TSTP Solution File: NUM830^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM830^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 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 : Mon Jul 18 13:56:55 EDT 2022
% Result : Theorem 2.42s 2.60s
% Output : Proof 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 32
% Syntax : Number of formulae : 110 ( 38 unt; 0 typ; 4 def)
% Number of atoms : 431 ( 42 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 439 ( 116 ~; 89 |; 4 &; 212 @)
% ( 0 <=>; 16 =>; 2 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 38 con; 0-2 aty)
% Number of variables : 44 ( 0 ^ 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(def_cPA_1,definition,
( cPA_1
= ( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 ) ) ) ).
thf(def_cPA_2,definition,
( cPA_2
= ( ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) ) ) ).
thf(def_cPA_3,definition,
( cPA_3
= ( ! [X1: n] :
( ( c_star @ X1 @ c0 )
= c0 ) ) ) ).
thf(def_cPA_4,definition,
( cPA_4
= ( ! [X1: n,X2: n] :
( ( c_star @ X1 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X1 @ X2 ) @ X1 ) ) ) ) ).
thf(cPA_THM1,conjecture,
( ~ ( ~ ( ~ ( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 )
=> ~ ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) )
=> ~ ! [X1: n] :
( ( c_star @ X1 @ c0 )
= c0 ) )
=> ~ ! [X1: n,X2: n] :
( ( c_star @ X1 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X1 @ X2 ) @ X1 ) ) )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 )
=> ~ ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) )
=> ~ ! [X1: n] :
( ( c_star @ X1 @ c0 )
= c0 ) )
=> ~ ! [X1: n,X2: n] :
( ( c_star @ X1 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X1 @ X2 ) @ X1 ) ) )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cPA_THM1]) ).
thf(ax1405,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1405) ).
thf(ax1406,axiom,
~ p1,
file('<stdin>',ax1406) ).
thf(ax1393,axiom,
( ~ p18
| p17 ),
file('<stdin>',ax1393) ).
thf(ax1387,axiom,
( ~ p11
| p19 ),
file('<stdin>',ax1387) ).
thf(ax1395,axiom,
( p2
| p11 ),
file('<stdin>',ax1395) ).
thf(ax1392,axiom,
( ~ p17
| p16 ),
file('<stdin>',ax1392) ).
thf(ax1394,axiom,
p18,
file('<stdin>',ax1394) ).
thf(ax1404,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax1404) ).
thf(ax1388,axiom,
( ~ p19
| p13 ),
file('<stdin>',ax1388) ).
thf(ax1391,axiom,
( ~ p16
| p3
| p15 ),
file('<stdin>',ax1391) ).
thf(ax1371,axiom,
( ~ p18
| p39 ),
file('<stdin>',ax1371) ).
thf(ax1389,axiom,
( ~ p14
| ~ p13
| ~ p12 ),
file('<stdin>',ax1389) ).
thf(ax1390,axiom,
( ~ p15
| p14 ),
file('<stdin>',ax1390) ).
thf(ax1233,axiom,
( ~ p39
| p144 ),
file('<stdin>',ax1233) ).
thf(ax1366,axiom,
( ~ p19
| p35 ),
file('<stdin>',ax1366) ).
thf(ax1232,axiom,
( ~ p144
| p12
| p143 ),
file('<stdin>',ax1232) ).
thf(ax1230,axiom,
( ~ p142
| ~ p35
| ~ p141 ),
file('<stdin>',ax1230) ).
thf(ax1231,axiom,
( ~ p143
| p142 ),
file('<stdin>',ax1231) ).
thf(ax1211,axiom,
( ~ p5
| p161 ),
file('<stdin>',ax1211) ).
thf(ax1201,axiom,
( ~ p161
| p169 ),
file('<stdin>',ax1201) ).
thf(ax1403,axiom,
p5,
file('<stdin>',ax1403) ).
thf(ax1189,axiom,
( p141
| ~ p155
| ~ p153 ),
file('<stdin>',ax1189) ).
thf(nax1,axiom,
( p1
<= ( ~ ( ~ ( ~ ( ! [X1: n] :
( ( fc_plus @ X1 @ fc0 )
= X1 )
=> ~ ! [X1: n,X2: n] :
( ( fc_plus @ X1 @ ( fcS @ X2 ) )
= ( fcS @ ( fc_plus @ X1 @ X2 ) ) ) )
=> ~ ! [X1: n] :
( ( fc_star @ X1 @ fc0 )
= fc0 ) )
=> ~ ! [X1: n,X2: n] :
( ( fc_star @ X1 @ ( fcS @ X2 ) )
= ( fc_plus @ ( fc_star @ X1 @ X2 ) @ X1 ) ) )
=> ( ( fc_star @ ( fcS @ ( fcS @ fc0 ) ) @ ( fcS @ ( fcS @ fc0 ) ) )
= ( fc_plus @ ( fcS @ ( fcS @ fc0 ) ) @ ( fcS @ ( fcS @ fc0 ) ) ) ) ) ),
file('<stdin>',nax1) ).
thf(ax1200,axiom,
( ~ p169
| ~ p167
| p155 ),
file('<stdin>',ax1200) ).
thf(ax1219,axiom,
p153,
file('<stdin>',ax1219) ).
thf(nax167,axiom,
( p167
<= ( ( fcS @ ( fcS @ fc0 ) )
= ( fc_plus @ ( fc_star @ ( fcS @ ( fcS @ fc0 ) ) @ fc0 ) @ ( fcS @ ( fcS @ fc0 ) ) ) ) ),
file('<stdin>',nax167) ).
thf(c_0_26,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1405]) ).
thf(c_0_27,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1406]) ).
thf(c_0_28,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_29,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_30,plain,
( ~ p18
| p17 ),
inference(fof_simplification,[status(thm)],[ax1393]) ).
thf(c_0_31,plain,
( ~ p11
| p19 ),
inference(fof_simplification,[status(thm)],[ax1387]) ).
thf(c_0_32,plain,
( p2
| p11 ),
inference(split_conjunct,[status(thm)],[ax1395]) ).
thf(c_0_33,plain,
~ p2,
inference(sr,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_34,plain,
( ~ p17
| p16 ),
inference(fof_simplification,[status(thm)],[ax1392]) ).
thf(c_0_35,plain,
( p17
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_36,plain,
p18,
inference(split_conjunct,[status(thm)],[ax1394]) ).
thf(c_0_37,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1404]) ).
thf(c_0_38,plain,
( ~ p19
| p13 ),
inference(fof_simplification,[status(thm)],[ax1388]) ).
thf(c_0_39,plain,
( p19
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_40,plain,
p11,
inference(sr,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_41,plain,
( ~ p16
| p3
| p15 ),
inference(fof_simplification,[status(thm)],[ax1391]) ).
thf(c_0_42,plain,
( p16
| ~ p17 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_43,plain,
p17,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
thf(c_0_44,plain,
( p1
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_45,plain,
( ~ p18
| p39 ),
inference(fof_simplification,[status(thm)],[ax1371]) ).
thf(c_0_46,plain,
( ~ p14
| ~ p13
| ~ p12 ),
inference(fof_simplification,[status(thm)],[ax1389]) ).
thf(c_0_47,plain,
( p13
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_48,plain,
p19,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
thf(c_0_49,plain,
( ~ p15
| p14 ),
inference(fof_simplification,[status(thm)],[ax1390]) ).
thf(c_0_50,plain,
( p3
| p15
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_51,plain,
p16,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
thf(c_0_52,plain,
~ p3,
inference(sr,[status(thm)],[c_0_44,c_0_29]) ).
thf(c_0_53,plain,
( ~ p39
| p144 ),
inference(fof_simplification,[status(thm)],[ax1233]) ).
thf(c_0_54,plain,
( p39
| ~ p18 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_55,plain,
( ~ p14
| ~ p13
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_56,plain,
p13,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
thf(c_0_57,plain,
( p14
| ~ p15 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_58,plain,
p15,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]),c_0_52]) ).
thf(c_0_59,plain,
( ~ p19
| p35 ),
inference(fof_simplification,[status(thm)],[ax1366]) ).
thf(c_0_60,plain,
( ~ p144
| p12
| p143 ),
inference(fof_simplification,[status(thm)],[ax1232]) ).
thf(c_0_61,plain,
( p144
| ~ p39 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_62,plain,
p39,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_36])]) ).
thf(c_0_63,plain,
( ~ p12
| ~ p14 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
thf(c_0_64,plain,
p14,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
thf(c_0_65,plain,
( ~ p142
| ~ p35
| ~ p141 ),
inference(fof_simplification,[status(thm)],[ax1230]) ).
thf(c_0_66,plain,
( p35
| ~ p19 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_67,plain,
( ~ p143
| p142 ),
inference(fof_simplification,[status(thm)],[ax1231]) ).
thf(c_0_68,plain,
( p12
| p143
| ~ p144 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
thf(c_0_69,plain,
p144,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).
thf(c_0_70,plain,
~ p12,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
thf(c_0_71,plain,
( ~ p5
| p161 ),
inference(fof_simplification,[status(thm)],[ax1211]) ).
thf(c_0_72,plain,
( ~ p142
| ~ p35
| ~ p141 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_73,plain,
p35,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_48])]) ).
thf(c_0_74,plain,
( p142
| ~ p143 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_75,plain,
p143,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]),c_0_70]) ).
thf(c_0_76,plain,
( ~ p161
| p169 ),
inference(fof_simplification,[status(thm)],[ax1201]) ).
thf(c_0_77,plain,
( p161
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
thf(c_0_78,plain,
p5,
inference(split_conjunct,[status(thm)],[ax1403]) ).
thf(c_0_79,plain,
( p141
| ~ p155
| ~ p153 ),
inference(fof_simplification,[status(thm)],[ax1189]) ).
thf(c_0_80,plain,
( ~ p141
| ~ p142 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).
thf(c_0_81,plain,
p142,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
thf(c_0_82,plain,
! [X2034: n,X2035: n,X2036: n,X2037: n,X2038: n,X2039: n] :
( ( ( ( fc_plus @ X2034 @ fc0 )
= X2034 )
| p1 )
& ( ( ( fc_plus @ X2035 @ ( fcS @ X2036 ) )
= ( fcS @ ( fc_plus @ X2035 @ X2036 ) ) )
| p1 )
& ( ( ( fc_star @ X2037 @ fc0 )
= fc0 )
| p1 )
& ( ( ( fc_star @ X2038 @ ( fcS @ X2039 ) )
= ( fc_plus @ ( fc_star @ X2038 @ X2039 ) @ X2038 ) )
| p1 )
& ( ( ( fc_star @ ( fcS @ ( fcS @ fc0 ) ) @ ( fcS @ ( fcS @ fc0 ) ) )
!= ( fc_plus @ ( fcS @ ( fcS @ fc0 ) ) @ ( fcS @ ( fcS @ fc0 ) ) ) )
| p1 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])]) ).
thf(c_0_83,plain,
( ~ p169
| ~ p167
| p155 ),
inference(fof_simplification,[status(thm)],[ax1200]) ).
thf(c_0_84,plain,
( p169
| ~ p161 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_85,plain,
p161,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
thf(c_0_86,plain,
( p141
| ~ p155
| ~ p153 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_87,plain,
p153,
inference(split_conjunct,[status(thm)],[ax1219]) ).
thf(c_0_88,plain,
~ p141,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
thf(c_0_89,plain,
( ( ( fcS @ ( fcS @ fc0 ) )
!= ( fc_plus @ ( fc_star @ ( fcS @ ( fcS @ fc0 ) ) @ fc0 ) @ ( fcS @ ( fcS @ fc0 ) ) ) )
| p167 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax167])]) ).
thf(c_0_90,plain,
! [X1: n] :
( ( ( fc_star @ X1 @ fc0 )
= fc0 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
thf(c_0_91,plain,
! [X1: n,X2: n] :
( ( ( fc_plus @ X1 @ ( fcS @ X2 ) )
= ( fcS @ ( fc_plus @ X1 @ X2 ) ) )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
thf(c_0_92,plain,
! [X1: n] :
( ( ( fc_plus @ X1 @ fc0 )
= X1 )
| p1 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
thf(c_0_93,plain,
( p155
| ~ p169
| ~ p167 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
thf(c_0_94,plain,
p169,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
thf(c_0_95,plain,
~ p155,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]),c_0_88]) ).
thf(c_0_96,plain,
( p167
| ( ( fcS @ ( fcS @ fc0 ) )
!= ( fc_plus @ ( fc_star @ ( fcS @ ( fcS @ fc0 ) ) @ fc0 ) @ ( fcS @ ( fcS @ fc0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
thf(c_0_97,plain,
! [X1: n] :
( ( fc_star @ X1 @ fc0 )
= fc0 ),
inference(sr,[status(thm)],[c_0_90,c_0_29]) ).
thf(c_0_98,plain,
! [X1: n,X2: n] :
( ( fc_plus @ X1 @ ( fcS @ X2 ) )
= ( fcS @ ( fc_plus @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[c_0_91,c_0_29]) ).
thf(c_0_99,plain,
! [X1: n] :
( ( fc_plus @ X1 @ fc0 )
= X1 ),
inference(sr,[status(thm)],[c_0_92,c_0_29]) ).
thf(c_0_100,plain,
~ p167,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]),c_0_95]) ).
thf(c_0_101,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_98]),c_0_98]),c_0_99])]),c_0_100]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 )
=> ~ ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) )
=> ~ ! [X1: n] :
( ( c_star @ X1 @ c0 )
= c0 ) )
=> ~ ! [X1: n,X2: n] :
( ( c_star @ X1 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X1 @ X2 ) @ X1 ) ) )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM830^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 15:25:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.42/2.60 % SZS status Theorem
% 2.42/2.60 % Mode: mode506
% 2.42/2.60 % Inferences: 19522
% 2.42/2.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------