TSTP Solution File: SWV405+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV405+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 16:24:45 EDT 2022
% Result : Theorem 0.70s 1.10s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV405+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Wed Jun 15 11:54:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.70/1.10 *** allocated 10000 integers for termspace/termends
% 0.70/1.10 *** allocated 10000 integers for clauses
% 0.70/1.10 *** allocated 10000 integers for justifications
% 0.70/1.10 Bliksem 1.12
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10 Automatic Strategy Selection
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10 Clauses:
% 0.70/1.10
% 0.70/1.10 { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.70/1.10 { less_than( X, Y ), less_than( Y, X ) }.
% 0.70/1.10 { less_than( X, X ) }.
% 0.70/1.10 { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.70/1.10 { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.70/1.10 { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.70/1.10 { less_than( bottom, X ) }.
% 0.70/1.10 { ! isnonempty_slb( create_slb ) }.
% 0.70/1.10 { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) ) }.
% 0.70/1.10 { ! contains_slb( create_slb, X ) }.
% 0.70/1.10 { ! contains_slb( insert_slb( X, pair( Y, T ) ), Z ), contains_slb( X, Z )
% 0.70/1.10 , Y = Z }.
% 0.70/1.10 { ! contains_slb( X, Z ), contains_slb( insert_slb( X, pair( Y, T ) ), Z )
% 0.70/1.10 }.
% 0.70/1.10 { ! Y = Z, contains_slb( insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.70/1.10 { ! pair_in_list( create_slb, X, Y ) }.
% 0.70/1.10 { ! pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U ), pair_in_list( X, Z
% 0.70/1.10 , U ), alpha1( Y, Z, T, U ) }.
% 0.70/1.10 { ! pair_in_list( X, Z, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z
% 0.70/1.10 , U ) }.
% 0.70/1.10 { ! alpha1( Y, Z, T, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U
% 0.70/1.10 ) }.
% 0.70/1.10 { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.70/1.10 { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.70/1.10 { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.70/1.10 { remove_slb( insert_slb( X, pair( Y, Z ) ), Y ) = X }.
% 0.70/1.10 { Y = Z, ! contains_slb( X, Z ), remove_slb( insert_slb( X, pair( Y, T ) )
% 0.70/1.10 , Z ) = insert_slb( remove_slb( X, Z ), pair( Y, T ) ) }.
% 0.70/1.10 { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y ) = Z }.
% 0.70/1.10 { Y = Z, ! contains_slb( X, Z ), lookup_slb( insert_slb( X, pair( Y, T ) )
% 0.70/1.10 , Z ) = lookup_slb( X, Z ) }.
% 0.70/1.10 { update_slb( create_slb, X ) = create_slb }.
% 0.70/1.10 { ! strictly_less_than( Y, X ), update_slb( insert_slb( Z, pair( T, Y ) ),
% 0.70/1.10 X ) = insert_slb( update_slb( Z, X ), pair( T, X ) ) }.
% 0.70/1.10 { ! less_than( X, Y ), update_slb( insert_slb( Z, pair( T, Y ) ), X ) =
% 0.70/1.10 insert_slb( update_slb( Z, X ), pair( T, Y ) ) }.
% 0.70/1.10 { succ_cpq( X, X ) }.
% 0.70/1.10 { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y, Z ) ) }.
% 0.70/1.10 { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y, Z ) ) }.
% 0.70/1.10 { ! succ_cpq( X, Y ), succ_cpq( X, findmin_cpq_eff( Y ) ) }.
% 0.70/1.10 { ! succ_cpq( X, Y ), succ_cpq( X, removemin_cpq_eff( Y ) ) }.
% 0.70/1.10 { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.70/1.10 { ! less_than( Y, X ), ! check_cpq( triple( Z, insert_slb( T, pair( X, Y )
% 0.70/1.10 ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.70/1.10 { ! less_than( Y, X ), ! check_cpq( triple( Z, T, U ) ), check_cpq( triple
% 0.70/1.10 ( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.70/1.10 { ! strictly_less_than( X, Y ), ! check_cpq( triple( Z, insert_slb( T, pair
% 0.70/1.10 ( X, Y ) ), U ) ) }.
% 0.70/1.10 { ! strictly_less_than( X, Y ), ! ||, check_cpq( triple( Z, insert_slb( T,
% 0.70/1.10 pair( X, Y ) ), U ) ) }.
% 0.70/1.10 { ! contains_cpq( triple( X, Y, Z ), T ), contains_slb( Y, T ) }.
% 0.70/1.10 { ! contains_slb( Y, T ), contains_cpq( triple( X, Y, Z ), T ) }.
% 0.70/1.10 { ! ok( triple( X, Y, bad ) ) }.
% 0.70/1.10 { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.70/1.10 { ok( triple( Y, Z, X ) ), X = bad }.
% 0.70/1.10 { insert_cpq( triple( X, Y, Z ), T ) = triple( insert_pqp( X, T ),
% 0.70/1.10 insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.70/1.10 { contains_slb( X, Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( Z, X,
% 0.70/1.10 bad ) }.
% 0.70/1.10 { ! contains_slb( X, Y ), ! less_than( lookup_slb( X, Y ), Y ), remove_cpq
% 0.70/1.10 ( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y )
% 0.70/1.10 , T ) }.
% 0.70/1.10 { ! contains_slb( X, Y ), ! strictly_less_than( Y, lookup_slb( X, Y ) ),
% 0.70/1.10 remove_cpq( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ),
% 0.70/1.10 remove_slb( X, Y ), bad ) }.
% 0.70/1.10 { findmin_cpq_eff( triple( X, create_slb, Y ) ) = triple( X, create_slb,
% 0.70/1.10 bad ) }.
% 0.70/1.10 { Y = create_slb, contains_slb( Y, findmin_pqp_res( X ) ), findmin_cpq_eff
% 0.70/1.10 ( triple( X, Y, Z ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) )
% 0.70/1.10 , bad ) }.
% 0.70/1.10 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), !
% 0.70/1.10 strictly_less_than( findmin_pqp_res( X ), lookup_slb( Y, findmin_pqp_res
% 0.70/1.10 ( X ) ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb(
% 0.70/1.10 Y, findmin_pqp_res( X ) ), bad ) }.
% 0.70/1.10 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! less_than(
% 0.70/1.10 lookup_slb( Y, findmin_pqp_res( X ) ), findmin_pqp_res( X ) ),
% 0.70/1.10 findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( Y,
% 0.70/1.10 findmin_pqp_res( X ) ), Z ) }.
% 0.70/1.10 { findmin_cpq_res( triple( X, create_slb, Y ) ) = bottom }.
% 0.70/1.10 { X = create_slb, findmin_cpq_res( triple( Y, X, Z ) ) = findmin_pqp_res( Y
% 0.70/1.10 ) }.
% 0.70/1.10 { removemin_cpq_eff( X ) = remove_cpq( findmin_cpq_eff( X ),
% 0.70/1.10 findmin_cpq_res( X ) ) }.
% 0.70/1.10 { removemin_cpq_res( X ) = findmin_cpq_res( X ) }.
% 0.70/1.10 { alpha3( skol1, skol3 ), ! pair_in_list( create_slb, X, Y ), less_than( Y
% 0.70/1.10 , X ) }.
% 0.70/1.10 { alpha3( skol1, skol3 ), ! check_cpq( triple( skol1, create_slb, skol3 ) )
% 0.70/1.10 }.
% 0.70/1.10 { ! alpha3( X, Y ), check_cpq( triple( X, create_slb, Y ) ) }.
% 0.70/1.10 { ! alpha3( X, Y ), alpha2 }.
% 0.70/1.10 { ! check_cpq( triple( X, create_slb, Y ) ), ! alpha2, alpha3( X, Y ) }.
% 0.70/1.10 { ! alpha2, pair_in_list( create_slb, skol2, skol4 ) }.
% 0.70/1.10 { ! alpha2, ! less_than( skol4, skol2 ) }.
% 0.70/1.10 { ! pair_in_list( create_slb, X, Y ), less_than( Y, X ), alpha2 }.
% 0.70/1.10
% 0.70/1.10 percentage equality = 0.268908, percentage horn = 0.796610
% 0.70/1.10 This is a problem with some equality
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10 Options Used:
% 0.70/1.10
% 0.70/1.10 useres = 1
% 0.70/1.10 useparamod = 1
% 0.70/1.10 useeqrefl = 1
% 0.70/1.10 useeqfact = 1
% 0.70/1.10 usefactor = 1
% 0.70/1.10 usesimpsplitting = 0
% 0.70/1.10 usesimpdemod = 5
% 0.70/1.10 usesimpres = 3
% 0.70/1.10
% 0.70/1.10 resimpinuse = 1000
% 0.70/1.10 resimpclauses = 20000
% 0.70/1.10 substype = eqrewr
% 0.70/1.10 backwardsubs = 1
% 0.70/1.10 selectoldest = 5
% 0.70/1.10
% 0.70/1.10 litorderings [0] = split
% 0.70/1.10 litorderings [1] = extend the termordering, first sorting on arguments
% 0.70/1.10
% 0.70/1.10 termordering = kbo
% 0.70/1.10
% 0.70/1.10 litapriori = 0
% 0.70/1.10 termapriori = 1
% 0.70/1.10 litaposteriori = 0
% 0.70/1.10 termaposteriori = 0
% 0.70/1.10 demodaposteriori = 0
% 0.70/1.10 ordereqreflfact = 0
% 0.70/1.10
% 0.70/1.10 litselect = negord
% 0.70/1.10
% 0.70/1.10 maxweight = 15
% 0.70/1.10 maxdepth = 30000
% 0.70/1.10 maxlength = 115
% 0.70/1.10 maxnrvars = 195
% 0.70/1.10 excuselevel = 1
% 0.70/1.10 increasemaxweight = 1
% 0.70/1.10
% 0.70/1.10 maxselected = 10000000
% 0.70/1.10 maxnrclauses = 10000000
% 0.70/1.10
% 0.70/1.10 showgenerated = 0
% 0.70/1.10 showkept = 0
% 0.70/1.10 showselected = 0
% 0.70/1.10 showdeleted = 0
% 0.70/1.10 showresimp = 1
% 0.70/1.10 showstatus = 2000
% 0.70/1.10
% 0.70/1.10 prologoutput = 0
% 0.70/1.10 nrgoals = 5000000
% 0.70/1.10 totalproof = 1
% 0.70/1.10
% 0.70/1.10 Symbols occurring in the translation:
% 0.70/1.10
% 0.70/1.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.70/1.10 . [1, 2] (w:1, o:32, a:1, s:1, b:0),
% 0.70/1.10 || [2, 0] (w:1, o:3, a:1, s:1, b:0),
% 0.70/1.10 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 0.70/1.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.10 less_than [38, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.70/1.10 strictly_less_than [39, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.70/1.10 bottom [40, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.70/1.10 create_slb [41, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.70/1.10 isnonempty_slb [42, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.70/1.10 pair [43, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.70/1.10 insert_slb [44, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.70/1.10 contains_slb [45, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.70/1.10 pair_in_list [47, 3] (w:1, o:71, a:1, s:1, b:0),
% 0.70/1.10 remove_slb [49, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.70/1.10 lookup_slb [50, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.70/1.10 update_slb [51, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.70/1.10 succ_cpq [52, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.70/1.10 insert_cpq [53, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.70/1.10 remove_cpq [54, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.70/1.10 findmin_cpq_eff [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.70/1.10 removemin_cpq_eff [56, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.70/1.10 triple [57, 3] (w:1, o:72, a:1, s:1, b:0),
% 0.70/1.10 check_cpq [58, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.70/1.10 contains_cpq [59, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.70/1.10 bad [60, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.70/1.10 ok [61, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.70/1.10 insert_pqp [62, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.70/1.10 remove_pqp [63, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.70/1.10 findmin_pqp_res [64, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.70/1.10 findmin_cpq_res [65, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.70/1.10 removemin_cpq_res [66, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.70/1.10 alpha1 [67, 4] (w:1, o:73, a:1, s:1, b:1),
% 0.70/1.10 alpha2 [68, 0] (w:1, o:9, a:1, s:1, b:1),
% 0.70/1.10 alpha3 [69, 2] (w:1, o:70, a:1, s:1, b:1),
% 0.70/1.10 skol1 [70, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.70/1.10 skol2 [71, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.70/1.10 skol3 [72, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.70/1.10 skol4 [73, 0] (w:1, o:18, a:1, s:1, b:1).
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10 Starting Search:
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10 Bliksems!, er is een bewijs:
% 0.70/1.10 % SZS status Theorem
% 0.70/1.10 % SZS output start Refutation
% 0.70/1.10
% 0.70/1.10 (13) {G0,W4,D2,L1,V2,M1} I { ! pair_in_list( create_slb, X, Y ) }.
% 0.70/1.10 (32) {G0,W5,D3,L1,V2,M1} I { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.70/1.10 (54) {G1,W3,D2,L1,V0,M1} I;r(32) { alpha3( skol1, skol3 ) }.
% 0.70/1.10 (55) {G0,W4,D2,L2,V2,M2} I { ! alpha3( X, Y ), alpha2 }.
% 0.70/1.10 (57) {G1,W1,D1,L1,V0,M1} I;r(13) { ! alpha2 }.
% 0.70/1.10 (66) {G2,W3,D2,L1,V2,M1} S(55);r(57) { ! alpha3( X, Y ) }.
% 0.70/1.10 (67) {G3,W0,D0,L0,V0,M0} R(66,54) { }.
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10 % SZS output end Refutation
% 0.70/1.10 found a proof!
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10 Unprocessed initial clauses:
% 0.70/1.10
% 0.70/1.10 (69) {G0,W9,D2,L3,V3,M3} { ! less_than( X, Z ), ! less_than( Z, Y ),
% 0.70/1.10 less_than( X, Y ) }.
% 0.70/1.10 (70) {G0,W6,D2,L2,V2,M2} { less_than( X, Y ), less_than( Y, X ) }.
% 0.70/1.10 (71) {G0,W3,D2,L1,V1,M1} { less_than( X, X ) }.
% 0.70/1.10 (72) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), less_than( X, Y )
% 0.70/1.10 }.
% 0.70/1.10 (73) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), ! less_than( Y, X
% 0.70/1.10 ) }.
% 0.70/1.10 (74) {G0,W9,D2,L3,V2,M3} { ! less_than( X, Y ), less_than( Y, X ),
% 0.70/1.10 strictly_less_than( X, Y ) }.
% 0.70/1.10 (75) {G0,W3,D2,L1,V1,M1} { less_than( bottom, X ) }.
% 0.70/1.10 (76) {G0,W2,D2,L1,V0,M1} { ! isnonempty_slb( create_slb ) }.
% 0.70/1.10 (77) {G0,W6,D4,L1,V3,M1} { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) )
% 0.70/1.10 }.
% 0.70/1.10 (78) {G0,W3,D2,L1,V1,M1} { ! contains_slb( create_slb, X ) }.
% 0.70/1.10 (79) {G0,W13,D4,L3,V4,M3} { ! contains_slb( insert_slb( X, pair( Y, T ) )
% 0.70/1.10 , Z ), contains_slb( X, Z ), Y = Z }.
% 0.70/1.10 (80) {G0,W10,D4,L2,V4,M2} { ! contains_slb( X, Z ), contains_slb(
% 0.70/1.10 insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.70/1.10 (81) {G0,W10,D4,L2,V4,M2} { ! Y = Z, contains_slb( insert_slb( X, pair( Y
% 0.70/1.10 , T ) ), Z ) }.
% 0.70/1.10 (82) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 0.70/1.10 (83) {G0,W17,D4,L3,V5,M3} { ! pair_in_list( insert_slb( X, pair( Y, T ) )
% 0.70/1.10 , Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 0.70/1.10 (84) {G0,W12,D4,L2,V5,M2} { ! pair_in_list( X, Z, U ), pair_in_list(
% 0.70/1.10 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.70/1.10 (85) {G0,W13,D4,L2,V5,M2} { ! alpha1( Y, Z, T, U ), pair_in_list(
% 0.70/1.10 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.70/1.10 (86) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.70/1.10 (87) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.70/1.10 (88) {G0,W11,D2,L3,V4,M3} { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.70/1.10 (89) {G0,W9,D5,L1,V3,M1} { remove_slb( insert_slb( X, pair( Y, Z ) ), Y )
% 0.70/1.10 = X }.
% 0.70/1.10 (90) {G0,W21,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), remove_slb(
% 0.70/1.10 insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 0.70/1.10 ( Y, T ) ) }.
% 0.70/1.10 (91) {G0,W9,D5,L1,V3,M1} { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y )
% 0.70/1.10 = Z }.
% 0.70/1.10 (92) {G0,W17,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), lookup_slb(
% 0.70/1.10 insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 0.70/1.10 (93) {G0,W5,D3,L1,V1,M1} { update_slb( create_slb, X ) = create_slb }.
% 0.70/1.10 (94) {G0,W18,D5,L2,V4,M2} { ! strictly_less_than( Y, X ), update_slb(
% 0.70/1.10 insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 0.70/1.10 ( T, X ) ) }.
% 0.70/1.10 (95) {G0,W18,D5,L2,V4,M2} { ! less_than( X, Y ), update_slb( insert_slb( Z
% 0.70/1.10 , pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 0.70/1.10 }.
% 0.70/1.10 (96) {G0,W3,D2,L1,V1,M1} { succ_cpq( X, X ) }.
% 0.70/1.10 (97) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y
% 0.70/1.10 , Z ) ) }.
% 0.70/1.10 (98) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y
% 0.70/1.10 , Z ) ) }.
% 0.70/1.10 (99) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.70/1.10 findmin_cpq_eff( Y ) ) }.
% 0.70/1.10 (100) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.70/1.10 removemin_cpq_eff( Y ) ) }.
% 0.70/1.10 (101) {G0,W5,D3,L1,V2,M1} { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.70/1.10 (102) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z,
% 0.70/1.10 insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.70/1.10 (103) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z,
% 0.70/1.10 T, U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.70/1.10 (104) {G0,W12,D5,L2,V5,M2} { ! strictly_less_than( X, Y ), ! check_cpq(
% 0.70/1.10 triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.70/1.10 (105) {G0,W13,D5,L3,V5,M3} { ! strictly_less_than( X, Y ), ! ||, check_cpq
% 0.70/1.10 ( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.70/1.10 (106) {G0,W9,D3,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z ), T ),
% 0.70/1.10 contains_slb( Y, T ) }.
% 0.70/1.10 (107) {G0,W9,D3,L2,V4,M2} { ! contains_slb( Y, T ), contains_cpq( triple(
% 0.70/1.10 X, Y, Z ), T ) }.
% 0.70/1.10 (108) {G0,W5,D3,L1,V2,M1} { ! ok( triple( X, Y, bad ) ) }.
% 0.70/1.10 (109) {G0,W6,D3,L2,V2,M2} { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.70/1.10 (110) {G0,W8,D3,L2,V3,M2} { ok( triple( Y, Z, X ) ), X = bad }.
% 0.70/1.10 (111) {G0,W17,D5,L1,V4,M1} { insert_cpq( triple( X, Y, Z ), T ) = triple(
% 0.70/1.10 insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.70/1.10 (112) {G0,W14,D4,L2,V4,M2} { contains_slb( X, Y ), remove_cpq( triple( Z,
% 0.70/1.10 X, T ), Y ) = triple( Z, X, bad ) }.
% 0.70/1.10 (113) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! less_than(
% 0.70/1.10 lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.70/1.10 remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 0.70/1.10 (114) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! strictly_less_than
% 0.70/1.10 ( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.70/1.10 remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 0.70/1.10 (115) {G0,W10,D4,L1,V2,M1} { findmin_cpq_eff( triple( X, create_slb, Y ) )
% 0.70/1.10 = triple( X, create_slb, bad ) }.
% 0.70/1.10 (116) {G0,W20,D5,L3,V3,M3} { Y = create_slb, contains_slb( Y,
% 0.70/1.10 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 0.70/1.10 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.70/1.10 (117) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.70/1.10 findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ),
% 0.70/1.10 lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 0.70/1.10 ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.70/1.10 (118) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.70/1.10 findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 0.70/1.10 ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 0.70/1.10 ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 0.70/1.10 (119) {G0,W7,D4,L1,V2,M1} { findmin_cpq_res( triple( X, create_slb, Y ) )
% 0.70/1.10 = bottom }.
% 0.70/1.10 (120) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res( triple( Y, X
% 0.70/1.10 , Z ) ) = findmin_pqp_res( Y ) }.
% 0.70/1.10 (121) {G0,W8,D4,L1,V1,M1} { removemin_cpq_eff( X ) = remove_cpq(
% 0.70/1.10 findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 0.70/1.10 (122) {G0,W5,D3,L1,V1,M1} { removemin_cpq_res( X ) = findmin_cpq_res( X )
% 0.70/1.10 }.
% 0.70/1.10 (123) {G0,W10,D2,L3,V2,M3} { alpha3( skol1, skol3 ), ! pair_in_list(
% 0.70/1.10 create_slb, X, Y ), less_than( Y, X ) }.
% 0.70/1.10 (124) {G0,W8,D3,L2,V0,M2} { alpha3( skol1, skol3 ), ! check_cpq( triple(
% 0.70/1.10 skol1, create_slb, skol3 ) ) }.
% 0.70/1.10 (125) {G0,W8,D3,L2,V2,M2} { ! alpha3( X, Y ), check_cpq( triple( X,
% 0.70/1.10 create_slb, Y ) ) }.
% 0.70/1.10 (126) {G0,W4,D2,L2,V2,M2} { ! alpha3( X, Y ), alpha2 }.
% 0.70/1.10 (127) {G0,W9,D3,L3,V2,M3} { ! check_cpq( triple( X, create_slb, Y ) ), !
% 0.70/1.10 alpha2, alpha3( X, Y ) }.
% 0.70/1.10 (128) {G0,W5,D2,L2,V0,M2} { ! alpha2, pair_in_list( create_slb, skol2,
% 0.70/1.10 skol4 ) }.
% 0.70/1.10 (129) {G0,W4,D2,L2,V0,M2} { ! alpha2, ! less_than( skol4, skol2 ) }.
% 0.70/1.10 (130) {G0,W8,D2,L3,V2,M3} { ! pair_in_list( create_slb, X, Y ), less_than
% 0.70/1.10 ( Y, X ), alpha2 }.
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10 Total Proof:
% 0.70/1.10
% 0.70/1.10 subsumption: (13) {G0,W4,D2,L1,V2,M1} I { ! pair_in_list( create_slb, X, Y
% 0.70/1.10 ) }.
% 0.70/1.10 parent0: (82) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 0.70/1.10 substitution0:
% 0.70/1.10 X := X
% 0.70/1.10 Y := Y
% 0.70/1.10 end
% 0.70/1.10 permutation0:
% 0.70/1.10 0 ==> 0
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 subsumption: (32) {G0,W5,D3,L1,V2,M1} I { check_cpq( triple( X, create_slb
% 0.70/1.10 , Y ) ) }.
% 0.70/1.10 parent0: (101) {G0,W5,D3,L1,V2,M1} { check_cpq( triple( X, create_slb, Y )
% 0.70/1.10 ) }.
% 0.70/1.10 substitution0:
% 0.70/1.10 X := X
% 0.70/1.10 Y := Y
% 0.70/1.10 end
% 0.70/1.10 permutation0:
% 0.70/1.10 0 ==> 0
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 resolution: (204) {G1,W3,D2,L1,V0,M1} { alpha3( skol1, skol3 ) }.
% 0.70/1.10 parent0[1]: (124) {G0,W8,D3,L2,V0,M2} { alpha3( skol1, skol3 ), !
% 0.70/1.10 check_cpq( triple( skol1, create_slb, skol3 ) ) }.
% 0.70/1.10 parent1[0]: (32) {G0,W5,D3,L1,V2,M1} I { check_cpq( triple( X, create_slb,
% 0.70/1.10 Y ) ) }.
% 0.70/1.10 substitution0:
% 0.70/1.10 end
% 0.70/1.10 substitution1:
% 0.70/1.10 X := skol1
% 0.70/1.10 Y := skol3
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 subsumption: (54) {G1,W3,D2,L1,V0,M1} I;r(32) { alpha3( skol1, skol3 ) }.
% 0.70/1.10 parent0: (204) {G1,W3,D2,L1,V0,M1} { alpha3( skol1, skol3 ) }.
% 0.70/1.10 substitution0:
% 0.70/1.10 end
% 0.70/1.10 permutation0:
% 0.70/1.10 0 ==> 0
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 subsumption: (55) {G0,W4,D2,L2,V2,M2} I { ! alpha3( X, Y ), alpha2 }.
% 0.70/1.10 parent0: (126) {G0,W4,D2,L2,V2,M2} { ! alpha3( X, Y ), alpha2 }.
% 0.70/1.10 substitution0:
% 0.70/1.10 X := X
% 0.70/1.10 Y := Y
% 0.70/1.10 end
% 0.70/1.10 permutation0:
% 0.70/1.10 0 ==> 0
% 0.70/1.10 1 ==> 1
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 *** allocated 15000 integers for clauses
% 0.70/1.10 resolution: (295) {G1,W1,D1,L1,V0,M1} { ! alpha2 }.
% 0.70/1.10 parent0[0]: (13) {G0,W4,D2,L1,V2,M1} I { ! pair_in_list( create_slb, X, Y )
% 0.70/1.10 }.
% 0.70/1.10 parent1[1]: (128) {G0,W5,D2,L2,V0,M2} { ! alpha2, pair_in_list( create_slb
% 0.70/1.10 , skol2, skol4 ) }.
% 0.70/1.10 substitution0:
% 0.70/1.10 X := skol2
% 0.70/1.10 Y := skol4
% 0.70/1.10 end
% 0.70/1.10 substitution1:
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 subsumption: (57) {G1,W1,D1,L1,V0,M1} I;r(13) { ! alpha2 }.
% 0.70/1.10 parent0: (295) {G1,W1,D1,L1,V0,M1} { ! alpha2 }.
% 0.70/1.10 substitution0:
% 0.70/1.10 end
% 0.70/1.10 permutation0:
% 0.70/1.10 0 ==> 0
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 resolution: (296) {G1,W3,D2,L1,V2,M1} { ! alpha3( X, Y ) }.
% 0.70/1.10 parent0[0]: (57) {G1,W1,D1,L1,V0,M1} I;r(13) { ! alpha2 }.
% 0.70/1.10 parent1[1]: (55) {G0,W4,D2,L2,V2,M2} I { ! alpha3( X, Y ), alpha2 }.
% 0.70/1.10 substitution0:
% 0.70/1.10 end
% 0.70/1.10 substitution1:
% 0.70/1.10 X := X
% 0.70/1.10 Y := Y
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 subsumption: (66) {G2,W3,D2,L1,V2,M1} S(55);r(57) { ! alpha3( X, Y ) }.
% 0.70/1.10 parent0: (296) {G1,W3,D2,L1,V2,M1} { ! alpha3( X, Y ) }.
% 0.70/1.10 substitution0:
% 0.70/1.10 X := X
% 0.70/1.10 Y := Y
% 0.70/1.10 end
% 0.70/1.10 permutation0:
% 0.70/1.10 0 ==> 0
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 resolution: (297) {G2,W0,D0,L0,V0,M0} { }.
% 0.70/1.10 parent0[0]: (66) {G2,W3,D2,L1,V2,M1} S(55);r(57) { ! alpha3( X, Y ) }.
% 0.70/1.10 parent1[0]: (54) {G1,W3,D2,L1,V0,M1} I;r(32) { alpha3( skol1, skol3 ) }.
% 0.70/1.10 substitution0:
% 0.70/1.10 X := skol1
% 0.70/1.10 Y := skol3
% 0.70/1.10 end
% 0.70/1.10 substitution1:
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 subsumption: (67) {G3,W0,D0,L0,V0,M0} R(66,54) { }.
% 0.70/1.10 parent0: (297) {G2,W0,D0,L0,V0,M0} { }.
% 0.70/1.10 substitution0:
% 0.70/1.10 end
% 0.70/1.10 permutation0:
% 0.70/1.10 end
% 0.70/1.10
% 0.70/1.10 Proof check complete!
% 0.70/1.10
% 0.70/1.10 Memory use:
% 0.70/1.10
% 0.70/1.10 space for terms: 2353
% 0.70/1.10 space for clauses: 5492
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10 clauses generated: 89
% 0.70/1.10 clauses kept: 68
% 0.70/1.10 clauses selected: 12
% 0.70/1.10 clauses deleted: 2
% 0.70/1.10 clauses inuse deleted: 0
% 0.70/1.10
% 0.70/1.10 subsentry: 1005
% 0.70/1.10 literals s-matched: 560
% 0.70/1.10 literals matched: 544
% 0.70/1.10 full subsumption: 228
% 0.70/1.10
% 0.70/1.10 checksum: 1816400583
% 0.70/1.10
% 0.70/1.10
% 0.70/1.10 Bliksem ended
%------------------------------------------------------------------------------