TSTP Solution File: ITP233_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP233_1 : TPTP v8.1.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 04:17:15 EDT 2022
% Result : Theorem 20.37s 14.41s
% Output : Proof 21.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 26
% Syntax : Number of formulae : 46 ( 23 unt; 15 typ; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 46 ( 37 ~; 1 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 16 ( 8 >; 8 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 33 ( 5 !; 26 ?; 33 :)
% 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(vEBT_vebt_insert_type,type,
vEBT_vebt_insert: ( 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_low_type,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(nth_VEBT_VEBT_type,type,
nth_VEBT_VEBT: ( list_VEBT_VEBT * nat ) > vEBT_VEBT ).
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(list_u1324408373059187874T_VEBT_type,type,
list_u1324408373059187874T_VEBT: ( list_VEBT_VEBT * nat * vEBT_VEBT ) > list_VEBT_VEBT ).
tff(i_type,type,
i: nat ).
tff(1,plain,
^ [Y4: nat] :
refl(
( ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4))
<=> ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y4: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4))
<=> ! [Y4: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4))
<=> ~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Y4))
<=> ~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Y4))
<=> ~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Y4)) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),Y4))
<=> ~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Y4)) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( ~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),Y4))
<=> ~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),Y4)) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),Y4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(9,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),Y4)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),Y4)),
inference(modus_ponens,[status(thm)],[9,7]) ).
tff(11,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),Y4)),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),Y4)),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),Y4)),
inference(modus_ponens,[status(thm)],[12,7]) ).
tff(14,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),Y4)),
inference(modus_ponens,[status(thm)],[13,7]) ).
tff(15,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Y4)),
inference(modus_ponens,[status(thm)],[14,6]) ).
tff(16,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Y4)),
inference(modus_ponens,[status(thm)],[15,5]) ).
tff(17,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na))),Y4)),
inference(modus_ponens,[status(thm)],[16,5]) ).
tff(18,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)),
inference(modus_ponens,[status(thm)],[17,4]) ).
tff(19,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)),
inference(modus_ponens,[status(thm)],[18,3]) ).
tff(20,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)),
inference(modus_ponens,[status(thm)],[19,3]) ).
tff(21,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)),
inference(modus_ponens,[status(thm)],[20,3]) ).
tff(22,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)),
inference(modus_ponens,[status(thm)],[21,3]) ).
tff(23,plain,
~ ? [Y4: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)),
inference(modus_ponens,[status(thm)],[22,3]) ).
tff(24,plain,
^ [Y4: nat] : refl($oeq(~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)),~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)))),
inference(bind,[status(th)],]) ).
tff(25,plain,
! [Y4: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)),
inference(nnf-neg,[status(sab)],[23,24]) ).
tff(26,plain,
! [Y4: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4)),
inference(modus_ponens,[status(thm)],[25,2]) ).
tff(27,plain,
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na)))
<=> pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__C166_C) ).
tff(29,plain,
pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ! [Y4: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),Y4))
| ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,29,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP233_1 : TPTP v8.1.0. Released v8.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Sep 1 05:21:35 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 20.37/14.41 % SZS status Theorem
% 20.37/14.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------