%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP239^1 : 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 : n022.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 12:39:50 PM UTC 2025
% Result : Theorem 12.21s 12.46s
% Output : Proof 12.21s
% 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_option_nat,type,
option_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_vEBT_vebt_member,type,
vEBT_vebt_member: vEBT_VEBT > nat > $o ).
thf(ty_summary,type,
summary: vEBT_VEBT ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_za,type,
za: nat ).
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_pr,type,
pr: nat ).
thf(ty_eigen__0,type,
eigen__0: 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_mi,type,
mi: nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_xa,type,
xa: nat ).
thf(ty_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(ty_one,type,
one: num ).
thf(ty_some_nat,type,
some_nat: nat > option_nat ).
thf(ty_vEBT_vebt_maxt,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
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_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(sP1,plain,
( sP1
<=> ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( za = ma ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( za = mi ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(conj_0,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
( ( some_nat @ eigen__0 )
= ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ pr ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ za,
introduced(assumption,[]) ).
thf(h3,assumption,
ord_less_nat @ za @ xa,
introduced(assumption,[]) ).
thf(h4,assumption,
( ~ sP3
=> sP2 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ( ord_less_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP3,
introduced(assumption,[]) ).
thf(h7,assumption,
sP2,
introduced(assumption,[]) ).
thf(h8,assumption,
( ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
!= ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ),
introduced(assumption,[]) ).
thf(fact_3_False,axiom,
~ sP3 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h8,h6,h4,h2,h3,h1,h0])],[h6,fact_3_False]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h9,h6,h4,h2,h3,h1,h0])],[h6,fact_3_False]) ).
thf(fact_4_aaa,axiom,
( ( ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
=> ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
thf(3,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[fact_4_aaa,1,2,h8,h9]) ).
thf(fact_66__092_060open_062z_A_092_060noteq_062_Ama_092_060close_062,axiom,
~ sP2 ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h8,h7,h4,h2,h3,h1,h0])],[h7,fact_66__092_060open_062z_A_092_060noteq_062_Ama_092_060close_062]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h9,h7,h4,h2,h3,h1,h0])],[h7,fact_66__092_060open_062z_A_092_060noteq_062_Ama_092_060close_062]) ).
thf(6,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h4,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[fact_4_aaa,4,5,h8,h9]) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h4,3,6,h6,h7]) ).
thf(h10,assumption,
ord_less_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(8,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h8,h10,h11,h5,h2,h3,h1,h0])],[h11,h0]) ).
thf(9,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h9,h10,h11,h5,h2,h3,h1,h0])],[h11,h0]) ).
thf(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h11,h5,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[fact_4_aaa,8,9,h8,h9]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h5,10,h10,h11]) ).
thf(fact_102__C20_C,axiom,
( ~ ( ~ sP3
=> sP2 )
=> ~ ( ( ord_less_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
=> ~ sP1 ) ) ).
thf(12,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[fact_102__C20_C,7,11,h4,h5]) ).
thf(fact_312__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Az_A_092_060and_062_Az_A_060_Ax_092_060close_062,axiom,
~ ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ za )
=> ~ ( ord_less_nat @ za @ xa ) ) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[fact_312__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Az_A_092_060and_062_Az_A_060_Ax_092_060close_062,12,h2,h3]) ).
thf(fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: nat] :
( ( some_nat @ X1 )
!= ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ pr ) ) ) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,13,h1]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP239^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.35 % Computer : n022.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Oct 10 14:27:08 EDT 2025
% 0.12/0.35 % CPUTime :
% 12.21/12.46 % SZS status Theorem
% 12.21/12.46 % Mode: mode9a:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 12.21/12.46 % Inferences: 0
% 12.21/12.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------