TSTP Solution File: ITP223^3 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP223^3 : TPTP v8.1.0. Released v8.1.0.
% 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 : 600s
% DateTime : Sun Jul 17 00:29:45 EDT 2022
% Result : Theorem 49.43s 49.43s
% Output : Proof 49.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 52 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 409 ( 35 equ; 0 cnn)
% Maximal formula atoms : 2 ( 7 avg)
% Number of connectives : 351 ( 20 ~; 14 |; 0 &; 310 @)
% ( 0 <=>; 6 =>; 1 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 53 con; 0-2 aty)
% Number of variables : 30 ( 0 ^ 30 !; 0 ?; 30 :)
% 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(pax9,axiom,
( p9
=> ( ( fplus_plus_real @ fone_one_real @ fone_one_real )
= ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) ) ),
file('<stdin>',pax9) ).
thf(pax150,axiom,
( p150
=> ( fsuc
= ( fplus_plus_nat @ fone_one_nat ) ) ),
file('<stdin>',pax150) ).
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(ax1641,axiom,
p9,
file('<stdin>',ax1641) ).
thf(pax140,axiom,
( p140
=> ! [X1769: nat] :
( ( fsemiri1314217659103216013at_int @ ( fsuc @ X1769 ) )
= ( fplus_plus_int @ fone_one_int @ ( fsemiri1314217659103216013at_int @ X1769 ) ) ) ),
file('<stdin>',pax140) ).
thf(ax1500,axiom,
p150,
file('<stdin>',ax1500) ).
thf(pax91,axiom,
( p91
=> ! [X1814: option4927543243414619207at_nat,X1815: nat,X1816: list_VEBT_VEBT,X1817: vEBT_VEBT] :
( ( fvEBT_VEBT_height @ ( fvEBT_Node @ X1814 @ X1815 @ X1816 @ X1817 ) )
= ( fplus_plus_nat @ fone_one_nat @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ X1817 @ ( fset_VEBT_VEBT2 @ X1816 ) ) ) ) ) ) ),
file('<stdin>',pax91) ).
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(ax1648,axiom,
p2,
file('<stdin>',ax1648) ).
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(ax1510,axiom,
p140,
file('<stdin>',ax1510) ).
thf(ax1649,axiom,
~ p1,
file('<stdin>',ax1649) ).
thf(ax1559,axiom,
p91,
file('<stdin>',ax1559) ).
thf(ax1646,axiom,
p4,
file('<stdin>',ax1646) ).
thf(c_0_14,plain,
( ~ p9
| ( ( fplus_plus_real @ fone_one_real @ fone_one_real )
= ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) ) ),
inference(fof_nnf,[status(thm)],[pax9]) ).
thf(c_0_15,plain,
( ~ p150
| ( fsuc
= ( fplus_plus_nat @ fone_one_nat ) ) ),
inference(fof_nnf,[status(thm)],[pax150]) ).
thf(c_0_16,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_17,plain,
( ( ( fplus_plus_real @ fone_one_real @ fone_one_real )
= ( fnumeral_numeral_real @ ( fbit0 @ fone ) ) )
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
p9,
inference(split_conjunct,[status(thm)],[ax1641]) ).
thf(c_0_19,plain,
! [X6692: nat] :
( ~ p140
| ( ( fsemiri1314217659103216013at_int @ ( fsuc @ X6692 ) )
= ( fplus_plus_int @ fone_one_int @ ( fsemiri1314217659103216013at_int @ X6692 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax140])])]) ).
thf(c_0_20,plain,
( ( fsuc
= ( fplus_plus_nat @ fone_one_nat ) )
| ~ p150 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,plain,
p150,
inference(split_conjunct,[status(thm)],[ax1500]) ).
thf(c_0_22,plain,
! [X6824: option4927543243414619207at_nat,X6825: nat,X6826: list_VEBT_VEBT,X6827: vEBT_VEBT] :
( ~ p91
| ( ( fvEBT_VEBT_height @ ( fvEBT_Node @ X6824 @ X6825 @ X6826 @ X6827 ) )
= ( fplus_plus_nat @ fone_one_nat @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ X6827 @ ( fset_VEBT_VEBT2 @ X6826 ) ) ) ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax91])])]) ).
thf(c_0_23,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_24,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_16]) ).
thf(c_0_25,plain,
( ( fnumeral_numeral_real @ ( fbit0 @ fone ) )
= ( fplus_plus_real @ fone_one_real @ fone_one_real ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
thf(c_0_26,plain,
p2,
inference(split_conjunct,[status(thm)],[ax1648]) ).
thf(c_0_27,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_28,plain,
! [X14: nat] :
( ( ( fsemiri1314217659103216013at_int @ ( fsuc @ X14 ) )
= ( fplus_plus_int @ fone_one_int @ ( fsemiri1314217659103216013at_int @ X14 ) ) )
| ~ p140 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_29,plain,
( fsuc
= ( fplus_plus_nat @ fone_one_nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
thf(c_0_30,plain,
p140,
inference(split_conjunct,[status(thm)],[ax1510]) ).
thf(c_0_31,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1649]) ).
thf(c_0_32,plain,
! [X14: nat,X653: vEBT_VEBT,X1814: option4927543243414619207at_nat,X654: list_VEBT_VEBT] :
( ( ( fvEBT_VEBT_height @ ( fvEBT_Node @ X1814 @ X14 @ X654 @ X653 ) )
= ( fplus_plus_nat @ fone_one_nat @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ X653 @ ( fset_VEBT_VEBT2 @ X654 ) ) ) ) ) )
| ~ p91 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_33,plain,
p91,
inference(split_conjunct,[status(thm)],[ax1559]) ).
thf(c_0_34,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_23]) ).
thf(c_0_35,plain,
( ( farchim7802044766580827645g_real @ ( flog @ ( fplus_plus_real @ fone_one_real @ fone_one_real ) @ ( fsemiri5074537144036343181t_real @ fm ) ) )
= ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ fsummary ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
thf(c_0_36,plain,
p4,
inference(split_conjunct,[status(thm)],[ax1646]) ).
thf(c_0_37,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_27]) ).
thf(c_0_38,plain,
! [X14: nat] :
( ( fplus_plus_int @ fone_one_int @ ( fsemiri1314217659103216013at_int @ X14 ) )
= ( fsemiri1314217659103216013at_int @ ( fplus_plus_nat @ fone_one_nat @ X14 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
thf(c_0_39,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_40,plain,
! [X14: nat,X653: vEBT_VEBT,X1814: option4927543243414619207at_nat,X654: list_VEBT_VEBT] :
( ( fvEBT_VEBT_height @ ( fvEBT_Node @ X1814 @ X14 @ X654 @ X653 ) )
= ( fplus_plus_nat @ fone_one_nat @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ X653 @ ( fset_VEBT_VEBT2 @ X654 ) ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
thf(c_0_41,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)],[inference(rw,[status(thm)],[c_0_34,c_0_25]),c_0_35]),c_0_36])]) ).
thf(c_0_42,plain,
( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ ( fvEBT_Node @ fnone_P5556105721700978146at_nat @ fdeg @ ftreeList @ fsummary ) ) )
!= ( fsemiri1314217659103216013at_int @ ( fplus_plus_nat @ fone_one_nat @ ( fvEBT_VEBT_height @ fsummary ) ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_25]),c_0_35]),c_0_38]),c_0_39]) ).
thf(c_0_43,plain,
! [X14: nat,X21: nat,X6824: option4927543243414619207at_nat,X1814: option4927543243414619207at_nat,X654: list_VEBT_VEBT,X653: vEBT_VEBT] :
( ( fvEBT_VEBT_height @ ( fvEBT_Node @ X1814 @ X14 @ X654 @ X653 ) )
= ( fvEBT_VEBT_height @ ( fvEBT_Node @ X6824 @ X21 @ X654 @ X653 ) ) ),
inference(spm,[status(thm)],[c_0_40,c_0_40]) ).
thf(c_0_44,plain,
( ( fsemiri1314217659103216013at_int @ ( fplus_plus_nat @ fone_one_nat @ ( flattic8265883725875713057ax_nat @ ( fimage_VEBT_VEBT_nat @ fvEBT_VEBT_height @ ( finsert_VEBT_VEBT @ fsummary @ ( fset_VEBT_VEBT2 @ ftreeList ) ) ) ) ) )
= ( fsemiri1314217659103216013at_int @ ( fplus_plus_nat @ fone_one_nat @ ( fvEBT_VEBT_height @ fsummary ) ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_41]),c_0_38]) ).
thf(c_0_45,plain,
! [X1814: option4927543243414619207at_nat,X14: nat] :
( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ ( fvEBT_Node @ X1814 @ X14 @ ftreeList @ fsummary ) ) )
!= ( fsemiri1314217659103216013at_int @ ( fplus_plus_nat @ fone_one_nat @ ( fvEBT_VEBT_height @ fsummary ) ) ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_46,plain,
! [X1814: option4927543243414619207at_nat,X14: nat] :
( ( fsemiri1314217659103216013at_int @ ( fvEBT_VEBT_height @ ( fvEBT_Node @ X1814 @ X14 @ ftreeList @ fsummary ) ) )
= ( fsemiri1314217659103216013at_int @ ( fplus_plus_nat @ fone_one_nat @ ( fvEBT_VEBT_height @ fsummary ) ) ) ),
inference(spm,[status(thm)],[c_0_44,c_0_40]) ).
thf(c_0_47,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_45,c_0_46]),
[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
% 0.11/0.13 % Problem : ITP223^3 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.13 % 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
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jun 3 08:43:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 49.43/49.43 % SZS status Theorem
% 49.43/49.43 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 49.43/49.43 % Inferences: 0
% 49.43/49.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------