TSTP Solution File: ITP257_1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : ITP257_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n016.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 May  4 08:10:07 EDT 2024

% Result   : Theorem 118.46s 23.59s
% Output   : CNFRefutation 118.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   49
% Syntax   : Number of formulae    :   71 (  32 unt;  39 typ;   0 def)
%            Number of atoms       :   32 (  31 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :   17 (   3 avg)
%            Number of types       :    9 (   9 usr)
%            Number of type conns  :   18 (  10   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   30 (  30 usr;  20 con; 0-3 aty)
%            Number of variables   :   15 (   0 sgn  15   !;   0   ?;  15   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_sort1,type,
    fun_nat_fun_nat_nat: $tType ).

tff(decl_sort2,type,
    nat: $tType ).

tff(decl_sort3,type,
    num: $tType ).

tff(decl_sort4,type,
    fun_nat_nat: $tType ).

tff(decl_sort5,type,
    vEBT_VEBT: $tType ).

tff(decl_sort6,type,
    option_nat: $tType ).

tff(decl_sort7,type,
    list_VEBT_VEBT: $tType ).

tff(decl_sort8,type,
    fun_num_nat: $tType ).

tff(decl_sort9,type,
    fun_num_num: $tType ).

tff(decl_1005,type,
    one_one_nat: nat ).

tff(decl_1012,type,
    plus_plus_nat: fun_nat_fun_nat_nat ).

tff(decl_1025,type,
    times_times_nat: fun_nat_fun_nat_nat ).

tff(decl_1157,type,
    list_u1324408373059187874T_VEBT: ( list_VEBT_VEBT * nat * vEBT_VEBT ) > list_VEBT_VEBT ).

tff(decl_1176,type,
    nth_VEBT_VEBT: ( list_VEBT_VEBT * nat ) > vEBT_VEBT ).

tff(decl_1201,type,
    suc: fun_nat_nat ).

tff(decl_1262,type,
    bit0: fun_num_num ).

tff(decl_1264,type,
    one: num ).

tff(decl_1272,type,
    numeral_numeral_nat: fun_num_nat ).

tff(decl_1280,type,
    some_nat: nat > option_nat ).

tff(decl_1291,type,
    the_nat: option_nat > nat ).

tff(decl_1369,type,
    power_power_nat: fun_nat_fun_nat_nat ).

tff(decl_1454,type,
    divide_divide_nat: fun_nat_fun_nat_nat ).

tff(decl_1603,type,
    vEBT_VEBT_high: fun_nat_fun_nat_nat ).

tff(decl_1605,type,
    vEBT_VEBT_low: fun_nat_fun_nat_nat ).

tff(decl_1616,type,
    vEBT_vebt_delete: ( vEBT_VEBT * nat ) > vEBT_VEBT ).

tff(decl_1637,type,
    vEBT_vebt_maxt: vEBT_VEBT > option_nat ).

tff(decl_1744,type,
    aa_nat_nat: ( fun_nat_nat * nat ) > nat ).

tff(decl_1772,type,
    aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).

tff(decl_1802,type,
    aa_num_nat: ( fun_num_nat * num ) > nat ).

tff(decl_1803,type,
    aa_num_num: ( fun_num_num * num ) > num ).

tff(decl_2126,type,
    deg: nat ).

tff(decl_2127,type,
    lx: nat ).

tff(decl_2129,type,
    ma: nat ).

tff(decl_2130,type,
    maxi: nat ).

tff(decl_2131,type,
    maxs: nat ).

tff(decl_2133,type,
    na: nat ).

tff(decl_2134,type,
    summary: vEBT_VEBT ).

tff(decl_2135,type,
    summin: nat ).

tff(decl_2136,type,
    treeList: list_VEBT_VEBT ).

tff(conj_0,conjecture,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,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_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na)),maxs)),maxi),
    file('/export/starexec/sandbox/tmp/tmp.e4NEMgAHin/E---3.1_17875.p',conj_0) ).

tff(fact_1414_add_Ocommute,axiom,
    ! [X4: nat,X5: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X4),X5) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X5),X4) ),
    file('/export/starexec/sandbox/tmp/tmp.e4NEMgAHin/E---3.1_17875.p',fact_1414_add_Ocommute) ).

tff(fact_12__092_060open_062treeList_A_091high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_A_Ilow_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_093_A_B_Athe_A_Ivebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_J_A_061_AtreeList_A_B_Amaxs_092_060close_062,axiom,
    nth_VEBT_VEBT(list_u1324408373059187874T_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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))))) = nth_VEBT_VEBT(treeList,maxs),
    file('/export/starexec/sandbox/tmp/tmp.e4NEMgAHin/E---3.1_17875.p',fact_12__092_060open_062treeList_A_091high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_A_Ilow_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_093_A_B_Athe_A_Ivebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_J_A_061_AtreeList_A_B_Amaxs_092_060close_062) ).

tff(fact_649_Suc__1,axiom,
    aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
    file('/export/starexec/sandbox/tmp/tmp.e4NEMgAHin/E---3.1_17875.p',fact_649_Suc__1) ).

tff(fact_364_option_Osel,axiom,
    ! [X329: nat] : ( the_nat(some_nat(X329)) = X329 ),
    file('/export/starexec/sandbox/tmp/tmp.e4NEMgAHin/E---3.1_17875.p',fact_364_option_Osel) ).

tff(fact_1380_mult_Ocommute,axiom,
    ! [X4: nat,X5: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X4),X5) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X5),X4) ),
    file('/export/starexec/sandbox/tmp/tmp.e4NEMgAHin/E---3.1_17875.p',fact_1380_mult_Ocommute) ).

tff(fact_19_True,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx) = ma,
    file('/export/starexec/sandbox/tmp/tmp.e4NEMgAHin/E---3.1_17875.p',fact_19_True) ).

tff(fact_16__092_060open_062Some_Amaxi_A_061_Avebt__maxt_A_ItreeList_A_B_Amaxs_J_092_060close_062,axiom,
    some_nat(maxi) = vEBT_vebt_maxt(nth_VEBT_VEBT(treeList,maxs)),
    file('/export/starexec/sandbox/tmp/tmp.e4NEMgAHin/E---3.1_17875.p',fact_16__092_060open_062Some_Amaxi_A_061_Avebt__maxt_A_ItreeList_A_B_Amaxs_J_092_060close_062) ).

tff(fact_6__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062,axiom,
    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/tmp/tmp.e4NEMgAHin/E---3.1_17875.p',fact_6__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062) ).

tff(fact_18__092_060open_062Some_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_092_060close_062,axiom,
    some_nat(maxs) = vEBT_vebt_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),
    file('/export/starexec/sandbox/tmp/tmp.e4NEMgAHin/E---3.1_17875.p',fact_18__092_060open_062Some_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_092_060close_062) ).

tff(c_0_10,negated_conjecture,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,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_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))))) != aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na)),maxs)),maxi),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

tff(c_0_11,plain,
    ! [X20648: nat,X20649: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X20648),X20649) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X20649),X20648) ),
    inference(variable_rename,[status(thm)],[fact_1414_add_Ocommute]) ).

tff(c_0_12,negated_conjecture,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,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_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))))) != aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na)),maxs)),maxi),
    inference(fof_nnf,[status(thm)],[c_0_10]) ).

tcf(c_0_13,plain,
    nth_VEBT_VEBT(list_u1324408373059187874T_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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))))) = nth_VEBT_VEBT(treeList,maxs),
    inference(split_conjunct,[status(thm)],[fact_12__092_060open_062treeList_A_091high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_A_Ilow_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_093_A_B_Athe_A_Ivebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_J_A_061_AtreeList_A_B_Amaxs_092_060close_062]) ).

tcf(c_0_14,plain,
    ! [X2: nat,X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

tcf(c_0_15,plain,
    aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
    inference(split_conjunct,[status(thm)],[fact_649_Suc__1]) ).

tff(c_0_16,plain,
    ! [X20848: nat] : ( the_nat(some_nat(X20848)) = X20848 ),
    inference(variable_rename,[status(thm)],[fact_364_option_Osel]) ).

tff(c_0_17,plain,
    ! [X20307: nat,X20308: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X20307),X20308) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X20308),X20307) ),
    inference(variable_rename,[status(thm)],[fact_1380_mult_Ocommute]) ).

tcf(c_0_18,plain,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx) = ma,
    inference(split_conjunct,[status(thm)],[fact_19_True]) ).

tcf(c_0_19,negated_conjecture,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,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_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))))) != aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na)),maxs)),maxi),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

tcf(c_0_20,plain,
    nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na),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,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(summary,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na))))) = nth_VEBT_VEBT(treeList,maxs),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_14]),c_0_15]),c_0_14]),c_0_15]),c_0_14]),c_0_15]) ).

tcf(c_0_21,plain,
    some_nat(maxi) = vEBT_vebt_maxt(nth_VEBT_VEBT(treeList,maxs)),
    inference(split_conjunct,[status(thm)],[fact_16__092_060open_062Some_Amaxi_A_061_Avebt__maxt_A_ItreeList_A_B_Amaxs_J_092_060close_062]) ).

tcf(c_0_22,plain,
    ! [X1: nat] : the_nat(some_nat(X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

tcf(c_0_23,plain,
    ! [X2: nat,X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

tcf(c_0_24,plain,
    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(split_conjunct,[status(thm)],[fact_6__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062]) ).

tcf(c_0_25,plain,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))),lx) = ma,
    inference(rw,[status(thm)],[c_0_18,c_0_15]) ).

tcf(c_0_26,plain,
    some_nat(maxs) = vEBT_vebt_maxt(vEBT_vebt_delete(summary,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,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),
    inference(split_conjunct,[status(thm)],[fact_18__092_060open_062Some_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_092_060close_062]) ).

tcf(c_0_27,negated_conjecture,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,maxi),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_nat_nat(suc,one_one_nat)))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(summary,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)))))) != aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,maxi),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,maxs),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_15]),c_0_15]),c_0_14]),c_0_15]),c_0_14]),c_0_15]),c_0_14]),c_0_15]),c_0_14]),c_0_15]),c_0_14]),c_0_15]),c_0_20]),c_0_21]),c_0_22]),c_0_14]),c_0_15]),c_0_23]),c_0_14]) ).

tcf(c_0_28,plain,
    aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_nat_nat(suc,one_one_nat)) = na,
    inference(rw,[status(thm)],[c_0_24,c_0_15]) ).

tcf(c_0_29,plain,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))) = ma,
    inference(rw,[status(thm)],[c_0_25,c_0_14]) ).

tcf(c_0_30,plain,
    vEBT_vebt_maxt(vEBT_vebt_delete(summary,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,ma),na))) = some_nat(maxs),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15]),c_0_25]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_22]),c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : ITP257_1 : TPTP v8.1.2. Released v8.0.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n016.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Fri May  3 13:13:46 EDT 2024
% 0.13/0.33  % CPUTime    : 
% 7.95/8.15  Running first-order model finding
% 7.95/8.15  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.e4NEMgAHin/E---3.1_17875.p
% 118.46/23.59  # Version: 3.1.0
% 118.46/23.59  # Preprocessing class: FMLLSMLLSSSNFFN.
% 118.46/23.59  # Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 118.46/23.59  # Starting new_bool_3 with 897s (3) cores
% 118.46/23.59  # Starting new_bool_1 with 897s (3) cores
% 118.46/23.59  # Starting sh5l with 299s (1) cores
% 118.46/23.59  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 299s (1) cores
% 118.46/23.59  # new_bool_1 with pid 18154 completed with status 0
% 118.46/23.59  # Result found by new_bool_1
% 118.46/23.59  # Preprocessing class: FMLLSMLLSSSNFFN.
% 118.46/23.59  # Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 118.46/23.59  # Starting new_bool_3 with 897s (3) cores
% 118.46/23.59  # Starting new_bool_1 with 897s (3) cores
% 118.46/23.59  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 118.46/23.59  # Search class: FGHSM-SMLM32-DFFFFFNN
% 118.46/23.59  # Scheduled 13 strats onto 3 cores with 896 seconds (896 total)
% 118.46/23.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 68s (1) cores
% 118.46/23.59  # Starting new_bool_1 with 90s (1) cores
% 118.46/23.59  # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 68s (1) cores
% 118.46/23.59  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with pid 18157 completed with status 0
% 118.46/23.59  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y
% 118.46/23.59  # Preprocessing class: FMLLSMLLSSSNFFN.
% 118.46/23.59  # Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 118.46/23.59  # Starting new_bool_3 with 897s (3) cores
% 118.46/23.59  # Starting new_bool_1 with 897s (3) cores
% 118.46/23.59  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 118.46/23.59  # Search class: FGHSM-SMLM32-DFFFFFNN
% 118.46/23.59  # Scheduled 13 strats onto 3 cores with 896 seconds (896 total)
% 118.46/23.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 68s (1) cores
% 118.46/23.59  # Preprocessing time       : 0.231 s
% 118.46/23.59  # Presaturation interreduction done
% 118.46/23.59  
% 118.46/23.59  # Proof found!
% 118.46/23.59  # SZS status Theorem
% 118.46/23.59  # SZS output start CNFRefutation
% See solution above
% 118.46/23.59  # Parsed axioms                        : 13716
% 118.46/23.59  # Removed by relevancy pruning/SinE    : 9660
% 118.46/23.59  # Initial clauses                      : 10374
% 118.46/23.59  # Removed in clause preprocessing      : 2006
% 118.46/23.59  # Initial clauses in saturation        : 8368
% 118.46/23.59  # Processed clauses                    : 10343
% 118.46/23.59  # ...of these trivial                  : 395
% 118.46/23.59  # ...subsumed                          : 1898
% 118.46/23.59  # ...remaining for further processing  : 8049
% 118.46/23.59  # Other redundant clauses eliminated   : 2368
% 118.46/23.59  # Clauses deleted for lack of memory   : 0
% 118.46/23.59  # Backward-subsumed                    : 71
% 118.46/23.59  # Backward-rewritten                   : 116
% 118.46/23.59  # Generated clauses                    : 6418
% 118.46/23.59  # ...of the previous two non-redundant : 4918
% 118.46/23.59  # ...aggressively subsumed             : 0
% 118.46/23.59  # Contextual simplify-reflections      : 97
% 118.46/23.59  # Paramodulations                      : 4727
% 118.46/23.59  # Factorizations                       : 3
% 118.46/23.59  # NegExts                              : 0
% 118.46/23.59  # Equation resolutions                 : 2407
% 118.46/23.59  # Disequality decompositions           : 0
% 118.46/23.59  # Total rewrite steps                  : 9316
% 118.46/23.59  # ...of those cached                   : 7915
% 118.46/23.59  # Propositional unsat checks           : 2
% 118.46/23.59  #    Propositional check models        : 2
% 118.46/23.59  #    Propositional check unsatisfiable : 0
% 118.46/23.59  #    Propositional clauses             : 0
% 118.46/23.59  #    Propositional clauses after purity: 0
% 118.46/23.59  #    Propositional unsat core size     : 0
% 118.46/23.59  #    Propositional preprocessing time  : 0.000
% 118.46/23.59  #    Propositional encoding time       : 0.069
% 118.46/23.59  #    Propositional solver time         : 0.009
% 118.46/23.59  #    Success case prop preproc time    : 0.000
% 118.46/23.59  #    Success case prop encoding time   : 0.000
% 118.46/23.59  #    Success case prop solver time     : 0.000
% 118.46/23.59  # Current number of processed clauses  : 833
% 118.46/23.59  #    Positive orientable unit clauses  : 310
% 118.46/23.59  #    Positive unorientable unit clauses: 9
% 118.46/23.59  #    Negative unit clauses             : 172
% 118.46/23.59  #    Non-unit-clauses                  : 342
% 118.46/23.59  # Current number of unprocessed clauses: 8531
% 118.46/23.59  # ...number of literals in the above   : 26881
% 118.46/23.59  # Current number of archived formulas  : 0
% 118.46/23.59  # Current number of archived clauses   : 5775
% 118.46/23.59  # Clause-clause subsumption calls (NU) : 25653431
% 118.46/23.59  # Rec. Clause-clause subsumption calls : 1145529
% 118.46/23.59  # Non-unit clause-clause subsumptions  : 1773
% 118.46/23.59  # Unit Clause-clause subsumption calls : 92037
% 118.46/23.59  # Rewrite failures with RHS unbound    : 0
% 118.46/23.59  # BW rewrite match attempts            : 8965
% 118.46/23.59  # BW rewrite match successes           : 447
% 118.46/23.59  # Condensation attempts                : 0
% 118.46/23.59  # Condensation successes               : 0
% 118.46/23.59  # Termbank termtop insertions          : 1813947
% 118.46/23.59  # Search garbage collected termcells   : 207819
% 118.46/23.59  
% 118.46/23.59  # -------------------------------------------------
% 118.46/23.59  # User time                : 14.040 s
% 118.46/23.59  # System time              : 0.158 s
% 118.46/23.59  # Total time               : 14.198 s
% 118.46/23.59  # Maximum resident set size: 55964 pages
% 118.46/23.59  
% 118.46/23.59  # -------------------------------------------------
% 118.46/23.59  # User time                : 41.010 s
% 118.46/23.59  # System time              : 0.439 s
% 118.46/23.59  # Total time               : 41.450 s
% 118.46/23.59  # Maximum resident set size: 30872 pages
% 118.46/23.59  % E---3.1 exiting
%------------------------------------------------------------------------------