TSTP Solution File: SWV395+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV395+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 : Wed Jul 20 16:24:43 EDT 2022
% Result : Theorem 0.72s 1.11s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV395+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n023.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Tue Jun 14 18:03:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.11 *** allocated 10000 integers for termspace/termends
% 0.72/1.11 *** allocated 10000 integers for clauses
% 0.72/1.11 *** allocated 10000 integers for justifications
% 0.72/1.11 Bliksem 1.12
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Automatic Strategy Selection
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Clauses:
% 0.72/1.11
% 0.72/1.11 { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.72/1.11 { less_than( X, Y ), less_than( Y, X ) }.
% 0.72/1.11 { less_than( X, X ) }.
% 0.72/1.11 { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.72/1.11 { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.72/1.11 { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.72/1.11 { less_than( bottom, X ) }.
% 0.72/1.11 { ! isnonempty_slb( create_slb ) }.
% 0.72/1.11 { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) ) }.
% 0.72/1.11 { ! contains_slb( create_slb, X ) }.
% 0.72/1.11 { ! contains_slb( insert_slb( X, pair( Y, T ) ), Z ), contains_slb( X, Z )
% 0.72/1.11 , Y = Z }.
% 0.72/1.11 { ! contains_slb( X, Z ), contains_slb( insert_slb( X, pair( Y, T ) ), Z )
% 0.72/1.11 }.
% 0.72/1.11 { ! Y = Z, contains_slb( insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.72/1.11 { ! pair_in_list( create_slb, X, Y ) }.
% 0.72/1.11 { ! pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U ), pair_in_list( X, Z
% 0.72/1.11 , U ), alpha1( Y, Z, T, U ) }.
% 0.72/1.11 { ! pair_in_list( X, Z, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z
% 0.72/1.11 , U ) }.
% 0.72/1.11 { ! alpha1( Y, Z, T, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U
% 0.72/1.11 ) }.
% 0.72/1.11 { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.72/1.11 { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.72/1.11 { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.72/1.11 { remove_slb( insert_slb( X, pair( Y, Z ) ), Y ) = X }.
% 0.72/1.11 { Y = Z, ! contains_slb( X, Z ), remove_slb( insert_slb( X, pair( Y, T ) )
% 0.72/1.11 , Z ) = insert_slb( remove_slb( X, Z ), pair( Y, T ) ) }.
% 0.72/1.11 { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y ) = Z }.
% 0.72/1.11 { Y = Z, ! contains_slb( X, Z ), lookup_slb( insert_slb( X, pair( Y, T ) )
% 0.72/1.11 , Z ) = lookup_slb( X, Z ) }.
% 0.72/1.11 { update_slb( create_slb, X ) = create_slb }.
% 0.72/1.11 { ! strictly_less_than( Y, X ), update_slb( insert_slb( Z, pair( T, Y ) ),
% 0.72/1.11 X ) = insert_slb( update_slb( Z, X ), pair( T, X ) ) }.
% 0.72/1.11 { ! less_than( X, Y ), update_slb( insert_slb( Z, pair( T, Y ) ), X ) =
% 0.72/1.11 insert_slb( update_slb( Z, X ), pair( T, Y ) ) }.
% 0.72/1.11 { succ_cpq( X, X ) }.
% 0.72/1.11 { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y, Z ) ) }.
% 0.72/1.11 { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y, Z ) ) }.
% 0.72/1.11 { ! succ_cpq( X, Y ), succ_cpq( X, findmin_cpq_eff( Y ) ) }.
% 0.72/1.11 { ! succ_cpq( X, Y ), succ_cpq( X, removemin_cpq_eff( Y ) ) }.
% 0.72/1.11 { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.72/1.11 { ! less_than( Y, X ), ! check_cpq( triple( Z, insert_slb( T, pair( X, Y )
% 0.72/1.11 ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.72/1.11 { ! less_than( Y, X ), ! check_cpq( triple( Z, T, U ) ), check_cpq( triple
% 0.72/1.11 ( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.72/1.11 { ! strictly_less_than( X, Y ), ! check_cpq( triple( Z, insert_slb( T, pair
% 0.72/1.11 ( X, Y ) ), U ) ) }.
% 0.72/1.11 { ! strictly_less_than( X, Y ), ! ||, check_cpq( triple( Z, insert_slb( T,
% 0.72/1.11 pair( X, Y ) ), U ) ) }.
% 0.72/1.11 { ! contains_cpq( triple( X, Y, Z ), T ), contains_slb( Y, T ) }.
% 0.72/1.11 { ! contains_slb( Y, T ), contains_cpq( triple( X, Y, Z ), T ) }.
% 0.72/1.11 { ! ok( triple( X, Y, bad ) ) }.
% 0.72/1.11 { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.72/1.11 { ok( triple( Y, Z, X ) ), X = bad }.
% 0.72/1.11 { insert_cpq( triple( X, Y, Z ), T ) = triple( insert_pqp( X, T ),
% 0.72/1.11 insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.72/1.11 { contains_slb( X, Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( Z, X,
% 0.72/1.11 bad ) }.
% 0.72/1.11 { ! contains_slb( X, Y ), ! less_than( lookup_slb( X, Y ), Y ), remove_cpq
% 0.72/1.11 ( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y )
% 0.72/1.11 , T ) }.
% 0.72/1.11 { ! contains_slb( X, Y ), ! strictly_less_than( Y, lookup_slb( X, Y ) ),
% 0.72/1.11 remove_cpq( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ),
% 0.72/1.11 remove_slb( X, Y ), bad ) }.
% 0.72/1.11 { findmin_cpq_eff( triple( X, create_slb, Y ) ) = triple( X, create_slb,
% 0.72/1.11 bad ) }.
% 0.72/1.11 { Y = create_slb, contains_slb( Y, findmin_pqp_res( X ) ), findmin_cpq_eff
% 0.72/1.11 ( triple( X, Y, Z ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) )
% 0.72/1.11 , bad ) }.
% 0.72/1.11 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), !
% 0.72/1.11 strictly_less_than( findmin_pqp_res( X ), lookup_slb( Y, findmin_pqp_res
% 0.72/1.11 ( X ) ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb(
% 0.72/1.11 Y, findmin_pqp_res( X ) ), bad ) }.
% 0.72/1.11 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! less_than(
% 0.72/1.11 lookup_slb( Y, findmin_pqp_res( X ) ), findmin_pqp_res( X ) ),
% 0.72/1.11 findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( Y,
% 0.72/1.11 findmin_pqp_res( X ) ), Z ) }.
% 0.72/1.11 { findmin_cpq_res( triple( X, create_slb, Y ) ) = bottom }.
% 0.72/1.11 { X = create_slb, findmin_cpq_res( triple( Y, X, Z ) ) = findmin_pqp_res( Y
% 0.72/1.11 ) }.
% 0.72/1.11 { removemin_cpq_eff( X ) = remove_cpq( findmin_cpq_eff( X ),
% 0.72/1.11 findmin_cpq_res( X ) ) }.
% 0.72/1.11 { removemin_cpq_res( X ) = findmin_cpq_res( X ) }.
% 0.72/1.11 { pair_in_list( create_slb, skol1, skol2 ) }.
% 0.72/1.11 { strictly_less_than( skol1, skol2 ) }.
% 0.72/1.11 { ok( remove_cpq( triple( skol3, create_slb, skol4 ), skol1 ) ) }.
% 0.72/1.11 { ! pair_in_list( remove_slb( create_slb, skol1 ), skol1, skol2 ) }.
% 0.72/1.11
% 0.72/1.11 percentage equality = 0.285714, percentage horn = 0.793103
% 0.72/1.11 This is a problem with some equality
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Options Used:
% 0.72/1.11
% 0.72/1.11 useres = 1
% 0.72/1.11 useparamod = 1
% 0.72/1.11 useeqrefl = 1
% 0.72/1.11 useeqfact = 1
% 0.72/1.11 usefactor = 1
% 0.72/1.11 usesimpsplitting = 0
% 0.72/1.11 usesimpdemod = 5
% 0.72/1.11 usesimpres = 3
% 0.72/1.11
% 0.72/1.11 resimpinuse = 1000
% 0.72/1.11 resimpclauses = 20000
% 0.72/1.11 substype = eqrewr
% 0.72/1.11 backwardsubs = 1
% 0.72/1.11 selectoldest = 5
% 0.72/1.11
% 0.72/1.11 litorderings [0] = split
% 0.72/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.11
% 0.72/1.11 termordering = kbo
% 0.72/1.11
% 0.72/1.11 litapriori = 0
% 0.72/1.11 termapriori = 1
% 0.72/1.11 litaposteriori = 0
% 0.72/1.11 termaposteriori = 0
% 0.72/1.11 demodaposteriori = 0
% 0.72/1.11 ordereqreflfact = 0
% 0.72/1.11
% 0.72/1.11 litselect = negord
% 0.72/1.11
% 0.72/1.11 maxweight = 15
% 0.72/1.11 maxdepth = 30000
% 0.72/1.11 maxlength = 115
% 0.72/1.11 maxnrvars = 195
% 0.72/1.11 excuselevel = 1
% 0.72/1.11 increasemaxweight = 1
% 0.72/1.11
% 0.72/1.11 maxselected = 10000000
% 0.72/1.11 maxnrclauses = 10000000
% 0.72/1.11
% 0.72/1.11 showgenerated = 0
% 0.72/1.11 showkept = 0
% 0.72/1.11 showselected = 0
% 0.72/1.11 showdeleted = 0
% 0.72/1.11 showresimp = 1
% 0.72/1.11 showstatus = 2000
% 0.72/1.11
% 0.72/1.11 prologoutput = 0
% 0.72/1.11 nrgoals = 5000000
% 0.72/1.11 totalproof = 1
% 0.72/1.11
% 0.72/1.11 Symbols occurring in the translation:
% 0.72/1.11
% 0.72/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.11 . [1, 2] (w:1, o:31, a:1, s:1, b:0),
% 0.72/1.11 || [2, 0] (w:1, o:3, a:1, s:1, b:0),
% 0.72/1.11 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.72/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.11 less_than [38, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.72/1.11 strictly_less_than [39, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.72/1.11 bottom [40, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.72/1.11 create_slb [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.72/1.11 isnonempty_slb [42, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.72/1.11 pair [43, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.72/1.11 insert_slb [44, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.72/1.11 contains_slb [45, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.72/1.11 pair_in_list [47, 3] (w:1, o:69, a:1, s:1, b:0),
% 0.72/1.11 remove_slb [49, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.72/1.11 lookup_slb [50, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.72/1.11 update_slb [51, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.72/1.11 succ_cpq [52, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.72/1.11 insert_cpq [53, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.72/1.11 remove_cpq [54, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.72/1.11 findmin_cpq_eff [55, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.72/1.11 removemin_cpq_eff [56, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.72/1.11 triple [57, 3] (w:1, o:70, a:1, s:1, b:0),
% 0.72/1.11 check_cpq [58, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.72/1.11 contains_cpq [59, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.72/1.11 bad [60, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.72/1.11 ok [61, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.72/1.11 insert_pqp [62, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.72/1.11 remove_pqp [63, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.72/1.11 findmin_pqp_res [64, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.72/1.11 findmin_cpq_res [65, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.72/1.11 removemin_cpq_res [66, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.72/1.11 alpha1 [67, 4] (w:1, o:71, a:1, s:1, b:1),
% 0.72/1.11 skol1 [68, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.72/1.11 skol2 [69, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.72/1.11 skol3 [70, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.72/1.11 skol4 [71, 0] (w:1, o:17, a:1, s:1, b:1).
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Starting Search:
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Bliksems!, er is een bewijs:
% 0.72/1.11 % SZS status Theorem
% 0.72/1.11 % SZS output start Refutation
% 0.72/1.11
% 0.72/1.11 (13) {G0,W4,D2,L1,V2,M1} I { ! pair_in_list( create_slb, X, Y ) }.
% 0.72/1.11 (54) {G1,W0,D0,L0,V0,M0} I;r(13) { }.
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 % SZS output end Refutation
% 0.72/1.11 found a proof!
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Unprocessed initial clauses:
% 0.72/1.11
% 0.72/1.11 (56) {G0,W9,D2,L3,V3,M3} { ! less_than( X, Z ), ! less_than( Z, Y ),
% 0.72/1.11 less_than( X, Y ) }.
% 0.72/1.11 (57) {G0,W6,D2,L2,V2,M2} { less_than( X, Y ), less_than( Y, X ) }.
% 0.72/1.11 (58) {G0,W3,D2,L1,V1,M1} { less_than( X, X ) }.
% 0.72/1.11 (59) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), less_than( X, Y )
% 0.72/1.11 }.
% 0.72/1.11 (60) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), ! less_than( Y, X
% 0.72/1.11 ) }.
% 0.72/1.11 (61) {G0,W9,D2,L3,V2,M3} { ! less_than( X, Y ), less_than( Y, X ),
% 0.72/1.11 strictly_less_than( X, Y ) }.
% 0.72/1.11 (62) {G0,W3,D2,L1,V1,M1} { less_than( bottom, X ) }.
% 0.72/1.11 (63) {G0,W2,D2,L1,V0,M1} { ! isnonempty_slb( create_slb ) }.
% 0.72/1.11 (64) {G0,W6,D4,L1,V3,M1} { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) )
% 0.72/1.11 }.
% 0.72/1.11 (65) {G0,W3,D2,L1,V1,M1} { ! contains_slb( create_slb, X ) }.
% 0.72/1.11 (66) {G0,W13,D4,L3,V4,M3} { ! contains_slb( insert_slb( X, pair( Y, T ) )
% 0.72/1.11 , Z ), contains_slb( X, Z ), Y = Z }.
% 0.72/1.11 (67) {G0,W10,D4,L2,V4,M2} { ! contains_slb( X, Z ), contains_slb(
% 0.72/1.11 insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.72/1.11 (68) {G0,W10,D4,L2,V4,M2} { ! Y = Z, contains_slb( insert_slb( X, pair( Y
% 0.72/1.11 , T ) ), Z ) }.
% 0.72/1.11 (69) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 0.72/1.11 (70) {G0,W17,D4,L3,V5,M3} { ! pair_in_list( insert_slb( X, pair( Y, T ) )
% 0.72/1.11 , Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 0.72/1.11 (71) {G0,W12,D4,L2,V5,M2} { ! pair_in_list( X, Z, U ), pair_in_list(
% 0.72/1.11 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.72/1.11 (72) {G0,W13,D4,L2,V5,M2} { ! alpha1( Y, Z, T, U ), pair_in_list(
% 0.72/1.11 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.72/1.11 (73) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.72/1.11 (74) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.72/1.11 (75) {G0,W11,D2,L3,V4,M3} { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.72/1.11 (76) {G0,W9,D5,L1,V3,M1} { remove_slb( insert_slb( X, pair( Y, Z ) ), Y )
% 0.72/1.11 = X }.
% 0.72/1.11 (77) {G0,W21,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), remove_slb(
% 0.72/1.11 insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 0.72/1.11 ( Y, T ) ) }.
% 0.72/1.11 (78) {G0,W9,D5,L1,V3,M1} { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y )
% 0.72/1.11 = Z }.
% 0.72/1.11 (79) {G0,W17,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), lookup_slb(
% 0.72/1.11 insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 0.72/1.11 (80) {G0,W5,D3,L1,V1,M1} { update_slb( create_slb, X ) = create_slb }.
% 0.72/1.11 (81) {G0,W18,D5,L2,V4,M2} { ! strictly_less_than( Y, X ), update_slb(
% 0.72/1.11 insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 0.72/1.11 ( T, X ) ) }.
% 0.72/1.11 (82) {G0,W18,D5,L2,V4,M2} { ! less_than( X, Y ), update_slb( insert_slb( Z
% 0.72/1.11 , pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 0.72/1.11 }.
% 0.72/1.11 (83) {G0,W3,D2,L1,V1,M1} { succ_cpq( X, X ) }.
% 0.72/1.11 (84) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y
% 0.72/1.11 , Z ) ) }.
% 0.72/1.11 (85) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y
% 0.72/1.11 , Z ) ) }.
% 0.72/1.11 (86) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.72/1.11 findmin_cpq_eff( Y ) ) }.
% 0.72/1.11 (87) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.72/1.11 removemin_cpq_eff( Y ) ) }.
% 0.72/1.11 (88) {G0,W5,D3,L1,V2,M1} { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.72/1.11 (89) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z,
% 0.72/1.11 insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.72/1.11 (90) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z, T
% 0.72/1.11 , U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.72/1.11 (91) {G0,W12,D5,L2,V5,M2} { ! strictly_less_than( X, Y ), ! check_cpq(
% 0.72/1.11 triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.72/1.11 (92) {G0,W13,D5,L3,V5,M3} { ! strictly_less_than( X, Y ), ! ||, check_cpq
% 0.72/1.11 ( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.72/1.11 (93) {G0,W9,D3,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z ), T ),
% 0.72/1.11 contains_slb( Y, T ) }.
% 0.72/1.11 (94) {G0,W9,D3,L2,V4,M2} { ! contains_slb( Y, T ), contains_cpq( triple( X
% 0.72/1.11 , Y, Z ), T ) }.
% 0.72/1.11 (95) {G0,W5,D3,L1,V2,M1} { ! ok( triple( X, Y, bad ) ) }.
% 0.72/1.11 (96) {G0,W6,D3,L2,V2,M2} { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.72/1.11 (97) {G0,W8,D3,L2,V3,M2} { ok( triple( Y, Z, X ) ), X = bad }.
% 0.72/1.11 (98) {G0,W17,D5,L1,V4,M1} { insert_cpq( triple( X, Y, Z ), T ) = triple(
% 0.72/1.11 insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.72/1.11 (99) {G0,W14,D4,L2,V4,M2} { contains_slb( X, Y ), remove_cpq( triple( Z, X
% 0.72/1.11 , T ), Y ) = triple( Z, X, bad ) }.
% 0.72/1.11 (100) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! less_than(
% 0.72/1.11 lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.72/1.11 remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 0.72/1.11 (101) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! strictly_less_than
% 0.72/1.11 ( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.72/1.11 remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 0.72/1.11 (102) {G0,W10,D4,L1,V2,M1} { findmin_cpq_eff( triple( X, create_slb, Y ) )
% 0.72/1.11 = triple( X, create_slb, bad ) }.
% 0.72/1.11 (103) {G0,W20,D5,L3,V3,M3} { Y = create_slb, contains_slb( Y,
% 0.72/1.11 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 0.72/1.11 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.72/1.11 (104) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.72/1.11 findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ),
% 0.72/1.11 lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 0.72/1.11 ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.72/1.11 (105) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.72/1.11 findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 0.72/1.11 ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 0.72/1.11 ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 0.72/1.11 (106) {G0,W7,D4,L1,V2,M1} { findmin_cpq_res( triple( X, create_slb, Y ) )
% 0.72/1.11 = bottom }.
% 0.72/1.11 (107) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res( triple( Y, X
% 0.72/1.11 , Z ) ) = findmin_pqp_res( Y ) }.
% 0.72/1.11 (108) {G0,W8,D4,L1,V1,M1} { removemin_cpq_eff( X ) = remove_cpq(
% 0.72/1.11 findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 0.72/1.11 (109) {G0,W5,D3,L1,V1,M1} { removemin_cpq_res( X ) = findmin_cpq_res( X )
% 0.72/1.11 }.
% 0.72/1.11 (110) {G0,W4,D2,L1,V0,M1} { pair_in_list( create_slb, skol1, skol2 ) }.
% 0.72/1.11 (111) {G0,W3,D2,L1,V0,M1} { strictly_less_than( skol1, skol2 ) }.
% 0.72/1.11 (112) {G0,W7,D4,L1,V0,M1} { ok( remove_cpq( triple( skol3, create_slb,
% 0.72/1.11 skol4 ), skol1 ) ) }.
% 0.72/1.11 (113) {G0,W6,D3,L1,V0,M1} { ! pair_in_list( remove_slb( create_slb, skol1
% 0.72/1.11 ), skol1, skol2 ) }.
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Total Proof:
% 0.72/1.11
% 0.72/1.11 subsumption: (13) {G0,W4,D2,L1,V2,M1} I { ! pair_in_list( create_slb, X, Y
% 0.72/1.11 ) }.
% 0.72/1.11 parent0: (69) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (163) {G1,W0,D0,L0,V0,M0} { }.
% 0.72/1.11 parent0[0]: (13) {G0,W4,D2,L1,V2,M1} I { ! pair_in_list( create_slb, X, Y )
% 0.72/1.11 }.
% 0.72/1.11 parent1[0]: (110) {G0,W4,D2,L1,V0,M1} { pair_in_list( create_slb, skol1,
% 0.72/1.11 skol2 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := skol1
% 0.72/1.11 Y := skol2
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (54) {G1,W0,D0,L0,V0,M0} I;r(13) { }.
% 0.72/1.11 parent0: (163) {G1,W0,D0,L0,V0,M0} { }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 Proof check complete!
% 0.72/1.11
% 0.72/1.11 Memory use:
% 0.72/1.11
% 0.72/1.11 space for terms: 2208
% 0.72/1.11 space for clauses: 4840
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 clauses generated: 55
% 0.72/1.11 clauses kept: 55
% 0.72/1.11 clauses selected: 0
% 0.72/1.11 clauses deleted: 0
% 0.72/1.11 clauses inuse deleted: 0
% 0.72/1.11
% 0.72/1.11 subsentry: 210
% 0.72/1.11 literals s-matched: 106
% 0.72/1.11 literals matched: 102
% 0.72/1.11 full subsumption: 36
% 0.72/1.11
% 0.72/1.11 checksum: -1816930428
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Bliksem ended
%------------------------------------------------------------------------------