%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP221^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Oct 14 12:39:44 PM UTC 2025
% Result : Theorem 173.11s 173.24s
% Output : Proof 173.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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_num,type,
num: $tType ).
thf(ty_info,type,
info: option4927543243414619207at_nat ).
thf(ty_summary,type,
summary: vEBT_VEBT ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_vEBT_VEBT_membermima,type,
vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
thf(ty_bit0,type,
bit0: num > num ).
thf(ty_deg,type,
deg: nat ).
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_vEBT_V5719532721284313246member,type,
vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
thf(ty_vEBT_Node,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(ty_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(ty_x,type,
x: nat ).
thf(sP1,plain,
( sP1
<=> ( ~ ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
=> ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
= ( ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x )
=> ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: vEBT_VEBT] :
( ( vEBT_V8194947554948674370ptions @ X1 )
= ( ^ [X2: nat] :
( ~ ( vEBT_V5719532721284313246member @ X1 @ X2 )
=> ( vEBT_VEBT_membermima @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP3
=> ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP5
=> ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( vEBT_V8194947554948674370ptions
= ( ^ [X1: vEBT_VEBT,X2: nat] :
( ~ ( vEBT_V5719532721284313246member @ X1 @ X2 )
=> ( vEBT_VEBT_membermima @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: nat] :
( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ X1 )
= ( ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ X1 )
=> ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) )
= ( ^ [X1: nat] :
( ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ X1 )
=> ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(conj_0,conjecture,
sP11 ).
thf(h0,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP1
| sP5
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP9
| ~ sP5
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| ~ sP6
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP8
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP8
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP2
| sP11
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP12
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP13
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP7
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP10
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_0_both__member__options__def,axiom,
sP10 ).
thf(fact_7__092_060open_062naive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Anaive__member_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,axiom,
sP4 ).
thf(fact_8__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Amembermima_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,axiom,
sP9 ).
thf(fact_10__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060or_062_Anaive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_092_060close_062,axiom,
sP1 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,fact_0_both__member__options__def,fact_7__092_060open_062naive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Anaive__member_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,fact_8__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Amembermima_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,fact_10__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060or_062_Anaive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_092_060close_062,h0]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP221^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.04/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Oct 10 14:06:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 173.11/173.24 % SZS status Theorem
% 173.11/173.24 % Mode: mode500:USE_SINE=true:SINE_TOLERANCE=1.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 173.11/173.24 % Inferences: 194
% 173.11/173.24 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------