%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG018+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 : Thu Jul 14 12:09:06 EDT 2022
% Result : Theorem 0.69s 1.06s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG018+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n021.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 9 01:57:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.06 *** allocated 10000 integers for termspace/termends
% 0.69/1.06 *** allocated 10000 integers for clauses
% 0.69/1.06 *** allocated 10000 integers for justifications
% 0.69/1.06 Bliksem 1.12
% 0.69/1.06
% 0.69/1.06
% 0.69/1.06 Automatic Strategy Selection
% 0.69/1.06
% 0.69/1.06
% 0.69/1.06 Clauses:
% 0.69/1.06
% 0.69/1.06 { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X, Y ) ) }.
% 0.69/1.06 { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X, Y ) ) }.
% 0.69/1.06 { sorti1( skol1 ) }.
% 0.69/1.06 { ! sorti1( X ), op1( X, X ) = skol1 }.
% 0.69/1.06 { ! sorti2( X ), sorti2( skol2( Y ) ) }.
% 0.69/1.06 { ! sorti2( X ), ! op2( skol2( X ), skol2( X ) ) = X }.
% 0.69/1.06 { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.69/1.06 { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.69/1.06 { ! sorti1( X ), ! sorti1( Y ), h( op1( X, Y ) ) = op2( h( X ), h( Y ) ) }
% 0.69/1.06 .
% 0.69/1.06 { ! sorti2( X ), ! sorti2( Y ), j( op2( X, Y ) ) = op1( j( X ), j( Y ) ) }
% 0.69/1.06 .
% 0.69/1.06 { ! sorti2( X ), h( j( X ) ) = X }.
% 0.69/1.06 { ! sorti1( X ), j( h( X ) ) = X }.
% 0.69/1.06
% 0.69/1.06 percentage equality = 0.222222, percentage horn = 1.000000
% 0.69/1.06 This is a problem with some equality
% 0.69/1.06
% 0.69/1.06
% 0.69/1.06
% 0.69/1.06 Options Used:
% 0.69/1.06
% 0.69/1.06 useres = 1
% 0.69/1.06 useparamod = 1
% 0.69/1.06 useeqrefl = 1
% 0.69/1.06 useeqfact = 1
% 0.69/1.06 usefactor = 1
% 0.69/1.06 usesimpsplitting = 0
% 0.69/1.06 usesimpdemod = 5
% 0.69/1.06 usesimpres = 3
% 0.69/1.06
% 0.69/1.06 resimpinuse = 1000
% 0.69/1.06 resimpclauses = 20000
% 0.69/1.06 substype = eqrewr
% 0.69/1.06 backwardsubs = 1
% 0.69/1.06 selectoldest = 5
% 0.69/1.06
% 0.69/1.06 litorderings [0] = split
% 0.69/1.06 litorderings [1] = extend the termordering, first sorting on arguments
% 0.69/1.06
% 0.69/1.06 termordering = kbo
% 0.69/1.06
% 0.69/1.06 litapriori = 0
% 0.69/1.06 termapriori = 1
% 0.69/1.06 litaposteriori = 0
% 0.69/1.06 termaposteriori = 0
% 0.69/1.06 demodaposteriori = 0
% 0.69/1.06 ordereqreflfact = 0
% 0.69/1.06
% 0.69/1.06 litselect = negord
% 0.69/1.06
% 0.69/1.06 maxweight = 15
% 0.69/1.06 maxdepth = 30000
% 0.69/1.06 maxlength = 115
% 0.69/1.06 maxnrvars = 195
% 0.69/1.06 excuselevel = 1
% 0.69/1.06 increasemaxweight = 1
% 0.69/1.06
% 0.69/1.06 maxselected = 10000000
% 0.69/1.06 maxnrclauses = 10000000
% 0.69/1.06
% 0.69/1.06 showgenerated = 0
% 0.69/1.06 showkept = 0
% 0.69/1.06 showselected = 0
% 0.69/1.06 showdeleted = 0
% 0.69/1.06 showresimp = 1
% 0.69/1.06 showstatus = 2000
% 0.69/1.06
% 0.69/1.06 prologoutput = 0
% 0.69/1.06 nrgoals = 5000000
% 0.69/1.06 totalproof = 1
% 0.69/1.06
% 0.69/1.06 Symbols occurring in the translation:
% 0.69/1.06
% 0.69/1.06 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.06 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.69/1.06 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.69/1.06 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.06 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.06 sorti1 [36, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.69/1.06 op1 [38, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.69/1.06 sorti2 [39, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.69/1.06 op2 [40, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.69/1.06 h [41, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.69/1.06 j [42, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.69/1.06 skol1 [49, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.69/1.06 skol2 [50, 1] (w:1, o:24, a:1, s:1, b:1).
% 0.69/1.06
% 0.69/1.06
% 0.69/1.06 Starting Search:
% 0.69/1.06
% 0.69/1.06 *** allocated 15000 integers for clauses
% 0.69/1.06 *** allocated 22500 integers for clauses
% 0.69/1.06 *** allocated 33750 integers for clauses
% 0.69/1.06 *** allocated 50625 integers for clauses
% 0.69/1.06
% 0.69/1.06 Bliksems!, er is een bewijs:
% 0.69/1.06 % SZS status Theorem
% 0.69/1.06 % SZS output start Refutation
% 0.69/1.06
% 0.69/1.06 (0) {G0,W8,D3,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X, Y
% 0.69/1.06 ) ) }.
% 0.69/1.06 (1) {G0,W8,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X, Y
% 0.69/1.06 ) ) }.
% 0.69/1.06 (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 0.69/1.06 (3) {G0,W7,D3,L2,V1,M2} I { ! sorti1( X ), op1( X, X ) ==> skol1 }.
% 0.69/1.06 (4) {G0,W5,D3,L2,V2,M2} I { ! sorti2( X ), sorti2( skol2( Y ) ) }.
% 0.69/1.06 (5) {G0,W9,D4,L2,V1,M2} I { ! sorti2( X ), ! op2( skol2( X ), skol2( X ) )
% 0.69/1.06 ==> X }.
% 0.69/1.06 (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.69/1.06 (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.69/1.06 (8) {G0,W14,D4,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), op2( h( X ), h(
% 0.69/1.06 Y ) ) ==> h( op1( X, Y ) ) }.
% 0.69/1.06 (10) {G0,W7,D4,L2,V1,M2} I { ! sorti2( X ), h( j( X ) ) ==> X }.
% 0.69/1.06 (13) {G1,W10,D4,L2,V1,M2} F(8);d(3) { ! sorti1( X ), op2( h( X ), h( X ) )
% 0.69/1.06 ==> h( skol1 ) }.
% 0.69/1.06 (17) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 0.69/1.06 (19) {G2,W3,D3,L1,V1,M1} R(17,4) { sorti2( skol2( X ) ) }.
% 0.69/1.06 (22) {G1,W9,D4,L3,V2,M3} R(0,6) { ! sorti1( X ), ! sorti1( Y ), sorti2( h(
% 0.69/1.06 op1( X, Y ) ) ) }.
% 0.69/1.06 (31) {G3,W4,D4,L1,V1,M1} R(19,7) { sorti1( j( skol2( X ) ) ) }.
% 0.69/1.06 (34) {G4,W5,D5,L1,V1,M1} R(31,6) { sorti2( h( j( skol2( X ) ) ) ) }.
% 0.69/1.06 (40) {G3,W7,D4,L2,V2,M2} R(1,19) { ! sorti2( X ), sorti2( op2( skol2( Y ),
% 0.69/1.06 X ) ) }.
% 0.69/1.06 (58) {G5,W6,D6,L1,V1,M1} R(34,7) { sorti1( j( h( j( skol2( X ) ) ) ) ) }.
% 0.69/1.06 (181) {G4,W6,D4,L1,V1,M1} R(40,17) { sorti2( op2( skol2( X ), h( skol1 ) )
% 0.69/1.06 ) }.
% 0.69/1.06 (196) {G5,W11,D7,L1,V1,M1} R(10,34) { h( j( h( j( skol2( X ) ) ) ) ) ==> h
% 0.69/1.06 ( j( skol2( X ) ) ) }.
% 0.69/1.06 (198) {G3,W7,D5,L1,V1,M1} R(10,19) { h( j( skol2( X ) ) ) ==> skol2( X )
% 0.69/1.06 }.
% 0.69/1.06 (205) {G5,W7,D5,L1,V1,M1} R(181,7) { sorti1( j( op2( skol2( X ), h( skol1 )
% 0.69/1.06 ) ) ) }.
% 0.69/1.06 (297) {G6,W8,D4,L1,V1,M1} R(13,58);d(196);d(198) { op2( skol2( X ), skol2(
% 0.69/1.06 X ) ) ==> h( skol1 ) }.
% 0.69/1.06 (565) {G7,W11,D4,L3,V2,M3} R(22,5);d(297) { ! sorti1( X ), ! sorti1( Y ), !
% 0.69/1.06 h( op1( X, Y ) ) ==> h( skol1 ) }.
% 0.69/1.06 (577) {G8,W2,D2,L1,V1,M1} F(565);d(3);q { ! sorti1( X ) }.
% 0.69/1.06 (578) {G9,W0,D0,L0,V0,M0} R(577,205) { }.
% 0.69/1.06
% 0.69/1.06
% 0.69/1.06 % SZS output end Refutation
% 0.69/1.06 found a proof!
% 0.69/1.06
% 0.69/1.06
% 0.69/1.06 Unprocessed initial clauses:
% 0.69/1.06
% 0.69/1.06 (580) {G0,W8,D3,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), sorti1( op1( X,
% 0.69/1.06 Y ) ) }.
% 0.69/1.06 (581) {G0,W8,D3,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), sorti2( op2( X,
% 0.69/1.06 Y ) ) }.
% 0.69/1.06 (582) {G0,W2,D2,L1,V0,M1} { sorti1( skol1 ) }.
% 0.69/1.06 (583) {G0,W7,D3,L2,V1,M2} { ! sorti1( X ), op1( X, X ) = skol1 }.
% 0.69/1.06 (584) {G0,W5,D3,L2,V2,M2} { ! sorti2( X ), sorti2( skol2( Y ) ) }.
% 0.69/1.06 (585) {G0,W9,D4,L2,V1,M2} { ! sorti2( X ), ! op2( skol2( X ), skol2( X ) )
% 0.69/1.06 = X }.
% 0.69/1.06 (586) {G0,W5,D3,L2,V1,M2} { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.69/1.06 (587) {G0,W5,D3,L2,V1,M2} { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.69/1.06 (588) {G0,W14,D4,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), h( op1( X, Y )
% 0.69/1.06 ) = op2( h( X ), h( Y ) ) }.
% 0.69/1.06 (589) {G0,W14,D4,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), j( op2( X, Y )
% 0.69/1.06 ) = op1( j( X ), j( Y ) ) }.
% 0.69/1.06 (590) {G0,W7,D4,L2,V1,M2} { ! sorti2( X ), h( j( X ) ) = X }.
% 0.69/1.06 (591) {G0,W7,D4,L2,V1,M2} { ! sorti1( X ), j( h( X ) ) = X }.
% 0.69/1.06
% 0.69/1.06
% 0.69/1.06 Total Proof:
% 0.69/1.06
% 0.69/1.06 subsumption: (0) {G0,W8,D3,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ),
% 0.69/1.06 sorti1( op1( X, Y ) ) }.
% 0.69/1.06 parent0: (580) {G0,W8,D3,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), sorti1
% 0.69/1.06 ( op1( X, Y ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 1 ==> 1
% 0.69/1.06 2 ==> 2
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (1) {G0,W8,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ),
% 0.69/1.06 sorti2( op2( X, Y ) ) }.
% 0.69/1.06 parent0: (581) {G0,W8,D3,L3,V2,M3} { ! sorti2( X ), ! sorti2( Y ), sorti2
% 0.69/1.06 ( op2( X, Y ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 1 ==> 1
% 0.69/1.06 2 ==> 2
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 0.69/1.06 parent0: (582) {G0,W2,D2,L1,V0,M1} { sorti1( skol1 ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (3) {G0,W7,D3,L2,V1,M2} I { ! sorti1( X ), op1( X, X ) ==>
% 0.69/1.06 skol1 }.
% 0.69/1.06 parent0: (583) {G0,W7,D3,L2,V1,M2} { ! sorti1( X ), op1( X, X ) = skol1
% 0.69/1.06 }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 1 ==> 1
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (4) {G0,W5,D3,L2,V2,M2} I { ! sorti2( X ), sorti2( skol2( Y )
% 0.69/1.06 ) }.
% 0.69/1.06 parent0: (584) {G0,W5,D3,L2,V2,M2} { ! sorti2( X ), sorti2( skol2( Y ) )
% 0.69/1.06 }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 1 ==> 1
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (5) {G0,W9,D4,L2,V1,M2} I { ! sorti2( X ), ! op2( skol2( X ),
% 0.69/1.06 skol2( X ) ) ==> X }.
% 0.69/1.06 parent0: (585) {G0,W9,D4,L2,V1,M2} { ! sorti2( X ), ! op2( skol2( X ),
% 0.69/1.06 skol2( X ) ) = X }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 1 ==> 1
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) )
% 0.69/1.06 }.
% 0.69/1.06 parent0: (586) {G0,W5,D3,L2,V1,M2} { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 1 ==> 1
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) )
% 0.69/1.06 }.
% 0.69/1.06 parent0: (587) {G0,W5,D3,L2,V1,M2} { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 1 ==> 1
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 eqswap: (619) {G0,W14,D4,L3,V2,M3} { op2( h( X ), h( Y ) ) = h( op1( X, Y
% 0.69/1.06 ) ), ! sorti1( X ), ! sorti1( Y ) }.
% 0.69/1.06 parent0[2]: (588) {G0,W14,D4,L3,V2,M3} { ! sorti1( X ), ! sorti1( Y ), h(
% 0.69/1.06 op1( X, Y ) ) = op2( h( X ), h( Y ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (8) {G0,W14,D4,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ), op2
% 0.69/1.06 ( h( X ), h( Y ) ) ==> h( op1( X, Y ) ) }.
% 0.69/1.06 parent0: (619) {G0,W14,D4,L3,V2,M3} { op2( h( X ), h( Y ) ) = h( op1( X, Y
% 0.69/1.06 ) ), ! sorti1( X ), ! sorti1( Y ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 2
% 0.69/1.06 1 ==> 0
% 0.69/1.06 2 ==> 1
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (10) {G0,W7,D4,L2,V1,M2} I { ! sorti2( X ), h( j( X ) ) ==> X
% 0.69/1.06 }.
% 0.69/1.06 parent0: (590) {G0,W7,D4,L2,V1,M2} { ! sorti2( X ), h( j( X ) ) = X }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 1 ==> 1
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 factor: (636) {G0,W12,D4,L2,V1,M2} { ! sorti1( X ), op2( h( X ), h( X ) )
% 0.69/1.06 ==> h( op1( X, X ) ) }.
% 0.69/1.06 parent0[0, 1]: (8) {G0,W14,D4,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ),
% 0.69/1.06 op2( h( X ), h( Y ) ) ==> h( op1( X, Y ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 Y := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 paramod: (637) {G1,W12,D4,L3,V1,M3} { op2( h( X ), h( X ) ) ==> h( skol1 )
% 0.69/1.06 , ! sorti1( X ), ! sorti1( X ) }.
% 0.69/1.06 parent0[1]: (3) {G0,W7,D3,L2,V1,M2} I { ! sorti1( X ), op1( X, X ) ==>
% 0.69/1.06 skol1 }.
% 0.69/1.06 parent1[1; 7]: (636) {G0,W12,D4,L2,V1,M2} { ! sorti1( X ), op2( h( X ), h
% 0.69/1.06 ( X ) ) ==> h( op1( X, X ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 factor: (640) {G1,W10,D4,L2,V1,M2} { op2( h( X ), h( X ) ) ==> h( skol1 )
% 0.69/1.06 , ! sorti1( X ) }.
% 0.69/1.06 parent0[1, 2]: (637) {G1,W12,D4,L3,V1,M3} { op2( h( X ), h( X ) ) ==> h(
% 0.69/1.06 skol1 ), ! sorti1( X ), ! sorti1( X ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (13) {G1,W10,D4,L2,V1,M2} F(8);d(3) { ! sorti1( X ), op2( h( X
% 0.69/1.06 ), h( X ) ) ==> h( skol1 ) }.
% 0.69/1.06 parent0: (640) {G1,W10,D4,L2,V1,M2} { op2( h( X ), h( X ) ) ==> h( skol1 )
% 0.69/1.06 , ! sorti1( X ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 1
% 0.69/1.06 1 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (641) {G1,W3,D3,L1,V0,M1} { sorti2( h( skol1 ) ) }.
% 0.69/1.06 parent0[0]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.69/1.06 parent1[0]: (2) {G0,W2,D2,L1,V0,M1} I { sorti1( skol1 ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := skol1
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (17) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 0.69/1.06 parent0: (641) {G1,W3,D3,L1,V0,M1} { sorti2( h( skol1 ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (642) {G1,W3,D3,L1,V1,M1} { sorti2( skol2( X ) ) }.
% 0.69/1.06 parent0[0]: (4) {G0,W5,D3,L2,V2,M2} I { ! sorti2( X ), sorti2( skol2( Y ) )
% 0.69/1.06 }.
% 0.69/1.06 parent1[0]: (17) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := h( skol1 )
% 0.69/1.06 Y := X
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (19) {G2,W3,D3,L1,V1,M1} R(17,4) { sorti2( skol2( X ) ) }.
% 0.69/1.06 parent0: (642) {G1,W3,D3,L1,V1,M1} { sorti2( skol2( X ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (643) {G1,W9,D4,L3,V2,M3} { sorti2( h( op1( X, Y ) ) ), !
% 0.69/1.06 sorti1( X ), ! sorti1( Y ) }.
% 0.69/1.06 parent0[0]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.69/1.06 parent1[2]: (0) {G0,W8,D3,L3,V2,M3} I { ! sorti1( X ), ! sorti1( Y ),
% 0.69/1.06 sorti1( op1( X, Y ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := op1( X, Y )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (22) {G1,W9,D4,L3,V2,M3} R(0,6) { ! sorti1( X ), ! sorti1( Y )
% 0.69/1.06 , sorti2( h( op1( X, Y ) ) ) }.
% 0.69/1.06 parent0: (643) {G1,W9,D4,L3,V2,M3} { sorti2( h( op1( X, Y ) ) ), ! sorti1
% 0.69/1.06 ( X ), ! sorti1( Y ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 2
% 0.69/1.06 1 ==> 0
% 0.69/1.06 2 ==> 1
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (645) {G1,W4,D4,L1,V1,M1} { sorti1( j( skol2( X ) ) ) }.
% 0.69/1.06 parent0[0]: (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.69/1.06 parent1[0]: (19) {G2,W3,D3,L1,V1,M1} R(17,4) { sorti2( skol2( X ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := skol2( X )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (31) {G3,W4,D4,L1,V1,M1} R(19,7) { sorti1( j( skol2( X ) ) )
% 0.69/1.06 }.
% 0.69/1.06 parent0: (645) {G1,W4,D4,L1,V1,M1} { sorti1( j( skol2( X ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (646) {G1,W5,D5,L1,V1,M1} { sorti2( h( j( skol2( X ) ) ) ) }.
% 0.69/1.06 parent0[0]: (6) {G0,W5,D3,L2,V1,M2} I { ! sorti1( X ), sorti2( h( X ) ) }.
% 0.69/1.06 parent1[0]: (31) {G3,W4,D4,L1,V1,M1} R(19,7) { sorti1( j( skol2( X ) ) )
% 0.69/1.06 }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := j( skol2( X ) )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (34) {G4,W5,D5,L1,V1,M1} R(31,6) { sorti2( h( j( skol2( X ) )
% 0.69/1.06 ) ) }.
% 0.69/1.06 parent0: (646) {G1,W5,D5,L1,V1,M1} { sorti2( h( j( skol2( X ) ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (647) {G1,W7,D4,L2,V2,M2} { ! sorti2( Y ), sorti2( op2( skol2
% 0.69/1.06 ( X ), Y ) ) }.
% 0.69/1.06 parent0[0]: (1) {G0,W8,D3,L3,V2,M3} I { ! sorti2( X ), ! sorti2( Y ),
% 0.69/1.06 sorti2( op2( X, Y ) ) }.
% 0.69/1.06 parent1[0]: (19) {G2,W3,D3,L1,V1,M1} R(17,4) { sorti2( skol2( X ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := skol2( X )
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (40) {G3,W7,D4,L2,V2,M2} R(1,19) { ! sorti2( X ), sorti2( op2
% 0.69/1.06 ( skol2( Y ), X ) ) }.
% 0.69/1.06 parent0: (647) {G1,W7,D4,L2,V2,M2} { ! sorti2( Y ), sorti2( op2( skol2( X
% 0.69/1.06 ), Y ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := Y
% 0.69/1.06 Y := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 1 ==> 1
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (649) {G1,W6,D6,L1,V1,M1} { sorti1( j( h( j( skol2( X ) ) ) )
% 0.69/1.06 ) }.
% 0.69/1.06 parent0[0]: (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.69/1.06 parent1[0]: (34) {G4,W5,D5,L1,V1,M1} R(31,6) { sorti2( h( j( skol2( X ) ) )
% 0.69/1.06 ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := h( j( skol2( X ) ) )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (58) {G5,W6,D6,L1,V1,M1} R(34,7) { sorti1( j( h( j( skol2( X )
% 0.69/1.06 ) ) ) ) }.
% 0.69/1.06 parent0: (649) {G1,W6,D6,L1,V1,M1} { sorti1( j( h( j( skol2( X ) ) ) ) )
% 0.69/1.06 }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (650) {G2,W6,D4,L1,V1,M1} { sorti2( op2( skol2( X ), h( skol1
% 0.69/1.06 ) ) ) }.
% 0.69/1.06 parent0[0]: (40) {G3,W7,D4,L2,V2,M2} R(1,19) { ! sorti2( X ), sorti2( op2(
% 0.69/1.06 skol2( Y ), X ) ) }.
% 0.69/1.06 parent1[0]: (17) {G1,W3,D3,L1,V0,M1} R(6,2) { sorti2( h( skol1 ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := h( skol1 )
% 0.69/1.06 Y := X
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (181) {G4,W6,D4,L1,V1,M1} R(40,17) { sorti2( op2( skol2( X ),
% 0.69/1.06 h( skol1 ) ) ) }.
% 0.69/1.06 parent0: (650) {G2,W6,D4,L1,V1,M1} { sorti2( op2( skol2( X ), h( skol1 ) )
% 0.69/1.06 ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 eqswap: (651) {G0,W7,D4,L2,V1,M2} { X ==> h( j( X ) ), ! sorti2( X ) }.
% 0.69/1.06 parent0[1]: (10) {G0,W7,D4,L2,V1,M2} I { ! sorti2( X ), h( j( X ) ) ==> X
% 0.69/1.06 }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (652) {G1,W11,D7,L1,V1,M1} { h( j( skol2( X ) ) ) ==> h( j( h
% 0.69/1.06 ( j( skol2( X ) ) ) ) ) }.
% 0.69/1.06 parent0[1]: (651) {G0,W7,D4,L2,V1,M2} { X ==> h( j( X ) ), ! sorti2( X )
% 0.69/1.06 }.
% 0.69/1.06 parent1[0]: (34) {G4,W5,D5,L1,V1,M1} R(31,6) { sorti2( h( j( skol2( X ) ) )
% 0.69/1.06 ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := h( j( skol2( X ) ) )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 eqswap: (653) {G1,W11,D7,L1,V1,M1} { h( j( h( j( skol2( X ) ) ) ) ) ==> h
% 0.69/1.06 ( j( skol2( X ) ) ) }.
% 0.69/1.06 parent0[0]: (652) {G1,W11,D7,L1,V1,M1} { h( j( skol2( X ) ) ) ==> h( j( h
% 0.69/1.06 ( j( skol2( X ) ) ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (196) {G5,W11,D7,L1,V1,M1} R(10,34) { h( j( h( j( skol2( X ) )
% 0.69/1.06 ) ) ) ==> h( j( skol2( X ) ) ) }.
% 0.69/1.06 parent0: (653) {G1,W11,D7,L1,V1,M1} { h( j( h( j( skol2( X ) ) ) ) ) ==> h
% 0.69/1.06 ( j( skol2( X ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 eqswap: (654) {G0,W7,D4,L2,V1,M2} { X ==> h( j( X ) ), ! sorti2( X ) }.
% 0.69/1.06 parent0[1]: (10) {G0,W7,D4,L2,V1,M2} I { ! sorti2( X ), h( j( X ) ) ==> X
% 0.69/1.06 }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (655) {G1,W7,D5,L1,V1,M1} { skol2( X ) ==> h( j( skol2( X ) )
% 0.69/1.06 ) }.
% 0.69/1.06 parent0[1]: (654) {G0,W7,D4,L2,V1,M2} { X ==> h( j( X ) ), ! sorti2( X )
% 0.69/1.06 }.
% 0.69/1.06 parent1[0]: (19) {G2,W3,D3,L1,V1,M1} R(17,4) { sorti2( skol2( X ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := skol2( X )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 eqswap: (656) {G1,W7,D5,L1,V1,M1} { h( j( skol2( X ) ) ) ==> skol2( X )
% 0.69/1.06 }.
% 0.69/1.06 parent0[0]: (655) {G1,W7,D5,L1,V1,M1} { skol2( X ) ==> h( j( skol2( X ) )
% 0.69/1.06 ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (198) {G3,W7,D5,L1,V1,M1} R(10,19) { h( j( skol2( X ) ) ) ==>
% 0.69/1.06 skol2( X ) }.
% 0.69/1.06 parent0: (656) {G1,W7,D5,L1,V1,M1} { h( j( skol2( X ) ) ) ==> skol2( X )
% 0.69/1.06 }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (657) {G1,W7,D5,L1,V1,M1} { sorti1( j( op2( skol2( X ), h(
% 0.69/1.06 skol1 ) ) ) ) }.
% 0.69/1.06 parent0[0]: (7) {G0,W5,D3,L2,V1,M2} I { ! sorti2( X ), sorti1( j( X ) ) }.
% 0.69/1.06 parent1[0]: (181) {G4,W6,D4,L1,V1,M1} R(40,17) { sorti2( op2( skol2( X ), h
% 0.69/1.06 ( skol1 ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := op2( skol2( X ), h( skol1 ) )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (205) {G5,W7,D5,L1,V1,M1} R(181,7) { sorti1( j( op2( skol2( X
% 0.69/1.06 ), h( skol1 ) ) ) ) }.
% 0.69/1.06 parent0: (657) {G1,W7,D5,L1,V1,M1} { sorti1( j( op2( skol2( X ), h( skol1
% 0.69/1.06 ) ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 eqswap: (658) {G1,W10,D4,L2,V1,M2} { h( skol1 ) ==> op2( h( X ), h( X ) )
% 0.69/1.06 , ! sorti1( X ) }.
% 0.69/1.06 parent0[1]: (13) {G1,W10,D4,L2,V1,M2} F(8);d(3) { ! sorti1( X ), op2( h( X
% 0.69/1.06 ), h( X ) ) ==> h( skol1 ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (661) {G2,W16,D8,L1,V1,M1} { h( skol1 ) ==> op2( h( j( h( j(
% 0.69/1.06 skol2( X ) ) ) ) ), h( j( h( j( skol2( X ) ) ) ) ) ) }.
% 0.69/1.06 parent0[1]: (658) {G1,W10,D4,L2,V1,M2} { h( skol1 ) ==> op2( h( X ), h( X
% 0.69/1.06 ) ), ! sorti1( X ) }.
% 0.69/1.06 parent1[0]: (58) {G5,W6,D6,L1,V1,M1} R(34,7) { sorti1( j( h( j( skol2( X )
% 0.69/1.06 ) ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := j( h( j( skol2( X ) ) ) )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 paramod: (663) {G3,W14,D8,L1,V1,M1} { h( skol1 ) ==> op2( h( j( h( j(
% 0.69/1.06 skol2( X ) ) ) ) ), h( j( skol2( X ) ) ) ) }.
% 0.69/1.06 parent0[0]: (196) {G5,W11,D7,L1,V1,M1} R(10,34) { h( j( h( j( skol2( X ) )
% 0.69/1.06 ) ) ) ==> h( j( skol2( X ) ) ) }.
% 0.69/1.06 parent1[0; 10]: (661) {G2,W16,D8,L1,V1,M1} { h( skol1 ) ==> op2( h( j( h(
% 0.69/1.06 j( skol2( X ) ) ) ) ), h( j( h( j( skol2( X ) ) ) ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 paramod: (666) {G4,W12,D8,L1,V1,M1} { h( skol1 ) ==> op2( h( j( h( j(
% 0.69/1.06 skol2( X ) ) ) ) ), skol2( X ) ) }.
% 0.69/1.06 parent0[0]: (198) {G3,W7,D5,L1,V1,M1} R(10,19) { h( j( skol2( X ) ) ) ==>
% 0.69/1.06 skol2( X ) }.
% 0.69/1.06 parent1[0; 10]: (663) {G3,W14,D8,L1,V1,M1} { h( skol1 ) ==> op2( h( j( h(
% 0.69/1.06 j( skol2( X ) ) ) ) ), h( j( skol2( X ) ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 paramod: (667) {G4,W10,D6,L1,V1,M1} { h( skol1 ) ==> op2( h( j( skol2( X )
% 0.69/1.06 ) ), skol2( X ) ) }.
% 0.69/1.06 parent0[0]: (198) {G3,W7,D5,L1,V1,M1} R(10,19) { h( j( skol2( X ) ) ) ==>
% 0.69/1.06 skol2( X ) }.
% 0.69/1.06 parent1[0; 6]: (666) {G4,W12,D8,L1,V1,M1} { h( skol1 ) ==> op2( h( j( h( j
% 0.69/1.06 ( skol2( X ) ) ) ) ), skol2( X ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 paramod: (668) {G4,W8,D4,L1,V1,M1} { h( skol1 ) ==> op2( skol2( X ), skol2
% 0.69/1.06 ( X ) ) }.
% 0.69/1.06 parent0[0]: (198) {G3,W7,D5,L1,V1,M1} R(10,19) { h( j( skol2( X ) ) ) ==>
% 0.69/1.06 skol2( X ) }.
% 0.69/1.06 parent1[0; 4]: (667) {G4,W10,D6,L1,V1,M1} { h( skol1 ) ==> op2( h( j(
% 0.69/1.06 skol2( X ) ) ), skol2( X ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 eqswap: (672) {G4,W8,D4,L1,V1,M1} { op2( skol2( X ), skol2( X ) ) ==> h(
% 0.69/1.06 skol1 ) }.
% 0.69/1.06 parent0[0]: (668) {G4,W8,D4,L1,V1,M1} { h( skol1 ) ==> op2( skol2( X ),
% 0.69/1.06 skol2( X ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (297) {G6,W8,D4,L1,V1,M1} R(13,58);d(196);d(198) { op2( skol2
% 0.69/1.06 ( X ), skol2( X ) ) ==> h( skol1 ) }.
% 0.69/1.06 parent0: (672) {G4,W8,D4,L1,V1,M1} { op2( skol2( X ), skol2( X ) ) ==> h(
% 0.69/1.06 skol1 ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 eqswap: (675) {G0,W9,D4,L2,V1,M2} { ! X ==> op2( skol2( X ), skol2( X ) )
% 0.69/1.06 , ! sorti2( X ) }.
% 0.69/1.06 parent0[1]: (5) {G0,W9,D4,L2,V1,M2} I { ! sorti2( X ), ! op2( skol2( X ),
% 0.69/1.06 skol2( X ) ) ==> X }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (677) {G1,W20,D6,L3,V2,M3} { ! h( op1( X, Y ) ) ==> op2( skol2
% 0.69/1.06 ( h( op1( X, Y ) ) ), skol2( h( op1( X, Y ) ) ) ), ! sorti1( X ), !
% 0.69/1.06 sorti1( Y ) }.
% 0.69/1.06 parent0[1]: (675) {G0,W9,D4,L2,V1,M2} { ! X ==> op2( skol2( X ), skol2( X
% 0.69/1.06 ) ), ! sorti2( X ) }.
% 0.69/1.06 parent1[2]: (22) {G1,W9,D4,L3,V2,M3} R(0,6) { ! sorti1( X ), ! sorti1( Y )
% 0.69/1.06 , sorti2( h( op1( X, Y ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := h( op1( X, Y ) )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 paramod: (681) {G2,W11,D4,L3,V2,M3} { ! h( op1( X, Y ) ) ==> h( skol1 ), !
% 0.69/1.06 sorti1( X ), ! sorti1( Y ) }.
% 0.69/1.06 parent0[0]: (297) {G6,W8,D4,L1,V1,M1} R(13,58);d(196);d(198) { op2( skol2(
% 0.69/1.06 X ), skol2( X ) ) ==> h( skol1 ) }.
% 0.69/1.06 parent1[0; 6]: (677) {G1,W20,D6,L3,V2,M3} { ! h( op1( X, Y ) ) ==> op2(
% 0.69/1.06 skol2( h( op1( X, Y ) ) ), skol2( h( op1( X, Y ) ) ) ), ! sorti1( X ), !
% 0.69/1.06 sorti1( Y ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := h( op1( X, Y ) )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (565) {G7,W11,D4,L3,V2,M3} R(22,5);d(297) { ! sorti1( X ), !
% 0.69/1.06 sorti1( Y ), ! h( op1( X, Y ) ) ==> h( skol1 ) }.
% 0.69/1.06 parent0: (681) {G2,W11,D4,L3,V2,M3} { ! h( op1( X, Y ) ) ==> h( skol1 ), !
% 0.69/1.06 sorti1( X ), ! sorti1( Y ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 Y := Y
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 2
% 0.69/1.06 1 ==> 0
% 0.69/1.06 2 ==> 1
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 factor: (688) {G7,W9,D4,L2,V1,M2} { ! sorti1( X ), ! h( op1( X, X ) ) ==>
% 0.69/1.06 h( skol1 ) }.
% 0.69/1.06 parent0[0, 1]: (565) {G7,W11,D4,L3,V2,M3} R(22,5);d(297) { ! sorti1( X ), !
% 0.69/1.06 sorti1( Y ), ! h( op1( X, Y ) ) ==> h( skol1 ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 Y := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 paramod: (689) {G1,W9,D3,L3,V1,M3} { ! h( skol1 ) ==> h( skol1 ), ! sorti1
% 0.69/1.06 ( X ), ! sorti1( X ) }.
% 0.69/1.06 parent0[1]: (3) {G0,W7,D3,L2,V1,M2} I { ! sorti1( X ), op1( X, X ) ==>
% 0.69/1.06 skol1 }.
% 0.69/1.06 parent1[1; 3]: (688) {G7,W9,D4,L2,V1,M2} { ! sorti1( X ), ! h( op1( X, X )
% 0.69/1.06 ) ==> h( skol1 ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 factor: (690) {G1,W7,D3,L2,V1,M2} { ! h( skol1 ) ==> h( skol1 ), ! sorti1
% 0.69/1.06 ( X ) }.
% 0.69/1.06 parent0[1, 2]: (689) {G1,W9,D3,L3,V1,M3} { ! h( skol1 ) ==> h( skol1 ), !
% 0.69/1.06 sorti1( X ), ! sorti1( X ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 eqrefl: (691) {G0,W2,D2,L1,V1,M1} { ! sorti1( X ) }.
% 0.69/1.06 parent0[0]: (690) {G1,W7,D3,L2,V1,M2} { ! h( skol1 ) ==> h( skol1 ), !
% 0.69/1.06 sorti1( X ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (577) {G8,W2,D2,L1,V1,M1} F(565);d(3);q { ! sorti1( X ) }.
% 0.69/1.06 parent0: (691) {G0,W2,D2,L1,V1,M1} { ! sorti1( X ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 0 ==> 0
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 resolution: (692) {G6,W0,D0,L0,V0,M0} { }.
% 0.69/1.06 parent0[0]: (577) {G8,W2,D2,L1,V1,M1} F(565);d(3);q { ! sorti1( X ) }.
% 0.69/1.06 parent1[0]: (205) {G5,W7,D5,L1,V1,M1} R(181,7) { sorti1( j( op2( skol2( X )
% 0.69/1.06 , h( skol1 ) ) ) ) }.
% 0.69/1.06 substitution0:
% 0.69/1.06 X := j( op2( skol2( X ), h( skol1 ) ) )
% 0.69/1.06 end
% 0.69/1.06 substitution1:
% 0.69/1.06 X := X
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 subsumption: (578) {G9,W0,D0,L0,V0,M0} R(577,205) { }.
% 0.69/1.06 parent0: (692) {G6,W0,D0,L0,V0,M0} { }.
% 0.69/1.06 substitution0:
% 0.69/1.06 end
% 0.69/1.06 permutation0:
% 0.69/1.06 end
% 0.69/1.06
% 0.69/1.06 Proof check complete!
% 0.69/1.06
% 0.69/1.06 Memory use:
% 0.69/1.06
% 0.69/1.06 space for terms: 7283
% 0.69/1.06 space for clauses: 37279
% 0.69/1.06
% 0.69/1.06
% 0.69/1.06 clauses generated: 1150
% 0.69/1.06 clauses kept: 579
% 0.69/1.06 clauses selected: 54
% 0.69/1.06 clauses deleted: 13
% 0.69/1.06 clauses inuse deleted: 0
% 0.69/1.06
% 0.69/1.06 subsentry: 2483
% 0.69/1.06 literals s-matched: 1243
% 0.69/1.06 literals matched: 1243
% 0.69/1.06 full subsumption: 602
% 0.69/1.06
% 0.69/1.06 checksum: 1002042813
% 0.69/1.06
% 0.69/1.06
% 0.69/1.06 Bliksem ended
%------------------------------------------------------------------------------