TSTP Solution File: LCL491+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL491+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %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 : 0s
% DateTime : Sun Jul 17 07:54:09 EDT 2022
% Result : Theorem 0.68s 1.11s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL491+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : bliksem %s
% 0.12/0.32 % Computer : n021.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sat Jul 2 23:15:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.68/1.09 *** allocated 10000 integers for termspace/termends
% 0.68/1.09 *** allocated 10000 integers for clauses
% 0.68/1.09 *** allocated 10000 integers for justifications
% 0.68/1.09 Bliksem 1.12
% 0.68/1.09
% 0.68/1.09
% 0.68/1.09 Automatic Strategy Selection
% 0.68/1.09
% 0.68/1.09
% 0.68/1.09 Clauses:
% 0.68/1.09
% 0.68/1.09 { ! modus_ponens, ! alpha1( X ), is_a_theorem( X ) }.
% 0.68/1.09 { alpha1( skol1 ), modus_ponens }.
% 0.68/1.09 { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.68/1.09 { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.68/1.09 { ! alpha1( X ), is_a_theorem( implies( skol2( X ), X ) ) }.
% 0.68/1.09 { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.68/1.09 { ! substitution_of_equivalents, ! is_a_theorem( equiv( X, Y ) ), X = Y }.
% 0.68/1.09 { is_a_theorem( equiv( skol3, skol28 ) ), substitution_of_equivalents }.
% 0.68/1.09 { ! skol3 = skol28, substitution_of_equivalents }.
% 0.68/1.09 { ! modus_tollens, is_a_theorem( implies( implies( not( Y ), not( X ) ),
% 0.68/1.09 implies( X, Y ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( implies( not( skol29 ), not( skol4 ) ), implies
% 0.68/1.09 ( skol4, skol29 ) ) ), modus_tollens }.
% 0.68/1.09 { ! implies_1, is_a_theorem( implies( X, implies( Y, X ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( skol5, implies( skol30, skol5 ) ) ), implies_1 }
% 0.68/1.09 .
% 0.68/1.09 { ! implies_2, is_a_theorem( implies( implies( X, implies( X, Y ) ),
% 0.68/1.09 implies( X, Y ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( implies( skol6, implies( skol6, skol31 ) ),
% 0.68/1.09 implies( skol6, skol31 ) ) ), implies_2 }.
% 0.68/1.09 { ! implies_3, is_a_theorem( implies( implies( X, Y ), implies( implies( Y
% 0.68/1.09 , Z ), implies( X, Z ) ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( implies( skol7, skol32 ), implies( implies(
% 0.68/1.09 skol32, skol50 ), implies( skol7, skol50 ) ) ) ), implies_3 }.
% 0.68/1.09 { ! and_1, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( and( skol8, skol33 ), skol8 ) ), and_1 }.
% 0.68/1.09 { ! and_2, is_a_theorem( implies( and( X, Y ), Y ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( and( skol9, skol34 ), skol34 ) ), and_2 }.
% 0.68/1.09 { ! and_3, is_a_theorem( implies( X, implies( Y, and( X, Y ) ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( skol10, implies( skol35, and( skol10, skol35 ) )
% 0.68/1.09 ) ), and_3 }.
% 0.68/1.09 { ! or_1, is_a_theorem( implies( X, or( X, Y ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( skol11, or( skol11, skol36 ) ) ), or_1 }.
% 0.68/1.09 { ! or_2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( skol37, or( skol12, skol37 ) ) ), or_2 }.
% 0.68/1.09 { ! or_3, is_a_theorem( implies( implies( X, Z ), implies( implies( Y, Z )
% 0.68/1.09 , implies( or( X, Y ), Z ) ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( implies( skol13, skol51 ), implies( implies(
% 0.68/1.09 skol38, skol51 ), implies( or( skol13, skol38 ), skol51 ) ) ) ), or_3 }.
% 0.68/1.09 { ! equivalence_1, is_a_theorem( implies( equiv( X, Y ), implies( X, Y ) )
% 0.68/1.09 ) }.
% 0.68/1.09 { ! is_a_theorem( implies( equiv( skol14, skol39 ), implies( skol14, skol39
% 0.68/1.09 ) ) ), equivalence_1 }.
% 0.68/1.09 { ! equivalence_2, is_a_theorem( implies( equiv( X, Y ), implies( Y, X ) )
% 0.68/1.09 ) }.
% 0.68/1.09 { ! is_a_theorem( implies( equiv( skol15, skol40 ), implies( skol40, skol15
% 0.68/1.09 ) ) ), equivalence_2 }.
% 0.68/1.09 { ! equivalence_3, is_a_theorem( implies( implies( X, Y ), implies( implies
% 0.68/1.09 ( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( implies( skol16, skol41 ), implies( implies(
% 0.68/1.09 skol41, skol16 ), equiv( skol16, skol41 ) ) ) ), equivalence_3 }.
% 0.68/1.09 { ! kn1, is_a_theorem( implies( X, and( X, X ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( skol17, and( skol17, skol17 ) ) ), kn1 }.
% 0.68/1.09 { ! kn2, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( and( skol18, skol42 ), skol18 ) ), kn2 }.
% 0.68/1.09 { ! kn3, is_a_theorem( implies( implies( X, Y ), implies( not( and( Y, Z )
% 0.68/1.09 ), not( and( Z, X ) ) ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( implies( skol19, skol43 ), implies( not( and(
% 0.68/1.09 skol43, skol52 ) ), not( and( skol52, skol19 ) ) ) ) ), kn3 }.
% 0.68/1.09 { ! cn1, is_a_theorem( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.68/1.09 implies( X, Z ) ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( implies( skol20, skol44 ), implies( implies(
% 0.68/1.09 skol44, skol53 ), implies( skol20, skol53 ) ) ) ), cn1 }.
% 0.68/1.09 { ! cn2, is_a_theorem( implies( X, implies( not( X ), Y ) ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( skol21, implies( not( skol21 ), skol45 ) ) ),
% 0.68/1.09 cn2 }.
% 0.68/1.09 { ! cn3, is_a_theorem( implies( implies( not( X ), X ), X ) ) }.
% 0.68/1.09 { ! is_a_theorem( implies( implies( not( skol22 ), skol22 ), skol22 ) ),
% 0.68/1.09 cn3 }.
% 0.68/1.11 { ! r1, is_a_theorem( implies( or( X, X ), X ) ) }.
% 0.68/1.11 { ! is_a_theorem( implies( or( skol23, skol23 ), skol23 ) ), r1 }.
% 0.68/1.11 { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.68/1.11 { ! is_a_theorem( implies( skol46, or( skol24, skol46 ) ) ), r2 }.
% 0.68/1.11 { ! r3, is_a_theorem( implies( or( X, Y ), or( Y, X ) ) ) }.
% 0.68/1.11 { ! is_a_theorem( implies( or( skol25, skol47 ), or( skol47, skol25 ) ) ),
% 0.68/1.11 r3 }.
% 0.68/1.11 { ! r4, is_a_theorem( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) )
% 0.68/1.11 }.
% 0.68/1.11 { ! is_a_theorem( implies( or( skol26, or( skol48, skol54 ) ), or( skol48,
% 0.68/1.11 or( skol26, skol54 ) ) ) ), r4 }.
% 0.68/1.11 { ! r5, is_a_theorem( implies( implies( Y, Z ), implies( or( X, Y ), or( X
% 0.68/1.11 , Z ) ) ) ) }.
% 0.68/1.11 { ! is_a_theorem( implies( implies( skol49, skol55 ), implies( or( skol27,
% 0.68/1.11 skol49 ), or( skol27, skol55 ) ) ) ), r5 }.
% 0.68/1.11 { ! op_or, or( X, Y ) = not( and( not( X ), not( Y ) ) ) }.
% 0.68/1.11 { ! op_and, and( X, Y ) = not( or( not( X ), not( Y ) ) ) }.
% 0.68/1.11 { ! op_implies_and, implies( X, Y ) = not( and( X, not( Y ) ) ) }.
% 0.68/1.11 { ! op_implies_or, implies( X, Y ) = or( not( X ), Y ) }.
% 0.68/1.11 { ! op_equiv, equiv( X, Y ) = and( implies( X, Y ), implies( Y, X ) ) }.
% 0.68/1.11 { op_implies_or }.
% 0.68/1.11 { op_and }.
% 0.68/1.11 { op_equiv }.
% 0.68/1.11 { modus_ponens }.
% 0.68/1.11 { r1 }.
% 0.68/1.11 { r2 }.
% 0.68/1.11 { r3 }.
% 0.68/1.11 { r4 }.
% 0.68/1.11 { r5 }.
% 0.68/1.11 { substitution_of_equivalents }.
% 0.68/1.11 { op_or }.
% 0.68/1.11 { op_implies_and }.
% 0.68/1.11 { op_equiv }.
% 0.68/1.11 { ! or_2 }.
% 0.68/1.11
% 0.68/1.11 percentage equality = 0.050000, percentage horn = 0.973333
% 0.68/1.11 This is a problem with some equality
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Options Used:
% 0.68/1.11
% 0.68/1.11 useres = 1
% 0.68/1.11 useparamod = 1
% 0.68/1.11 useeqrefl = 1
% 0.68/1.11 useeqfact = 1
% 0.68/1.11 usefactor = 1
% 0.68/1.11 usesimpsplitting = 0
% 0.68/1.11 usesimpdemod = 5
% 0.68/1.11 usesimpres = 3
% 0.68/1.11
% 0.68/1.11 resimpinuse = 1000
% 0.68/1.11 resimpclauses = 20000
% 0.68/1.11 substype = eqrewr
% 0.68/1.11 backwardsubs = 1
% 0.68/1.11 selectoldest = 5
% 0.68/1.11
% 0.68/1.11 litorderings [0] = split
% 0.68/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.68/1.11
% 0.68/1.11 termordering = kbo
% 0.68/1.11
% 0.68/1.11 litapriori = 0
% 0.68/1.11 termapriori = 1
% 0.68/1.11 litaposteriori = 0
% 0.68/1.11 termaposteriori = 0
% 0.68/1.11 demodaposteriori = 0
% 0.68/1.11 ordereqreflfact = 0
% 0.68/1.11
% 0.68/1.11 litselect = negord
% 0.68/1.11
% 0.68/1.11 maxweight = 15
% 0.68/1.11 maxdepth = 30000
% 0.68/1.11 maxlength = 115
% 0.68/1.11 maxnrvars = 195
% 0.68/1.11 excuselevel = 1
% 0.68/1.11 increasemaxweight = 1
% 0.68/1.11
% 0.68/1.11 maxselected = 10000000
% 0.68/1.11 maxnrclauses = 10000000
% 0.68/1.11
% 0.68/1.11 showgenerated = 0
% 0.68/1.11 showkept = 0
% 0.68/1.11 showselected = 0
% 0.68/1.11 showdeleted = 0
% 0.68/1.11 showresimp = 1
% 0.68/1.11 showstatus = 2000
% 0.68/1.11
% 0.68/1.11 prologoutput = 0
% 0.68/1.11 nrgoals = 5000000
% 0.68/1.11 totalproof = 1
% 0.68/1.11
% 0.68/1.11 Symbols occurring in the translation:
% 0.68/1.11
% 0.68/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.68/1.11 . [1, 2] (w:1, o:106, a:1, s:1, b:0),
% 0.68/1.11 ! [4, 1] (w:0, o:97, a:1, s:1, b:0),
% 0.68/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.68/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.68/1.11 modus_ponens [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.68/1.11 is_a_theorem [38, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.68/1.11 implies [39, 2] (w:1, o:130, a:1, s:1, b:0),
% 0.68/1.11 substitution_of_equivalents [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.68/1.11 equiv [41, 2] (w:1, o:131, a:1, s:1, b:0),
% 0.68/1.11 modus_tollens [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.68/1.11 not [43, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.68/1.11 implies_1 [44, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.68/1.11 implies_2 [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.68/1.11 implies_3 [46, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.68/1.11 and_1 [48, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.68/1.11 and [49, 2] (w:1, o:132, a:1, s:1, b:0),
% 0.68/1.11 and_2 [50, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.68/1.11 and_3 [51, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.68/1.11 or_1 [52, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.68/1.11 or [53, 2] (w:1, o:133, a:1, s:1, b:0),
% 0.68/1.11 or_2 [54, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.68/1.11 or_3 [55, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.68/1.11 equivalence_1 [56, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.68/1.11 equivalence_2 [57, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.68/1.11 equivalence_3 [58, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.68/1.11 kn1 [59, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.68/1.11 kn2 [61, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.68/1.11 kn3 [63, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.68/1.11 cn1 [65, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.68/1.11 cn2 [66, 0] (w:1, o:36, a:1, s:1, b:0),
% 0.68/1.11 cn3 [67, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.68/1.11 r1 [68, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.68/1.11 r2 [69, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.68/1.11 r3 [70, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.68/1.11 r4 [71, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.68/1.11 r5 [72, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.68/1.11 op_or [73, 0] (w:1, o:38, a:1, s:1, b:0),
% 0.68/1.11 op_and [74, 0] (w:1, o:39, a:1, s:1, b:0),
% 0.68/1.11 op_implies_and [75, 0] (w:1, o:40, a:1, s:1, b:0),
% 0.68/1.11 op_implies_or [76, 0] (w:1, o:41, a:1, s:1, b:0),
% 0.68/1.11 op_equiv [77, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.68/1.11 alpha1 [78, 1] (w:1, o:104, a:1, s:1, b:1),
% 0.68/1.11 skol1 [79, 0] (w:1, o:43, a:1, s:1, b:1),
% 0.68/1.11 skol2 [80, 1] (w:1, o:105, a:1, s:1, b:1),
% 0.68/1.11 skol3 [81, 0] (w:1, o:54, a:1, s:1, b:1),
% 0.68/1.11 skol4 [82, 0] (w:1, o:65, a:1, s:1, b:1),
% 0.68/1.11 skol5 [83, 0] (w:1, o:76, a:1, s:1, b:1),
% 0.68/1.11 skol6 [84, 0] (w:1, o:83, a:1, s:1, b:1),
% 0.68/1.11 skol7 [85, 0] (w:1, o:84, a:1, s:1, b:1),
% 0.68/1.11 skol8 [86, 0] (w:1, o:85, a:1, s:1, b:1),
% 0.68/1.11 skol9 [87, 0] (w:1, o:86, a:1, s:1, b:1),
% 0.68/1.11 skol10 [88, 0] (w:1, o:87, a:1, s:1, b:1),
% 0.68/1.11 skol11 [89, 0] (w:1, o:88, a:1, s:1, b:1),
% 0.68/1.11 skol12 [90, 0] (w:1, o:89, a:1, s:1, b:1),
% 0.68/1.11 skol13 [91, 0] (w:1, o:90, a:1, s:1, b:1),
% 0.68/1.11 skol14 [92, 0] (w:1, o:91, a:1, s:1, b:1),
% 0.68/1.11 skol15 [93, 0] (w:1, o:92, a:1, s:1, b:1),
% 0.68/1.11 skol16 [94, 0] (w:1, o:93, a:1, s:1, b:1),
% 0.68/1.11 skol17 [95, 0] (w:1, o:94, a:1, s:1, b:1),
% 0.68/1.11 skol18 [96, 0] (w:1, o:95, a:1, s:1, b:1),
% 0.68/1.11 skol19 [97, 0] (w:1, o:96, a:1, s:1, b:1),
% 0.68/1.11 skol20 [98, 0] (w:1, o:44, a:1, s:1, b:1),
% 0.68/1.11 skol21 [99, 0] (w:1, o:45, a:1, s:1, b:1),
% 0.68/1.11 skol22 [100, 0] (w:1, o:46, a:1, s:1, b:1),
% 0.68/1.11 skol23 [101, 0] (w:1, o:47, a:1, s:1, b:1),
% 0.68/1.11 skol24 [102, 0] (w:1, o:48, a:1, s:1, b:1),
% 0.68/1.11 skol25 [103, 0] (w:1, o:49, a:1, s:1, b:1),
% 0.68/1.11 skol26 [104, 0] (w:1, o:50, a:1, s:1, b:1),
% 0.68/1.11 skol27 [105, 0] (w:1, o:51, a:1, s:1, b:1),
% 0.68/1.11 skol28 [106, 0] (w:1, o:52, a:1, s:1, b:1),
% 0.68/1.11 skol29 [107, 0] (w:1, o:53, a:1, s:1, b:1),
% 0.68/1.11 skol30 [108, 0] (w:1, o:55, a:1, s:1, b:1),
% 0.68/1.11 skol31 [109, 0] (w:1, o:56, a:1, s:1, b:1),
% 0.68/1.11 skol32 [110, 0] (w:1, o:57, a:1, s:1, b:1),
% 0.68/1.11 skol33 [111, 0] (w:1, o:58, a:1, s:1, b:1),
% 0.68/1.11 skol34 [112, 0] (w:1, o:59, a:1, s:1, b:1),
% 0.68/1.11 skol35 [113, 0] (w:1, o:60, a:1, s:1, b:1),
% 0.68/1.11 skol36 [114, 0] (w:1, o:61, a:1, s:1, b:1),
% 0.68/1.11 skol37 [115, 0] (w:1, o:62, a:1, s:1, b:1),
% 0.68/1.11 skol38 [116, 0] (w:1, o:63, a:1, s:1, b:1),
% 0.68/1.11 skol39 [117, 0] (w:1, o:64, a:1, s:1, b:1),
% 0.68/1.11 skol40 [118, 0] (w:1, o:66, a:1, s:1, b:1),
% 0.68/1.11 skol41 [119, 0] (w:1, o:67, a:1, s:1, b:1),
% 0.68/1.11 skol42 [120, 0] (w:1, o:68, a:1, s:1, b:1),
% 0.68/1.11 skol43 [121, 0] (w:1, o:69, a:1, s:1, b:1),
% 0.68/1.11 skol44 [122, 0] (w:1, o:70, a:1, s:1, b:1),
% 0.68/1.11 skol45 [123, 0] (w:1, o:71, a:1, s:1, b:1),
% 0.68/1.11 skol46 [124, 0] (w:1, o:72, a:1, s:1, b:1),
% 0.68/1.11 skol47 [125, 0] (w:1, o:73, a:1, s:1, b:1),
% 0.68/1.11 skol48 [126, 0] (w:1, o:74, a:1, s:1, b:1),
% 0.68/1.11 skol49 [127, 0] (w:1, o:75, a:1, s:1, b:1),
% 0.68/1.11 skol50 [128, 0] (w:1, o:77, a:1, s:1, b:1),
% 0.68/1.11 skol51 [129, 0] (w:1, o:78, a:1, s:1, b:1),
% 0.68/1.11 skol52 [130, 0] (w:1, o:79, a:1, s:1, b:1),
% 0.68/1.11 skol53 [131, 0] (w:1, o:80, a:1, s:1, b:1),
% 0.68/1.11 skol54 [132, 0] (w:1, o:81, a:1, s:1, b:1),
% 0.68/1.11 skol55 [133, 0] (w:1, o:82, a:1, s:1, b:1).
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Starting Search:
% 0.68/1.11
% 0.68/1.11 *** allocated 15000 integers for clauses
% 0.68/1.11 *** allocated 22500 integers for clauses
% 0.68/1.11 *** allocated 33750 integers for clauses
% 0.68/1.11 *** allocated 50625 integers for clauses
% 0.68/1.11 *** allocated 15000 integers for termspace/termends
% 0.68/1.11 *** allocated 75937 integers for clauses
% 0.68/1.11 Resimplifying inuse:
% 0.68/1.11 Done
% 0.68/1.11
% 0.68/1.11 *** allocated 22500 integers for termspace/termends
% 0.68/1.11
% 0.68/1.11 Bliksems!, er is een bewijs:
% 0.68/1.11 % SZS status Theorem
% 0.68/1.11 % SZS output start Refutation
% 0.68/1.11
% 0.68/1.11 (26) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( skol37, or( skol12,
% 0.68/1.11 skol37 ) ) ), or_2 }.
% 0.68/1.11 (49) {G0,W7,D4,L2,V2,M2} I { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) )
% 0.68/1.11 }.
% 0.68/1.11 (67) {G0,W1,D1,L1,V0,M1} I { r2 }.
% 0.68/1.11 (74) {G0,W1,D1,L1,V0,M1} I { ! or_2 }.
% 0.68/1.11 (76) {G1,W6,D4,L1,V2,M1} S(49);r(67) { is_a_theorem( implies( Y, or( X, Y )
% 0.68/1.11 ) ) }.
% 0.68/1.11 (1149) {G2,W0,D0,L0,V0,M0} S(26);r(76);r(74) { }.
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 % SZS output end Refutation
% 0.68/1.11 found a proof!
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Unprocessed initial clauses:
% 0.68/1.11
% 0.68/1.11 (1151) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ), is_a_theorem(
% 0.68/1.11 X ) }.
% 0.68/1.11 (1152) {G0,W3,D2,L2,V0,M2} { alpha1( skol1 ), modus_ponens }.
% 0.68/1.11 (1153) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.68/1.11 (1154) {G0,W5,D3,L2,V2,M2} { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.68/1.11 (1155) {G0,W7,D4,L2,V1,M2} { ! alpha1( X ), is_a_theorem( implies( skol2(
% 0.68/1.11 X ), X ) ) }.
% 0.68/1.11 (1156) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem( implies
% 0.68/1.11 ( Y, X ) ), alpha1( X ) }.
% 0.68/1.11 (1157) {G0,W8,D3,L3,V2,M3} { ! substitution_of_equivalents, ! is_a_theorem
% 0.68/1.11 ( equiv( X, Y ) ), X = Y }.
% 0.68/1.11 (1158) {G0,W5,D3,L2,V0,M2} { is_a_theorem( equiv( skol3, skol28 ) ),
% 0.68/1.11 substitution_of_equivalents }.
% 0.68/1.11 (1159) {G0,W4,D2,L2,V0,M2} { ! skol3 = skol28, substitution_of_equivalents
% 0.68/1.11 }.
% 0.68/1.11 (1160) {G0,W11,D5,L2,V2,M2} { ! modus_tollens, is_a_theorem( implies(
% 0.68/1.11 implies( not( Y ), not( X ) ), implies( X, Y ) ) ) }.
% 0.68/1.11 (1161) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 0.68/1.11 skol29 ), not( skol4 ) ), implies( skol4, skol29 ) ) ), modus_tollens }.
% 0.68/1.11 (1162) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies( X,
% 0.68/1.11 implies( Y, X ) ) ) }.
% 0.68/1.11 (1163) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol5, implies(
% 0.68/1.11 skol30, skol5 ) ) ), implies_1 }.
% 0.68/1.11 (1164) {G0,W11,D5,L2,V2,M2} { ! implies_2, is_a_theorem( implies( implies
% 0.68/1.11 ( X, implies( X, Y ) ), implies( X, Y ) ) ) }.
% 0.68/1.11 (1165) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol6,
% 0.68/1.11 implies( skol6, skol31 ) ), implies( skol6, skol31 ) ) ), implies_2 }.
% 0.68/1.11 (1166) {G0,W13,D5,L2,V3,M2} { ! implies_3, is_a_theorem( implies( implies
% 0.68/1.11 ( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 0.68/1.11 (1167) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol7,
% 0.68/1.11 skol32 ), implies( implies( skol32, skol50 ), implies( skol7, skol50 ) )
% 0.68/1.11 ) ), implies_3 }.
% 0.68/1.11 (1168) {G0,W7,D4,L2,V2,M2} { ! and_1, is_a_theorem( implies( and( X, Y ),
% 0.68/1.11 X ) ) }.
% 0.68/1.11 (1169) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol8, skol33 )
% 0.68/1.11 , skol8 ) ), and_1 }.
% 0.68/1.11 (1170) {G0,W7,D4,L2,V2,M2} { ! and_2, is_a_theorem( implies( and( X, Y ),
% 0.68/1.11 Y ) ) }.
% 0.68/1.11 (1171) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol9, skol34 )
% 0.68/1.11 , skol34 ) ), and_2 }.
% 0.68/1.11 (1172) {G0,W9,D5,L2,V2,M2} { ! and_3, is_a_theorem( implies( X, implies( Y
% 0.68/1.11 , and( X, Y ) ) ) ) }.
% 0.68/1.11 (1173) {G0,W9,D5,L2,V0,M2} { ! is_a_theorem( implies( skol10, implies(
% 0.68/1.11 skol35, and( skol10, skol35 ) ) ) ), and_3 }.
% 0.68/1.11 (1174) {G0,W7,D4,L2,V2,M2} { ! or_1, is_a_theorem( implies( X, or( X, Y )
% 0.68/1.11 ) ) }.
% 0.68/1.11 (1175) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol11, or( skol11,
% 0.68/1.11 skol36 ) ) ), or_1 }.
% 0.68/1.11 (1176) {G0,W7,D4,L2,V2,M2} { ! or_2, is_a_theorem( implies( Y, or( X, Y )
% 0.68/1.11 ) ) }.
% 0.68/1.11 (1177) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol37, or( skol12,
% 0.68/1.11 skol37 ) ) ), or_2 }.
% 0.68/1.11 (1178) {G0,W15,D6,L2,V3,M2} { ! or_3, is_a_theorem( implies( implies( X, Z
% 0.68/1.11 ), implies( implies( Y, Z ), implies( or( X, Y ), Z ) ) ) ) }.
% 0.68/1.11 (1179) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol13,
% 0.68/1.11 skol51 ), implies( implies( skol38, skol51 ), implies( or( skol13, skol38
% 0.68/1.11 ), skol51 ) ) ) ), or_3 }.
% 0.68/1.11 (1180) {G0,W9,D4,L2,V2,M2} { ! equivalence_1, is_a_theorem( implies( equiv
% 0.68/1.11 ( X, Y ), implies( X, Y ) ) ) }.
% 0.68/1.11 (1181) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol14,
% 0.68/1.11 skol39 ), implies( skol14, skol39 ) ) ), equivalence_1 }.
% 0.68/1.11 (1182) {G0,W9,D4,L2,V2,M2} { ! equivalence_2, is_a_theorem( implies( equiv
% 0.68/1.11 ( X, Y ), implies( Y, X ) ) ) }.
% 0.68/1.11 (1183) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol15,
% 0.68/1.11 skol40 ), implies( skol40, skol15 ) ) ), equivalence_2 }.
% 0.68/1.11 (1184) {G0,W13,D5,L2,V2,M2} { ! equivalence_3, is_a_theorem( implies(
% 0.68/1.11 implies( X, Y ), implies( implies( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.68/1.11 (1185) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol16,
% 0.68/1.11 skol41 ), implies( implies( skol41, skol16 ), equiv( skol16, skol41 ) ) )
% 0.68/1.11 ), equivalence_3 }.
% 0.68/1.11 (1186) {G0,W7,D4,L2,V1,M2} { ! kn1, is_a_theorem( implies( X, and( X, X )
% 0.68/1.11 ) ) }.
% 0.68/1.11 (1187) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol17, and( skol17
% 0.68/1.11 , skol17 ) ) ), kn1 }.
% 0.68/1.11 (1188) {G0,W7,D4,L2,V2,M2} { ! kn2, is_a_theorem( implies( and( X, Y ), X
% 0.68/1.11 ) ) }.
% 0.68/1.11 (1189) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol18, skol42
% 0.68/1.11 ), skol18 ) ), kn2 }.
% 0.68/1.11 (1190) {G0,W15,D6,L2,V3,M2} { ! kn3, is_a_theorem( implies( implies( X, Y
% 0.68/1.11 ), implies( not( and( Y, Z ) ), not( and( Z, X ) ) ) ) ) }.
% 0.68/1.11 (1191) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol19,
% 0.68/1.11 skol43 ), implies( not( and( skol43, skol52 ) ), not( and( skol52, skol19
% 0.68/1.11 ) ) ) ) ), kn3 }.
% 0.68/1.11 (1192) {G0,W13,D5,L2,V3,M2} { ! cn1, is_a_theorem( implies( implies( X, Y
% 0.68/1.11 ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 0.68/1.11 (1193) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol20,
% 0.68/1.11 skol44 ), implies( implies( skol44, skol53 ), implies( skol20, skol53 ) )
% 0.68/1.11 ) ), cn1 }.
% 0.68/1.11 (1194) {G0,W8,D5,L2,V2,M2} { ! cn2, is_a_theorem( implies( X, implies( not
% 0.68/1.11 ( X ), Y ) ) ) }.
% 0.68/1.11 (1195) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( skol21, implies( not
% 0.68/1.11 ( skol21 ), skol45 ) ) ), cn2 }.
% 0.68/1.11 (1196) {G0,W8,D5,L2,V1,M2} { ! cn3, is_a_theorem( implies( implies( not( X
% 0.68/1.11 ), X ), X ) ) }.
% 0.68/1.11 (1197) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not( skol22
% 0.68/1.11 ), skol22 ), skol22 ) ), cn3 }.
% 0.68/1.11 (1198) {G0,W7,D4,L2,V1,M2} { ! r1, is_a_theorem( implies( or( X, X ), X )
% 0.68/1.11 ) }.
% 0.68/1.11 (1199) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol23, skol23 )
% 0.68/1.11 , skol23 ) ), r1 }.
% 0.68/1.11 (1200) {G0,W7,D4,L2,V2,M2} { ! r2, is_a_theorem( implies( Y, or( X, Y ) )
% 0.68/1.11 ) }.
% 0.68/1.11 (1201) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol46, or( skol24,
% 0.68/1.11 skol46 ) ) ), r2 }.
% 0.68/1.11 (1202) {G0,W9,D4,L2,V2,M2} { ! r3, is_a_theorem( implies( or( X, Y ), or(
% 0.68/1.11 Y, X ) ) ) }.
% 0.68/1.11 (1203) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol25, skol47 )
% 0.68/1.11 , or( skol47, skol25 ) ) ), r3 }.
% 0.68/1.11 (1204) {G0,W13,D5,L2,V3,M2} { ! r4, is_a_theorem( implies( or( X, or( Y, Z
% 0.68/1.11 ) ), or( Y, or( X, Z ) ) ) ) }.
% 0.68/1.11 (1205) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( or( skol26, or(
% 0.68/1.11 skol48, skol54 ) ), or( skol48, or( skol26, skol54 ) ) ) ), r4 }.
% 0.68/1.11 (1206) {G0,W13,D5,L2,V3,M2} { ! r5, is_a_theorem( implies( implies( Y, Z )
% 0.68/1.11 , implies( or( X, Y ), or( X, Z ) ) ) ) }.
% 0.68/1.11 (1207) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol49,
% 0.68/1.11 skol55 ), implies( or( skol27, skol49 ), or( skol27, skol55 ) ) ) ), r5
% 0.68/1.11 }.
% 0.68/1.11 (1208) {G0,W11,D5,L2,V2,M2} { ! op_or, or( X, Y ) = not( and( not( X ),
% 0.68/1.11 not( Y ) ) ) }.
% 0.68/1.11 (1209) {G0,W11,D5,L2,V2,M2} { ! op_and, and( X, Y ) = not( or( not( X ),
% 0.68/1.11 not( Y ) ) ) }.
% 0.68/1.11 (1210) {G0,W10,D5,L2,V2,M2} { ! op_implies_and, implies( X, Y ) = not( and
% 0.68/1.11 ( X, not( Y ) ) ) }.
% 0.68/1.11 (1211) {G0,W9,D4,L2,V2,M2} { ! op_implies_or, implies( X, Y ) = or( not( X
% 0.68/1.11 ), Y ) }.
% 0.68/1.11 (1212) {G0,W12,D4,L2,V2,M2} { ! op_equiv, equiv( X, Y ) = and( implies( X
% 0.68/1.11 , Y ), implies( Y, X ) ) }.
% 0.68/1.11 (1213) {G0,W1,D1,L1,V0,M1} { op_implies_or }.
% 0.68/1.11 (1214) {G0,W1,D1,L1,V0,M1} { op_and }.
% 0.68/1.11 (1215) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 0.68/1.11 (1216) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 0.68/1.11 (1217) {G0,W1,D1,L1,V0,M1} { r1 }.
% 0.68/1.11 (1218) {G0,W1,D1,L1,V0,M1} { r2 }.
% 0.68/1.11 (1219) {G0,W1,D1,L1,V0,M1} { r3 }.
% 0.68/1.11 (1220) {G0,W1,D1,L1,V0,M1} { r4 }.
% 0.68/1.11 (1221) {G0,W1,D1,L1,V0,M1} { r5 }.
% 0.68/1.11 (1222) {G0,W1,D1,L1,V0,M1} { substitution_of_equivalents }.
% 0.68/1.11 (1223) {G0,W1,D1,L1,V0,M1} { op_or }.
% 0.68/1.11 (1224) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 0.68/1.11 (1225) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 0.68/1.11 (1226) {G0,W1,D1,L1,V0,M1} { ! or_2 }.
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Total Proof:
% 0.68/1.11
% 0.68/1.11 subsumption: (26) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( skol37,
% 0.68/1.11 or( skol12, skol37 ) ) ), or_2 }.
% 0.68/1.11 parent0: (1177) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol37, or
% 0.68/1.11 ( skol12, skol37 ) ) ), or_2 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 1 ==> 1
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (49) {G0,W7,D4,L2,V2,M2} I { ! r2, is_a_theorem( implies( Y,
% 0.68/1.11 or( X, Y ) ) ) }.
% 0.68/1.11 parent0: (1200) {G0,W7,D4,L2,V2,M2} { ! r2, is_a_theorem( implies( Y, or(
% 0.68/1.11 X, Y ) ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 Y := Y
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 1 ==> 1
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (67) {G0,W1,D1,L1,V0,M1} I { r2 }.
% 0.68/1.11 parent0: (1218) {G0,W1,D1,L1,V0,M1} { r2 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (74) {G0,W1,D1,L1,V0,M1} I { ! or_2 }.
% 0.68/1.11 parent0: (1226) {G0,W1,D1,L1,V0,M1} { ! or_2 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 resolution: (1245) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( X, or( Y,
% 0.68/1.11 X ) ) ) }.
% 0.68/1.11 parent0[0]: (49) {G0,W7,D4,L2,V2,M2} I { ! r2, is_a_theorem( implies( Y, or
% 0.68/1.11 ( X, Y ) ) ) }.
% 0.68/1.11 parent1[0]: (67) {G0,W1,D1,L1,V0,M1} I { r2 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := Y
% 0.68/1.11 Y := X
% 0.68/1.11 end
% 0.68/1.11 substitution1:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (76) {G1,W6,D4,L1,V2,M1} S(49);r(67) { is_a_theorem( implies(
% 0.68/1.11 Y, or( X, Y ) ) ) }.
% 0.68/1.11 parent0: (1245) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( X, or( Y, X )
% 0.68/1.11 ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := Y
% 0.68/1.11 Y := X
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 resolution: (1246) {G1,W1,D1,L1,V0,M1} { or_2 }.
% 0.68/1.11 parent0[0]: (26) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( skol37,
% 0.68/1.11 or( skol12, skol37 ) ) ), or_2 }.
% 0.68/1.11 parent1[0]: (76) {G1,W6,D4,L1,V2,M1} S(49);r(67) { is_a_theorem( implies( Y
% 0.68/1.11 , or( X, Y ) ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 substitution1:
% 0.68/1.11 X := skol12
% 0.68/1.11 Y := skol37
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 resolution: (1247) {G1,W0,D0,L0,V0,M0} { }.
% 0.68/1.11 parent0[0]: (74) {G0,W1,D1,L1,V0,M1} I { ! or_2 }.
% 0.68/1.11 parent1[0]: (1246) {G1,W1,D1,L1,V0,M1} { or_2 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 substitution1:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (1149) {G2,W0,D0,L0,V0,M0} S(26);r(76);r(74) { }.
% 0.68/1.11 parent0: (1247) {G1,W0,D0,L0,V0,M0} { }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 Proof check complete!
% 0.68/1.11
% 0.68/1.11 Memory use:
% 0.68/1.11
% 0.68/1.11 space for terms: 15751
% 0.68/1.11 space for clauses: 57929
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 clauses generated: 1745
% 0.68/1.11 clauses kept: 1150
% 0.68/1.11 clauses selected: 103
% 0.68/1.11 clauses deleted: 16
% 0.68/1.11 clauses inuse deleted: 3
% 0.68/1.11
% 0.68/1.11 subsentry: 1629
% 0.68/1.11 literals s-matched: 1462
% 0.68/1.11 literals matched: 1461
% 0.68/1.11 full subsumption: 131
% 0.68/1.11
% 0.68/1.11 checksum: 641385785
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Bliksem ended
%------------------------------------------------------------------------------