%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP257_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:55:01 PM UTC 2026
% Result : Theorem 8.93s 3.86s
% Output : CNFRefutation 8.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 32 unt; 0 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 ( 4 avg)
% Number of types : 9 ( 9 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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_1006,type,
one_one_nat: nat ).
tff(decl_1013,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
tff(decl_1026,type,
times_times_nat: fun_nat_fun_nat_nat ).
tff(decl_1158,type,
list_u1324408373059187874T_VEBT: ( vEBT_VEBT * ( nat * list_VEBT_VEBT ) ) > list_VEBT_VEBT ).
tff(decl_1177,type,
nth_VEBT_VEBT: ( nat * list_VEBT_VEBT ) > vEBT_VEBT ).
tff(decl_1202,type,
suc: fun_nat_nat ).
tff(decl_1263,type,
bit0: fun_num_num ).
tff(decl_1265,type,
one: num ).
tff(decl_1273,type,
numeral_numeral_nat: fun_num_nat ).
tff(decl_1281,type,
some_nat: nat > option_nat ).
tff(decl_1292,type,
the_nat: option_nat > nat ).
tff(decl_1370,type,
power_power_nat: fun_nat_fun_nat_nat ).
tff(decl_1455,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
tff(decl_1604,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(decl_1606,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(decl_1617,type,
vEBT_vebt_delete: ( nat * vEBT_VEBT ) > vEBT_VEBT ).
tff(decl_1638,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
tff(decl_1745,type,
aa_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(decl_1773,type,
aa_nat_fun_nat_nat: ( nat * fun_nat_fun_nat_nat ) > fun_nat_nat ).
tff(decl_1803,type,
aa_num_nat: ( num * fun_num_nat ) > nat ).
tff(decl_1804,type,
aa_num_num: ( num * fun_num_num ) > num ).
tff(decl_2127,type,
deg: nat ).
tff(decl_2128,type,
lx: nat ).
tff(decl_2130,type,
ma: nat ).
tff(decl_2131,type,
maxi: nat ).
tff(decl_2132,type,
maxs: nat ).
tff(decl_2134,type,
na: nat ).
tff(decl_2135,type,
summary: vEBT_VEBT ).
tff(decl_2136,type,
summin: nat ).
tff(decl_2137,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/benchmark/theBenchmark.p',conj_0) ).
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/benchmark/theBenchmark.p',fact_19_True) ).
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/benchmark/theBenchmark.p',fact_649_Suc__1) ).
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/benchmark/theBenchmark.p',fact_1414_add_Ocommute) ).
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/benchmark/theBenchmark.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(fact_364_option_Osel,axiom,
! [X329: nat] : ( the_nat(some_nat(X329)) = X329 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_option_Osel) ).
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/benchmark/theBenchmark.p',fact_6__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062) ).
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/benchmark/theBenchmark.p',fact_1380_mult_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/benchmark/theBenchmark.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_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/benchmark/theBenchmark.p',fact_16__092_060open_062Some_Amaxi_A_061_Avebt__maxt_A_ItreeList_A_B_Amaxs_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(assume_negation,[status(cth)],[conj_0]) ).
tcf(c_0_11,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_12,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_13,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_14,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)],[c_0_10]) ).
tcf(c_0_15,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_11,c_0_12]) ).
tcf(c_0_16,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_13]) ).
tcf(c_0_17,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]) ).
tff(c_0_18,plain,
! [X20848: nat] : ( the_nat(some_nat(X20848)) = X20848 ),
inference(variable_rename,[status(thm)],[fact_364_option_Osel]) ).
tff(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(fof_nnf,[status(thm)],[c_0_14]) ).
tcf(c_0_20,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]) ).
tff(c_0_21,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_22,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_23,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_15,c_0_16]) ).
tcf(c_0_24,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_17,c_0_12]),c_0_15]) ).
tcf(c_0_25,plain,
! [X1: nat] : the_nat(some_nat(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_26,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_19]) ).
tcf(c_0_27,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_20,c_0_12]) ).
tcf(c_0_28,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_21]) ).
tcf(c_0_29,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,ma),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,ma),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,ma),na))),maxs) = 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)],[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_22,c_0_16]),c_0_12]),c_0_23]),c_0_16]),c_0_12]),c_0_23]),c_0_16]),c_0_12]),c_0_23]),c_0_16]),c_0_12]),c_0_23]),c_0_24]),c_0_25]) ).
tcf(c_0_30,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]) ).
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)],[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)],[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_26,c_0_12]),c_0_12]),c_0_27]),c_0_16]),c_0_12]),c_0_23]),c_0_24]),c_0_25]),c_0_28]),c_0_16]),c_0_12]),c_0_23]),c_0_16]),c_0_12]),c_0_23]),c_0_16]),c_0_12]),c_0_23]),c_0_16]),c_0_12]),c_0_23]),c_0_24]),c_0_25]),c_0_29]),c_0_30]),c_0_25]),c_0_16]),c_0_12]),c_0_28]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP257_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n003.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 20 22:22:46 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.12/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.93/3.86 % Version: 3.5.1
% 8.93/3.86 % Preprocessing class: FMLLSMLLSSSNFFN.
% 8.93/3.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.93/3.86 % Starting new_bool_3 with 900s (3) cores
% 8.93/3.86 % Starting new_bool_1 with 900s (3) cores
% 8.93/3.86 % Starting sh5l with 300s (1) cores
% 8.93/3.86 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 8.93/3.86 % new_bool_3 with pid 2736272 completed with status 0
% 8.93/3.86 % Result found by new_bool_3
% 8.93/3.86 % Preprocessing class: FMLLSMLLSSSNFFN.
% 8.93/3.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.93/3.86 % Starting new_bool_3 with 900s (3) cores
% 8.93/3.86 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 8.93/3.86 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 8.93/3.86 % Search class: FGHSM-SMLM32-DFFFFFNN
% 8.93/3.86 % Scheduled 13 strats onto 3 cores with 899 seconds (899 total)
% 8.93/3.86 % Starting SubtermCWHack with 81s (1) cores
% 8.93/3.86 % Starting new_bool_3 with 90s (1) cores
% 8.93/3.86 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 8.93/3.86 % new_bool_3 with pid 2736277 completed with status 0
% 8.93/3.86 % Result found by new_bool_3
% 8.93/3.86 % Preprocessing class: FMLLSMLLSSSNFFN.
% 8.93/3.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.93/3.86 % Starting new_bool_3 with 900s (3) cores
% 8.93/3.86 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 8.93/3.86 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 8.93/3.86 % Search class: FGHSM-SMLM32-DFFFFFNN
% 8.93/3.86 % Scheduled 13 strats onto 3 cores with 899 seconds (899 total)
% 8.93/3.86 % Starting SubtermCWHack with 81s (1) cores
% 8.93/3.86 % Starting new_bool_3 with 90s (1) cores
% 8.93/3.86 % Preprocessing time : 0.292 s
% 8.93/3.86 % Presaturation interreduction done
% 8.93/3.86
% 8.93/3.86 % Proof found!
% 8.93/3.86 % SZS status Theorem
% 8.93/3.86 % SZS output start CNFRefutation
% See solution above
% 8.93/3.86 % Parsed axioms : 13716
% 8.93/3.86 % Removed by relevancy pruning/SinE : 9660
% 8.93/3.86 % Initial clauses : 10374
% 8.93/3.86 % Removed in clause preprocessing : 2006
% 8.93/3.86 % Initial clauses in saturation : 8368
% 8.93/3.86 % Processed clauses : 2667
% 8.93/3.86 % ...of these trivial : 207
% 8.93/3.86 % ...subsumed : 562
% 8.93/3.86 % ...remaining for further processing : 1897
% 8.93/3.86 % Other redundant clauses eliminated : 515
% 8.93/3.86 % Clauses deleted for lack of memory : 0
% 8.93/3.86 % Backward-subsumed : 8
% 8.93/3.86 % Backward-rewritten : 72
% 8.93/3.86 % Generated clauses : 485
% 8.93/3.86 % ...of the previous two non-redundant : 213
% 8.93/3.86 % ...aggressively subsumed : 0
% 8.93/3.86 % Contextual simplify-reflections : 1
% 8.93/3.86 % Paramodulations : 0
% 8.93/3.86 % Factorizations : 0
% 8.93/3.86 % NegExts : 0
% 8.93/3.86 % Equation resolutions : 515
% 8.93/3.86 % Disequality decompositions : 0
% 8.93/3.86 % Total rewrite steps : 1327
% 8.93/3.86 % ...of those cached : 922
% 8.93/3.86 % Propositional unsat checks : 0
% 8.93/3.86 % Propositional check models : 0
% 8.93/3.86 % Propositional check unsatisfiable : 0
% 8.93/3.86 % Propositional clauses : 0
% 8.93/3.86 % Propositional clauses after purity: 0
% 8.93/3.86 % Propositional unsat core size : 0
% 8.93/3.86 % Propositional preprocessing time : 0.000
% 8.93/3.86 % Propositional encoding time : 0.000
% 8.93/3.86 % Propositional solver time : 0.000
% 8.93/3.86 % Success case prop preproc time : 0.000
% 8.93/3.86 % Success case prop encoding time : 0.000
% 8.93/3.86 % Success case prop solver time : 0.000
% 8.93/3.86 % Current number of processed clauses : 1332
% 8.93/3.86 % Positive orientable unit clauses : 450
% 8.93/3.86 % Positive unorientable unit clauses: 21
% 8.93/3.86 % Negative unit clauses : 174
% 8.93/3.86 % Non-unit-clauses : 687
% 8.93/3.86 % Current number of unprocessed clauses: 5914
% 8.93/3.86 % ...number of literals in the above : 26734
% 8.93/3.86 % Current number of archived formulas : 0
% 8.93/3.86 % Current number of archived clauses : 80
% 8.93/3.86 % Clause-clause subsumption calls (NU) : 91738
% 8.93/3.86 % Rec. Clause-clause subsumption calls : 55374
% 8.93/3.86 % Non-unit clause-clause subsumptions : 413
% 8.93/3.86 % Unit Clause-clause subsumption calls : 11736
% 8.93/3.86 % Rewrite failures with RHS unbound : 0
% 8.93/3.86 % BW rewrite match attempts : 3010
% 8.93/3.86 % BW rewrite match successes : 276
% 8.93/3.86 % Condensation attempts : 0
% 8.93/3.86 % Condensation successes : 0
% 8.93/3.86 % Termbank termtop insertions : 1190374
% 8.93/3.86 % Search garbage collected termcells : 207817
% 8.93/3.86
% 8.93/3.86 % -------------------------------------------------
% 8.93/3.86 % User time : 2.106 s
% 8.93/3.86 % System time : 0.163 s
% 8.93/3.86 % Total time : 2.269 s
% 8.93/3.86 % Maximum resident set size: 57768 pages
% 8.93/3.86
% 8.93/3.86 % -------------------------------------------------
% 8.93/3.86 % User time : 4.025 s
% 8.93/3.86 % System time : 0.392 s
% 8.93/3.86 % Total time : 4.417 s
% 8.93/3.86 % Maximum resident set size: 33792 pages
% 8.93/3.86 % E exiting
%------------------------------------------------------------------------------