%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU354+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Jul 19 07:12:41 EDT 2022
% Result : Theorem 0.73s 1.10s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU354+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sat Jun 18 21:23:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.08 *** allocated 10000 integers for termspace/termends
% 0.73/1.08 *** allocated 10000 integers for clauses
% 0.73/1.08 *** allocated 10000 integers for justifications
% 0.73/1.08 Bliksem 1.12
% 0.73/1.08
% 0.73/1.08
% 0.73/1.08 Automatic Strategy Selection
% 0.73/1.08
% 0.73/1.08
% 0.73/1.08 Clauses:
% 0.73/1.08
% 0.73/1.08 { ! in( X, Y ), ! in( Y, X ) }.
% 0.73/1.08 { ! v1_membered( X ), ! element( Y, X ), v1_xcmplx_0( Y ) }.
% 0.73/1.08 { ! v2_membered( X ), ! element( Y, X ), v1_xcmplx_0( Y ) }.
% 0.73/1.08 { ! v2_membered( X ), ! element( Y, X ), v1_xreal_0( Y ) }.
% 0.73/1.08 { ! v3_membered( X ), ! element( Y, X ), v1_xcmplx_0( Y ) }.
% 0.73/1.08 { ! v3_membered( X ), ! element( Y, X ), v1_xreal_0( Y ) }.
% 0.73/1.08 { ! v3_membered( X ), ! element( Y, X ), v1_rat_1( Y ) }.
% 0.73/1.08 { ! v4_membered( X ), ! element( Y, X ), alpha1( Y ) }.
% 0.73/1.08 { ! v4_membered( X ), ! element( Y, X ), v1_rat_1( Y ) }.
% 0.73/1.08 { ! alpha1( X ), v1_xcmplx_0( X ) }.
% 0.73/1.08 { ! alpha1( X ), v1_xreal_0( X ) }.
% 0.73/1.08 { ! alpha1( X ), v1_int_1( X ) }.
% 0.73/1.08 { ! v1_xcmplx_0( X ), ! v1_xreal_0( X ), ! v1_int_1( X ), alpha1( X ) }.
% 0.73/1.08 { ! v5_membered( X ), ! element( Y, X ), alpha2( Y ) }.
% 0.73/1.08 { ! v5_membered( X ), ! element( Y, X ), v1_rat_1( Y ) }.
% 0.73/1.08 { ! alpha2( X ), alpha7( X ) }.
% 0.73/1.08 { ! alpha2( X ), v1_int_1( X ) }.
% 0.73/1.08 { ! alpha7( X ), ! v1_int_1( X ), alpha2( X ) }.
% 0.73/1.08 { ! alpha7( X ), v1_xcmplx_0( X ) }.
% 0.73/1.08 { ! alpha7( X ), natural( X ) }.
% 0.73/1.08 { ! alpha7( X ), v1_xreal_0( X ) }.
% 0.73/1.08 { ! v1_xcmplx_0( X ), ! natural( X ), ! v1_xreal_0( X ), alpha7( X ) }.
% 0.73/1.08 { ! empty( X ), alpha3( X ) }.
% 0.73/1.08 { ! empty( X ), v5_membered( X ) }.
% 0.73/1.08 { ! alpha3( X ), alpha8( X ) }.
% 0.73/1.08 { ! alpha3( X ), v4_membered( X ) }.
% 0.73/1.08 { ! alpha8( X ), ! v4_membered( X ), alpha3( X ) }.
% 0.73/1.08 { ! alpha8( X ), v1_membered( X ) }.
% 0.73/1.08 { ! alpha8( X ), v2_membered( X ) }.
% 0.73/1.08 { ! alpha8( X ), v3_membered( X ) }.
% 0.73/1.08 { ! v1_membered( X ), ! v2_membered( X ), ! v3_membered( X ), alpha8( X ) }
% 0.73/1.08 .
% 0.73/1.08 { ! v1_membered( X ), ! element( Y, powerset( X ) ), v1_membered( Y ) }.
% 0.73/1.08 { ! v2_membered( X ), ! element( Y, powerset( X ) ), v1_membered( Y ) }.
% 0.73/1.08 { ! v2_membered( X ), ! element( Y, powerset( X ) ), v2_membered( Y ) }.
% 0.73/1.08 { ! v3_membered( X ), ! element( Y, powerset( X ) ), v1_membered( Y ) }.
% 0.73/1.08 { ! v3_membered( X ), ! element( Y, powerset( X ) ), v2_membered( Y ) }.
% 0.73/1.08 { ! v3_membered( X ), ! element( Y, powerset( X ) ), v3_membered( Y ) }.
% 0.73/1.08 { ! v4_membered( X ), ! element( Y, powerset( X ) ), alpha4( Y ) }.
% 0.73/1.08 { ! v4_membered( X ), ! element( Y, powerset( X ) ), v4_membered( Y ) }.
% 0.73/1.08 { ! alpha4( X ), v1_membered( X ) }.
% 0.73/1.08 { ! alpha4( X ), v2_membered( X ) }.
% 0.73/1.08 { ! alpha4( X ), v3_membered( X ) }.
% 0.73/1.08 { ! v1_membered( X ), ! v2_membered( X ), ! v3_membered( X ), alpha4( X ) }
% 0.73/1.08 .
% 0.73/1.08 { ! v5_membered( X ), v4_membered( X ) }.
% 0.73/1.08 { ! v5_membered( X ), ! element( Y, powerset( X ) ), alpha5( Y ) }.
% 0.73/1.08 { ! v5_membered( X ), ! element( Y, powerset( X ) ), v5_membered( Y ) }.
% 0.73/1.08 { ! alpha5( X ), alpha9( X ) }.
% 0.73/1.08 { ! alpha5( X ), v4_membered( X ) }.
% 0.73/1.08 { ! alpha9( X ), ! v4_membered( X ), alpha5( X ) }.
% 0.73/1.08 { ! alpha9( X ), v1_membered( X ) }.
% 0.73/1.08 { ! alpha9( X ), v2_membered( X ) }.
% 0.73/1.08 { ! alpha9( X ), v3_membered( X ) }.
% 0.73/1.08 { ! v1_membered( X ), ! v2_membered( X ), ! v3_membered( X ), alpha9( X ) }
% 0.73/1.08 .
% 0.73/1.08 { ! v4_membered( X ), v3_membered( X ) }.
% 0.73/1.08 { ! v3_membered( X ), v2_membered( X ) }.
% 0.73/1.08 { ! v2_membered( X ), v1_membered( X ) }.
% 0.73/1.08 { ! element( Y, X ), ! proper_element( Y, X ), ! Y = union( X ) }.
% 0.73/1.08 { ! element( Y, X ), Y = union( X ), proper_element( Y, X ) }.
% 0.73/1.08 { element( k1_pcomps_1( X ), powerset( powerset( X ) ) ) }.
% 0.73/1.08 { && }.
% 0.73/1.08 { && }.
% 0.73/1.08 { && }.
% 0.73/1.08 { ! element( Y, powerset( powerset( X ) ) ), element( union_of_subsets( X,
% 0.73/1.08 Y ), powerset( X ) ) }.
% 0.73/1.08 { && }.
% 0.73/1.08 { element( skol1( X ), X ) }.
% 0.73/1.08 { ! empty( powerset( X ) ) }.
% 0.73/1.08 { empty( empty_set ) }.
% 0.73/1.08 { v1_membered( empty_set ) }.
% 0.73/1.08 { v2_membered( empty_set ) }.
% 0.73/1.08 { v3_membered( empty_set ) }.
% 0.73/1.08 { v4_membered( empty_set ) }.
% 0.73/1.08 { v5_membered( empty_set ) }.
% 0.73/1.08 { ! empty( skol2 ) }.
% 0.73/1.08 { v1_membered( skol2 ) }.
% 0.73/1.08 { v2_membered( skol2 ) }.
% 0.73/1.08 { v3_membered( skol2 ) }.
% 0.73/1.08 { v4_membered( skol2 ) }.
% 0.73/1.08 { v5_membered( skol2 ) }.
% 0.73/1.08 { empty( X ), ! empty( skol3( Y ) ) }.
% 0.73/1.08 { empty( X ), element( skol3( X ), powerset( X ) ) }.
% 0.73/1.08 { empty( skol4( Y ) ) }.
% 0.73/1.08 { element( skol4( X ), powerset( X ) ) }.
% 0.73/1.08 { element( skol5( X ), powerset( X ) ) }.
% 0.73/1.08 { ! proper_element( skol5( X ), powerset( X ) ) }.
% 0.73/1.08 { k1_pcomps_1( X ) = powerset( X ) }.
% 0.73/1.08 { ! element( Y, powerset( powerset( X ) ) ), union_of_subsets( X, Y ) =
% 0.73/1.10 union( Y ) }.
% 0.73/1.10 { subset( X, X ) }.
% 0.73/1.10 { ! in( X, Y ), element( X, Y ) }.
% 0.73/1.10 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.73/1.10 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.73/1.10 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.73/1.10 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.73/1.10 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.73/1.10 { element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 { alpha6( skol6, skol7 ), ! skol7 = skol6 }.
% 0.73/1.10 { alpha6( skol6, skol7 ), ! proper_element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 { ! alpha6( X, Y ), proper_element( Y, powerset( X ) ) }.
% 0.73/1.10 { ! alpha6( X, Y ), Y = X }.
% 0.73/1.10 { ! proper_element( Y, powerset( X ) ), ! Y = X, alpha6( X, Y ) }.
% 0.73/1.10 { ! empty( X ), X = empty_set }.
% 0.73/1.10 { ! in( X, Y ), ! empty( Y ) }.
% 0.73/1.10 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.73/1.10 { union( powerset( X ) ) = X }.
% 0.73/1.10
% 0.73/1.10 percentage equality = 0.046296, percentage horn = 0.970000
% 0.73/1.10 This is a problem with some equality
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 Options Used:
% 0.73/1.10
% 0.73/1.10 useres = 1
% 0.73/1.10 useparamod = 1
% 0.73/1.10 useeqrefl = 1
% 0.73/1.10 useeqfact = 1
% 0.73/1.10 usefactor = 1
% 0.73/1.10 usesimpsplitting = 0
% 0.73/1.10 usesimpdemod = 5
% 0.73/1.10 usesimpres = 3
% 0.73/1.10
% 0.73/1.10 resimpinuse = 1000
% 0.73/1.10 resimpclauses = 20000
% 0.73/1.10 substype = eqrewr
% 0.73/1.10 backwardsubs = 1
% 0.73/1.10 selectoldest = 5
% 0.73/1.10
% 0.73/1.10 litorderings [0] = split
% 0.73/1.10 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.10
% 0.73/1.10 termordering = kbo
% 0.73/1.10
% 0.73/1.10 litapriori = 0
% 0.73/1.10 termapriori = 1
% 0.73/1.10 litaposteriori = 0
% 0.73/1.10 termaposteriori = 0
% 0.73/1.10 demodaposteriori = 0
% 0.73/1.10 ordereqreflfact = 0
% 0.73/1.10
% 0.73/1.10 litselect = negord
% 0.73/1.10
% 0.73/1.10 maxweight = 15
% 0.73/1.10 maxdepth = 30000
% 0.73/1.10 maxlength = 115
% 0.73/1.10 maxnrvars = 195
% 0.73/1.10 excuselevel = 1
% 0.73/1.10 increasemaxweight = 1
% 0.73/1.10
% 0.73/1.10 maxselected = 10000000
% 0.73/1.10 maxnrclauses = 10000000
% 0.73/1.10
% 0.73/1.10 showgenerated = 0
% 0.73/1.10 showkept = 0
% 0.73/1.10 showselected = 0
% 0.73/1.10 showdeleted = 0
% 0.73/1.10 showresimp = 1
% 0.73/1.10 showstatus = 2000
% 0.73/1.10
% 0.73/1.10 prologoutput = 0
% 0.73/1.10 nrgoals = 5000000
% 0.73/1.10 totalproof = 1
% 0.73/1.10
% 0.73/1.10 Symbols occurring in the translation:
% 0.73/1.10
% 0.73/1.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.10 . [1, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.73/1.10 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 0.73/1.10 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.73/1.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.10 in [37, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.73/1.10 v1_membered [38, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.73/1.10 element [39, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.73/1.10 v1_xcmplx_0 [40, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.73/1.10 v2_membered [41, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.73/1.10 v1_xreal_0 [42, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.10 v3_membered [43, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.73/1.10 v1_rat_1 [44, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.73/1.10 v4_membered [45, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.73/1.10 v1_int_1 [46, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.73/1.10 v5_membered [47, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.73/1.10 natural [48, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.73/1.10 empty [49, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.73/1.10 powerset [50, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.73/1.10 proper_element [51, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.73/1.10 union [52, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.73/1.10 k1_pcomps_1 [53, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.73/1.10 union_of_subsets [54, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.73/1.10 empty_set [55, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.73/1.10 subset [56, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.73/1.10 alpha1 [58, 1] (w:1, o:32, a:1, s:1, b:1),
% 0.73/1.10 alpha2 [59, 1] (w:1, o:33, a:1, s:1, b:1),
% 0.73/1.10 alpha3 [60, 1] (w:1, o:34, a:1, s:1, b:1),
% 0.73/1.10 alpha4 [61, 1] (w:1, o:35, a:1, s:1, b:1),
% 0.73/1.10 alpha5 [62, 1] (w:1, o:36, a:1, s:1, b:1),
% 0.73/1.10 alpha6 [63, 2] (w:1, o:73, a:1, s:1, b:1),
% 0.73/1.10 alpha7 [64, 1] (w:1, o:37, a:1, s:1, b:1),
% 0.73/1.10 alpha8 [65, 1] (w:1, o:38, a:1, s:1, b:1),
% 0.73/1.10 alpha9 [66, 1] (w:1, o:39, a:1, s:1, b:1),
% 0.73/1.10 skol1 [67, 1] (w:1, o:40, a:1, s:1, b:1),
% 0.73/1.10 skol2 [68, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.73/1.10 skol3 [69, 1] (w:1, o:41, a:1, s:1, b:1),
% 0.73/1.10 skol4 [70, 1] (w:1, o:42, a:1, s:1, b:1),
% 0.73/1.10 skol5 [71, 1] (w:1, o:43, a:1, s:1, b:1),
% 0.73/1.10 skol6 [72, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.73/1.10 skol7 [73, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 Starting Search:
% 0.73/1.10
% 0.73/1.10 *** allocated 15000 integers for clauses
% 0.73/1.10 *** allocated 22500 integers for clauses
% 0.73/1.10 *** allocated 33750 integers for clauses
% 0.73/1.10 *** allocated 50625 integers for clauses
% 0.73/1.10 *** allocated 15000 integers for termspace/termends
% 0.73/1.10
% 0.73/1.10 Bliksems!, er is een bewijs:
% 0.73/1.10 % SZS status Theorem
% 0.73/1.10 % SZS output start Refutation
% 0.73/1.10
% 0.73/1.10 (56) {G0,W10,D3,L3,V2,M3} I { ! element( Y, X ), ! proper_element( Y, X ),
% 0.73/1.10 ! Y = union( X ) }.
% 0.73/1.10 (57) {G0,W10,D3,L3,V2,M3} I { ! element( Y, X ), Y = union( X ),
% 0.73/1.10 proper_element( Y, X ) }.
% 0.73/1.10 (90) {G0,W4,D3,L1,V0,M1} I { element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 (91) {G0,W6,D2,L2,V0,M2} I { alpha6( skol6, skol7 ), ! skol7 ==> skol6 }.
% 0.73/1.10 (92) {G0,W7,D3,L2,V0,M2} I { alpha6( skol6, skol7 ), ! proper_element(
% 0.73/1.10 skol7, powerset( skol6 ) ) }.
% 0.73/1.10 (93) {G0,W7,D3,L2,V2,M2} I { ! alpha6( X, Y ), proper_element( Y, powerset
% 0.73/1.10 ( X ) ) }.
% 0.73/1.10 (94) {G0,W6,D2,L2,V2,M2} I { ! alpha6( X, Y ), Y = X }.
% 0.73/1.10 (99) {G0,W5,D4,L1,V1,M1} I { union( powerset( X ) ) ==> X }.
% 0.73/1.10 (513) {G1,W7,D3,L2,V0,M2} R(57,90);d(99) { proper_element( skol7, powerset
% 0.73/1.10 ( skol6 ) ), skol7 ==> skol6 }.
% 0.73/1.10 (979) {G1,W7,D3,L2,V0,M2} R(92,57);d(99);r(94) { ! element( skol7, powerset
% 0.73/1.10 ( skol6 ) ), skol7 ==> skol6 }.
% 0.73/1.10 (988) {G2,W4,D3,L1,V0,M1} R(93,91);d(513);q { proper_element( skol7,
% 0.73/1.10 powerset( skol6 ) ) }.
% 0.73/1.10 (993) {G3,W0,D0,L0,V0,M0} R(988,56);d(979);d(99);q;r(90) { }.
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 % SZS output end Refutation
% 0.73/1.10 found a proof!
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 Unprocessed initial clauses:
% 0.73/1.10
% 0.73/1.10 (995) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.73/1.10 (996) {G0,W7,D2,L3,V2,M3} { ! v1_membered( X ), ! element( Y, X ),
% 0.73/1.10 v1_xcmplx_0( Y ) }.
% 0.73/1.10 (997) {G0,W7,D2,L3,V2,M3} { ! v2_membered( X ), ! element( Y, X ),
% 0.73/1.10 v1_xcmplx_0( Y ) }.
% 0.73/1.10 (998) {G0,W7,D2,L3,V2,M3} { ! v2_membered( X ), ! element( Y, X ),
% 0.73/1.10 v1_xreal_0( Y ) }.
% 0.73/1.10 (999) {G0,W7,D2,L3,V2,M3} { ! v3_membered( X ), ! element( Y, X ),
% 0.73/1.10 v1_xcmplx_0( Y ) }.
% 0.73/1.10 (1000) {G0,W7,D2,L3,V2,M3} { ! v3_membered( X ), ! element( Y, X ),
% 0.73/1.10 v1_xreal_0( Y ) }.
% 0.73/1.10 (1001) {G0,W7,D2,L3,V2,M3} { ! v3_membered( X ), ! element( Y, X ),
% 0.73/1.10 v1_rat_1( Y ) }.
% 0.73/1.10 (1002) {G0,W7,D2,L3,V2,M3} { ! v4_membered( X ), ! element( Y, X ), alpha1
% 0.73/1.10 ( Y ) }.
% 0.73/1.10 (1003) {G0,W7,D2,L3,V2,M3} { ! v4_membered( X ), ! element( Y, X ),
% 0.73/1.10 v1_rat_1( Y ) }.
% 0.73/1.10 (1004) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), v1_xcmplx_0( X ) }.
% 0.73/1.10 (1005) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), v1_xreal_0( X ) }.
% 0.73/1.10 (1006) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), v1_int_1( X ) }.
% 0.73/1.10 (1007) {G0,W8,D2,L4,V1,M4} { ! v1_xcmplx_0( X ), ! v1_xreal_0( X ), !
% 0.73/1.10 v1_int_1( X ), alpha1( X ) }.
% 0.73/1.10 (1008) {G0,W7,D2,L3,V2,M3} { ! v5_membered( X ), ! element( Y, X ), alpha2
% 0.73/1.10 ( Y ) }.
% 0.73/1.10 (1009) {G0,W7,D2,L3,V2,M3} { ! v5_membered( X ), ! element( Y, X ),
% 0.73/1.10 v1_rat_1( Y ) }.
% 0.73/1.10 (1010) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), alpha7( X ) }.
% 0.73/1.10 (1011) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), v1_int_1( X ) }.
% 0.73/1.10 (1012) {G0,W6,D2,L3,V1,M3} { ! alpha7( X ), ! v1_int_1( X ), alpha2( X )
% 0.73/1.10 }.
% 0.73/1.10 (1013) {G0,W4,D2,L2,V1,M2} { ! alpha7( X ), v1_xcmplx_0( X ) }.
% 0.73/1.10 (1014) {G0,W4,D2,L2,V1,M2} { ! alpha7( X ), natural( X ) }.
% 0.73/1.10 (1015) {G0,W4,D2,L2,V1,M2} { ! alpha7( X ), v1_xreal_0( X ) }.
% 0.73/1.10 (1016) {G0,W8,D2,L4,V1,M4} { ! v1_xcmplx_0( X ), ! natural( X ), !
% 0.73/1.10 v1_xreal_0( X ), alpha7( X ) }.
% 0.73/1.10 (1017) {G0,W4,D2,L2,V1,M2} { ! empty( X ), alpha3( X ) }.
% 0.73/1.10 (1018) {G0,W4,D2,L2,V1,M2} { ! empty( X ), v5_membered( X ) }.
% 0.73/1.10 (1019) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), alpha8( X ) }.
% 0.73/1.10 (1020) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), v4_membered( X ) }.
% 0.73/1.10 (1021) {G0,W6,D2,L3,V1,M3} { ! alpha8( X ), ! v4_membered( X ), alpha3( X
% 0.73/1.10 ) }.
% 0.73/1.10 (1022) {G0,W4,D2,L2,V1,M2} { ! alpha8( X ), v1_membered( X ) }.
% 0.73/1.10 (1023) {G0,W4,D2,L2,V1,M2} { ! alpha8( X ), v2_membered( X ) }.
% 0.73/1.10 (1024) {G0,W4,D2,L2,V1,M2} { ! alpha8( X ), v3_membered( X ) }.
% 0.73/1.10 (1025) {G0,W8,D2,L4,V1,M4} { ! v1_membered( X ), ! v2_membered( X ), !
% 0.73/1.10 v3_membered( X ), alpha8( X ) }.
% 0.73/1.10 (1026) {G0,W8,D3,L3,V2,M3} { ! v1_membered( X ), ! element( Y, powerset( X
% 0.73/1.10 ) ), v1_membered( Y ) }.
% 0.73/1.10 (1027) {G0,W8,D3,L3,V2,M3} { ! v2_membered( X ), ! element( Y, powerset( X
% 0.73/1.10 ) ), v1_membered( Y ) }.
% 0.73/1.10 (1028) {G0,W8,D3,L3,V2,M3} { ! v2_membered( X ), ! element( Y, powerset( X
% 0.73/1.10 ) ), v2_membered( Y ) }.
% 0.73/1.10 (1029) {G0,W8,D3,L3,V2,M3} { ! v3_membered( X ), ! element( Y, powerset( X
% 0.73/1.10 ) ), v1_membered( Y ) }.
% 0.73/1.10 (1030) {G0,W8,D3,L3,V2,M3} { ! v3_membered( X ), ! element( Y, powerset( X
% 0.73/1.10 ) ), v2_membered( Y ) }.
% 0.73/1.10 (1031) {G0,W8,D3,L3,V2,M3} { ! v3_membered( X ), ! element( Y, powerset( X
% 0.73/1.10 ) ), v3_membered( Y ) }.
% 0.73/1.10 (1032) {G0,W8,D3,L3,V2,M3} { ! v4_membered( X ), ! element( Y, powerset( X
% 0.73/1.10 ) ), alpha4( Y ) }.
% 0.73/1.10 (1033) {G0,W8,D3,L3,V2,M3} { ! v4_membered( X ), ! element( Y, powerset( X
% 0.73/1.10 ) ), v4_membered( Y ) }.
% 0.73/1.10 (1034) {G0,W4,D2,L2,V1,M2} { ! alpha4( X ), v1_membered( X ) }.
% 0.73/1.10 (1035) {G0,W4,D2,L2,V1,M2} { ! alpha4( X ), v2_membered( X ) }.
% 0.73/1.10 (1036) {G0,W4,D2,L2,V1,M2} { ! alpha4( X ), v3_membered( X ) }.
% 0.73/1.10 (1037) {G0,W8,D2,L4,V1,M4} { ! v1_membered( X ), ! v2_membered( X ), !
% 0.73/1.10 v3_membered( X ), alpha4( X ) }.
% 0.73/1.10 (1038) {G0,W4,D2,L2,V1,M2} { ! v5_membered( X ), v4_membered( X ) }.
% 0.73/1.10 (1039) {G0,W8,D3,L3,V2,M3} { ! v5_membered( X ), ! element( Y, powerset( X
% 0.73/1.10 ) ), alpha5( Y ) }.
% 0.73/1.10 (1040) {G0,W8,D3,L3,V2,M3} { ! v5_membered( X ), ! element( Y, powerset( X
% 0.73/1.10 ) ), v5_membered( Y ) }.
% 0.73/1.10 (1041) {G0,W4,D2,L2,V1,M2} { ! alpha5( X ), alpha9( X ) }.
% 0.73/1.10 (1042) {G0,W4,D2,L2,V1,M2} { ! alpha5( X ), v4_membered( X ) }.
% 0.73/1.10 (1043) {G0,W6,D2,L3,V1,M3} { ! alpha9( X ), ! v4_membered( X ), alpha5( X
% 0.73/1.10 ) }.
% 0.73/1.10 (1044) {G0,W4,D2,L2,V1,M2} { ! alpha9( X ), v1_membered( X ) }.
% 0.73/1.10 (1045) {G0,W4,D2,L2,V1,M2} { ! alpha9( X ), v2_membered( X ) }.
% 0.73/1.10 (1046) {G0,W4,D2,L2,V1,M2} { ! alpha9( X ), v3_membered( X ) }.
% 0.73/1.10 (1047) {G0,W8,D2,L4,V1,M4} { ! v1_membered( X ), ! v2_membered( X ), !
% 0.73/1.10 v3_membered( X ), alpha9( X ) }.
% 0.73/1.10 (1048) {G0,W4,D2,L2,V1,M2} { ! v4_membered( X ), v3_membered( X ) }.
% 0.73/1.10 (1049) {G0,W4,D2,L2,V1,M2} { ! v3_membered( X ), v2_membered( X ) }.
% 0.73/1.10 (1050) {G0,W4,D2,L2,V1,M2} { ! v2_membered( X ), v1_membered( X ) }.
% 0.73/1.10 (1051) {G0,W10,D3,L3,V2,M3} { ! element( Y, X ), ! proper_element( Y, X )
% 0.73/1.10 , ! Y = union( X ) }.
% 0.73/1.10 (1052) {G0,W10,D3,L3,V2,M3} { ! element( Y, X ), Y = union( X ),
% 0.73/1.10 proper_element( Y, X ) }.
% 0.73/1.10 (1053) {G0,W6,D4,L1,V1,M1} { element( k1_pcomps_1( X ), powerset( powerset
% 0.73/1.10 ( X ) ) ) }.
% 0.73/1.10 (1054) {G0,W1,D1,L1,V0,M1} { && }.
% 0.73/1.10 (1055) {G0,W1,D1,L1,V0,M1} { && }.
% 0.73/1.10 (1056) {G0,W1,D1,L1,V0,M1} { && }.
% 0.73/1.10 (1057) {G0,W11,D4,L2,V2,M2} { ! element( Y, powerset( powerset( X ) ) ),
% 0.73/1.10 element( union_of_subsets( X, Y ), powerset( X ) ) }.
% 0.73/1.10 (1058) {G0,W1,D1,L1,V0,M1} { && }.
% 0.73/1.10 (1059) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.73/1.10 (1060) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 0.73/1.10 (1061) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.73/1.10 (1062) {G0,W2,D2,L1,V0,M1} { v1_membered( empty_set ) }.
% 0.73/1.10 (1063) {G0,W2,D2,L1,V0,M1} { v2_membered( empty_set ) }.
% 0.73/1.10 (1064) {G0,W2,D2,L1,V0,M1} { v3_membered( empty_set ) }.
% 0.73/1.10 (1065) {G0,W2,D2,L1,V0,M1} { v4_membered( empty_set ) }.
% 0.73/1.10 (1066) {G0,W2,D2,L1,V0,M1} { v5_membered( empty_set ) }.
% 0.73/1.10 (1067) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.73/1.10 (1068) {G0,W2,D2,L1,V0,M1} { v1_membered( skol2 ) }.
% 0.73/1.10 (1069) {G0,W2,D2,L1,V0,M1} { v2_membered( skol2 ) }.
% 0.73/1.10 (1070) {G0,W2,D2,L1,V0,M1} { v3_membered( skol2 ) }.
% 0.73/1.10 (1071) {G0,W2,D2,L1,V0,M1} { v4_membered( skol2 ) }.
% 0.73/1.10 (1072) {G0,W2,D2,L1,V0,M1} { v5_membered( skol2 ) }.
% 0.73/1.10 (1073) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol3( Y ) ) }.
% 0.73/1.10 (1074) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol3( X ), powerset( X
% 0.73/1.10 ) ) }.
% 0.73/1.10 (1075) {G0,W3,D3,L1,V1,M1} { empty( skol4( Y ) ) }.
% 0.73/1.10 (1076) {G0,W5,D3,L1,V1,M1} { element( skol4( X ), powerset( X ) ) }.
% 0.73/1.10 (1077) {G0,W5,D3,L1,V1,M1} { element( skol5( X ), powerset( X ) ) }.
% 0.73/1.10 (1078) {G0,W5,D3,L1,V1,M1} { ! proper_element( skol5( X ), powerset( X ) )
% 0.73/1.10 }.
% 0.73/1.10 (1079) {G0,W5,D3,L1,V1,M1} { k1_pcomps_1( X ) = powerset( X ) }.
% 0.73/1.10 (1080) {G0,W11,D4,L2,V2,M2} { ! element( Y, powerset( powerset( X ) ) ),
% 0.73/1.10 union_of_subsets( X, Y ) = union( Y ) }.
% 0.73/1.10 (1081) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.73/1.10 (1082) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.73/1.10 (1083) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.73/1.10 (1084) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.73/1.10 }.
% 0.73/1.10 (1085) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.73/1.10 }.
% 0.73/1.10 (1086) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 0.73/1.10 , element( X, Y ) }.
% 0.73/1.10 (1087) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ),
% 0.73/1.10 ! empty( Z ) }.
% 0.73/1.10 (1088) {G0,W4,D3,L1,V0,M1} { element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 (1089) {G0,W6,D2,L2,V0,M2} { alpha6( skol6, skol7 ), ! skol7 = skol6 }.
% 0.73/1.10 (1090) {G0,W7,D3,L2,V0,M2} { alpha6( skol6, skol7 ), ! proper_element(
% 0.73/1.10 skol7, powerset( skol6 ) ) }.
% 0.73/1.10 (1091) {G0,W7,D3,L2,V2,M2} { ! alpha6( X, Y ), proper_element( Y, powerset
% 0.73/1.10 ( X ) ) }.
% 0.73/1.10 (1092) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), Y = X }.
% 0.73/1.10 (1093) {G0,W10,D3,L3,V2,M3} { ! proper_element( Y, powerset( X ) ), ! Y =
% 0.73/1.10 X, alpha6( X, Y ) }.
% 0.73/1.10 (1094) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.73/1.10 (1095) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.73/1.10 (1096) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.73/1.10 (1097) {G0,W5,D4,L1,V1,M1} { union( powerset( X ) ) = X }.
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 Total Proof:
% 0.73/1.10
% 0.73/1.10 subsumption: (56) {G0,W10,D3,L3,V2,M3} I { ! element( Y, X ), !
% 0.73/1.10 proper_element( Y, X ), ! Y = union( X ) }.
% 0.73/1.10 parent0: (1051) {G0,W10,D3,L3,V2,M3} { ! element( Y, X ), ! proper_element
% 0.73/1.10 ( Y, X ), ! Y = union( X ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 1
% 0.73/1.10 2 ==> 2
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (57) {G0,W10,D3,L3,V2,M3} I { ! element( Y, X ), Y = union( X
% 0.73/1.10 ), proper_element( Y, X ) }.
% 0.73/1.10 parent0: (1052) {G0,W10,D3,L3,V2,M3} { ! element( Y, X ), Y = union( X ),
% 0.73/1.10 proper_element( Y, X ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 1
% 0.73/1.10 2 ==> 2
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (90) {G0,W4,D3,L1,V0,M1} I { element( skol7, powerset( skol6 )
% 0.73/1.10 ) }.
% 0.73/1.10 parent0: (1088) {G0,W4,D3,L1,V0,M1} { element( skol7, powerset( skol6 ) )
% 0.73/1.10 }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (91) {G0,W6,D2,L2,V0,M2} I { alpha6( skol6, skol7 ), ! skol7
% 0.73/1.10 ==> skol6 }.
% 0.73/1.10 parent0: (1089) {G0,W6,D2,L2,V0,M2} { alpha6( skol6, skol7 ), ! skol7 =
% 0.73/1.10 skol6 }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 1
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (92) {G0,W7,D3,L2,V0,M2} I { alpha6( skol6, skol7 ), !
% 0.73/1.10 proper_element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 parent0: (1090) {G0,W7,D3,L2,V0,M2} { alpha6( skol6, skol7 ), !
% 0.73/1.10 proper_element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 1
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (93) {G0,W7,D3,L2,V2,M2} I { ! alpha6( X, Y ), proper_element
% 0.73/1.10 ( Y, powerset( X ) ) }.
% 0.73/1.10 parent0: (1091) {G0,W7,D3,L2,V2,M2} { ! alpha6( X, Y ), proper_element( Y
% 0.73/1.10 , powerset( X ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 1
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (94) {G0,W6,D2,L2,V2,M2} I { ! alpha6( X, Y ), Y = X }.
% 0.73/1.10 parent0: (1092) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), Y = X }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 1
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (99) {G0,W5,D4,L1,V1,M1} I { union( powerset( X ) ) ==> X }.
% 0.73/1.10 parent0: (1097) {G0,W5,D4,L1,V1,M1} { union( powerset( X ) ) = X }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 eqswap: (1144) {G0,W10,D3,L3,V2,M3} { union( Y ) = X, ! element( X, Y ),
% 0.73/1.10 proper_element( X, Y ) }.
% 0.73/1.10 parent0[1]: (57) {G0,W10,D3,L3,V2,M3} I { ! element( Y, X ), Y = union( X )
% 0.73/1.10 , proper_element( Y, X ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := Y
% 0.73/1.10 Y := X
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (1146) {G1,W9,D4,L2,V0,M2} { union( powerset( skol6 ) ) =
% 0.73/1.10 skol7, proper_element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 parent0[1]: (1144) {G0,W10,D3,L3,V2,M3} { union( Y ) = X, ! element( X, Y
% 0.73/1.10 ), proper_element( X, Y ) }.
% 0.73/1.10 parent1[0]: (90) {G0,W4,D3,L1,V0,M1} I { element( skol7, powerset( skol6 )
% 0.73/1.10 ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := skol7
% 0.73/1.10 Y := powerset( skol6 )
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 paramod: (1147) {G1,W7,D3,L2,V0,M2} { skol6 = skol7, proper_element( skol7
% 0.73/1.10 , powerset( skol6 ) ) }.
% 0.73/1.10 parent0[0]: (99) {G0,W5,D4,L1,V1,M1} I { union( powerset( X ) ) ==> X }.
% 0.73/1.10 parent1[0; 1]: (1146) {G1,W9,D4,L2,V0,M2} { union( powerset( skol6 ) ) =
% 0.73/1.10 skol7, proper_element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := skol6
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 eqswap: (1148) {G1,W7,D3,L2,V0,M2} { skol7 = skol6, proper_element( skol7
% 0.73/1.10 , powerset( skol6 ) ) }.
% 0.73/1.10 parent0[0]: (1147) {G1,W7,D3,L2,V0,M2} { skol6 = skol7, proper_element(
% 0.73/1.10 skol7, powerset( skol6 ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (513) {G1,W7,D3,L2,V0,M2} R(57,90);d(99) { proper_element(
% 0.73/1.10 skol7, powerset( skol6 ) ), skol7 ==> skol6 }.
% 0.73/1.10 parent0: (1148) {G1,W7,D3,L2,V0,M2} { skol7 = skol6, proper_element( skol7
% 0.73/1.10 , powerset( skol6 ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 1
% 0.73/1.10 1 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 eqswap: (1149) {G0,W10,D3,L3,V2,M3} { union( Y ) = X, ! element( X, Y ),
% 0.73/1.10 proper_element( X, Y ) }.
% 0.73/1.10 parent0[1]: (57) {G0,W10,D3,L3,V2,M3} I { ! element( Y, X ), Y = union( X )
% 0.73/1.10 , proper_element( Y, X ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := Y
% 0.73/1.10 Y := X
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (1152) {G1,W12,D4,L3,V0,M3} { alpha6( skol6, skol7 ), union(
% 0.73/1.10 powerset( skol6 ) ) = skol7, ! element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 parent0[1]: (92) {G0,W7,D3,L2,V0,M2} I { alpha6( skol6, skol7 ), !
% 0.73/1.10 proper_element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 parent1[2]: (1149) {G0,W10,D3,L3,V2,M3} { union( Y ) = X, ! element( X, Y
% 0.73/1.10 ), proper_element( X, Y ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 X := skol7
% 0.73/1.10 Y := powerset( skol6 )
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 paramod: (1153) {G1,W10,D3,L3,V0,M3} { skol6 = skol7, alpha6( skol6, skol7
% 0.73/1.10 ), ! element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 parent0[0]: (99) {G0,W5,D4,L1,V1,M1} I { union( powerset( X ) ) ==> X }.
% 0.73/1.10 parent1[1; 1]: (1152) {G1,W12,D4,L3,V0,M3} { alpha6( skol6, skol7 ), union
% 0.73/1.10 ( powerset( skol6 ) ) = skol7, ! element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := skol6
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (1156) {G1,W10,D3,L3,V0,M3} { skol7 = skol6, skol6 = skol7, !
% 0.73/1.10 element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 parent0[0]: (94) {G0,W6,D2,L2,V2,M2} I { ! alpha6( X, Y ), Y = X }.
% 0.73/1.10 parent1[1]: (1153) {G1,W10,D3,L3,V0,M3} { skol6 = skol7, alpha6( skol6,
% 0.73/1.10 skol7 ), ! element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := skol6
% 0.73/1.10 Y := skol7
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 eqswap: (1158) {G1,W10,D3,L3,V0,M3} { skol7 = skol6, skol7 = skol6, !
% 0.73/1.10 element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 parent0[1]: (1156) {G1,W10,D3,L3,V0,M3} { skol7 = skol6, skol6 = skol7, !
% 0.73/1.10 element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 factor: (1160) {G1,W7,D3,L2,V0,M2} { skol7 = skol6, ! element( skol7,
% 0.73/1.10 powerset( skol6 ) ) }.
% 0.73/1.10 parent0[0, 1]: (1158) {G1,W10,D3,L3,V0,M3} { skol7 = skol6, skol7 = skol6
% 0.73/1.10 , ! element( skol7, powerset( skol6 ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (979) {G1,W7,D3,L2,V0,M2} R(92,57);d(99);r(94) { ! element(
% 0.73/1.10 skol7, powerset( skol6 ) ), skol7 ==> skol6 }.
% 0.73/1.10 parent0: (1160) {G1,W7,D3,L2,V0,M2} { skol7 = skol6, ! element( skol7,
% 0.73/1.10 powerset( skol6 ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 1
% 0.73/1.10 1 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 eqswap: (1161) {G0,W6,D2,L2,V0,M2} { ! skol6 ==> skol7, alpha6( skol6,
% 0.73/1.10 skol7 ) }.
% 0.73/1.10 parent0[1]: (91) {G0,W6,D2,L2,V0,M2} I { alpha6( skol6, skol7 ), ! skol7
% 0.73/1.10 ==> skol6 }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (1163) {G1,W7,D3,L2,V0,M2} { proper_element( skol7, powerset(
% 0.73/1.10 skol6 ) ), ! skol6 ==> skol7 }.
% 0.73/1.10 parent0[0]: (93) {G0,W7,D3,L2,V2,M2} I { ! alpha6( X, Y ), proper_element(
% 0.73/1.10 Y, powerset( X ) ) }.
% 0.73/1.10 parent1[1]: (1161) {G0,W6,D2,L2,V0,M2} { ! skol6 ==> skol7, alpha6( skol6
% 0.73/1.10 , skol7 ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := skol6
% 0.73/1.10 Y := skol7
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 paramod: (1165) {G2,W11,D3,L3,V0,M3} { ! skol6 ==> skol6, proper_element(
% 0.73/1.10 skol7, powerset( skol6 ) ), proper_element( skol7, powerset( skol6 ) )
% 0.73/1.10 }.
% 0.73/1.10 parent0[1]: (513) {G1,W7,D3,L2,V0,M2} R(57,90);d(99) { proper_element(
% 0.73/1.10 skol7, powerset( skol6 ) ), skol7 ==> skol6 }.
% 0.73/1.10 parent1[1; 3]: (1163) {G1,W7,D3,L2,V0,M2} { proper_element( skol7,
% 0.73/1.10 powerset( skol6 ) ), ! skol6 ==> skol7 }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 factor: (1176) {G2,W7,D3,L2,V0,M2} { ! skol6 ==> skol6, proper_element(
% 0.73/1.10 skol7, powerset( skol6 ) ) }.
% 0.73/1.10 parent0[1, 2]: (1165) {G2,W11,D3,L3,V0,M3} { ! skol6 ==> skol6,
% 0.73/1.10 proper_element( skol7, powerset( skol6 ) ), proper_element( skol7,
% 0.73/1.10 powerset( skol6 ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 eqrefl: (1177) {G0,W4,D3,L1,V0,M1} { proper_element( skol7, powerset(
% 0.73/1.10 skol6 ) ) }.
% 0.73/1.10 parent0[0]: (1176) {G2,W7,D3,L2,V0,M2} { ! skol6 ==> skol6, proper_element
% 0.73/1.11 ( skol7, powerset( skol6 ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (988) {G2,W4,D3,L1,V0,M1} R(93,91);d(513);q { proper_element(
% 0.73/1.11 skol7, powerset( skol6 ) ) }.
% 0.73/1.11 parent0: (1177) {G0,W4,D3,L1,V0,M1} { proper_element( skol7, powerset(
% 0.73/1.11 skol6 ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 eqswap: (1178) {G0,W10,D3,L3,V2,M3} { ! union( Y ) = X, ! element( X, Y )
% 0.73/1.11 , ! proper_element( X, Y ) }.
% 0.73/1.11 parent0[2]: (56) {G0,W10,D3,L3,V2,M3} I { ! element( Y, X ), !
% 0.73/1.11 proper_element( Y, X ), ! Y = union( X ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := Y
% 0.73/1.11 Y := X
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (1181) {G1,W9,D4,L2,V0,M2} { ! union( powerset( skol6 ) ) =
% 0.73/1.11 skol7, ! element( skol7, powerset( skol6 ) ) }.
% 0.73/1.11 parent0[2]: (1178) {G0,W10,D3,L3,V2,M3} { ! union( Y ) = X, ! element( X,
% 0.73/1.11 Y ), ! proper_element( X, Y ) }.
% 0.73/1.11 parent1[0]: (988) {G2,W4,D3,L1,V0,M1} R(93,91);d(513);q { proper_element(
% 0.73/1.11 skol7, powerset( skol6 ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := skol7
% 0.73/1.11 Y := powerset( skol6 )
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 paramod: (1182) {G2,W13,D4,L3,V0,M3} { ! union( powerset( skol6 ) ) =
% 0.73/1.11 skol6, ! element( skol7, powerset( skol6 ) ), ! element( skol7, powerset
% 0.73/1.11 ( skol6 ) ) }.
% 0.73/1.11 parent0[1]: (979) {G1,W7,D3,L2,V0,M2} R(92,57);d(99);r(94) { ! element(
% 0.73/1.11 skol7, powerset( skol6 ) ), skol7 ==> skol6 }.
% 0.73/1.11 parent1[0; 5]: (1181) {G1,W9,D4,L2,V0,M2} { ! union( powerset( skol6 ) ) =
% 0.73/1.11 skol7, ! element( skol7, powerset( skol6 ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 factor: (1195) {G2,W9,D4,L2,V0,M2} { ! union( powerset( skol6 ) ) = skol6
% 0.73/1.11 , ! element( skol7, powerset( skol6 ) ) }.
% 0.73/1.11 parent0[1, 2]: (1182) {G2,W13,D4,L3,V0,M3} { ! union( powerset( skol6 ) )
% 0.73/1.11 = skol6, ! element( skol7, powerset( skol6 ) ), ! element( skol7,
% 0.73/1.11 powerset( skol6 ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 paramod: (2329) {G1,W7,D3,L2,V0,M2} { ! skol6 = skol6, ! element( skol7,
% 0.73/1.11 powerset( skol6 ) ) }.
% 0.73/1.11 parent0[0]: (99) {G0,W5,D4,L1,V1,M1} I { union( powerset( X ) ) ==> X }.
% 0.73/1.11 parent1[0; 2]: (1195) {G2,W9,D4,L2,V0,M2} { ! union( powerset( skol6 ) ) =
% 0.73/1.11 skol6, ! element( skol7, powerset( skol6 ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := skol6
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 eqrefl: (2330) {G0,W4,D3,L1,V0,M1} { ! element( skol7, powerset( skol6 ) )
% 0.73/1.11 }.
% 0.73/1.11 parent0[0]: (2329) {G1,W7,D3,L2,V0,M2} { ! skol6 = skol6, ! element( skol7
% 0.73/1.11 , powerset( skol6 ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (2331) {G1,W0,D0,L0,V0,M0} { }.
% 0.73/1.11 parent0[0]: (2330) {G0,W4,D3,L1,V0,M1} { ! element( skol7, powerset( skol6
% 0.73/1.11 ) ) }.
% 0.73/1.11 parent1[0]: (90) {G0,W4,D3,L1,V0,M1} I { element( skol7, powerset( skol6 )
% 0.73/1.11 ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (993) {G3,W0,D0,L0,V0,M0} R(988,56);d(979);d(99);q;r(90) {
% 0.73/1.11 }.
% 0.73/1.11 parent0: (2331) {G1,W0,D0,L0,V0,M0} { }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 Proof check complete!
% 0.73/1.11
% 0.73/1.11 Memory use:
% 0.73/1.11
% 0.73/1.11 space for terms: 10406
% 0.73/1.11 space for clauses: 44141
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 clauses generated: 2533
% 0.73/1.11 clauses kept: 994
% 0.73/1.11 clauses selected: 261
% 0.73/1.11 clauses deleted: 7
% 0.73/1.11 clauses inuse deleted: 0
% 0.73/1.11
% 0.73/1.11 subsentry: 8261
% 0.73/1.11 literals s-matched: 7997
% 0.73/1.11 literals matched: 7997
% 0.73/1.11 full subsumption: 105
% 0.73/1.11
% 0.73/1.11 checksum: 1770951564
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Bliksem ended
%------------------------------------------------------------------------------