TSTP Solution File: LCL506+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL506+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 07:54:16 EDT 2022
% Result : Theorem 0.69s 1.08s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL506+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jul 4 21:00:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.69/1.08 *** allocated 10000 integers for termspace/termends
% 0.69/1.08 *** allocated 10000 integers for clauses
% 0.69/1.08 *** allocated 10000 integers for justifications
% 0.69/1.08 Bliksem 1.12
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Automatic Strategy Selection
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Clauses:
% 0.69/1.08
% 0.69/1.08 { ! modus_ponens, ! alpha1( X ), is_a_theorem( X ) }.
% 0.69/1.08 { alpha1( skol1 ), modus_ponens }.
% 0.69/1.08 { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.69/1.08 { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.69/1.08 { ! alpha1( X ), is_a_theorem( implies( skol2( X ), X ) ) }.
% 0.69/1.08 { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.69/1.08 { ! substitution_of_equivalents, ! is_a_theorem( equiv( X, Y ) ), X = Y }.
% 0.69/1.08 { is_a_theorem( equiv( skol3, skol28 ) ), substitution_of_equivalents }.
% 0.69/1.08 { ! skol3 = skol28, substitution_of_equivalents }.
% 0.69/1.08 { ! modus_tollens, is_a_theorem( implies( implies( not( Y ), not( X ) ),
% 0.69/1.08 implies( X, Y ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( implies( not( skol29 ), not( skol4 ) ), implies
% 0.69/1.08 ( skol4, skol29 ) ) ), modus_tollens }.
% 0.69/1.08 { ! implies_1, is_a_theorem( implies( X, implies( Y, X ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( skol5, implies( skol30, skol5 ) ) ), implies_1 }
% 0.69/1.08 .
% 0.69/1.08 { ! implies_2, is_a_theorem( implies( implies( X, implies( X, Y ) ),
% 0.69/1.08 implies( X, Y ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( implies( skol6, implies( skol6, skol31 ) ),
% 0.69/1.08 implies( skol6, skol31 ) ) ), implies_2 }.
% 0.69/1.08 { ! implies_3, is_a_theorem( implies( implies( X, Y ), implies( implies( Y
% 0.69/1.08 , Z ), implies( X, Z ) ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( implies( skol7, skol32 ), implies( implies(
% 0.69/1.08 skol32, skol50 ), implies( skol7, skol50 ) ) ) ), implies_3 }.
% 0.69/1.08 { ! and_1, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( and( skol8, skol33 ), skol8 ) ), and_1 }.
% 0.69/1.08 { ! and_2, is_a_theorem( implies( and( X, Y ), Y ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( and( skol9, skol34 ), skol34 ) ), and_2 }.
% 0.69/1.08 { ! and_3, is_a_theorem( implies( X, implies( Y, and( X, Y ) ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( skol10, implies( skol35, and( skol10, skol35 ) )
% 0.69/1.08 ) ), and_3 }.
% 0.69/1.08 { ! or_1, is_a_theorem( implies( X, or( X, Y ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( skol11, or( skol11, skol36 ) ) ), or_1 }.
% 0.69/1.08 { ! or_2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( skol37, or( skol12, skol37 ) ) ), or_2 }.
% 0.69/1.08 { ! or_3, is_a_theorem( implies( implies( X, Z ), implies( implies( Y, Z )
% 0.69/1.08 , implies( or( X, Y ), Z ) ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( implies( skol13, skol51 ), implies( implies(
% 0.69/1.08 skol38, skol51 ), implies( or( skol13, skol38 ), skol51 ) ) ) ), or_3 }.
% 0.69/1.08 { ! equivalence_1, is_a_theorem( implies( equiv( X, Y ), implies( X, Y ) )
% 0.69/1.08 ) }.
% 0.69/1.08 { ! is_a_theorem( implies( equiv( skol14, skol39 ), implies( skol14, skol39
% 0.69/1.08 ) ) ), equivalence_1 }.
% 0.69/1.08 { ! equivalence_2, is_a_theorem( implies( equiv( X, Y ), implies( Y, X ) )
% 0.69/1.08 ) }.
% 0.69/1.08 { ! is_a_theorem( implies( equiv( skol15, skol40 ), implies( skol40, skol15
% 0.69/1.08 ) ) ), equivalence_2 }.
% 0.69/1.08 { ! equivalence_3, is_a_theorem( implies( implies( X, Y ), implies( implies
% 0.69/1.08 ( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( implies( skol16, skol41 ), implies( implies(
% 0.69/1.08 skol41, skol16 ), equiv( skol16, skol41 ) ) ) ), equivalence_3 }.
% 0.69/1.08 { ! kn1, is_a_theorem( implies( X, and( X, X ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( skol17, and( skol17, skol17 ) ) ), kn1 }.
% 0.69/1.08 { ! kn2, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( and( skol18, skol42 ), skol18 ) ), kn2 }.
% 0.69/1.08 { ! kn3, is_a_theorem( implies( implies( X, Y ), implies( not( and( Y, Z )
% 0.69/1.08 ), not( and( Z, X ) ) ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( implies( skol19, skol43 ), implies( not( and(
% 0.69/1.08 skol43, skol52 ) ), not( and( skol52, skol19 ) ) ) ) ), kn3 }.
% 0.69/1.08 { ! cn1, is_a_theorem( implies( implies( X, Y ), implies( implies( Y, Z ),
% 0.69/1.08 implies( X, Z ) ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( implies( skol20, skol44 ), implies( implies(
% 0.69/1.08 skol44, skol53 ), implies( skol20, skol53 ) ) ) ), cn1 }.
% 0.69/1.08 { ! cn2, is_a_theorem( implies( X, implies( not( X ), Y ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( skol21, implies( not( skol21 ), skol45 ) ) ),
% 0.69/1.08 cn2 }.
% 0.69/1.08 { ! cn3, is_a_theorem( implies( implies( not( X ), X ), X ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( implies( not( skol22 ), skol22 ), skol22 ) ),
% 0.69/1.08 cn3 }.
% 0.69/1.08 { ! r1, is_a_theorem( implies( or( X, X ), X ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( or( skol23, skol23 ), skol23 ) ), r1 }.
% 0.69/1.08 { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( skol46, or( skol24, skol46 ) ) ), r2 }.
% 0.69/1.08 { ! r3, is_a_theorem( implies( or( X, Y ), or( Y, X ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( or( skol25, skol47 ), or( skol47, skol25 ) ) ),
% 0.69/1.08 r3 }.
% 0.69/1.08 { ! r4, is_a_theorem( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) )
% 0.69/1.08 }.
% 0.69/1.08 { ! is_a_theorem( implies( or( skol26, or( skol48, skol54 ) ), or( skol48,
% 0.69/1.08 or( skol26, skol54 ) ) ) ), r4 }.
% 0.69/1.08 { ! r5, is_a_theorem( implies( implies( Y, Z ), implies( or( X, Y ), or( X
% 0.69/1.08 , Z ) ) ) ) }.
% 0.69/1.08 { ! is_a_theorem( implies( implies( skol49, skol55 ), implies( or( skol27,
% 0.69/1.08 skol49 ), or( skol27, skol55 ) ) ) ), r5 }.
% 0.69/1.08 { ! op_or, or( X, Y ) = not( and( not( X ), not( Y ) ) ) }.
% 0.69/1.08 { ! op_and, and( X, Y ) = not( or( not( X ), not( Y ) ) ) }.
% 0.69/1.08 { ! op_implies_and, implies( X, Y ) = not( and( X, not( Y ) ) ) }.
% 0.69/1.08 { ! op_implies_or, implies( X, Y ) = or( not( X ), Y ) }.
% 0.69/1.08 { ! op_equiv, equiv( X, Y ) = and( implies( X, Y ), implies( Y, X ) ) }.
% 0.69/1.08 { op_or }.
% 0.69/1.08 { op_implies_and }.
% 0.69/1.08 { op_equiv }.
% 0.69/1.08 { modus_ponens }.
% 0.69/1.08 { kn1 }.
% 0.69/1.08 { kn2 }.
% 0.69/1.08 { kn3 }.
% 0.69/1.08 { substitution_of_equivalents }.
% 0.69/1.08 { op_or }.
% 0.69/1.08 { op_implies_and }.
% 0.69/1.08 { op_equiv }.
% 0.69/1.08 { ! and_1 }.
% 0.69/1.08
% 0.69/1.08 percentage equality = 0.051471, percentage horn = 0.971831
% 0.69/1.08 This is a problem with some equality
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Options Used:
% 0.69/1.08
% 0.69/1.08 useres = 1
% 0.69/1.08 useparamod = 1
% 0.69/1.08 useeqrefl = 1
% 0.69/1.08 useeqfact = 1
% 0.69/1.08 usefactor = 1
% 0.69/1.08 usesimpsplitting = 0
% 0.69/1.08 usesimpdemod = 5
% 0.69/1.08 usesimpres = 3
% 0.69/1.08
% 0.69/1.08 resimpinuse = 1000
% 0.69/1.08 resimpclauses = 20000
% 0.69/1.08 substype = eqrewr
% 0.69/1.08 backwardsubs = 1
% 0.69/1.08 selectoldest = 5
% 0.69/1.08
% 0.69/1.08 litorderings [0] = split
% 0.69/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.69/1.08
% 0.69/1.08 termordering = kbo
% 0.69/1.08
% 0.69/1.08 litapriori = 0
% 0.69/1.08 termapriori = 1
% 0.69/1.08 litaposteriori = 0
% 0.69/1.08 termaposteriori = 0
% 0.69/1.08 demodaposteriori = 0
% 0.69/1.08 ordereqreflfact = 0
% 0.69/1.08
% 0.69/1.08 litselect = negord
% 0.69/1.08
% 0.69/1.08 maxweight = 15
% 0.69/1.08 maxdepth = 30000
% 0.69/1.08 maxlength = 115
% 0.69/1.08 maxnrvars = 195
% 0.69/1.08 excuselevel = 1
% 0.69/1.08 increasemaxweight = 1
% 0.69/1.08
% 0.69/1.08 maxselected = 10000000
% 0.69/1.08 maxnrclauses = 10000000
% 0.69/1.08
% 0.69/1.08 showgenerated = 0
% 0.69/1.08 showkept = 0
% 0.69/1.08 showselected = 0
% 0.69/1.08 showdeleted = 0
% 0.69/1.08 showresimp = 1
% 0.69/1.08 showstatus = 2000
% 0.69/1.08
% 0.69/1.08 prologoutput = 0
% 0.69/1.08 nrgoals = 5000000
% 0.69/1.08 totalproof = 1
% 0.69/1.08
% 0.69/1.08 Symbols occurring in the translation:
% 0.69/1.08
% 0.69/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.08 . [1, 2] (w:1, o:106, a:1, s:1, b:0),
% 0.69/1.08 ! [4, 1] (w:0, o:97, a:1, s:1, b:0),
% 0.69/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.08 modus_ponens [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.69/1.08 is_a_theorem [38, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.69/1.08 implies [39, 2] (w:1, o:130, a:1, s:1, b:0),
% 0.69/1.08 substitution_of_equivalents [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.69/1.08 equiv [41, 2] (w:1, o:131, a:1, s:1, b:0),
% 0.69/1.08 modus_tollens [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.69/1.08 not [43, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.69/1.08 implies_1 [44, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.69/1.08 implies_2 [45, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.69/1.08 implies_3 [46, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.69/1.08 and_1 [48, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.69/1.08 and [49, 2] (w:1, o:132, a:1, s:1, b:0),
% 0.69/1.08 and_2 [50, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.69/1.08 and_3 [51, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.69/1.08 or_1 [52, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.69/1.08 or [53, 2] (w:1, o:133, a:1, s:1, b:0),
% 0.69/1.08 or_2 [54, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.69/1.08 or_3 [55, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.69/1.08 equivalence_1 [56, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.69/1.08 equivalence_2 [57, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.69/1.08 equivalence_3 [58, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.69/1.08 kn1 [59, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.69/1.08 kn2 [61, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.69/1.08 kn3 [63, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.69/1.08 cn1 [65, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.69/1.08 cn2 [66, 0] (w:1, o:36, a:1, s:1, b:0),
% 0.69/1.08 cn3 [67, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.69/1.08 r1 [68, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.69/1.08 r2 [69, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.69/1.08 r3 [70, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.69/1.08 r4 [71, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.69/1.08 r5 [72, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.69/1.08 op_or [73, 0] (w:1, o:38, a:1, s:1, b:0),
% 0.69/1.08 op_and [74, 0] (w:1, o:39, a:1, s:1, b:0),
% 0.69/1.08 op_implies_and [75, 0] (w:1, o:40, a:1, s:1, b:0),
% 0.69/1.08 op_implies_or [76, 0] (w:1, o:41, a:1, s:1, b:0),
% 0.69/1.08 op_equiv [77, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.69/1.08 alpha1 [78, 1] (w:1, o:104, a:1, s:1, b:1),
% 0.69/1.08 skol1 [79, 0] (w:1, o:43, a:1, s:1, b:1),
% 0.69/1.08 skol2 [80, 1] (w:1, o:105, a:1, s:1, b:1),
% 0.69/1.08 skol3 [81, 0] (w:1, o:54, a:1, s:1, b:1),
% 0.69/1.08 skol4 [82, 0] (w:1, o:65, a:1, s:1, b:1),
% 0.69/1.08 skol5 [83, 0] (w:1, o:76, a:1, s:1, b:1),
% 0.69/1.08 skol6 [84, 0] (w:1, o:83, a:1, s:1, b:1),
% 0.69/1.08 skol7 [85, 0] (w:1, o:84, a:1, s:1, b:1),
% 0.69/1.08 skol8 [86, 0] (w:1, o:85, a:1, s:1, b:1),
% 0.69/1.08 skol9 [87, 0] (w:1, o:86, a:1, s:1, b:1),
% 0.69/1.08 skol10 [88, 0] (w:1, o:87, a:1, s:1, b:1),
% 0.69/1.08 skol11 [89, 0] (w:1, o:88, a:1, s:1, b:1),
% 0.69/1.08 skol12 [90, 0] (w:1, o:89, a:1, s:1, b:1),
% 0.69/1.08 skol13 [91, 0] (w:1, o:90, a:1, s:1, b:1),
% 0.69/1.08 skol14 [92, 0] (w:1, o:91, a:1, s:1, b:1),
% 0.69/1.08 skol15 [93, 0] (w:1, o:92, a:1, s:1, b:1),
% 0.69/1.08 skol16 [94, 0] (w:1, o:93, a:1, s:1, b:1),
% 0.69/1.08 skol17 [95, 0] (w:1, o:94, a:1, s:1, b:1),
% 0.69/1.08 skol18 [96, 0] (w:1, o:95, a:1, s:1, b:1),
% 0.69/1.08 skol19 [97, 0] (w:1, o:96, a:1, s:1, b:1),
% 0.69/1.08 skol20 [98, 0] (w:1, o:44, a:1, s:1, b:1),
% 0.69/1.08 skol21 [99, 0] (w:1, o:45, a:1, s:1, b:1),
% 0.69/1.08 skol22 [100, 0] (w:1, o:46, a:1, s:1, b:1),
% 0.69/1.08 skol23 [101, 0] (w:1, o:47, a:1, s:1, b:1),
% 0.69/1.08 skol24 [102, 0] (w:1, o:48, a:1, s:1, b:1),
% 0.69/1.08 skol25 [103, 0] (w:1, o:49, a:1, s:1, b:1),
% 0.69/1.08 skol26 [104, 0] (w:1, o:50, a:1, s:1, b:1),
% 0.69/1.08 skol27 [105, 0] (w:1, o:51, a:1, s:1, b:1),
% 0.69/1.08 skol28 [106, 0] (w:1, o:52, a:1, s:1, b:1),
% 0.69/1.08 skol29 [107, 0] (w:1, o:53, a:1, s:1, b:1),
% 0.69/1.08 skol30 [108, 0] (w:1, o:55, a:1, s:1, b:1),
% 0.69/1.08 skol31 [109, 0] (w:1, o:56, a:1, s:1, b:1),
% 0.69/1.08 skol32 [110, 0] (w:1, o:57, a:1, s:1, b:1),
% 0.69/1.08 skol33 [111, 0] (w:1, o:58, a:1, s:1, b:1),
% 0.69/1.08 skol34 [112, 0] (w:1, o:59, a:1, s:1, b:1),
% 0.69/1.08 skol35 [113, 0] (w:1, o:60, a:1, s:1, b:1),
% 0.69/1.08 skol36 [114, 0] (w:1, o:61, a:1, s:1, b:1),
% 0.69/1.08 skol37 [115, 0] (w:1, o:62, a:1, s:1, b:1),
% 0.69/1.08 skol38 [116, 0] (w:1, o:63, a:1, s:1, b:1),
% 0.69/1.08 skol39 [117, 0] (w:1, o:64, a:1, s:1, b:1),
% 0.69/1.08 skol40 [118, 0] (w:1, o:66, a:1, s:1, b:1),
% 0.69/1.08 skol41 [119, 0] (w:1, o:67, a:1, s:1, b:1),
% 0.69/1.08 skol42 [120, 0] (w:1, o:68, a:1, s:1, b:1),
% 0.69/1.08 skol43 [121, 0] (w:1, o:69, a:1, s:1, b:1),
% 0.69/1.08 skol44 [122, 0] (w:1, o:70, a:1, s:1, b:1),
% 0.69/1.08 skol45 [123, 0] (w:1, o:71, a:1, s:1, b:1),
% 0.69/1.08 skol46 [124, 0] (w:1, o:72, a:1, s:1, b:1),
% 0.69/1.08 skol47 [125, 0] (w:1, o:73, a:1, s:1, b:1),
% 0.69/1.08 skol48 [126, 0] (w:1, o:74, a:1, s:1, b:1),
% 0.69/1.08 skol49 [127, 0] (w:1, o:75, a:1, s:1, b:1),
% 0.69/1.08 skol50 [128, 0] (w:1, o:77, a:1, s:1, b:1),
% 0.69/1.08 skol51 [129, 0] (w:1, o:78, a:1, s:1, b:1),
% 0.69/1.08 skol52 [130, 0] (w:1, o:79, a:1, s:1, b:1),
% 0.69/1.08 skol53 [131, 0] (w:1, o:80, a:1, s:1, b:1),
% 0.69/1.08 skol54 [132, 0] (w:1, o:81, a:1, s:1, b:1),
% 0.69/1.08 skol55 [133, 0] (w:1, o:82, a:1, s:1, b:1).
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Starting Search:
% 0.69/1.08
% 0.69/1.08 *** allocated 15000 integers for clauses
% 0.69/1.08 *** allocated 22500 integers for clauses
% 0.69/1.08 *** allocated 33750 integers for clauses
% 0.69/1.08 *** allocated 50625 integers for clauses
% 0.69/1.08
% 0.69/1.08 Bliksems!, er is een bewijs:
% 0.69/1.08 % SZS status Theorem
% 0.69/1.08 % SZS output start Refutation
% 0.69/1.08
% 0.69/1.08 (18) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( and( skol8, skol33 )
% 0.69/1.08 , skol8 ) ), and_1 }.
% 0.69/1.08 (37) {G0,W7,D4,L2,V2,M2} I { ! kn2, is_a_theorem( implies( and( X, Y ), X )
% 0.69/1.08 ) }.
% 0.69/1.08 (67) {G0,W1,D1,L1,V0,M1} I { kn2 }.
% 0.69/1.08 (70) {G0,W1,D1,L1,V0,M1} I { ! and_1 }.
% 0.69/1.08 (72) {G1,W6,D4,L1,V2,M1} S(37);r(67) { is_a_theorem( implies( and( X, Y ),
% 0.69/1.08 X ) ) }.
% 0.69/1.08 (592) {G2,W0,D0,L0,V0,M0} S(18);r(72);r(70) { }.
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 % SZS output end Refutation
% 0.69/1.08 found a proof!
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Unprocessed initial clauses:
% 0.69/1.08
% 0.69/1.08 (594) {G0,W5,D2,L3,V1,M3} { ! modus_ponens, ! alpha1( X ), is_a_theorem( X
% 0.69/1.08 ) }.
% 0.69/1.08 (595) {G0,W3,D2,L2,V0,M2} { alpha1( skol1 ), modus_ponens }.
% 0.69/1.08 (596) {G0,W3,D2,L2,V0,M2} { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.69/1.08 (597) {G0,W5,D3,L2,V2,M2} { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.69/1.08 (598) {G0,W7,D4,L2,V1,M2} { ! alpha1( X ), is_a_theorem( implies( skol2( X
% 0.69/1.08 ), X ) ) }.
% 0.69/1.08 (599) {G0,W8,D3,L3,V2,M3} { ! is_a_theorem( Y ), ! is_a_theorem( implies(
% 0.69/1.08 Y, X ) ), alpha1( X ) }.
% 0.69/1.08 (600) {G0,W8,D3,L3,V2,M3} { ! substitution_of_equivalents, ! is_a_theorem
% 0.69/1.08 ( equiv( X, Y ) ), X = Y }.
% 0.69/1.08 (601) {G0,W5,D3,L2,V0,M2} { is_a_theorem( equiv( skol3, skol28 ) ),
% 0.69/1.08 substitution_of_equivalents }.
% 0.69/1.08 (602) {G0,W4,D2,L2,V0,M2} { ! skol3 = skol28, substitution_of_equivalents
% 0.69/1.08 }.
% 0.69/1.08 (603) {G0,W11,D5,L2,V2,M2} { ! modus_tollens, is_a_theorem( implies(
% 0.69/1.08 implies( not( Y ), not( X ) ), implies( X, Y ) ) ) }.
% 0.69/1.08 (604) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not( skol29
% 0.69/1.08 ), not( skol4 ) ), implies( skol4, skol29 ) ) ), modus_tollens }.
% 0.69/1.08 (605) {G0,W7,D4,L2,V2,M2} { ! implies_1, is_a_theorem( implies( X, implies
% 0.69/1.08 ( Y, X ) ) ) }.
% 0.69/1.08 (606) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol5, implies(
% 0.69/1.08 skol30, skol5 ) ) ), implies_1 }.
% 0.69/1.08 (607) {G0,W11,D5,L2,V2,M2} { ! implies_2, is_a_theorem( implies( implies(
% 0.69/1.08 X, implies( X, Y ) ), implies( X, Y ) ) ) }.
% 0.69/1.08 (608) {G0,W11,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol6,
% 0.69/1.08 implies( skol6, skol31 ) ), implies( skol6, skol31 ) ) ), implies_2 }.
% 0.69/1.08 (609) {G0,W13,D5,L2,V3,M2} { ! implies_3, is_a_theorem( implies( implies(
% 0.69/1.08 X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 0.69/1.08 (610) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol7,
% 0.69/1.08 skol32 ), implies( implies( skol32, skol50 ), implies( skol7, skol50 ) )
% 0.69/1.08 ) ), implies_3 }.
% 0.69/1.08 (611) {G0,W7,D4,L2,V2,M2} { ! and_1, is_a_theorem( implies( and( X, Y ), X
% 0.69/1.08 ) ) }.
% 0.69/1.08 (612) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol8, skol33 )
% 0.69/1.08 , skol8 ) ), and_1 }.
% 0.69/1.08 (613) {G0,W7,D4,L2,V2,M2} { ! and_2, is_a_theorem( implies( and( X, Y ), Y
% 0.69/1.08 ) ) }.
% 0.69/1.08 (614) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol9, skol34 )
% 0.69/1.08 , skol34 ) ), and_2 }.
% 0.69/1.08 (615) {G0,W9,D5,L2,V2,M2} { ! and_3, is_a_theorem( implies( X, implies( Y
% 0.69/1.08 , and( X, Y ) ) ) ) }.
% 0.69/1.08 (616) {G0,W9,D5,L2,V0,M2} { ! is_a_theorem( implies( skol10, implies(
% 0.69/1.08 skol35, and( skol10, skol35 ) ) ) ), and_3 }.
% 0.69/1.08 (617) {G0,W7,D4,L2,V2,M2} { ! or_1, is_a_theorem( implies( X, or( X, Y ) )
% 0.69/1.08 ) }.
% 0.69/1.08 (618) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol11, or( skol11,
% 0.69/1.08 skol36 ) ) ), or_1 }.
% 0.69/1.08 (619) {G0,W7,D4,L2,V2,M2} { ! or_2, is_a_theorem( implies( Y, or( X, Y ) )
% 0.69/1.08 ) }.
% 0.69/1.08 (620) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol37, or( skol12,
% 0.69/1.08 skol37 ) ) ), or_2 }.
% 0.69/1.08 (621) {G0,W15,D6,L2,V3,M2} { ! or_3, is_a_theorem( implies( implies( X, Z
% 0.69/1.08 ), implies( implies( Y, Z ), implies( or( X, Y ), Z ) ) ) ) }.
% 0.69/1.08 (622) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol13,
% 0.69/1.08 skol51 ), implies( implies( skol38, skol51 ), implies( or( skol13, skol38
% 0.69/1.08 ), skol51 ) ) ) ), or_3 }.
% 0.69/1.08 (623) {G0,W9,D4,L2,V2,M2} { ! equivalence_1, is_a_theorem( implies( equiv
% 0.69/1.08 ( X, Y ), implies( X, Y ) ) ) }.
% 0.69/1.08 (624) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol14, skol39
% 0.69/1.08 ), implies( skol14, skol39 ) ) ), equivalence_1 }.
% 0.69/1.08 (625) {G0,W9,D4,L2,V2,M2} { ! equivalence_2, is_a_theorem( implies( equiv
% 0.69/1.08 ( X, Y ), implies( Y, X ) ) ) }.
% 0.69/1.08 (626) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( equiv( skol15, skol40
% 0.69/1.08 ), implies( skol40, skol15 ) ) ), equivalence_2 }.
% 0.69/1.08 (627) {G0,W13,D5,L2,V2,M2} { ! equivalence_3, is_a_theorem( implies(
% 0.69/1.08 implies( X, Y ), implies( implies( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.69/1.08 (628) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol16,
% 0.69/1.08 skol41 ), implies( implies( skol41, skol16 ), equiv( skol16, skol41 ) ) )
% 0.69/1.08 ), equivalence_3 }.
% 0.69/1.08 (629) {G0,W7,D4,L2,V1,M2} { ! kn1, is_a_theorem( implies( X, and( X, X ) )
% 0.69/1.08 ) }.
% 0.69/1.08 (630) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol17, and( skol17,
% 0.69/1.08 skol17 ) ) ), kn1 }.
% 0.69/1.08 (631) {G0,W7,D4,L2,V2,M2} { ! kn2, is_a_theorem( implies( and( X, Y ), X )
% 0.69/1.08 ) }.
% 0.69/1.08 (632) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol18, skol42 )
% 0.69/1.08 , skol18 ) ), kn2 }.
% 0.69/1.08 (633) {G0,W15,D6,L2,V3,M2} { ! kn3, is_a_theorem( implies( implies( X, Y )
% 0.69/1.08 , implies( not( and( Y, Z ) ), not( and( Z, X ) ) ) ) ) }.
% 0.69/1.08 (634) {G0,W15,D6,L2,V0,M2} { ! is_a_theorem( implies( implies( skol19,
% 0.69/1.08 skol43 ), implies( not( and( skol43, skol52 ) ), not( and( skol52, skol19
% 0.69/1.08 ) ) ) ) ), kn3 }.
% 0.69/1.08 (635) {G0,W13,D5,L2,V3,M2} { ! cn1, is_a_theorem( implies( implies( X, Y )
% 0.69/1.08 , implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 0.69/1.08 (636) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol20,
% 0.69/1.08 skol44 ), implies( implies( skol44, skol53 ), implies( skol20, skol53 ) )
% 0.69/1.08 ) ), cn1 }.
% 0.69/1.08 (637) {G0,W8,D5,L2,V2,M2} { ! cn2, is_a_theorem( implies( X, implies( not
% 0.69/1.08 ( X ), Y ) ) ) }.
% 0.69/1.08 (638) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( skol21, implies( not
% 0.69/1.08 ( skol21 ), skol45 ) ) ), cn2 }.
% 0.69/1.08 (639) {G0,W8,D5,L2,V1,M2} { ! cn3, is_a_theorem( implies( implies( not( X
% 0.69/1.08 ), X ), X ) ) }.
% 0.69/1.08 (640) {G0,W8,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( not( skol22
% 0.69/1.08 ), skol22 ), skol22 ) ), cn3 }.
% 0.69/1.08 (641) {G0,W7,D4,L2,V1,M2} { ! r1, is_a_theorem( implies( or( X, X ), X ) )
% 0.69/1.08 }.
% 0.69/1.08 (642) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol23, skol23 )
% 0.69/1.08 , skol23 ) ), r1 }.
% 0.69/1.08 (643) {G0,W7,D4,L2,V2,M2} { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) )
% 0.69/1.08 }.
% 0.69/1.08 (644) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( skol46, or( skol24,
% 0.69/1.08 skol46 ) ) ), r2 }.
% 0.69/1.08 (645) {G0,W9,D4,L2,V2,M2} { ! r3, is_a_theorem( implies( or( X, Y ), or( Y
% 0.69/1.08 , X ) ) ) }.
% 0.69/1.08 (646) {G0,W9,D4,L2,V0,M2} { ! is_a_theorem( implies( or( skol25, skol47 )
% 0.69/1.08 , or( skol47, skol25 ) ) ), r3 }.
% 0.69/1.08 (647) {G0,W13,D5,L2,V3,M2} { ! r4, is_a_theorem( implies( or( X, or( Y, Z
% 0.69/1.08 ) ), or( Y, or( X, Z ) ) ) ) }.
% 0.69/1.08 (648) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( or( skol26, or(
% 0.69/1.08 skol48, skol54 ) ), or( skol48, or( skol26, skol54 ) ) ) ), r4 }.
% 0.69/1.08 (649) {G0,W13,D5,L2,V3,M2} { ! r5, is_a_theorem( implies( implies( Y, Z )
% 0.69/1.08 , implies( or( X, Y ), or( X, Z ) ) ) ) }.
% 0.69/1.08 (650) {G0,W13,D5,L2,V0,M2} { ! is_a_theorem( implies( implies( skol49,
% 0.69/1.08 skol55 ), implies( or( skol27, skol49 ), or( skol27, skol55 ) ) ) ), r5
% 0.69/1.08 }.
% 0.69/1.08 (651) {G0,W11,D5,L2,V2,M2} { ! op_or, or( X, Y ) = not( and( not( X ), not
% 0.69/1.08 ( Y ) ) ) }.
% 0.69/1.08 (652) {G0,W11,D5,L2,V2,M2} { ! op_and, and( X, Y ) = not( or( not( X ),
% 0.69/1.08 not( Y ) ) ) }.
% 0.69/1.08 (653) {G0,W10,D5,L2,V2,M2} { ! op_implies_and, implies( X, Y ) = not( and
% 0.69/1.08 ( X, not( Y ) ) ) }.
% 0.69/1.08 (654) {G0,W9,D4,L2,V2,M2} { ! op_implies_or, implies( X, Y ) = or( not( X
% 0.69/1.08 ), Y ) }.
% 0.69/1.08 (655) {G0,W12,D4,L2,V2,M2} { ! op_equiv, equiv( X, Y ) = and( implies( X,
% 0.69/1.08 Y ), implies( Y, X ) ) }.
% 0.69/1.08 (656) {G0,W1,D1,L1,V0,M1} { op_or }.
% 0.69/1.08 (657) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 0.69/1.08 (658) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 0.69/1.08 (659) {G0,W1,D1,L1,V0,M1} { modus_ponens }.
% 0.69/1.08 (660) {G0,W1,D1,L1,V0,M1} { kn1 }.
% 0.69/1.08 (661) {G0,W1,D1,L1,V0,M1} { kn2 }.
% 0.69/1.08 (662) {G0,W1,D1,L1,V0,M1} { kn3 }.
% 0.69/1.08 (663) {G0,W1,D1,L1,V0,M1} { substitution_of_equivalents }.
% 0.69/1.08 (664) {G0,W1,D1,L1,V0,M1} { op_or }.
% 0.69/1.08 (665) {G0,W1,D1,L1,V0,M1} { op_implies_and }.
% 0.69/1.08 (666) {G0,W1,D1,L1,V0,M1} { op_equiv }.
% 0.69/1.08 (667) {G0,W1,D1,L1,V0,M1} { ! and_1 }.
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Total Proof:
% 0.69/1.08
% 0.69/1.08 subsumption: (18) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( and(
% 0.69/1.08 skol8, skol33 ), skol8 ) ), and_1 }.
% 0.69/1.08 parent0: (612) {G0,W7,D4,L2,V0,M2} { ! is_a_theorem( implies( and( skol8,
% 0.69/1.08 skol33 ), skol8 ) ), and_1 }.
% 0.69/1.08 substitution0:
% 0.69/1.08 end
% 0.69/1.08 permutation0:
% 0.69/1.08 0 ==> 0
% 0.69/1.08 1 ==> 1
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 subsumption: (37) {G0,W7,D4,L2,V2,M2} I { ! kn2, is_a_theorem( implies( and
% 0.69/1.08 ( X, Y ), X ) ) }.
% 0.69/1.08 parent0: (631) {G0,W7,D4,L2,V2,M2} { ! kn2, is_a_theorem( implies( and( X
% 0.69/1.08 , Y ), X ) ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := X
% 0.69/1.08 Y := Y
% 0.69/1.08 end
% 0.69/1.08 permutation0:
% 0.69/1.08 0 ==> 0
% 0.69/1.08 1 ==> 1
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 subsumption: (67) {G0,W1,D1,L1,V0,M1} I { kn2 }.
% 0.69/1.08 parent0: (661) {G0,W1,D1,L1,V0,M1} { kn2 }.
% 0.69/1.08 substitution0:
% 0.69/1.08 end
% 0.69/1.08 permutation0:
% 0.69/1.08 0 ==> 0
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 subsumption: (70) {G0,W1,D1,L1,V0,M1} I { ! and_1 }.
% 0.69/1.08 parent0: (667) {G0,W1,D1,L1,V0,M1} { ! and_1 }.
% 0.69/1.08 substitution0:
% 0.69/1.08 end
% 0.69/1.08 permutation0:
% 0.69/1.08 0 ==> 0
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 resolution: (686) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( and( X, Y )
% 0.69/1.08 , X ) ) }.
% 0.69/1.08 parent0[0]: (37) {G0,W7,D4,L2,V2,M2} I { ! kn2, is_a_theorem( implies( and
% 0.69/1.09 ( X, Y ), X ) ) }.
% 0.69/1.09 parent1[0]: (67) {G0,W1,D1,L1,V0,M1} I { kn2 }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 Y := Y
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (72) {G1,W6,D4,L1,V2,M1} S(37);r(67) { is_a_theorem( implies(
% 0.69/1.09 and( X, Y ), X ) ) }.
% 0.69/1.09 parent0: (686) {G1,W6,D4,L1,V2,M1} { is_a_theorem( implies( and( X, Y ), X
% 0.69/1.09 ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 Y := Y
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (687) {G1,W1,D1,L1,V0,M1} { and_1 }.
% 0.69/1.09 parent0[0]: (18) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( and(
% 0.69/1.09 skol8, skol33 ), skol8 ) ), and_1 }.
% 0.69/1.09 parent1[0]: (72) {G1,W6,D4,L1,V2,M1} S(37);r(67) { is_a_theorem( implies(
% 0.69/1.09 and( X, Y ), X ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 X := skol8
% 0.69/1.09 Y := skol33
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (688) {G1,W0,D0,L0,V0,M0} { }.
% 0.69/1.09 parent0[0]: (70) {G0,W1,D1,L1,V0,M1} I { ! and_1 }.
% 0.69/1.09 parent1[0]: (687) {G1,W1,D1,L1,V0,M1} { and_1 }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (592) {G2,W0,D0,L0,V0,M0} S(18);r(72);r(70) { }.
% 0.69/1.09 parent0: (688) {G1,W0,D0,L0,V0,M0} { }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 Proof check complete!
% 0.69/1.09
% 0.69/1.09 Memory use:
% 0.69/1.09
% 0.69/1.09 space for terms: 8595
% 0.69/1.09 space for clauses: 33684
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 clauses generated: 957
% 0.69/1.09 clauses kept: 593
% 0.69/1.09 clauses selected: 65
% 0.69/1.09 clauses deleted: 11
% 0.69/1.09 clauses inuse deleted: 0
% 0.69/1.09
% 0.69/1.09 subsentry: 882
% 0.69/1.09 literals s-matched: 757
% 0.69/1.09 literals matched: 756
% 0.69/1.09 full subsumption: 64
% 0.69/1.09
% 0.69/1.09 checksum: 1595179251
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Bliksem ended
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