TSTP Solution File: SWV408+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV408+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 16:24:46 EDT 2022
% Result : Theorem 0.96s 1.34s
% Output : Refutation 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV408+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Wed Jun 15 16:53:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.09 *** allocated 10000 integers for termspace/termends
% 0.69/1.09 *** allocated 10000 integers for clauses
% 0.69/1.09 *** allocated 10000 integers for justifications
% 0.69/1.09 Bliksem 1.12
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Automatic Strategy Selection
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Clauses:
% 0.69/1.09
% 0.69/1.09 { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.69/1.09 { less_than( X, Y ), less_than( Y, X ) }.
% 0.69/1.09 { less_than( X, X ) }.
% 0.69/1.09 { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.69/1.09 { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.69/1.09 { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.69/1.09 { less_than( bottom, X ) }.
% 0.69/1.09 { ! isnonempty_slb( create_slb ) }.
% 0.69/1.09 { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) ) }.
% 0.69/1.09 { ! contains_slb( create_slb, X ) }.
% 0.69/1.09 { ! contains_slb( insert_slb( X, pair( Y, T ) ), Z ), contains_slb( X, Z )
% 0.69/1.09 , Y = Z }.
% 0.69/1.09 { ! contains_slb( X, Z ), contains_slb( insert_slb( X, pair( Y, T ) ), Z )
% 0.69/1.09 }.
% 0.69/1.09 { ! Y = Z, contains_slb( insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.69/1.09 { ! pair_in_list( create_slb, X, Y ) }.
% 0.69/1.09 { ! pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U ), pair_in_list( X, Z
% 0.69/1.09 , U ), alpha1( Y, Z, T, U ) }.
% 0.69/1.09 { ! pair_in_list( X, Z, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z
% 0.69/1.09 , U ) }.
% 0.69/1.09 { ! alpha1( Y, Z, T, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U
% 0.69/1.09 ) }.
% 0.69/1.09 { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.69/1.09 { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.69/1.09 { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.69/1.09 { remove_slb( insert_slb( X, pair( Y, Z ) ), Y ) = X }.
% 0.69/1.09 { Y = Z, ! contains_slb( X, Z ), remove_slb( insert_slb( X, pair( Y, T ) )
% 0.69/1.09 , Z ) = insert_slb( remove_slb( X, Z ), pair( Y, T ) ) }.
% 0.69/1.09 { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y ) = Z }.
% 0.69/1.09 { Y = Z, ! contains_slb( X, Z ), lookup_slb( insert_slb( X, pair( Y, T ) )
% 0.69/1.09 , Z ) = lookup_slb( X, Z ) }.
% 0.69/1.09 { update_slb( create_slb, X ) = create_slb }.
% 0.69/1.09 { ! strictly_less_than( Y, X ), update_slb( insert_slb( Z, pair( T, Y ) ),
% 0.69/1.09 X ) = insert_slb( update_slb( Z, X ), pair( T, X ) ) }.
% 0.69/1.09 { ! less_than( X, Y ), update_slb( insert_slb( Z, pair( T, Y ) ), X ) =
% 0.69/1.09 insert_slb( update_slb( Z, X ), pair( T, Y ) ) }.
% 0.69/1.09 { succ_cpq( X, X ) }.
% 0.69/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y, Z ) ) }.
% 0.69/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y, Z ) ) }.
% 0.69/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, findmin_cpq_eff( Y ) ) }.
% 0.69/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, removemin_cpq_eff( Y ) ) }.
% 0.69/1.09 { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.69/1.09 { ! less_than( Y, X ), ! check_cpq( triple( Z, insert_slb( T, pair( X, Y )
% 0.69/1.09 ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.69/1.09 { ! less_than( Y, X ), ! check_cpq( triple( Z, T, U ) ), check_cpq( triple
% 0.69/1.09 ( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.69/1.09 { ! strictly_less_than( X, Y ), ! check_cpq( triple( Z, insert_slb( T, pair
% 0.69/1.09 ( X, Y ) ), U ) ) }.
% 0.69/1.09 { ! strictly_less_than( X, Y ), ! ||, check_cpq( triple( Z, insert_slb( T,
% 0.69/1.09 pair( X, Y ) ), U ) ) }.
% 0.69/1.09 { ! contains_cpq( triple( X, Y, Z ), T ), contains_slb( Y, T ) }.
% 0.69/1.09 { ! contains_slb( Y, T ), contains_cpq( triple( X, Y, Z ), T ) }.
% 0.69/1.09 { ! ok( triple( X, Y, bad ) ) }.
% 0.69/1.09 { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.69/1.09 { ok( triple( Y, Z, X ) ), X = bad }.
% 0.69/1.09 { insert_cpq( triple( X, Y, Z ), T ) = triple( insert_pqp( X, T ),
% 0.69/1.09 insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.69/1.09 { contains_slb( X, Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( Z, X,
% 0.69/1.09 bad ) }.
% 0.69/1.09 { ! contains_slb( X, Y ), ! less_than( lookup_slb( X, Y ), Y ), remove_cpq
% 0.69/1.09 ( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y )
% 0.69/1.09 , T ) }.
% 0.69/1.09 { ! contains_slb( X, Y ), ! strictly_less_than( Y, lookup_slb( X, Y ) ),
% 0.69/1.09 remove_cpq( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ),
% 0.69/1.09 remove_slb( X, Y ), bad ) }.
% 0.69/1.09 { findmin_cpq_eff( triple( X, create_slb, Y ) ) = triple( X, create_slb,
% 0.69/1.09 bad ) }.
% 0.69/1.09 { Y = create_slb, contains_slb( Y, findmin_pqp_res( X ) ), findmin_cpq_eff
% 0.69/1.09 ( triple( X, Y, Z ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) )
% 0.69/1.09 , bad ) }.
% 0.69/1.09 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), !
% 0.69/1.09 strictly_less_than( findmin_pqp_res( X ), lookup_slb( Y, findmin_pqp_res
% 0.69/1.09 ( X ) ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb(
% 0.69/1.09 Y, findmin_pqp_res( X ) ), bad ) }.
% 0.69/1.09 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! less_than(
% 0.69/1.09 lookup_slb( Y, findmin_pqp_res( X ) ), findmin_pqp_res( X ) ),
% 0.96/1.34 findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( Y,
% 0.96/1.34 findmin_pqp_res( X ) ), Z ) }.
% 0.96/1.34 { findmin_cpq_res( triple( X, create_slb, Y ) ) = bottom }.
% 0.96/1.34 { X = create_slb, findmin_cpq_res( triple( Y, X, Z ) ) = findmin_pqp_res( Y
% 0.96/1.34 ) }.
% 0.96/1.34 { removemin_cpq_eff( X ) = remove_cpq( findmin_cpq_eff( X ),
% 0.96/1.34 findmin_cpq_res( X ) ) }.
% 0.96/1.34 { removemin_cpq_res( X ) = findmin_cpq_res( X ) }.
% 0.96/1.34 { ! contains_slb( X, Y ), pair_in_list( X, Y, skol1( X, Y ) ) }.
% 0.96/1.34 { ! pair_in_list( X, Y, T ), ! strictly_less_than( T, Z ), pair_in_list(
% 0.96/1.34 update_slb( X, Z ), Y, Z ) }.
% 0.96/1.34 { ! pair_in_list( X, Y, Z ), ! less_than( T, Z ), pair_in_list( update_slb
% 0.96/1.34 ( X, T ), Y, Z ) }.
% 0.96/1.34 { contains_slb( skol3, skol4 ) }.
% 0.96/1.34 { strictly_less_than( skol4, findmin_cpq_res( triple( skol2, skol3, skol5 )
% 0.96/1.34 ) ) }.
% 0.96/1.34 { ! pair_in_list( update_slb( skol3, findmin_pqp_res( skol2 ) ), skol4,
% 0.96/1.34 findmin_pqp_res( skol2 ) ) }.
% 0.96/1.34 { ! pair_in_list( update_slb( skol3, findmin_pqp_res( skol2 ) ), skol4, X )
% 0.96/1.34 , ! less_than( findmin_pqp_res( skol2 ), X ) }.
% 0.96/1.34
% 0.96/1.34 percentage equality = 0.264463, percentage horn = 0.803279
% 0.96/1.34 This is a problem with some equality
% 0.96/1.34
% 0.96/1.34
% 0.96/1.34
% 0.96/1.34 Options Used:
% 0.96/1.34
% 0.96/1.34 useres = 1
% 0.96/1.34 useparamod = 1
% 0.96/1.34 useeqrefl = 1
% 0.96/1.34 useeqfact = 1
% 0.96/1.34 usefactor = 1
% 0.96/1.34 usesimpsplitting = 0
% 0.96/1.34 usesimpdemod = 5
% 0.96/1.34 usesimpres = 3
% 0.96/1.34
% 0.96/1.34 resimpinuse = 1000
% 0.96/1.34 resimpclauses = 20000
% 0.96/1.34 substype = eqrewr
% 0.96/1.34 backwardsubs = 1
% 0.96/1.34 selectoldest = 5
% 0.96/1.34
% 0.96/1.34 litorderings [0] = split
% 0.96/1.34 litorderings [1] = extend the termordering, first sorting on arguments
% 0.96/1.34
% 0.96/1.34 termordering = kbo
% 0.96/1.34
% 0.96/1.34 litapriori = 0
% 0.96/1.34 termapriori = 1
% 0.96/1.34 litaposteriori = 0
% 0.96/1.34 termaposteriori = 0
% 0.96/1.34 demodaposteriori = 0
% 0.96/1.34 ordereqreflfact = 0
% 0.96/1.34
% 0.96/1.34 litselect = negord
% 0.96/1.34
% 0.96/1.34 maxweight = 15
% 0.96/1.34 maxdepth = 30000
% 0.96/1.34 maxlength = 115
% 0.96/1.34 maxnrvars = 195
% 0.96/1.34 excuselevel = 1
% 0.96/1.34 increasemaxweight = 1
% 0.96/1.34
% 0.96/1.34 maxselected = 10000000
% 0.96/1.34 maxnrclauses = 10000000
% 0.96/1.34
% 0.96/1.34 showgenerated = 0
% 0.96/1.34 showkept = 0
% 0.96/1.34 showselected = 0
% 0.96/1.34 showdeleted = 0
% 0.96/1.34 showresimp = 1
% 0.96/1.34 showstatus = 2000
% 0.96/1.34
% 0.96/1.34 prologoutput = 0
% 0.96/1.34 nrgoals = 5000000
% 0.96/1.34 totalproof = 1
% 0.96/1.34
% 0.96/1.34 Symbols occurring in the translation:
% 0.96/1.34
% 0.96/1.34 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.96/1.34 . [1, 2] (w:1, o:31, a:1, s:1, b:0),
% 0.96/1.34 || [2, 0] (w:1, o:3, a:1, s:1, b:0),
% 0.96/1.34 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.96/1.34 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.34 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.34 less_than [38, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.96/1.34 strictly_less_than [39, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.96/1.34 bottom [40, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.96/1.34 create_slb [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.96/1.34 isnonempty_slb [42, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.96/1.34 pair [43, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.96/1.34 insert_slb [44, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.96/1.34 contains_slb [45, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.96/1.34 pair_in_list [47, 3] (w:1, o:70, a:1, s:1, b:0),
% 0.96/1.34 remove_slb [49, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.96/1.34 lookup_slb [50, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.96/1.34 update_slb [51, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.96/1.34 succ_cpq [52, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.96/1.34 insert_cpq [53, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.96/1.34 remove_cpq [54, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.96/1.34 findmin_cpq_eff [55, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.96/1.34 removemin_cpq_eff [56, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.96/1.34 triple [57, 3] (w:1, o:71, a:1, s:1, b:0),
% 0.96/1.34 check_cpq [58, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.96/1.34 contains_cpq [59, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.96/1.34 bad [60, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.96/1.34 ok [61, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.96/1.34 insert_pqp [62, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.96/1.34 remove_pqp [63, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.96/1.34 findmin_pqp_res [64, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.96/1.34 findmin_cpq_res [65, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.96/1.34 removemin_cpq_res [66, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.96/1.34 alpha1 [67, 4] (w:1, o:72, a:1, s:1, b:1),
% 0.96/1.34 skol1 [68, 2] (w:1, o:69, a:1, s:1, b:1),
% 0.96/1.34 skol2 [69, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.96/1.34 skol3 [70, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.96/1.34 skol4 [71, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.96/1.34 skol5 [72, 0] (w:1, o:17, a:1, s:1, b:1).
% 0.96/1.34
% 0.96/1.34
% 0.96/1.34 Starting Search:
% 0.96/1.34
% 0.96/1.34 *** allocated 15000 integers for clauses
% 0.96/1.34 *** allocated 22500 integers for clauses
% 0.96/1.34 *** allocated 33750 integers for clauses
% 0.96/1.34 *** allocated 15000 integers for termspace/termends
% 0.96/1.34 *** allocated 50625 integers for clauses
% 0.96/1.34 *** allocated 22500 integers for termspace/termends
% 0.96/1.34 *** allocated 75937 integers for clauses
% 0.96/1.34 Resimplifying inuse:
% 0.96/1.34 Done
% 0.96/1.34
% 0.96/1.34 *** allocated 33750 integers for termspace/termends
% 0.96/1.34 *** allocated 113905 integers for clauses
% 0.96/1.34 *** allocated 50625 integers for termspace/termends
% 0.96/1.34
% 0.96/1.34 Intermediate Status:
% 0.96/1.34 Generated: 3931
% 0.96/1.34 Kept: 2001
% 0.96/1.34 Inuse: 133
% 0.96/1.34 Deleted: 4
% 0.96/1.34 Deletedinuse: 1
% 0.96/1.34
% 0.96/1.34 Resimplifying inuse:
% 0.96/1.34 Done
% 0.96/1.34
% 0.96/1.34 *** allocated 170857 integers for clauses
% 0.96/1.34 *** allocated 75937 integers for termspace/termends
% 0.96/1.34 Resimplifying inuse:
% 0.96/1.34 Done
% 0.96/1.34
% 0.96/1.34 *** allocated 256285 integers for clauses
% 0.96/1.34 *** allocated 113905 integers for termspace/termends
% 0.96/1.34
% 0.96/1.34 Intermediate Status:
% 0.96/1.34 Generated: 8915
% 0.96/1.34 Kept: 4013
% 0.96/1.34 Inuse: 184
% 0.96/1.34 Deleted: 5
% 0.96/1.34 Deletedinuse: 1
% 0.96/1.34
% 0.96/1.34 Resimplifying inuse:
% 0.96/1.34 Done
% 0.96/1.34
% 0.96/1.34 *** allocated 384427 integers for clauses
% 0.96/1.34 Resimplifying inuse:
% 0.96/1.34 Done
% 0.96/1.34
% 0.96/1.34 *** allocated 170857 integers for termspace/termends
% 0.96/1.34
% 0.96/1.34 Intermediate Status:
% 0.96/1.34 Generated: 17718
% 0.96/1.34 Kept: 6590
% 0.96/1.34 Inuse: 289
% 0.96/1.34 Deleted: 22
% 0.96/1.34 Deletedinuse: 10
% 0.96/1.34
% 0.96/1.34 Resimplifying inuse:
% 0.96/1.34 Done
% 0.96/1.34
% 0.96/1.34
% 0.96/1.34 Bliksems!, er is een bewijs:
% 0.96/1.34 % SZS status Theorem
% 0.96/1.34 % SZS output start Refutation
% 0.96/1.34
% 0.96/1.34 (1) {G0,W6,D2,L2,V2,M2} I { less_than( X, Y ), less_than( Y, X ) }.
% 0.96/1.34 (5) {G1,W6,D2,L2,V2,M2} I;r(1) { less_than( Y, X ), strictly_less_than( X,
% 0.96/1.34 Y ) }.
% 0.96/1.34 (54) {G0,W9,D3,L2,V2,M2} I { ! contains_slb( X, Y ), pair_in_list( X, Y,
% 0.96/1.34 skol1( X, Y ) ) }.
% 0.96/1.34 (55) {G0,W13,D3,L3,V4,M3} I { ! pair_in_list( X, Y, T ), !
% 0.96/1.34 strictly_less_than( T, Z ), pair_in_list( update_slb( X, Z ), Y, Z ) }.
% 0.96/1.34 (56) {G0,W13,D3,L3,V4,M3} I { ! pair_in_list( X, Y, Z ), ! less_than( T, Z
% 0.96/1.34 ), pair_in_list( update_slb( X, T ), Y, Z ) }.
% 0.96/1.34 (57) {G0,W3,D2,L1,V0,M1} I { contains_slb( skol3, skol4 ) }.
% 0.96/1.34 (59) {G0,W8,D4,L1,V0,M1} I { ! pair_in_list( update_slb( skol3,
% 0.96/1.34 findmin_pqp_res( skol2 ) ), skol4, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.34 (60) {G0,W11,D4,L2,V1,M2} I { ! pair_in_list( update_slb( skol3,
% 0.96/1.34 findmin_pqp_res( skol2 ) ), skol4, X ), ! less_than( findmin_pqp_res(
% 0.96/1.34 skol2 ), X ) }.
% 0.96/1.34 (4101) {G1,W6,D3,L1,V0,M1} R(54,57) { pair_in_list( skol3, skol4, skol1(
% 0.96/1.34 skol3, skol4 ) ) }.
% 0.96/1.34 (4444) {G1,W8,D3,L2,V1,M2} R(59,55) { ! pair_in_list( skol3, skol4, X ), !
% 0.96/1.34 strictly_less_than( X, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.34 (4608) {G1,W8,D3,L2,V1,M2} R(60,56);f { ! less_than( findmin_pqp_res( skol2
% 0.96/1.34 ), X ), ! pair_in_list( skol3, skol4, X ) }.
% 0.96/1.34 (7522) {G2,W4,D2,L1,V1,M1} R(4608,5);r(4444) { ! pair_in_list( skol3, skol4
% 0.96/1.34 , X ) }.
% 0.96/1.34 (7537) {G3,W0,D0,L0,V0,M0} R(7522,4101) { }.
% 0.96/1.34
% 0.96/1.34
% 0.96/1.34 % SZS output end Refutation
% 0.96/1.34 found a proof!
% 0.96/1.34
% 0.96/1.34
% 0.96/1.34 Unprocessed initial clauses:
% 0.96/1.34
% 0.96/1.34 (7539) {G0,W9,D2,L3,V3,M3} { ! less_than( X, Z ), ! less_than( Z, Y ),
% 0.96/1.34 less_than( X, Y ) }.
% 0.96/1.34 (7540) {G0,W6,D2,L2,V2,M2} { less_than( X, Y ), less_than( Y, X ) }.
% 0.96/1.34 (7541) {G0,W3,D2,L1,V1,M1} { less_than( X, X ) }.
% 0.96/1.34 (7542) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), less_than( X, Y
% 0.96/1.34 ) }.
% 0.96/1.34 (7543) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), ! less_than( Y
% 0.96/1.34 , X ) }.
% 0.96/1.34 (7544) {G0,W9,D2,L3,V2,M3} { ! less_than( X, Y ), less_than( Y, X ),
% 0.96/1.34 strictly_less_than( X, Y ) }.
% 0.96/1.34 (7545) {G0,W3,D2,L1,V1,M1} { less_than( bottom, X ) }.
% 0.96/1.34 (7546) {G0,W2,D2,L1,V0,M1} { ! isnonempty_slb( create_slb ) }.
% 0.96/1.34 (7547) {G0,W6,D4,L1,V3,M1} { isnonempty_slb( insert_slb( X, pair( Y, Z ) )
% 0.96/1.34 ) }.
% 0.96/1.34 (7548) {G0,W3,D2,L1,V1,M1} { ! contains_slb( create_slb, X ) }.
% 0.96/1.34 (7549) {G0,W13,D4,L3,V4,M3} { ! contains_slb( insert_slb( X, pair( Y, T )
% 0.96/1.34 ), Z ), contains_slb( X, Z ), Y = Z }.
% 0.96/1.34 (7550) {G0,W10,D4,L2,V4,M2} { ! contains_slb( X, Z ), contains_slb(
% 0.96/1.34 insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.96/1.34 (7551) {G0,W10,D4,L2,V4,M2} { ! Y = Z, contains_slb( insert_slb( X, pair(
% 0.96/1.34 Y, T ) ), Z ) }.
% 0.96/1.34 (7552) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 0.96/1.34 (7553) {G0,W17,D4,L3,V5,M3} { ! pair_in_list( insert_slb( X, pair( Y, T )
% 0.96/1.34 ), Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 0.96/1.34 (7554) {G0,W12,D4,L2,V5,M2} { ! pair_in_list( X, Z, U ), pair_in_list(
% 0.96/1.34 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.96/1.34 (7555) {G0,W13,D4,L2,V5,M2} { ! alpha1( Y, Z, T, U ), pair_in_list(
% 0.96/1.34 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.96/1.34 (7556) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.96/1.34 (7557) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.96/1.34 (7558) {G0,W11,D2,L3,V4,M3} { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.96/1.34 (7559) {G0,W9,D5,L1,V3,M1} { remove_slb( insert_slb( X, pair( Y, Z ) ), Y
% 0.96/1.34 ) = X }.
% 0.96/1.34 (7560) {G0,W21,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), remove_slb(
% 0.96/1.34 insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 0.96/1.34 ( Y, T ) ) }.
% 0.96/1.34 (7561) {G0,W9,D5,L1,V3,M1} { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y
% 0.96/1.34 ) = Z }.
% 0.96/1.34 (7562) {G0,W17,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), lookup_slb(
% 0.96/1.34 insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 0.96/1.34 (7563) {G0,W5,D3,L1,V1,M1} { update_slb( create_slb, X ) = create_slb }.
% 0.96/1.34 (7564) {G0,W18,D5,L2,V4,M2} { ! strictly_less_than( Y, X ), update_slb(
% 0.96/1.34 insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 0.96/1.34 ( T, X ) ) }.
% 0.96/1.34 (7565) {G0,W18,D5,L2,V4,M2} { ! less_than( X, Y ), update_slb( insert_slb
% 0.96/1.34 ( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 0.96/1.34 }.
% 0.96/1.34 (7566) {G0,W3,D2,L1,V1,M1} { succ_cpq( X, X ) }.
% 0.96/1.34 (7567) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq(
% 0.96/1.34 Y, Z ) ) }.
% 0.96/1.34 (7568) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq(
% 0.96/1.34 Y, Z ) ) }.
% 0.96/1.34 (7569) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.96/1.34 findmin_cpq_eff( Y ) ) }.
% 0.96/1.34 (7570) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.96/1.34 removemin_cpq_eff( Y ) ) }.
% 0.96/1.34 (7571) {G0,W5,D3,L1,V2,M1} { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.96/1.34 (7572) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z
% 0.96/1.34 , insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) )
% 0.96/1.34 }.
% 0.96/1.34 (7573) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z
% 0.96/1.34 , T, U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) )
% 0.96/1.34 }.
% 0.96/1.34 (7574) {G0,W12,D5,L2,V5,M2} { ! strictly_less_than( X, Y ), ! check_cpq(
% 0.96/1.34 triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.96/1.34 (7575) {G0,W13,D5,L3,V5,M3} { ! strictly_less_than( X, Y ), ! ||,
% 0.96/1.34 check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.96/1.34 (7576) {G0,W9,D3,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z ), T ),
% 0.96/1.34 contains_slb( Y, T ) }.
% 0.96/1.34 (7577) {G0,W9,D3,L2,V4,M2} { ! contains_slb( Y, T ), contains_cpq( triple
% 0.96/1.34 ( X, Y, Z ), T ) }.
% 0.96/1.34 (7578) {G0,W5,D3,L1,V2,M1} { ! ok( triple( X, Y, bad ) ) }.
% 0.96/1.34 (7579) {G0,W6,D3,L2,V2,M2} { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.96/1.34 (7580) {G0,W8,D3,L2,V3,M2} { ok( triple( Y, Z, X ) ), X = bad }.
% 0.96/1.34 (7581) {G0,W17,D5,L1,V4,M1} { insert_cpq( triple( X, Y, Z ), T ) = triple
% 0.96/1.34 ( insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.96/1.34 (7582) {G0,W14,D4,L2,V4,M2} { contains_slb( X, Y ), remove_cpq( triple( Z
% 0.96/1.34 , X, T ), Y ) = triple( Z, X, bad ) }.
% 0.96/1.34 (7583) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! less_than(
% 0.96/1.34 lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.96/1.34 remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 0.96/1.34 (7584) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! strictly_less_than
% 0.96/1.34 ( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.96/1.34 remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 0.96/1.34 (7585) {G0,W10,D4,L1,V2,M1} { findmin_cpq_eff( triple( X, create_slb, Y )
% 0.96/1.34 ) = triple( X, create_slb, bad ) }.
% 0.96/1.34 (7586) {G0,W20,D5,L3,V3,M3} { Y = create_slb, contains_slb( Y,
% 0.96/1.34 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 0.96/1.34 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.96/1.34 (7587) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.96/1.34 findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ),
% 0.96/1.34 lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 0.96/1.34 ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.96/1.34 (7588) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.96/1.35 findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 0.96/1.35 ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 0.96/1.35 ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 0.96/1.35 (7589) {G0,W7,D4,L1,V2,M1} { findmin_cpq_res( triple( X, create_slb, Y ) )
% 0.96/1.35 = bottom }.
% 0.96/1.35 (7590) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res( triple( Y,
% 0.96/1.35 X, Z ) ) = findmin_pqp_res( Y ) }.
% 0.96/1.35 (7591) {G0,W8,D4,L1,V1,M1} { removemin_cpq_eff( X ) = remove_cpq(
% 0.96/1.35 findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 0.96/1.35 (7592) {G0,W5,D3,L1,V1,M1} { removemin_cpq_res( X ) = findmin_cpq_res( X )
% 0.96/1.35 }.
% 0.96/1.35 (7593) {G0,W9,D3,L2,V2,M2} { ! contains_slb( X, Y ), pair_in_list( X, Y,
% 0.96/1.35 skol1( X, Y ) ) }.
% 0.96/1.35 (7594) {G0,W13,D3,L3,V4,M3} { ! pair_in_list( X, Y, T ), !
% 0.96/1.35 strictly_less_than( T, Z ), pair_in_list( update_slb( X, Z ), Y, Z ) }.
% 0.96/1.35 (7595) {G0,W13,D3,L3,V4,M3} { ! pair_in_list( X, Y, Z ), ! less_than( T, Z
% 0.96/1.35 ), pair_in_list( update_slb( X, T ), Y, Z ) }.
% 0.96/1.35 (7596) {G0,W3,D2,L1,V0,M1} { contains_slb( skol3, skol4 ) }.
% 0.96/1.35 (7597) {G0,W7,D4,L1,V0,M1} { strictly_less_than( skol4, findmin_cpq_res(
% 0.96/1.35 triple( skol2, skol3, skol5 ) ) ) }.
% 0.96/1.35 (7598) {G0,W8,D4,L1,V0,M1} { ! pair_in_list( update_slb( skol3,
% 0.96/1.35 findmin_pqp_res( skol2 ) ), skol4, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.35 (7599) {G0,W11,D4,L2,V1,M2} { ! pair_in_list( update_slb( skol3,
% 0.96/1.35 findmin_pqp_res( skol2 ) ), skol4, X ), ! less_than( findmin_pqp_res(
% 0.96/1.35 skol2 ), X ) }.
% 0.96/1.35
% 0.96/1.35
% 0.96/1.35 Total Proof:
% 0.96/1.35
% 0.96/1.35 subsumption: (1) {G0,W6,D2,L2,V2,M2} I { less_than( X, Y ), less_than( Y, X
% 0.96/1.35 ) }.
% 0.96/1.35 parent0: (7540) {G0,W6,D2,L2,V2,M2} { less_than( X, Y ), less_than( Y, X )
% 0.96/1.35 }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 Y := Y
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 1 ==> 1
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 resolution: (7609) {G1,W9,D2,L3,V2,M3} { less_than( Y, X ),
% 0.96/1.35 strictly_less_than( X, Y ), less_than( Y, X ) }.
% 0.96/1.35 parent0[0]: (7544) {G0,W9,D2,L3,V2,M3} { ! less_than( X, Y ), less_than( Y
% 0.96/1.35 , X ), strictly_less_than( X, Y ) }.
% 0.96/1.35 parent1[0]: (1) {G0,W6,D2,L2,V2,M2} I { less_than( X, Y ), less_than( Y, X
% 0.96/1.35 ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 Y := Y
% 0.96/1.35 end
% 0.96/1.35 substitution1:
% 0.96/1.35 X := X
% 0.96/1.35 Y := Y
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 factor: (7610) {G1,W6,D2,L2,V2,M2} { less_than( X, Y ), strictly_less_than
% 0.96/1.35 ( Y, X ) }.
% 0.96/1.35 parent0[0, 2]: (7609) {G1,W9,D2,L3,V2,M3} { less_than( Y, X ),
% 0.96/1.35 strictly_less_than( X, Y ), less_than( Y, X ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := Y
% 0.96/1.35 Y := X
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (5) {G1,W6,D2,L2,V2,M2} I;r(1) { less_than( Y, X ),
% 0.96/1.35 strictly_less_than( X, Y ) }.
% 0.96/1.35 parent0: (7610) {G1,W6,D2,L2,V2,M2} { less_than( X, Y ),
% 0.96/1.35 strictly_less_than( Y, X ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := Y
% 0.96/1.35 Y := X
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 1 ==> 1
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (54) {G0,W9,D3,L2,V2,M2} I { ! contains_slb( X, Y ),
% 0.96/1.35 pair_in_list( X, Y, skol1( X, Y ) ) }.
% 0.96/1.35 parent0: (7593) {G0,W9,D3,L2,V2,M2} { ! contains_slb( X, Y ), pair_in_list
% 0.96/1.35 ( X, Y, skol1( X, Y ) ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 Y := Y
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 1 ==> 1
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (55) {G0,W13,D3,L3,V4,M3} I { ! pair_in_list( X, Y, T ), !
% 0.96/1.35 strictly_less_than( T, Z ), pair_in_list( update_slb( X, Z ), Y, Z ) }.
% 0.96/1.35 parent0: (7594) {G0,W13,D3,L3,V4,M3} { ! pair_in_list( X, Y, T ), !
% 0.96/1.35 strictly_less_than( T, Z ), pair_in_list( update_slb( X, Z ), Y, Z ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 Y := Y
% 0.96/1.35 Z := Z
% 0.96/1.35 T := T
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 1 ==> 1
% 0.96/1.35 2 ==> 2
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (56) {G0,W13,D3,L3,V4,M3} I { ! pair_in_list( X, Y, Z ), !
% 0.96/1.35 less_than( T, Z ), pair_in_list( update_slb( X, T ), Y, Z ) }.
% 0.96/1.35 parent0: (7595) {G0,W13,D3,L3,V4,M3} { ! pair_in_list( X, Y, Z ), !
% 0.96/1.35 less_than( T, Z ), pair_in_list( update_slb( X, T ), Y, Z ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 Y := Y
% 0.96/1.35 Z := Z
% 0.96/1.35 T := T
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 1 ==> 1
% 0.96/1.35 2 ==> 2
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (57) {G0,W3,D2,L1,V0,M1} I { contains_slb( skol3, skol4 ) }.
% 0.96/1.35 parent0: (7596) {G0,W3,D2,L1,V0,M1} { contains_slb( skol3, skol4 ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (59) {G0,W8,D4,L1,V0,M1} I { ! pair_in_list( update_slb( skol3
% 0.96/1.35 , findmin_pqp_res( skol2 ) ), skol4, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.35 parent0: (7598) {G0,W8,D4,L1,V0,M1} { ! pair_in_list( update_slb( skol3,
% 0.96/1.35 findmin_pqp_res( skol2 ) ), skol4, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (60) {G0,W11,D4,L2,V1,M2} I { ! pair_in_list( update_slb(
% 0.96/1.35 skol3, findmin_pqp_res( skol2 ) ), skol4, X ), ! less_than(
% 0.96/1.35 findmin_pqp_res( skol2 ), X ) }.
% 0.96/1.35 parent0: (7599) {G0,W11,D4,L2,V1,M2} { ! pair_in_list( update_slb( skol3,
% 0.96/1.35 findmin_pqp_res( skol2 ) ), skol4, X ), ! less_than( findmin_pqp_res(
% 0.96/1.35 skol2 ), X ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 1 ==> 1
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 resolution: (7881) {G1,W6,D3,L1,V0,M1} { pair_in_list( skol3, skol4, skol1
% 0.96/1.35 ( skol3, skol4 ) ) }.
% 0.96/1.35 parent0[0]: (54) {G0,W9,D3,L2,V2,M2} I { ! contains_slb( X, Y ),
% 0.96/1.35 pair_in_list( X, Y, skol1( X, Y ) ) }.
% 0.96/1.35 parent1[0]: (57) {G0,W3,D2,L1,V0,M1} I { contains_slb( skol3, skol4 ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := skol3
% 0.96/1.35 Y := skol4
% 0.96/1.35 end
% 0.96/1.35 substitution1:
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (4101) {G1,W6,D3,L1,V0,M1} R(54,57) { pair_in_list( skol3,
% 0.96/1.35 skol4, skol1( skol3, skol4 ) ) }.
% 0.96/1.35 parent0: (7881) {G1,W6,D3,L1,V0,M1} { pair_in_list( skol3, skol4, skol1(
% 0.96/1.35 skol3, skol4 ) ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 resolution: (7882) {G1,W8,D3,L2,V1,M2} { ! pair_in_list( skol3, skol4, X )
% 0.96/1.35 , ! strictly_less_than( X, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.35 parent0[0]: (59) {G0,W8,D4,L1,V0,M1} I { ! pair_in_list( update_slb( skol3
% 0.96/1.35 , findmin_pqp_res( skol2 ) ), skol4, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.35 parent1[2]: (55) {G0,W13,D3,L3,V4,M3} I { ! pair_in_list( X, Y, T ), !
% 0.96/1.35 strictly_less_than( T, Z ), pair_in_list( update_slb( X, Z ), Y, Z ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 end
% 0.96/1.35 substitution1:
% 0.96/1.35 X := skol3
% 0.96/1.35 Y := skol4
% 0.96/1.35 Z := findmin_pqp_res( skol2 )
% 0.96/1.35 T := X
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (4444) {G1,W8,D3,L2,V1,M2} R(59,55) { ! pair_in_list( skol3,
% 0.96/1.35 skol4, X ), ! strictly_less_than( X, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.35 parent0: (7882) {G1,W8,D3,L2,V1,M2} { ! pair_in_list( skol3, skol4, X ), !
% 0.96/1.35 strictly_less_than( X, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 1 ==> 1
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 resolution: (7883) {G1,W12,D3,L3,V1,M3} { ! less_than( findmin_pqp_res(
% 0.96/1.35 skol2 ), X ), ! pair_in_list( skol3, skol4, X ), ! less_than(
% 0.96/1.35 findmin_pqp_res( skol2 ), X ) }.
% 0.96/1.35 parent0[0]: (60) {G0,W11,D4,L2,V1,M2} I { ! pair_in_list( update_slb( skol3
% 0.96/1.35 , findmin_pqp_res( skol2 ) ), skol4, X ), ! less_than( findmin_pqp_res(
% 0.96/1.35 skol2 ), X ) }.
% 0.96/1.35 parent1[2]: (56) {G0,W13,D3,L3,V4,M3} I { ! pair_in_list( X, Y, Z ), !
% 0.96/1.35 less_than( T, Z ), pair_in_list( update_slb( X, T ), Y, Z ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 end
% 0.96/1.35 substitution1:
% 0.96/1.35 X := skol3
% 0.96/1.35 Y := skol4
% 0.96/1.35 Z := X
% 0.96/1.35 T := findmin_pqp_res( skol2 )
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 factor: (7884) {G1,W8,D3,L2,V1,M2} { ! less_than( findmin_pqp_res( skol2 )
% 0.96/1.35 , X ), ! pair_in_list( skol3, skol4, X ) }.
% 0.96/1.35 parent0[0, 2]: (7883) {G1,W12,D3,L3,V1,M3} { ! less_than( findmin_pqp_res
% 0.96/1.35 ( skol2 ), X ), ! pair_in_list( skol3, skol4, X ), ! less_than(
% 0.96/1.35 findmin_pqp_res( skol2 ), X ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (4608) {G1,W8,D3,L2,V1,M2} R(60,56);f { ! less_than(
% 0.96/1.35 findmin_pqp_res( skol2 ), X ), ! pair_in_list( skol3, skol4, X ) }.
% 0.96/1.35 parent0: (7884) {G1,W8,D3,L2,V1,M2} { ! less_than( findmin_pqp_res( skol2
% 0.96/1.35 ), X ), ! pair_in_list( skol3, skol4, X ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 1 ==> 1
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 resolution: (7885) {G2,W8,D3,L2,V1,M2} { ! pair_in_list( skol3, skol4, X )
% 0.96/1.35 , strictly_less_than( X, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.35 parent0[0]: (4608) {G1,W8,D3,L2,V1,M2} R(60,56);f { ! less_than(
% 0.96/1.35 findmin_pqp_res( skol2 ), X ), ! pair_in_list( skol3, skol4, X ) }.
% 0.96/1.35 parent1[0]: (5) {G1,W6,D2,L2,V2,M2} I;r(1) { less_than( Y, X ),
% 0.96/1.35 strictly_less_than( X, Y ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 end
% 0.96/1.35 substitution1:
% 0.96/1.35 X := X
% 0.96/1.35 Y := findmin_pqp_res( skol2 )
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 resolution: (7886) {G2,W8,D2,L2,V1,M2} { ! pair_in_list( skol3, skol4, X )
% 0.96/1.35 , ! pair_in_list( skol3, skol4, X ) }.
% 0.96/1.35 parent0[1]: (4444) {G1,W8,D3,L2,V1,M2} R(59,55) { ! pair_in_list( skol3,
% 0.96/1.35 skol4, X ), ! strictly_less_than( X, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.35 parent1[1]: (7885) {G2,W8,D3,L2,V1,M2} { ! pair_in_list( skol3, skol4, X )
% 0.96/1.35 , strictly_less_than( X, findmin_pqp_res( skol2 ) ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 end
% 0.96/1.35 substitution1:
% 0.96/1.35 X := X
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 factor: (7887) {G2,W4,D2,L1,V1,M1} { ! pair_in_list( skol3, skol4, X ) }.
% 0.96/1.35 parent0[0, 1]: (7886) {G2,W8,D2,L2,V1,M2} { ! pair_in_list( skol3, skol4,
% 0.96/1.35 X ), ! pair_in_list( skol3, skol4, X ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (7522) {G2,W4,D2,L1,V1,M1} R(4608,5);r(4444) { ! pair_in_list
% 0.96/1.35 ( skol3, skol4, X ) }.
% 0.96/1.35 parent0: (7887) {G2,W4,D2,L1,V1,M1} { ! pair_in_list( skol3, skol4, X )
% 0.96/1.35 }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := X
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 0 ==> 0
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 resolution: (7888) {G2,W0,D0,L0,V0,M0} { }.
% 0.96/1.35 parent0[0]: (7522) {G2,W4,D2,L1,V1,M1} R(4608,5);r(4444) { ! pair_in_list(
% 0.96/1.35 skol3, skol4, X ) }.
% 0.96/1.35 parent1[0]: (4101) {G1,W6,D3,L1,V0,M1} R(54,57) { pair_in_list( skol3,
% 0.96/1.35 skol4, skol1( skol3, skol4 ) ) }.
% 0.96/1.35 substitution0:
% 0.96/1.35 X := skol1( skol3, skol4 )
% 0.96/1.35 end
% 0.96/1.35 substitution1:
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 subsumption: (7537) {G3,W0,D0,L0,V0,M0} R(7522,4101) { }.
% 0.96/1.35 parent0: (7888) {G2,W0,D0,L0,V0,M0} { }.
% 0.96/1.35 substitution0:
% 0.96/1.35 end
% 0.96/1.35 permutation0:
% 0.96/1.35 end
% 0.96/1.35
% 0.96/1.35 Proof check complete!
% 0.96/1.35
% 0.96/1.35 Memory use:
% 0.96/1.35
% 0.96/1.35 space for terms: 134164
% 0.96/1.35 space for clauses: 362301
% 0.96/1.35
% 0.96/1.35
% 0.96/1.35 clauses generated: 28793
% 0.96/1.35 clauses kept: 7538
% 0.96/1.35 clauses selected: 362
% 0.96/1.35 clauses deleted: 23
% 0.96/1.35 clauses inuse deleted: 10
% 0.96/1.35
% 0.96/1.35 subsentry: 35245
% 0.96/1.35 literals s-matched: 24027
% 0.96/1.35 literals matched: 23632
% 0.96/1.35 full subsumption: 7547
% 0.96/1.35
% 0.96/1.35 checksum: -100084707
% 0.96/1.35
% 0.96/1.35
% 0.96/1.35 Bliksem ended
%------------------------------------------------------------------------------