%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE093+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 01:37:08 EDT 2022
% Result : Theorem 0.88s 1.26s
% Output : Refutation 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE093+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Thu Jun 16 12:53:26 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.88/1.26 *** allocated 10000 integers for termspace/termends
% 0.88/1.26 *** allocated 10000 integers for clauses
% 0.88/1.26 *** allocated 10000 integers for justifications
% 0.88/1.26 Bliksem 1.12
% 0.88/1.26
% 0.88/1.26
% 0.88/1.26 Automatic Strategy Selection
% 0.88/1.26
% 0.88/1.26
% 0.88/1.26 Clauses:
% 0.88/1.26
% 0.88/1.26 { addition( X, Y ) = addition( Y, X ) }.
% 0.88/1.26 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.88/1.26 { addition( X, zero ) = X }.
% 0.88/1.26 { addition( X, X ) = X }.
% 0.88/1.26 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.88/1.26 multiplication( X, Y ), Z ) }.
% 0.88/1.26 { multiplication( X, one ) = X }.
% 0.88/1.26 { multiplication( one, X ) = X }.
% 0.88/1.26 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.88/1.26 , multiplication( X, Z ) ) }.
% 0.88/1.26 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.88/1.26 , multiplication( Y, Z ) ) }.
% 0.88/1.26 { multiplication( X, zero ) = zero }.
% 0.88/1.26 { multiplication( zero, X ) = zero }.
% 0.88/1.26 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.88/1.26 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.88/1.26 { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 0.88/1.26 { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 0.88/1.26 { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication(
% 0.88/1.26 star( X ), Z ), Y ) }.
% 0.88/1.26 { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 0.88/1.26 , star( Y ) ), X ) }.
% 0.88/1.26 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.88/1.26 ( X ), X ) }.
% 0.88/1.26 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.88/1.26 ) ) }.
% 0.88/1.26 { addition( domain( X ), one ) = one }.
% 0.88/1.26 { domain( zero ) = zero }.
% 0.88/1.26 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.88/1.26 { ! domain( star( skol1 ) ) = one }.
% 0.88/1.26
% 0.88/1.26 percentage equality = 0.703704, percentage horn = 1.000000
% 0.88/1.26 This is a problem with some equality
% 0.88/1.26
% 0.88/1.26
% 0.88/1.26
% 0.88/1.26 Options Used:
% 0.88/1.26
% 0.88/1.26 useres = 1
% 0.88/1.26 useparamod = 1
% 0.88/1.26 useeqrefl = 1
% 0.88/1.26 useeqfact = 1
% 0.88/1.26 usefactor = 1
% 0.88/1.26 usesimpsplitting = 0
% 0.88/1.26 usesimpdemod = 5
% 0.88/1.26 usesimpres = 3
% 0.88/1.26
% 0.88/1.26 resimpinuse = 1000
% 0.88/1.26 resimpclauses = 20000
% 0.88/1.26 substype = eqrewr
% 0.88/1.26 backwardsubs = 1
% 0.88/1.26 selectoldest = 5
% 0.88/1.26
% 0.88/1.26 litorderings [0] = split
% 0.88/1.26 litorderings [1] = extend the termordering, first sorting on arguments
% 0.88/1.26
% 0.88/1.26 termordering = kbo
% 0.88/1.26
% 0.88/1.26 litapriori = 0
% 0.88/1.26 termapriori = 1
% 0.88/1.26 litaposteriori = 0
% 0.88/1.26 termaposteriori = 0
% 0.88/1.26 demodaposteriori = 0
% 0.88/1.26 ordereqreflfact = 0
% 0.88/1.26
% 0.88/1.26 litselect = negord
% 0.88/1.26
% 0.88/1.26 maxweight = 15
% 0.88/1.26 maxdepth = 30000
% 0.88/1.26 maxlength = 115
% 0.88/1.26 maxnrvars = 195
% 0.88/1.26 excuselevel = 1
% 0.88/1.26 increasemaxweight = 1
% 0.88/1.26
% 0.88/1.26 maxselected = 10000000
% 0.88/1.26 maxnrclauses = 10000000
% 0.88/1.26
% 0.88/1.26 showgenerated = 0
% 0.88/1.26 showkept = 0
% 0.88/1.26 showselected = 0
% 0.88/1.26 showdeleted = 0
% 0.88/1.26 showresimp = 1
% 0.88/1.26 showstatus = 2000
% 0.88/1.26
% 0.88/1.26 prologoutput = 0
% 0.88/1.26 nrgoals = 5000000
% 0.88/1.26 totalproof = 1
% 0.88/1.26
% 0.88/1.26 Symbols occurring in the translation:
% 0.88/1.26
% 0.88/1.26 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.88/1.26 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.88/1.26 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.88/1.26 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.26 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.26 addition [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.88/1.26 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.88/1.26 multiplication [40, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.88/1.26 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.88/1.26 leq [42, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.88/1.26 star [43, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.88/1.26 domain [45, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.88/1.26 skol1 [47, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.88/1.26
% 0.88/1.26
% 0.88/1.26 Starting Search:
% 0.88/1.26
% 0.88/1.26 *** allocated 15000 integers for clauses
% 0.88/1.26 *** allocated 22500 integers for clauses
% 0.88/1.26 *** allocated 33750 integers for clauses
% 0.88/1.26 *** allocated 50625 integers for clauses
% 0.88/1.26 *** allocated 75937 integers for clauses
% 0.88/1.26 *** allocated 15000 integers for termspace/termends
% 0.88/1.26 Resimplifying inuse:
% 0.88/1.26 Done
% 0.88/1.26
% 0.88/1.26 *** allocated 113905 integers for clauses
% 0.88/1.26 *** allocated 22500 integers for termspace/termends
% 0.88/1.26
% 0.88/1.26 Bliksems!, er is een bewijs:
% 0.88/1.26 % SZS status Theorem
% 0.88/1.26 % SZS output start Refutation
% 0.88/1.26
% 0.88/1.26 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.88/1.26 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 0.88/1.26 addition( Z, Y ), X ) }.
% 0.88/1.26 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.88/1.26 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.88/1.26 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.88/1.26 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.88/1.26 (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 0.88/1.26 , X ) ), star( X ) ) }.
% 0.88/1.26 (17) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.88/1.26 ) ==> multiplication( domain( X ), X ) }.
% 0.88/1.26 (19) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> one }.
% 0.88/1.26 (21) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y ) ) ==>
% 0.88/1.26 domain( addition( X, Y ) ) }.
% 0.88/1.26 (22) {G0,W5,D4,L1,V0,M1} I { ! domain( star( skol1 ) ) ==> one }.
% 0.88/1.26 (25) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 0.88/1.26 addition( Y, X ) }.
% 0.88/1.26 (29) {G1,W6,D4,L1,V1,M1} P(19,0) { addition( one, domain( X ) ) ==> one }.
% 0.88/1.26 (37) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y, leq( X, Y )
% 0.88/1.26 }.
% 0.88/1.26 (203) {G2,W4,D3,L1,V0,M1} P(5,17);d(29) { domain( one ) ==> one }.
% 0.88/1.26 (251) {G3,W6,D4,L1,V1,M1} P(203,21);d(29) { domain( addition( one, X ) )
% 0.88/1.26 ==> one }.
% 0.88/1.26 (268) {G4,W7,D3,L2,V1,M2} P(11,251) { domain( X ) ==> one, ! leq( one, X )
% 0.88/1.26 }.
% 0.88/1.26 (295) {G5,W4,D3,L1,V0,M1} R(268,22) { ! leq( one, star( skol1 ) ) }.
% 0.88/1.26 (308) {G2,W5,D3,L1,V2,M1} R(25,37) { leq( X, addition( Y, X ) ) }.
% 0.88/1.26 (325) {G3,W5,D3,L1,V2,M1} P(0,308) { leq( Y, addition( Y, X ) ) }.
% 0.88/1.26 (335) {G4,W7,D4,L1,V3,M1} P(1,325) { leq( X, addition( addition( X, Y ), Z
% 0.88/1.26 ) ) }.
% 0.88/1.26 (747) {G5,W8,D3,L2,V3,M2} P(11,335) { leq( X, Z ), ! leq( addition( X, Y )
% 0.88/1.26 , Z ) }.
% 0.88/1.26 (1680) {G6,W4,D3,L1,V1,M1} R(747,14) { leq( one, star( X ) ) }.
% 0.88/1.26 (1741) {G7,W0,D0,L0,V0,M0} R(1680,295) { }.
% 0.88/1.26
% 0.88/1.26
% 0.88/1.26 % SZS output end Refutation
% 0.88/1.26 found a proof!
% 0.88/1.26
% 0.88/1.26
% 0.88/1.26 Unprocessed initial clauses:
% 0.88/1.26
% 0.88/1.26 (1743) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.88/1.26 (1744) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.88/1.26 addition( Z, Y ), X ) }.
% 0.88/1.26 (1745) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.88/1.26 (1746) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.88/1.26 (1747) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.88/1.26 = multiplication( multiplication( X, Y ), Z ) }.
% 0.88/1.26 (1748) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.88/1.26 (1749) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.88/1.26 (1750) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.88/1.26 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.88/1.26 (1751) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.88/1.26 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.88/1.26 (1752) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.88/1.26 (1753) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.88/1.26 (1754) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.88/1.26 (1755) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.88/1.26 (1756) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( X, star(
% 0.88/1.26 X ) ) ), star( X ) ) }.
% 0.88/1.26 (1757) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( star( X )
% 0.88/1.26 , X ) ), star( X ) ) }.
% 0.88/1.26 (1758) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z )
% 0.88/1.26 , Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 0.88/1.26 (1759) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z )
% 0.88/1.26 , X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 0.88/1.26 (1760) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X
% 0.88/1.26 ) ) = multiplication( domain( X ), X ) }.
% 0.88/1.26 (1761) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 0.88/1.26 multiplication( X, domain( Y ) ) ) }.
% 0.88/1.26 (1762) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 0.88/1.26 (1763) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.88/1.26 (1764) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition(
% 0.88/1.26 domain( X ), domain( Y ) ) }.
% 0.88/1.26 (1765) {G0,W5,D4,L1,V0,M1} { ! domain( star( skol1 ) ) = one }.
% 0.88/1.26
% 0.88/1.26
% 0.88/1.26 Total Proof:
% 0.88/1.26
% 0.88/1.26 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.88/1.26 ) }.
% 0.88/1.26 parent0: (1743) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.88/1.26 }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.88/1.26 ==> addition( addition( Z, Y ), X ) }.
% 0.88/1.26 parent0: (1744) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 0.88/1.26 addition( addition( Z, Y ), X ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 Z := Z
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.88/1.26 parent0: (1746) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.88/1.26 parent0: (1748) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.88/1.26 ==> Y }.
% 0.88/1.26 parent0: (1754) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.88/1.26 }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 1 ==> 1
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.88/1.26 , Y ) }.
% 0.88/1.26 parent0: (1755) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.88/1.26 }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 1 ==> 1
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 0.88/1.26 multiplication( star( X ), X ) ), star( X ) ) }.
% 0.88/1.26 parent0: (1757) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication(
% 0.88/1.26 star( X ), X ) ), star( X ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (17) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.88/1.26 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.88/1.26 parent0: (1760) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain
% 0.88/1.26 ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (19) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.88/1.26 one }.
% 0.88/1.26 parent0: (1762) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one
% 0.88/1.26 }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1854) {G0,W10,D4,L1,V2,M1} { addition( domain( X ), domain( Y ) )
% 0.88/1.26 = domain( addition( X, Y ) ) }.
% 0.88/1.26 parent0[0]: (1764) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) =
% 0.88/1.26 addition( domain( X ), domain( Y ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (21) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 0.88/1.26 ) ) ==> domain( addition( X, Y ) ) }.
% 0.88/1.26 parent0: (1854) {G0,W10,D4,L1,V2,M1} { addition( domain( X ), domain( Y )
% 0.88/1.26 ) = domain( addition( X, Y ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (22) {G0,W5,D4,L1,V0,M1} I { ! domain( star( skol1 ) ) ==> one
% 0.88/1.26 }.
% 0.88/1.26 parent0: (1765) {G0,W5,D4,L1,V0,M1} { ! domain( star( skol1 ) ) = one }.
% 0.88/1.26 substitution0:
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1874) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.88/1.26 addition( X, addition( Y, Z ) ) }.
% 0.88/1.26 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.88/1.26 ==> addition( addition( Z, Y ), X ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Z
% 0.88/1.26 Y := Y
% 0.88/1.26 Z := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1880) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 0.88/1.26 addition( X, Y ) }.
% 0.88/1.26 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.88/1.26 parent1[0; 8]: (1874) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 0.88/1.26 ) ==> addition( X, addition( Y, Z ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Y
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 Z := Y
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (25) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 0.88/1.26 X ) ==> addition( Y, X ) }.
% 0.88/1.26 parent0: (1880) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 0.88/1.26 addition( X, Y ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Y
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1885) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X ), one )
% 0.88/1.26 }.
% 0.88/1.26 parent0[0]: (19) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.88/1.26 one }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1886) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X ) )
% 0.88/1.26 }.
% 0.88/1.26 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.88/1.26 }.
% 0.88/1.26 parent1[0; 2]: (1885) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X )
% 0.88/1.26 , one ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := domain( X )
% 0.88/1.26 Y := one
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1889) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.88/1.26 }.
% 0.88/1.26 parent0[0]: (1886) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X
% 0.88/1.26 ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (29) {G1,W6,D4,L1,V1,M1} P(19,0) { addition( one, domain( X )
% 0.88/1.26 ) ==> one }.
% 0.88/1.26 parent0: (1889) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.88/1.26 }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1890) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.88/1.26 }.
% 0.88/1.26 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.88/1.26 Y ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1891) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 0.88/1.26 ) }.
% 0.88/1.26 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.88/1.26 }.
% 0.88/1.26 parent1[0; 3]: (1890) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.88/1.26 ( X, Y ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Y
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := Y
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1894) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X )
% 0.88/1.26 }.
% 0.88/1.26 parent0[0]: (1891) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 0.88/1.26 , X ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (37) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 0.88/1.26 leq( X, Y ) }.
% 0.88/1.26 parent0: (1894) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 0.88/1.26 ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Y
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 1 ==> 1
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1896) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ), X ) ==>
% 0.88/1.26 addition( X, multiplication( domain( X ), X ) ) }.
% 0.88/1.26 parent0[0]: (17) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.88/1.26 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1899) {G1,W9,D4,L1,V0,M1} { multiplication( domain( one ), one )
% 0.88/1.26 ==> addition( one, domain( one ) ) }.
% 0.88/1.26 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.88/1.26 parent1[0; 7]: (1896) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ),
% 0.88/1.26 X ) ==> addition( X, multiplication( domain( X ), X ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := domain( one )
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := one
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1900) {G1,W7,D4,L1,V0,M1} { domain( one ) ==> addition( one,
% 0.88/1.26 domain( one ) ) }.
% 0.88/1.26 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.88/1.26 parent1[0; 1]: (1899) {G1,W9,D4,L1,V0,M1} { multiplication( domain( one )
% 0.88/1.26 , one ) ==> addition( one, domain( one ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := domain( one )
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1903) {G2,W4,D3,L1,V0,M1} { domain( one ) ==> one }.
% 0.88/1.26 parent0[0]: (29) {G1,W6,D4,L1,V1,M1} P(19,0) { addition( one, domain( X ) )
% 0.88/1.26 ==> one }.
% 0.88/1.26 parent1[0; 3]: (1900) {G1,W7,D4,L1,V0,M1} { domain( one ) ==> addition(
% 0.88/1.26 one, domain( one ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := one
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (203) {G2,W4,D3,L1,V0,M1} P(5,17);d(29) { domain( one ) ==>
% 0.88/1.26 one }.
% 0.88/1.26 parent0: (1903) {G2,W4,D3,L1,V0,M1} { domain( one ) ==> one }.
% 0.88/1.26 substitution0:
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1906) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) ==>
% 0.88/1.26 addition( domain( X ), domain( Y ) ) }.
% 0.88/1.26 parent0[0]: (21) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 0.88/1.26 ) ) ==> domain( addition( X, Y ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1908) {G1,W9,D4,L1,V1,M1} { domain( addition( one, X ) ) ==>
% 0.88/1.26 addition( one, domain( X ) ) }.
% 0.88/1.26 parent0[0]: (203) {G2,W4,D3,L1,V0,M1} P(5,17);d(29) { domain( one ) ==> one
% 0.88/1.26 }.
% 0.88/1.26 parent1[0; 6]: (1906) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) )
% 0.88/1.26 ==> addition( domain( X ), domain( Y ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := one
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1910) {G2,W6,D4,L1,V1,M1} { domain( addition( one, X ) ) ==> one
% 0.88/1.26 }.
% 0.88/1.26 parent0[0]: (29) {G1,W6,D4,L1,V1,M1} P(19,0) { addition( one, domain( X ) )
% 0.88/1.26 ==> one }.
% 0.88/1.26 parent1[0; 5]: (1908) {G1,W9,D4,L1,V1,M1} { domain( addition( one, X ) )
% 0.88/1.26 ==> addition( one, domain( X ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (251) {G3,W6,D4,L1,V1,M1} P(203,21);d(29) { domain( addition(
% 0.88/1.26 one, X ) ) ==> one }.
% 0.88/1.26 parent0: (1910) {G2,W6,D4,L1,V1,M1} { domain( addition( one, X ) ) ==> one
% 0.88/1.26 }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1913) {G3,W6,D4,L1,V1,M1} { one ==> domain( addition( one, X ) )
% 0.88/1.26 }.
% 0.88/1.26 parent0[0]: (251) {G3,W6,D4,L1,V1,M1} P(203,21);d(29) { domain( addition(
% 0.88/1.26 one, X ) ) ==> one }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1914) {G1,W7,D3,L2,V1,M2} { one ==> domain( X ), ! leq( one, X )
% 0.88/1.26 }.
% 0.88/1.26 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.88/1.26 ==> Y }.
% 0.88/1.26 parent1[0; 3]: (1913) {G3,W6,D4,L1,V1,M1} { one ==> domain( addition( one
% 0.88/1.26 , X ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := one
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1915) {G1,W7,D3,L2,V1,M2} { domain( X ) ==> one, ! leq( one, X )
% 0.88/1.26 }.
% 0.88/1.26 parent0[0]: (1914) {G1,W7,D3,L2,V1,M2} { one ==> domain( X ), ! leq( one,
% 0.88/1.26 X ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (268) {G4,W7,D3,L2,V1,M2} P(11,251) { domain( X ) ==> one, !
% 0.88/1.26 leq( one, X ) }.
% 0.88/1.26 parent0: (1915) {G1,W7,D3,L2,V1,M2} { domain( X ) ==> one, ! leq( one, X )
% 0.88/1.26 }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 1 ==> 1
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1916) {G4,W7,D3,L2,V1,M2} { one ==> domain( X ), ! leq( one, X )
% 0.88/1.26 }.
% 0.88/1.26 parent0[0]: (268) {G4,W7,D3,L2,V1,M2} P(11,251) { domain( X ) ==> one, !
% 0.88/1.26 leq( one, X ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1917) {G0,W5,D4,L1,V0,M1} { ! one ==> domain( star( skol1 ) ) }.
% 0.88/1.26 parent0[0]: (22) {G0,W5,D4,L1,V0,M1} I { ! domain( star( skol1 ) ) ==> one
% 0.88/1.26 }.
% 0.88/1.26 substitution0:
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 resolution: (1918) {G1,W4,D3,L1,V0,M1} { ! leq( one, star( skol1 ) ) }.
% 0.88/1.26 parent0[0]: (1917) {G0,W5,D4,L1,V0,M1} { ! one ==> domain( star( skol1 ) )
% 0.88/1.26 }.
% 0.88/1.26 parent1[0]: (1916) {G4,W7,D3,L2,V1,M2} { one ==> domain( X ), ! leq( one,
% 0.88/1.26 X ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := star( skol1 )
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (295) {G5,W4,D3,L1,V0,M1} R(268,22) { ! leq( one, star( skol1
% 0.88/1.26 ) ) }.
% 0.88/1.26 parent0: (1918) {G1,W4,D3,L1,V0,M1} { ! leq( one, star( skol1 ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1919) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 0.88/1.26 addition( X, Y ), Y ) }.
% 0.88/1.26 parent0[0]: (25) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 0.88/1.26 ) ==> addition( Y, X ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Y
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 eqswap: (1920) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X )
% 0.88/1.26 }.
% 0.88/1.26 parent0[0]: (37) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 0.88/1.26 leq( X, Y ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Y
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 resolution: (1921) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 0.88/1.26 parent0[0]: (1920) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 0.88/1.26 , X ) }.
% 0.88/1.26 parent1[0]: (1919) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 0.88/1.26 addition( X, Y ), Y ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := addition( X, Y )
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (308) {G2,W5,D3,L1,V2,M1} R(25,37) { leq( X, addition( Y, X )
% 0.88/1.26 ) }.
% 0.88/1.26 parent0: (1921) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Y
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1922) {G1,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.88/1.26 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.88/1.26 }.
% 0.88/1.26 parent1[0; 2]: (308) {G2,W5,D3,L1,V2,M1} R(25,37) { leq( X, addition( Y, X
% 0.88/1.26 ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Y
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (325) {G3,W5,D3,L1,V2,M1} P(0,308) { leq( Y, addition( Y, X )
% 0.88/1.26 ) }.
% 0.88/1.26 parent0: (1922) {G1,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Y
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1925) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.88/1.26 Z ) ) }.
% 0.88/1.26 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.88/1.26 ==> addition( addition( Z, Y ), X ) }.
% 0.88/1.26 parent1[0; 2]: (325) {G3,W5,D3,L1,V2,M1} P(0,308) { leq( Y, addition( Y, X
% 0.88/1.26 ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := Z
% 0.88/1.26 Y := Y
% 0.88/1.26 Z := X
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := addition( Y, Z )
% 0.88/1.26 Y := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (335) {G4,W7,D4,L1,V3,M1} P(1,325) { leq( X, addition(
% 0.88/1.26 addition( X, Y ), Z ) ) }.
% 0.88/1.26 parent0: (1925) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.88/1.26 Z ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 Z := Z
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 paramod: (1927) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y )
% 0.88/1.26 , Z ) }.
% 0.88/1.26 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.88/1.26 ==> Y }.
% 0.88/1.26 parent1[0; 2]: (335) {G4,W7,D4,L1,V3,M1} P(1,325) { leq( X, addition(
% 0.88/1.26 addition( X, Y ), Z ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := addition( X, Y )
% 0.88/1.26 Y := Z
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 Z := Z
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (747) {G5,W8,D3,L2,V3,M2} P(11,335) { leq( X, Z ), ! leq(
% 0.88/1.26 addition( X, Y ), Z ) }.
% 0.88/1.26 parent0: (1927) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y )
% 0.88/1.26 , Z ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 Y := Y
% 0.88/1.26 Z := Z
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 1 ==> 1
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 resolution: (1931) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 0.88/1.26 parent0[1]: (747) {G5,W8,D3,L2,V3,M2} P(11,335) { leq( X, Z ), ! leq(
% 0.88/1.26 addition( X, Y ), Z ) }.
% 0.88/1.26 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 0.88/1.26 ( star( X ), X ) ), star( X ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := one
% 0.88/1.26 Y := multiplication( star( X ), X )
% 0.88/1.26 Z := star( X )
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (1680) {G6,W4,D3,L1,V1,M1} R(747,14) { leq( one, star( X ) )
% 0.88/1.26 }.
% 0.88/1.26 parent0: (1931) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 0.88/1.26 substitution0:
% 0.88/1.26 X := X
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 0 ==> 0
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 resolution: (1932) {G6,W0,D0,L0,V0,M0} { }.
% 0.88/1.26 parent0[0]: (295) {G5,W4,D3,L1,V0,M1} R(268,22) { ! leq( one, star( skol1 )
% 0.88/1.26 ) }.
% 0.88/1.26 parent1[0]: (1680) {G6,W4,D3,L1,V1,M1} R(747,14) { leq( one, star( X ) )
% 0.88/1.26 }.
% 0.88/1.26 substitution0:
% 0.88/1.26 end
% 0.88/1.26 substitution1:
% 0.88/1.26 X := skol1
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 subsumption: (1741) {G7,W0,D0,L0,V0,M0} R(1680,295) { }.
% 0.88/1.26 parent0: (1932) {G6,W0,D0,L0,V0,M0} { }.
% 0.88/1.26 substitution0:
% 0.88/1.26 end
% 0.88/1.26 permutation0:
% 0.88/1.26 end
% 0.88/1.26
% 0.88/1.26 Proof check complete!
% 0.88/1.26
% 0.88/1.26 Memory use:
% 0.88/1.26
% 0.88/1.26 space for terms: 20718
% 0.88/1.26 space for clauses: 102884
% 0.88/1.26
% 0.88/1.26
% 0.88/1.26 clauses generated: 11663
% 0.88/1.26 clauses kept: 1742
% 0.88/1.26 clauses selected: 235
% 0.88/1.26 clauses deleted: 16
% 0.88/1.26 clauses inuse deleted: 4
% 0.88/1.26
% 0.88/1.26 subsentry: 15160
% 0.88/1.26 literals s-matched: 11636
% 0.88/1.26 literals matched: 11427
% 0.88/1.26 full subsumption: 1038
% 0.88/1.26
% 0.88/1.26 checksum: 152882550
% 0.88/1.26
% 0.88/1.26
% 0.88/1.26 Bliksem ended
%------------------------------------------------------------------------------