TSTP Solution File: ITP104^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP104^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 00:29:07 EDT 2022
% Result : Theorem 74.01s 74.52s
% Output : Proof 74.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 36
% Syntax : Number of formulae : 130 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 391 ( 23 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 335 ( 120 ~; 108 |; 0 &; 102 @)
% ( 0 <=>; 4 =>; 1 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 45 con; 0-2 aty)
% Number of variables : 0 ( 0 ^ 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(conj_1,conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
= k ) ).
thf(h0,negated_conjecture,
( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
!= k,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(ax1374,axiom,
( ~ p9
| p96 ),
file('<stdin>',ax1374) ).
thf(ax1370,axiom,
( ~ p10
| ~ p100 ),
file('<stdin>',ax1370) ).
thf(ax1238,axiom,
( ~ p96
| p232 ),
file('<stdin>',ax1238) ).
thf(ax1463,axiom,
p9,
file('<stdin>',ax1463) ).
thf(ax1391,axiom,
( ~ p7
| p79 ),
file('<stdin>',ax1391) ).
thf(ax1169,axiom,
( ~ p237
| p312 ),
file('<stdin>',ax1169) ).
thf(ax1233,axiom,
( ~ p237
| p238 ),
file('<stdin>',ax1233) ).
thf(ax1164,axiom,
( ~ p310
| p49
| ~ p315
| ~ p310 ),
file('<stdin>',ax1164) ).
thf(ax1462,axiom,
p10,
file('<stdin>',ax1462) ).
thf(ax1239,axiom,
( ~ p232
| p231 ),
file('<stdin>',ax1239) ).
thf(ax187,axiom,
( ~ p237
| p1059 ),
file('<stdin>',ax187) ).
thf(ax1235,axiom,
( ~ p79
| p235 ),
file('<stdin>',ax1235) ).
thf(ax1465,axiom,
p7,
file('<stdin>',ax1465) ).
thf(ax1168,axiom,
( ~ p312
| p313 ),
file('<stdin>',ax1168) ).
thf(ax1234,axiom,
p237,
file('<stdin>',ax1234) ).
thf(ax1367,axiom,
( ~ p10
| ~ p103 ),
file('<stdin>',ax1367) ).
thf(ax1153,axiom,
( ~ p238
| p323 ),
file('<stdin>',ax1153) ).
thf(ax1170,axiom,
( p100
| p310 ),
file('<stdin>',ax1170) ).
thf(ax1423,axiom,
~ p49,
file('<stdin>',ax1423) ).
thf(ax1240,axiom,
( ~ p231
| ~ p48
| p230 ),
file('<stdin>',ax1240) ).
thf(ax186,axiom,
( ~ p1059
| p1060 ),
file('<stdin>',ax186) ).
thf(ax1236,axiom,
( ~ p235
| p234 ),
file('<stdin>',ax1236) ).
thf(ax1167,axiom,
( ~ p313
| ~ p310
| p311 ),
file('<stdin>',ax1167) ).
thf(ax610,axiom,
( ~ p543
| p321
| ~ p543
| ~ p557 ),
file('<stdin>',ax610) ).
thf(ax1152,axiom,
( ~ p323
| ~ p321
| p315 ),
file('<stdin>',ax1152) ).
thf(ax185,axiom,
( ~ p1060
| ~ p230
| p1058 ),
file('<stdin>',ax185) ).
thf(ax1424,axiom,
p48,
file('<stdin>',ax1424) ).
thf(ax1237,axiom,
( ~ p234
| ~ p48
| p233 ),
file('<stdin>',ax1237) ).
thf(pax311,axiom,
( p311
=> ( fk
= ( fsize_size_list_a @ f__1 ) ) ),
file('<stdin>',pax311) ).
thf(ax852,axiom,
( p103
| p543 ),
file('<stdin>',ax852) ).
thf(pax1058,axiom,
( p1058
=> ( fk
= ( fsize_size_list_a @ ( fnth_list_a @ ( flistSl97544552lice_a @ fxs @ fk ) @ fm ) ) ) ),
file('<stdin>',pax1058) ).
thf(pax233,axiom,
( p233
=> ( ( fnth_list_a @ ( flistSl1174287072ice2_a @ fxs @ fk ) @ fm )
= ( fnth_list_a @ ( flistSl97544552lice_a @ fxs @ fk ) @ fm ) ) ),
file('<stdin>',pax233) ).
thf(pax543,axiom,
( p543
=> ( ( fsize_size_list_a @ f__4 )
= ( fsize_size_list_a @ ( fnth_list_a @ ( flistSl1174287072ice2_a @ fxs @ fk ) @ fm ) ) ) ),
file('<stdin>',pax543) ).
thf(nax557,axiom,
( p557
<= ( ( fsize_size_list_a @ f__4 )
= ( fsize_size_list_a @ f__1 ) ) ),
file('<stdin>',nax557) ).
thf(c_0_34,plain,
( ~ p9
| p96 ),
inference(fof_simplification,[status(thm)],[ax1374]) ).
thf(c_0_35,plain,
( ~ p10
| ~ p100 ),
inference(fof_simplification,[status(thm)],[ax1370]) ).
thf(c_0_36,plain,
( ~ p96
| p232 ),
inference(fof_simplification,[status(thm)],[ax1238]) ).
thf(c_0_37,plain,
( p96
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_38,plain,
p9,
inference(split_conjunct,[status(thm)],[ax1463]) ).
thf(c_0_39,plain,
( ~ p7
| p79 ),
inference(fof_simplification,[status(thm)],[ax1391]) ).
thf(c_0_40,plain,
( ~ p237
| p312 ),
inference(fof_simplification,[status(thm)],[ax1169]) ).
thf(c_0_41,plain,
( ~ p237
| p238 ),
inference(fof_simplification,[status(thm)],[ax1233]) ).
thf(c_0_42,plain,
( ~ p310
| p49
| ~ p315
| ~ p310 ),
inference(fof_simplification,[status(thm)],[ax1164]) ).
thf(c_0_43,plain,
( ~ p10
| ~ p100 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_44,plain,
p10,
inference(split_conjunct,[status(thm)],[ax1462]) ).
thf(c_0_45,plain,
( ~ p232
| p231 ),
inference(fof_simplification,[status(thm)],[ax1239]) ).
thf(c_0_46,plain,
( p232
| ~ p96 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_47,plain,
p96,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
thf(c_0_48,plain,
( ~ p237
| p1059 ),
inference(fof_simplification,[status(thm)],[ax187]) ).
thf(c_0_49,plain,
( ~ p79
| p235 ),
inference(fof_simplification,[status(thm)],[ax1235]) ).
thf(c_0_50,plain,
( p79
| ~ p7 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_51,plain,
p7,
inference(split_conjunct,[status(thm)],[ax1465]) ).
thf(c_0_52,plain,
( ~ p312
| p313 ),
inference(fof_simplification,[status(thm)],[ax1168]) ).
thf(c_0_53,plain,
( p312
| ~ p237 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_54,plain,
p237,
inference(split_conjunct,[status(thm)],[ax1234]) ).
thf(c_0_55,plain,
( ~ p10
| ~ p103 ),
inference(fof_simplification,[status(thm)],[ax1367]) ).
thf(c_0_56,plain,
( ~ p238
| p323 ),
inference(fof_simplification,[status(thm)],[ax1153]) ).
thf(c_0_57,plain,
( p238
| ~ p237 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_58,plain,
( p49
| ~ p310
| ~ p315
| ~ p310 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_59,plain,
( p100
| p310 ),
inference(split_conjunct,[status(thm)],[ax1170]) ).
thf(c_0_60,plain,
~ p100,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
thf(c_0_61,plain,
~ p49,
inference(fof_simplification,[status(thm)],[ax1423]) ).
thf(c_0_62,plain,
( ~ p231
| ~ p48
| p230 ),
inference(fof_simplification,[status(thm)],[ax1240]) ).
thf(c_0_63,plain,
( p231
| ~ p232 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_64,plain,
p232,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
thf(c_0_65,plain,
( ~ p1059
| p1060 ),
inference(fof_simplification,[status(thm)],[ax186]) ).
thf(c_0_66,plain,
( p1059
| ~ p237 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_67,plain,
( ~ p235
| p234 ),
inference(fof_simplification,[status(thm)],[ax1236]) ).
thf(c_0_68,plain,
( p235
| ~ p79 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_69,plain,
p79,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).
thf(c_0_70,plain,
( ~ p313
| ~ p310
| p311 ),
inference(fof_simplification,[status(thm)],[ax1167]) ).
thf(c_0_71,plain,
( p313
| ~ p312 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_72,plain,
p312,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]) ).
thf(c_0_73,plain,
( ~ p543
| p321
| ~ p543
| ~ p557 ),
inference(fof_simplification,[status(thm)],[ax610]) ).
thf(c_0_74,plain,
( ~ p10
| ~ p103 ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_75,plain,
( ~ p323
| ~ p321
| p315 ),
inference(fof_simplification,[status(thm)],[ax1152]) ).
thf(c_0_76,plain,
( p323
| ~ p238 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_77,plain,
p238,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_54])]) ).
thf(c_0_78,plain,
( p49
| ~ p310
| ~ p315 ),
inference(cn,[status(thm)],[c_0_58]) ).
thf(c_0_79,plain,
p310,
inference(sr,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_80,plain,
~ p49,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_81,plain,
( ~ p1060
| ~ p230
| p1058 ),
inference(fof_simplification,[status(thm)],[ax185]) ).
thf(c_0_82,plain,
( p230
| ~ p231
| ~ p48 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_83,plain,
p48,
inference(split_conjunct,[status(thm)],[ax1424]) ).
thf(c_0_84,plain,
p231,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
thf(c_0_85,plain,
( p1060
| ~ p1059 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_86,plain,
p1059,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_54])]) ).
thf(c_0_87,plain,
( ~ p234
| ~ p48
| p233 ),
inference(fof_simplification,[status(thm)],[ax1237]) ).
thf(c_0_88,plain,
( p234
| ~ p235 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_89,plain,
p235,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
thf(c_0_90,plain,
( ~ p311
| ( fk
= ( fsize_size_list_a @ f__1 ) ) ),
inference(fof_nnf,[status(thm)],[pax311]) ).
thf(c_0_91,plain,
( p311
| ~ p313
| ~ p310 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
thf(c_0_92,plain,
p313,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).
thf(c_0_93,plain,
( p321
| ~ p543
| ~ p543
| ~ p557 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_94,plain,
( p103
| p543 ),
inference(split_conjunct,[status(thm)],[ax852]) ).
thf(c_0_95,plain,
~ p103,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_44])]) ).
thf(c_0_96,plain,
( p315
| ~ p323
| ~ p321 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
thf(c_0_97,plain,
p323,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
thf(c_0_98,plain,
~ p315,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79])]),c_0_80]) ).
thf(c_0_99,plain,
( ~ p1058
| ( fk
= ( fsize_size_list_a @ ( fnth_list_a @ ( flistSl97544552lice_a @ fxs @ fk ) @ fm ) ) ) ),
inference(fof_nnf,[status(thm)],[pax1058]) ).
thf(c_0_100,plain,
( p1058
| ~ p1060
| ~ p230 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
thf(c_0_101,plain,
p230,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83]),c_0_84])]) ).
thf(c_0_102,plain,
p1060,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]) ).
thf(c_0_103,plain,
( ~ p233
| ( ( fnth_list_a @ ( flistSl1174287072ice2_a @ fxs @ fk ) @ fm )
= ( fnth_list_a @ ( flistSl97544552lice_a @ fxs @ fk ) @ fm ) ) ),
inference(fof_nnf,[status(thm)],[pax233]) ).
thf(c_0_104,plain,
( p233
| ~ p234
| ~ p48 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
thf(c_0_105,plain,
p234,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89])]) ).
thf(c_0_106,plain,
( ~ p543
| ( ( fsize_size_list_a @ f__4 )
= ( fsize_size_list_a @ ( fnth_list_a @ ( flistSl1174287072ice2_a @ fxs @ fk ) @ fm ) ) ) ),
inference(fof_nnf,[status(thm)],[pax543]) ).
thf(c_0_107,plain,
( ( ( fsize_size_list_a @ f__4 )
!= ( fsize_size_list_a @ f__1 ) )
| p557 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax557])]) ).
thf(c_0_108,plain,
( ( fk
= ( fsize_size_list_a @ f__1 ) )
| ~ p311 ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
thf(c_0_109,plain,
p311,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_79]),c_0_92])]) ).
thf(c_0_110,plain,
( p321
| ~ p543
| ~ p557 ),
inference(cn,[status(thm)],[c_0_93]) ).
thf(c_0_111,plain,
p543,
inference(sr,[status(thm)],[c_0_94,c_0_95]) ).
thf(c_0_112,plain,
~ p321,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97])]),c_0_98]) ).
thf(c_0_113,plain,
( ( fk
= ( fsize_size_list_a @ ( fnth_list_a @ ( flistSl97544552lice_a @ fxs @ fk ) @ fm ) ) )
| ~ p1058 ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
thf(c_0_114,plain,
p1058,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101]),c_0_102])]) ).
thf(c_0_115,plain,
( ( ( fnth_list_a @ ( flistSl1174287072ice2_a @ fxs @ fk ) @ fm )
= ( fnth_list_a @ ( flistSl97544552lice_a @ fxs @ fk ) @ fm ) )
| ~ p233 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
thf(c_0_116,plain,
p233,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_83]),c_0_105])]) ).
thf(c_0_117,plain,
( ( ( fsize_size_list_a @ f__4 )
= ( fsize_size_list_a @ ( fnth_list_a @ ( flistSl1174287072ice2_a @ fxs @ fk ) @ fm ) ) )
| ~ p543 ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
thf(c_0_118,plain,
( p557
| ( ( fsize_size_list_a @ f__4 )
!= ( fsize_size_list_a @ f__1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
thf(c_0_119,plain,
( ( fsize_size_list_a @ f__1 )
= fk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109])]) ).
thf(c_0_120,plain,
~ p557,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]),c_0_112]) ).
thf(c_0_121,plain,
( ( fsize_size_list_a @ ( fnth_list_a @ ( flistSl97544552lice_a @ fxs @ fk ) @ fm ) )
= fk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
thf(c_0_122,plain,
( ( fnth_list_a @ ( flistSl97544552lice_a @ fxs @ fk ) @ fm )
= ( fnth_list_a @ ( flistSl1174287072ice2_a @ fxs @ fk ) @ fm ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_116])]) ).
thf(c_0_123,plain,
( ( fsize_size_list_a @ ( fnth_list_a @ ( flistSl1174287072ice2_a @ fxs @ fk ) @ fm ) )
= ( fsize_size_list_a @ f__4 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_111])]) ).
thf(c_0_124,plain,
( fsize_size_list_a @ f__4 )
!= fk,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119]),c_0_120]) ).
thf(c_0_125,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122]),c_0_123]),c_0_124]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
= k ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP104^1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n018.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 : Thu Jun 2 19:50:15 EDT 2022
% 0.12/0.35 % CPUTime :
% 74.01/74.52 % SZS status Theorem
% 74.01/74.52 % Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 74.01/74.52 % Inferences: 591
% 74.01/74.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------