%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP256_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 : Sat Jun 21 05:12:22 AM UTC 2025
% Result : Theorem 37.01s 37.21s
% Output : Proof 37.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 42 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 272 ( 42 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 419 ( 201 ~; 109 |; 36 &)
% ( 64 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 144 ( 136 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
tff(pp_type,type,
pp: bool > $o ).
tff(aa_set8260762808118238015T_bool_type,type,
aa_set8260762808118238015T_bool: ( fun_se448528567104302406T_bool * set_VEBT_VEBT ) > bool ).
tff(set_VEBT_VEBT2_type,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
tff(treeList_type,type,
treeList: list_VEBT_VEBT ).
tff(aa_VEB289770264548726718T_bool_type,type,
aa_VEB289770264548726718T_bool: ( fun_VE7346385682144900493T_bool * vEBT_VEBT ) > fun_se448528567104302406T_bool ).
tff(nth_VEBT_VEBT_type,type,
nth_VEBT_VEBT: ( list_VEBT_VEBT * nat ) > vEBT_VEBT ).
tff(aa_nat_nat_type,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(na_type,type,
na: nat ).
tff(aa_nat_fun_nat_nat_type,type,
aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).
tff(xa_type,type,
xa: nat ).
tff(vEBT_VEBT_high_type,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(member_VEBT_VEBT_type,type,
member_VEBT_VEBT: fun_VE7346385682144900493T_bool ).
tff(aa_nat_bool_type,type,
aa_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(aa_VEB4832260192069861672t_bool_type,type,
aa_VEB4832260192069861672t_bool: ( fun_VE3763956218935105199t_bool * vEBT_VEBT ) > fun_nat_bool ).
tff(vEBT_vebt_delete_type,type,
vEBT_vebt_delete: ( vEBT_VEBT * nat ) > vEBT_VEBT ).
tff(vEBT_V8194947554948674370ptions_type,type,
vEBT_V8194947554948674370ptions: fun_VE3763956218935105199t_bool ).
tff(vEBT_invar_vebt_type,type,
vEBT_invar_vebt: vEBT_VEBT > fun_nat_bool ).
tff(size_s6755466524823107622T_VEBT_type,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
tff(aa_nat_fun_nat_bool_type,type,
aa_nat_fun_nat_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(ord_less_nat_type,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(1,plain,
( ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na))
<=> ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(3,plain,
~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),Xa)),Xb)) )
| pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na)) ),
inference(tautology,[status(thm)],[]) ).
tff(5,plain,
( ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),Xa)),Xb)) ) ),
inference(unit_resolution,[status(thm)],[4,3]) ).
tff(6,plain,
^ [X2: vEBT_VEBT] :
refl(( ( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) )
<=> ( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) )
<=> ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [X2: vEBT_VEBT] :
rewrite(( ( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) )
<=> ( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) )
<=> ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) )
<=> ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) ) ),
inference(transitivity,[status(thm)],[9,7]) ).
tff(11,plain,
^ [X2: vEBT_VEBT] :
rewrite(( ( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) )
<=> ( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) )
<=> ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) )
<=> ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
^ [X2: vEBT_VEBT] :
trans(monotonicity(rewrite(( ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) )
<=> ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) )),
( ( pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
=> ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) )
<=> ( pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
=> ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) ) )),
rewrite(( ( pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
=> ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) )
<=> ( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) ) )),
( ( pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
=> ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) )
<=> ( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [X2: vEBT_VEBT] :
( pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
=> ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) )
<=> ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [X2: vEBT_VEBT] :
( pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
=> ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23__C4_OIH_C_I1_J) ).
tff(17,plain,
! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ( pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
& ! [Xa: nat,Xb: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb))
<=> ( ( Xa != Xb )
& pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) ) ) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) ),
inference(modus_ponens,[status(thm)],[20,10]) ).
tff(22,plain,
( ( ~ ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) )
| ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),Xa)),Xb)) ) ) )
<=> ( ~ ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) )
| ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),Xa)),Xb)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) )
| ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),Xa)),Xb)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [X2: vEBT_VEBT] :
( ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,X2),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(X2),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X2),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(X2,Xa)),Xb)) ) ) )
| ~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),set_VEBT_VEBT2(treeList)))
| ~ ( ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
~ ( ( ( Xa = Xb )
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Xb)) )
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),Xa)),Xb)) ) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),set_VEBT_VEBT2(treeList))),
inference(unit_resolution,[status(thm)],[24,21,5]) ).
tff(26,plain,
^ [N: nat,Xs: list_VEBT_VEBT] :
refl(( ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) )
<=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) )
<=> ! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) )
<=> ! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
^ [N: nat,Xs: list_VEBT_VEBT] :
rewrite(( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
=> pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) )
<=> ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [N: nat,Xs: list_VEBT_VEBT] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
=> pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) )
<=> ! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [N: nat,Xs: list_VEBT_VEBT] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
=> pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_nth__mem) ).
tff(32,plain,
! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),size_s6755466524823107622T_VEBT(treeList)))
<=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),size_s6755466524823107622T_VEBT(treeList))) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),size_s6755466524823107622T_VEBT(treeList))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062high_Ax_An_A_060_Alength_AtreeList_092_060close_062) ).
tff(38,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),size_s6755466524823107622T_VEBT(treeList))),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( ~ ! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),size_s6755466524823107622T_VEBT(treeList)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),set_VEBT_VEBT2(treeList))) )
<=> ( ~ ! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),size_s6755466524823107622T_VEBT(treeList)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),set_VEBT_VEBT2(treeList))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),size_s6755466524823107622T_VEBT(treeList)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),set_VEBT_VEBT2(treeList))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [N: nat,Xs: list_VEBT_VEBT] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,N),size_s6755466524823107622T_VEBT(Xs)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(Xs,N)),set_VEBT_VEBT2(Xs))) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),size_s6755466524823107622T_VEBT(treeList)))
| pp(aa_set8260762808118238015T_bool(aa_VEB289770264548726718T_bool(member_VEBT_VEBT,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),set_VEBT_VEBT2(treeList))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
$false,
inference(unit_resolution,[status(thm)],[41,38,35,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ITP256_1 : TPTP v9.0.0. Released v8.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 18:36:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 37.01/37.21 % SZS status Theorem
% 37.01/37.21 % SZS output start Proof
% See solution above
% 37.96/38.16 % E exiting
%------------------------------------------------------------------------------