%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP224^1 : 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 : 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 : 300s
% DateTime : Tue Oct 14 12:39:45 PM UTC 2025
% Result : Theorem 220.58s 219.48s
% Output : Proof 220.58s
% 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_info,type,
info: option4927543243414619207at_nat ).
thf(ty_summary,type,
summary: vEBT_VEBT ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_deg,type,
deg: nat ).
thf(ty_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_vEBT_Node,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(ty_vEBT_invar_vebt,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(sP1,plain,
( sP1
<=> ( ( vEBT_invar_vebt @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: vEBT_VEBT,X2: nat] :
( ( vEBT_invar_vebt @ X1 @ X2 )
=> ( ord_less_nat @ zero_zero_nat @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( vEBT_invar_vebt @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ zero_zero_nat ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat] :
( ( vEBT_invar_vebt @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ X1 )
=> ( ord_less_nat @ zero_zero_nat @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(conj_9,conjecture,
ord_less_eq_nat @ n @ zero_zero_nat ).
thf(h0,negated_conjecture,
~ ( ord_less_eq_nat @ n @ zero_zero_nat ),
inference(assume_negation,[status(cth)],[conj_9]) ).
thf(1,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP5
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP1
| ~ sP3
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_679_less__numeral__extra_I3_J,axiom,
~ sP4 ).
thf(fact_482_deg__not__0,axiom,
sP2 ).
thf(fact_6_Node_Oprems,axiom,
sP3 ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,fact_679_less__numeral__extra_I3_J,fact_482_deg__not__0,fact_6_Node_Oprems]) ).
thf(0,theorem,
ord_less_eq_nat @ n @ zero_zero_nat,
inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ITP224^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.08/0.13 % 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 : 300
% 0.12/0.34 % DateTime : Fri Oct 10 14:09:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 220.58/219.48 % SZS status Theorem
% 220.58/219.48 % Mode: mode490:USE_SINE=true:SINE_TOLERANCE=5.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 220.58/219.48 % Inferences: 547
% 220.58/219.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------