subst > $o] :
@+[B: subst] :
~ ( ( A @ ( comp @ ( sk47 @ A ) @ B ) @ ( sub @ ( sk48 @ A ) @ B ) @ ( sk49 @ A ) )
=> ( A @ ( sk47 @ A ) @ ( sk48 @ A ) @ ( comp @ B @ ( sk49 @ A ) ) ) ) ) ) ).
thf(sk51_def,definition,
( sk51
= ( ^ [A: subst > term > subst > $o] :
@+[B: term] :
~ ( ( A @ id @ B @ id )
=> ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( ap @ ( sub @ B @ id ) @ C ) @ id ) ) ) ) ) ).
thf(sk52_def,definition,
( sk52
= ( ^ [A: subst > term > subst > $o] :
@+[B: term] :
~ ( ( A @ id @ B @ id )
=> ( A @ id @ ( ap @ ( sub @ ( sk51 @ A ) @ id ) @ B ) @ id ) ) ) ) ).
thf(sk53_def,definition,
( sk53
= ( @+[A: term] :
~ ? [B: subst > term > term] :
( ( sub @ A @ ( push @ one @ sh ) )
= ( B @ sh @ one ) ) ) ) ).
thf(1,conjecture,
hoasinduction_lem3b_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoasinduction_lem3b_gthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term,B: term,C: subst] :
( ( sub @ ( ap @ A @ B ) @ C )
= ( ap @ ( sub @ A @ C ) @ ( sub @ B @ C ) ) )
=> ( ! [A: term,B: subst] :
( ( sub @ one @ ( push @ A @ B ) )
= A )
=> ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ! [A: term,B: subst] :
( ( sub @ ( lam @ A ) @ B )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ B @ sh ) ) ) ) )
=> ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: subst] :
( ( comp @ id @ A )
= A )
=> ( ! [A: term,B: subst] :
( ( comp @ sh @ ( push @ A @ B ) )
= B )
=> ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: term,B: subst,C: subst] :
( ( comp @ ( push @ A @ B ) @ C )
= ( push @ ( sub @ A @ C ) @ ( comp @ B @ C ) ) )
=> ( ! [A: subst] :
( ( comp @ A @ id )
= A )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [A: subst] :
( ( push @ ( sub @ one @ A ) @ ( comp @ sh @ A ) )
= A )
=> ( ( var @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) )
=> ( ! [A: term > $o] :
( ( A @ one )
=> ( ! [B: term] :
( ( var @ B )
=> ( ( A @ B )
=> ( A @ ( sub @ B @ sh ) ) ) )
=> ! [B: term] :
( ( var @ B )
=> ( A @ B ) ) ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) )
=> ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) )
=> ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) )
=> ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) )
=> ( ! [A: term] :
~ ( var @ ( lam @ A ) )
=> ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ( A @ B )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) )
=> ( ! [A: term > $o,B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( ( A @ B )
=> ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ ( push @ B @ C ) ) ) ) ) )
=> ( ! [A: term > $o] :
( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( A @ ( sub @ B @ C ) ) ) ) )
=> ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) )
=> ( ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
& ! [A: subst] :
( ( comp @ id @ A )
= A )
& ! [A: subst] :
( ( comp @ A @ id )
= A ) )
=> ( ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ ( sub @ A @ id ) @ C )
= ( ap @ ( sub @ B @ id ) @ D ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ ( sub @ A @ id ) @ C )
= ( ap @ ( sub @ B @ id ) @ D ) )
=> ( C = D ) )
=> ( ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ! [B: subst > term > term] :
( ! [C: subst,D: term,E: subst] :
( ( sub @ ( B @ C @ D ) @ E )
= ( B @ ( comp @ C @ E ) @ ( sub @ D @ E ) ) )
=> ( ( ( lam @ ( A @ sh @ one ) )
= ( lam @ ( B @ sh @ one ) ) )
=> ! [C: subst,D: term] :
( ( A @ C @ D )
= ( B @ C @ D ) ) ) ) )
=> ( ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ! [B: term,C: term] :
( ( lam @ ( A @ sh @ one ) )
!= ( ap @ ( sub @ B @ id ) @ C ) ) )
=> ( ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( A @ sh @ one ) ) @ id ) ) )
=> ( ! [A: term,B: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
=> ( ! [A: subst > term > subst > $o] :
( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ B @ C @ ( comp @ E @ D ) )
=> ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D ) )
=> ( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D )
=> ( A @ B @ C @ ( comp @ E @ D ) ) )
=> ( ! [B: term] :
( ( var @ ( sub @ B @ id ) )
=> ( A @ id @ B @ id ) )
=> ! [B: term] :
( ( var @ B )
=> ( A @ id @ B @ id ) ) ) ) )
=> ( ! [A: subst > term > subst > $o] :
( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ B @ C @ ( comp @ E @ D ) )
=> ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D ) )
=> ( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D )
=> ( A @ B @ C @ ( comp @ E @ D ) ) )
=> ( ! [B: term,C: term] :
( ( A @ id @ B @ id )
=> ( ( A @ id @ C @ id )
=> ( A @ id @ ( ap @ ( sub @ B @ id ) @ C ) @ id ) ) )
=> ! [B: term,C: term] :
( ( A @ id @ B @ id )
=> ( ( A @ id @ C @ id )
=> ( A @ id @ ( ap @ B @ C ) @ id ) ) ) ) ) )
=> ! [A: term] :
? [B: subst > term > term] :
( ( sub @ A @ ( push @ one @ sh ) )
= ( B @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: term,B: term,C: subst] :
( ( sub @ ( ap @ A @ B ) @ C )
= ( ap @ ( sub @ A @ C ) @ ( sub @ B @ C ) ) )
=> ( ! [A: term,B: subst] :
( ( sub @ one @ ( push @ A @ B ) )
= A )
=> ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ! [A: term,B: subst] :
( ( sub @ ( lam @ A ) @ B )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ B @ sh ) ) ) ) )
=> ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: subst] :
( ( comp @ id @ A )
= A )
=> ( ! [A: term,B: subst] :
( ( comp @ sh @ ( push @ A @ B ) )
= B )
=> ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: term,B: subst,C: subst] :
( ( comp @ ( push @ A @ B ) @ C )
= ( push @ ( sub @ A @ C ) @ ( comp @ B @ C ) ) )
=> ( ! [A: subst] :
( ( comp @ A @ id )
= A )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [A: subst] :
( ( push @ ( sub @ one @ A ) @ ( comp @ sh @ A ) )
= A )
=> ( ( var @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) )
=> ( ! [A: term > $o] :
( ( A @ one )
=> ( ! [B: term] :
( ( var @ B )
=> ( ( A @ B )
=> ( A @ ( sub @ B @ sh ) ) ) )
=> ! [B: term] :
( ( var @ B )
=> ( A @ B ) ) ) )
=> ( ! [A: term,B: term] :
( ? [C: term,D: term] :
( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) )
=> ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) )
=> ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) )
=> ( ~ ? [A: term,B: term,C: term] :
( ( lam @ A )
= ( ap @ B @ C ) )
=> ( ~ ? [A: term,B: term] : ( var @ ( ap @ A @ B ) )
=> ( ~ ? [A: term] : ( var @ ( lam @ A ) )
=> ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term] :
( ( A @ B )
=> ! [C: term] :
( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ( A @ B )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) )
=> ( ! [A: term > $o,B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( ( A @ B )
=> ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ ( push @ B @ C ) ) ) ) ) )
=> ( ! [A: term > $o] :
( ! [B: term] :
( ( A @ B )
=> ! [C: term] :
( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( A @ ( sub @ B @ C ) ) ) ) )
=> ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term] :
( ( A @ B )
=> ! [C: term] :
( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) )
=> ( ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
& ! [A: subst] :
( ( comp @ id @ A )
= A )
& ! [A: subst] :
( ( comp @ A @ id )
= A ) )
=> ( ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) )
=> ( ! [A: term,B: term] :
( ? [C: term,D: term] :
( ( ap @ ( sub @ A @ id ) @ C )
= ( ap @ ( sub @ B @ id ) @ D ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ ( sub @ A @ id ) @ C )
= ( ap @ ( sub @ B @ id ) @ D ) )
=> ( C = D ) )
=> ( ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ! [B: subst > term > term] :
( ! [C: subst,D: term,E: subst] :
( ( sub @ ( B @ C @ D ) @ E )
= ( B @ ( comp @ C @ E ) @ ( sub @ D @ E ) ) )
=> ( ( ( lam @ ( A @ sh @ one ) )
= ( lam @ ( B @ sh @ one ) ) )
=> ! [C: subst,D: term] :
( ( A @ C @ D )
= ( B @ C @ D ) ) ) ) )
=> ( ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ~ ? [B: term,C: term] :
( ( lam @ ( A @ sh @ one ) )
= ( ap @ ( sub @ B @ id ) @ C ) ) )
=> ( ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( A @ sh @ one ) ) @ id ) ) )
=> ( ~ ? [A: term,B: term] : ( var @ ( sub @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
=> ( ! [A: subst > term > subst > $o] :
( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ B @ C @ ( comp @ E @ D ) )
=> ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D ) )
=> ( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D )
=> ( A @ B @ C @ ( comp @ E @ D ) ) )
=> ( ! [B: term] :
( ( var @ ( sub @ B @ id ) )
=> ( A @ id @ B @ id ) )
=> ! [B: term] :
( ( var @ B )
=> ( A @ id @ B @ id ) ) ) ) )
=> ( ! [A: subst > term > subst > $o] :
( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ B @ C @ ( comp @ E @ D ) )
=> ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D ) )
=> ( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D )
=> ( A @ B @ C @ ( comp @ E @ D ) ) )
=> ( ! [B: term] :
( ( A @ id @ B @ id )
=> ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( ap @ ( sub @ B @ id ) @ C ) @ id ) ) )
=> ! [B: term] :
( ( A @ id @ B @ id )
=> ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( ap @ B @ C ) @ id ) ) ) ) ) )
=> ! [A: term] :
? [B: subst > term > term] :
( ( sub @ A @ ( push @ one @ sh ) )
= ( B @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [ZZZK: subst > term > term,ZZZJ: term,ZZZI: term,ZZZH: subst > term > subst > $o,ZZZG: term,ZZZF: subst > term > subst > $o,ZZZE: term,ZZZD: term,ZZZC: subst > term > term,ZZZB: term,ZZZA: term,ZZZ: subst > term > term,ZZY: term,ZZX: subst,ZZW: subst > term > term,ZZV: subst > term > term,ZZU: term,ZZT: term,ZZS: term,ZZR: term,ZZQ: term,ZZP: term,ZZO: term,ZZN: term,ZZM: term,ZZL: subst,ZZK: subst,ZZJ: term,ZZI: subst,ZZH: subst,ZZG: subst,ZZF: subst,ZZE: subst,ZZD: term,ZZC: term,ZZB: term > $o,ZZA: subst,ZZ: term,ZY: term,ZX: term > $o,ZW: term,ZV: subst,ZU: term,ZT: term > $o,ZS: term,ZR: term > $o,ZQ: term,ZP: term,ZO: term,ZN: term,ZM: term,ZL: term,ZK: term,ZJ: term,ZI: term,ZH: term,ZG: term,ZF: term,ZE: term,ZD: term,ZC: term,ZB: term,ZA: term,Z: term,Y: term,X: term > $o,W: term,V: subst,U: subst,T: subst,S: subst,R: term,Q: subst,P: subst,O: subst,N: subst,M: term,L: subst,K: subst,J: subst,I: term,H: subst,G: term,F: term,E: subst,D: term,C: subst,B: term,A: term] :
( ( ( sub @ ( ap @ A @ B ) @ C )
= ( ap @ ( sub @ A @ C ) @ ( sub @ B @ C ) ) )
& ( ( sub @ one @ ( push @ D @ E ) )
= D )
& ( ( sub @ F @ id )
= F )
& ( ( sub @ ( lam @ G ) @ H )
= ( lam @ ( sub @ G @ ( push @ one @ ( comp @ H @ sh ) ) ) ) )
& ( ( sub @ ( sub @ I @ J ) @ K )
= ( sub @ I @ ( comp @ J @ K ) ) )
& ( ( comp @ id @ L )
= L )
& ( ( comp @ sh @ ( push @ M @ N ) )
= N )
& ( ( comp @ ( comp @ O @ P ) @ Q )
= ( comp @ O @ ( comp @ P @ Q ) ) )
& ( ( comp @ ( push @ R @ S ) @ T )
= ( push @ ( sub @ R @ T ) @ ( comp @ S @ T ) ) )
& ( ( comp @ U @ id )
= U )
& ( ( push @ one @ sh )
= id )
& ( ( push @ ( sub @ one @ V ) @ ( comp @ sh @ V ) )
= V )
& ( var @ one )
& ( ~ ( var @ W )
| ( var @ ( sub @ W @ sh ) ) )
& ( ~ ( X @ one )
| ( var @ ( sk1 @ X ) )
| ~ ( var @ Y )
| ( X @ Y ) )
& ( ~ ( X @ one )
| ( X @ ( sk1 @ X ) )
| ~ ( var @ Y )
| ( X @ Y ) )
& ( ~ ( X @ one )
| ~ ( X @ ( sub @ ( sk1 @ X ) @ sh ) )
| ~ ( var @ Y )
| ( X @ Y ) )
& ( ( ( ap @ Z @ ZB )
!= ( ap @ ZA @ ZC ) )
| ( Z = ZA ) )
& ( ( ( ap @ ZD @ ZF )
!= ( ap @ ZE @ ZG ) )
| ( ZF = ZG ) )
& ( ( ( lam @ ZH )
!= ( lam @ ZI ) )
| ( ZH = ZI ) )
& ( ( ( sub @ ZJ @ sh )
!= ( sub @ ZK @ sh ) )
| ( ZJ = ZK ) )
& ( ( lam @ ZL )
!= ( ap @ ZM @ ZN ) )
& ~ ( var @ ( ap @ ZO @ ZP ) )
& ~ ( var @ ( lam @ ZQ ) )
& ( ( var @ ( sk3 @ ZR ) )
| ( sk2 @ ZR ) )
& ( ~ ( ZR @ ( sk3 @ ZR ) )
| ( sk2 @ ZR ) )
& ( ~ ( sk2 @ ZR )
| ( ZR @ ( sk4 @ ZR ) )
| ( ZR @ ( sk6 @ ZR ) )
| ( ZR @ ZS ) )
& ( ~ ( sk2 @ ZR )
| ( ZR @ ( sk4 @ ZR ) )
| ~ ( ZR @ ( lam @ ( sk6 @ ZR ) ) )
| ( ZR @ ZS ) )
& ( ~ ( sk2 @ ZR )
| ( ZR @ ( sk5 @ ZR ) )
| ( ZR @ ( sk6 @ ZR ) )
| ( ZR @ ZS ) )
& ( ~ ( sk2 @ ZR )
| ( ZR @ ( sk5 @ ZR ) )
| ~ ( ZR @ ( lam @ ( sk6 @ ZR ) ) )
| ( ZR @ ZS ) )
& ( ~ ( sk2 @ ZR )
| ~ ( ZR @ ( ap @ ( sk4 @ ZR ) @ ( sk5 @ ZR ) ) )
| ( ZR @ ( sk6 @ ZR ) )
| ( ZR @ ZS ) )
& ( ~ ( sk2 @ ZR )
| ~ ( ZR @ ( ap @ ( sk4 @ ZR ) @ ( sk5 @ ZR ) ) )
| ~ ( ZR @ ( lam @ ( sk6 @ ZR ) ) )
| ( ZR @ ZS ) )
& ( ( var @ ( sk7 @ ZV @ ZU @ ZT ) )
| ~ ( ZT @ ZU )
| ~ ( var @ ZW )
| ( ZT @ ( sub @ ZW @ ( push @ ZU @ ZV ) ) ) )
& ( ~ ( ZT @ ( sub @ ( sk7 @ ZV @ ZU @ ZT ) @ ZV ) )
| ~ ( ZT @ ZU )
| ~ ( var @ ZW )
| ( ZT @ ( sub @ ZW @ ( push @ ZU @ ZV ) ) ) )
& ( ( ZX @ ( sk9 @ ZX ) )
| ( sk8 @ ZX ) )
& ( ( ZX @ ( sk10 @ ZX ) )
| ( sk8 @ ZX ) )
& ( ~ ( ZX @ ( ap @ ( sk9 @ ZX ) @ ( sk10 @ ZX ) ) )
| ( sk8 @ ZX ) )
& ( ~ ( sk8 @ ZX )
| ~ ( ZX @ ZY )
| ( ZX @ ( sub @ ( sk12 @ ZX ) @ ( push @ ZY @ id ) ) )
| ( sk11 @ ZX ) )
& ( ~ ( sk8 @ ZX )
| ~ ( ZX @ ( lam @ ( sk12 @ ZX ) ) )
| ( sk11 @ ZX ) )
& ( ~ ( sk8 @ ZX )
| ~ ( sk11 @ ZX )
| ( var @ ( sk13 @ ZZA @ ZZ @ ZX ) )
| ( ZX @ ( sub @ ZZ @ ZZA ) ) )
& ( ~ ( sk8 @ ZX )
| ~ ( sk11 @ ZX )
| ~ ( ZX @ ( sub @ ( sk13 @ ZZA @ ZZ @ ZX ) @ ZZA ) )
| ( ZX @ ( sub @ ZZ @ ZZA ) ) )
& ( ( var @ ( sk15 @ ZZB ) )
| ( sk14 @ ZZB ) )
& ( ~ ( ZZB @ ( sk15 @ ZZB ) )
| ( sk14 @ ZZB ) )
& ( ~ ( sk14 @ ZZB )
| ( ZZB @ ( sk17 @ ZZB ) )
| ( sk16 @ ZZB ) )
& ( ~ ( sk14 @ ZZB )
| ( ZZB @ ( sk18 @ ZZB ) )
| ( sk16 @ ZZB ) )
& ( ~ ( sk14 @ ZZB )
| ~ ( ZZB @ ( ap @ ( sk17 @ ZZB ) @ ( sk18 @ ZZB ) ) )
| ( sk16 @ ZZB ) )
& ( ~ ( sk14 @ ZZB )
| ~ ( sk16 @ ZZB )
| ~ ( ZZB @ ZZC )
| ( ZZB @ ( sub @ ( sk19 @ ZZB ) @ ( push @ ZZC @ id ) ) )
| ( ZZB @ ZZD ) )
& ( ~ ( sk14 @ ZZB )
| ~ ( sk16 @ ZZB )
| ~ ( ZZB @ ( lam @ ( sk19 @ ZZB ) ) )
| ( ZZB @ ZZD ) )
& ( ( comp @ ( comp @ ZZE @ ZZF ) @ ZZG )
= ( comp @ ZZE @ ( comp @ ZZF @ ZZG ) ) )
& ( ( comp @ id @ ZZH )
= ZZH )
& ( ( comp @ ZZI @ id )
= ZZI )
& ( ( sub @ ( sub @ ZZJ @ ZZK ) @ ZZL )
= ( sub @ ZZJ @ ( comp @ ZZK @ ZZL ) ) )
& ( ( sub @ ZZM @ id )
= ZZM )
& ( ( ( ap @ ( sub @ ZZN @ id ) @ ZZP )
!= ( ap @ ( sub @ ZZO @ id ) @ ZZQ ) )
| ( ZZN = ZZO ) )
& ( ( ( ap @ ( sub @ ZZR @ id ) @ ZZT )
!= ( ap @ ( sub @ ZZS @ id ) @ ZZU ) )
| ( ZZT = ZZU ) )
& ( ( ( sub @ ( ZZV @ ( sk20 @ ZZV ) @ ( sk21 @ ZZV ) ) @ ( sk22 @ ZZV ) )
!= ( ZZV @ ( comp @ ( sk20 @ ZZV ) @ ( sk22 @ ZZV ) ) @ ( sub @ ( sk21 @ ZZV ) @ ( sk22 @ ZZV ) ) ) )
| ( ( sub @ ( ZZW @ ( sk23 @ ZZW @ ZZV ) @ ( sk24 @ ZZW @ ZZV ) ) @ ( sk25 @ ZZW @ ZZV ) )
!= ( ZZW @ ( comp @ ( sk23 @ ZZW @ ZZV ) @ ( sk25 @ ZZW @ ZZV ) ) @ ( sub @ ( sk24 @ ZZW @ ZZV ) @ ( sk25 @ ZZW @ ZZV ) ) ) )
| ( ( lam @ ( ZZV @ sh @ one ) )
!= ( lam @ ( ZZW @ sh @ one ) ) )
| ( ( ZZV @ ZZX @ ZZY )
= ( ZZW @ ZZX @ ZZY ) ) )
& ( ( ( sub @ ( ZZZ @ ( sk26 @ ZZZ ) @ ( sk27 @ ZZZ ) ) @ ( sk28 @ ZZZ ) )
!= ( ZZZ @ ( comp @ ( sk26 @ ZZZ ) @ ( sk28 @ ZZZ ) ) @ ( sub @ ( sk27 @ ZZZ ) @ ( sk28 @ ZZZ ) ) ) )
| ( ( lam @ ( ZZZ @ sh @ one ) )
!= ( ap @ ( sub @ ZZZA @ id ) @ ZZZB ) ) )
& ( ( ( sub @ ( ZZZC @ ( sk29 @ ZZZC ) @ ( sk30 @ ZZZC ) ) @ ( sk31 @ ZZZC ) )
!= ( ZZZC @ ( comp @ ( sk29 @ ZZZC ) @ ( sk31 @ ZZZC ) ) @ ( sub @ ( sk30 @ ZZZC ) @ ( sk31 @ ZZZC ) ) ) )
| ~ ( var @ ( sub @ ( lam @ ( ZZZC @ sh @ one ) ) @ id ) ) )
& ~ ( var @ ( sub @ ( ap @ ( sub @ ZZZD @ id ) @ ZZZE ) @ id ) )
& ( ( ZZZF @ ( sk33 @ ZZZF ) @ ( sk34 @ ZZZF ) @ ( comp @ ( sk36 @ ZZZF ) @ ( sk35 @ ZZZF ) ) )
| ( sk32 @ ZZZF ) )
& ( ~ ( ZZZF @ ( comp @ ( sk33 @ ZZZF ) @ ( sk36 @ ZZZF ) ) @ ( sub @ ( sk34 @ ZZZF ) @ ( sk36 @ ZZZF ) ) @ ( sk35 @ ZZZF ) )
| ( sk32 @ ZZZF ) )
& ( ~ ( sk32 @ ZZZF )
| ( ZZZF @ ( comp @ ( sk37 @ ZZZF ) @ ( sk40 @ ZZZF ) ) @ ( sub @ ( sk38 @ ZZZF ) @ ( sk40 @ ZZZF ) ) @ ( sk39 @ ZZZF ) )
| ( var @ ( sub @ ( sk41 @ ZZZF ) @ id ) )
| ~ ( var @ ZZZG )
| ( ZZZF @ id @ ZZZG @ id ) )
& ( ~ ( sk32 @ ZZZF )
| ( ZZZF @ ( comp @ ( sk37 @ ZZZF ) @ ( sk40 @ ZZZF ) ) @ ( sub @ ( sk38 @ ZZZF ) @ ( sk40 @ ZZZF ) ) @ ( sk39 @ ZZZF ) )
| ~ ( ZZZF @ id @ ( sk41 @ ZZZF ) @ id )
| ~ ( var @ ZZZG )
| ( ZZZF @ id @ ZZZG @ id ) )
& ( ~ ( sk32 @ ZZZF )
| ~ ( ZZZF @ ( sk37 @ ZZZF ) @ ( sk38 @ ZZZF ) @ ( comp @ ( sk40 @ ZZZF ) @ ( sk39 @ ZZZF ) ) )
| ( var @ ( sub @ ( sk41 @ ZZZF ) @ id ) )
| ~ ( var @ ZZZG )
| ( ZZZF @ id @ ZZZG @ id ) )
& ( ~ ( sk32 @ ZZZF )
| ~ ( ZZZF @ ( sk37 @ ZZZF ) @ ( sk38 @ ZZZF ) @ ( comp @ ( sk40 @ ZZZF ) @ ( sk39 @ ZZZF ) ) )
| ~ ( ZZZF @ id @ ( sk41 @ ZZZF ) @ id )
| ~ ( var @ ZZZG )
| ( ZZZF @ id @ ZZZG @ id ) )
& ( ( ZZZH @ ( sk43 @ ZZZH ) @ ( sk44 @ ZZZH ) @ ( comp @ ( sk46 @ ZZZH ) @ ( sk45 @ ZZZH ) ) )
| ( sk42 @ ZZZH ) )
& ( ~ ( ZZZH @ ( comp @ ( sk43 @ ZZZH ) @ ( sk46 @ ZZZH ) ) @ ( sub @ ( sk44 @ ZZZH ) @ ( sk46 @ ZZZH ) ) @ ( sk45 @ ZZZH ) )
| ( sk42 @ ZZZH ) )
& ( ~ ( sk42 @ ZZZH )
| ( ZZZH @ ( comp @ ( sk47 @ ZZZH ) @ ( sk50 @ ZZZH ) ) @ ( sub @ ( sk48 @ ZZZH ) @ ( sk50 @ ZZZH ) ) @ ( sk49 @ ZZZH ) )
| ( ZZZH @ id @ ( sk51 @ ZZZH ) @ id )
| ~ ( ZZZH @ id @ ZZZI @ id )
| ~ ( ZZZH @ id @ ZZZJ @ id )
| ( ZZZH @ id @ ( ap @ ZZZI @ ZZZJ ) @ id ) )
& ( ~ ( sk42 @ ZZZH )
| ( ZZZH @ ( comp @ ( sk47 @ ZZZH ) @ ( sk50 @ ZZZH ) ) @ ( sub @ ( sk48 @ ZZZH ) @ ( sk50 @ ZZZH ) ) @ ( sk49 @ ZZZH ) )
| ( ZZZH @ id @ ( sk52 @ ZZZH ) @ id )
| ~ ( ZZZH @ id @ ZZZI @ id )
| ~ ( ZZZH @ id @ ZZZJ @ id )
| ( ZZZH @ id @ ( ap @ ZZZI @ ZZZJ ) @ id ) )
& ( ~ ( sk42 @ ZZZH )
| ( ZZZH @ ( comp @ ( sk47 @ ZZZH ) @ ( sk50 @ ZZZH ) ) @ ( sub @ ( sk48 @ ZZZH ) @ ( sk50 @ ZZZH ) ) @ ( sk49 @ ZZZH ) )
| ~ ( ZZZH @ id @ ( ap @ ( sub @ ( sk51 @ ZZZH ) @ id ) @ ( sk52 @ ZZZH ) ) @ id )
| ~ ( ZZZH @ id @ ZZZI @ id )
| ~ ( ZZZH @ id @ ZZZJ @ id )
| ( ZZZH @ id @ ( ap @ ZZZI @ ZZZJ ) @ id ) )
& ( ~ ( sk42 @ ZZZH )
| ~ ( ZZZH @ ( sk47 @ ZZZH ) @ ( sk48 @ ZZZH ) @ ( comp @ ( sk50 @ ZZZH ) @ ( sk49 @ ZZZH ) ) )
| ( ZZZH @ id @ ( sk51 @ ZZZH ) @ id )
| ~ ( ZZZH @ id @ ZZZI @ id )
| ~ ( ZZZH @ id @ ZZZJ @ id )
| ( ZZZH @ id @ ( ap @ ZZZI @ ZZZJ ) @ id ) )
& ( ~ ( sk42 @ ZZZH )
| ~ ( ZZZH @ ( sk47 @ ZZZH ) @ ( sk48 @ ZZZH ) @ ( comp @ ( sk50 @ ZZZH ) @ ( sk49 @ ZZZH ) ) )
| ( ZZZH @ id @ ( sk52 @ ZZZH ) @ id )
| ~ ( ZZZH @ id @ ZZZI @ id )
| ~ ( ZZZH @ id @ ZZZJ @ id )
| ( ZZZH @ id @ ( ap @ ZZZI @ ZZZJ ) @ id ) )
& ( ~ ( sk42 @ ZZZH )
| ~ ( ZZZH @ ( sk47 @ ZZZH ) @ ( sk48 @ ZZZH ) @ ( comp @ ( sk50 @ ZZZH ) @ ( sk49 @ ZZZH ) ) )
| ~ ( ZZZH @ id @ ( ap @ ( sub @ ( sk51 @ ZZZH ) @ id ) @ ( sk52 @ ZZZH ) ) @ id )
| ~ ( ZZZH @ id @ ZZZI @ id )
| ~ ( ZZZH @ id @ ZZZJ @ id )
| ( ZZZH @ id @ ( ap @ ZZZI @ ZZZJ ) @ id ) )
& ( ( sub @ sk53 @ ( push @ one @ sh ) )
!= ( ZZZK @ sh @ one ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(30,plain,
! [A: subst > term > term] :
( ( sub @ sk53 @ ( push @ one @ sh ) )
!= ( A @ sh @ one ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(210,plain,
! [A: subst > term > term] :
( ( sub @ sk53 @ ( push @ one @ sh ) )
!= ( A @ sh @ one ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(211,plain,
! [A: subst > term > term] :
( ( sub @ sk53 @ ( push @ one @ sh ) )
!= ( A @ sh @ one ) ),
inference(simp,[status(thm)],[210]) ).
thf(42,plain,
( ( push @ one @ sh )
= id ),
inference(cnfConj,[status(thm)],[5]) ).
thf(107,plain,
( ( push @ one @ sh )
= id ),
inference(lifteq,[status(thm)],[42]) ).
thf(230,plain,
! [A: subst > term > term] :
( ( sub @ sk53 @ id )
!= ( A @ sh @ one ) ),
inference(rewrite,[status(thm)],[211,107]) ).
thf(231,plain,
$false,
inference(pre_uni,[status(thm)],[230:[bind(A,$thf( ^ [B: subst] : ^ [C: term] : ( sub @ sk53 @ id ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG267^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n008.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 17:35:39 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.91/0.63 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.77/0.98 % [INFO] Parsing done (349ms).
% 1.77/1.00 % [INFO] Running in sequential loop mode.
% 3.24/1.33 % [INFO] eprover registered as external prover.
% 3.24/1.33 % [INFO] Scanning for conjecture ...
% 4.61/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 4.99/1.81 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 4.99/1.82 % [INFO] Problem is higher-order (TPTP THF).
% 4.99/1.82 % [INFO] Type checking passed.
% 4.99/1.82 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 11.90/3.69 % [INFO] Killing All external provers ...
% 12.36/3.70 % Time passed: 3350ms (effective reasoning time: 2697ms)
% 12.36/3.70 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 12.36/3.70 % Axioms used in derivation (0):
% 12.36/3.70 % No. of inferences in proof: 12
% 12.36/3.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3350 ms resp. 2697 ms w/o parsing
% 14.36/4.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.36/4.08 % [INFO] Killing All external provers ...
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