%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP223^3 : 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 : n021.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 113.55s 113.18s
% Output : Proof 113.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 46 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 371 ( 31 equ; 0 cnn)
% Maximal formula atoms : 2 ( 8 avg)
% Number of connectives : 339 ( 18 ~; 12 |; 0 &; 303 @)
% ( 0 <=>; 5 =>; 1 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 49 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ ( vEBT_Node @ none_P5556105721700978146at_nat @ deg @ treeList @ summary ) ) )
= ( plus_plus_int @ one_one_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ m ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ ( vEBT_Node @ none_P5556105721700978146at_nat @ deg @ treeList @ summary ) ) )
!= ( plus_plus_int @ one_one_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ m ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(pax2,axiom,
( p2
=> ( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ fsummary ) )
= ( farchim7802044766580827645g_real @ ( flog @ ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) @ ( fsemiri5074537144036343181t_real @ fm ) ) ) ) ),
file('<stdin>',pax2) ).
thf(pax44,axiom,
( p44
=> ! [X209: option4927543243414619207at_nat,X210: nat,X211: list_VEBT_VEBT,X212: vEBT_VEBT] :
( ( fvEBT_VEBT_height @ ( fvEBT_Node @ X209 @ X210 @ X211 @ X212 ) )
= ( fplus_plus_nat @ fone_one_nat @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ X212 @ ( fset_VEBT_VEBT2 @ X211 ) ) ) ) ) ) ),
file('<stdin>',pax44) ).
thf(pax24,axiom,
( p24
=> ! [X220: nat,X219: nat] :
( ( fsemiri1314217659103216013at_int @ ( fplus_plus_nat @ X220 @ X219 ) )
= ( fplus_plus_int @ ( fsemiri1314217659103216013at_int @ X220 ) @ ( fsemiri1314217659103216013at_int @ X219 ) ) ) ),
file('<stdin>',pax24) ).
thf(pax26,axiom,
( p26
=> ( ( fsemiri1314217659103216013at_int @ fone_one_nat )
= fone_one_int ) ),
file('<stdin>',pax26) ).
thf(nax1,axiom,
( p1
<= ( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ ( fvEBT_Node @ fnone_P5556105721700978146at_nat @ fdeg @ ftreeList @ fsummary ) ) )
= ( fplus_plus_int @ fone_one_int @ ( farchim7802044766580827645g_real @ ( flog @ ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) @ ( fsemiri5074537144036343181t_real @ fm ) ) ) ) ) ),
file('<stdin>',nax1) ).
thf(ax514,axiom,
p2,
file('<stdin>',ax514) ).
thf(ax515,axiom,
~ p1,
file('<stdin>',ax515) ).
thf(ax472,axiom,
p44,
file('<stdin>',ax472) ).
thf(ax492,axiom,
p24,
file('<stdin>',ax492) ).
thf(ax490,axiom,
p26,
file('<stdin>',ax490) ).
thf(pax4,axiom,
( p4
=> ( ( fsemiri1314217659103216013at_int @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ fsummary @ ( fset_VEBT_VEBT2 @ ftreeList ) ) ) ) )
= ( farchim7802044766580827645g_real @ ( flog @ ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) @ ( fsemiri5074537144036343181t_real @ fm ) ) ) ) ),
file('<stdin>',pax4) ).
thf(ax512,axiom,
p4,
file('<stdin>',ax512) ).
thf(c_0_12,plain,
( ~ p2
| ( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ fsummary ) )
= ( farchim7802044766580827645g_real @ ( flog @ ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) @ ( fsemiri5074537144036343181t_real @ fm ) ) ) ) ),
inference(fof_nnf,[status(thm)],[pax2]) ).
thf(c_0_13,plain,
! [X1283: option4927543243414619207at_nat,X1284: nat,X1285: list_VEBT_VEBT,X1286: vEBT_VEBT] :
( ~ p44
| ( ( fvEBT_VEBT_height @ ( fvEBT_Node @ X1283 @ X1284 @ X1285 @ X1286 ) )
= ( fplus_plus_nat @ fone_one_nat @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ X1286 @ ( fset_VEBT_VEBT2 @ X1285 ) ) ) ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax44])])]) ).
thf(c_0_14,plain,
! [X1321: nat,X1322: nat] :
( ~ p24
| ( ( fsemiri1314217659103216013at_int @ ( fplus_plus_nat @ X1321 @ X1322 ) )
= ( fplus_plus_int @ ( fsemiri1314217659103216013at_int @ X1321 ) @ ( fsemiri1314217659103216013at_int @ X1322 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax24])])]) ).
thf(c_0_15,plain,
( ~ p26
| ( ( fsemiri1314217659103216013at_int @ fone_one_nat )
= fone_one_int ) ),
inference(fof_nnf,[status(thm)],[pax26]) ).
thf(c_0_16,plain,
( ( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ ( fvEBT_Node @ fnone_P5556105721700978146at_nat @ fdeg @ ftreeList @ fsummary ) ) )
!= ( fplus_plus_int @ fone_one_int @ ( farchim7802044766580827645g_real @ ( flog @ ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) @ ( fsemiri5074537144036343181t_real @ fm ) ) ) ) )
| p1 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])]) ).
thf(c_0_17,plain,
( ( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ fsummary ) )
= ( farchim7802044766580827645g_real @ ( flog @ ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) @ ( fsemiri5074537144036343181t_real @ fm ) ) ) )
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
p2,
inference(split_conjunct,[status(thm)],[ax514]) ).
thf(c_0_19,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax515]) ).
thf(c_0_20,plain,
! [X5: nat,X209: option4927543243414619207at_nat,X166: vEBT_VEBT,X165: list_VEBT_VEBT] :
( ( ( fvEBT_VEBT_height @ ( fvEBT_Node @ X209 @ X5 @ X165 @ X166 ) )
= ( fplus_plus_nat @ fone_one_nat @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ X166 @ ( fset_VEBT_VEBT2 @ X165 ) ) ) ) ) )
| ~ p44 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_21,plain,
p44,
inference(split_conjunct,[status(thm)],[ax472]) ).
thf(c_0_22,plain,
! [X5: nat,X6: nat] :
( ( ( fsemiri1314217659103216013at_int @ ( fplus_plus_nat @ X5 @ X6 ) )
= ( fplus_plus_int @ ( fsemiri1314217659103216013at_int @ X5 ) @ ( fsemiri1314217659103216013at_int @ X6 ) ) )
| ~ p24 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_23,plain,
p24,
inference(split_conjunct,[status(thm)],[ax492]) ).
thf(c_0_24,plain,
( ( ( fsemiri1314217659103216013at_int @ fone_one_nat )
= fone_one_int )
| ~ p26 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_25,plain,
p26,
inference(split_conjunct,[status(thm)],[ax490]) ).
thf(c_0_26,plain,
( ~ p4
| ( ( fsemiri1314217659103216013at_int @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ fsummary @ ( fset_VEBT_VEBT2 @ ftreeList ) ) ) ) )
= ( farchim7802044766580827645g_real @ ( flog @ ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) @ ( fsemiri5074537144036343181t_real @ fm ) ) ) ) ),
inference(fof_nnf,[status(thm)],[pax4]) ).
thf(c_0_27,plain,
( p1
| ( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ ( fvEBT_Node @ fnone_P5556105721700978146at_nat @ fdeg @ ftreeList @ fsummary ) ) )
!= ( fplus_plus_int @ fone_one_int @ ( farchim7802044766580827645g_real @ ( flog @ ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) @ ( fsemiri5074537144036343181t_real @ fm ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_28,plain,
( ( farchim7802044766580827645g_real @ ( flog @ ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) @ ( fsemiri5074537144036343181t_real @ fm ) ) )
= ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ fsummary ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
thf(c_0_29,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_30,plain,
! [X5: nat,X209: option4927543243414619207at_nat,X166: vEBT_VEBT,X165: list_VEBT_VEBT] :
( ( fvEBT_VEBT_height @ ( fvEBT_Node @ X209 @ X5 @ X165 @ X166 ) )
= ( fplus_plus_nat @ fone_one_nat @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ X166 @ ( fset_VEBT_VEBT2 @ X165 ) ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
thf(c_0_31,plain,
! [X5: nat,X6: nat] :
( ( fsemiri1314217659103216013at_int @ ( fplus_plus_nat @ X5 @ X6 ) )
= ( fplus_plus_int @ ( fsemiri1314217659103216013at_int @ X5 ) @ ( fsemiri1314217659103216013at_int @ X6 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_32,plain,
( ( fsemiri1314217659103216013at_int @ fone_one_nat )
= fone_one_int ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
thf(c_0_33,plain,
( ( ( fsemiri1314217659103216013at_int @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ fsummary @ ( fset_VEBT_VEBT2 @ ftreeList ) ) ) ) )
= ( farchim7802044766580827645g_real @ ( flog @ ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) @ ( fsemiri5074537144036343181t_real @ fm ) ) ) )
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_34,plain,
p4,
inference(split_conjunct,[status(thm)],[ax512]) ).
thf(c_0_35,plain,
( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ ( fvEBT_Node @ fnone_P5556105721700978146at_nat @ fdeg @ ftreeList @ fsummary ) ) )
!= ( fplus_plus_int @ fone_one_int @ ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ fsummary ) ) ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_36,plain,
! [X5: nat,X6: nat,X165: list_VEBT_VEBT,X1283: option4927543243414619207at_nat,X209: option4927543243414619207at_nat,X166: vEBT_VEBT] :
( ( fvEBT_VEBT_height @ ( fvEBT_Node @ X209 @ X5 @ X165 @ X166 ) )
= ( fvEBT_VEBT_height @ ( fvEBT_Node @ X1283 @ X6 @ X165 @ X166 ) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_30]) ).
thf(c_0_37,plain,
! [X5: nat,X209: option4927543243414619207at_nat,X166: vEBT_VEBT,X165: list_VEBT_VEBT] :
( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ ( fvEBT_Node @ X209 @ X5 @ X165 @ X166 ) ) )
= ( fplus_plus_int @ fone_one_int @ ( fsemiri1314217659103216013at_int @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ X166 @ ( fset_VEBT_VEBT2 @ X165 ) ) ) ) ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_32]) ).
thf(c_0_38,plain,
( ( fsemiri1314217659103216013at_int @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ fsummary @ ( fset_VEBT_VEBT2 @ ftreeList ) ) ) ) )
= ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ fsummary ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_28]),c_0_34])]) ).
thf(c_0_39,plain,
! [X209: option4927543243414619207at_nat,X5: nat] :
( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ ( fvEBT_Node @ X209 @ X5 @ ftreeList @ fsummary ) ) )
!= ( fplus_plus_int @ fone_one_int @ ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ fsummary ) ) ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_40,plain,
! [X209: option4927543243414619207at_nat,X5: nat] :
( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ ( fvEBT_Node @ X209 @ X5 @ ftreeList @ fsummary ) ) )
= ( fplus_plus_int @ fone_one_int @ ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ fsummary ) ) ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_41,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_39,c_0_40]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ ( vEBT_Node @ none_P5556105721700978146at_nat @ deg @ treeList @ summary ) ) )
= ( plus_plus_int @ one_one_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ m ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP223^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n021.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 14:08:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 113.55/113.18 % SZS status Theorem
% 113.55/113.18 % Mode: mode505:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=256:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 113.55/113.18 % Inferences: 0
% 113.55/113.18 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------