TSTP Solution File: NUM816^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM816^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 : Mon Jul 18 13:56:52 EDT 2022
% Result : Theorem 36.79s 37.21s
% Output : Proof 36.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 29
% Syntax : Number of formulae : 102 ( 33 unt; 0 typ; 2 def)
% Number of atoms : 384 ( 68 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 344 ( 117 ~; 86 |; 3 &; 102 @)
% ( 0 <=>; 33 =>; 3 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 30 con; 0-2 aty)
% Number of variables : 38 ( 2 ^ 36 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(def_cEVEN1,definition,
( cEVEN1
= ( ^ [X1: $i] :
! [X2: $i > $o] :
( ~ ( ( X2 @ c0 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) ) ) ).
thf(def_cODD1,definition,
( cODD1
= ( ^ [X1: $i] :
~ ( cEVEN1 @ X1 ) ) ) ).
thf(cTHM406,conjecture,
( ~ ( ! [X1: $i] :
( ( cS @ X1 )
!= c0 )
=> ~ ! [X1: $i,X2: $i] :
( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: $i > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) ) )
=> ( X1 @ ( cS @ c0 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ! [X1: $i] :
( ( cS @ X1 )
!= c0 )
=> ~ ! [X1: $i,X2: $i] :
( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: $i > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) ) )
=> ( X1 @ ( cS @ c0 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM406]) ).
thf(ax1291,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1291) ).
thf(ax1292,axiom,
~ p1,
file('<stdin>',ax1292) ).
thf(ax1276,axiom,
( ~ p14
| p17 ),
file('<stdin>',ax1276) ).
thf(ax1275,axiom,
( ~ p17
| p18 ),
file('<stdin>',ax1275) ).
thf(ax1280,axiom,
p14,
file('<stdin>',ax1280) ).
thf(ax1287,axiom,
( ~ p4
| ~ p6 ),
file('<stdin>',ax1287) ).
thf(ax1289,axiom,
( p2
| p4 ),
file('<stdin>',ax1289) ).
thf(pax4,axiom,
( p4
=> ! [X1: $i] :
( ( fcS @ X1 )
!= fc0 ) ),
file('<stdin>',pax4) ).
thf(nax41,axiom,
( p41
<= ( ( fcS @ fc0 )
= ( fcS @ fc0 ) ) ),
file('<stdin>',nax41) ).
thf(ax1274,axiom,
( ~ p18
| ~ p13
| p6 ),
file('<stdin>',ax1274) ).
thf(ax1252,axiom,
( ~ p38
| p45 ),
file('<stdin>',ax1252) ).
thf(pax705,axiom,
( p705
=> ! [X1: $i] :
( ( X1
= ( fcS @ fc0 ) )
=> ( X1 = fc0 ) ) ),
file('<stdin>',pax705) ).
thf(ax387,axiom,
( ~ p736
| ~ p41
| p13 ),
file('<stdin>',ax387) ).
thf(ax1265,axiom,
( ~ p3
| p27 ),
file('<stdin>',ax1265) ).
thf(ax1290,axiom,
( p1
| p3 ),
file('<stdin>',ax1290) ).
thf(ax617,axiom,
( ~ p45
| p558 ),
file('<stdin>',ax617) ).
thf(ax1260,axiom,
p38,
file('<stdin>',ax1260) ).
thf(nax705,axiom,
( p705
<= ! [X1: $i] :
( ( X1
= ( fcS @ fc0 ) )
=> ( X1 = fc0 ) ) ),
file('<stdin>',nax705) ).
thf(ax1284,axiom,
( ~ p5
| p9 ),
file('<stdin>',ax1284) ).
thf(ax1288,axiom,
( p2
| p5 ),
file('<stdin>',ax1288) ).
thf(ax388,axiom,
( ~ p737
| p736 ),
file('<stdin>',ax388) ).
thf(pax557,axiom,
( p557
=> ! [X1: $i] :
( ( X1 = fc0 )
=> ( ~ ( ( fc0
!= ( fcS @ X1 ) )
=> ~ ! [X2: $i] :
( ( X2
!= ( fcS @ fc0 ) )
=> ( ( fcS @ ( fcS @ X2 ) )
!= ( fcS @ fc0 ) ) ) )
=> ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) ) ) ) ),
file('<stdin>',pax557) ).
thf(ax616,axiom,
( ~ p558
| ~ p27
| p557 ),
file('<stdin>',ax616) ).
thf(pax9,axiom,
( p9
=> ! [X1: $i] :
( ( ( fcS @ fc0 )
= ( fcS @ X1 ) )
=> ( fc0 = X1 ) ) ),
file('<stdin>',pax9) ).
thf(nax737,axiom,
( p737
<= ! [X1: $i] :
( ( X1
= ( fcS @ fc0 ) )
=> ( fc0 = X1 ) ) ),
file('<stdin>',nax737) ).
thf(c_0_25,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1291]) ).
thf(c_0_26,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1292]) ).
thf(c_0_27,plain,
( ~ p14
| p17 ),
inference(fof_simplification,[status(thm)],[ax1276]) ).
thf(c_0_28,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_29,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_30,plain,
( ~ p17
| p18 ),
inference(fof_simplification,[status(thm)],[ax1275]) ).
thf(c_0_31,plain,
( p17
| ~ p14 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_32,plain,
p14,
inference(split_conjunct,[status(thm)],[ax1280]) ).
thf(c_0_33,plain,
( ~ p4
| ~ p6 ),
inference(fof_simplification,[status(thm)],[ax1287]) ).
thf(c_0_34,plain,
( p2
| p4 ),
inference(split_conjunct,[status(thm)],[ax1289]) ).
thf(c_0_35,plain,
~ p2,
inference(sr,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_36,plain,
! [X2230: $i] :
( ~ p4
| ( ( fcS @ X2230 )
!= fc0 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax4])])])]) ).
thf(c_0_37,plain,
( ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| p41 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax41])]) ).
thf(c_0_38,plain,
( ~ p18
| ~ p13
| p6 ),
inference(fof_simplification,[status(thm)],[ax1274]) ).
thf(c_0_39,plain,
( p18
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_40,plain,
p17,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
thf(c_0_41,plain,
( ~ p4
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_42,plain,
p4,
inference(sr,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_43,plain,
( ~ p38
| p45 ),
inference(fof_simplification,[status(thm)],[ax1252]) ).
thf(c_0_44,plain,
! [X674: $i] :
( ~ p705
| ( X674
!= ( fcS @ fc0 ) )
| ( X674 = fc0 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax705])])]) ).
thf(c_0_45,plain,
! [X1: $i] :
( ~ p4
| ( ( fcS @ X1 )
!= fc0 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_46,plain,
( ~ p736
| ~ p41
| p13 ),
inference(fof_simplification,[status(thm)],[ax387]) ).
thf(c_0_47,plain,
( p41
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_48,plain,
( p6
| ~ p18
| ~ p13 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_49,plain,
p18,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
thf(c_0_50,plain,
~ p6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
thf(c_0_51,plain,
( ~ p3
| p27 ),
inference(fof_simplification,[status(thm)],[ax1265]) ).
thf(c_0_52,plain,
( p1
| p3 ),
inference(split_conjunct,[status(thm)],[ax1290]) ).
thf(c_0_53,plain,
( ~ p45
| p558 ),
inference(fof_simplification,[status(thm)],[ax617]) ).
thf(c_0_54,plain,
( p45
| ~ p38 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_55,plain,
p38,
inference(split_conjunct,[status(thm)],[ax1260]) ).
thf(c_0_56,plain,
( ( ( esk336_0
= ( fcS @ fc0 ) )
| p705 )
& ( ( esk336_0 != fc0 )
| p705 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax705])])])])]) ).
thf(c_0_57,plain,
! [X1: $i] :
( ( X1 = fc0 )
| ~ p705
| ( X1
!= ( fcS @ fc0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_58,plain,
! [X1: $i] :
( ( fcS @ X1 )
!= fc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_42])]) ).
thf(c_0_59,plain,
( ~ p5
| p9 ),
inference(fof_simplification,[status(thm)],[ax1284]) ).
thf(c_0_60,plain,
( p2
| p5 ),
inference(split_conjunct,[status(thm)],[ax1288]) ).
thf(c_0_61,plain,
( ~ p737
| p736 ),
inference(fof_simplification,[status(thm)],[ax388]) ).
thf(c_0_62,plain,
( p13
| ~ p736
| ~ p41 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_63,plain,
p41,
inference(cn,[status(thm)],[c_0_47]) ).
thf(c_0_64,plain,
~ p13,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),c_0_50]) ).
thf(c_0_65,plain,
! [X1044: $i] :
( ( ( ( esk521_1 @ X1044 )
!= ( fcS @ fc0 ) )
| ( fc0
= ( fcS @ X1044 ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ( X1044 != fc0 )
| ~ p557 )
& ( ( ( fcS @ ( fcS @ ( esk521_1 @ X1044 ) ) )
= ( fcS @ fc0 ) )
| ( fc0
= ( fcS @ X1044 ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ( X1044 != fc0 )
| ~ p557 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax557])])])])])]) ).
thf(c_0_66,plain,
( ~ p558
| ~ p27
| p557 ),
inference(fof_simplification,[status(thm)],[ax616]) ).
thf(c_0_67,plain,
( p27
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
thf(c_0_68,plain,
p3,
inference(sr,[status(thm)],[c_0_52,c_0_29]) ).
thf(c_0_69,plain,
( p558
| ~ p45 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_70,plain,
p45,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
thf(c_0_71,plain,
! [X2220: $i] :
( ~ p9
| ( ( fcS @ fc0 )
!= ( fcS @ X2220 ) )
| ( fc0 = X2220 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax9])])]) ).
thf(c_0_72,plain,
( ( esk336_0
= ( fcS @ fc0 ) )
| p705 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_73,plain,
~ p705,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_57]),c_0_58]) ).
thf(c_0_74,plain,
( p9
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_75,plain,
p5,
inference(sr,[status(thm)],[c_0_60,c_0_35]) ).
thf(c_0_76,plain,
( ( ( esk297_0
= ( fcS @ fc0 ) )
| p737 )
& ( ( fc0 != esk297_0 )
| p737 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax737])])])])]) ).
thf(c_0_77,plain,
( p736
| ~ p737 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_78,plain,
~ p736,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]),c_0_64]) ).
thf(c_0_79,plain,
! [X1: $i] :
( ( ( fcS @ ( fcS @ ( esk521_1 @ X1 ) ) )
= ( fcS @ fc0 ) )
| ( fc0
= ( fcS @ X1 ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ( X1 != fc0 )
| ~ p557 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_80,plain,
( p557
| ~ p558
| ~ p27 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
thf(c_0_81,plain,
p27,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
thf(c_0_82,plain,
p558,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
thf(c_0_83,plain,
! [X1: $i] :
( ( fc0 = X1 )
| ~ p9
| ( ( fcS @ fc0 )
!= ( fcS @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
thf(c_0_84,plain,
( ( fcS @ fc0 )
= esk336_0 ),
inference(sr,[status(thm)],[c_0_72,c_0_73]) ).
thf(c_0_85,plain,
p9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
thf(c_0_86,plain,
( ( esk297_0
= ( fcS @ fc0 ) )
| p737 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_87,plain,
~ p737,
inference(sr,[status(thm)],[c_0_77,c_0_78]) ).
thf(c_0_88,plain,
! [X1: $i] :
( ( fc0
= ( fcS @ X1 ) )
| ( ( fcS @ ( fcS @ ( esk521_1 @ X1 ) ) )
= ( fcS @ fc0 ) )
| ( X1 != fc0 )
| ~ p557 ),
inference(cn,[status(thm)],[c_0_79]) ).
thf(c_0_89,plain,
p557,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_82])]) ).
thf(c_0_90,plain,
! [X1: $i] :
( ( fc0 = X1 )
| ( ( fcS @ X1 )
!= esk336_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84]),c_0_85])]) ).
thf(c_0_91,plain,
esk336_0 = esk297_0,
inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_86,c_0_87]),c_0_84]) ).
thf(c_0_92,plain,
( ( fcS @ ( fcS @ ( esk521_1 @ fc0 ) ) )
= esk336_0 ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_84]),c_0_89])]),c_0_58])]) ).
thf(c_0_93,plain,
! [X1: $i] :
( ( fc0 = X1 )
| ( ( fcS @ X1 )
!= esk297_0 ) ),
inference(rw,[status(thm)],[c_0_90,c_0_91]) ).
thf(c_0_94,plain,
( ( fcS @ ( fcS @ ( esk521_1 @ fc0 ) ) )
= esk297_0 ),
inference(rw,[status(thm)],[c_0_92,c_0_91]) ).
thf(c_0_95,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_58]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ~ ( ! [X1: $i] :
( ( cS @ X1 )
!= c0 )
=> ~ ! [X1: $i,X2: $i] :
( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: $i > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) ) )
=> ( X1 @ ( cS @ c0 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM816^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n027.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 : 600
% 0.12/0.34 % DateTime : Tue Jul 5 16:06:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 36.79/37.21 % SZS status Theorem
% 36.79/37.21 % Mode: mode485
% 36.79/37.21 % Inferences: 33
% 36.79/37.21 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------