%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUN088+3 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.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 : Mon Jul 18 16:19:18 EDT 2022
% Result : Theorem 0.73s 1.12s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUN088+3 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Thu Jun 2 09:31:31 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.73/1.12 *** allocated 10000 integers for termspace/termends
% 0.73/1.12 *** allocated 10000 integers for clauses
% 0.73/1.12 *** allocated 10000 integers for justifications
% 0.73/1.12 Bliksem 1.12
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 Automatic Strategy Selection
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 Clauses:
% 0.73/1.12
% 0.73/1.12 { alpha1( skol1, X ), r1( X ) }.
% 0.73/1.12 { alpha1( skol1, X ), X = skol1 }.
% 0.73/1.12 { ! alpha1( X, Y ), ! r1( Y ) }.
% 0.73/1.12 { ! alpha1( X, Y ), ! Y = X }.
% 0.73/1.12 { r1( Y ), Y = X, alpha1( X, Y ) }.
% 0.73/1.12 { alpha2( X, skol2( X ), Y ), r2( X, Y ) }.
% 0.73/1.12 { alpha2( X, skol2( X ), Y ), Y = skol2( X ) }.
% 0.73/1.12 { ! alpha2( X, Y, Z ), ! r2( X, Z ) }.
% 0.73/1.12 { ! alpha2( X, Y, Z ), ! Z = Y }.
% 0.73/1.12 { r2( X, Z ), Z = Y, alpha2( X, Y, Z ) }.
% 0.73/1.12 { alpha3( X, Y, skol3( X, Y ), Z ), r3( X, Y, Z ) }.
% 0.73/1.12 { alpha3( X, Y, skol3( X, Y ), Z ), Z = skol3( X, Y ) }.
% 0.73/1.12 { ! alpha3( X, Y, Z, T ), ! r3( X, Y, T ) }.
% 0.73/1.12 { ! alpha3( X, Y, Z, T ), ! T = Z }.
% 0.73/1.12 { r3( X, Y, T ), T = Z, alpha3( X, Y, Z, T ) }.
% 0.73/1.12 { alpha4( X, Y, skol4( X, Y ), Z ), r4( X, Y, Z ) }.
% 0.73/1.12 { alpha4( X, Y, skol4( X, Y ), Z ), Z = skol4( X, Y ) }.
% 0.73/1.12 { ! alpha4( X, Y, Z, T ), ! r4( X, Y, T ) }.
% 0.73/1.12 { ! alpha4( X, Y, Z, T ), ! T = Z }.
% 0.73/1.12 { r4( X, Y, T ), T = Z, alpha4( X, Y, Z, T ) }.
% 0.73/1.12 { r2( Y, skol18( Z, Y ) ) }.
% 0.73/1.12 { r3( X, skol18( X, Y ), skol12( X, Y ) ) }.
% 0.73/1.12 { skol12( X, Y ) = skol5( X, Y ) }.
% 0.73/1.12 { r2( skol21( X, Y ), skol5( X, Y ) ) }.
% 0.73/1.12 { r3( X, Y, skol21( X, Y ) ) }.
% 0.73/1.12 { r2( Y, skol19( Z, Y ) ) }.
% 0.73/1.12 { r4( X, skol19( X, Y ), skol13( X, Y ) ) }.
% 0.73/1.12 { skol13( X, Y ) = skol6( X, Y ) }.
% 0.73/1.12 { r3( skol22( X, Y ), X, skol6( X, Y ) ) }.
% 0.73/1.12 { r4( X, Y, skol22( X, Y ) ) }.
% 0.73/1.12 { ! r2( X, T ), ! T = Z, ! r2( Y, Z ), X = Y }.
% 0.73/1.12 { r1( skol14( Y ) ) }.
% 0.73/1.12 { r3( X, skol14( X ), skol7( X ) ) }.
% 0.73/1.12 { skol7( X ) = X }.
% 0.73/1.12 { r1( skol15( Z ) ) }.
% 0.73/1.12 { skol8( Y ) = skol15( Y ) }.
% 0.73/1.12 { r1( skol20( Y ) ) }.
% 0.73/1.12 { r4( X, skol20( X ), skol8( X ) ) }.
% 0.73/1.12 { alpha5( X ), r2( skol16( Y ), skol9( Y ) ) }.
% 0.73/1.12 { alpha5( X ), X = skol9( X ) }.
% 0.73/1.12 { ! alpha5( X ), r1( skol10( Y ) ) }.
% 0.73/1.12 { ! alpha5( X ), X = skol10( X ) }.
% 0.73/1.12 { ! r1( Y ), ! X = Y, alpha5( X ) }.
% 0.73/1.12 { ! r1( Y ), ! Y = X, ! r2( Z, X ) }.
% 0.73/1.12 { skol11 = skol17 }.
% 0.73/1.12 { r2( skol11, skol17 ) }.
% 0.73/1.12 { r1( skol11 ) }.
% 0.73/1.12
% 0.73/1.12 percentage equality = 0.280488, percentage horn = 0.702128
% 0.73/1.12 This is a problem with some equality
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 Options Used:
% 0.73/1.12
% 0.73/1.12 useres = 1
% 0.73/1.12 useparamod = 1
% 0.73/1.12 useeqrefl = 1
% 0.73/1.12 useeqfact = 1
% 0.73/1.12 usefactor = 1
% 0.73/1.12 usesimpsplitting = 0
% 0.73/1.12 usesimpdemod = 5
% 0.73/1.12 usesimpres = 3
% 0.73/1.12
% 0.73/1.12 resimpinuse = 1000
% 0.73/1.12 resimpclauses = 20000
% 0.73/1.12 substype = eqrewr
% 0.73/1.12 backwardsubs = 1
% 0.73/1.12 selectoldest = 5
% 0.73/1.12
% 0.73/1.12 litorderings [0] = split
% 0.73/1.12 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.12
% 0.73/1.12 termordering = kbo
% 0.73/1.12
% 0.73/1.12 litapriori = 0
% 0.73/1.12 termapriori = 1
% 0.73/1.12 litaposteriori = 0
% 0.73/1.12 termaposteriori = 0
% 0.73/1.12 demodaposteriori = 0
% 0.73/1.12 ordereqreflfact = 0
% 0.73/1.12
% 0.73/1.12 litselect = negord
% 0.73/1.12
% 0.73/1.12 maxweight = 15
% 0.73/1.12 maxdepth = 30000
% 0.73/1.12 maxlength = 115
% 0.73/1.12 maxnrvars = 195
% 0.73/1.12 excuselevel = 1
% 0.73/1.12 increasemaxweight = 1
% 0.73/1.12
% 0.73/1.12 maxselected = 10000000
% 0.73/1.12 maxnrclauses = 10000000
% 0.73/1.12
% 0.73/1.12 showgenerated = 0
% 0.73/1.12 showkept = 0
% 0.73/1.12 showselected = 0
% 0.73/1.12 showdeleted = 0
% 0.73/1.12 showresimp = 1
% 0.73/1.12 showstatus = 2000
% 0.73/1.12
% 0.73/1.12 prologoutput = 0
% 0.73/1.12 nrgoals = 5000000
% 0.73/1.12 totalproof = 1
% 0.73/1.12
% 0.73/1.12 Symbols occurring in the translation:
% 0.73/1.12
% 0.73/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.12 . [1, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.73/1.12 ! [4, 1] (w:0, o:53, a:1, s:1, b:0),
% 0.73/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.12 r1 [37, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.73/1.12 r2 [41, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.73/1.12 r3 [46, 3] (w:1, o:105, a:1, s:1, b:0),
% 0.73/1.12 r4 [51, 3] (w:1, o:106, a:1, s:1, b:0),
% 0.73/1.12 alpha1 [83, 2] (w:1, o:94, a:1, s:1, b:1),
% 0.73/1.12 alpha2 [84, 3] (w:1, o:107, a:1, s:1, b:1),
% 0.73/1.12 alpha3 [85, 4] (w:1, o:108, a:1, s:1, b:1),
% 0.73/1.12 alpha4 [86, 4] (w:1, o:109, a:1, s:1, b:1),
% 0.73/1.12 alpha5 [87, 1] (w:1, o:59, a:1, s:1, b:1),
% 0.73/1.12 skol1 [88, 0] (w:1, o:50, a:1, s:1, b:1),
% 0.73/1.12 skol2 [89, 1] (w:1, o:64, a:1, s:1, b:1),
% 0.73/1.12 skol3 [90, 2] (w:1, o:97, a:1, s:1, b:1),
% 0.73/1.12 skol4 [91, 2] (w:1, o:98, a:1, s:1, b:1),
% 0.73/1.12 skol5 [92, 2] (w:1, o:99, a:1, s:1, b:1),
% 0.73/1.12 skol6 [93, 2] (w:1, o:100, a:1, s:1, b:1),
% 0.73/1.12 skol7 [94, 1] (w:1, o:65, a:1, s:1, b:1),
% 0.73/1.12 skol8 [95, 1] (w:1, o:66, a:1, s:1, b:1),
% 0.73/1.12 skol9 [96, 1] (w:1, o:67, a:1, s:1, b:1),
% 0.73/1.12 skol10 [97, 1] (w:1, o:60, a:1, s:1, b:1),
% 0.73/1.12 skol11 [98, 0] (w:1, o:51, a:1, s:1, b:1),
% 0.73/1.12 skol12 [99, 2] (w:1, o:101, a:1, s:1, b:1),
% 0.73/1.12 skol13 [100, 2] (w:1, o:102, a:1, s:1, b:1),
% 0.73/1.12 skol14 [101, 1] (w:1, o:61, a:1, s:1, b:1),
% 0.73/1.12 skol15 [102, 1] (w:1, o:62, a:1, s:1, b:1),
% 0.73/1.12 skol16 [103, 1] (w:1, o:63, a:1, s:1, b:1),
% 0.73/1.12 skol17 [104, 0] (w:1, o:52, a:1, s:1, b:1),
% 0.73/1.12 skol18 [105, 2] (w:1, o:103, a:1, s:1, b:1),
% 0.73/1.12 skol19 [106, 2] (w:1, o:104, a:1, s:1, b:1),
% 0.73/1.12 skol20 [107, 1] (w:1, o:68, a:1, s:1, b:1),
% 0.73/1.12 skol21 [108, 2] (w:1, o:95, a:1, s:1, b:1),
% 0.73/1.12 skol22 [109, 2] (w:1, o:96, a:1, s:1, b:1).
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 Starting Search:
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 Bliksems!, er is een bewijs:
% 0.73/1.12 % SZS status Theorem
% 0.73/1.12 % SZS output start Refutation
% 0.73/1.12
% 0.73/1.12 (0) {G0,W5,D2,L2,V1,M2} I { alpha1( skol1, X ), r1( X ) }.
% 0.73/1.12 (1) {G0,W6,D2,L2,V1,M2} I { alpha1( skol1, X ), X = skol1 }.
% 0.73/1.12 (2) {G0,W5,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! r1( Y ) }.
% 0.73/1.12 (3) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! Y = X }.
% 0.73/1.12 (43) {G0,W8,D2,L3,V3,M3} I { ! r1( Y ), ! Y = X, ! r2( Z, X ) }.
% 0.73/1.12 (44) {G0,W3,D2,L1,V0,M1} I { skol17 ==> skol11 }.
% 0.73/1.12 (45) {G1,W3,D2,L1,V0,M1} I;d(44) { r2( skol11, skol11 ) }.
% 0.73/1.12 (46) {G0,W2,D2,L1,V0,M1} I { r1( skol11 ) }.
% 0.73/1.12 (47) {G1,W3,D2,L1,V1,M1} Q(3) { ! alpha1( X, X ) }.
% 0.73/1.12 (53) {G1,W5,D2,L2,V2,M2} Q(43) { ! r1( X ), ! r2( Y, X ) }.
% 0.73/1.12 (54) {G2,W2,D2,L1,V0,M1} R(0,47) { r1( skol1 ) }.
% 0.73/1.12 (69) {G1,W3,D2,L1,V1,M1} R(2,46) { ! alpha1( X, skol11 ) }.
% 0.73/1.12 (70) {G2,W3,D2,L1,V0,M1} R(69,1) { skol11 ==> skol1 }.
% 0.73/1.12 (71) {G3,W3,D2,L1,V0,M1} P(70,45) { r2( skol1, skol1 ) }.
% 0.73/1.12 (97) {G4,W0,D0,L0,V0,M0} R(53,71);r(54) { }.
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 % SZS output end Refutation
% 0.73/1.12 found a proof!
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 Unprocessed initial clauses:
% 0.73/1.12
% 0.73/1.12 (99) {G0,W5,D2,L2,V1,M2} { alpha1( skol1, X ), r1( X ) }.
% 0.73/1.12 (100) {G0,W6,D2,L2,V1,M2} { alpha1( skol1, X ), X = skol1 }.
% 0.73/1.12 (101) {G0,W5,D2,L2,V2,M2} { ! alpha1( X, Y ), ! r1( Y ) }.
% 0.73/1.12 (102) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), ! Y = X }.
% 0.73/1.12 (103) {G0,W8,D2,L3,V2,M3} { r1( Y ), Y = X, alpha1( X, Y ) }.
% 0.73/1.12 (104) {G0,W8,D3,L2,V2,M2} { alpha2( X, skol2( X ), Y ), r2( X, Y ) }.
% 0.73/1.12 (105) {G0,W9,D3,L2,V2,M2} { alpha2( X, skol2( X ), Y ), Y = skol2( X ) }.
% 0.73/1.12 (106) {G0,W7,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), ! r2( X, Z ) }.
% 0.73/1.12 (107) {G0,W7,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), ! Z = Y }.
% 0.73/1.12 (108) {G0,W10,D2,L3,V3,M3} { r2( X, Z ), Z = Y, alpha2( X, Y, Z ) }.
% 0.73/1.12 (109) {G0,W11,D3,L2,V3,M2} { alpha3( X, Y, skol3( X, Y ), Z ), r3( X, Y, Z
% 0.73/1.12 ) }.
% 0.73/1.12 (110) {G0,W12,D3,L2,V3,M2} { alpha3( X, Y, skol3( X, Y ), Z ), Z = skol3(
% 0.73/1.12 X, Y ) }.
% 0.73/1.12 (111) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), ! r3( X, Y, T ) }.
% 0.73/1.12 (112) {G0,W8,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), ! T = Z }.
% 0.73/1.12 (113) {G0,W12,D2,L3,V4,M3} { r3( X, Y, T ), T = Z, alpha3( X, Y, Z, T )
% 0.73/1.12 }.
% 0.73/1.12 (114) {G0,W11,D3,L2,V3,M2} { alpha4( X, Y, skol4( X, Y ), Z ), r4( X, Y, Z
% 0.73/1.12 ) }.
% 0.73/1.12 (115) {G0,W12,D3,L2,V3,M2} { alpha4( X, Y, skol4( X, Y ), Z ), Z = skol4(
% 0.73/1.12 X, Y ) }.
% 0.73/1.12 (116) {G0,W9,D2,L2,V4,M2} { ! alpha4( X, Y, Z, T ), ! r4( X, Y, T ) }.
% 0.73/1.12 (117) {G0,W8,D2,L2,V4,M2} { ! alpha4( X, Y, Z, T ), ! T = Z }.
% 0.73/1.12 (118) {G0,W12,D2,L3,V4,M3} { r4( X, Y, T ), T = Z, alpha4( X, Y, Z, T )
% 0.73/1.12 }.
% 0.73/1.12 (119) {G0,W5,D3,L1,V2,M1} { r2( Y, skol18( Z, Y ) ) }.
% 0.73/1.12 (120) {G0,W8,D3,L1,V2,M1} { r3( X, skol18( X, Y ), skol12( X, Y ) ) }.
% 0.73/1.12 (121) {G0,W7,D3,L1,V2,M1} { skol12( X, Y ) = skol5( X, Y ) }.
% 0.73/1.12 (122) {G0,W7,D3,L1,V2,M1} { r2( skol21( X, Y ), skol5( X, Y ) ) }.
% 0.73/1.12 (123) {G0,W6,D3,L1,V2,M1} { r3( X, Y, skol21( X, Y ) ) }.
% 0.73/1.12 (124) {G0,W5,D3,L1,V2,M1} { r2( Y, skol19( Z, Y ) ) }.
% 0.73/1.12 (125) {G0,W8,D3,L1,V2,M1} { r4( X, skol19( X, Y ), skol13( X, Y ) ) }.
% 0.73/1.12 (126) {G0,W7,D3,L1,V2,M1} { skol13( X, Y ) = skol6( X, Y ) }.
% 0.73/1.12 (127) {G0,W8,D3,L1,V2,M1} { r3( skol22( X, Y ), X, skol6( X, Y ) ) }.
% 0.73/1.12 (128) {G0,W6,D3,L1,V2,M1} { r4( X, Y, skol22( X, Y ) ) }.
% 0.73/1.12 (129) {G0,W12,D2,L4,V4,M4} { ! r2( X, T ), ! T = Z, ! r2( Y, Z ), X = Y
% 0.73/1.12 }.
% 0.73/1.12 (130) {G0,W3,D3,L1,V1,M1} { r1( skol14( Y ) ) }.
% 0.73/1.12 (131) {G0,W6,D3,L1,V1,M1} { r3( X, skol14( X ), skol7( X ) ) }.
% 0.73/1.12 (132) {G0,W4,D3,L1,V1,M1} { skol7( X ) = X }.
% 0.73/1.12 (133) {G0,W3,D3,L1,V1,M1} { r1( skol15( Z ) ) }.
% 0.73/1.12 (134) {G0,W5,D3,L1,V1,M1} { skol8( Y ) = skol15( Y ) }.
% 0.73/1.12 (135) {G0,W3,D3,L1,V1,M1} { r1( skol20( Y ) ) }.
% 0.73/1.12 (136) {G0,W6,D3,L1,V1,M1} { r4( X, skol20( X ), skol8( X ) ) }.
% 0.73/1.12 (137) {G0,W7,D3,L2,V2,M2} { alpha5( X ), r2( skol16( Y ), skol9( Y ) ) }.
% 0.73/1.12 (138) {G0,W6,D3,L2,V1,M2} { alpha5( X ), X = skol9( X ) }.
% 0.73/1.12 (139) {G0,W5,D3,L2,V2,M2} { ! alpha5( X ), r1( skol10( Y ) ) }.
% 0.73/1.12 (140) {G0,W6,D3,L2,V1,M2} { ! alpha5( X ), X = skol10( X ) }.
% 0.73/1.12 (141) {G0,W7,D2,L3,V2,M3} { ! r1( Y ), ! X = Y, alpha5( X ) }.
% 0.73/1.12 (142) {G0,W8,D2,L3,V3,M3} { ! r1( Y ), ! Y = X, ! r2( Z, X ) }.
% 0.73/1.12 (143) {G0,W3,D2,L1,V0,M1} { skol11 = skol17 }.
% 0.73/1.12 (144) {G0,W3,D2,L1,V0,M1} { r2( skol11, skol17 ) }.
% 0.73/1.12 (145) {G0,W2,D2,L1,V0,M1} { r1( skol11 ) }.
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 Total Proof:
% 0.73/1.12
% 0.73/1.12 subsumption: (0) {G0,W5,D2,L2,V1,M2} I { alpha1( skol1, X ), r1( X ) }.
% 0.73/1.12 parent0: (99) {G0,W5,D2,L2,V1,M2} { alpha1( skol1, X ), r1( X ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 1 ==> 1
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (1) {G0,W6,D2,L2,V1,M2} I { alpha1( skol1, X ), X = skol1 }.
% 0.73/1.12 parent0: (100) {G0,W6,D2,L2,V1,M2} { alpha1( skol1, X ), X = skol1 }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 1 ==> 1
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (2) {G0,W5,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! r1( Y ) }.
% 0.73/1.12 parent0: (101) {G0,W5,D2,L2,V2,M2} { ! alpha1( X, Y ), ! r1( Y ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 Y := Y
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 1 ==> 1
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (3) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! Y = X }.
% 0.73/1.12 parent0: (102) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), ! Y = X }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 Y := Y
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 1 ==> 1
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (43) {G0,W8,D2,L3,V3,M3} I { ! r1( Y ), ! Y = X, ! r2( Z, X )
% 0.73/1.12 }.
% 0.73/1.12 parent0: (142) {G0,W8,D2,L3,V3,M3} { ! r1( Y ), ! Y = X, ! r2( Z, X ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 Y := Y
% 0.73/1.12 Z := Z
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 1 ==> 1
% 0.73/1.12 2 ==> 2
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 eqswap: (194) {G0,W3,D2,L1,V0,M1} { skol17 = skol11 }.
% 0.73/1.12 parent0[0]: (143) {G0,W3,D2,L1,V0,M1} { skol11 = skol17 }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (44) {G0,W3,D2,L1,V0,M1} I { skol17 ==> skol11 }.
% 0.73/1.12 parent0: (194) {G0,W3,D2,L1,V0,M1} { skol17 = skol11 }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 paramod: (266) {G1,W3,D2,L1,V0,M1} { r2( skol11, skol11 ) }.
% 0.73/1.12 parent0[0]: (44) {G0,W3,D2,L1,V0,M1} I { skol17 ==> skol11 }.
% 0.73/1.12 parent1[0; 2]: (144) {G0,W3,D2,L1,V0,M1} { r2( skol11, skol17 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 substitution1:
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (45) {G1,W3,D2,L1,V0,M1} I;d(44) { r2( skol11, skol11 ) }.
% 0.73/1.12 parent0: (266) {G1,W3,D2,L1,V0,M1} { r2( skol11, skol11 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (46) {G0,W2,D2,L1,V0,M1} I { r1( skol11 ) }.
% 0.73/1.12 parent0: (145) {G0,W2,D2,L1,V0,M1} { r1( skol11 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 eqswap: (290) {G0,W6,D2,L2,V2,M2} { ! Y = X, ! alpha1( Y, X ) }.
% 0.73/1.12 parent0[1]: (3) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! Y = X }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := Y
% 0.73/1.12 Y := X
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 eqrefl: (291) {G0,W3,D2,L1,V1,M1} { ! alpha1( X, X ) }.
% 0.73/1.12 parent0[0]: (290) {G0,W6,D2,L2,V2,M2} { ! Y = X, ! alpha1( Y, X ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 Y := X
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (47) {G1,W3,D2,L1,V1,M1} Q(3) { ! alpha1( X, X ) }.
% 0.73/1.12 parent0: (291) {G0,W3,D2,L1,V1,M1} { ! alpha1( X, X ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 eqswap: (292) {G0,W8,D2,L3,V3,M3} { ! Y = X, ! r1( X ), ! r2( Z, Y ) }.
% 0.73/1.12 parent0[1]: (43) {G0,W8,D2,L3,V3,M3} I { ! r1( Y ), ! Y = X, ! r2( Z, X )
% 0.73/1.12 }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := Y
% 0.73/1.12 Y := X
% 0.73/1.12 Z := Z
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 eqrefl: (293) {G0,W5,D2,L2,V2,M2} { ! r1( X ), ! r2( Y, X ) }.
% 0.73/1.12 parent0[0]: (292) {G0,W8,D2,L3,V3,M3} { ! Y = X, ! r1( X ), ! r2( Z, Y )
% 0.73/1.12 }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 Y := X
% 0.73/1.12 Z := Y
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (53) {G1,W5,D2,L2,V2,M2} Q(43) { ! r1( X ), ! r2( Y, X ) }.
% 0.73/1.12 parent0: (293) {G0,W5,D2,L2,V2,M2} { ! r1( X ), ! r2( Y, X ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 Y := Y
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 1 ==> 1
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 resolution: (294) {G1,W2,D2,L1,V0,M1} { r1( skol1 ) }.
% 0.73/1.12 parent0[0]: (47) {G1,W3,D2,L1,V1,M1} Q(3) { ! alpha1( X, X ) }.
% 0.73/1.12 parent1[0]: (0) {G0,W5,D2,L2,V1,M2} I { alpha1( skol1, X ), r1( X ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := skol1
% 0.73/1.12 end
% 0.73/1.12 substitution1:
% 0.73/1.12 X := skol1
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (54) {G2,W2,D2,L1,V0,M1} R(0,47) { r1( skol1 ) }.
% 0.73/1.12 parent0: (294) {G1,W2,D2,L1,V0,M1} { r1( skol1 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 resolution: (295) {G1,W3,D2,L1,V1,M1} { ! alpha1( X, skol11 ) }.
% 0.73/1.12 parent0[1]: (2) {G0,W5,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! r1( Y ) }.
% 0.73/1.12 parent1[0]: (46) {G0,W2,D2,L1,V0,M1} I { r1( skol11 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 Y := skol11
% 0.73/1.12 end
% 0.73/1.12 substitution1:
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (69) {G1,W3,D2,L1,V1,M1} R(2,46) { ! alpha1( X, skol11 ) }.
% 0.73/1.12 parent0: (295) {G1,W3,D2,L1,V1,M1} { ! alpha1( X, skol11 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 eqswap: (296) {G0,W6,D2,L2,V1,M2} { skol1 = X, alpha1( skol1, X ) }.
% 0.73/1.12 parent0[1]: (1) {G0,W6,D2,L2,V1,M2} I { alpha1( skol1, X ), X = skol1 }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := X
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 resolution: (297) {G1,W3,D2,L1,V0,M1} { skol1 = skol11 }.
% 0.73/1.12 parent0[0]: (69) {G1,W3,D2,L1,V1,M1} R(2,46) { ! alpha1( X, skol11 ) }.
% 0.73/1.12 parent1[1]: (296) {G0,W6,D2,L2,V1,M2} { skol1 = X, alpha1( skol1, X ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := skol1
% 0.73/1.12 end
% 0.73/1.12 substitution1:
% 0.73/1.12 X := skol11
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 eqswap: (298) {G1,W3,D2,L1,V0,M1} { skol11 = skol1 }.
% 0.73/1.12 parent0[0]: (297) {G1,W3,D2,L1,V0,M1} { skol1 = skol11 }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (70) {G2,W3,D2,L1,V0,M1} R(69,1) { skol11 ==> skol1 }.
% 0.73/1.12 parent0: (298) {G1,W3,D2,L1,V0,M1} { skol11 = skol1 }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 paramod: (301) {G2,W3,D2,L1,V0,M1} { r2( skol11, skol1 ) }.
% 0.73/1.12 parent0[0]: (70) {G2,W3,D2,L1,V0,M1} R(69,1) { skol11 ==> skol1 }.
% 0.73/1.12 parent1[0; 2]: (45) {G1,W3,D2,L1,V0,M1} I;d(44) { r2( skol11, skol11 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 substitution1:
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 paramod: (302) {G3,W3,D2,L1,V0,M1} { r2( skol1, skol1 ) }.
% 0.73/1.12 parent0[0]: (70) {G2,W3,D2,L1,V0,M1} R(69,1) { skol11 ==> skol1 }.
% 0.73/1.12 parent1[0; 1]: (301) {G2,W3,D2,L1,V0,M1} { r2( skol11, skol1 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 substitution1:
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (71) {G3,W3,D2,L1,V0,M1} P(70,45) { r2( skol1, skol1 ) }.
% 0.73/1.12 parent0: (302) {G3,W3,D2,L1,V0,M1} { r2( skol1, skol1 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 0 ==> 0
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 resolution: (303) {G2,W2,D2,L1,V0,M1} { ! r1( skol1 ) }.
% 0.73/1.12 parent0[1]: (53) {G1,W5,D2,L2,V2,M2} Q(43) { ! r1( X ), ! r2( Y, X ) }.
% 0.73/1.12 parent1[0]: (71) {G3,W3,D2,L1,V0,M1} P(70,45) { r2( skol1, skol1 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 X := skol1
% 0.73/1.12 Y := skol1
% 0.73/1.12 end
% 0.73/1.12 substitution1:
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 resolution: (304) {G3,W0,D0,L0,V0,M0} { }.
% 0.73/1.12 parent0[0]: (303) {G2,W2,D2,L1,V0,M1} { ! r1( skol1 ) }.
% 0.73/1.12 parent1[0]: (54) {G2,W2,D2,L1,V0,M1} R(0,47) { r1( skol1 ) }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 substitution1:
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 subsumption: (97) {G4,W0,D0,L0,V0,M0} R(53,71);r(54) { }.
% 0.73/1.12 parent0: (304) {G3,W0,D0,L0,V0,M0} { }.
% 0.73/1.12 substitution0:
% 0.73/1.12 end
% 0.73/1.12 permutation0:
% 0.73/1.12 end
% 0.73/1.12
% 0.73/1.12 Proof check complete!
% 0.73/1.12
% 0.73/1.12 Memory use:
% 0.73/1.12
% 0.73/1.12 space for terms: 1468
% 0.73/1.12 space for clauses: 5609
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 clauses generated: 207
% 0.73/1.12 clauses kept: 98
% 0.73/1.12 clauses selected: 37
% 0.73/1.12 clauses deleted: 0
% 0.73/1.12 clauses inuse deleted: 0
% 0.73/1.12
% 0.73/1.12 subsentry: 764
% 0.73/1.12 literals s-matched: 534
% 0.73/1.12 literals matched: 534
% 0.73/1.12 full subsumption: 55
% 0.73/1.12
% 0.73/1.12 checksum: 56428111
% 0.73/1.12
% 0.73/1.12
% 0.73/1.12 Bliksem ended
%------------------------------------------------------------------------------