TSTP Solution File: ITP256_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP256_1 : TPTP v8.1.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 Sep 17 04:17:46 EDT 2022
% Result : Theorem 56.54s 37.09s
% Output : Proof 57.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 42
% Syntax : Number of formulae : 67 ( 14 unt; 21 typ; 0 def)
% Number of atoms : 278 ( 42 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 423 ( 203 ~; 109 |; 36 &)
% ( 66 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 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 : 22 ( 13 >; 9 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-2 aty)
% Number of variables : 144 ( 136 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
tff(pp_type,type,
pp: bool > $o ).
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(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(ma_type,type,
ma: nat ).
tff(vEBT_VEBT_high_type,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(treeList_type,type,
treeList: list_VEBT_VEBT ).
tff(vEBT_V8194947554948674370ptions_type,type,
vEBT_V8194947554948674370ptions: fun_VE3763956218935105199t_bool ).
tff(vEBT_vebt_delete_type,type,
vEBT_vebt_delete: ( vEBT_VEBT * nat ) > vEBT_VEBT ).
tff(vEBT_invar_vebt_type,type,
vEBT_invar_vebt: vEBT_VEBT > fun_nat_bool ).
tff(xa_type,type,
xa: nat ).
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(aa_VEB289770264548726718T_bool_type,type,
aa_VEB289770264548726718T_bool: ( fun_VE7346385682144900493T_bool * vEBT_VEBT ) > fun_se448528567104302406T_bool ).
tff(member_VEBT_VEBT_type,type,
member_VEBT_VEBT: fun_VE7346385682144900493T_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,ma),na))),na)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,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(3,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
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)),
inference(modus_ponens,[status(thm)],[3,2]) ).
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,ma),na))),na)),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,ma),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
( 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,ma),na)),Xa)),Xb))
<=> ~ ( ( 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,ma),na))),Xb)) ) )
| pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,ma),na))),na)) ),
inference(tautology,[status(thm)],]) ).
tff(7,plain,
( ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,ma),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
( 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,ma),na)),Xa)),Xb))
<=> ~ ( ( 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,ma),na))),Xb)) ) ) ),
inference(unit_resolution,[status(thm)],[6,5]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,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(12,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)],[11]) ).
tff(13,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/sandbox/benchmark/theBenchmark.p',fact_137_nth__mem) ).
tff(14,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)],[13,12]) ).
tff(15,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)],[14,10]) ).
tff(16,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)],[15]) ).
tff(17,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)],[16,9]) ).
tff(18,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,ma),na)),size_s6755466524823107622T_VEBT(treeList))) ),
inference(rewrite,[status(thm)],]) ).
tff(19,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(20,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/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062high_Ax_An_A_060_Alength_AtreeList_092_060close_062) ).
tff(21,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)],[20,19]) ).
tff(22,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,ma),na)),size_s6755466524823107622T_VEBT(treeList))),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,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,ma),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,ma),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,ma),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,ma),na))),set_VEBT_VEBT2(treeList))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,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,ma),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,ma),na))),set_VEBT_VEBT2(treeList))) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,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,ma),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,ma),na))),set_VEBT_VEBT2(treeList))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,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,ma),na))),set_VEBT_VEBT2(treeList))),
inference(unit_resolution,[status(thm)],[25,22,17]) ).
tff(27,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] :
( 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(28,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)],[27]) ).
tff(29,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] :
( 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(30,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)],[29]) ).
tff(31,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(transitivity,[status(thm)],[30,28]) ).
tff(32,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] :
( 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(33,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)],[32]) ).
tff(34,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(35,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(36,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)],[35]) ).
tff(37,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/sandbox/benchmark/theBenchmark.p',fact_23__C4_OIH_C_I1_J) ).
tff(38,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)],[37,36]) ).
tff(39,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)],[38,34]) ).
tff(40,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)],[39]) ).
tff(41,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)],[40,33]) ).
tff(42,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)],[41,31]) ).
tff(43,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)) ) ) ) )
| ~ 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,ma),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,ma),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
( 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,ma),na)),Xa)),Xb))
<=> ~ ( ( 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,ma),na))),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)) ) ) ) )
| ~ 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,ma),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,ma),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
( 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,ma),na)),Xa)),Xb))
<=> ~ ( ( 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,ma),na))),Xb)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,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)) ) ) ) )
| ~ 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,ma),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,ma),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
( 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,ma),na)),Xa)),Xb))
<=> ~ ( ( 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,ma),na))),Xb)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,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)) ) ) ) )
| ~ 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,ma),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,ma),na))),na))
| ~ ! [Xa: nat,Xb: nat] :
( 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,ma),na)),Xa)),Xb))
<=> ~ ( ( 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,ma),na))),Xb)) ) ) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,42,26,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ITP256_1 : TPTP v8.1.0. Released v8.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 06:15:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 56.54/37.09 % SZS status Theorem
% 56.54/37.09 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------