TSTP Solution File: KLE052+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE052+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 01:36:55 EDT 2022
% Result : Theorem 0.49s 1.01s
% Output : Refutation 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : KLE052+1 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.09 % Command : bliksem %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % DateTime : Thu Jun 16 13:41:45 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.49/1.01 *** allocated 10000 integers for termspace/termends
% 0.49/1.01 *** allocated 10000 integers for clauses
% 0.49/1.01 *** allocated 10000 integers for justifications
% 0.49/1.01 Bliksem 1.12
% 0.49/1.01
% 0.49/1.01
% 0.49/1.01 Automatic Strategy Selection
% 0.49/1.01
% 0.49/1.01
% 0.49/1.01 Clauses:
% 0.49/1.01
% 0.49/1.01 { addition( X, Y ) = addition( Y, X ) }.
% 0.49/1.01 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.49/1.01 { addition( X, zero ) = X }.
% 0.49/1.01 { addition( X, X ) = X }.
% 0.49/1.01 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.49/1.01 multiplication( X, Y ), Z ) }.
% 0.49/1.01 { multiplication( X, one ) = X }.
% 0.49/1.01 { multiplication( one, X ) = X }.
% 0.49/1.01 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.49/1.01 , multiplication( X, Z ) ) }.
% 0.49/1.01 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.49/1.01 , multiplication( Y, Z ) ) }.
% 0.49/1.01 { multiplication( X, zero ) = zero }.
% 0.49/1.01 { multiplication( zero, X ) = zero }.
% 0.49/1.01 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.49/1.01 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.49/1.01 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.49/1.01 ( X ), X ) }.
% 0.49/1.01 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.49/1.01 ) ) }.
% 0.49/1.01 { addition( domain( X ), one ) = one }.
% 0.49/1.01 { domain( zero ) = zero }.
% 0.49/1.01 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.49/1.01 { ! multiplication( domain( skol1 ), skol1 ) = skol1 }.
% 0.49/1.01
% 0.49/1.01 percentage equality = 0.904762, percentage horn = 1.000000
% 0.49/1.01 This is a pure equality problem
% 0.49/1.01
% 0.49/1.01
% 0.49/1.01
% 0.49/1.01 Options Used:
% 0.49/1.01
% 0.49/1.01 useres = 1
% 0.49/1.01 useparamod = 1
% 0.49/1.01 useeqrefl = 1
% 0.49/1.01 useeqfact = 1
% 0.49/1.01 usefactor = 1
% 0.49/1.01 usesimpsplitting = 0
% 0.49/1.01 usesimpdemod = 5
% 0.49/1.01 usesimpres = 3
% 0.49/1.01
% 0.49/1.01 resimpinuse = 1000
% 0.49/1.01 resimpclauses = 20000
% 0.49/1.01 substype = eqrewr
% 0.49/1.01 backwardsubs = 1
% 0.49/1.01 selectoldest = 5
% 0.49/1.01
% 0.49/1.01 litorderings [0] = split
% 0.49/1.01 litorderings [1] = extend the termordering, first sorting on arguments
% 0.49/1.01
% 0.49/1.01 termordering = kbo
% 0.49/1.01
% 0.49/1.01 litapriori = 0
% 0.49/1.01 termapriori = 1
% 0.49/1.01 litaposteriori = 0
% 0.49/1.01 termaposteriori = 0
% 0.49/1.01 demodaposteriori = 0
% 0.49/1.01 ordereqreflfact = 0
% 0.49/1.01
% 0.49/1.01 litselect = negord
% 0.49/1.01
% 0.49/1.01 maxweight = 15
% 0.49/1.01 maxdepth = 30000
% 0.49/1.01 maxlength = 115
% 0.49/1.01 maxnrvars = 195
% 0.49/1.01 excuselevel = 1
% 0.49/1.01 increasemaxweight = 1
% 0.49/1.01
% 0.49/1.01 maxselected = 10000000
% 0.49/1.01 maxnrclauses = 10000000
% 0.49/1.01
% 0.49/1.01 showgenerated = 0
% 0.49/1.01 showkept = 0
% 0.49/1.01 showselected = 0
% 0.49/1.01 showdeleted = 0
% 0.49/1.01 showresimp = 1
% 0.49/1.01 showstatus = 2000
% 0.49/1.01
% 0.49/1.01 prologoutput = 0
% 0.49/1.01 nrgoals = 5000000
% 0.49/1.01 totalproof = 1
% 0.49/1.01
% 0.49/1.01 Symbols occurring in the translation:
% 0.49/1.01
% 0.49/1.01 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.49/1.01 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 0.49/1.01 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.49/1.01 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.49/1.01 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.49/1.01 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.49/1.01 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.49/1.01 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.49/1.01 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.49/1.01 leq [42, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.49/1.01 domain [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.49/1.01 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.49/1.01
% 0.49/1.01
% 0.49/1.01 Starting Search:
% 0.49/1.01
% 0.49/1.01 *** allocated 15000 integers for clauses
% 0.49/1.01 *** allocated 22500 integers for clauses
% 0.49/1.01 *** allocated 33750 integers for clauses
% 0.49/1.01 *** allocated 50625 integers for clauses
% 0.49/1.01 *** allocated 75937 integers for clauses
% 0.49/1.01 *** allocated 15000 integers for termspace/termends
% 0.49/1.01 Resimplifying inuse:
% 0.49/1.01 Done
% 0.49/1.01
% 0.49/1.01 *** allocated 22500 integers for termspace/termends
% 0.49/1.01 *** allocated 113905 integers for clauses
% 0.49/1.01 *** allocated 33750 integers for termspace/termends
% 0.49/1.01
% 0.49/1.01 Intermediate Status:
% 0.49/1.01 Generated: 14368
% 0.49/1.01 Kept: 2005
% 0.49/1.01 Inuse: 224
% 0.49/1.01 Deleted: 13
% 0.49/1.01 Deletedinuse: 5
% 0.49/1.01
% 0.49/1.01 Resimplifying inuse:
% 0.49/1.01 Done
% 0.49/1.01
% 0.49/1.01 *** allocated 170857 integers for clauses
% 0.49/1.01
% 0.49/1.01 Bliksems!, er is een bewijs:
% 0.49/1.01 % SZS status Theorem
% 0.49/1.01 % SZS output start Refutation
% 0.49/1.01
% 0.49/1.01 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.49/1.01 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.49/1.01 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.49/1.01 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.49/1.01 (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.49/1.01 ) ==> multiplication( domain( X ), X ) }.
% 0.49/1.01 (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> one }.
% 0.49/1.01 (18) {G0,W6,D4,L1,V0,M1} I { ! multiplication( domain( skol1 ), skol1 ) ==>
% 0.49/1.01 skol1 }.
% 0.49/1.01 (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) ) ==> one }.
% 0.49/1.01 (78) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication( Y, X ) ) =
% 0.49/1.01 multiplication( addition( one, Y ), X ) }.
% 0.49/1.01 (2400) {G2,W6,D4,L1,V1,M1} P(78,13);d(20);d(6) { multiplication( domain( X
% 0.49/1.01 ), X ) ==> X }.
% 0.49/1.01 (2411) {G3,W0,D0,L0,V0,M0} R(2400,18) { }.
% 0.49/1.01
% 0.49/1.01
% 0.49/1.01 % SZS output end Refutation
% 0.49/1.01 found a proof!
% 0.49/1.01
% 0.49/1.01
% 0.49/1.01 Unprocessed initial clauses:
% 0.49/1.01
% 0.49/1.01 (2413) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.49/1.01 (2414) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.49/1.01 addition( Z, Y ), X ) }.
% 0.49/1.01 (2415) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.49/1.01 (2416) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.49/1.01 (2417) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.49/1.01 = multiplication( multiplication( X, Y ), Z ) }.
% 0.49/1.01 (2418) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.49/1.01 (2419) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.49/1.01 (2420) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.49/1.01 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.49/1.01 (2421) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.49/1.01 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.49/1.01 (2422) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.49/1.01 (2423) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.49/1.01 (2424) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.49/1.01 (2425) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.49/1.01 (2426) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X
% 0.49/1.01 ) ) = multiplication( domain( X ), X ) }.
% 0.49/1.01 (2427) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 0.49/1.01 multiplication( X, domain( Y ) ) ) }.
% 0.49/1.01 (2428) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 0.49/1.01 (2429) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.49/1.01 (2430) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition(
% 0.49/1.01 domain( X ), domain( Y ) ) }.
% 0.49/1.01 (2431) {G0,W6,D4,L1,V0,M1} { ! multiplication( domain( skol1 ), skol1 ) =
% 0.49/1.01 skol1 }.
% 0.49/1.01
% 0.49/1.01
% 0.49/1.01 Total Proof:
% 0.49/1.01
% 0.49/1.01 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.49/1.01 ) }.
% 0.49/1.01 parent0: (2413) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.49/1.01 }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 Y := Y
% 0.49/1.01 end
% 0.49/1.01 permutation0:
% 0.49/1.01 0 ==> 0
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.49/1.01 parent0: (2419) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01 permutation0:
% 0.49/1.01 0 ==> 0
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 eqswap: (2445) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.49/1.01 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.49/1.01 parent0[0]: (2421) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 0.49/1.01 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 Y := Y
% 0.49/1.01 Z := Z
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.49/1.01 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.49/1.01 parent0: (2445) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.49/1.01 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 Y := Y
% 0.49/1.01 Z := Z
% 0.49/1.01 end
% 0.49/1.01 permutation0:
% 0.49/1.01 0 ==> 0
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.49/1.01 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.49/1.01 parent0: (2426) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain
% 0.49/1.01 ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01 permutation0:
% 0.49/1.01 0 ==> 0
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 subsumption: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.49/1.01 one }.
% 0.49/1.01 parent0: (2428) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one
% 0.49/1.01 }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01 permutation0:
% 0.49/1.01 0 ==> 0
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 subsumption: (18) {G0,W6,D4,L1,V0,M1} I { ! multiplication( domain( skol1 )
% 0.49/1.01 , skol1 ) ==> skol1 }.
% 0.49/1.01 parent0: (2431) {G0,W6,D4,L1,V0,M1} { ! multiplication( domain( skol1 ),
% 0.49/1.01 skol1 ) = skol1 }.
% 0.49/1.01 substitution0:
% 0.49/1.01 end
% 0.49/1.01 permutation0:
% 0.49/1.01 0 ==> 0
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 eqswap: (2492) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X ), one )
% 0.49/1.01 }.
% 0.49/1.01 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.49/1.01 one }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 paramod: (2493) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X ) )
% 0.49/1.01 }.
% 0.49/1.01 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.49/1.01 }.
% 0.49/1.01 parent1[0; 2]: (2492) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X )
% 0.49/1.01 , one ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := domain( X )
% 0.49/1.01 Y := one
% 0.49/1.01 end
% 0.49/1.01 substitution1:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 eqswap: (2496) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.49/1.01 }.
% 0.49/1.01 parent0[0]: (2493) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X
% 0.49/1.01 ) ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 subsumption: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X )
% 0.49/1.01 ) ==> one }.
% 0.49/1.01 parent0: (2496) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.49/1.01 }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01 permutation0:
% 0.49/1.01 0 ==> 0
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 eqswap: (2498) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 0.49/1.01 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 0.49/1.01 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.49/1.01 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 Y := Z
% 0.49/1.01 Z := Y
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 paramod: (2499) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X )
% 0.49/1.01 , Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.49/1.01 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.49/1.01 parent1[0; 7]: (2498) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X,
% 0.49/1.01 Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 0.49/1.01 }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := Y
% 0.49/1.01 end
% 0.49/1.01 substitution1:
% 0.49/1.01 X := one
% 0.49/1.01 Y := Y
% 0.49/1.01 Z := X
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 eqswap: (2501) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y )
% 0.49/1.01 ) ==> multiplication( addition( one, X ), Y ) }.
% 0.49/1.01 parent0[0]: (2499) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X
% 0.49/1.01 ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 Y := Y
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 subsumption: (78) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.49/1.01 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.49/1.01 parent0: (2501) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y )
% 0.49/1.01 ) ==> multiplication( addition( one, X ), Y ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := Y
% 0.49/1.01 Y := X
% 0.49/1.01 end
% 0.49/1.01 permutation0:
% 0.49/1.01 0 ==> 0
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 eqswap: (2503) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, Y ),
% 0.49/1.01 X ) = addition( X, multiplication( Y, X ) ) }.
% 0.49/1.01 parent0[0]: (78) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.49/1.01 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 Y := Y
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 paramod: (2508) {G1,W11,D5,L1,V1,M1} { multiplication( addition( one,
% 0.49/1.01 domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 0.49/1.01 parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.49/1.01 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.49/1.01 parent1[0; 7]: (2503) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one
% 0.49/1.01 , Y ), X ) = addition( X, multiplication( Y, X ) ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01 substitution1:
% 0.49/1.01 X := X
% 0.49/1.01 Y := domain( X )
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 paramod: (2509) {G2,W8,D4,L1,V1,M1} { multiplication( one, X ) =
% 0.49/1.01 multiplication( domain( X ), X ) }.
% 0.49/1.01 parent0[0]: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 0.49/1.01 ==> one }.
% 0.49/1.01 parent1[0; 2]: (2508) {G1,W11,D5,L1,V1,M1} { multiplication( addition( one
% 0.49/1.01 , domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01 substitution1:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 paramod: (2510) {G1,W6,D4,L1,V1,M1} { X = multiplication( domain( X ), X )
% 0.49/1.01 }.
% 0.49/1.01 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.49/1.01 parent1[0; 1]: (2509) {G2,W8,D4,L1,V1,M1} { multiplication( one, X ) =
% 0.49/1.01 multiplication( domain( X ), X ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01 substitution1:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 eqswap: (2511) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) = X
% 0.49/1.01 }.
% 0.49/1.01 parent0[0]: (2510) {G1,W6,D4,L1,V1,M1} { X = multiplication( domain( X ),
% 0.49/1.01 X ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 subsumption: (2400) {G2,W6,D4,L1,V1,M1} P(78,13);d(20);d(6) {
% 0.49/1.01 multiplication( domain( X ), X ) ==> X }.
% 0.49/1.01 parent0: (2511) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) = X
% 0.49/1.01 }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01 permutation0:
% 0.49/1.01 0 ==> 0
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 eqswap: (2512) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain( X ), X
% 0.49/1.01 ) }.
% 0.49/1.01 parent0[0]: (2400) {G2,W6,D4,L1,V1,M1} P(78,13);d(20);d(6) { multiplication
% 0.49/1.01 ( domain( X ), X ) ==> X }.
% 0.49/1.01 substitution0:
% 0.49/1.01 X := X
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 eqswap: (2513) {G0,W6,D4,L1,V0,M1} { ! skol1 ==> multiplication( domain(
% 0.49/1.01 skol1 ), skol1 ) }.
% 0.49/1.01 parent0[0]: (18) {G0,W6,D4,L1,V0,M1} I { ! multiplication( domain( skol1 )
% 0.49/1.01 , skol1 ) ==> skol1 }.
% 0.49/1.01 substitution0:
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 resolution: (2514) {G1,W0,D0,L0,V0,M0} { }.
% 0.49/1.01 parent0[0]: (2513) {G0,W6,D4,L1,V0,M1} { ! skol1 ==> multiplication(
% 0.49/1.01 domain( skol1 ), skol1 ) }.
% 0.49/1.01 parent1[0]: (2512) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain( X )
% 0.49/1.01 , X ) }.
% 0.49/1.01 substitution0:
% 0.49/1.01 end
% 0.49/1.01 substitution1:
% 0.49/1.01 X := skol1
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 subsumption: (2411) {G3,W0,D0,L0,V0,M0} R(2400,18) { }.
% 0.49/1.01 parent0: (2514) {G1,W0,D0,L0,V0,M0} { }.
% 0.49/1.01 substitution0:
% 0.49/1.01 end
% 0.49/1.01 permutation0:
% 0.49/1.01 end
% 0.49/1.01
% 0.49/1.01 Proof check complete!
% 0.49/1.01
% 0.49/1.01 Memory use:
% 0.49/1.01
% 0.49/1.01 space for terms: 30448
% 0.49/1.01 space for clauses: 124707
% 0.49/1.01
% 0.49/1.01
% 0.49/1.01 clauses generated: 17992
% 0.49/1.01 clauses kept: 2412
% 0.49/1.01 clauses selected: 250
% 0.49/1.01 clauses deleted: 18
% 0.49/1.01 clauses inuse deleted: 6
% 0.49/1.01
% 0.49/1.01 subsentry: 38292
% 0.49/1.01 literals s-matched: 26182
% 0.49/1.01 literals matched: 25050
% 0.49/1.01 full subsumption: 3121
% 0.49/1.01
% 0.49/1.01 checksum: -1593391094
% 0.49/1.01
% 0.49/1.01
% 0.49/1.01 Bliksem ended
%------------------------------------------------------------------------------