%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP257^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Wed Sep 30 08:04:57 AM UTC 2026
% Result : Theorem 84.20s 30.10s
% Output : CNFRefutation 84.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 586 ( 3 ~; 0 |; 0 &; 583 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 5 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 11 con; 0-3 aty)
% Number of variables : 19 ( 12 ^; 7 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
num: $tType ).
thf(decl_sort3,type,
vEBT_VEBT: $tType ).
thf(decl_sort4,type,
list_VEBT_VEBT: $tType ).
thf(decl_sort5,type,
option_nat: $tType ).
thf(decl_214,type,
plus_plus_nat: nat > nat > nat ).
thf(decl_227,type,
times_times_nat: nat > nat > nat ).
thf(decl_364,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(decl_383,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(decl_469,type,
bit0: num > num ).
thf(decl_471,type,
one: num ).
thf(decl_479,type,
numeral_numeral_nat: num > nat ).
thf(decl_487,type,
some_nat: nat > option_nat ).
thf(decl_498,type,
the_nat: option_nat > nat ).
thf(decl_576,type,
power_power_nat: nat > nat > nat ).
thf(decl_661,type,
divide_divide_nat: nat > nat > nat ).
thf(decl_810,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(decl_812,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(decl_823,type,
vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
thf(decl_844,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
thf(decl_873,type,
deg: nat ).
thf(decl_874,type,
lx: nat ).
thf(decl_876,type,
ma: nat ).
thf(decl_877,type,
maxi: nat ).
thf(decl_878,type,
maxs: nat ).
thf(decl_880,type,
na: nat ).
thf(decl_881,type,
summary: vEBT_VEBT ).
thf(decl_882,type,
summin: nat ).
thf(decl_883,type,
treeList: list_VEBT_VEBT ).
thf(fact_1414_add_Ocommute,axiom,
( plus_plus_nat
= ( ^ [X2159: nat,X2160: nat] : ( plus_plus_nat @ X2160 @ X2159 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WyO5MJEAul/E---3.1_662119.p',fact_1414_add_Ocommute) ).
thf(fact_19_True,axiom,
( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= ma ),
file('/export/starexec/sandbox2/tmp/tmp.WyO5MJEAul/E---3.1_662119.p',fact_19_True) ).
thf(conj_0,conjecture,
( ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) )
= ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) @ maxs ) @ maxi ) ),
file('/export/starexec/sandbox2/tmp/tmp.WyO5MJEAul/E---3.1_662119.p',conj_0) ).
thf(fact_1380_mult_Ocommute,axiom,
( times_times_nat
= ( ^ [X2063: nat,X2064: nat] : ( times_times_nat @ X2064 @ X2063 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WyO5MJEAul/E---3.1_662119.p',fact_1380_mult_Ocommute) ).
thf(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 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WyO5MJEAul/E---3.1_662119.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) ).
thf(fact_364_option_Osel,axiom,
! [X334: nat] :
( ( the_nat @ ( some_nat @ X334 ) )
= X334 ),
file('/export/starexec/sandbox2/tmp/tmp.WyO5MJEAul/E---3.1_662119.p',fact_364_option_Osel) ).
thf(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 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
= ( nth_VEBT_VEBT @ treeList @ maxs ) ),
file('/export/starexec/sandbox2/tmp/tmp.WyO5MJEAul/E---3.1_662119.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) ).
thf(fact_6__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062,axiom,
( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= na ),
file('/export/starexec/sandbox2/tmp/tmp.WyO5MJEAul/E---3.1_662119.p',fact_6__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062) ).
thf(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/sandbox2/tmp/tmp.WyO5MJEAul/E---3.1_662119.p',fact_16__092_060open_062Some_Amaxi_A_061_Avebt__maxt_A_ItreeList_A_B_Amaxs_J_092_060close_062) ).
thf(c_0_9,plain,
( plus_plus_nat
= ( ^ [Z0: nat,Z1: nat] : ( plus_plus_nat @ Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[fact_1414_add_Ocommute]) ).
thf(c_0_10,plain,
( plus_plus_nat
= ( ^ [Z0: nat,Z1: nat] : ( plus_plus_nat @ Z1 @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,plain,
( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= ma ),
inference(split_conjunct,[status(thm)],[fact_19_True]) ).
thf(c_0_12,plain,
! [X2: nat,X1: nat] :
( ( plus_plus_nat @ X1 @ X2 )
= ( plus_plus_nat @ X2 @ X1 ) ),
inference(arg_cong,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
( ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) )
!= ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) @ maxs ) @ maxi ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_14,plain,
( times_times_nat
= ( ^ [Z0: nat,Z1: nat] : ( times_times_nat @ Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[fact_1380_mult_Ocommute]) ).
thf(c_0_15,plain,
( ( some_nat @ maxs )
= ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( 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]) ).
thf(c_0_16,plain,
( ( plus_plus_nat @ lx @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) )
= ma ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_17,plain,
! [X27858: nat] :
( ( the_nat @ ( some_nat @ X27858 ) )
= X27858 ),
inference(variable_rename,[status(thm)],[fact_364_option_Osel]) ).
thf(c_0_18,negated_conjecture,
( ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) )
!= ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) @ maxs ) @ maxi ) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
thf(c_0_19,plain,
( times_times_nat
= ( ^ [Z0: nat,Z1: nat] : ( times_times_nat @ Z1 @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( 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]) ).
thf(c_0_21,plain,
( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ma @ na ) ) )
= ( some_nat @ maxs ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_12]),c_0_16]) ).
thf(c_0_22,plain,
! [X1: nat] :
( ( the_nat @ ( some_nat @ X1 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
( ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) )
!= ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) @ maxs ) @ maxi ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,plain,
( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= na ),
inference(split_conjunct,[status(thm)],[fact_6__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062]) ).
thf(c_0_25,plain,
! [X2: nat,X1: nat] :
( ( times_times_nat @ X1 @ X2 )
= ( times_times_nat @ X2 @ X1 ) ),
inference(arg_cong,[status(thm)],[c_0_19]) ).
thf(c_0_26,plain,
( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ma @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ma @ na ) ) @ ( 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)],[c_0_20,c_0_12]),c_0_16]),c_0_12]),c_0_16]),c_0_12]),c_0_16]),c_0_12]),c_0_16]),c_0_21]),c_0_22]) ).
thf(c_0_27,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]) ).
thf(c_0_28,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)],[c_0_23,c_0_24]),c_0_12]),c_0_16]),c_0_21]),c_0_22]),c_0_25]),c_0_12]),c_0_16]),c_0_12]),c_0_16]),c_0_12]),c_0_16]),c_0_12]),c_0_16]),c_0_21]),c_0_22]),c_0_26]),c_0_27]),c_0_22]),c_0_12]),c_0_25]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP257^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.03 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.11 % Computer : n012.cluster.edu
% 0.07/0.11 % Model : x86_64 x86_64
% 0.07/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.11 % Memory : 8046.5625MB
% 0.07/0.11 % OS : Linux 6.8.0-71-generic
% 0.07/0.11 % CPULimit : 300
% 0.07/0.11 % WCLimit : 300
% 0.07/0.11 % DateTime : Tue Sep 29 20:39:18 UTC 2026
% 0.07/0.12 % CPUTime :
% 0.07/0.12 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.14 Running higher-order theorem proving
% 1.93/2.06 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.WyO5MJEAul/E---3.1_662119.p
% 84.20/30.10 % Version: 3.5.1-ho
% 84.20/30.10 % partial match(1): HMLMSMSMSSLCHFA
% 84.20/30.10 % Preprocessing class: HMLMSMLMSSLCHFA.
% 84.20/30.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.20/30.10 % Starting new_ho_10 with 1500s (5) cores
% 84.20/30.10 % Starting sh5l with 300s (1) cores
% 84.20/30.10 % Starting new_bool_1 with 300s (1) cores
% 84.20/30.10 % Starting new_bool_2 with 300s (1) cores
% 84.20/30.10 % new_bool_2 with pid 662317 completed with status 0
% 84.20/30.10 % Result found by new_bool_2
% 84.20/30.10 % partial match(1): HMLMSMSMSSLCHFA
% 84.20/30.10 % Preprocessing class: HMLMSMLMSSLCHFA.
% 84.20/30.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.20/30.10 % Starting new_ho_10 with 1500s (5) cores
% 84.20/30.10 % Starting sh5l with 300s (1) cores
% 84.20/30.10 % Starting new_bool_1 with 300s (1) cores
% 84.20/30.10 % Starting new_bool_2 with 300s (1) cores
% 84.20/30.10 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 84.20/30.10 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 84.20/30.10 % Search class: HGHSM-SMLM32-DHFFFSBN
% 84.20/30.10 % Scheduled 5 strats onto 1 cores with 299 seconds (299 total)
% 84.20/30.10 % Starting SubtermCWHack with 30s (1) cores
% 84.20/30.10 % SubtermCWHack with pid 662429 completed with status 0
% 84.20/30.10 % Result found by SubtermCWHack
% 84.20/30.10 % partial match(1): HMLMSMSMSSLCHFA
% 84.20/30.10 % Preprocessing class: HMLMSMLMSSLCHFA.
% 84.20/30.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.20/30.10 % Starting new_ho_10 with 1500s (5) cores
% 84.20/30.10 % Starting sh5l with 300s (1) cores
% 84.20/30.10 % Starting new_bool_1 with 300s (1) cores
% 84.20/30.10 % Starting new_bool_2 with 300s (1) cores
% 84.20/30.10 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 84.20/30.10 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 84.20/30.10 % Search class: HGHSM-SMLM32-DHFFFSBN
% 84.20/30.10 % Scheduled 5 strats onto 1 cores with 299 seconds (299 total)
% 84.20/30.10 % Starting SubtermCWHack with 30s (1) cores
% 84.20/30.10 % Preprocessing time : 0.104 s
% 84.20/30.10
% 84.20/30.10 % Proof found!
% 84.20/30.10 % SZS status Theorem
% 84.20/30.10 % SZS output start CNFRefutation
% See solution above
% 84.20/30.10 % Parsed axioms : 11194
% 84.20/30.10 % Removed by relevancy pruning/SinE : 7823
% 84.20/30.10 % Initial clauses : 8528
% 84.20/30.10 % Removed in clause preprocessing : 1919
% 84.20/30.10 % Initial clauses in saturation : 6609
% 84.20/30.10 % Processed clauses : 60764
% 84.20/30.10 % ...of these trivial : 2439
% 84.20/30.10 % ...subsumed : 41061
% 84.20/30.10 % ...remaining for further processing : 17263
% 84.20/30.10 % Other redundant clauses eliminated : 2610
% 84.20/30.10 % Clauses deleted for lack of memory : 0
% 84.20/30.10 % Backward-subsumed : 264
% 84.20/30.10 % Backward-rewritten : 497
% 84.20/30.10 % Generated clauses : 395513
% 84.20/30.10 % ...of the previous two non-redundant : 318448
% 84.20/30.10 % ...aggressively subsumed : 0
% 84.20/30.10 % Contextual simplify-reflections : 85
% 84.20/30.10 % Paramodulations : 392789
% 84.20/30.10 % Factorizations : 29
% 84.20/30.10 % NegExts : 0
% 84.20/30.10 % Equation resolutions : 2689
% 84.20/30.10 % Disequality decompositions : 0
% 84.20/30.10 % Total rewrite steps : 200600
% 84.20/30.10 % ...of those cached : 185291
% 84.20/30.10 % Propositional unsat checks : 0
% 84.20/30.10 % Propositional check models : 0
% 84.20/30.10 % Propositional check unsatisfiable : 0
% 84.20/30.10 % Propositional clauses : 0
% 84.20/30.10 % Propositional clauses after purity: 0
% 84.20/30.10 % Propositional unsat core size : 0
% 84.20/30.10 % Propositional preprocessing time : 0.000
% 84.20/30.10 % Propositional encoding time : 0.000
% 84.20/30.10 % Propositional solver time : 0.000
% 84.20/30.10 % Success case prop preproc time : 0.000
% 84.20/30.10 % Success case prop encoding time : 0.000
% 84.20/30.10 % Success case prop solver time : 0.000
% 84.20/30.10 % Current number of processed clauses : 15804
% 84.20/30.10 % Positive orientable unit clauses : 10194
% 84.20/30.10 % Positive unorientable unit clauses: 41
% 84.20/30.10 % Negative unit clauses : 2205
% 84.20/30.10 % Non-unit-clauses : 3364
% 84.20/30.10 % Current number of unprocessed clauses: 263892
% 84.20/30.10 % ...number of literals in the above : 935268
% 84.20/30.10 % Current number of archived formulas : 0
% 84.20/30.10 % Current number of archived clauses : 764
% 84.20/30.10 % Clause-clause subsumption calls (NU) : 5433149
% 84.20/30.10 % Rec. Clause-clause subsumption calls : 1066236
% 84.20/30.10 % Non-unit clause-clause subsumptions : 2185
% 84.20/30.10 % Unit Clause-clause subsumption calls : 2576488
% 84.20/30.10 % Rewrite failures with RHS unbound : 8
% 84.20/30.10 % BW rewrite match attempts : 15371
% 84.20/30.10 % BW rewrite match successes : 8285
% 84.20/30.10 % Condensation attempts : 0
% 84.20/30.10 % Condensation successes : 0
% 84.20/30.10 % Termbank termtop insertions : 65402353
% 84.20/30.10 % Search garbage collected termcells : 180821
% 84.20/30.10
% 84.20/30.10 % -------------------------------------------------
% 84.20/30.10 % User time : 26.859 s
% 84.20/30.10 % System time : 0.258 s
% 84.20/30.10 % Total time : 27.117 s
% 84.20/30.10 % Maximum resident set size: 47920 pages
% 84.20/30.10
% 84.20/30.10 % -------------------------------------------------
% 84.20/30.10 % User time : 27.574 s
% 84.20/30.10 % System time : 0.289 s
% 84.20/30.10 % Total time : 27.863 s
% 84.20/30.10 % Maximum resident set size: 30720 pages
% 84.20/30.10 % E exiting
%------------------------------------------------------------------------------