%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP272_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:12:30 AM UTC 2025
% Result : Theorem 29.08s 29.30s
% Output : Proof 29.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 63 ( 28 ~; 24 |; 0 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 12 prp; 0-1 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-2 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(pp_type,type,
pp: bool > $o ).
tff(aa_nat_bool_type,type,
aa_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(na_type,type,
na: nat ).
tff(vEBT_invar_vebt_type,type,
vEBT_invar_vebt: vEBT_VEBT > fun_nat_bool ).
tff(vEBT_vebt_delete_type,type,
vEBT_vebt_delete: ( vEBT_VEBT * nat ) > vEBT_VEBT ).
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(the_nat_type,type,
the_nat: option_nat > nat ).
tff(vEBT_vebt_mint_type,type,
vEBT_vebt_mint: vEBT_VEBT > option_nat ).
tff(nth_VEBT_VEBT_type,type,
nth_VEBT_VEBT: ( list_VEBT_VEBT * nat ) > vEBT_VEBT ).
tff(summary_type,type,
summary: vEBT_VEBT ).
tff(treeList_type,type,
treeList: list_VEBT_VEBT ).
tff(power_power_nat_type,type,
power_power_nat: fun_nat_fun_nat_nat ).
tff(times_times_nat_type,type,
times_times_nat: fun_nat_fun_nat_nat ).
tff(plus_plus_nat_type,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
tff(vEBT_VEBT_low_type,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(vEBT_VEBT_high_type,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(1,plain,
( ~ pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),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,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na))
<=> ~ pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),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,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),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,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(3,plain,
~ pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),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,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),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,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na))
<=> pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062invar__vebt_A_ItreeList_A_B_Ahigh_A_Ithe_A_Ivebt__mint_Asummary_J_A_K_A2_A_094_A_Ideg_Adiv_A2_J_A_L_Athe_A_Ivebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__mint_Asummary_J_J_J_J_A_Ideg_Adiv_A2_J_J_An_092_060close_062) ).
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,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [T: vEBT_VEBT,N: nat,X: nat] :
refl(( ( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) )
<=> ( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) )
<=> ! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) )
<=> ! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [T: vEBT_VEBT,N: nat,X: nat] :
rewrite(( ( pp(aa_nat_bool(vEBT_invar_vebt(T),N))
=> pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) )
<=> ( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [T: vEBT_VEBT,N: nat,X: nat] :
( pp(aa_nat_bool(vEBT_invar_vebt(T),N))
=> pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) )
<=> ! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [T: vEBT_VEBT,N: nat,X: nat] :
( pp(aa_nat_bool(vEBT_invar_vebt(T),N))
=> pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_delete__pres__valid) ).
tff(13,plain,
! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) )
| ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),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,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)) )
<=> ( ~ ! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) )
| ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),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,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) )
| ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),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,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [T: vEBT_VEBT,N: nat,X: nat] :
( ~ pp(aa_nat_bool(vEBT_invar_vebt(T),N))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(T,X)),N)) )
| ~ pp(aa_nat_bool(vEBT_invar_vebt(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na))
| pp(aa_nat_bool(vEBT_invar_vebt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),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,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,the_nat(vEBT_vebt_mint(summary))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_mint(nth_VEBT_VEBT(treeList,the_nat(vEBT_vebt_mint(summary))))))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),na)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP272_1 : TPTP v9.0.0. Released v8.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 Jun 19 18:42:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 29.08/29.30 % SZS status Theorem
% 29.08/29.30 % SZS output start Proof
% See solution above
% 30.05/30.26 % E exiting
%------------------------------------------------------------------------------