TSTP Solution File: LCL452+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL452+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.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 07:53:53 EDT 2022
% Result : Theorem 1.33s 1.71s
% Output : Refutation 1.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL452+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n008.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 % DateTime : Mon Jul 4 23:41:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.10 *** allocated 10000 integers for termspace/termends
% 0.44/1.10 *** allocated 10000 integers for clauses
% 0.44/1.10 *** allocated 10000 integers for justifications
% 0.44/1.10 Bliksem 1.12
% 0.44/1.10
% 0.44/1.10
% 0.44/1.10 Automatic Strategy Selection
% 0.44/1.10
% 0.44/1.10
% 0.44/1.10 Clauses:
% 0.44/1.10
% 0.44/1.10 { ! modus_ponens, ! alpha1( X ), is_a_theorem( X ) }.
% 0.44/1.10 { alpha1( skol1 ), modus_ponens }.
% 0.44/1.10 { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.44/1.10 { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.44/1.10 { ! alpha1( X ), is_a_theorem( implies( skol2( X ), X ) ) }.
% 0.44/1.10 { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.44/1.10 { ! substitution_of_equivalents, ! is_a_theorem( equiv( X, Y ) ), X = Y }.
% 0.44/1.10 { is_a_theorem( equiv( skol3, skol28 ) ), substitution_of_equivalents }.
% 0.44/1.10 { ! skol3 = skol28, substitution_of_equivalents }.
% 0.44/1.10 { ! modus_tollens, is_a_theorem( implies( implies( not( Y ), not( X ) ),
% 0.44/1.10 implies( X, Y ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( implies( not( skol29 ), not( skol4 ) ), implies
% 0.44/1.10 ( skol4, skol29 ) ) ), modus_tollens }.
% 0.44/1.10 { ! implies_1, is_a_theorem( implies( X, implies( Y, X ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( skol5, implies( skol30, skol5 ) ) ), implies_1 }
% 0.44/1.10 .
% 0.44/1.10 { ! implies_2, is_a_theorem( implies( implies( X, implies( X, Y ) ),
% 0.44/1.10 implies( X, Y ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( implies( skol6, implies( skol6, skol31 ) ),
% 0.44/1.10 implies( skol6, skol31 ) ) ), implies_2 }.
% 0.44/1.10 { ! implies_3, is_a_theorem( implies( implies( X, Y ), implies( implies( Y
% 0.44/1.10 , Z ), implies( X, Z ) ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( implies( skol7, skol32 ), implies( implies(
% 0.44/1.10 skol32, skol50 ), implies( skol7, skol50 ) ) ) ), implies_3 }.
% 0.44/1.10 { ! and_1, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( and( skol8, skol33 ), skol8 ) ), and_1 }.
% 0.44/1.10 { ! and_2, is_a_theorem( implies( and( X, Y ), Y ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( and( skol9, skol34 ), skol34 ) ), and_2 }.
% 0.44/1.10 { ! and_3, is_a_theorem( implies( X, implies( Y, and( X, Y ) ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( skol10, implies( skol35, and( skol10, skol35 ) )
% 0.44/1.10 ) ), and_3 }.
% 0.44/1.10 { ! or_1, is_a_theorem( implies( X, or( X, Y ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( skol11, or( skol11, skol36 ) ) ), or_1 }.
% 0.44/1.10 { ! or_2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( skol37, or( skol12, skol37 ) ) ), or_2 }.
% 0.44/1.10 { ! or_3, is_a_theorem( implies( implies( X, Z ), implies( implies( Y, Z )
% 0.44/1.10 , implies( or( X, Y ), Z ) ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( implies( skol13, skol51 ), implies( implies(
% 0.44/1.10 skol38, skol51 ), implies( or( skol13, skol38 ), skol51 ) ) ) ), or_3 }.
% 0.44/1.10 { ! equivalence_1, is_a_theorem( implies( equiv( X, Y ), implies( X, Y ) )
% 0.44/1.10 ) }.
% 0.44/1.10 { ! is_a_theorem( implies( equiv( skol14, skol39 ), implies( skol14, skol39
% 0.44/1.10 ) ) ), equivalence_1 }.
% 0.44/1.10 { ! equivalence_2, is_a_theorem( implies( equiv( X, Y ), implies( Y, X ) )
% 0.44/1.10 ) }.
% 0.44/1.10 { ! is_a_theorem( implies( equiv( skol15, skol40 ), implies( skol40, skol15
% 0.44/1.10 ) ) ), equivalence_2 }.
% 0.44/1.10 { ! equivalence_3, is_a_theorem( implies( implies( X, Y ), implies( implies
% 0.44/1.10 ( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( implies( skol16, skol41 ), implies( implies(
% 0.44/1.10 skol41, skol16 ), equiv( skol16, skol41 ) ) ) ), equivalence_3 }.
% 0.44/1.10 { ! kn1, is_a_theorem( implies( X, and( X, X ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( skol17, and( skol17, skol17 ) ) ), kn1 }.
% 0.44/1.10 { ! kn2, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( and( skol18, skol42 ), skol18 ) ), kn2 }.
% 0.44/1.10 { ! kn3, is_a_theorem( implies( implies( X, Y ), implies( not( and( Y, Z )
% 0.44/1.10 ), not( and( Z, X ) ) ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( implies( skol19, skol43 ), implies( not( and(
% 0.44/1.10 skol43, skol52 ) ), not( and( skol52, skol19 ) ) ) ) ), kn3 }.
% 0.44/1.10 { ! cn1, is_a_theorem( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.44/1.10 implies( X, Z ) ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( implies( skol20, skol44 ), implies( implies(
% 0.44/1.10 skol44, skol53 ), implies( skol20, skol53 ) ) ) ), cn1 }.
% 0.44/1.10 { ! cn2, is_a_theorem( implies( X, implies( not( X ), Y ) ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( skol21, implies( not( skol21 ), skol45 ) ) ),
% 0.44/1.10 cn2 }.
% 0.44/1.10 { ! cn3, is_a_theorem( implies( implies( not( X ), X ), X ) ) }.
% 0.44/1.10 { ! is_a_theorem( implies( implies( not( skol22 ), skol22 ), skol22 ) ),
% 0.44/1.10 cn3 }.
% 0.44/1.14 { ! r1, is_a_theorem( implies( or( X, X ), X ) ) }.
% 0.44/1.14 { ! is_a_theorem( implies( or( skol23, skol23 ), skol23 ) ), r1 }.
% 0.44/1.14 { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.44/1.14 { ! is_a_theorem( implies( skol46, or( skol24, skol46 ) ) ), r2 }.
% 0.44/1.14 { ! r3, is_a_theorem( implies( or( X, Y ), or( Y, X ) ) ) }.
% 0.44/1.14 { ! is_a_theorem( implies( or( skol25, skol47 ), or( skol47, skol25 ) ) ),
% 0.44/1.14 r3 }.
% 0.44/1.14 { ! r4, is_a_theorem( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) )
% 0.44/1.14 }.
% 0.44/1.14 { ! is_a_theorem( implies( or( skol26, or( skol48, skol54 ) ), or( skol48,
% 0.44/1.14 or( skol26, skol54 ) ) ) ), r4 }.
% 0.44/1.14 { ! r5, is_a_theorem( implies( implies( Y, Z ), implies( or( X, Y ), or( X
% 0.44/1.14 , Z ) ) ) ) }.
% 0.44/1.14 { ! is_a_theorem( implies( implies( skol49, skol55 ), implies( or( skol27,
% 0.44/1.14 skol49 ), or( skol27, skol55 ) ) ) ), r5 }.
% 0.44/1.14 { ! op_or, or( X, Y ) = not( and( not( X ), not( Y ) ) ) }.
% 0.44/1.14 { ! op_and, and( X, Y ) = not( or( not( X ), not( Y ) ) ) }.
% 0.44/1.14 { ! op_implies_and, implies( X, Y ) = not( and( X, not( Y ) ) ) }.
% 0.44/1.14 { ! op_implies_or, implies( X, Y ) = or( not( X ), Y ) }.
% 0.44/1.14 { ! op_equiv, equiv( X, Y ) = and( implies( X, Y ), implies( Y, X ) ) }.
% 0.44/1.14 { op_or }.
% 0.44/1.14 { op_implies_and }.
% 0.44/1.14 { op_equiv }.
% 0.44/1.14 { modus_ponens }.
% 0.44/1.14 { modus_tollens }.
% 0.44/1.14 { implies_1 }.
% 0.44/1.14 { implies_2 }.
% 0.44/1.14 { implies_3 }.
% 0.44/1.14 { and_1 }.
% 0.44/1.14 { and_2 }.
% 0.44/1.14 { and_3 }.
% 0.44/1.14 { or_1 }.
% 0.44/1.14 { or_2 }.
% 0.44/1.14 { or_3 }.
% 0.44/1.14 { equivalence_1 }.
% 0.44/1.14 { equivalence_2 }.
% 0.44/1.14 { equivalence_3 }.
% 0.44/1.14 { substitution_of_equivalents }.
% 0.44/1.14 { op_or }.
% 0.44/1.14 { op_implies }.
% 0.44/1.14 { op_equiv }.
% 0.44/1.14 { ! cn2 }.
% 0.44/1.14
% 0.44/1.14 percentage equality = 0.047619, percentage horn = 0.975610
% 0.44/1.14 This is a problem with some equality
% 0.44/1.14
% 0.44/1.14
% 0.44/1.14
% 0.44/1.14 Options Used:
% 0.44/1.14
% 0.44/1.14 useres = 1
% 0.44/1.14 useparamod = 1
% 0.44/1.14 useeqrefl = 1
% 0.44/1.14 useeqfact = 1
% 0.44/1.14 usefactor = 1
% 0.44/1.14 usesimpsplitting = 0
% 0.44/1.14 usesimpdemod = 5
% 0.44/1.14 usesimpres = 3
% 0.44/1.14
% 0.44/1.14 resimpinuse = 1000
% 0.44/1.14 resimpclauses = 20000
% 0.44/1.14 substype = eqrewr
% 0.44/1.14 backwardsubs = 1
% 0.44/1.14 selectoldest = 5
% 0.44/1.14
% 0.44/1.14 litorderings [0] = split
% 0.44/1.14 litorderings [1] = extend the termordering, first sorting on arguments
% 0.44/1.14
% 0.44/1.14 termordering = kbo
% 0.44/1.14
% 0.44/1.14 litapriori = 0
% 0.44/1.14 termapriori = 1
% 0.44/1.14 litaposteriori = 0
% 0.44/1.14 termaposteriori = 0
% 0.44/1.14 demodaposteriori = 0
% 0.44/1.14 ordereqreflfact = 0
% 0.44/1.14
% 0.44/1.14 litselect = negord
% 0.44/1.14
% 0.44/1.14 maxweight = 15
% 0.44/1.14 maxdepth = 30000
% 0.44/1.14 maxlength = 115
% 0.44/1.14 maxnrvars = 195
% 0.44/1.14 excuselevel = 1
% 0.44/1.14 increasemaxweight = 1
% 0.44/1.14
% 0.44/1.14 maxselected = 10000000
% 0.44/1.14 maxnrclauses = 10000000
% 0.44/1.14
% 0.44/1.14 showgenerated = 0
% 0.44/1.14 showkept = 0
% 0.44/1.14 showselected = 0
% 0.44/1.14 showdeleted = 0
% 0.44/1.14 showresimp = 1
% 0.44/1.14 showstatus = 2000
% 0.44/1.14
% 0.44/1.14 prologoutput = 0
% 0.44/1.14 nrgoals = 5000000
% 0.44/1.14 totalproof = 1
% 0.44/1.14
% 0.44/1.14 Symbols occurring in the translation:
% 0.44/1.14
% 0.44/1.14 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.44/1.14 . [1, 2] (w:1, o:107, a:1, s:1, b:0),
% 0.44/1.14 ! [4, 1] (w:0, o:98, a:1, s:1, b:0),
% 0.44/1.14 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.14 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.14 modus_ponens [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.44/1.14 is_a_theorem [38, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.44/1.14 implies [39, 2] (w:1, o:131, a:1, s:1, b:0),
% 0.44/1.14 substitution_of_equivalents [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.44/1.14 equiv [41, 2] (w:1, o:132, a:1, s:1, b:0),
% 0.44/1.14 modus_tollens [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.44/1.14 not [43, 1] (w:1, o:104, a:1, s:1, b:0),
% 0.44/1.14 implies_1 [44, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.44/1.14 implies_2 [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.44/1.14 implies_3 [46, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.44/1.14 and_1 [48, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.44/1.14 and [49, 2] (w:1, o:133, a:1, s:1, b:0),
% 0.44/1.14 and_2 [50, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.44/1.14 and_3 [51, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.44/1.14 or_1 [52, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.44/1.14 or [53, 2] (w:1, o:134, a:1, s:1, b:0),
% 0.44/1.14 or_2 [54, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.44/1.14 or_3 [55, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.44/1.14 equivalence_1 [56, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.44/1.14 equivalence_2 [57, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.44/1.14 equivalence_3 [58, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.44/1.14 kn1 [59, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.44/1.14 kn2 [61, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.44/1.14 kn3 [63, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.44/1.14 cn1 [65, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.33/1.71 cn2 [66, 0] (w:1, o:36, a:1, s:1, b:0),
% 1.33/1.71 cn3 [67, 0] (w:1, o:37, a:1, s:1, b:0),
% 1.33/1.71 r1 [68, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.33/1.71 r2 [69, 0] (w:1, o:10, a:1, s:1, b:0),
% 1.33/1.71 r3 [70, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.33/1.71 r4 [71, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.33/1.71 r5 [72, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.33/1.71 op_or [73, 0] (w:1, o:38, a:1, s:1, b:0),
% 1.33/1.71 op_and [74, 0] (w:1, o:39, a:1, s:1, b:0),
% 1.33/1.71 op_implies_and [75, 0] (w:1, o:40, a:1, s:1, b:0),
% 1.33/1.71 op_implies_or [76, 0] (w:1, o:41, a:1, s:1, b:0),
% 1.33/1.71 op_equiv [77, 0] (w:1, o:42, a:1, s:1, b:0),
% 1.33/1.71 op_implies [78, 0] (w:1, o:43, a:1, s:1, b:0),
% 1.33/1.71 alpha1 [79, 1] (w:1, o:105, a:1, s:1, b:1),
% 1.33/1.71 skol1 [80, 0] (w:1, o:44, a:1, s:1, b:1),
% 1.33/1.71 skol2 [81, 1] (w:1, o:106, a:1, s:1, b:1),
% 1.33/1.71 skol3 [82, 0] (w:1, o:55, a:1, s:1, b:1),
% 1.33/1.71 skol4 [83, 0] (w:1, o:66, a:1, s:1, b:1),
% 1.33/1.71 skol5 [84, 0] (w:1, o:77, a:1, s:1, b:1),
% 1.33/1.71 skol6 [85, 0] (w:1, o:84, a:1, s:1, b:1),
% 1.33/1.71 skol7 [86, 0] (w:1, o:85, a:1, s:1, b:1),
% 1.33/1.71 skol8 [87, 0] (w:1, o:86, a:1, s:1, b:1),
% 1.33/1.71 skol9 [88, 0] (w:1, o:87, a:1, s:1, b:1),
% 1.33/1.71 skol10 [89, 0] (w:1, o:88, a:1, s:1, b:1),
% 1.33/1.71 skol11 [90, 0] (w:1, o:89, a:1, s:1, b:1),
% 1.33/1.71 skol12 [91, 0] (w:1, o:90, a:1, s:1, b:1),
% 1.33/1.71 skol13 [92, 0] (w:1, o:91, a:1, s:1, b:1),
% 1.33/1.71 skol14 [93, 0] (w:1, o:92, a:1, s:1, b:1),
% 1.33/1.71 skol15 [94, 0] (w:1, o:93, a:1, s:1, b:1),
% 1.33/1.71 skol16 [95, 0] (w:1, o:94, a:1, s:1, b:1),
% 1.33/1.71 skol17 [96, 0] (w:1, o:95, a:1, s:1, b:1),
% 1.33/1.71 skol18 [97, 0] (w:1, o:96, a:1, s:1, b:1),
% 1.33/1.71 skol19 [98, 0] (w:1, o:97, a:1, s:1, b:1),
% 1.33/1.71 skol20 [99, 0] (w:1, o:45, a:1, s:1, b:1),
% 1.33/1.71 skol21 [100, 0] (w:1, o:46, a:1, s:1, b:1),
% 1.33/1.71 skol22 [101, 0] (w:1, o:47, a:1, s:1, b:1),
% 1.33/1.71 skol23 [102, 0] (w:1, o:48, a:1, s:1, b:1),
% 1.33/1.71 skol24 [103, 0] (w:1, o:49, a:1, s:1, b:1),
% 1.33/1.71 skol25 [104, 0] (w:1, o:50, a:1, s:1, b:1),
% 1.33/1.71 skol26 [105, 0] (w:1, o:51, a:1, s:1, b:1),
% 1.33/1.71 skol27 [106, 0] (w:1, o:52, a:1, s:1, b:1),
% 1.33/1.71 skol28 [107, 0] (w:1, o:53, a:1, s:1, b:1),
% 1.33/1.71 skol29 [108, 0] (w:1, o:54, a:1, s:1, b:1),
% 1.33/1.71 skol30 [109, 0] (w:1, o:56, a:1, s:1, b:1),
% 1.33/1.71 skol31 [110, 0] (w:1, o:57, a:1, s:1, b:1),
% 1.33/1.71 skol32 [111, 0] (w:1, o:58, a:1, s:1, b:1),
% 1.33/1.71 skol33 [112, 0] (w:1, o:59, a:1, s:1, b:1),
% 1.33/1.71 skol34 [113, 0] (w:1, o:60, a:1, s:1, b:1),
% 1.33/1.71 skol35 [114, 0] (w:1, o:61, a:1, s:1, b:1),
% 1.33/1.71 skol36 [115, 0] (w:1, o:62, a:1, s:1, b:1),
% 1.33/1.71 skol37 [116, 0] (w:1, o:63, a:1, s:1, b:1),
% 1.33/1.71 skol38 [117, 0] (w:1, o:64, a:1, s:1, b:1),
% 1.33/1.71 skol39 [118, 0] (w:1, o:65, a:1, s:1, b:1),
% 1.33/1.71 skol40 [119, 0] (w:1, o:67, a:1, s:1, b:1),
% 1.33/1.71 skol41 [120, 0] (w:1, o:68, a:1, s:1, b:1),
% 1.33/1.71 skol42 [121, 0] (w:1, o:69, a:1, s:1, b:1),
% 1.33/1.71 skol43 [122, 0] (w:1, o:70, a:1, s:1, b:1),
% 1.33/1.71 skol44 [123, 0] (w:1, o:71, a:1, s:1, b:1),
% 1.33/1.71 skol45 [124, 0] (w:1, o:72, a:1, s:1, b:1),
% 1.33/1.71 skol46 [125, 0] (w:1, o:73, a:1, s:1, b:1),
% 1.33/1.71 skol47 [126, 0] (w:1, o:74, a:1, s:1, b:1),
% 1.33/1.71 skol48 [127, 0] (w:1, o:75, a:1, s:1, b:1),
% 1.33/1.71 skol49 [128, 0] (w:1, o:76, a:1, s:1, b:1),
% 1.33/1.71 skol50 [129, 0] (w:1, o:78, a:1, s:1, b:1),
% 1.33/1.71 skol51 [130, 0] (w:1, o:79, a:1, s:1, b:1),
% 1.33/1.71 skol52 [131, 0] (w:1, o:80, a:1, s:1, b:1),
% 1.33/1.71 skol53 [132, 0] (w:1, o:81, a:1, s:1, b:1),
% 1.33/1.71 skol54 [133, 0] (w:1, o:82, a:1, s:1, b:1),
% 1.33/1.71 skol55 [134, 0] (w:1, o:83, a:1, s:1, b:1).
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Starting Search:
% 1.33/1.71
% 1.33/1.71 *** allocated 15000 integers for clauses
% 1.33/1.71 *** allocated 22500 integers for clauses
% 1.33/1.71 *** allocated 33750 integers for clauses
% 1.33/1.71 *** allocated 50625 integers for clauses
% 1.33/1.71 *** allocated 15000 integers for termspace/termends
% 1.33/1.71 *** allocated 75937 integers for clauses
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 *** allocated 22500 integers for termspace/termends
% 1.33/1.71 *** allocated 113905 integers for clauses
% 1.33/1.71 *** allocated 33750 integers for termspace/termends
% 1.33/1.71
% 1.33/1.71 Intermediate Status:
% 1.33/1.71 Generated: 4061
% 1.33/1.71 Kept: 2017
% 1.33/1.71 Inuse: 159
% 1.33/1.71 Deleted: 63
% 1.33/1.71 Deletedinuse: 20
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 *** allocated 170857 integers for clauses
% 1.33/1.71 *** allocated 50625 integers for termspace/termends
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 *** allocated 256285 integers for clauses
% 1.33/1.71
% 1.33/1.71 Intermediate Status:
% 1.33/1.71 Generated: 7724
% 1.33/1.71 Kept: 4123
% 1.33/1.71 Inuse: 246
% 1.33/1.71 Deleted: 70
% 1.33/1.71 Deletedinuse: 20
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 *** allocated 75937 integers for termspace/termends
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 *** allocated 384427 integers for clauses
% 1.33/1.71 *** allocated 113905 integers for termspace/termends
% 1.33/1.71
% 1.33/1.71 Intermediate Status:
% 1.33/1.71 Generated: 12292
% 1.33/1.71 Kept: 6814
% 1.33/1.71 Inuse: 324
% 1.33/1.71 Deleted: 87
% 1.33/1.71 Deletedinuse: 20
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 *** allocated 576640 integers for clauses
% 1.33/1.71 *** allocated 170857 integers for termspace/termends
% 1.33/1.71
% 1.33/1.71 Intermediate Status:
% 1.33/1.71 Generated: 15609
% 1.33/1.71 Kept: 9295
% 1.33/1.71 Inuse: 350
% 1.33/1.71 Deleted: 91
% 1.33/1.71 Deletedinuse: 20
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Intermediate Status:
% 1.33/1.71 Generated: 19034
% 1.33/1.71 Kept: 11349
% 1.33/1.71 Inuse: 382
% 1.33/1.71 Deleted: 97
% 1.33/1.71 Deletedinuse: 20
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 *** allocated 256285 integers for termspace/termends
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 *** allocated 864960 integers for clauses
% 1.33/1.71
% 1.33/1.71 Intermediate Status:
% 1.33/1.71 Generated: 24226
% 1.33/1.71 Kept: 14504
% 1.33/1.71 Inuse: 426
% 1.33/1.71 Deleted: 105
% 1.33/1.71 Deletedinuse: 20
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Intermediate Status:
% 1.33/1.71 Generated: 26934
% 1.33/1.71 Kept: 16559
% 1.33/1.71 Inuse: 432
% 1.33/1.71 Deleted: 105
% 1.33/1.71 Deletedinuse: 20
% 1.33/1.71
% 1.33/1.71 *** allocated 384427 integers for termspace/termends
% 1.33/1.71
% 1.33/1.71 Intermediate Status:
% 1.33/1.71 Generated: 29568
% 1.33/1.71 Kept: 18573
% 1.33/1.71 Inuse: 436
% 1.33/1.71 Deleted: 105
% 1.33/1.71 Deletedinuse: 20
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 *** allocated 1297440 integers for clauses
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71 Resimplifying clauses:
% 1.33/1.71 Done
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Intermediate Status:
% 1.33/1.71 Generated: 32221
% 1.33/1.71 Kept: 20573
% 1.33/1.71 Inuse: 457
% 1.33/1.71 Deleted: 354
% 1.33/1.71 Deletedinuse: 20
% 1.33/1.71
% 1.33/1.71 Resimplifying inuse:
% 1.33/1.71
% 1.33/1.71 Bliksems!, er is een bewijs:
% 1.33/1.71 % SZS status Theorem
% 1.33/1.71 % SZS output start Refutation
% 1.33/1.71
% 1.33/1.71 (23) {G0,W7,D4,L2,V2,M2} I { ! or_1, is_a_theorem( implies( X, or( X, Y ) )
% 1.33/1.71 ) }.
% 1.33/1.71 (44) {G0,W8,D5,L2,V0,M2} I { ! is_a_theorem( implies( skol21, implies( not
% 1.33/1.71 ( skol21 ), skol45 ) ) ), cn2 }.
% 1.33/1.71 (57) {G0,W11,D5,L2,V2,M2} I { ! op_or, not( and( not( X ), not( Y ) ) ) ==>
% 1.33/1.71 or( X, Y ) }.
% 1.33/1.71 (59) {G0,W10,D5,L2,V2,M2} I { ! op_implies_and, not( and( X, not( Y ) ) )
% 1.33/1.71 ==> implies( X, Y ) }.
% 1.33/1.71 (62) {G0,W1,D1,L1,V0,M1} I { op_or }.
% 1.33/1.71 (63) {G0,W1,D1,L1,V0,M1} I { op_implies_and }.
% 1.33/1.71 (73) {G0,W1,D1,L1,V0,M1} I { or_1 }.
% 1.33/1.71 (81) {G0,W1,D1,L1,V0,M1} I { ! cn2 }.
% 1.33/1.71 (662) {G1,W6,D4,L1,V2,M1} S(23);r(73) { is_a_theorem( implies( X, or( X, Y
% 1.33/1.71 ) ) ) }.
% 1.33/1.71 (1989) {G1,W7,D5,L1,V0,M1} S(44);r(81) { ! is_a_theorem( implies( skol21,
% 1.33/1.71 implies( not( skol21 ), skol45 ) ) ) }.
% 1.33/1.71 (2816) {G1,W10,D5,L1,V2,M1} S(57);r(62) { not( and( not( X ), not( Y ) ) )
% 1.33/1.71 ==> or( X, Y ) }.
% 1.33/1.71 (2956) {G1,W9,D5,L1,V2,M1} S(59);r(63) { not( and( X, not( Y ) ) ) ==>
% 1.33/1.71 implies( X, Y ) }.
% 1.33/1.71 (20457) {G2,W8,D4,L1,V2,M1} S(2816);d(2956) { implies( not( X ), Y ) ==> or
% 1.33/1.71 ( X, Y ) }.
% 1.33/1.71 (20746) {G3,W0,D0,L0,V0,M0} S(1989);d(20457);r(662) { }.
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 % SZS output end Refutation
% 1.33/1.71 found a proof!
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Unprocessed initial clauses:
% 1.33/1.71
% 1.33/1.71 (20748) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ), is_a_theorem
% 1.33/1.71 ( X ) }.
% 1.33/1.71 (20749) {G0,W3,D2,L2,V0,M2} { alpha1( skol1 ), modus_ponens }.
% 1.33/1.71 (20750) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol1 ), modus_ponens }.
% 1.33/1.71 (20751) {G0,W5,D3,L2,V2,M2} { ! alpha1( X ), is_a_theorem( skol2( Y ) )
% 1.33/1.71 }.
% 1.33/1.71 (20752) {G0,W7,D4,L2,V1,M2} { ! alpha1( X ), is_a_theorem( implies( skol2
% 1.33/1.71 ( X ), X ) ) }.
% 1.33/1.71 (20753) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem( implies
% 1.33/1.71 ( Y, X ) ), alpha1( X ) }.
% 1.33/1.71 (20754) {G0,W8,D3,L3,V2,M3} { ! substitution_of_equivalents, !
% 1.33/1.71 is_a_theorem( equiv( X, Y ) ), X = Y }.
% 1.33/1.71 (20755) {G0,W5,D3,L2,V0,M2} { is_a_theorem( equiv( skol3, skol28 ) ),
% 1.33/1.71 substitution_of_equivalents }.
% 1.33/1.71 (20756) {G0,W4,D2,L2,V0,M2} { ! skol3 = skol28,
% 1.33/1.71 substitution_of_equivalents }.
% 1.33/1.71 (20757) {G0,W11,D5,L2,V2,M2} { ! modus_tollens, is_a_theorem( implies(
% 1.33/1.71 implies( not( Y ), not( X ) ), implies( X, Y ) ) ) }.
% 1.33/1.71 (20758) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 1.33/1.71 skol29 ), not( skol4 ) ), implies( skol4, skol29 ) ) ), modus_tollens }.
% 1.33/1.71 (20759) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies( X,
% 1.33/1.71 implies( Y, X ) ) ) }.
% 1.33/1.71 (20760) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol5, implies(
% 1.33/1.71 skol30, skol5 ) ) ), implies_1 }.
% 1.33/1.71 (20761) {G0,W11,D5,L2,V2,M2} { ! implies_2, is_a_theorem( implies( implies
% 1.33/1.71 ( X, implies( X, Y ) ), implies( X, Y ) ) ) }.
% 1.33/1.71 (20762) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol6,
% 1.33/1.71 implies( skol6, skol31 ) ), implies( skol6, skol31 ) ) ), implies_2 }.
% 1.33/1.71 (20763) {G0,W13,D5,L2,V3,M2} { ! implies_3, is_a_theorem( implies( implies
% 1.33/1.71 ( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 1.33/1.71 (20764) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol7,
% 1.33/1.71 skol32 ), implies( implies( skol32, skol50 ), implies( skol7, skol50 ) )
% 1.33/1.71 ) ), implies_3 }.
% 1.33/1.71 (20765) {G0,W7,D4,L2,V2,M2} { ! and_1, is_a_theorem( implies( and( X, Y )
% 1.33/1.71 , X ) ) }.
% 1.33/1.71 (20766) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol8, skol33
% 1.33/1.71 ), skol8 ) ), and_1 }.
% 1.33/1.71 (20767) {G0,W7,D4,L2,V2,M2} { ! and_2, is_a_theorem( implies( and( X, Y )
% 1.33/1.71 , Y ) ) }.
% 1.33/1.71 (20768) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol9, skol34
% 1.33/1.71 ), skol34 ) ), and_2 }.
% 1.33/1.71 (20769) {G0,W9,D5,L2,V2,M2} { ! and_3, is_a_theorem( implies( X, implies(
% 1.33/1.71 Y, and( X, Y ) ) ) ) }.
% 1.33/1.71 (20770) {G0,W9,D5,L2,V0,M2} { ! is_a_theorem( implies( skol10, implies(
% 1.33/1.71 skol35, and( skol10, skol35 ) ) ) ), and_3 }.
% 1.33/1.71 (20771) {G0,W7,D4,L2,V2,M2} { ! or_1, is_a_theorem( implies( X, or( X, Y )
% 1.33/1.71 ) ) }.
% 1.33/1.71 (20772) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol11, or( skol11
% 1.33/1.71 , skol36 ) ) ), or_1 }.
% 1.33/1.71 (20773) {G0,W7,D4,L2,V2,M2} { ! or_2, is_a_theorem( implies( Y, or( X, Y )
% 1.33/1.71 ) ) }.
% 1.33/1.71 (20774) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol37, or( skol12
% 1.33/1.71 , skol37 ) ) ), or_2 }.
% 1.33/1.71 (20775) {G0,W15,D6,L2,V3,M2} { ! or_3, is_a_theorem( implies( implies( X,
% 1.33/1.71 Z ), implies( implies( Y, Z ), implies( or( X, Y ), Z ) ) ) ) }.
% 1.33/1.71 (20776) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol13,
% 1.33/1.71 skol51 ), implies( implies( skol38, skol51 ), implies( or( skol13, skol38
% 1.33/1.71 ), skol51 ) ) ) ), or_3 }.
% 1.33/1.71 (20777) {G0,W9,D4,L2,V2,M2} { ! equivalence_1, is_a_theorem( implies(
% 1.33/1.71 equiv( X, Y ), implies( X, Y ) ) ) }.
% 1.33/1.71 (20778) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol14,
% 1.33/1.71 skol39 ), implies( skol14, skol39 ) ) ), equivalence_1 }.
% 1.33/1.71 (20779) {G0,W9,D4,L2,V2,M2} { ! equivalence_2, is_a_theorem( implies(
% 1.33/1.71 equiv( X, Y ), implies( Y, X ) ) ) }.
% 1.33/1.71 (20780) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol15,
% 1.33/1.71 skol40 ), implies( skol40, skol15 ) ) ), equivalence_2 }.
% 1.33/1.71 (20781) {G0,W13,D5,L2,V2,M2} { ! equivalence_3, is_a_theorem( implies(
% 1.33/1.71 implies( X, Y ), implies( implies( Y, X ), equiv( X, Y ) ) ) ) }.
% 1.33/1.71 (20782) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol16,
% 1.33/1.71 skol41 ), implies( implies( skol41, skol16 ), equiv( skol16, skol41 ) ) )
% 1.33/1.71 ), equivalence_3 }.
% 1.33/1.71 (20783) {G0,W7,D4,L2,V1,M2} { ! kn1, is_a_theorem( implies( X, and( X, X )
% 1.33/1.71 ) ) }.
% 1.33/1.71 (20784) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol17, and( skol17
% 1.33/1.71 , skol17 ) ) ), kn1 }.
% 1.33/1.71 (20785) {G0,W7,D4,L2,V2,M2} { ! kn2, is_a_theorem( implies( and( X, Y ), X
% 1.33/1.71 ) ) }.
% 1.33/1.71 (20786) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol18, skol42
% 1.33/1.71 ), skol18 ) ), kn2 }.
% 1.33/1.71 (20787) {G0,W15,D6,L2,V3,M2} { ! kn3, is_a_theorem( implies( implies( X, Y
% 1.33/1.71 ), implies( not( and( Y, Z ) ), not( and( Z, X ) ) ) ) ) }.
% 1.33/1.71 (20788) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol19,
% 1.33/1.71 skol43 ), implies( not( and( skol43, skol52 ) ), not( and( skol52, skol19
% 1.33/1.71 ) ) ) ) ), kn3 }.
% 1.33/1.71 (20789) {G0,W13,D5,L2,V3,M2} { ! cn1, is_a_theorem( implies( implies( X, Y
% 1.33/1.71 ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 1.33/1.71 (20790) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol20,
% 1.33/1.71 skol44 ), implies( implies( skol44, skol53 ), implies( skol20, skol53 ) )
% 1.33/1.71 ) ), cn1 }.
% 1.33/1.71 (20791) {G0,W8,D5,L2,V2,M2} { ! cn2, is_a_theorem( implies( X, implies(
% 1.33/1.71 not( X ), Y ) ) ) }.
% 1.33/1.71 (20792) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( skol21, implies(
% 1.33/1.71 not( skol21 ), skol45 ) ) ), cn2 }.
% 1.33/1.71 (20793) {G0,W8,D5,L2,V1,M2} { ! cn3, is_a_theorem( implies( implies( not(
% 1.33/1.71 X ), X ), X ) ) }.
% 1.33/1.71 (20794) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 1.33/1.71 skol22 ), skol22 ), skol22 ) ), cn3 }.
% 1.33/1.71 (20795) {G0,W7,D4,L2,V1,M2} { ! r1, is_a_theorem( implies( or( X, X ), X )
% 1.33/1.71 ) }.
% 1.33/1.71 (20796) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol23, skol23
% 1.33/1.71 ), skol23 ) ), r1 }.
% 1.33/1.71 (20797) {G0,W7,D4,L2,V2,M2} { ! r2, is_a_theorem( implies( Y, or( X, Y ) )
% 1.33/1.71 ) }.
% 1.33/1.71 (20798) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol46, or( skol24
% 1.33/1.71 , skol46 ) ) ), r2 }.
% 1.33/1.71 (20799) {G0,W9,D4,L2,V2,M2} { ! r3, is_a_theorem( implies( or( X, Y ), or
% 1.33/1.71 ( Y, X ) ) ) }.
% 1.33/1.71 (20800) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol25, skol47
% 1.33/1.71 ), or( skol47, skol25 ) ) ), r3 }.
% 1.33/1.71 (20801) {G0,W13,D5,L2,V3,M2} { ! r4, is_a_theorem( implies( or( X, or( Y,
% 1.33/1.71 Z ) ), or( Y, or( X, Z ) ) ) ) }.
% 1.33/1.71 (20802) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( or( skol26, or(
% 1.33/1.71 skol48, skol54 ) ), or( skol48, or( skol26, skol54 ) ) ) ), r4 }.
% 1.33/1.71 (20803) {G0,W13,D5,L2,V3,M2} { ! r5, is_a_theorem( implies( implies( Y, Z
% 1.33/1.71 ), implies( or( X, Y ), or( X, Z ) ) ) ) }.
% 1.33/1.71 (20804) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol49,
% 1.33/1.71 skol55 ), implies( or( skol27, skol49 ), or( skol27, skol55 ) ) ) ), r5
% 1.33/1.71 }.
% 1.33/1.71 (20805) {G0,W11,D5,L2,V2,M2} { ! op_or, or( X, Y ) = not( and( not( X ),
% 1.33/1.71 not( Y ) ) ) }.
% 1.33/1.71 (20806) {G0,W11,D5,L2,V2,M2} { ! op_and, and( X, Y ) = not( or( not( X ),
% 1.33/1.71 not( Y ) ) ) }.
% 1.33/1.71 (20807) {G0,W10,D5,L2,V2,M2} { ! op_implies_and, implies( X, Y ) = not(
% 1.33/1.71 and( X, not( Y ) ) ) }.
% 1.33/1.71 (20808) {G0,W9,D4,L2,V2,M2} { ! op_implies_or, implies( X, Y ) = or( not(
% 1.33/1.71 X ), Y ) }.
% 1.33/1.71 (20809) {G0,W12,D4,L2,V2,M2} { ! op_equiv, equiv( X, Y ) = and( implies( X
% 1.33/1.71 , Y ), implies( Y, X ) ) }.
% 1.33/1.71 (20810) {G0,W1,D1,L1,V0,M1} { op_or }.
% 1.33/1.71 (20811) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 1.33/1.71 (20812) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 1.33/1.71 (20813) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 1.33/1.71 (20814) {G0,W1,D1,L1,V0,M1} { modus_tollens }.
% 1.33/1.71 (20815) {G0,W1,D1,L1,V0,M1} { implies_1 }.
% 1.33/1.71 (20816) {G0,W1,D1,L1,V0,M1} { implies_2 }.
% 1.33/1.71 (20817) {G0,W1,D1,L1,V0,M1} { implies_3 }.
% 1.33/1.71 (20818) {G0,W1,D1,L1,V0,M1} { and_1 }.
% 1.33/1.71 (20819) {G0,W1,D1,L1,V0,M1} { and_2 }.
% 1.33/1.71 (20820) {G0,W1,D1,L1,V0,M1} { and_3 }.
% 1.33/1.71 (20821) {G0,W1,D1,L1,V0,M1} { or_1 }.
% 1.33/1.71 (20822) {G0,W1,D1,L1,V0,M1} { or_2 }.
% 1.33/1.71 (20823) {G0,W1,D1,L1,V0,M1} { or_3 }.
% 1.33/1.71 (20824) {G0,W1,D1,L1,V0,M1} { equivalence_1 }.
% 1.33/1.71 (20825) {G0,W1,D1,L1,V0,M1} { equivalence_2 }.
% 1.33/1.71 (20826) {G0,W1,D1,L1,V0,M1} { equivalence_3 }.
% 1.33/1.71 (20827) {G0,W1,D1,L1,V0,M1} { substitution_of_equivalents }.
% 1.33/1.71 (20828) {G0,W1,D1,L1,V0,M1} { op_or }.
% 1.33/1.71 (20829) {G0,W1,D1,L1,V0,M1} { op_implies }.
% 1.33/1.71 (20830) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 1.33/1.71 (20831) {G0,W1,D1,L1,V0,M1} { ! cn2 }.
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Total Proof:
% 1.33/1.71
% 1.33/1.71 subsumption: (23) {G0,W7,D4,L2,V2,M2} I { ! or_1, is_a_theorem( implies( X
% 1.33/1.71 , or( X, Y ) ) ) }.
% 1.33/1.71 parent0: (20771) {G0,W7,D4,L2,V2,M2} { ! or_1, is_a_theorem( implies( X,
% 1.33/1.71 or( X, Y ) ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (44) {G0,W8,D5,L2,V0,M2} I { ! is_a_theorem( implies( skol21,
% 1.33/1.71 implies( not( skol21 ), skol45 ) ) ), cn2 }.
% 1.33/1.71 parent0: (20792) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( skol21,
% 1.33/1.71 implies( not( skol21 ), skol45 ) ) ), cn2 }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 eqswap: (20838) {G0,W11,D5,L2,V2,M2} { not( and( not( X ), not( Y ) ) ) =
% 1.33/1.71 or( X, Y ), ! op_or }.
% 1.33/1.71 parent0[1]: (20805) {G0,W11,D5,L2,V2,M2} { ! op_or, or( X, Y ) = not( and
% 1.33/1.71 ( not( X ), not( Y ) ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (57) {G0,W11,D5,L2,V2,M2} I { ! op_or, not( and( not( X ), not
% 1.33/1.71 ( Y ) ) ) ==> or( X, Y ) }.
% 1.33/1.71 parent0: (20838) {G0,W11,D5,L2,V2,M2} { not( and( not( X ), not( Y ) ) ) =
% 1.33/1.71 or( X, Y ), ! op_or }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 1
% 1.33/1.71 1 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 eqswap: (20843) {G0,W10,D5,L2,V2,M2} { not( and( X, not( Y ) ) ) = implies
% 1.33/1.71 ( X, Y ), ! op_implies_and }.
% 1.33/1.71 parent0[1]: (20807) {G0,W10,D5,L2,V2,M2} { ! op_implies_and, implies( X, Y
% 1.33/1.71 ) = not( and( X, not( Y ) ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (59) {G0,W10,D5,L2,V2,M2} I { ! op_implies_and, not( and( X,
% 1.33/1.71 not( Y ) ) ) ==> implies( X, Y ) }.
% 1.33/1.71 parent0: (20843) {G0,W10,D5,L2,V2,M2} { not( and( X, not( Y ) ) ) =
% 1.33/1.71 implies( X, Y ), ! op_implies_and }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 1
% 1.33/1.71 1 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (62) {G0,W1,D1,L1,V0,M1} I { op_or }.
% 1.33/1.71 parent0: (20810) {G0,W1,D1,L1,V0,M1} { op_or }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (63) {G0,W1,D1,L1,V0,M1} I { op_implies_and }.
% 1.33/1.71 parent0: (20811) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (73) {G0,W1,D1,L1,V0,M1} I { or_1 }.
% 1.33/1.71 parent0: (20821) {G0,W1,D1,L1,V0,M1} { or_1 }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (81) {G0,W1,D1,L1,V0,M1} I { ! cn2 }.
% 1.33/1.71 parent0: (20831) {G0,W1,D1,L1,V0,M1} { ! cn2 }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (20872) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( X, or( X
% 1.33/1.71 , Y ) ) ) }.
% 1.33/1.71 parent0[0]: (23) {G0,W7,D4,L2,V2,M2} I { ! or_1, is_a_theorem( implies( X,
% 1.33/1.71 or( X, Y ) ) ) }.
% 1.33/1.71 parent1[0]: (73) {G0,W1,D1,L1,V0,M1} I { or_1 }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (662) {G1,W6,D4,L1,V2,M1} S(23);r(73) { is_a_theorem( implies
% 1.33/1.71 ( X, or( X, Y ) ) ) }.
% 1.33/1.71 parent0: (20872) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( X, or( X, Y
% 1.33/1.71 ) ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (20873) {G1,W7,D5,L1,V0,M1} { ! is_a_theorem( implies( skol21
% 1.33/1.71 , implies( not( skol21 ), skol45 ) ) ) }.
% 1.33/1.71 parent0[0]: (81) {G0,W1,D1,L1,V0,M1} I { ! cn2 }.
% 1.33/1.71 parent1[1]: (44) {G0,W8,D5,L2,V0,M2} I { ! is_a_theorem( implies( skol21,
% 1.33/1.71 implies( not( skol21 ), skol45 ) ) ), cn2 }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (1989) {G1,W7,D5,L1,V0,M1} S(44);r(81) { ! is_a_theorem(
% 1.33/1.71 implies( skol21, implies( not( skol21 ), skol45 ) ) ) }.
% 1.33/1.71 parent0: (20873) {G1,W7,D5,L1,V0,M1} { ! is_a_theorem( implies( skol21,
% 1.33/1.71 implies( not( skol21 ), skol45 ) ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (20875) {G1,W10,D5,L1,V2,M1} { not( and( not( X ), not( Y ) )
% 1.33/1.71 ) ==> or( X, Y ) }.
% 1.33/1.71 parent0[0]: (57) {G0,W11,D5,L2,V2,M2} I { ! op_or, not( and( not( X ), not
% 1.33/1.71 ( Y ) ) ) ==> or( X, Y ) }.
% 1.33/1.71 parent1[0]: (62) {G0,W1,D1,L1,V0,M1} I { op_or }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (2816) {G1,W10,D5,L1,V2,M1} S(57);r(62) { not( and( not( X ),
% 1.33/1.71 not( Y ) ) ) ==> or( X, Y ) }.
% 1.33/1.71 parent0: (20875) {G1,W10,D5,L1,V2,M1} { not( and( not( X ), not( Y ) ) )
% 1.33/1.71 ==> or( X, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (20878) {G1,W9,D5,L1,V2,M1} { not( and( X, not( Y ) ) ) ==>
% 1.33/1.71 implies( X, Y ) }.
% 1.33/1.71 parent0[0]: (59) {G0,W10,D5,L2,V2,M2} I { ! op_implies_and, not( and( X,
% 1.33/1.71 not( Y ) ) ) ==> implies( X, Y ) }.
% 1.33/1.71 parent1[0]: (63) {G0,W1,D1,L1,V0,M1} I { op_implies_and }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (2956) {G1,W9,D5,L1,V2,M1} S(59);r(63) { not( and( X, not( Y )
% 1.33/1.71 ) ) ==> implies( X, Y ) }.
% 1.33/1.71 parent0: (20878) {G1,W9,D5,L1,V2,M1} { not( and( X, not( Y ) ) ) ==>
% 1.33/1.71 implies( X, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 paramod: (20882) {G2,W8,D4,L1,V2,M1} { implies( not( X ), Y ) ==> or( X, Y
% 1.33/1.71 ) }.
% 1.33/1.71 parent0[0]: (2956) {G1,W9,D5,L1,V2,M1} S(59);r(63) { not( and( X, not( Y )
% 1.33/1.71 ) ) ==> implies( X, Y ) }.
% 1.33/1.71 parent1[0; 1]: (2816) {G1,W10,D5,L1,V2,M1} S(57);r(62) { not( and( not( X )
% 1.33/1.71 , not( Y ) ) ) ==> or( X, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := not( X )
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (20457) {G2,W8,D4,L1,V2,M1} S(2816);d(2956) { implies( not( X
% 1.33/1.71 ), Y ) ==> or( X, Y ) }.
% 1.33/1.71 parent0: (20882) {G2,W8,D4,L1,V2,M1} { implies( not( X ), Y ) ==> or( X, Y
% 1.33/1.71 ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 paramod: (20885) {G2,W6,D4,L1,V0,M1} { ! is_a_theorem( implies( skol21, or
% 1.33/1.71 ( skol21, skol45 ) ) ) }.
% 1.33/1.71 parent0[0]: (20457) {G2,W8,D4,L1,V2,M1} S(2816);d(2956) { implies( not( X )
% 1.33/1.71 , Y ) ==> or( X, Y ) }.
% 1.33/1.71 parent1[0; 4]: (1989) {G1,W7,D5,L1,V0,M1} S(44);r(81) { ! is_a_theorem(
% 1.33/1.71 implies( skol21, implies( not( skol21 ), skol45 ) ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := skol21
% 1.33/1.71 Y := skol45
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (20886) {G2,W0,D0,L0,V0,M0} { }.
% 1.33/1.71 parent0[0]: (20885) {G2,W6,D4,L1,V0,M1} { ! is_a_theorem( implies( skol21
% 1.33/1.71 , or( skol21, skol45 ) ) ) }.
% 1.33/1.71 parent1[0]: (662) {G1,W6,D4,L1,V2,M1} S(23);r(73) { is_a_theorem( implies(
% 1.33/1.71 X, or( X, Y ) ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := skol21
% 1.33/1.71 Y := skol45
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (20746) {G3,W0,D0,L0,V0,M0} S(1989);d(20457);r(662) { }.
% 1.33/1.71 parent0: (20886) {G2,W0,D0,L0,V0,M0} { }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 Proof check complete!
% 1.33/1.71
% 1.33/1.71 Memory use:
% 1.33/1.71
% 1.33/1.71 space for terms: 305801
% 1.33/1.71 space for clauses: 931048
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 clauses generated: 32435
% 1.33/1.71 clauses kept: 20747
% 1.33/1.71 clauses selected: 460
% 1.33/1.71 clauses deleted: 356
% 1.33/1.71 clauses inuse deleted: 22
% 1.33/1.71
% 1.33/1.71 subsentry: 147819
% 1.33/1.71 literals s-matched: 74762
% 1.33/1.71 literals matched: 74742
% 1.33/1.71 full subsumption: 37567
% 1.33/1.71
% 1.33/1.71 checksum: -722309295
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Bliksem ended
%------------------------------------------------------------------------------