%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP221_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:12:05 AM UTC 2025
% Result : Theorem 38.84s 39.01s
% Output : Proof 39.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 98 ( 26 ~; 43 |; 0 &)
% ( 25 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 13 prp; 0-1 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-4 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(pp_type,type,
pp: bool > $o ).
tff(aa_nat_bool_type,type,
aa_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(aa_nat_nat_type,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(aa_num_nat_type,type,
aa_num_nat: ( fun_num_nat * num ) > nat ).
tff(aa_num_num_type,type,
aa_num_num: ( fun_num_num * num ) > num ).
tff(one_type,type,
one: num ).
tff(bit0_type,type,
bit0: fun_num_num ).
tff(numeral_numeral_nat_type,type,
numeral_numeral_nat: fun_num_nat ).
tff(aa_nat_fun_nat_nat_type,type,
aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).
tff(deg_type,type,
deg: nat ).
tff(divide_divide_nat_type,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
tff(x_type,type,
x: nat ).
tff(vEBT_VEBT_low_type,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(vEBT_V5719532721284313246member_type,type,
vEBT_V5719532721284313246member: vEBT_VEBT > fun_nat_bool ).
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_Node_type,type,
vEBT_Node: ( option4927543243414619207at_nat * nat * list_VEBT_VEBT * vEBT_VEBT ) > vEBT_VEBT ).
tff(summary_type,type,
summary: vEBT_VEBT ).
tff(info_type,type,
info: option4927543243414619207at_nat ).
tff(vEBT_VEBT_membermima_type,type,
vEBT_VEBT_membermima: vEBT_VEBT > fun_nat_bool ).
tff(aa_VEB4832260192069861672t_bool_type,type,
aa_VEB4832260192069861672t_bool: ( fun_VE3763956218935105199t_bool * vEBT_VEBT ) > fun_nat_bool ).
tff(vEBT_V8194947554948674370ptions_type,type,
vEBT_V8194947554948674370ptions: fun_VE3763956218935105199t_bool ).
tff(1,plain,
^ [T: vEBT_VEBT,X: nat] :
refl(( ( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) )
<=> ( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T: vEBT_VEBT,X: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) )
<=> ! [T: vEBT_VEBT,X: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T: vEBT_VEBT,X: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) )
<=> ! [T: vEBT_VEBT,X: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T: vEBT_VEBT,X: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_both__member__options__def) ).
tff(5,plain,
! [T: vEBT_VEBT,X: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T: vEBT_VEBT,X: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T: vEBT_VEBT,X: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T: vEBT_VEBT,X: nat] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,T),X))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(T),X))
| pp(aa_nat_bool(vEBT_VEBT_membermima(T),X)) ) )
| ( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_Node(info,deg,treeList,summary)),x))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_Node(info,deg,treeList,summary)),x))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)) ) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_Node(info,deg,treeList,summary)),x))
<=> ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_Node(info,deg,treeList,summary)),x)) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_Node(info,deg,treeList,summary)),x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(12,plain,
~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_Node(info,deg,treeList,summary)),x)),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( ~ ( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_Node(info,deg,treeList,summary)),x))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)) ) )
| pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_Node(info,deg,treeList,summary)),x))
| ~ ( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(14,plain,
( ~ ( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_Node(info,deg,treeList,summary)),x))
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)) ) )
| ~ ( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)) ) ),
inference(unit_resolution,[status(thm)],[13,12]) ).
tff(15,plain,
~ ( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)) ),
inference(unit_resolution,[status(thm)],[14,9]) ).
tff(16,plain,
( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x)) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
~ pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x)),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
( ( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) )
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
=> pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x)) )
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
( pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
=> pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__092_060open_062naive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Anaive__member_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062) ).
tff(21,plain,
( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
~ pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),
inference(unit_resolution,[status(thm)],[22,17]) ).
tff(24,plain,
( pp(aa_nat_bool(vEBT_V5719532721284313246member(vEBT_Node(info,deg,treeList,summary)),x))
| pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)) ),
inference(tautology,[status(thm)],[]) ).
tff(25,plain,
~ pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)),
inference(unit_resolution,[status(thm)],[24,15]) ).
tff(26,plain,
( ( pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) )
<=> ( pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
=> pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)) )
<=> ( pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
( pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
=> pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Amembermima_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062) ).
tff(29,plain,
( pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_Node(info,deg,treeList,summary)),x))
| ~ pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
inference(modus_ponens,[status(thm)],[29,26]) ).
tff(31,plain,
~ pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),
inference(unit_resolution,[status(thm)],[30,25]) ).
tff(32,plain,
( ( pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
| pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) )
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
| pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
| pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) )
<=> ( pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
| pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
( pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
| pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060or_062_Anaive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_092_060close_062) ).
tff(35,plain,
( pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
| pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( pp(aa_nat_bool(vEBT_V5719532721284313246member(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))
| pp(aa_nat_bool(vEBT_VEBT_membermima(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,x),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ),
inference(modus_ponens,[status(thm)],[35,32]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,31,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ITP221_1 : TPTP v9.0.0. Released v8.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 18:32:05 EDT 2025
% 0.11/0.32 % CPUTime :
% 38.84/39.01 % SZS status Theorem
% 38.84/39.01 % SZS output start Proof
% See solution above
% 39.74/39.91 % E exiting
%------------------------------------------------------------------------------