TSTP Solution File: LCL469+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL469+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n005.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 07:54:01 EDT 2022
% Result : Theorem 1.45s 1.86s
% Output : Refutation 1.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL469+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11 % Command : bliksem %s
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Mon Jul 4 02:05:52 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.68/1.07 *** allocated 10000 integers for termspace/termends
% 0.68/1.07 *** allocated 10000 integers for clauses
% 0.68/1.07 *** allocated 10000 integers for justifications
% 0.68/1.07 Bliksem 1.12
% 0.68/1.07
% 0.68/1.07
% 0.68/1.07 Automatic Strategy Selection
% 0.68/1.07
% 0.68/1.07
% 0.68/1.07 Clauses:
% 0.68/1.07
% 0.68/1.07 { ! modus_ponens, ! alpha1( X ), is_a_theorem( X ) }.
% 0.68/1.07 { alpha1( skol1 ), modus_ponens }.
% 0.68/1.07 { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.68/1.07 { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.68/1.07 { ! alpha1( X ), is_a_theorem( implies( skol2( X ), X ) ) }.
% 0.68/1.07 { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.68/1.07 { ! substitution_of_equivalents, ! is_a_theorem( equiv( X, Y ) ), X = Y }.
% 0.68/1.07 { is_a_theorem( equiv( skol3, skol28 ) ), substitution_of_equivalents }.
% 0.68/1.07 { ! skol3 = skol28, substitution_of_equivalents }.
% 0.68/1.07 { ! modus_tollens, is_a_theorem( implies( implies( not( Y ), not( X ) ),
% 0.68/1.07 implies( X, Y ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( implies( not( skol29 ), not( skol4 ) ), implies
% 0.68/1.07 ( skol4, skol29 ) ) ), modus_tollens }.
% 0.68/1.07 { ! implies_1, is_a_theorem( implies( X, implies( Y, X ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( skol5, implies( skol30, skol5 ) ) ), implies_1 }
% 0.68/1.07 .
% 0.68/1.07 { ! implies_2, is_a_theorem( implies( implies( X, implies( X, Y ) ),
% 0.68/1.07 implies( X, Y ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( implies( skol6, implies( skol6, skol31 ) ),
% 0.68/1.07 implies( skol6, skol31 ) ) ), implies_2 }.
% 0.68/1.07 { ! implies_3, is_a_theorem( implies( implies( X, Y ), implies( implies( Y
% 0.68/1.07 , Z ), implies( X, Z ) ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( implies( skol7, skol32 ), implies( implies(
% 0.68/1.07 skol32, skol50 ), implies( skol7, skol50 ) ) ) ), implies_3 }.
% 0.68/1.07 { ! and_1, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( and( skol8, skol33 ), skol8 ) ), and_1 }.
% 0.68/1.07 { ! and_2, is_a_theorem( implies( and( X, Y ), Y ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( and( skol9, skol34 ), skol34 ) ), and_2 }.
% 0.68/1.07 { ! and_3, is_a_theorem( implies( X, implies( Y, and( X, Y ) ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( skol10, implies( skol35, and( skol10, skol35 ) )
% 0.68/1.07 ) ), and_3 }.
% 0.68/1.07 { ! or_1, is_a_theorem( implies( X, or( X, Y ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( skol11, or( skol11, skol36 ) ) ), or_1 }.
% 0.68/1.07 { ! or_2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( skol37, or( skol12, skol37 ) ) ), or_2 }.
% 0.68/1.07 { ! or_3, is_a_theorem( implies( implies( X, Z ), implies( implies( Y, Z )
% 0.68/1.07 , implies( or( X, Y ), Z ) ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( implies( skol13, skol51 ), implies( implies(
% 0.68/1.07 skol38, skol51 ), implies( or( skol13, skol38 ), skol51 ) ) ) ), or_3 }.
% 0.68/1.07 { ! equivalence_1, is_a_theorem( implies( equiv( X, Y ), implies( X, Y ) )
% 0.68/1.07 ) }.
% 0.68/1.07 { ! is_a_theorem( implies( equiv( skol14, skol39 ), implies( skol14, skol39
% 0.68/1.07 ) ) ), equivalence_1 }.
% 0.68/1.07 { ! equivalence_2, is_a_theorem( implies( equiv( X, Y ), implies( Y, X ) )
% 0.68/1.07 ) }.
% 0.68/1.07 { ! is_a_theorem( implies( equiv( skol15, skol40 ), implies( skol40, skol15
% 0.68/1.07 ) ) ), equivalence_2 }.
% 0.68/1.07 { ! equivalence_3, is_a_theorem( implies( implies( X, Y ), implies( implies
% 0.68/1.07 ( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( implies( skol16, skol41 ), implies( implies(
% 0.68/1.07 skol41, skol16 ), equiv( skol16, skol41 ) ) ) ), equivalence_3 }.
% 0.68/1.07 { ! kn1, is_a_theorem( implies( X, and( X, X ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( skol17, and( skol17, skol17 ) ) ), kn1 }.
% 0.68/1.07 { ! kn2, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( and( skol18, skol42 ), skol18 ) ), kn2 }.
% 0.68/1.07 { ! kn3, is_a_theorem( implies( implies( X, Y ), implies( not( and( Y, Z )
% 0.68/1.07 ), not( and( Z, X ) ) ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( implies( skol19, skol43 ), implies( not( and(
% 0.68/1.07 skol43, skol52 ) ), not( and( skol52, skol19 ) ) ) ) ), kn3 }.
% 0.68/1.07 { ! cn1, is_a_theorem( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.68/1.07 implies( X, Z ) ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( implies( skol20, skol44 ), implies( implies(
% 0.68/1.07 skol44, skol53 ), implies( skol20, skol53 ) ) ) ), cn1 }.
% 0.68/1.07 { ! cn2, is_a_theorem( implies( X, implies( not( X ), Y ) ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( skol21, implies( not( skol21 ), skol45 ) ) ),
% 0.68/1.07 cn2 }.
% 0.68/1.07 { ! cn3, is_a_theorem( implies( implies( not( X ), X ), X ) ) }.
% 0.68/1.07 { ! is_a_theorem( implies( implies( not( skol22 ), skol22 ), skol22 ) ),
% 0.68/1.07 cn3 }.
% 0.79/1.19 { ! r1, is_a_theorem( implies( or( X, X ), X ) ) }.
% 0.79/1.19 { ! is_a_theorem( implies( or( skol23, skol23 ), skol23 ) ), r1 }.
% 0.79/1.19 { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.79/1.19 { ! is_a_theorem( implies( skol46, or( skol24, skol46 ) ) ), r2 }.
% 0.79/1.19 { ! r3, is_a_theorem( implies( or( X, Y ), or( Y, X ) ) ) }.
% 0.79/1.19 { ! is_a_theorem( implies( or( skol25, skol47 ), or( skol47, skol25 ) ) ),
% 0.79/1.19 r3 }.
% 0.79/1.19 { ! r4, is_a_theorem( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) )
% 0.79/1.19 }.
% 0.79/1.19 { ! is_a_theorem( implies( or( skol26, or( skol48, skol54 ) ), or( skol48,
% 0.79/1.19 or( skol26, skol54 ) ) ) ), r4 }.
% 0.79/1.19 { ! r5, is_a_theorem( implies( implies( Y, Z ), implies( or( X, Y ), or( X
% 0.79/1.19 , Z ) ) ) ) }.
% 0.79/1.19 { ! is_a_theorem( implies( implies( skol49, skol55 ), implies( or( skol27,
% 0.79/1.19 skol49 ), or( skol27, skol55 ) ) ) ), r5 }.
% 0.79/1.19 { ! op_or, or( X, Y ) = not( and( not( X ), not( Y ) ) ) }.
% 0.79/1.19 { ! op_and, and( X, Y ) = not( or( not( X ), not( Y ) ) ) }.
% 0.79/1.19 { ! op_implies_and, implies( X, Y ) = not( and( X, not( Y ) ) ) }.
% 0.79/1.19 { ! op_implies_or, implies( X, Y ) = or( not( X ), Y ) }.
% 0.79/1.19 { ! op_equiv, equiv( X, Y ) = and( implies( X, Y ), implies( Y, X ) ) }.
% 0.79/1.19 { op_or }.
% 0.79/1.19 { op_implies }.
% 0.79/1.19 { op_equiv }.
% 0.79/1.19 { modus_ponens }.
% 0.79/1.19 { cn1 }.
% 0.79/1.19 { cn2 }.
% 0.79/1.19 { cn3 }.
% 0.79/1.19 { substitution_of_equivalents }.
% 0.79/1.19 { op_or }.
% 0.79/1.19 { op_implies_and }.
% 0.79/1.19 { op_equiv }.
% 0.79/1.19 { ! or_1 }.
% 0.79/1.19
% 0.79/1.19 percentage equality = 0.051095, percentage horn = 0.972222
% 0.79/1.19 This is a problem with some equality
% 0.79/1.19
% 0.79/1.19
% 0.79/1.19
% 0.79/1.19 Options Used:
% 0.79/1.19
% 0.79/1.19 useres = 1
% 0.79/1.19 useparamod = 1
% 0.79/1.19 useeqrefl = 1
% 0.79/1.19 useeqfact = 1
% 0.79/1.19 usefactor = 1
% 0.79/1.19 usesimpsplitting = 0
% 0.79/1.19 usesimpdemod = 5
% 0.79/1.19 usesimpres = 3
% 0.79/1.19
% 0.79/1.19 resimpinuse = 1000
% 0.79/1.19 resimpclauses = 20000
% 0.79/1.19 substype = eqrewr
% 0.79/1.19 backwardsubs = 1
% 0.79/1.19 selectoldest = 5
% 0.79/1.19
% 0.79/1.19 litorderings [0] = split
% 0.79/1.19 litorderings [1] = extend the termordering, first sorting on arguments
% 0.79/1.19
% 0.79/1.19 termordering = kbo
% 0.79/1.19
% 0.79/1.19 litapriori = 0
% 0.79/1.19 termapriori = 1
% 0.79/1.19 litaposteriori = 0
% 0.79/1.19 termaposteriori = 0
% 0.79/1.19 demodaposteriori = 0
% 0.79/1.19 ordereqreflfact = 0
% 0.79/1.19
% 0.79/1.19 litselect = negord
% 0.79/1.19
% 0.79/1.19 maxweight = 15
% 0.79/1.19 maxdepth = 30000
% 0.79/1.19 maxlength = 115
% 0.79/1.19 maxnrvars = 195
% 0.79/1.19 excuselevel = 1
% 0.79/1.19 increasemaxweight = 1
% 0.79/1.19
% 0.79/1.19 maxselected = 10000000
% 0.79/1.19 maxnrclauses = 10000000
% 0.79/1.19
% 0.79/1.19 showgenerated = 0
% 0.79/1.19 showkept = 0
% 0.79/1.19 showselected = 0
% 0.79/1.19 showdeleted = 0
% 0.79/1.19 showresimp = 1
% 0.79/1.19 showstatus = 2000
% 0.79/1.19
% 0.79/1.19 prologoutput = 0
% 0.79/1.19 nrgoals = 5000000
% 0.79/1.19 totalproof = 1
% 0.79/1.19
% 0.79/1.19 Symbols occurring in the translation:
% 0.79/1.19
% 0.79/1.19 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.79/1.19 . [1, 2] (w:1, o:107, a:1, s:1, b:0),
% 0.79/1.19 ! [4, 1] (w:0, o:98, a:1, s:1, b:0),
% 0.79/1.19 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.79/1.19 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.79/1.19 modus_ponens [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.79/1.19 is_a_theorem [38, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.79/1.19 implies [39, 2] (w:1, o:131, a:1, s:1, b:0),
% 0.79/1.19 substitution_of_equivalents [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.79/1.19 equiv [41, 2] (w:1, o:132, a:1, s:1, b:0),
% 0.79/1.19 modus_tollens [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.79/1.19 not [43, 1] (w:1, o:104, a:1, s:1, b:0),
% 0.79/1.19 implies_1 [44, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.79/1.19 implies_2 [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.79/1.19 implies_3 [46, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.79/1.19 and_1 [48, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.79/1.19 and [49, 2] (w:1, o:133, a:1, s:1, b:0),
% 0.79/1.19 and_2 [50, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.79/1.19 and_3 [51, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.79/1.19 or_1 [52, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.79/1.19 or [53, 2] (w:1, o:134, a:1, s:1, b:0),
% 0.79/1.19 or_2 [54, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.79/1.19 or_3 [55, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.79/1.19 equivalence_1 [56, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.79/1.19 equivalence_2 [57, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.79/1.19 equivalence_3 [58, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.79/1.19 kn1 [59, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.79/1.19 kn2 [61, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.79/1.19 kn3 [63, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.79/1.19 cn1 [65, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.79/1.19 cn2 [66, 0] (w:1, o:36, a:1, s:1, b:0),
% 0.79/1.19 cn3 [67, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.79/1.19 r1 [68, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.79/1.19 r2 [69, 0] (w:1, o:10, a:1, s:1, b:0),
% 1.45/1.86 r3 [70, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.45/1.86 r4 [71, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.45/1.86 r5 [72, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.45/1.86 op_or [73, 0] (w:1, o:38, a:1, s:1, b:0),
% 1.45/1.86 op_and [74, 0] (w:1, o:39, a:1, s:1, b:0),
% 1.45/1.86 op_implies_and [75, 0] (w:1, o:40, a:1, s:1, b:0),
% 1.45/1.86 op_implies_or [76, 0] (w:1, o:41, a:1, s:1, b:0),
% 1.45/1.86 op_equiv [77, 0] (w:1, o:42, a:1, s:1, b:0),
% 1.45/1.86 op_implies [78, 0] (w:1, o:43, a:1, s:1, b:0),
% 1.45/1.86 alpha1 [79, 1] (w:1, o:105, a:1, s:1, b:1),
% 1.45/1.86 skol1 [80, 0] (w:1, o:44, a:1, s:1, b:1),
% 1.45/1.86 skol2 [81, 1] (w:1, o:106, a:1, s:1, b:1),
% 1.45/1.86 skol3 [82, 0] (w:1, o:55, a:1, s:1, b:1),
% 1.45/1.86 skol4 [83, 0] (w:1, o:66, a:1, s:1, b:1),
% 1.45/1.86 skol5 [84, 0] (w:1, o:77, a:1, s:1, b:1),
% 1.45/1.86 skol6 [85, 0] (w:1, o:84, a:1, s:1, b:1),
% 1.45/1.86 skol7 [86, 0] (w:1, o:85, a:1, s:1, b:1),
% 1.45/1.86 skol8 [87, 0] (w:1, o:86, a:1, s:1, b:1),
% 1.45/1.86 skol9 [88, 0] (w:1, o:87, a:1, s:1, b:1),
% 1.45/1.86 skol10 [89, 0] (w:1, o:88, a:1, s:1, b:1),
% 1.45/1.86 skol11 [90, 0] (w:1, o:89, a:1, s:1, b:1),
% 1.45/1.86 skol12 [91, 0] (w:1, o:90, a:1, s:1, b:1),
% 1.45/1.86 skol13 [92, 0] (w:1, o:91, a:1, s:1, b:1),
% 1.45/1.86 skol14 [93, 0] (w:1, o:92, a:1, s:1, b:1),
% 1.45/1.86 skol15 [94, 0] (w:1, o:93, a:1, s:1, b:1),
% 1.45/1.86 skol16 [95, 0] (w:1, o:94, a:1, s:1, b:1),
% 1.45/1.86 skol17 [96, 0] (w:1, o:95, a:1, s:1, b:1),
% 1.45/1.86 skol18 [97, 0] (w:1, o:96, a:1, s:1, b:1),
% 1.45/1.86 skol19 [98, 0] (w:1, o:97, a:1, s:1, b:1),
% 1.45/1.86 skol20 [99, 0] (w:1, o:45, a:1, s:1, b:1),
% 1.45/1.86 skol21 [100, 0] (w:1, o:46, a:1, s:1, b:1),
% 1.45/1.86 skol22 [101, 0] (w:1, o:47, a:1, s:1, b:1),
% 1.45/1.86 skol23 [102, 0] (w:1, o:48, a:1, s:1, b:1),
% 1.45/1.86 skol24 [103, 0] (w:1, o:49, a:1, s:1, b:1),
% 1.45/1.86 skol25 [104, 0] (w:1, o:50, a:1, s:1, b:1),
% 1.45/1.86 skol26 [105, 0] (w:1, o:51, a:1, s:1, b:1),
% 1.45/1.86 skol27 [106, 0] (w:1, o:52, a:1, s:1, b:1),
% 1.45/1.86 skol28 [107, 0] (w:1, o:53, a:1, s:1, b:1),
% 1.45/1.86 skol29 [108, 0] (w:1, o:54, a:1, s:1, b:1),
% 1.45/1.86 skol30 [109, 0] (w:1, o:56, a:1, s:1, b:1),
% 1.45/1.86 skol31 [110, 0] (w:1, o:57, a:1, s:1, b:1),
% 1.45/1.86 skol32 [111, 0] (w:1, o:58, a:1, s:1, b:1),
% 1.45/1.86 skol33 [112, 0] (w:1, o:59, a:1, s:1, b:1),
% 1.45/1.86 skol34 [113, 0] (w:1, o:60, a:1, s:1, b:1),
% 1.45/1.86 skol35 [114, 0] (w:1, o:61, a:1, s:1, b:1),
% 1.45/1.86 skol36 [115, 0] (w:1, o:62, a:1, s:1, b:1),
% 1.45/1.86 skol37 [116, 0] (w:1, o:63, a:1, s:1, b:1),
% 1.45/1.86 skol38 [117, 0] (w:1, o:64, a:1, s:1, b:1),
% 1.45/1.86 skol39 [118, 0] (w:1, o:65, a:1, s:1, b:1),
% 1.45/1.86 skol40 [119, 0] (w:1, o:67, a:1, s:1, b:1),
% 1.45/1.86 skol41 [120, 0] (w:1, o:68, a:1, s:1, b:1),
% 1.45/1.86 skol42 [121, 0] (w:1, o:69, a:1, s:1, b:1),
% 1.45/1.86 skol43 [122, 0] (w:1, o:70, a:1, s:1, b:1),
% 1.45/1.86 skol44 [123, 0] (w:1, o:71, a:1, s:1, b:1),
% 1.45/1.86 skol45 [124, 0] (w:1, o:72, a:1, s:1, b:1),
% 1.45/1.86 skol46 [125, 0] (w:1, o:73, a:1, s:1, b:1),
% 1.45/1.86 skol47 [126, 0] (w:1, o:74, a:1, s:1, b:1),
% 1.45/1.86 skol48 [127, 0] (w:1, o:75, a:1, s:1, b:1),
% 1.45/1.86 skol49 [128, 0] (w:1, o:76, a:1, s:1, b:1),
% 1.45/1.86 skol50 [129, 0] (w:1, o:78, a:1, s:1, b:1),
% 1.45/1.86 skol51 [130, 0] (w:1, o:79, a:1, s:1, b:1),
% 1.45/1.86 skol52 [131, 0] (w:1, o:80, a:1, s:1, b:1),
% 1.45/1.86 skol53 [132, 0] (w:1, o:81, a:1, s:1, b:1),
% 1.45/1.86 skol54 [133, 0] (w:1, o:82, a:1, s:1, b:1),
% 1.45/1.86 skol55 [134, 0] (w:1, o:83, a:1, s:1, b:1).
% 1.45/1.86
% 1.45/1.86
% 1.45/1.86 Starting Search:
% 1.45/1.86
% 1.45/1.86 *** allocated 15000 integers for clauses
% 1.45/1.86 *** allocated 22500 integers for clauses
% 1.45/1.86 *** allocated 33750 integers for clauses
% 1.45/1.86 *** allocated 50625 integers for clauses
% 1.45/1.86 *** allocated 15000 integers for termspace/termends
% 1.45/1.86 *** allocated 75937 integers for clauses
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 *** allocated 22500 integers for termspace/termends
% 1.45/1.86 *** allocated 113905 integers for clauses
% 1.45/1.86 *** allocated 33750 integers for termspace/termends
% 1.45/1.86
% 1.45/1.86 Intermediate Status:
% 1.45/1.86 Generated: 3829
% 1.45/1.86 Kept: 2045
% 1.45/1.86 Inuse: 165
% 1.45/1.86 Deleted: 35
% 1.45/1.86 Deletedinuse: 3
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 *** allocated 170857 integers for clauses
% 1.45/1.86 *** allocated 50625 integers for termspace/termends
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 *** allocated 75937 integers for termspace/termends
% 1.45/1.86 *** allocated 256285 integers for clauses
% 1.45/1.86
% 1.45/1.86 Intermediate Status:
% 1.45/1.86 Generated: 7770
% 1.45/1.86 Kept: 4061
% 1.45/1.86 Inuse: 256
% 1.45/1.86 Deleted: 41
% 1.45/1.86 Deletedinuse: 6
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 *** allocated 113905 integers for termspace/termends
% 1.45/1.86
% 1.45/1.86 Intermediate Status:
% 1.45/1.86 Generated: 11625
% 1.45/1.86 Kept: 6074
% 1.45/1.86 Inuse: 323
% 1.45/1.86 Deleted: 53
% 1.45/1.86 Deletedinuse: 7
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 *** allocated 384427 integers for clauses
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 *** allocated 170857 integers for termspace/termends
% 1.45/1.86
% 1.45/1.86 Intermediate Status:
% 1.45/1.86 Generated: 15647
% 1.45/1.86 Kept: 8710
% 1.45/1.86 Inuse: 356
% 1.45/1.86 Deleted: 57
% 1.45/1.86 Deletedinuse: 7
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 *** allocated 576640 integers for clauses
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86
% 1.45/1.86 Intermediate Status:
% 1.45/1.86 Generated: 18766
% 1.45/1.86 Kept: 10714
% 1.45/1.86 Inuse: 371
% 1.45/1.86 Deleted: 57
% 1.45/1.86 Deletedinuse: 7
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 *** allocated 256285 integers for termspace/termends
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86
% 1.45/1.86 Intermediate Status:
% 1.45/1.86 Generated: 21481
% 1.45/1.86 Kept: 12741
% 1.45/1.86 Inuse: 396
% 1.45/1.86 Deleted: 59
% 1.45/1.86 Deletedinuse: 7
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 *** allocated 864960 integers for clauses
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86
% 1.45/1.86 Intermediate Status:
% 1.45/1.86 Generated: 24462
% 1.45/1.86 Kept: 14746
% 1.45/1.86 Inuse: 424
% 1.45/1.86 Deleted: 59
% 1.45/1.86 Deletedinuse: 7
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 *** allocated 384427 integers for termspace/termends
% 1.45/1.86
% 1.45/1.86 Intermediate Status:
% 1.45/1.86 Generated: 27957
% 1.45/1.86 Kept: 16771
% 1.45/1.86 Inuse: 462
% 1.45/1.86 Deleted: 59
% 1.45/1.86 Deletedinuse: 7
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86
% 1.45/1.86 Intermediate Status:
% 1.45/1.86 Generated: 31982
% 1.45/1.86 Kept: 18798
% 1.45/1.86 Inuse: 484
% 1.45/1.86 Deleted: 97
% 1.45/1.86 Deletedinuse: 20
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 Resimplifying clauses:
% 1.45/1.86 Done
% 1.45/1.86
% 1.45/1.86 Resimplifying inuse:
% 1.45/1.86
% 1.45/1.86 Bliksems!, er is een bewijs:
% 1.45/1.86 % SZS status Theorem
% 1.45/1.86 % SZS output start Refutation
% 1.45/1.86
% 1.45/1.86 (24) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( skol11, or( skol11,
% 1.45/1.86 skol36 ) ) ), or_1 }.
% 1.45/1.86 (43) {G0,W8,D5,L2,V2,M2} I { ! cn2, is_a_theorem( implies( X, implies( not
% 1.45/1.86 ( X ), Y ) ) ) }.
% 1.45/1.86 (57) {G0,W11,D5,L2,V2,M2} I { ! op_or, not( and( not( X ), not( Y ) ) ) ==>
% 1.45/1.86 or( X, Y ) }.
% 1.45/1.86 (59) {G0,W10,D5,L2,V2,M2} I { ! op_implies_and, not( and( X, not( Y ) ) )
% 1.45/1.86 ==> implies( X, Y ) }.
% 1.45/1.86 (62) {G0,W1,D1,L1,V0,M1} I { op_or }.
% 1.45/1.86 (67) {G0,W1,D1,L1,V0,M1} I { cn2 }.
% 1.45/1.86 (70) {G0,W1,D1,L1,V0,M1} I { op_implies_and }.
% 1.45/1.86 (71) {G0,W1,D1,L1,V0,M1} I { ! or_1 }.
% 1.45/1.86 (811) {G1,W6,D4,L1,V0,M1} S(24);r(71) { ! is_a_theorem( implies( skol11, or
% 1.45/1.86 ( skol11, skol36 ) ) ) }.
% 1.45/1.86 (1776) {G1,W7,D5,L1,V2,M1} S(43);r(67) { is_a_theorem( implies( X, implies
% 1.45/1.86 ( not( X ), Y ) ) ) }.
% 1.45/1.86 (2725) {G1,W10,D5,L1,V2,M1} S(57);r(62) { not( and( not( X ), not( Y ) ) )
% 1.45/1.86 ==> or( X, Y ) }.
% 1.45/1.86 (2877) {G1,W9,D5,L1,V2,M1} S(59);r(70) { not( and( X, not( Y ) ) ) ==>
% 1.45/1.86 implies( X, Y ) }.
% 1.45/1.86 (20113) {G2,W8,D4,L1,V2,M1} S(2725);d(2877) { implies( not( X ), Y ) ==> or
% 1.45/1.86 ( X, Y ) }.
% 1.45/1.86 (20651) {G3,W6,D4,L1,V2,M1} S(1776);d(20113) { is_a_theorem( implies( X, or
% 1.45/1.86 ( X, Y ) ) ) }.
% 1.45/1.86 (20654) {G4,W0,D0,L0,V0,M0} S(811);r(20651) { }.
% 1.45/1.86
% 1.45/1.86
% 1.45/1.86 % SZS output end Refutation
% 1.45/1.86 found a proof!
% 1.45/1.86
% 1.45/1.86
% 1.45/1.86 Unprocessed initial clauses:
% 1.45/1.86
% 1.45/1.86 (20656) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ), is_a_theorem
% 1.45/1.86 ( X ) }.
% 1.45/1.86 (20657) {G0,W3,D2,L2,V0,M2} { alpha1( skol1 ), modus_ponens }.
% 1.45/1.86 (20658) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol1 ), modus_ponens }.
% 1.45/1.86 (20659) {G0,W5,D3,L2,V2,M2} { ! alpha1( X ), is_a_theorem( skol2( Y ) )
% 1.45/1.86 }.
% 1.45/1.86 (20660) {G0,W7,D4,L2,V1,M2} { ! alpha1( X ), is_a_theorem( implies( skol2
% 1.45/1.86 ( X ), X ) ) }.
% 1.45/1.86 (20661) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem( implies
% 1.45/1.86 ( Y, X ) ), alpha1( X ) }.
% 1.45/1.86 (20662) {G0,W8,D3,L3,V2,M3} { ! substitution_of_equivalents, !
% 1.45/1.86 is_a_theorem( equiv( X, Y ) ), X = Y }.
% 1.45/1.86 (20663) {G0,W5,D3,L2,V0,M2} { is_a_theorem( equiv( skol3, skol28 ) ),
% 1.45/1.86 substitution_of_equivalents }.
% 1.45/1.86 (20664) {G0,W4,D2,L2,V0,M2} { ! skol3 = skol28,
% 1.45/1.86 substitution_of_equivalents }.
% 1.45/1.86 (20665) {G0,W11,D5,L2,V2,M2} { ! modus_tollens, is_a_theorem( implies(
% 1.45/1.86 implies( not( Y ), not( X ) ), implies( X, Y ) ) ) }.
% 1.45/1.86 (20666) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 1.45/1.86 skol29 ), not( skol4 ) ), implies( skol4, skol29 ) ) ), modus_tollens }.
% 1.45/1.86 (20667) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies( X,
% 1.45/1.86 implies( Y, X ) ) ) }.
% 1.45/1.86 (20668) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol5, implies(
% 1.45/1.86 skol30, skol5 ) ) ), implies_1 }.
% 1.45/1.86 (20669) {G0,W11,D5,L2,V2,M2} { ! implies_2, is_a_theorem( implies( implies
% 1.45/1.86 ( X, implies( X, Y ) ), implies( X, Y ) ) ) }.
% 1.45/1.86 (20670) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol6,
% 1.45/1.86 implies( skol6, skol31 ) ), implies( skol6, skol31 ) ) ), implies_2 }.
% 1.45/1.86 (20671) {G0,W13,D5,L2,V3,M2} { ! implies_3, is_a_theorem( implies( implies
% 1.45/1.86 ( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 1.45/1.86 (20672) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol7,
% 1.45/1.86 skol32 ), implies( implies( skol32, skol50 ), implies( skol7, skol50 ) )
% 1.45/1.86 ) ), implies_3 }.
% 1.45/1.86 (20673) {G0,W7,D4,L2,V2,M2} { ! and_1, is_a_theorem( implies( and( X, Y )
% 1.45/1.86 , X ) ) }.
% 1.45/1.86 (20674) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol8, skol33
% 1.45/1.86 ), skol8 ) ), and_1 }.
% 1.45/1.86 (20675) {G0,W7,D4,L2,V2,M2} { ! and_2, is_a_theorem( implies( and( X, Y )
% 1.45/1.86 , Y ) ) }.
% 1.45/1.86 (20676) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol9, skol34
% 1.45/1.86 ), skol34 ) ), and_2 }.
% 1.45/1.86 (20677) {G0,W9,D5,L2,V2,M2} { ! and_3, is_a_theorem( implies( X, implies(
% 1.45/1.86 Y, and( X, Y ) ) ) ) }.
% 1.45/1.86 (20678) {G0,W9,D5,L2,V0,M2} { ! is_a_theorem( implies( skol10, implies(
% 1.45/1.86 skol35, and( skol10, skol35 ) ) ) ), and_3 }.
% 1.45/1.86 (20679) {G0,W7,D4,L2,V2,M2} { ! or_1, is_a_theorem( implies( X, or( X, Y )
% 1.45/1.86 ) ) }.
% 1.45/1.86 (20680) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol11, or( skol11
% 1.45/1.86 , skol36 ) ) ), or_1 }.
% 1.45/1.86 (20681) {G0,W7,D4,L2,V2,M2} { ! or_2, is_a_theorem( implies( Y, or( X, Y )
% 1.45/1.86 ) ) }.
% 1.45/1.86 (20682) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol37, or( skol12
% 1.45/1.86 , skol37 ) ) ), or_2 }.
% 1.45/1.86 (20683) {G0,W15,D6,L2,V3,M2} { ! or_3, is_a_theorem( implies( implies( X,
% 1.45/1.86 Z ), implies( implies( Y, Z ), implies( or( X, Y ), Z ) ) ) ) }.
% 1.45/1.86 (20684) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol13,
% 1.45/1.86 skol51 ), implies( implies( skol38, skol51 ), implies( or( skol13, skol38
% 1.45/1.86 ), skol51 ) ) ) ), or_3 }.
% 1.45/1.86 (20685) {G0,W9,D4,L2,V2,M2} { ! equivalence_1, is_a_theorem( implies(
% 1.45/1.86 equiv( X, Y ), implies( X, Y ) ) ) }.
% 1.45/1.86 (20686) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol14,
% 1.45/1.86 skol39 ), implies( skol14, skol39 ) ) ), equivalence_1 }.
% 1.45/1.86 (20687) {G0,W9,D4,L2,V2,M2} { ! equivalence_2, is_a_theorem( implies(
% 1.45/1.86 equiv( X, Y ), implies( Y, X ) ) ) }.
% 1.45/1.86 (20688) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol15,
% 1.45/1.86 skol40 ), implies( skol40, skol15 ) ) ), equivalence_2 }.
% 1.45/1.86 (20689) {G0,W13,D5,L2,V2,M2} { ! equivalence_3, is_a_theorem( implies(
% 1.45/1.86 implies( X, Y ), implies( implies( Y, X ), equiv( X, Y ) ) ) ) }.
% 1.45/1.86 (20690) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol16,
% 1.45/1.86 skol41 ), implies( implies( skol41, skol16 ), equiv( skol16, skol41 ) ) )
% 1.45/1.86 ), equivalence_3 }.
% 1.45/1.86 (20691) {G0,W7,D4,L2,V1,M2} { ! kn1, is_a_theorem( implies( X, and( X, X )
% 1.45/1.86 ) ) }.
% 1.45/1.86 (20692) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol17, and( skol17
% 1.45/1.86 , skol17 ) ) ), kn1 }.
% 1.45/1.86 (20693) {G0,W7,D4,L2,V2,M2} { ! kn2, is_a_theorem( implies( and( X, Y ), X
% 1.45/1.86 ) ) }.
% 1.45/1.86 (20694) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol18, skol42
% 1.45/1.86 ), skol18 ) ), kn2 }.
% 1.45/1.86 (20695) {G0,W15,D6,L2,V3,M2} { ! kn3, is_a_theorem( implies( implies( X, Y
% 1.45/1.86 ), implies( not( and( Y, Z ) ), not( and( Z, X ) ) ) ) ) }.
% 1.45/1.86 (20696) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol19,
% 1.45/1.86 skol43 ), implies( not( and( skol43, skol52 ) ), not( and( skol52, skol19
% 1.45/1.86 ) ) ) ) ), kn3 }.
% 1.45/1.86 (20697) {G0,W13,D5,L2,V3,M2} { ! cn1, is_a_theorem( implies( implies( X, Y
% 1.45/1.86 ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 1.45/1.86 (20698) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol20,
% 1.45/1.86 skol44 ), implies( implies( skol44, skol53 ), implies( skol20, skol53 ) )
% 1.45/1.86 ) ), cn1 }.
% 1.45/1.86 (20699) {G0,W8,D5,L2,V2,M2} { ! cn2, is_a_theorem( implies( X, implies(
% 1.45/1.86 not( X ), Y ) ) ) }.
% 1.45/1.86 (20700) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( skol21, implies(
% 1.45/1.86 not( skol21 ), skol45 ) ) ), cn2 }.
% 1.45/1.86 (20701) {G0,W8,D5,L2,V1,M2} { ! cn3, is_a_theorem( implies( implies( not(
% 1.45/1.86 X ), X ), X ) ) }.
% 1.45/1.86 (20702) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not(
% 1.45/1.86 skol22 ), skol22 ), skol22 ) ), cn3 }.
% 1.45/1.86 (20703) {G0,W7,D4,L2,V1,M2} { ! r1, is_a_theorem( implies( or( X, X ), X )
% 1.45/1.86 ) }.
% 1.45/1.86 (20704) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol23, skol23
% 1.45/1.86 ), skol23 ) ), r1 }.
% 1.45/1.86 (20705) {G0,W7,D4,L2,V2,M2} { ! r2, is_a_theorem( implies( Y, or( X, Y ) )
% 1.45/1.86 ) }.
% 1.45/1.86 (20706) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol46, or( skol24
% 1.45/1.86 , skol46 ) ) ), r2 }.
% 1.45/1.86 (20707) {G0,W9,D4,L2,V2,M2} { ! r3, is_a_theorem( implies( or( X, Y ), or
% 1.45/1.86 ( Y, X ) ) ) }.
% 1.45/1.86 (20708) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol25, skol47
% 1.45/1.86 ), or( skol47, skol25 ) ) ), r3 }.
% 1.45/1.86 (20709) {G0,W13,D5,L2,V3,M2} { ! r4, is_a_theorem( implies( or( X, or( Y,
% 1.45/1.86 Z ) ), or( Y, or( X, Z ) ) ) ) }.
% 1.45/1.86 (20710) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( or( skol26, or(
% 1.45/1.86 skol48, skol54 ) ), or( skol48, or( skol26, skol54 ) ) ) ), r4 }.
% 1.45/1.86 (20711) {G0,W13,D5,L2,V3,M2} { ! r5, is_a_theorem( implies( implies( Y, Z
% 1.45/1.86 ), implies( or( X, Y ), or( X, Z ) ) ) ) }.
% 1.45/1.86 (20712) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol49,
% 1.45/1.86 skol55 ), implies( or( skol27, skol49 ), or( skol27, skol55 ) ) ) ), r5
% 1.45/1.86 }.
% 1.45/1.86 (20713) {G0,W11,D5,L2,V2,M2} { ! op_or, or( X, Y ) = not( and( not( X ),
% 1.45/1.86 not( Y ) ) ) }.
% 1.45/1.86 (20714) {G0,W11,D5,L2,V2,M2} { ! op_and, and( X, Y ) = not( or( not( X ),
% 1.45/1.86 not( Y ) ) ) }.
% 1.45/1.86 (20715) {G0,W10,D5,L2,V2,M2} { ! op_implies_and, implies( X, Y ) = not(
% 1.45/1.86 and( X, not( Y ) ) ) }.
% 1.45/1.86 (20716) {G0,W9,D4,L2,V2,M2} { ! op_implies_or, implies( X, Y ) = or( not(
% 1.45/1.86 X ), Y ) }.
% 1.45/1.86 (20717) {G0,W12,D4,L2,V2,M2} { ! op_equiv, equiv( X, Y ) = and( implies( X
% 1.45/1.86 , Y ), implies( Y, X ) ) }.
% 1.45/1.86 (20718) {G0,W1,D1,L1,V0,M1} { op_or }.
% 1.45/1.86 (20719) {G0,W1,D1,L1,V0,M1} { op_implies }.
% 1.45/1.86 (20720) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 1.45/1.86 (20721) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 1.45/1.86 (20722) {G0,W1,D1,L1,V0,M1} { cn1 }.
% 1.45/1.86 (20723) {G0,W1,D1,L1,V0,M1} { cn2 }.
% 1.45/1.86 (20724) {G0,W1,D1,L1,V0,M1} { cn3 }.
% 1.45/1.86 (20725) {G0,W1,D1,L1,V0,M1} { substitution_of_equivalents }.
% 1.45/1.86 (20726) {G0,W1,D1,L1,V0,M1} { op_or }.
% 1.45/1.86 (20727) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 1.45/1.86 (20728) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 1.45/1.86 (20729) {G0,W1,D1,L1,V0,M1} { ! or_1 }.
% 1.45/1.86
% 1.45/1.86
% 1.45/1.86 Total Proof:
% 1.45/1.86
% 1.45/1.86 subsumption: (24) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( skol11,
% 1.45/1.86 or( skol11, skol36 ) ) ), or_1 }.
% 1.45/1.86 parent0: (20680) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol11, or
% 1.45/1.86 ( skol11, skol36 ) ) ), or_1 }.
% 1.45/1.86 substitution0:
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 1 ==> 1
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (43) {G0,W8,D5,L2,V2,M2} I { ! cn2, is_a_theorem( implies( X,
% 1.45/1.86 implies( not( X ), Y ) ) ) }.
% 1.45/1.86 parent0: (20699) {G0,W8,D5,L2,V2,M2} { ! cn2, is_a_theorem( implies( X,
% 1.45/1.86 implies( not( X ), Y ) ) ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 1 ==> 1
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 eqswap: (20736) {G0,W11,D5,L2,V2,M2} { not( and( not( X ), not( Y ) ) ) =
% 1.45/1.86 or( X, Y ), ! op_or }.
% 1.45/1.86 parent0[1]: (20713) {G0,W11,D5,L2,V2,M2} { ! op_or, or( X, Y ) = not( and
% 1.45/1.86 ( not( X ), not( Y ) ) ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (57) {G0,W11,D5,L2,V2,M2} I { ! op_or, not( and( not( X ), not
% 1.45/1.86 ( Y ) ) ) ==> or( X, Y ) }.
% 1.45/1.86 parent0: (20736) {G0,W11,D5,L2,V2,M2} { not( and( not( X ), not( Y ) ) ) =
% 1.45/1.86 or( X, Y ), ! op_or }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 1
% 1.45/1.86 1 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 eqswap: (20741) {G0,W10,D5,L2,V2,M2} { not( and( X, not( Y ) ) ) = implies
% 1.45/1.86 ( X, Y ), ! op_implies_and }.
% 1.45/1.86 parent0[1]: (20715) {G0,W10,D5,L2,V2,M2} { ! op_implies_and, implies( X, Y
% 1.45/1.86 ) = not( and( X, not( Y ) ) ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (59) {G0,W10,D5,L2,V2,M2} I { ! op_implies_and, not( and( X,
% 1.45/1.86 not( Y ) ) ) ==> implies( X, Y ) }.
% 1.45/1.86 parent0: (20741) {G0,W10,D5,L2,V2,M2} { not( and( X, not( Y ) ) ) =
% 1.45/1.86 implies( X, Y ), ! op_implies_and }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 1
% 1.45/1.86 1 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (62) {G0,W1,D1,L1,V0,M1} I { op_or }.
% 1.45/1.86 parent0: (20718) {G0,W1,D1,L1,V0,M1} { op_or }.
% 1.45/1.86 substitution0:
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (67) {G0,W1,D1,L1,V0,M1} I { cn2 }.
% 1.45/1.86 parent0: (20723) {G0,W1,D1,L1,V0,M1} { cn2 }.
% 1.45/1.86 substitution0:
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (70) {G0,W1,D1,L1,V0,M1} I { op_implies_and }.
% 1.45/1.86 parent0: (20727) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 1.45/1.86 substitution0:
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (71) {G0,W1,D1,L1,V0,M1} I { ! or_1 }.
% 1.45/1.86 parent0: (20729) {G0,W1,D1,L1,V0,M1} { ! or_1 }.
% 1.45/1.86 substitution0:
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 resolution: (20770) {G1,W6,D4,L1,V0,M1} { ! is_a_theorem( implies( skol11
% 1.45/1.86 , or( skol11, skol36 ) ) ) }.
% 1.45/1.86 parent0[0]: (71) {G0,W1,D1,L1,V0,M1} I { ! or_1 }.
% 1.45/1.86 parent1[1]: (24) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( skol11,
% 1.45/1.86 or( skol11, skol36 ) ) ), or_1 }.
% 1.45/1.86 substitution0:
% 1.45/1.86 end
% 1.45/1.86 substitution1:
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (811) {G1,W6,D4,L1,V0,M1} S(24);r(71) { ! is_a_theorem(
% 1.45/1.86 implies( skol11, or( skol11, skol36 ) ) ) }.
% 1.45/1.86 parent0: (20770) {G1,W6,D4,L1,V0,M1} { ! is_a_theorem( implies( skol11, or
% 1.45/1.86 ( skol11, skol36 ) ) ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 resolution: (20771) {G1,W7,D5,L1,V2,M1} { is_a_theorem( implies( X,
% 1.45/1.86 implies( not( X ), Y ) ) ) }.
% 1.45/1.86 parent0[0]: (43) {G0,W8,D5,L2,V2,M2} I { ! cn2, is_a_theorem( implies( X,
% 1.45/1.86 implies( not( X ), Y ) ) ) }.
% 1.45/1.86 parent1[0]: (67) {G0,W1,D1,L1,V0,M1} I { cn2 }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 substitution1:
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (1776) {G1,W7,D5,L1,V2,M1} S(43);r(67) { is_a_theorem( implies
% 1.45/1.86 ( X, implies( not( X ), Y ) ) ) }.
% 1.45/1.86 parent0: (20771) {G1,W7,D5,L1,V2,M1} { is_a_theorem( implies( X, implies(
% 1.45/1.86 not( X ), Y ) ) ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 resolution: (20773) {G1,W10,D5,L1,V2,M1} { not( and( not( X ), not( Y ) )
% 1.45/1.86 ) ==> or( X, Y ) }.
% 1.45/1.86 parent0[0]: (57) {G0,W11,D5,L2,V2,M2} I { ! op_or, not( and( not( X ), not
% 1.45/1.86 ( Y ) ) ) ==> or( X, Y ) }.
% 1.45/1.86 parent1[0]: (62) {G0,W1,D1,L1,V0,M1} I { op_or }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 substitution1:
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (2725) {G1,W10,D5,L1,V2,M1} S(57);r(62) { not( and( not( X ),
% 1.45/1.86 not( Y ) ) ) ==> or( X, Y ) }.
% 1.45/1.86 parent0: (20773) {G1,W10,D5,L1,V2,M1} { not( and( not( X ), not( Y ) ) )
% 1.45/1.86 ==> or( X, Y ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 resolution: (20776) {G1,W9,D5,L1,V2,M1} { not( and( X, not( Y ) ) ) ==>
% 1.45/1.86 implies( X, Y ) }.
% 1.45/1.86 parent0[0]: (59) {G0,W10,D5,L2,V2,M2} I { ! op_implies_and, not( and( X,
% 1.45/1.86 not( Y ) ) ) ==> implies( X, Y ) }.
% 1.45/1.86 parent1[0]: (70) {G0,W1,D1,L1,V0,M1} I { op_implies_and }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 substitution1:
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (2877) {G1,W9,D5,L1,V2,M1} S(59);r(70) { not( and( X, not( Y )
% 1.45/1.86 ) ) ==> implies( X, Y ) }.
% 1.45/1.86 parent0: (20776) {G1,W9,D5,L1,V2,M1} { not( and( X, not( Y ) ) ) ==>
% 1.45/1.86 implies( X, Y ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 paramod: (20780) {G2,W8,D4,L1,V2,M1} { implies( not( X ), Y ) ==> or( X, Y
% 1.45/1.86 ) }.
% 1.45/1.86 parent0[0]: (2877) {G1,W9,D5,L1,V2,M1} S(59);r(70) { not( and( X, not( Y )
% 1.45/1.86 ) ) ==> implies( X, Y ) }.
% 1.45/1.86 parent1[0; 1]: (2725) {G1,W10,D5,L1,V2,M1} S(57);r(62) { not( and( not( X )
% 1.45/1.86 , not( Y ) ) ) ==> or( X, Y ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := not( X )
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 substitution1:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (20113) {G2,W8,D4,L1,V2,M1} S(2725);d(2877) { implies( not( X
% 1.45/1.86 ), Y ) ==> or( X, Y ) }.
% 1.45/1.86 parent0: (20780) {G2,W8,D4,L1,V2,M1} { implies( not( X ), Y ) ==> or( X, Y
% 1.45/1.86 ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 paramod: (20783) {G2,W6,D4,L1,V2,M1} { is_a_theorem( implies( X, or( X, Y
% 1.45/1.86 ) ) ) }.
% 1.45/1.86 parent0[0]: (20113) {G2,W8,D4,L1,V2,M1} S(2725);d(2877) { implies( not( X )
% 1.45/1.86 , Y ) ==> or( X, Y ) }.
% 1.45/1.86 parent1[0; 3]: (1776) {G1,W7,D5,L1,V2,M1} S(43);r(67) { is_a_theorem(
% 1.45/1.86 implies( X, implies( not( X ), Y ) ) ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 substitution1:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (20651) {G3,W6,D4,L1,V2,M1} S(1776);d(20113) { is_a_theorem(
% 1.45/1.86 implies( X, or( X, Y ) ) ) }.
% 1.45/1.86 parent0: (20783) {G2,W6,D4,L1,V2,M1} { is_a_theorem( implies( X, or( X, Y
% 1.45/1.86 ) ) ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 X := X
% 1.45/1.86 Y := Y
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 0 ==> 0
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 resolution: (20784) {G2,W0,D0,L0,V0,M0} { }.
% 1.45/1.86 parent0[0]: (811) {G1,W6,D4,L1,V0,M1} S(24);r(71) { ! is_a_theorem( implies
% 1.45/1.86 ( skol11, or( skol11, skol36 ) ) ) }.
% 1.45/1.86 parent1[0]: (20651) {G3,W6,D4,L1,V2,M1} S(1776);d(20113) { is_a_theorem(
% 1.45/1.86 implies( X, or( X, Y ) ) ) }.
% 1.45/1.86 substitution0:
% 1.45/1.86 end
% 1.45/1.86 substitution1:
% 1.45/1.86 X := skol11
% 1.45/1.86 Y := skol36
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 subsumption: (20654) {G4,W0,D0,L0,V0,M0} S(811);r(20651) { }.
% 1.45/1.86 parent0: (20784) {G2,W0,D0,L0,V0,M0} { }.
% 1.45/1.86 substitution0:
% 1.45/1.86 end
% 1.45/1.86 permutation0:
% 1.45/1.86 end
% 1.45/1.86
% 1.45/1.86 Proof check complete!
% 1.45/1.86
% 1.45/1.86 Memory use:
% 1.45/1.86
% 1.45/1.86 space for terms: 316916
% 1.45/1.86 space for clauses: 841492
% 1.45/1.86
% 1.45/1.86
% 1.45/1.86 clauses generated: 36128
% 1.45/1.86 clauses kept: 20655
% 1.45/1.86 clauses selected: 506
% 1.45/1.86 clauses deleted: 1117
% 1.45/1.86 clauses inuse deleted: 85
% 1.45/1.86
% 1.45/1.86 subsentry: 86326
% 1.45/1.86 literals s-matched: 55675
% 1.45/1.86 literals matched: 55646
% 1.45/1.86 full subsumption: 10848
% 1.45/1.86
% 1.45/1.86 checksum: 705313960
% 1.45/1.86
% 1.45/1.86
% 1.45/1.86 Bliksem ended
%------------------------------------------------------------------------------