TSTP Solution File: NUM817^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM817^5 : 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 : n026.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 37.16s 37.18s
% Output : Proof 37.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 31
% Syntax : Number of formulae : 141 ( 43 unt; 0 typ; 2 def)
% Number of atoms : 937 ( 184 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 723 ( 195 ~; 156 |; 13 &; 298 @)
% ( 0 <=>; 56 =>; 5 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 31 con; 0-2 aty)
% Number of variables : 52 ( 2 ^ 50 !; 0 ?; 52 :)
% 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(cTHM405,conjecture,
( ~ ( ! [X1: $i] :
( ( cS @ X1 )
!= c0 )
=> ~ ! [X1: $i,X2: $i] :
( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: $i] :
~ ~ ! [X2: $i > $o] :
( ~ ( ( X2 @ c0 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ! [X1: $i] :
( ( cS @ X1 )
!= c0 )
=> ~ ! [X1: $i,X2: $i] :
( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: $i,X2: $i > $o] :
( ~ ( ( X2 @ c0 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cTHM405]) ).
thf(ax1297,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1297) ).
thf(ax1298,axiom,
~ p1,
file('<stdin>',ax1298) ).
thf(ax1283,axiom,
( ~ p13
| p16 ),
file('<stdin>',ax1283) ).
thf(ax1291,axiom,
( ~ p5
| p8 ),
file('<stdin>',ax1291) ).
thf(ax1294,axiom,
( p2
| p5 ),
file('<stdin>',ax1294) ).
thf(ax1113,axiom,
( ~ p16
| p154 ),
file('<stdin>',ax1113) ).
thf(ax1287,axiom,
p13,
file('<stdin>',ax1287) ).
thf(ax1280,axiom,
( ~ p4
| ~ p18 ),
file('<stdin>',ax1280) ).
thf(ax1295,axiom,
( p2
| p4 ),
file('<stdin>',ax1295) ).
thf(ax1199,axiom,
( ~ p8
| p89 ),
file('<stdin>',ax1199) ).
thf(ax1112,axiom,
( ~ p154
| ~ p83
| p18 ),
file('<stdin>',ax1112) ).
thf(ax1200,axiom,
( ~ p89
| ~ p84
| p83 ),
file('<stdin>',ax1200) ).
thf(pax598,axiom,
( p598
=> ( ~ ( ( ( fcS @ fc0 )
= ( fcS @ fc0 ) )
=> ~ ! [X1: $i] :
( ( ( fcS @ fc0 )
= X1 )
=> ( ( fcS @ fc0 )
= ( fcS @ ( fcS @ X1 ) ) ) ) )
=> ( ( fcS @ fc0 )
= fc0 ) ) ),
file('<stdin>',pax598) ).
thf(pax4,axiom,
( p4
=> ! [X1: $i] :
( ( fcS @ X1 )
!= fc0 ) ),
file('<stdin>',pax4) ).
thf(nax84,axiom,
( p84
<= ( ( fcS @ fc0 )
= ( fcS @ ( fcS @ ( fcS @ fc0 ) ) ) ) ),
file('<stdin>',nax84) ).
thf(nax598,axiom,
( p598
<= ( ~ ( ( ( fcS @ fc0 )
= ( fcS @ fc0 ) )
=> ~ ! [X1: $i] :
( ( ( fcS @ fc0 )
= X1 )
=> ( ( fcS @ fc0 )
= ( fcS @ ( fcS @ X1 ) ) ) ) )
=> ( ( fcS @ fc0 )
= fc0 ) ) ),
file('<stdin>',nax598) ).
thf(pax623,axiom,
( p623
=> ( ~ ( ( fc0 = fc0 )
=> ~ ! [X1: $i] :
( ( ( fcS @ fc0 )
= X1 )
=> ( ( fcS @ fc0 )
= ( fcS @ ( fcS @ X1 ) ) ) ) )
=> ( ( fcS @ fc0 )
= fc0 ) ) ),
file('<stdin>',pax623) ).
thf(nax623,axiom,
( p623
<= ( ~ ( ( fc0 = fc0 )
=> ~ ! [X1: $i] :
( ( ( fcS @ fc0 )
= X1 )
=> ( ( fcS @ fc0 )
= ( fcS @ ( fcS @ X1 ) ) ) ) )
=> ( ( fcS @ fc0 )
= fc0 ) ) ),
file('<stdin>',nax623) ).
thf(pax363,axiom,
( p363
=> ( ~ ( ( ( fcS @ fc0 )
= ( fcS @ fc0 ) )
=> ~ ! [X1: $i] :
( ( X1
= ( fcS @ fc0 ) )
=> ( ( fcS @ ( fcS @ X1 ) )
= ( fcS @ fc0 ) ) ) )
=> ( fc0
= ( fcS @ fc0 ) ) ) ),
file('<stdin>',pax363) ).
thf(nax363,axiom,
( p363
<= ( ~ ( ( ( fcS @ fc0 )
= ( fcS @ fc0 ) )
=> ~ ! [X1: $i] :
( ( X1
= ( fcS @ fc0 ) )
=> ( ( fcS @ ( fcS @ X1 ) )
= ( fcS @ fc0 ) ) ) )
=> ( fc0
= ( fcS @ fc0 ) ) ) ),
file('<stdin>',nax363) ).
thf(ax1279,axiom,
( ~ p3
| p19 ),
file('<stdin>',ax1279) ).
thf(ax1296,axiom,
( p1
| p3 ),
file('<stdin>',ax1296) ).
thf(pax192,axiom,
( p192
=> ( ~ ( ( fc0
!= ( fcS @ fc0 ) )
=> ~ ! [X1: $i] :
( ( X1
!= ( fcS @ fc0 ) )
=> ( ( fcS @ ( fcS @ X1 ) )
!= ( fcS @ fc0 ) ) ) )
=> ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) ) ) ),
file('<stdin>',pax192) ).
thf(ax1066,axiom,
( ~ p19
| p192 ),
file('<stdin>',ax1066) ).
thf(pax396,axiom,
( p396
=> ( ~ ( ( fc0 = fc0 )
=> ~ ! [X1: $i] :
( ( X1
= ( fcS @ fc0 ) )
=> ( ( fcS @ ( fcS @ X1 ) )
= ( fcS @ fc0 ) ) ) )
=> ( fc0
= ( fcS @ fc0 ) ) ) ),
file('<stdin>',pax396) ).
thf(nax396,axiom,
( p396
<= ( ~ ( ( fc0 = fc0 )
=> ~ ! [X1: $i] :
( ( X1
= ( fcS @ fc0 ) )
=> ( ( fcS @ ( fcS @ X1 ) )
= ( fcS @ fc0 ) ) ) )
=> ( fc0
= ( fcS @ fc0 ) ) ) ),
file('<stdin>',nax396) ).
thf(pax5,axiom,
( p5
=> ! [X1: $i,X2: $i] :
( ( ( fcS @ X1 )
= ( fcS @ X2 ) )
=> ( X1 = X2 ) ) ),
file('<stdin>',pax5) ).
thf(c_0_27,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1297]) ).
thf(c_0_28,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1298]) ).
thf(c_0_29,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_30,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_31,plain,
( ~ p13
| p16 ),
inference(fof_simplification,[status(thm)],[ax1283]) ).
thf(c_0_32,plain,
( ~ p5
| p8 ),
inference(fof_simplification,[status(thm)],[ax1291]) ).
thf(c_0_33,plain,
( p2
| p5 ),
inference(split_conjunct,[status(thm)],[ax1294]) ).
thf(c_0_34,plain,
~ p2,
inference(sr,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_35,plain,
( ~ p16
| p154 ),
inference(fof_simplification,[status(thm)],[ax1113]) ).
thf(c_0_36,plain,
( p16
| ~ p13 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_37,plain,
p13,
inference(split_conjunct,[status(thm)],[ax1287]) ).
thf(c_0_38,plain,
( ~ p4
| ~ p18 ),
inference(fof_simplification,[status(thm)],[ax1280]) ).
thf(c_0_39,plain,
( p2
| p4 ),
inference(split_conjunct,[status(thm)],[ax1295]) ).
thf(c_0_40,plain,
( ~ p8
| p89 ),
inference(fof_simplification,[status(thm)],[ax1199]) ).
thf(c_0_41,plain,
( p8
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_42,plain,
p5,
inference(sr,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_43,plain,
( ~ p154
| ~ p83
| p18 ),
inference(fof_simplification,[status(thm)],[ax1112]) ).
thf(c_0_44,plain,
( p154
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_45,plain,
p16,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
thf(c_0_46,plain,
( ~ p4
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_47,plain,
p4,
inference(sr,[status(thm)],[c_0_39,c_0_34]) ).
thf(c_0_48,plain,
( ~ p89
| ~ p84
| p83 ),
inference(fof_simplification,[status(thm)],[ax1200]) ).
thf(c_0_49,plain,
( p89
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_50,plain,
p8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
thf(c_0_51,plain,
( p18
| ~ p154
| ~ p83 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_52,plain,
p154,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
thf(c_0_53,plain,
~ p18,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
thf(c_0_54,plain,
( ( ( ( fcS @ fc0 )
= esk435_0 )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ( ( fcS @ fc0 )
= fc0 )
| ~ p598 )
& ( ( ( fcS @ fc0 )
!= ( fcS @ ( fcS @ esk435_0 ) ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ( ( fcS @ fc0 )
= fc0 )
| ~ p598 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax598])])])]) ).
thf(c_0_55,plain,
! [X2278: $i] :
( ~ p4
| ( ( fcS @ X2278 )
!= 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_56,plain,
( ( ( fcS @ fc0 )
!= ( fcS @ ( fcS @ ( fcS @ fc0 ) ) ) )
| p84 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax84])]) ).
thf(c_0_57,plain,
( p83
| ~ p89
| ~ p84 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_58,plain,
p89,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
thf(c_0_59,plain,
~ p83,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]),c_0_53]) ).
thf(c_0_60,plain,
( ( ( fcS @ fc0 )
= esk435_0 )
| ( ( fcS @ fc0 )
= fc0 )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ~ p598 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_61,plain,
! [X1: $i] :
( ~ p4
| ( ( fcS @ X1 )
!= fc0 ) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_62,plain,
! [X873: $i] :
( ( ( ( fcS @ fc0 )
= ( fcS @ fc0 ) )
| p598 )
& ( ( ( fcS @ fc0 )
!= X873 )
| ( ( fcS @ fc0 )
= ( fcS @ ( fcS @ X873 ) ) )
| p598 )
& ( ( ( fcS @ fc0 )
!= fc0 )
| p598 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax598])])])])]) ).
thf(c_0_63,plain,
( p84
| ( ( fcS @ fc0 )
!= ( fcS @ ( fcS @ ( fcS @ fc0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_64,plain,
~ p84,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]),c_0_59]) ).
thf(c_0_65,plain,
( ( ( fcS @ fc0 )
= fc0 )
| ( ( fcS @ fc0 )
!= ( fcS @ ( fcS @ esk435_0 ) ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ~ p598 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_66,plain,
( ( ( fcS @ fc0 )
= fc0 )
| ( ( fcS @ fc0 )
= esk435_0 )
| ~ p598 ),
inference(cn,[status(thm)],[c_0_60]) ).
thf(c_0_67,plain,
! [X1: $i] :
( ( fcS @ X1 )
!= fc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_47])]) ).
thf(c_0_68,plain,
! [X1: $i] :
( ( ( fcS @ fc0 )
= ( fcS @ ( fcS @ X1 ) ) )
| p598
| ( ( fcS @ fc0 )
!= X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_69,plain,
( fcS @ ( fcS @ ( fcS @ fc0 ) ) )
!= ( fcS @ fc0 ),
inference(sr,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_70,plain,
( ( ( ( fcS @ fc0 )
= esk386_0 )
| ( fc0 != fc0 )
| ( ( fcS @ fc0 )
= fc0 )
| ~ p623 )
& ( ( ( fcS @ fc0 )
!= ( fcS @ ( fcS @ esk386_0 ) ) )
| ( fc0 != fc0 )
| ( ( fcS @ fc0 )
= fc0 )
| ~ p623 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax623])])])]) ).
thf(c_0_71,plain,
( ( ( fcS @ fc0 )
= fc0 )
| ( ( fcS @ fc0 )
!= ( fcS @ ( fcS @ esk435_0 ) ) )
| ~ p598 ),
inference(cn,[status(thm)],[c_0_65]) ).
thf(c_0_72,plain,
( ( ( fcS @ fc0 )
= esk435_0 )
| ~ p598 ),
inference(sr,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_73,plain,
p598,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_68]),c_0_69]) ).
thf(c_0_74,plain,
( ( ( fcS @ fc0 )
= fc0 )
| ( ( fcS @ fc0 )
!= ( fcS @ ( fcS @ esk386_0 ) ) )
| ( fc0 != fc0 )
| ~ p623 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
thf(c_0_75,plain,
( ( ( fcS @ fc0 )
= esk386_0 )
| ( ( fcS @ fc0 )
= fc0 )
| ( fc0 != fc0 )
| ~ p623 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
thf(c_0_76,plain,
! [X775: $i] :
( ( ( fc0 = fc0 )
| p623 )
& ( ( ( fcS @ fc0 )
!= X775 )
| ( ( fcS @ fc0 )
= ( fcS @ ( fcS @ X775 ) ) )
| p623 )
& ( ( ( fcS @ fc0 )
!= fc0 )
| p623 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax623])])])])]) ).
thf(c_0_77,plain,
( ( ( fcS @ ( fcS @ esk435_0 ) )
!= ( fcS @ fc0 ) )
| ~ p598 ),
inference(sr,[status(thm)],[c_0_71,c_0_67]) ).
thf(c_0_78,plain,
( ( fcS @ fc0 )
= esk435_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).
thf(c_0_79,plain,
( ( ( esk775_0
= ( fcS @ fc0 ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ( fc0
= ( fcS @ fc0 ) )
| ~ p363 )
& ( ( ( fcS @ ( fcS @ esk775_0 ) )
!= ( fcS @ fc0 ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ( fc0
= ( fcS @ fc0 ) )
| ~ p363 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax363])])])]) ).
thf(c_0_80,plain,
( ( ( fcS @ fc0 )
= fc0 )
| ( ( fcS @ fc0 )
!= ( fcS @ ( fcS @ esk386_0 ) ) )
| ~ p623 ),
inference(cn,[status(thm)],[c_0_74]) ).
thf(c_0_81,plain,
( ( ( fcS @ fc0 )
= fc0 )
| ( ( fcS @ fc0 )
= esk386_0 )
| ~ p623 ),
inference(cn,[status(thm)],[c_0_75]) ).
thf(c_0_82,plain,
! [X1: $i] :
( ( ( fcS @ fc0 )
= ( fcS @ ( fcS @ X1 ) ) )
| p623
| ( ( fcS @ fc0 )
!= X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_83,plain,
( fcS @ ( fcS @ esk435_0 ) )
!= esk435_0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_73])]),c_0_78]) ).
thf(c_0_84,plain,
( ( fc0
= ( fcS @ fc0 ) )
| ( ( fcS @ ( fcS @ esk775_0 ) )
!= ( fcS @ fc0 ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ~ p363 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_85,plain,
( ( ( fcS @ ( fcS @ esk386_0 ) )
!= ( fcS @ fc0 ) )
| ~ p623 ),
inference(sr,[status(thm)],[c_0_80,c_0_67]) ).
thf(c_0_86,plain,
( ( ( fcS @ fc0 )
= esk386_0 )
| ~ p623 ),
inference(sr,[status(thm)],[c_0_81,c_0_67]) ).
thf(c_0_87,plain,
p623,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_78]),c_0_78])]),c_0_83]) ).
thf(c_0_88,plain,
( ( fc0
= ( fcS @ fc0 ) )
| ( ( fcS @ ( fcS @ esk775_0 ) )
!= ( fcS @ fc0 ) )
| ~ p363 ),
inference(cn,[status(thm)],[c_0_84]) ).
thf(c_0_89,plain,
( ( esk775_0
= ( fcS @ fc0 ) )
| ( fc0
= ( fcS @ fc0 ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ~ p363 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_90,plain,
! [X1553: $i] :
( ( ( ( fcS @ fc0 )
= ( fcS @ fc0 ) )
| p363 )
& ( ( X1553
!= ( fcS @ fc0 ) )
| ( ( fcS @ ( fcS @ X1553 ) )
= ( fcS @ fc0 ) )
| p363 )
& ( ( fc0
!= ( fcS @ fc0 ) )
| p363 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax363])])])])]) ).
thf(c_0_91,plain,
( ( ( fcS @ ( fcS @ esk386_0 ) )
!= esk435_0 )
| ~ p623 ),
inference(rw,[status(thm)],[c_0_85,c_0_78]) ).
thf(c_0_92,plain,
esk435_0 = esk386_0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]),c_0_78]) ).
thf(c_0_93,plain,
( ~ p3
| p19 ),
inference(fof_simplification,[status(thm)],[ax1279]) ).
thf(c_0_94,plain,
( p1
| p3 ),
inference(split_conjunct,[status(thm)],[ax1296]) ).
thf(c_0_95,plain,
( ( ( fcS @ ( fcS @ esk775_0 ) )
!= ( fcS @ fc0 ) )
| ~ p363 ),
inference(sr,[status(thm)],[c_0_88,c_0_67]) ).
thf(c_0_96,plain,
( ( fc0
= ( fcS @ fc0 ) )
| ( esk775_0
= ( fcS @ fc0 ) )
| ~ p363 ),
inference(cn,[status(thm)],[c_0_89]) ).
thf(c_0_97,plain,
! [X1: $i] :
( ( ( fcS @ ( fcS @ X1 ) )
= ( fcS @ fc0 ) )
| p363
| ( X1
!= ( fcS @ fc0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
thf(c_0_98,plain,
( fcS @ ( fcS @ esk386_0 ) )
!= esk386_0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_87])]),c_0_92]) ).
thf(c_0_99,plain,
( ( ( esk991_0
!= ( fcS @ fc0 ) )
| ( fc0
= ( fcS @ fc0 ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ~ p192 )
& ( ( ( fcS @ ( fcS @ esk991_0 ) )
= ( fcS @ fc0 ) )
| ( fc0
= ( fcS @ fc0 ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ~ p192 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax192])])])])]) ).
thf(c_0_100,plain,
( ~ p19
| p192 ),
inference(fof_simplification,[status(thm)],[ax1066]) ).
thf(c_0_101,plain,
( p19
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_102,plain,
p3,
inference(sr,[status(thm)],[c_0_94,c_0_30]) ).
thf(c_0_103,plain,
( ( ( esk712_0
= ( fcS @ fc0 ) )
| ( fc0 != fc0 )
| ( fc0
= ( fcS @ fc0 ) )
| ~ p396 )
& ( ( ( fcS @ ( fcS @ esk712_0 ) )
!= ( fcS @ fc0 ) )
| ( fc0 != fc0 )
| ( fc0
= ( fcS @ fc0 ) )
| ~ p396 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax396])])])]) ).
thf(c_0_104,plain,
( ( ( fcS @ ( fcS @ esk775_0 ) )
!= esk435_0 )
| ~ p363 ),
inference(rw,[status(thm)],[c_0_95,c_0_78]) ).
thf(c_0_105,plain,
( ( ( fcS @ fc0 )
= esk775_0 )
| ~ p363 ),
inference(sr,[status(thm)],[c_0_96,c_0_67]) ).
thf(c_0_106,plain,
p363,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_78]),c_0_92]),c_0_78]),c_0_92])]),c_0_98]) ).
thf(c_0_107,plain,
( ( ( fcS @ ( fcS @ esk991_0 ) )
= ( fcS @ fc0 ) )
| ( fc0
= ( fcS @ fc0 ) )
| ( ( fcS @ fc0 )
!= ( fcS @ fc0 ) )
| ~ p192 ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
thf(c_0_108,plain,
( p192
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
thf(c_0_109,plain,
p19,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
thf(c_0_110,plain,
( ( esk712_0
= ( fcS @ fc0 ) )
| ( fc0
= ( fcS @ fc0 ) )
| ( fc0 != fc0 )
| ~ p396 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
thf(c_0_111,plain,
! [X1427: $i] :
( ( ( fc0 = fc0 )
| p396 )
& ( ( X1427
!= ( fcS @ fc0 ) )
| ( ( fcS @ ( fcS @ X1427 ) )
= ( fcS @ fc0 ) )
| p396 )
& ( ( fc0
!= ( fcS @ fc0 ) )
| p396 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax396])])])])]) ).
thf(c_0_112,plain,
( ( ( fcS @ ( fcS @ esk775_0 ) )
!= esk386_0 )
| ~ p363 ),
inference(rw,[status(thm)],[c_0_104,c_0_92]) ).
thf(c_0_113,plain,
esk386_0 = esk775_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]),c_0_78]),c_0_92]) ).
thf(c_0_114,plain,
( ( fc0
= ( fcS @ fc0 ) )
| ( ( fcS @ ( fcS @ esk991_0 ) )
= ( fcS @ fc0 ) )
| ~ p192 ),
inference(cn,[status(thm)],[c_0_107]) ).
thf(c_0_115,plain,
p192,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109])]) ).
thf(c_0_116,plain,
( ( fc0
= ( fcS @ fc0 ) )
| ( esk712_0
= ( fcS @ fc0 ) )
| ~ p396 ),
inference(cn,[status(thm)],[c_0_110]) ).
thf(c_0_117,plain,
! [X1: $i] :
( ( ( fcS @ ( fcS @ X1 ) )
= ( fcS @ fc0 ) )
| p396
| ( X1
!= ( fcS @ fc0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
thf(c_0_118,plain,
( fcS @ ( fcS @ esk775_0 ) )
!= esk775_0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_106])]),c_0_113]) ).
thf(c_0_119,plain,
( ( fcS @ ( fcS @ esk991_0 ) )
= ( fcS @ fc0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]),c_0_67]) ).
thf(c_0_120,plain,
! [X2274: $i,X2275: $i] :
( ~ p5
| ( ( fcS @ X2274 )
!= ( fcS @ X2275 ) )
| ( X2274 = X2275 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).
thf(c_0_121,plain,
( ( fcS @ fc0 )
= esk386_0 ),
inference(rw,[status(thm)],[c_0_78,c_0_92]) ).
thf(c_0_122,plain,
( ( ( fcS @ fc0 )
= esk712_0 )
| ~ p396 ),
inference(sr,[status(thm)],[c_0_116,c_0_67]) ).
thf(c_0_123,plain,
p396,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_78]),c_0_92]),c_0_113]),c_0_78]),c_0_92]),c_0_113])]),c_0_118]) ).
thf(c_0_124,plain,
( ( fcS @ ( fcS @ esk991_0 ) )
= esk435_0 ),
inference(rw,[status(thm)],[c_0_119,c_0_78]) ).
thf(c_0_125,plain,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ p5
| ( ( fcS @ X1 )
!= ( fcS @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
thf(c_0_126,plain,
( ( fcS @ fc0 )
= esk775_0 ),
inference(rw,[status(thm)],[c_0_121,c_0_113]) ).
thf(c_0_127,plain,
esk775_0 = esk712_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123])]),c_0_78]),c_0_92]),c_0_113]) ).
thf(c_0_128,plain,
( ( fcS @ ( fcS @ esk991_0 ) )
= esk386_0 ),
inference(rw,[status(thm)],[c_0_124,c_0_92]) ).
thf(c_0_129,plain,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( fcS @ X1 )
!= ( fcS @ X2 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_42])]) ).
thf(c_0_130,plain,
( ( fcS @ fc0 )
= esk712_0 ),
inference(rw,[status(thm)],[c_0_126,c_0_127]) ).
thf(c_0_131,plain,
( ( fcS @ ( fcS @ esk991_0 ) )
= esk775_0 ),
inference(rw,[status(thm)],[c_0_128,c_0_113]) ).
thf(c_0_132,plain,
! [X1: $i] :
( ( X1 = fc0 )
| ( ( fcS @ X1 )
!= esk712_0 ) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
thf(c_0_133,plain,
( ( fcS @ ( fcS @ esk991_0 ) )
= esk712_0 ),
inference(rw,[status(thm)],[c_0_131,c_0_127]) ).
thf(c_0_134,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_67]),
[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] :
~ ~ ! [X2: $i > $o] :
( ~ ( ( X2 @ c0 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ ( cS @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM817^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jul 6 00:29:08 EDT 2022
% 0.11/0.33 % CPUTime :
% 37.16/37.18 % SZS status Theorem
% 37.16/37.18 % Mode: mode485
% 37.16/37.18 % Inferences: 36
% 37.16/37.18 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------