%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE063+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 01:36:58 EDT 2022
% Result : Theorem 0.73s 1.18s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE063+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 16 11:07:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.73/1.18 *** allocated 10000 integers for termspace/termends
% 0.73/1.18 *** allocated 10000 integers for clauses
% 0.73/1.18 *** allocated 10000 integers for justifications
% 0.73/1.18 Bliksem 1.12
% 0.73/1.18
% 0.73/1.18
% 0.73/1.18 Automatic Strategy Selection
% 0.73/1.18
% 0.73/1.18
% 0.73/1.18 Clauses:
% 0.73/1.18
% 0.73/1.18 { addition( X, Y ) = addition( Y, X ) }.
% 0.73/1.18 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.73/1.18 { addition( X, zero ) = X }.
% 0.73/1.18 { addition( X, X ) = X }.
% 0.73/1.18 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.73/1.18 multiplication( X, Y ), Z ) }.
% 0.73/1.18 { multiplication( X, one ) = X }.
% 0.73/1.18 { multiplication( one, X ) = X }.
% 0.73/1.18 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.73/1.18 , multiplication( X, Z ) ) }.
% 0.73/1.18 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.73/1.18 , multiplication( Y, Z ) ) }.
% 0.73/1.18 { multiplication( X, zero ) = zero }.
% 0.73/1.18 { multiplication( zero, X ) = zero }.
% 0.73/1.18 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.73/1.18 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.73/1.18 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.73/1.18 ( X ), X ) }.
% 0.73/1.18 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.73/1.18 ) ) }.
% 0.73/1.18 { addition( domain( X ), one ) = one }.
% 0.73/1.18 { domain( zero ) = zero }.
% 0.73/1.18 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.73/1.18 { addition( skol1, multiplication( domain( skol2 ), skol1 ) ) =
% 0.73/1.18 multiplication( domain( skol2 ), skol1 ) }.
% 0.73/1.18 { ! addition( domain( skol1 ), domain( skol2 ) ) = domain( skol2 ) }.
% 0.73/1.18
% 0.73/1.18 percentage equality = 0.909091, percentage horn = 1.000000
% 0.73/1.18 This is a pure equality problem
% 0.73/1.18
% 0.73/1.18
% 0.73/1.18
% 0.73/1.18 Options Used:
% 0.73/1.18
% 0.73/1.18 useres = 1
% 0.73/1.18 useparamod = 1
% 0.73/1.18 useeqrefl = 1
% 0.73/1.18 useeqfact = 1
% 0.73/1.18 usefactor = 1
% 0.73/1.18 usesimpsplitting = 0
% 0.73/1.18 usesimpdemod = 5
% 0.73/1.18 usesimpres = 3
% 0.73/1.18
% 0.73/1.18 resimpinuse = 1000
% 0.73/1.18 resimpclauses = 20000
% 0.73/1.18 substype = eqrewr
% 0.73/1.18 backwardsubs = 1
% 0.73/1.18 selectoldest = 5
% 0.73/1.18
% 0.73/1.18 litorderings [0] = split
% 0.73/1.18 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.18
% 0.73/1.18 termordering = kbo
% 0.73/1.18
% 0.73/1.18 litapriori = 0
% 0.73/1.18 termapriori = 1
% 0.73/1.18 litaposteriori = 0
% 0.73/1.18 termaposteriori = 0
% 0.73/1.18 demodaposteriori = 0
% 0.73/1.18 ordereqreflfact = 0
% 0.73/1.18
% 0.73/1.18 litselect = negord
% 0.73/1.18
% 0.73/1.18 maxweight = 15
% 0.73/1.18 maxdepth = 30000
% 0.73/1.18 maxlength = 115
% 0.73/1.18 maxnrvars = 195
% 0.73/1.18 excuselevel = 1
% 0.73/1.18 increasemaxweight = 1
% 0.73/1.18
% 0.73/1.18 maxselected = 10000000
% 0.73/1.18 maxnrclauses = 10000000
% 0.73/1.18
% 0.73/1.18 showgenerated = 0
% 0.73/1.18 showkept = 0
% 0.73/1.18 showselected = 0
% 0.73/1.18 showdeleted = 0
% 0.73/1.18 showresimp = 1
% 0.73/1.18 showstatus = 2000
% 0.73/1.18
% 0.73/1.18 prologoutput = 0
% 0.73/1.18 nrgoals = 5000000
% 0.73/1.18 totalproof = 1
% 0.73/1.18
% 0.73/1.18 Symbols occurring in the translation:
% 0.73/1.18
% 0.73/1.18 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.18 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.18 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.73/1.18 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.18 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.18 addition [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.73/1.18 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.73/1.18 multiplication [40, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.73/1.18 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.73/1.18 leq [42, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.73/1.18 domain [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.73/1.18 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.73/1.18 skol2 [47, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.73/1.18
% 0.73/1.18
% 0.73/1.18 Starting Search:
% 0.73/1.18
% 0.73/1.18 *** allocated 15000 integers for clauses
% 0.73/1.18 *** allocated 22500 integers for clauses
% 0.73/1.18 *** allocated 33750 integers for clauses
% 0.73/1.18 *** allocated 50625 integers for clauses
% 0.73/1.18 *** allocated 75937 integers for clauses
% 0.73/1.18 *** allocated 15000 integers for termspace/termends
% 0.73/1.18 Resimplifying inuse:
% 0.73/1.18 Done
% 0.73/1.18
% 0.73/1.18 *** allocated 113905 integers for clauses
% 0.73/1.18
% 0.73/1.18 Bliksems!, er is een bewijs:
% 0.73/1.18 % SZS status Theorem
% 0.73/1.18 % SZS output start Refutation
% 0.73/1.18
% 0.73/1.18 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.73/1.18 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 0.73/1.18 addition( Z, Y ), X ) }.
% 0.73/1.18 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.73/1.18 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.73/1.18 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.73/1.18 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.73/1.18 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.73/1.18 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.73/1.18 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.73/1.18 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.73/1.18 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.73/1.18 (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.73/1.18 ) ==> multiplication( domain( X ), X ) }.
% 0.73/1.18 (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) )
% 0.73/1.18 ==> domain( multiplication( X, Y ) ) }.
% 0.73/1.18 (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> one }.
% 0.73/1.18 (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y ) ) ==>
% 0.73/1.18 domain( addition( X, Y ) ) }.
% 0.73/1.18 (18) {G0,W11,D5,L1,V0,M1} I { addition( skol1, multiplication( domain(
% 0.73/1.18 skol2 ), skol1 ) ) ==> multiplication( domain( skol2 ), skol1 ) }.
% 0.73/1.18 (19) {G1,W7,D4,L1,V0,M1} I;d(17) { ! domain( addition( skol1, skol2 ) ) ==>
% 0.73/1.18 domain( skol2 ) }.
% 0.73/1.18 (21) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) ) ==> one }.
% 0.73/1.18 (24) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 0.73/1.18 addition( Y, X ) }.
% 0.73/1.18 (28) {G2,W7,D4,L1,V0,M1} P(0,19) { ! domain( addition( skol2, skol1 ) ) ==>
% 0.73/1.18 domain( skol2 ) }.
% 0.73/1.18 (35) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y, leq( X, Y )
% 0.73/1.18 }.
% 0.73/1.18 (42) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X, Y ), X ) =
% 0.73/1.18 multiplication( X, addition( Y, one ) ) }.
% 0.73/1.18 (54) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 0.73/1.18 }.
% 0.73/1.18 (62) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication( Y, X ) ) =
% 0.73/1.18 multiplication( addition( one, Y ), X ) }.
% 0.73/1.18 (100) {G2,W4,D3,L1,V0,M1} P(5,13);d(21) { domain( one ) ==> one }.
% 0.73/1.18 (137) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) ) ==> domain(
% 0.73/1.18 X ) }.
% 0.73/1.18 (152) {G3,W6,D4,L1,V1,M1} P(100,17);d(15) { domain( addition( X, one ) )
% 0.73/1.18 ==> one }.
% 0.73/1.18 (216) {G2,W5,D3,L1,V2,M1} R(24,35) { leq( X, addition( Y, X ) ) }.
% 0.73/1.18 (233) {G3,W5,D3,L1,V2,M1} P(0,216) { leq( Y, addition( Y, X ) ) }.
% 0.73/1.18 (241) {G4,W7,D4,L1,V2,M1} P(17,233) { leq( domain( X ), domain( addition( X
% 0.73/1.18 , Y ) ) ) }.
% 0.73/1.18 (332) {G4,W9,D5,L1,V2,M1} P(152,14);d(5) { domain( multiplication( Y,
% 0.73/1.18 addition( X, one ) ) ) ==> domain( Y ) }.
% 0.73/1.18 (1080) {G5,W7,D4,L1,V2,M1} P(42,241);d(332) { leq( domain( multiplication(
% 0.73/1.18 X, Y ) ), domain( X ) ) }.
% 0.73/1.18 (1213) {G2,W6,D4,L1,V0,M1} P(62,18);d(21);d(6) { multiplication( domain(
% 0.73/1.18 skol2 ), skol1 ) ==> skol1 }.
% 0.73/1.18 (1243) {G6,W5,D3,L1,V0,M1} P(1213,1080);d(137) { leq( domain( skol1 ),
% 0.73/1.18 domain( skol2 ) ) }.
% 0.73/1.18 (1257) {G7,W0,D0,L0,V0,M0} R(1243,54);d(17);r(28) { }.
% 0.73/1.18
% 0.73/1.18
% 0.73/1.18 % SZS output end Refutation
% 0.73/1.18 found a proof!
% 0.73/1.18
% 0.73/1.18 *** allocated 22500 integers for termspace/termends
% 0.73/1.18
% 0.73/1.18 Unprocessed initial clauses:
% 0.73/1.18
% 0.73/1.18 (1259) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.73/1.18 (1260) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.73/1.18 addition( Z, Y ), X ) }.
% 0.73/1.18 (1261) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.73/1.18 (1262) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.73/1.18 (1263) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.73/1.18 = multiplication( multiplication( X, Y ), Z ) }.
% 0.73/1.18 (1264) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.73/1.18 (1265) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.73/1.18 (1266) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.73/1.18 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.73/1.18 (1267) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.73/1.18 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.73/1.18 (1268) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.73/1.18 (1269) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.73/1.18 (1270) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.73/1.18 (1271) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.73/1.18 (1272) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X
% 0.73/1.18 ) ) = multiplication( domain( X ), X ) }.
% 0.73/1.18 (1273) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 0.73/1.18 multiplication( X, domain( Y ) ) ) }.
% 0.73/1.18 (1274) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 0.73/1.18 (1275) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.73/1.18 (1276) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition(
% 0.73/1.18 domain( X ), domain( Y ) ) }.
% 0.73/1.18 (1277) {G0,W11,D5,L1,V0,M1} { addition( skol1, multiplication( domain(
% 0.73/1.18 skol2 ), skol1 ) ) = multiplication( domain( skol2 ), skol1 ) }.
% 0.73/1.18 (1278) {G0,W8,D4,L1,V0,M1} { ! addition( domain( skol1 ), domain( skol2 )
% 0.73/1.18 ) = domain( skol2 ) }.
% 0.73/1.18
% 0.73/1.18
% 0.73/1.18 Total Proof:
% 0.73/1.18
% 0.73/1.18 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.73/1.18 ) }.
% 0.73/1.18 parent0: (1259) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.73/1.18 }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.73/1.18 ==> addition( addition( Z, Y ), X ) }.
% 0.73/1.18 parent0: (1260) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 0.73/1.18 addition( addition( Z, Y ), X ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 Z := Z
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.73/1.18 parent0: (1262) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.73/1.18 parent0: (1264) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.73/1.18 parent0: (1265) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1300) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.73/1.18 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.73/1.18 parent0[0]: (1266) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 0.73/1.18 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 Z := Z
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.73/1.18 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.73/1.18 parent0: (1300) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.73/1.18 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 Z := Z
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1308) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.73/1.18 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.73/1.18 parent0[0]: (1267) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 0.73/1.18 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 Z := Z
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.73/1.18 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.73/1.18 parent0: (1308) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.73/1.18 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 Z := Z
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.73/1.18 ==> Y }.
% 0.73/1.18 parent0: (1270) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.73/1.18 }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 1 ==> 1
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.73/1.18 , Y ) }.
% 0.73/1.18 parent0: (1271) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.73/1.18 }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 1 ==> 1
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.73/1.18 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.73/1.18 parent0: (1272) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain
% 0.73/1.18 ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1358) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 0.73/1.18 ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.73/1.18 parent0[0]: (1273) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) )
% 0.73/1.18 = domain( multiplication( X, domain( Y ) ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X,
% 0.73/1.18 domain( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.73/1.18 parent0: (1358) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain(
% 0.73/1.18 Y ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.73/1.18 one }.
% 0.73/1.18 parent0: (1274) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one
% 0.73/1.18 }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1390) {G0,W10,D4,L1,V2,M1} { addition( domain( X ), domain( Y ) )
% 0.73/1.18 = domain( addition( X, Y ) ) }.
% 0.73/1.18 parent0[0]: (1276) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) =
% 0.73/1.18 addition( domain( X ), domain( Y ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 0.73/1.18 ) ) ==> domain( addition( X, Y ) ) }.
% 0.73/1.18 parent0: (1390) {G0,W10,D4,L1,V2,M1} { addition( domain( X ), domain( Y )
% 0.73/1.18 ) = domain( addition( X, Y ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (18) {G0,W11,D5,L1,V0,M1} I { addition( skol1, multiplication
% 0.73/1.18 ( domain( skol2 ), skol1 ) ) ==> multiplication( domain( skol2 ), skol1 )
% 0.73/1.18 }.
% 0.73/1.18 parent0: (1277) {G0,W11,D5,L1,V0,M1} { addition( skol1, multiplication(
% 0.73/1.18 domain( skol2 ), skol1 ) ) = multiplication( domain( skol2 ), skol1 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1450) {G1,W7,D4,L1,V0,M1} { ! domain( addition( skol1, skol2 ) )
% 0.73/1.18 = domain( skol2 ) }.
% 0.73/1.18 parent0[0]: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 0.73/1.18 ) ) ==> domain( addition( X, Y ) ) }.
% 0.73/1.18 parent1[0; 2]: (1278) {G0,W8,D4,L1,V0,M1} { ! addition( domain( skol1 ),
% 0.73/1.18 domain( skol2 ) ) = domain( skol2 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := skol1
% 0.73/1.18 Y := skol2
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (19) {G1,W7,D4,L1,V0,M1} I;d(17) { ! domain( addition( skol1,
% 0.73/1.18 skol2 ) ) ==> domain( skol2 ) }.
% 0.73/1.18 parent0: (1450) {G1,W7,D4,L1,V0,M1} { ! domain( addition( skol1, skol2 ) )
% 0.73/1.18 = domain( skol2 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1452) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X ), one )
% 0.73/1.18 }.
% 0.73/1.18 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.73/1.18 one }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1453) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X ) )
% 0.73/1.18 }.
% 0.73/1.18 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.73/1.18 }.
% 0.73/1.18 parent1[0; 2]: (1452) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X )
% 0.73/1.18 , one ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := domain( X )
% 0.73/1.18 Y := one
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1456) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.73/1.18 }.
% 0.73/1.18 parent0[0]: (1453) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X
% 0.73/1.18 ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (21) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X )
% 0.73/1.18 ) ==> one }.
% 0.73/1.18 parent0: (1456) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.73/1.18 }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1458) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.73/1.18 addition( X, addition( Y, Z ) ) }.
% 0.73/1.18 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.73/1.18 ==> addition( addition( Z, Y ), X ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Z
% 0.73/1.18 Y := Y
% 0.73/1.18 Z := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1464) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 0.73/1.18 addition( X, Y ) }.
% 0.73/1.18 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.73/1.18 parent1[0; 8]: (1458) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 0.73/1.18 ) ==> addition( X, addition( Y, Z ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 Z := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (24) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 0.73/1.18 X ) ==> addition( Y, X ) }.
% 0.73/1.18 parent0: (1464) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 0.73/1.18 addition( X, Y ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1469) {G1,W7,D4,L1,V0,M1} { ! domain( skol2 ) ==> domain(
% 0.73/1.18 addition( skol1, skol2 ) ) }.
% 0.73/1.18 parent0[0]: (19) {G1,W7,D4,L1,V0,M1} I;d(17) { ! domain( addition( skol1,
% 0.73/1.18 skol2 ) ) ==> domain( skol2 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1470) {G1,W7,D4,L1,V0,M1} { ! domain( skol2 ) ==> domain(
% 0.73/1.18 addition( skol2, skol1 ) ) }.
% 0.73/1.18 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.73/1.18 }.
% 0.73/1.18 parent1[0; 5]: (1469) {G1,W7,D4,L1,V0,M1} { ! domain( skol2 ) ==> domain(
% 0.73/1.18 addition( skol1, skol2 ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := skol1
% 0.73/1.18 Y := skol2
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1473) {G1,W7,D4,L1,V0,M1} { ! domain( addition( skol2, skol1 ) )
% 0.73/1.18 ==> domain( skol2 ) }.
% 0.73/1.18 parent0[0]: (1470) {G1,W7,D4,L1,V0,M1} { ! domain( skol2 ) ==> domain(
% 0.73/1.18 addition( skol2, skol1 ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (28) {G2,W7,D4,L1,V0,M1} P(0,19) { ! domain( addition( skol2,
% 0.73/1.18 skol1 ) ) ==> domain( skol2 ) }.
% 0.73/1.18 parent0: (1473) {G1,W7,D4,L1,V0,M1} { ! domain( addition( skol2, skol1 ) )
% 0.73/1.18 ==> domain( skol2 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1474) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.73/1.18 }.
% 0.73/1.18 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.73/1.18 Y ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1475) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 0.73/1.18 ) }.
% 0.73/1.18 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.73/1.18 }.
% 0.73/1.18 parent1[0; 3]: (1474) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.73/1.18 ( X, Y ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1478) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X )
% 0.73/1.18 }.
% 0.73/1.18 parent0[0]: (1475) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 0.73/1.18 , X ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (35) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 0.73/1.18 leq( X, Y ) }.
% 0.73/1.18 parent0: (1478) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 0.73/1.18 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 1 ==> 1
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1480) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 0.73/1.18 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.73/1.18 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.73/1.18 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 Z := Z
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1482) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( Y, one
% 0.73/1.18 ) ) ==> addition( multiplication( X, Y ), X ) }.
% 0.73/1.18 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.73/1.18 parent1[0; 10]: (1480) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 0.73/1.18 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 0.73/1.18 }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 Z := one
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1484) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), X
% 0.73/1.18 ) ==> multiplication( X, addition( Y, one ) ) }.
% 0.73/1.18 parent0[0]: (1482) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( Y,
% 0.73/1.18 one ) ) ==> addition( multiplication( X, Y ), X ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (42) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X
% 0.73/1.18 , Y ), X ) = multiplication( X, addition( Y, one ) ) }.
% 0.73/1.18 parent0: (1484) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), X
% 0.73/1.18 ) ==> multiplication( X, addition( Y, one ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1485) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.73/1.18 }.
% 0.73/1.18 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.73/1.18 ==> Y }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1486) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 0.73/1.18 ) }.
% 0.73/1.18 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.73/1.18 }.
% 0.73/1.18 parent1[0; 2]: (1485) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 0.73/1.18 ( X, Y ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1489) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X )
% 0.73/1.18 }.
% 0.73/1.18 parent0[0]: (1486) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 0.73/1.18 , X ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (54) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 0.73/1.18 leq( X, Y ) }.
% 0.73/1.18 parent0: (1489) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 0.73/1.18 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 1 ==> 1
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1491) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 0.73/1.18 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 0.73/1.18 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.73/1.18 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Z
% 0.73/1.18 Z := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1492) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X )
% 0.73/1.18 , Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.73/1.18 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.73/1.18 parent1[0; 7]: (1491) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X,
% 0.73/1.18 Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 0.73/1.18 }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := one
% 0.73/1.18 Y := Y
% 0.73/1.18 Z := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1494) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y )
% 0.73/1.18 ) ==> multiplication( addition( one, X ), Y ) }.
% 0.73/1.18 parent0[0]: (1492) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X
% 0.73/1.18 ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (62) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.73/1.18 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.73/1.18 parent0: (1494) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y )
% 0.73/1.18 ) ==> multiplication( addition( one, X ), Y ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1497) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ), X ) ==>
% 0.73/1.18 addition( X, multiplication( domain( X ), X ) ) }.
% 0.73/1.18 parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.73/1.18 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1500) {G1,W9,D4,L1,V0,M1} { multiplication( domain( one ), one )
% 0.73/1.18 ==> addition( one, domain( one ) ) }.
% 0.73/1.18 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.73/1.18 parent1[0; 7]: (1497) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ),
% 0.73/1.18 X ) ==> addition( X, multiplication( domain( X ), X ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := domain( one )
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := one
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1501) {G1,W7,D4,L1,V0,M1} { domain( one ) ==> addition( one,
% 0.73/1.18 domain( one ) ) }.
% 0.73/1.18 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.73/1.18 parent1[0; 1]: (1500) {G1,W9,D4,L1,V0,M1} { multiplication( domain( one )
% 0.73/1.18 , one ) ==> addition( one, domain( one ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := domain( one )
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1504) {G2,W4,D3,L1,V0,M1} { domain( one ) ==> one }.
% 0.73/1.18 parent0[0]: (21) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 0.73/1.18 ==> one }.
% 0.73/1.18 parent1[0; 3]: (1501) {G1,W7,D4,L1,V0,M1} { domain( one ) ==> addition(
% 0.73/1.18 one, domain( one ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := one
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (100) {G2,W4,D3,L1,V0,M1} P(5,13);d(21) { domain( one ) ==>
% 0.73/1.18 one }.
% 0.73/1.18 parent0: (1504) {G2,W4,D3,L1,V0,M1} { domain( one ) ==> one }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1507) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) ==>
% 0.73/1.18 domain( multiplication( X, domain( Y ) ) ) }.
% 0.73/1.18 parent0[0]: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 0.73/1.18 ( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1510) {G1,W8,D4,L1,V1,M1} { domain( multiplication( one, X ) )
% 0.73/1.18 ==> domain( domain( X ) ) }.
% 0.73/1.18 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.73/1.18 parent1[0; 6]: (1507) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y
% 0.73/1.18 ) ) ==> domain( multiplication( X, domain( Y ) ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := domain( X )
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := one
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1512) {G1,W6,D4,L1,V1,M1} { domain( X ) ==> domain( domain( X )
% 0.73/1.18 ) }.
% 0.73/1.18 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.73/1.18 parent1[0; 2]: (1510) {G1,W8,D4,L1,V1,M1} { domain( multiplication( one, X
% 0.73/1.18 ) ) ==> domain( domain( X ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1513) {G1,W6,D4,L1,V1,M1} { domain( domain( X ) ) ==> domain( X )
% 0.73/1.18 }.
% 0.73/1.18 parent0[0]: (1512) {G1,W6,D4,L1,V1,M1} { domain( X ) ==> domain( domain( X
% 0.73/1.18 ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (137) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) )
% 0.73/1.18 ==> domain( X ) }.
% 0.73/1.18 parent0: (1513) {G1,W6,D4,L1,V1,M1} { domain( domain( X ) ) ==> domain( X
% 0.73/1.18 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1515) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) ==>
% 0.73/1.18 addition( domain( X ), domain( Y ) ) }.
% 0.73/1.18 parent0[0]: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 0.73/1.18 ) ) ==> domain( addition( X, Y ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1518) {G1,W9,D4,L1,V1,M1} { domain( addition( X, one ) ) ==>
% 0.73/1.18 addition( domain( X ), one ) }.
% 0.73/1.18 parent0[0]: (100) {G2,W4,D3,L1,V0,M1} P(5,13);d(21) { domain( one ) ==> one
% 0.73/1.18 }.
% 0.73/1.18 parent1[0; 8]: (1515) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) )
% 0.73/1.18 ==> addition( domain( X ), domain( Y ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 Y := one
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1519) {G1,W6,D4,L1,V1,M1} { domain( addition( X, one ) ) ==> one
% 0.73/1.18 }.
% 0.73/1.18 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.73/1.18 one }.
% 0.73/1.18 parent1[0; 5]: (1518) {G1,W9,D4,L1,V1,M1} { domain( addition( X, one ) )
% 0.73/1.18 ==> addition( domain( X ), one ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (152) {G3,W6,D4,L1,V1,M1} P(100,17);d(15) { domain( addition(
% 0.73/1.18 X, one ) ) ==> one }.
% 0.73/1.18 parent0: (1519) {G1,W6,D4,L1,V1,M1} { domain( addition( X, one ) ) ==> one
% 0.73/1.18 }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1521) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 0.73/1.18 addition( X, Y ), Y ) }.
% 0.73/1.18 parent0[0]: (24) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 0.73/1.18 ) ==> addition( Y, X ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1522) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X )
% 0.73/1.18 }.
% 0.73/1.18 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 0.73/1.18 leq( X, Y ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 resolution: (1523) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 0.73/1.18 parent0[0]: (1522) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 0.73/1.18 , X ) }.
% 0.73/1.18 parent1[0]: (1521) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 0.73/1.18 addition( X, Y ), Y ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := addition( X, Y )
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (216) {G2,W5,D3,L1,V2,M1} R(24,35) { leq( X, addition( Y, X )
% 0.73/1.18 ) }.
% 0.73/1.18 parent0: (1523) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1524) {G1,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.73/1.18 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.73/1.18 }.
% 0.73/1.18 parent1[0; 2]: (216) {G2,W5,D3,L1,V2,M1} R(24,35) { leq( X, addition( Y, X
% 0.73/1.18 ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (233) {G3,W5,D3,L1,V2,M1} P(0,216) { leq( Y, addition( Y, X )
% 0.73/1.18 ) }.
% 0.73/1.18 parent0: (1524) {G1,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1527) {G1,W7,D4,L1,V2,M1} { leq( domain( X ), domain( addition(
% 0.73/1.18 X, Y ) ) ) }.
% 0.73/1.18 parent0[0]: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 0.73/1.18 ) ) ==> domain( addition( X, Y ) ) }.
% 0.73/1.18 parent1[0; 3]: (233) {G3,W5,D3,L1,V2,M1} P(0,216) { leq( Y, addition( Y, X
% 0.73/1.18 ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := domain( Y )
% 0.73/1.18 Y := domain( X )
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (241) {G4,W7,D4,L1,V2,M1} P(17,233) { leq( domain( X ), domain
% 0.73/1.18 ( addition( X, Y ) ) ) }.
% 0.73/1.18 parent0: (1527) {G1,W7,D4,L1,V2,M1} { leq( domain( X ), domain( addition(
% 0.73/1.18 X, Y ) ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1529) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) ==>
% 0.73/1.18 domain( multiplication( X, domain( Y ) ) ) }.
% 0.73/1.18 parent0[0]: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 0.73/1.18 ( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1531) {G1,W11,D5,L1,V2,M1} { domain( multiplication( X, addition
% 0.73/1.18 ( Y, one ) ) ) ==> domain( multiplication( X, one ) ) }.
% 0.73/1.18 parent0[0]: (152) {G3,W6,D4,L1,V1,M1} P(100,17);d(15) { domain( addition( X
% 0.73/1.18 , one ) ) ==> one }.
% 0.73/1.18 parent1[0; 10]: (1529) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y
% 0.73/1.18 ) ) ==> domain( multiplication( X, domain( Y ) ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 Y := addition( Y, one )
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1532) {G1,W9,D5,L1,V2,M1} { domain( multiplication( X, addition
% 0.73/1.18 ( Y, one ) ) ) ==> domain( X ) }.
% 0.73/1.18 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.73/1.18 parent1[0; 8]: (1531) {G1,W11,D5,L1,V2,M1} { domain( multiplication( X,
% 0.73/1.18 addition( Y, one ) ) ) ==> domain( multiplication( X, one ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (332) {G4,W9,D5,L1,V2,M1} P(152,14);d(5) { domain(
% 0.73/1.18 multiplication( Y, addition( X, one ) ) ) ==> domain( Y ) }.
% 0.73/1.18 parent0: (1532) {G1,W9,D5,L1,V2,M1} { domain( multiplication( X, addition
% 0.73/1.18 ( Y, one ) ) ) ==> domain( X ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1536) {G2,W11,D5,L1,V2,M1} { leq( domain( multiplication( X, Y )
% 0.73/1.18 ), domain( multiplication( X, addition( Y, one ) ) ) ) }.
% 0.73/1.18 parent0[0]: (42) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X
% 0.73/1.18 , Y ), X ) = multiplication( X, addition( Y, one ) ) }.
% 0.73/1.18 parent1[0; 6]: (241) {G4,W7,D4,L1,V2,M1} P(17,233) { leq( domain( X ),
% 0.73/1.18 domain( addition( X, Y ) ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := multiplication( X, Y )
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1537) {G3,W7,D4,L1,V2,M1} { leq( domain( multiplication( X, Y )
% 0.73/1.18 ), domain( X ) ) }.
% 0.73/1.18 parent0[0]: (332) {G4,W9,D5,L1,V2,M1} P(152,14);d(5) { domain(
% 0.73/1.18 multiplication( Y, addition( X, one ) ) ) ==> domain( Y ) }.
% 0.73/1.18 parent1[0; 5]: (1536) {G2,W11,D5,L1,V2,M1} { leq( domain( multiplication(
% 0.73/1.18 X, Y ) ), domain( multiplication( X, addition( Y, one ) ) ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (1080) {G5,W7,D4,L1,V2,M1} P(42,241);d(332) { leq( domain(
% 0.73/1.18 multiplication( X, Y ) ), domain( X ) ) }.
% 0.73/1.18 parent0: (1537) {G3,W7,D4,L1,V2,M1} { leq( domain( multiplication( X, Y )
% 0.73/1.18 ), domain( X ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1538) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, Y ),
% 0.73/1.18 X ) = addition( X, multiplication( Y, X ) ) }.
% 0.73/1.18 parent0[0]: (62) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.73/1.18 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := X
% 0.73/1.18 Y := Y
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1542) {G1,W11,D5,L1,V0,M1} { multiplication( addition( one,
% 0.73/1.18 domain( skol2 ) ), skol1 ) = multiplication( domain( skol2 ), skol1 ) }.
% 0.73/1.18 parent0[0]: (18) {G0,W11,D5,L1,V0,M1} I { addition( skol1, multiplication(
% 0.73/1.18 domain( skol2 ), skol1 ) ) ==> multiplication( domain( skol2 ), skol1 )
% 0.73/1.18 }.
% 0.73/1.18 parent1[0; 7]: (1538) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one
% 0.73/1.18 , Y ), X ) = addition( X, multiplication( Y, X ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := skol1
% 0.73/1.18 Y := domain( skol2 )
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1543) {G2,W8,D4,L1,V0,M1} { multiplication( one, skol1 ) =
% 0.73/1.18 multiplication( domain( skol2 ), skol1 ) }.
% 0.73/1.18 parent0[0]: (21) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 0.73/1.18 ==> one }.
% 0.73/1.18 parent1[0; 2]: (1542) {G1,W11,D5,L1,V0,M1} { multiplication( addition( one
% 0.73/1.18 , domain( skol2 ) ), skol1 ) = multiplication( domain( skol2 ), skol1 )
% 0.73/1.18 }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := skol2
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1544) {G1,W6,D4,L1,V0,M1} { skol1 = multiplication( domain(
% 0.73/1.18 skol2 ), skol1 ) }.
% 0.73/1.18 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.73/1.18 parent1[0; 1]: (1543) {G2,W8,D4,L1,V0,M1} { multiplication( one, skol1 ) =
% 0.73/1.18 multiplication( domain( skol2 ), skol1 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := skol1
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1545) {G1,W6,D4,L1,V0,M1} { multiplication( domain( skol2 ),
% 0.73/1.18 skol1 ) = skol1 }.
% 0.73/1.18 parent0[0]: (1544) {G1,W6,D4,L1,V0,M1} { skol1 = multiplication( domain(
% 0.73/1.18 skol2 ), skol1 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (1213) {G2,W6,D4,L1,V0,M1} P(62,18);d(21);d(6) {
% 0.73/1.18 multiplication( domain( skol2 ), skol1 ) ==> skol1 }.
% 0.73/1.18 parent0: (1545) {G1,W6,D4,L1,V0,M1} { multiplication( domain( skol2 ),
% 0.73/1.18 skol1 ) = skol1 }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1548) {G3,W6,D4,L1,V0,M1} { leq( domain( skol1 ), domain( domain
% 0.73/1.18 ( skol2 ) ) ) }.
% 0.73/1.18 parent0[0]: (1213) {G2,W6,D4,L1,V0,M1} P(62,18);d(21);d(6) { multiplication
% 0.73/1.18 ( domain( skol2 ), skol1 ) ==> skol1 }.
% 0.73/1.18 parent1[0; 2]: (1080) {G5,W7,D4,L1,V2,M1} P(42,241);d(332) { leq( domain(
% 0.73/1.18 multiplication( X, Y ) ), domain( X ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 X := domain( skol2 )
% 0.73/1.18 Y := skol1
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1549) {G2,W5,D3,L1,V0,M1} { leq( domain( skol1 ), domain( skol2
% 0.73/1.18 ) ) }.
% 0.73/1.18 parent0[0]: (137) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) )
% 0.73/1.18 ==> domain( X ) }.
% 0.73/1.18 parent1[0; 3]: (1548) {G3,W6,D4,L1,V0,M1} { leq( domain( skol1 ), domain(
% 0.73/1.18 domain( skol2 ) ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := skol2
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (1243) {G6,W5,D3,L1,V0,M1} P(1213,1080);d(137) { leq( domain(
% 0.73/1.18 skol1 ), domain( skol2 ) ) }.
% 0.73/1.18 parent0: (1549) {G2,W5,D3,L1,V0,M1} { leq( domain( skol1 ), domain( skol2
% 0.73/1.18 ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 0 ==> 0
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1550) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X )
% 0.73/1.18 }.
% 0.73/1.18 parent0[0]: (54) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 0.73/1.18 leq( X, Y ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := Y
% 0.73/1.18 Y := X
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 eqswap: (1552) {G2,W7,D4,L1,V0,M1} { ! domain( skol2 ) ==> domain(
% 0.73/1.18 addition( skol2, skol1 ) ) }.
% 0.73/1.18 parent0[0]: (28) {G2,W7,D4,L1,V0,M1} P(0,19) { ! domain( addition( skol2,
% 0.73/1.18 skol1 ) ) ==> domain( skol2 ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 resolution: (1553) {G2,W8,D4,L1,V0,M1} { domain( skol2 ) ==> addition(
% 0.73/1.18 domain( skol2 ), domain( skol1 ) ) }.
% 0.73/1.18 parent0[1]: (1550) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 0.73/1.18 , X ) }.
% 0.73/1.18 parent1[0]: (1243) {G6,W5,D3,L1,V0,M1} P(1213,1080);d(137) { leq( domain(
% 0.73/1.18 skol1 ), domain( skol2 ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := domain( skol2 )
% 0.73/1.18 Y := domain( skol1 )
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 paramod: (1554) {G1,W7,D4,L1,V0,M1} { domain( skol2 ) ==> domain( addition
% 0.73/1.18 ( skol2, skol1 ) ) }.
% 0.73/1.18 parent0[0]: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 0.73/1.18 ) ) ==> domain( addition( X, Y ) ) }.
% 0.73/1.18 parent1[0; 3]: (1553) {G2,W8,D4,L1,V0,M1} { domain( skol2 ) ==> addition(
% 0.73/1.18 domain( skol2 ), domain( skol1 ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 X := skol2
% 0.73/1.18 Y := skol1
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 resolution: (1555) {G2,W0,D0,L0,V0,M0} { }.
% 0.73/1.18 parent0[0]: (1552) {G2,W7,D4,L1,V0,M1} { ! domain( skol2 ) ==> domain(
% 0.73/1.18 addition( skol2, skol1 ) ) }.
% 0.73/1.18 parent1[0]: (1554) {G1,W7,D4,L1,V0,M1} { domain( skol2 ) ==> domain(
% 0.73/1.18 addition( skol2, skol1 ) ) }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 substitution1:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 subsumption: (1257) {G7,W0,D0,L0,V0,M0} R(1243,54);d(17);r(28) { }.
% 0.73/1.18 parent0: (1555) {G2,W0,D0,L0,V0,M0} { }.
% 0.73/1.18 substitution0:
% 0.73/1.18 end
% 0.73/1.18 permutation0:
% 0.73/1.18 end
% 0.73/1.18
% 0.73/1.18 Proof check complete!
% 0.73/1.18
% 0.73/1.18 Memory use:
% 0.73/1.18
% 0.73/1.18 space for terms: 14943
% 0.73/1.18 space for clauses: 79903
% 0.73/1.18
% 0.73/1.18
% 0.73/1.18 clauses generated: 8989
% 0.73/1.18 clauses kept: 1258
% 0.73/1.18 clauses selected: 188
% 0.73/1.18 clauses deleted: 11
% 0.73/1.18 clauses inuse deleted: 5
% 0.73/1.18
% 0.73/1.18 subsentry: 10865
% 0.73/1.18 literals s-matched: 8174
% 0.73/1.18 literals matched: 8100
% 0.73/1.18 full subsumption: 516
% 0.73/1.18
% 0.73/1.18 checksum: -346549630
% 0.73/1.18
% 0.73/1.18
% 0.73/1.18 Bliksem ended
%------------------------------------------------------------------------------