%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP256^1 : 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 : n008.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 12:39:54 PM UTC 2025
% Result : Theorem 27.22s 27.18s
% Output : Proof 27.22s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_vEBT_VEBT,type,
vEBT_VEBT: $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_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_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_vEBT_vebt_delete,type,
vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_member_VEBT_VEBT,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(ty_na,type,
na: nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_set_VEBT_VEBT2,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(ty_xa,type,
xa: nat ).
thf(ty_vEBT_V8194947554948674370ptions,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(ty_size_s6755466524823107622T_VEBT,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
thf(ty_vEBT_invar_vebt,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: list_VEBT_VEBT] :
( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( size_s6755466524823107622T_VEBT @ X1 ) )
=> ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ X1 @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat,X2: list_VEBT_VEBT] :
( ( ord_less_nat @ X1 @ ( size_s6755466524823107622T_VEBT @ X2 ) )
=> ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ X2 @ X1 ) @ ( set_VEBT_VEBT2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ treeList ) )
=> ~ ( ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ na )
=> ~ ! [X1: nat,X2: nat] :
( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X1 ) @ X2 )
= ( ~ ( ( X1 != X2 )
=> ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
=> ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ treeList ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ na )
=> ~ ! [X1: nat,X2: nat] :
( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X1 ) @ X2 )
= ( ~ ( ( X1 != X2 )
=> ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ na ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
=> ~ ( ( vEBT_invar_vebt @ X1 @ na )
=> ~ ! [X2: nat,X3: nat] :
( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X1 @ X2 ) @ X3 )
= ( ~ ( ( X2 != X3 )
=> ~ ( vEBT_V8194947554948674370ptions @ X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ treeList ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(conj_0,conjecture,
sP7 ).
thf(h0,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( sP5
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| ~ sP6
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| ~ sP9
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_8__092_060open_062high_Ax_An_A_060_Alength_AtreeList_092_060close_062,axiom,
sP6 ).
thf(fact_23__C4_OIH_C_I1_J,axiom,
sP8 ).
thf(fact_137_nth__mem,axiom,
sP2 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,fact_8__092_060open_062high_Ax_An_A_060_Alength_AtreeList_092_060close_062,fact_23__C4_OIH_C_I1_J,fact_137_nth__mem,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP256^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Oct 10 14:54:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 27.22/27.18 % SZS status Theorem
% 27.22/27.18 % Mode: mode9:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 27.22/27.18 % Inferences: 3813
% 27.22/27.18 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------