TSTP Solution File: ITP278^3 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP278^3 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : 600s
% DateTime : Sun Jul 17 00:30:26 EDT 2022
% Result : Theorem 95.68s 94.66s
% Output : Proof 95.68s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_product_prod_nat_nat,type,
product_prod_nat_nat: $tType ).
thf(ty_vEBT_VEBT,type,
vEBT_VEBT: $tType ).
thf(ty_option4927543243414619207at_nat,type,
option4927543243414619207at_nat: $tType ).
thf(ty_list_VEBT_VEBT,type,
list_VEBT_VEBT: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_set_VEBT_VEBT,type,
set_VEBT_VEBT: $tType ).
thf(ty_num,type,
num: $tType ).
thf(ty_treeList2,type,
treeList2: list_VEBT_VEBT ).
thf(ty_eigen__12,type,
eigen__12: vEBT_VEBT ).
thf(ty_info,type,
info: option4927543243414619207at_nat ).
thf(ty_summary,type,
summary: vEBT_VEBT ).
thf(ty_plus_plus_nat,type,
plus_plus_nat: nat > nat > nat ).
thf(ty_eigen__2,type,
eigen__2: option4927543243414619207at_nat ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_eigen__25,type,
eigen__25: option4927543243414619207at_nat ).
thf(ty_summary2,type,
summary2: vEBT_VEBT ).
thf(ty_sa,type,
sa: vEBT_VEBT ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_eigen__24,type,
eigen__24: vEBT_VEBT ).
thf(ty_eigen__1,type,
eigen__1: vEBT_VEBT ).
thf(ty_eigen__0,type,
eigen__0: list_VEBT_VEBT ).
thf(ty_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_some_P7363390416028606310at_nat,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
thf(ty_bit0,type,
bit0: num > num ).
thf(ty_deg,type,
deg: nat ).
thf(ty_eigen__11,type,
eigen__11: list_VEBT_VEBT ).
thf(ty_eigen__10,type,
eigen__10: option4927543243414619207at_nat ).
thf(ty_member_VEBT_VEBT,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(ty_mi,type,
mi: nat ).
thf(ty_eigen__8,type,
eigen__8: list_VEBT_VEBT ).
thf(ty_na,type,
na: nat ).
thf(ty_eigen__13,type,
eigen__13: option4927543243414619207at_nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_eigen__9,type,
eigen__9: vEBT_VEBT ).
thf(ty_set_VEBT_VEBT2,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(ty_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(ty_one,type,
one: num ).
thf(ty_vEBT_V8194947554948674370ptions,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(ty_eigen__23,type,
eigen__23: list_VEBT_VEBT ).
thf(ty_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_size_s6755466524823107622T_VEBT,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
thf(ty_ma,type,
ma: nat ).
thf(ty_vEBT_Node,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(ty_product_Pair_nat_nat,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(ty_m,type,
m: nat ).
thf(ty_vEBT_invar_vebt,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(sP1,plain,
( sP1
<=> ( deg = deg ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( mi = ma ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sa
= ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList2 @ summary2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sa = sa ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: vEBT_VEBT,X2: vEBT_VEBT] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: list_VEBT_VEBT,X2: list_VEBT_VEBT] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sa
= ( vEBT_Node @ info @ deg @ treeList @ summary ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( treeList = treeList2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( info
= ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( summary2 = summary ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( treeList2 = treeList ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( summary = summary2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: vEBT_VEBT] :
( ( summary2 = X1 )
=> ( X1 = summary2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( vEBT_Node @ info @ deg @ treeList @ summary )
= ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList2 @ summary2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP10
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP11
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: list_VEBT_VEBT] :
( ( treeList2 = X1 )
=> ( X1 = treeList2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(conj_0,conjecture,
sP3 ).
thf(h0,negated_conjecture,
~ sP3,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
! [X1: nat] :
( ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ( ( ( vEBT_VEBT_high @ ma @ na )
= X1 )
=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
=> ~ ! [X2: nat] :
( ~ ( ( ( vEBT_VEBT_high @ X2 @ na )
= X1 )
=> ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
=> ~ ( ( ord_less_nat @ mi @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
! [X1: nat] :
( ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ( ( ( vEBT_VEBT_high @ ma @ na )
= X1 )
=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ X1 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
=> ~ ! [X2: nat] :
( ~ ( ( ( vEBT_VEBT_high @ X2 @ na )
= X1 )
=> ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ X1 ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
=> ~ ( ( ord_less_nat @ mi @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: vEBT_VEBT,X2: option4927543243414619207at_nat] :
( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ X2 @ deg @ eigen__0 @ X1 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__0 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ X1 @ m ) )
=> ~ ! [X3: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ eigen__0 ) )
=> ( vEBT_invar_vebt @ X3 @ na ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: option4927543243414619207at_nat] :
( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ X1 @ deg @ eigen__0 @ eigen__1 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__0 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__1 @ m ) )
=> ~ ! [X2: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ eigen__0 ) )
=> ( vEBT_invar_vebt @ X2 @ na ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__2 @ deg @ eigen__0 @ eigen__1 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__0 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__1 @ m ) )
=> ~ ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ eigen__0 ) )
=> ( vEBT_invar_vebt @ X1 @ na ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__2 @ deg @ eigen__0 @ eigen__1 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__0 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__1 @ m ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ eigen__0 ) )
=> ( vEBT_invar_vebt @ X1 @ na ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__2 @ deg @ eigen__0 @ eigen__1 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__0 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
vEBT_invar_vebt @ eigen__1 @ m,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ( sa
= ( vEBT_Node @ eigen__2 @ deg @ eigen__0 @ eigen__1 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
( ( size_s6755466524823107622T_VEBT @ eigen__0 )
= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
( sa
= ( vEBT_Node @ eigen__2 @ deg @ eigen__0 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
( deg
= ( plus_plus_nat @ na @ m ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( sP7
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ treeList )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ summary @ m ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
=> ( vEBT_invar_vebt @ X1 @ na ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( sP7
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ treeList )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
vEBT_invar_vebt @ summary @ m,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP7
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
( ( size_s6755466524823107622T_VEBT @ treeList )
= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP7,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h23,assumption,
! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList2 ) )
=> ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h22,h21,h14,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h1,h1,h0])],[h1,h22]) ).
thf(2,plain,
( sP14
| ~ sP9
| ~ sP1
| ~ sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
sP1,
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| sP3
| ~ sP4
| ~ sP14 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP15
| ~ sP10
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP13
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP16
| ~ sP11
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP17
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
sP6,
inference(eq_sym,[status(thm)],]) ).
thf(13,plain,
sP5,
inference(eq_sym,[status(thm)],]) ).
thf(fact_9__092_060open_062treeList_A_061_AtreeList_H_092_060close_062,axiom,
sP11 ).
thf(fact_2_infsplit,axiom,
sP9 ).
thf(fact_0__092_060open_062summary_A_061_Asummary_H_092_060close_062,axiom,
sP10 ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h21,h14,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h1,h1,h0])],[2,3,4,5,6,7,8,9,10,11,12,13,h0,h21,fact_9__092_060open_062treeList_A_061_AtreeList_H_092_060close_062,fact_2_infsplit,fact_0__092_060open_062summary_A_061_Asummary_H_092_060close_062]) ).
thf(fact_20_case4_I8_J,axiom,
( sP2
=> ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList2 ) )
=> ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ) ) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h21,h14,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h1,h1,h0]),tab_imp(discharge,[h22]),tab_imp(discharge,[h23])],[fact_20_case4_I8_J,1,14,h22,h23]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h1,h1,h0]),tab_negimp(discharge,[h21,h14])],[h19,15,h21,h14]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h1,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,16,h19,h20]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h1,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,17,h17,h18]) ).
thf(fact_737_sprop1,axiom,
~ ( ~ ( ~ ( ~ ( sP7
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ treeList )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ summary @ m ) )
=> ~ ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
=> ( vEBT_invar_vebt @ X1 @ na ) ) ) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h1,h1,h0]),tab_negimp(discharge,[h15,h16])],[fact_737_sprop1,18,h15,h16]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h6,h5,h4,h1,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,19,h13,h14]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h6,h5,h4,h1,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,20,h11,h12]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h5,h4,h1,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,21,h9,h10]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h4,h1,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,22,h7,h8]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h1,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,23,h6]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h1,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,24,h5]) ).
thf(fact_750__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062treeList_H_Asummary_H_Ainfo_O_As_A_061_ANode_Ainfo_Adeg_AtreeList_H_Asummary_H_A_092_060and_062_Adeg_A_061_An_A_L_Am_A_092_060and_062_Alength_AtreeList_H_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_H_Am_A_092_060and_062_A_I_092_060forall_062t_092_060in_062set_AtreeList_H_O_Ainvar__vebt_At_An_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: list_VEBT_VEBT,X2: vEBT_VEBT,X3: option4927543243414619207at_nat] :
( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ X3 @ deg @ X1 @ X2 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ X1 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ X2 @ m ) )
=> ~ ! [X4: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ X1 ) )
=> ( vEBT_invar_vebt @ X4 @ na ) ) ) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[fact_750__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062treeList_H_Asummary_H_Ainfo_O_As_A_061_ANode_Ainfo_Adeg_AtreeList_H_Asummary_H_A_092_060and_062_Adeg_A_061_An_A_L_Am_A_092_060and_062_Alength_AtreeList_H_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_H_Am_A_092_060and_062_A_I_092_060forall_062t_092_060in_062set_AtreeList_H_O_Ainvar__vebt_At_An_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,25,h4]) ).
thf(h24,assumption,
~ ! [X1: vEBT_VEBT,X2: option4927543243414619207at_nat] :
( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ X2 @ deg @ eigen__8 @ X1 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__8 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ X1 @ m ) )
=> ~ ! [X3: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ eigen__8 ) )
=> ( vEBT_invar_vebt @ X3 @ na ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ! [X1: option4927543243414619207at_nat] :
( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ X1 @ deg @ eigen__8 @ eigen__9 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__8 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__9 @ m ) )
=> ~ ! [X2: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ eigen__8 ) )
=> ( vEBT_invar_vebt @ X2 @ na ) ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ ( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__10 @ deg @ eigen__8 @ eigen__9 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__8 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__9 @ m ) )
=> ~ ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ eigen__8 ) )
=> ( vEBT_invar_vebt @ X1 @ na ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__10 @ deg @ eigen__8 @ eigen__9 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__8 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__9 @ m ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ eigen__8 ) )
=> ( vEBT_invar_vebt @ X1 @ na ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__10 @ deg @ eigen__8 @ eigen__9 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__8 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
vEBT_invar_vebt @ eigen__9 @ m,
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( ( sa
= ( vEBT_Node @ eigen__10 @ deg @ eigen__8 @ eigen__9 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) ),
introduced(assumption,[]) ).
thf(h32,assumption,
( ( size_s6755466524823107622T_VEBT @ eigen__8 )
= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ),
introduced(assumption,[]) ).
thf(h33,assumption,
( sa
= ( vEBT_Node @ eigen__10 @ deg @ eigen__8 @ eigen__9 ) ),
introduced(assumption,[]) ).
thf(27,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h22,h21,h14,h19,h20,h17,h18,h15,h16,h33,h14,h31,h32,h29,h30,h27,h28,h26,h25,h24,h3,h1,h0])],[h1,h22]) ).
thf(28,plain,
( sP14
| ~ sP9
| ~ sP1
| ~ sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
sP1,
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP7
| sP3
| ~ sP4
| ~ sP14 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP15
| ~ sP10
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP13
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP5
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP16
| ~ sP11
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP17
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP6
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
sP6,
inference(eq_sym,[status(thm)],]) ).
thf(39,plain,
sP5,
inference(eq_sym,[status(thm)],]) ).
thf(40,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h21,h14,h19,h20,h17,h18,h15,h16,h33,h14,h31,h32,h29,h30,h27,h28,h26,h25,h24,h3,h1,h0])],[28,29,30,31,32,33,34,35,36,37,38,39,h0,h21,fact_9__092_060open_062treeList_A_061_AtreeList_H_092_060close_062,fact_2_infsplit,fact_0__092_060open_062summary_A_061_Asummary_H_092_060close_062]) ).
thf(41,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h21,h14,h19,h20,h17,h18,h15,h16,h33,h14,h31,h32,h29,h30,h27,h28,h26,h25,h24,h3,h1,h0]),tab_imp(discharge,[h22]),tab_imp(discharge,[h23])],[fact_20_case4_I8_J,27,40,h22,h23]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h33,h14,h31,h32,h29,h30,h27,h28,h26,h25,h24,h3,h1,h0]),tab_negimp(discharge,[h21,h14])],[h19,41,h21,h14]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h33,h14,h31,h32,h29,h30,h27,h28,h26,h25,h24,h3,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,42,h19,h20]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h33,h14,h31,h32,h29,h30,h27,h28,h26,h25,h24,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,43,h17,h18]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h14,h31,h32,h29,h30,h27,h28,h26,h25,h24,h3,h1,h0]),tab_negimp(discharge,[h15,h16])],[fact_737_sprop1,44,h15,h16]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h32,h29,h30,h27,h28,h26,h25,h24,h3,h1,h0]),tab_negimp(discharge,[h33,h14])],[h31,45,h33,h14]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h30,h27,h28,h26,h25,h24,h3,h1,h0]),tab_negimp(discharge,[h31,h32])],[h29,46,h31,h32]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h26,h25,h24,h3,h1,h0]),tab_negimp(discharge,[h29,h30])],[h27,47,h29,h30]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h25,h24,h3,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,48,h27,h28]) ).
thf(50,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h24,h3,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__10)],[h25,49,h26]) ).
thf(51,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h3,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__9)],[h24,50,h25]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__8)],[fact_750__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062treeList_H_Asummary_H_Ainfo_O_As_A_061_ANode_Ainfo_Adeg_AtreeList_H_Asummary_H_A_092_060and_062_Adeg_A_061_An_A_L_Am_A_092_060and_062_Alength_AtreeList_H_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_H_Am_A_092_060and_062_A_I_092_060forall_062t_092_060in_062set_AtreeList_H_O_Ainvar__vebt_At_An_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,51,h24]) ).
thf(fact_1658_case4_I11_J,axiom,
( ~ sP2
=> ! [X1: nat] :
( ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ( ( ( vEBT_VEBT_high @ ma @ na )
= X1 )
=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ X1 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
=> ~ ! [X2: nat] :
( ~ ( ( ( vEBT_VEBT_high @ X2 @ na )
= X1 )
=> ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ X1 ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
=> ~ ( ( ord_less_nat @ mi @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ) ) ).
thf(53,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h3])],[fact_1658_case4_I11_J,26,52,h1,h3]) ).
thf(h34,assumption,
~ ! [X1: vEBT_VEBT,X2: option4927543243414619207at_nat] :
( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ X2 @ deg @ eigen__11 @ X1 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__11 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ X1 @ m ) )
=> ~ ! [X3: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ eigen__11 ) )
=> ( vEBT_invar_vebt @ X3 @ na ) ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
~ ! [X1: option4927543243414619207at_nat] :
( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ X1 @ deg @ eigen__11 @ eigen__12 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__11 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__12 @ m ) )
=> ~ ! [X2: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ eigen__11 ) )
=> ( vEBT_invar_vebt @ X2 @ na ) ) ),
introduced(assumption,[]) ).
thf(h36,assumption,
~ ( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__13 @ deg @ eigen__11 @ eigen__12 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__11 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__12 @ m ) )
=> ~ ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ eigen__11 ) )
=> ( vEBT_invar_vebt @ X1 @ na ) ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__13 @ deg @ eigen__11 @ eigen__12 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__11 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__12 @ m ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ eigen__11 ) )
=> ( vEBT_invar_vebt @ X1 @ na ) ),
introduced(assumption,[]) ).
thf(h39,assumption,
~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__13 @ deg @ eigen__11 @ eigen__12 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__11 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ),
introduced(assumption,[]) ).
thf(h40,assumption,
vEBT_invar_vebt @ eigen__12 @ m,
introduced(assumption,[]) ).
thf(h41,assumption,
~ ( ( sa
= ( vEBT_Node @ eigen__13 @ deg @ eigen__11 @ eigen__12 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) ),
introduced(assumption,[]) ).
thf(h42,assumption,
( ( size_s6755466524823107622T_VEBT @ eigen__11 )
= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ),
introduced(assumption,[]) ).
thf(h43,assumption,
( sa
= ( vEBT_Node @ eigen__13 @ deg @ eigen__11 @ eigen__12 ) ),
introduced(assumption,[]) ).
thf(54,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h22,h21,h14,h19,h20,h17,h18,h15,h16,h43,h14,h41,h42,h39,h40,h37,h38,h36,h35,h34,h1,h2,h0])],[h1,h22]) ).
thf(55,plain,
sP1,
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP14
| ~ sP9
| ~ sP1
| ~ sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP7
| sP3
| ~ sP4
| ~ sP14 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP15
| ~ sP10
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP13
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP5
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP16
| ~ sP11
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP17
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP6
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
sP6,
inference(eq_sym,[status(thm)],]) ).
thf(66,plain,
sP5,
inference(eq_sym,[status(thm)],]) ).
thf(67,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h21,h14,h19,h20,h17,h18,h15,h16,h43,h14,h41,h42,h39,h40,h37,h38,h36,h35,h34,h1,h2,h0])],[55,56,57,58,59,60,61,62,63,64,65,66,h0,h21,fact_9__092_060open_062treeList_A_061_AtreeList_H_092_060close_062,fact_2_infsplit,fact_0__092_060open_062summary_A_061_Asummary_H_092_060close_062]) ).
thf(68,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h21,h14,h19,h20,h17,h18,h15,h16,h43,h14,h41,h42,h39,h40,h37,h38,h36,h35,h34,h1,h2,h0]),tab_imp(discharge,[h22]),tab_imp(discharge,[h23])],[fact_20_case4_I8_J,54,67,h22,h23]) ).
thf(69,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h43,h14,h41,h42,h39,h40,h37,h38,h36,h35,h34,h1,h2,h0]),tab_negimp(discharge,[h21,h14])],[h19,68,h21,h14]) ).
thf(70,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h43,h14,h41,h42,h39,h40,h37,h38,h36,h35,h34,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h17,69,h19,h20]) ).
thf(71,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h43,h14,h41,h42,h39,h40,h37,h38,h36,h35,h34,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h15,70,h17,h18]) ).
thf(72,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h43,h14,h41,h42,h39,h40,h37,h38,h36,h35,h34,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[fact_737_sprop1,71,h15,h16]) ).
thf(73,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h42,h39,h40,h37,h38,h36,h35,h34,h1,h2,h0]),tab_negimp(discharge,[h43,h14])],[h41,72,h43,h14]) ).
thf(74,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h39,h40,h37,h38,h36,h35,h34,h1,h2,h0]),tab_negimp(discharge,[h41,h42])],[h39,73,h41,h42]) ).
thf(75,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h37,h38,h36,h35,h34,h1,h2,h0]),tab_negimp(discharge,[h39,h40])],[h37,74,h39,h40]) ).
thf(76,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h35,h34,h1,h2,h0]),tab_negimp(discharge,[h37,h38])],[h36,75,h37,h38]) ).
thf(77,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h35,h34,h1,h2,h0]),tab_negall(discharge,[h36]),tab_negall(eigenvar,eigen__13)],[h35,76,h36]) ).
thf(78,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h34,h1,h2,h0]),tab_negall(discharge,[h35]),tab_negall(eigenvar,eigen__12)],[h34,77,h35]) ).
thf(79,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h34]),tab_negall(eigenvar,eigen__11)],[fact_750__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062treeList_H_Asummary_H_Ainfo_O_As_A_061_ANode_Ainfo_Adeg_AtreeList_H_Asummary_H_A_092_060and_062_Adeg_A_061_An_A_L_Am_A_092_060and_062_Alength_AtreeList_H_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_H_Am_A_092_060and_062_A_I_092_060forall_062t_092_060in_062set_AtreeList_H_O_Ainvar__vebt_At_An_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,78,h34]) ).
thf(h44,assumption,
~ ! [X1: vEBT_VEBT,X2: option4927543243414619207at_nat] :
( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ X2 @ deg @ eigen__23 @ X1 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__23 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ X1 @ m ) )
=> ~ ! [X3: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ eigen__23 ) )
=> ( vEBT_invar_vebt @ X3 @ na ) ) ),
introduced(assumption,[]) ).
thf(h45,assumption,
~ ! [X1: option4927543243414619207at_nat] :
( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ X1 @ deg @ eigen__23 @ eigen__24 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__23 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__24 @ m ) )
=> ~ ! [X2: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ eigen__23 ) )
=> ( vEBT_invar_vebt @ X2 @ na ) ) ),
introduced(assumption,[]) ).
thf(h46,assumption,
~ ( ~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__25 @ deg @ eigen__23 @ eigen__24 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__23 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__24 @ m ) )
=> ~ ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ eigen__23 ) )
=> ( vEBT_invar_vebt @ X1 @ na ) ) ),
introduced(assumption,[]) ).
thf(h47,assumption,
~ ( ~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__25 @ deg @ eigen__23 @ eigen__24 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__23 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
=> ~ ( vEBT_invar_vebt @ eigen__24 @ m ) ),
introduced(assumption,[]) ).
thf(h48,assumption,
! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ eigen__23 ) )
=> ( vEBT_invar_vebt @ X1 @ na ) ),
introduced(assumption,[]) ).
thf(h49,assumption,
~ ( ~ ( ( sa
= ( vEBT_Node @ eigen__25 @ deg @ eigen__23 @ eigen__24 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) )
=> ( ( size_s6755466524823107622T_VEBT @ eigen__23 )
!= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ),
introduced(assumption,[]) ).
thf(h50,assumption,
vEBT_invar_vebt @ eigen__24 @ m,
introduced(assumption,[]) ).
thf(h51,assumption,
~ ( ( sa
= ( vEBT_Node @ eigen__25 @ deg @ eigen__23 @ eigen__24 ) )
=> ( deg
!= ( plus_plus_nat @ na @ m ) ) ),
introduced(assumption,[]) ).
thf(h52,assumption,
( ( size_s6755466524823107622T_VEBT @ eigen__23 )
= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ),
introduced(assumption,[]) ).
thf(h53,assumption,
( sa
= ( vEBT_Node @ eigen__25 @ deg @ eigen__23 @ eigen__24 ) ),
introduced(assumption,[]) ).
thf(80,plain,
( sP14
| ~ sP9
| ~ sP1
| ~ sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(82,plain,
sP1,
inference(prop_rule,[status(thm)],]) ).
thf(83,plain,
( ~ sP7
| sP3
| ~ sP4
| ~ sP14 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(84,plain,
( ~ sP15
| ~ sP10
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(85,plain,
( ~ sP13
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(86,plain,
( ~ sP5
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(87,plain,
( ~ sP16
| ~ sP11
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(88,plain,
( ~ sP17
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(89,plain,
( ~ sP6
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(90,plain,
sP6,
inference(eq_sym,[status(thm)],]) ).
thf(91,plain,
sP5,
inference(eq_sym,[status(thm)],]) ).
thf(92,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h21,h14,h19,h20,h17,h18,h15,h16,h53,h14,h51,h52,h49,h50,h47,h48,h46,h45,h44,h3,h2,h0])],[80,81,82,83,84,85,86,87,88,89,90,91,h0,h21,fact_9__092_060open_062treeList_A_061_AtreeList_H_092_060close_062,fact_2_infsplit,fact_0__092_060open_062summary_A_061_Asummary_H_092_060close_062]) ).
thf(93,plain,
sP1,
inference(prop_rule,[status(thm)],]) ).
thf(94,plain,
( sP14
| ~ sP9
| ~ sP1
| ~ sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(95,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(96,plain,
( ~ sP7
| sP3
| ~ sP4
| ~ sP14 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(97,plain,
( ~ sP15
| ~ sP10
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(98,plain,
( ~ sP13
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(99,plain,
( ~ sP5
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(100,plain,
( ~ sP16
| ~ sP11
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(101,plain,
( ~ sP17
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(102,plain,
( ~ sP6
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(103,plain,
sP6,
inference(eq_sym,[status(thm)],]) ).
thf(104,plain,
sP5,
inference(eq_sym,[status(thm)],]) ).
thf(105,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h21,h14,h19,h20,h17,h18,h15,h16,h53,h14,h51,h52,h49,h50,h47,h48,h46,h45,h44,h3,h2,h0])],[93,94,95,96,97,98,99,100,101,102,103,104,h0,h21,fact_9__092_060open_062treeList_A_061_AtreeList_H_092_060close_062,fact_2_infsplit,fact_0__092_060open_062summary_A_061_Asummary_H_092_060close_062]) ).
thf(106,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h21,h14,h19,h20,h17,h18,h15,h16,h53,h14,h51,h52,h49,h50,h47,h48,h46,h45,h44,h3,h2,h0]),tab_imp(discharge,[h22]),tab_imp(discharge,[h23])],[fact_20_case4_I8_J,92,105,h22,h23]) ).
thf(107,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h53,h14,h51,h52,h49,h50,h47,h48,h46,h45,h44,h3,h2,h0]),tab_negimp(discharge,[h21,h14])],[h19,106,h21,h14]) ).
thf(108,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h53,h14,h51,h52,h49,h50,h47,h48,h46,h45,h44,h3,h2,h0]),tab_negimp(discharge,[h19,h20])],[h17,107,h19,h20]) ).
thf(109,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h53,h14,h51,h52,h49,h50,h47,h48,h46,h45,h44,h3,h2,h0]),tab_negimp(discharge,[h17,h18])],[h15,108,h17,h18]) ).
thf(110,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h53,h14,h51,h52,h49,h50,h47,h48,h46,h45,h44,h3,h2,h0]),tab_negimp(discharge,[h15,h16])],[fact_737_sprop1,109,h15,h16]) ).
thf(111,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h51,h52,h49,h50,h47,h48,h46,h45,h44,h3,h2,h0]),tab_negimp(discharge,[h53,h14])],[h51,110,h53,h14]) ).
thf(112,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h49,h50,h47,h48,h46,h45,h44,h3,h2,h0]),tab_negimp(discharge,[h51,h52])],[h49,111,h51,h52]) ).
thf(113,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h47,h48,h46,h45,h44,h3,h2,h0]),tab_negimp(discharge,[h49,h50])],[h47,112,h49,h50]) ).
thf(114,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h46,h45,h44,h3,h2,h0]),tab_negimp(discharge,[h47,h48])],[h46,113,h47,h48]) ).
thf(115,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h45,h44,h3,h2,h0]),tab_negall(discharge,[h46]),tab_negall(eigenvar,eigen__25)],[h45,114,h46]) ).
thf(116,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h44,h3,h2,h0]),tab_negall(discharge,[h45]),tab_negall(eigenvar,eigen__24)],[h44,115,h45]) ).
thf(117,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h0]),tab_negall(discharge,[h44]),tab_negall(eigenvar,eigen__23)],[fact_750__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062treeList_H_Asummary_H_Ainfo_O_As_A_061_ANode_Ainfo_Adeg_AtreeList_H_Asummary_H_A_092_060and_062_Adeg_A_061_An_A_L_Am_A_092_060and_062_Alength_AtreeList_H_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_H_Am_A_092_060and_062_A_I_092_060forall_062t_092_060in_062set_AtreeList_H_O_Ainvar__vebt_At_An_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,116,h44]) ).
thf(118,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h3])],[fact_1658_case4_I11_J,79,117,h1,h3]) ).
thf(fact_1786_acd,axiom,
( ~ sP2
=> ! [X1: nat] :
( ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ( ( ( vEBT_VEBT_high @ ma @ na )
= X1 )
=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
=> ~ ! [X2: nat] :
( ~ ( ( ( vEBT_VEBT_high @ X2 @ na )
= X1 )
=> ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
=> ~ ( ( ord_less_nat @ mi @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ) ) ).
thf(119,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_1786_acd,53,118,h1,h2]) ).
thf(0,theorem,
sP3,
inference(contra,[status(thm),contra(discharge,[h0])],[119,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP278^3 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 2 21:17:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 95.68/94.66 % SZS status Theorem
% 95.68/94.66 % Mode: mode81:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 95.68/94.66 % Inferences: 7802
% 95.68/94.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------