TSTP Solution File: SWV417+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV417+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 16:24:48 EDT 2022
% Result : Theorem 0.89s 1.30s
% Output : Refutation 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV417+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Wed Jun 15 09:18:55 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.49/1.15 *** allocated 10000 integers for termspace/termends
% 0.49/1.15 *** allocated 10000 integers for clauses
% 0.49/1.15 *** allocated 10000 integers for justifications
% 0.49/1.15 Bliksem 1.12
% 0.49/1.15
% 0.49/1.15
% 0.49/1.15 Automatic Strategy Selection
% 0.49/1.15
% 0.49/1.15
% 0.49/1.15 Clauses:
% 0.49/1.15
% 0.49/1.15 { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.49/1.15 { less_than( X, Y ), less_than( Y, X ) }.
% 0.49/1.15 { less_than( X, X ) }.
% 0.49/1.15 { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.49/1.15 { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.49/1.15 { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.49/1.15 { less_than( bottom, X ) }.
% 0.49/1.15 { ! isnonempty_pq( create_pq ) }.
% 0.49/1.15 { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.49/1.15 { ! contains_pq( create_pq, X ) }.
% 0.49/1.15 { ! contains_pq( insert_pq( X, Y ), Z ), contains_pq( X, Z ), Y = Z }.
% 0.49/1.15 { ! contains_pq( X, Z ), contains_pq( insert_pq( X, Y ), Z ) }.
% 0.49/1.15 { ! Y = Z, contains_pq( insert_pq( X, Y ), Z ) }.
% 0.49/1.15 { ! issmallestelement_pq( X, Y ), ! contains_pq( X, Z ), less_than( Y, Z )
% 0.49/1.15 }.
% 0.49/1.15 { ! less_than( Y, skol1( Z, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.49/1.15 { contains_pq( X, skol1( X, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.49/1.15 { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 0.49/1.15 { ! contains_pq( X, Z ), Y = Z, remove_pq( insert_pq( X, Y ), Z ) =
% 0.49/1.15 insert_pq( remove_pq( X, Z ), Y ) }.
% 0.49/1.15 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_eff( X
% 0.49/1.15 , Y ) = X }.
% 0.49/1.15 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_res( X
% 0.49/1.15 , Y ) = Y }.
% 0.49/1.15 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_eff(
% 0.49/1.15 X, Y ) = remove_pq( X, Y ) }.
% 0.49/1.15 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_res(
% 0.49/1.15 X, Y ) = Y }.
% 0.49/1.15 { insert_pq( insert_pq( X, Y ), Z ) = insert_pq( insert_pq( X, Z ), Y ) }.
% 0.49/1.15 { ! isnonempty_slb( create_slb ) }.
% 0.49/1.15 { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) ) }.
% 0.49/1.15 { ! contains_slb( create_slb, X ) }.
% 0.49/1.15 { ! contains_slb( insert_slb( X, pair( Y, T ) ), Z ), contains_slb( X, Z )
% 0.49/1.15 , Y = Z }.
% 0.49/1.15 { ! contains_slb( X, Z ), contains_slb( insert_slb( X, pair( Y, T ) ), Z )
% 0.49/1.15 }.
% 0.49/1.15 { ! Y = Z, contains_slb( insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.49/1.15 { ! pair_in_list( create_slb, X, Y ) }.
% 0.49/1.15 { ! pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U ), pair_in_list( X, Z
% 0.49/1.15 , U ), alpha1( Y, Z, T, U ) }.
% 0.49/1.15 { ! pair_in_list( X, Z, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z
% 0.49/1.15 , U ) }.
% 0.49/1.15 { ! alpha1( Y, Z, T, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U
% 0.49/1.15 ) }.
% 0.49/1.15 { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.49/1.15 { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.49/1.15 { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.49/1.15 { remove_slb( insert_slb( X, pair( Y, Z ) ), Y ) = X }.
% 0.49/1.15 { Y = Z, ! contains_slb( X, Z ), remove_slb( insert_slb( X, pair( Y, T ) )
% 0.49/1.15 , Z ) = insert_slb( remove_slb( X, Z ), pair( Y, T ) ) }.
% 0.49/1.15 { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y ) = Z }.
% 0.49/1.15 { Y = Z, ! contains_slb( X, Z ), lookup_slb( insert_slb( X, pair( Y, T ) )
% 0.49/1.15 , Z ) = lookup_slb( X, Z ) }.
% 0.49/1.15 { update_slb( create_slb, X ) = create_slb }.
% 0.49/1.15 { ! strictly_less_than( Y, X ), update_slb( insert_slb( Z, pair( T, Y ) ),
% 0.49/1.15 X ) = insert_slb( update_slb( Z, X ), pair( T, X ) ) }.
% 0.49/1.15 { ! less_than( X, Y ), update_slb( insert_slb( Z, pair( T, Y ) ), X ) =
% 0.49/1.15 insert_slb( update_slb( Z, X ), pair( T, Y ) ) }.
% 0.49/1.15 { succ_cpq( X, X ) }.
% 0.49/1.15 { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y, Z ) ) }.
% 0.49/1.15 { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y, Z ) ) }.
% 0.49/1.15 { ! succ_cpq( X, Y ), succ_cpq( X, findmin_cpq_eff( Y ) ) }.
% 0.49/1.15 { ! succ_cpq( X, Y ), succ_cpq( X, removemin_cpq_eff( Y ) ) }.
% 0.49/1.15 { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.49/1.15 { ! less_than( Y, X ), ! check_cpq( triple( Z, insert_slb( T, pair( X, Y )
% 0.49/1.15 ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.49/1.15 { ! less_than( Y, X ), ! check_cpq( triple( Z, T, U ) ), check_cpq( triple
% 0.49/1.15 ( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.49/1.15 { ! strictly_less_than( X, Y ), ! check_cpq( triple( Z, insert_slb( T, pair
% 0.49/1.15 ( X, Y ) ), U ) ) }.
% 0.49/1.15 { ! strictly_less_than( X, Y ), ! ||, check_cpq( triple( Z, insert_slb( T,
% 0.49/1.15 pair( X, Y ) ), U ) ) }.
% 0.49/1.15 { ! contains_cpq( triple( X, Y, Z ), T ), contains_slb( Y, T ) }.
% 0.49/1.15 { ! contains_slb( Y, T ), contains_cpq( triple( X, Y, Z ), T ) }.
% 0.49/1.15 { ! ok( triple( X, Y, bad ) ) }.
% 0.49/1.15 { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.49/1.15 { ok( triple( Y, Z, X ) ), X = bad }.
% 0.82/1.20 { insert_cpq( triple( X, Y, Z ), T ) = triple( insert_pqp( X, T ),
% 0.82/1.20 insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.82/1.20 { contains_slb( X, Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( Z, X,
% 0.82/1.20 bad ) }.
% 0.82/1.20 { ! contains_slb( X, Y ), ! less_than( lookup_slb( X, Y ), Y ), remove_cpq
% 0.82/1.20 ( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y )
% 0.82/1.20 , T ) }.
% 0.82/1.20 { ! contains_slb( X, Y ), ! strictly_less_than( Y, lookup_slb( X, Y ) ),
% 0.82/1.20 remove_cpq( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ),
% 0.82/1.20 remove_slb( X, Y ), bad ) }.
% 0.82/1.20 { findmin_cpq_eff( triple( X, create_slb, Y ) ) = triple( X, create_slb,
% 0.82/1.20 bad ) }.
% 0.82/1.20 { Y = create_slb, contains_slb( Y, findmin_pqp_res( X ) ), findmin_cpq_eff
% 0.82/1.20 ( triple( X, Y, Z ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) )
% 0.82/1.20 , bad ) }.
% 0.82/1.20 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), !
% 0.82/1.20 strictly_less_than( findmin_pqp_res( X ), lookup_slb( Y, findmin_pqp_res
% 0.82/1.20 ( X ) ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb(
% 0.82/1.20 Y, findmin_pqp_res( X ) ), bad ) }.
% 0.82/1.20 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! less_than(
% 0.82/1.20 lookup_slb( Y, findmin_pqp_res( X ) ), findmin_pqp_res( X ) ),
% 0.82/1.20 findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( Y,
% 0.82/1.20 findmin_pqp_res( X ) ), Z ) }.
% 0.82/1.20 { findmin_cpq_res( triple( X, create_slb, Y ) ) = bottom }.
% 0.82/1.20 { X = create_slb, findmin_cpq_res( triple( Y, X, Z ) ) = findmin_pqp_res( Y
% 0.82/1.20 ) }.
% 0.82/1.20 { removemin_cpq_eff( X ) = remove_cpq( findmin_cpq_eff( X ),
% 0.82/1.20 findmin_cpq_res( X ) ) }.
% 0.82/1.20 { removemin_cpq_res( X ) = findmin_cpq_res( X ) }.
% 0.82/1.20 { i( triple( X, create_slb, Y ) ) = create_pq }.
% 0.82/1.20 { i( triple( X, insert_slb( Y, pair( T, U ) ), Z ) ) = insert_pq( i( triple
% 0.82/1.20 ( X, Y, Z ) ), T ) }.
% 0.82/1.20 { ! pi_sharp_remove( X, Y ), contains_pq( X, Y ) }.
% 0.82/1.20 { ! contains_pq( X, Y ), pi_sharp_remove( X, Y ) }.
% 0.82/1.20 { ! pi_remove( X, Y ), pi_sharp_remove( i( X ), Y ) }.
% 0.82/1.20 { ! pi_sharp_remove( i( X ), Y ), pi_remove( X, Y ) }.
% 0.82/1.20 { ! pi_sharp_find_min( X, Y ), contains_pq( X, Y ) }.
% 0.82/1.20 { ! pi_sharp_find_min( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.82/1.20 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_find_min
% 0.82/1.20 ( X, Y ) }.
% 0.82/1.20 { ! pi_find_min( X ), pi_sharp_find_min( i( X ), skol2( X ) ) }.
% 0.82/1.20 { ! pi_sharp_find_min( i( X ), Y ), pi_find_min( X ) }.
% 0.82/1.20 { ! pi_sharp_removemin( X, Y ), contains_pq( X, Y ) }.
% 0.82/1.20 { ! pi_sharp_removemin( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.82/1.20 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_removemin
% 0.82/1.20 ( X, Y ) }.
% 0.82/1.20 { ! pi_removemin( X ), pi_sharp_find_min( i( X ), skol3( X ) ) }.
% 0.82/1.20 { ! pi_sharp_find_min( i( X ), Y ), pi_removemin( X ) }.
% 0.82/1.20 { ! phi( X ), alpha2( skol4( Y ) ) }.
% 0.82/1.20 { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 0.82/1.20 { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X ) }.
% 0.82/1.20 { ! alpha2( X ), ok( X ) }.
% 0.82/1.20 { ! alpha2( X ), check_cpq( X ) }.
% 0.82/1.20 { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 0.82/1.20 { ! phi( findmin_cpq_eff( triple( X, Y, Z ) ) ), pi_sharp_find_min( i(
% 0.82/1.20 triple( X, Y, Z ) ), findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 0.82/1.20 { pi_find_min( triple( skol5, skol6, skol7 ) ) }.
% 0.82/1.20 { phi( findmin_cpq_eff( triple( skol5, skol6, skol7 ) ) ) }.
% 0.82/1.20 { ! pi_sharp_find_min( i( triple( skol5, skol6, skol7 ) ), X ), !
% 0.82/1.20 findmin_cpq_res( triple( skol5, skol6, skol7 ) ) = findmin_pq_res( i(
% 0.82/1.20 triple( skol5, skol6, skol7 ) ), X ) }.
% 0.82/1.20
% 0.82/1.20 percentage equality = 0.231959, percentage horn = 0.843750
% 0.82/1.20 This is a problem with some equality
% 0.82/1.20
% 0.82/1.20
% 0.82/1.20
% 0.82/1.20 Options Used:
% 0.82/1.20
% 0.82/1.20 useres = 1
% 0.82/1.20 useparamod = 1
% 0.82/1.20 useeqrefl = 1
% 0.82/1.20 useeqfact = 1
% 0.82/1.20 usefactor = 1
% 0.82/1.20 usesimpsplitting = 0
% 0.82/1.20 usesimpdemod = 5
% 0.82/1.20 usesimpres = 3
% 0.82/1.20
% 0.82/1.20 resimpinuse = 1000
% 0.82/1.20 resimpclauses = 20000
% 0.82/1.20 substype = eqrewr
% 0.82/1.20 backwardsubs = 1
% 0.82/1.20 selectoldest = 5
% 0.82/1.20
% 0.82/1.20 litorderings [0] = split
% 0.82/1.20 litorderings [1] = extend the termordering, first sorting on arguments
% 0.82/1.20
% 0.82/1.20 termordering = kbo
% 0.82/1.20
% 0.82/1.20 litapriori = 0
% 0.82/1.20 termapriori = 1
% 0.82/1.20 litaposteriori = 0
% 0.82/1.20 termaposteriori = 0
% 0.82/1.20 demodaposteriori = 0
% 0.82/1.20 ordereqreflfact = 0
% 0.82/1.20
% 0.82/1.20 litselect = negord
% 0.82/1.20
% 0.82/1.20 maxweight = 15
% 0.82/1.20 maxdepth = 30000
% 0.82/1.20 maxlength = 115
% 0.82/1.20 maxnrvars = 195
% 0.82/1.20 excuselevel = 1
% 0.82/1.20 increasemaxweight = 1
% 0.82/1.20
% 0.89/1.30 maxselected = 10000000
% 0.89/1.30 maxnrclauses = 10000000
% 0.89/1.30
% 0.89/1.30 showgenerated = 0
% 0.89/1.30 showkept = 0
% 0.89/1.30 showselected = 0
% 0.89/1.30 showdeleted = 0
% 0.89/1.30 showresimp = 1
% 0.89/1.30 showstatus = 2000
% 0.89/1.30
% 0.89/1.30 prologoutput = 0
% 0.89/1.30 nrgoals = 5000000
% 0.89/1.30 totalproof = 1
% 0.89/1.30
% 0.89/1.30 Symbols occurring in the translation:
% 0.89/1.30
% 0.89/1.30 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.89/1.30 . [1, 2] (w:1, o:40, a:1, s:1, b:0),
% 0.89/1.30 || [2, 0] (w:1, o:3, a:1, s:1, b:0),
% 0.89/1.30 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.89/1.30 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.30 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.30 less_than [38, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.89/1.30 strictly_less_than [39, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.89/1.30 bottom [40, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.89/1.30 create_pq [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.89/1.30 isnonempty_pq [42, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.89/1.30 insert_pq [43, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.89/1.30 contains_pq [44, 2] (w:1, o:73, a:1, s:1, b:0),
% 0.89/1.30 issmallestelement_pq [45, 2] (w:1, o:74, a:1, s:1, b:0),
% 0.89/1.30 remove_pq [46, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.89/1.30 findmin_pq_eff [47, 2] (w:1, o:75, a:1, s:1, b:0),
% 0.89/1.30 findmin_pq_res [48, 2] (w:1, o:76, a:1, s:1, b:0),
% 0.89/1.30 removemin_pq_eff [49, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.89/1.30 removemin_pq_res [50, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.89/1.30 create_slb [51, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.89/1.30 isnonempty_slb [52, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.89/1.30 pair [53, 2] (w:1, o:77, a:1, s:1, b:0),
% 0.89/1.30 insert_slb [54, 2] (w:1, o:78, a:1, s:1, b:0),
% 0.89/1.30 contains_slb [55, 2] (w:1, o:79, a:1, s:1, b:0),
% 0.89/1.30 pair_in_list [57, 3] (w:1, o:91, a:1, s:1, b:0),
% 0.89/1.30 remove_slb [59, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.89/1.30 lookup_slb [60, 2] (w:1, o:80, a:1, s:1, b:0),
% 0.89/1.30 update_slb [61, 2] (w:1, o:81, a:1, s:1, b:0),
% 0.89/1.30 succ_cpq [62, 2] (w:1, o:82, a:1, s:1, b:0),
% 0.89/1.30 insert_cpq [63, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.89/1.30 remove_cpq [64, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.89/1.30 findmin_cpq_eff [65, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.89/1.30 removemin_cpq_eff [66, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.89/1.30 triple [67, 3] (w:1, o:92, a:1, s:1, b:0),
% 0.89/1.30 check_cpq [68, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.89/1.30 contains_cpq [69, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.89/1.30 bad [70, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.89/1.30 ok [71, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.89/1.30 insert_pqp [72, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.89/1.30 remove_pqp [73, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.89/1.30 findmin_pqp_res [74, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.89/1.30 findmin_cpq_res [75, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.89/1.30 removemin_cpq_res [76, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.89/1.30 i [77, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.89/1.30 pi_sharp_remove [78, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.89/1.30 pi_remove [79, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.89/1.30 pi_sharp_find_min [80, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.89/1.30 pi_find_min [81, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.89/1.30 pi_sharp_removemin [82, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.89/1.30 pi_removemin [83, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.89/1.30 phi [84, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.89/1.30 alpha1 [85, 4] (w:1, o:93, a:1, s:1, b:1),
% 0.89/1.30 alpha2 [86, 1] (w:1, o:36, a:1, s:1, b:1),
% 0.89/1.30 skol1 [87, 2] (w:1, o:90, a:1, s:1, b:1),
% 0.89/1.30 skol2 [88, 1] (w:1, o:37, a:1, s:1, b:1),
% 0.89/1.30 skol3 [89, 1] (w:1, o:38, a:1, s:1, b:1),
% 0.89/1.30 skol4 [90, 1] (w:1, o:39, a:1, s:1, b:1),
% 0.89/1.30 skol5 [91, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.89/1.30 skol6 [92, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.89/1.30 skol7 [93, 0] (w:1, o:17, a:1, s:1, b:1).
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 Starting Search:
% 0.89/1.30
% 0.89/1.30 *** allocated 15000 integers for clauses
% 0.89/1.30 *** allocated 22500 integers for clauses
% 0.89/1.30 *** allocated 33750 integers for clauses
% 0.89/1.30 *** allocated 15000 integers for termspace/termends
% 0.89/1.30 *** allocated 50625 integers for clauses
% 0.89/1.30 *** allocated 22500 integers for termspace/termends
% 0.89/1.30 *** allocated 75937 integers for clauses
% 0.89/1.30 Resimplifying inuse:
% 0.89/1.30 Done
% 0.89/1.30
% 0.89/1.30 *** allocated 33750 integers for termspace/termends
% 0.89/1.30 *** allocated 113905 integers for clauses
% 0.89/1.30 *** allocated 50625 integers for termspace/termends
% 0.89/1.30
% 0.89/1.30 Intermediate Status:
% 0.89/1.30 Generated: 3892
% 0.89/1.30 Kept: 2010
% 0.89/1.30 Inuse: 158
% 0.89/1.30 Deleted: 4
% 0.89/1.30 Deletedinuse: 3
% 0.89/1.30
% 0.89/1.30 *** allocated 170857 integers for clauses
% 0.89/1.30 Resimplifying inuse:
% 0.89/1.30 Done
% 0.89/1.30
% 0.89/1.30 *** allocated 75937 integers for termspace/termends
% 0.89/1.30 Resimplifying inuse:
% 0.89/1.30 Done
% 0.89/1.30
% 0.89/1.30 *** allocated 256285 integers for clauses
% 0.89/1.30 *** allocated 113905 integers for termspace/termends
% 0.89/1.30
% 0.89/1.30 Intermediate Status:
% 0.89/1.30 Generated: 8213
% 0.89/1.30 Kept: 4253
% 0.89/1.30 Inuse: 235
% 0.89/1.30 Deleted: 4
% 0.89/1.30 Deletedinuse: 3
% 0.89/1.30
% 0.89/1.30 Resimplifying inuse:
% 0.89/1.30 Done
% 0.89/1.30
% 0.89/1.30 *** allocated 384427 integers for clauses
% 0.89/1.30 Resimplifying inuse:
% 0.89/1.30 Done
% 0.89/1.30
% 0.89/1.30 *** allocated 170857 integers for termspace/termends
% 0.89/1.30
% 0.89/1.30 Bliksems!, er is een bewijs:
% 0.89/1.30 % SZS status Theorem
% 0.89/1.30 % SZS output start Refutation
% 0.89/1.30
% 0.89/1.30 (9) {G0,W3,D2,L1,V1,M1} I { ! contains_pq( create_pq, X ) }.
% 0.89/1.30 (19) {G0,W11,D3,L3,V2,M3} I { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.89/1.30 ( X, Y ), findmin_pq_res( X, Y ) ==> Y }.
% 0.89/1.30 (67) {G0,W11,D4,L2,V3,M2} I { X = create_slb, findmin_cpq_res( triple( Y, X
% 0.89/1.30 , Z ) ) ==> findmin_pqp_res( Y ) }.
% 0.89/1.30 (70) {G0,W7,D4,L1,V2,M1} I { i( triple( X, create_slb, Y ) ) ==> create_pq
% 0.89/1.30 }.
% 0.89/1.30 (76) {G0,W6,D2,L2,V2,M2} I { ! pi_sharp_find_min( X, Y ), contains_pq( X, Y
% 0.89/1.30 ) }.
% 0.89/1.30 (77) {G0,W6,D2,L2,V2,M2} I { ! pi_sharp_find_min( X, Y ),
% 0.89/1.30 issmallestelement_pq( X, Y ) }.
% 0.89/1.30 (79) {G0,W7,D3,L2,V1,M2} I { ! pi_find_min( X ), pi_sharp_find_min( i( X )
% 0.89/1.30 , skol2( X ) ) }.
% 0.89/1.30 (80) {G0,W6,D3,L2,V2,M2} I { ! pi_sharp_find_min( i( X ), Y ), pi_find_min
% 0.89/1.30 ( X ) }.
% 0.89/1.30 (84) {G0,W7,D3,L2,V1,M2} I { ! pi_removemin( X ), pi_sharp_find_min( i( X )
% 0.89/1.30 , skol3( X ) ) }.
% 0.89/1.30 (85) {G0,W6,D3,L2,V2,M2} I { ! pi_sharp_find_min( i( X ), Y ), pi_removemin
% 0.89/1.30 ( X ) }.
% 0.89/1.30 (92) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( X, Y, Z ) ) )
% 0.89/1.30 , pi_sharp_find_min( i( triple( X, Y, Z ) ), findmin_cpq_res( triple( X,
% 0.89/1.30 Y, Z ) ) ) }.
% 0.89/1.30 (93) {G0,W5,D3,L1,V0,M1} I { pi_find_min( triple( skol5, skol6, skol7 ) )
% 0.89/1.30 }.
% 0.89/1.30 (94) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple( skol5, skol6,
% 0.89/1.30 skol7 ) ) ) }.
% 0.89/1.30 (95) {G0,W20,D5,L2,V1,M2} I { ! pi_sharp_find_min( i( triple( skol5, skol6
% 0.89/1.30 , skol7 ) ), X ), ! findmin_pq_res( i( triple( skol5, skol6, skol7 ) ), X
% 0.89/1.30 ) ==> findmin_cpq_res( triple( skol5, skol6, skol7 ) ) }.
% 0.89/1.30 (197) {G1,W3,D2,L1,V1,M1} R(76,9) { ! pi_sharp_find_min( create_pq, X ) }.
% 0.89/1.30 (410) {G1,W8,D3,L2,V2,M2} R(19,76);r(77) { findmin_pq_res( X, Y ) ==> Y, !
% 0.89/1.30 pi_sharp_find_min( X, Y ) }.
% 0.89/1.30 (814) {G1,W4,D2,L2,V1,M2} R(84,80) { ! pi_removemin( X ), pi_find_min( X )
% 0.89/1.30 }.
% 0.89/1.30 (867) {G2,W7,D3,L2,V1,M2} R(79,814) { pi_sharp_find_min( i( X ), skol2( X )
% 0.89/1.30 ), ! pi_removemin( X ) }.
% 0.89/1.30 (870) {G1,W4,D2,L2,V1,M2} R(79,85) { ! pi_find_min( X ), pi_removemin( X )
% 0.89/1.30 }.
% 0.89/1.30 (892) {G2,W5,D3,L1,V0,M1} R(870,93) { pi_removemin( triple( skol5, skol6,
% 0.89/1.30 skol7 ) ) }.
% 0.89/1.30 (2231) {G3,W5,D3,L1,V2,M1} P(70,867);r(197) { ! pi_removemin( triple( X,
% 0.89/1.30 create_slb, Y ) ) }.
% 0.89/1.30 (5240) {G4,W8,D4,L1,V2,M1} P(67,892);r(2231) { findmin_cpq_res( triple( X,
% 0.89/1.30 skol6, Y ) ) ==> findmin_pqp_res( X ) }.
% 0.89/1.30 (5782) {G5,W8,D4,L1,V0,M1} R(92,94);d(5240) { pi_sharp_find_min( i( triple
% 0.89/1.30 ( skol5, skol6, skol7 ) ), findmin_pqp_res( skol5 ) ) }.
% 0.89/1.30 (5947) {G5,W11,D4,L2,V1,M2} S(95);d(410);d(5240) { ! pi_sharp_find_min( i(
% 0.89/1.30 triple( skol5, skol6, skol7 ) ), X ), ! X = findmin_pqp_res( skol5 ) }.
% 0.89/1.30 (5948) {G6,W0,D0,L0,V0,M0} Q(5947);r(5782) { }.
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 % SZS output end Refutation
% 0.89/1.30 found a proof!
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 Unprocessed initial clauses:
% 0.89/1.30
% 0.89/1.30 (5950) {G0,W9,D2,L3,V3,M3} { ! less_than( X, Z ), ! less_than( Z, Y ),
% 0.89/1.30 less_than( X, Y ) }.
% 0.89/1.30 (5951) {G0,W6,D2,L2,V2,M2} { less_than( X, Y ), less_than( Y, X ) }.
% 0.89/1.30 (5952) {G0,W3,D2,L1,V1,M1} { less_than( X, X ) }.
% 0.89/1.30 (5953) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), less_than( X, Y
% 0.89/1.30 ) }.
% 0.89/1.30 (5954) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), ! less_than( Y
% 0.89/1.30 , X ) }.
% 0.89/1.30 (5955) {G0,W9,D2,L3,V2,M3} { ! less_than( X, Y ), less_than( Y, X ),
% 0.89/1.30 strictly_less_than( X, Y ) }.
% 0.89/1.30 (5956) {G0,W3,D2,L1,V1,M1} { less_than( bottom, X ) }.
% 0.89/1.30 (5957) {G0,W2,D2,L1,V0,M1} { ! isnonempty_pq( create_pq ) }.
% 0.89/1.30 (5958) {G0,W4,D3,L1,V2,M1} { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.89/1.30 (5959) {G0,W3,D2,L1,V1,M1} { ! contains_pq( create_pq, X ) }.
% 0.89/1.30 (5960) {G0,W11,D3,L3,V3,M3} { ! contains_pq( insert_pq( X, Y ), Z ),
% 0.89/1.30 contains_pq( X, Z ), Y = Z }.
% 0.89/1.30 (5961) {G0,W8,D3,L2,V3,M2} { ! contains_pq( X, Z ), contains_pq( insert_pq
% 0.89/1.30 ( X, Y ), Z ) }.
% 0.89/1.30 (5962) {G0,W8,D3,L2,V3,M2} { ! Y = Z, contains_pq( insert_pq( X, Y ), Z )
% 0.89/1.30 }.
% 0.89/1.30 (5963) {G0,W9,D2,L3,V3,M3} { ! issmallestelement_pq( X, Y ), ! contains_pq
% 0.89/1.30 ( X, Z ), less_than( Y, Z ) }.
% 0.89/1.30 (5964) {G0,W8,D3,L2,V3,M2} { ! less_than( Y, skol1( Z, Y ) ),
% 0.89/1.30 issmallestelement_pq( X, Y ) }.
% 0.89/1.30 (5965) {G0,W8,D3,L2,V2,M2} { contains_pq( X, skol1( X, Y ) ),
% 0.89/1.30 issmallestelement_pq( X, Y ) }.
% 0.89/1.30 (5966) {G0,W7,D4,L1,V2,M1} { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 0.89/1.30 (5967) {G0,W17,D4,L3,V3,M3} { ! contains_pq( X, Z ), Y = Z, remove_pq(
% 0.89/1.30 insert_pq( X, Y ), Z ) = insert_pq( remove_pq( X, Z ), Y ) }.
% 0.89/1.30 (5968) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 0.89/1.30 issmallestelement_pq( X, Y ), findmin_pq_eff( X, Y ) = X }.
% 0.89/1.30 (5969) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 0.89/1.30 issmallestelement_pq( X, Y ), findmin_pq_res( X, Y ) = Y }.
% 0.89/1.30 (5970) {G0,W13,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 0.89/1.30 issmallestelement_pq( X, Y ), removemin_pq_eff( X, Y ) = remove_pq( X, Y
% 0.89/1.30 ) }.
% 0.89/1.30 (5971) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 0.89/1.30 issmallestelement_pq( X, Y ), removemin_pq_res( X, Y ) = Y }.
% 0.89/1.30 (5972) {G0,W11,D4,L1,V3,M1} { insert_pq( insert_pq( X, Y ), Z ) =
% 0.89/1.30 insert_pq( insert_pq( X, Z ), Y ) }.
% 0.89/1.30 (5973) {G0,W2,D2,L1,V0,M1} { ! isnonempty_slb( create_slb ) }.
% 0.89/1.30 (5974) {G0,W6,D4,L1,V3,M1} { isnonempty_slb( insert_slb( X, pair( Y, Z ) )
% 0.89/1.30 ) }.
% 0.89/1.30 (5975) {G0,W3,D2,L1,V1,M1} { ! contains_slb( create_slb, X ) }.
% 0.89/1.30 (5976) {G0,W13,D4,L3,V4,M3} { ! contains_slb( insert_slb( X, pair( Y, T )
% 0.89/1.30 ), Z ), contains_slb( X, Z ), Y = Z }.
% 0.89/1.30 (5977) {G0,W10,D4,L2,V4,M2} { ! contains_slb( X, Z ), contains_slb(
% 0.89/1.30 insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.89/1.30 (5978) {G0,W10,D4,L2,V4,M2} { ! Y = Z, contains_slb( insert_slb( X, pair(
% 0.89/1.30 Y, T ) ), Z ) }.
% 0.89/1.30 (5979) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 0.89/1.30 (5980) {G0,W17,D4,L3,V5,M3} { ! pair_in_list( insert_slb( X, pair( Y, T )
% 0.89/1.30 ), Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 0.89/1.30 (5981) {G0,W12,D4,L2,V5,M2} { ! pair_in_list( X, Z, U ), pair_in_list(
% 0.89/1.30 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.89/1.30 (5982) {G0,W13,D4,L2,V5,M2} { ! alpha1( Y, Z, T, U ), pair_in_list(
% 0.89/1.30 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.89/1.30 (5983) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.89/1.30 (5984) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.89/1.30 (5985) {G0,W11,D2,L3,V4,M3} { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.89/1.30 (5986) {G0,W9,D5,L1,V3,M1} { remove_slb( insert_slb( X, pair( Y, Z ) ), Y
% 0.89/1.30 ) = X }.
% 0.89/1.30 (5987) {G0,W21,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), remove_slb(
% 0.89/1.30 insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 0.89/1.30 ( Y, T ) ) }.
% 0.89/1.30 (5988) {G0,W9,D5,L1,V3,M1} { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y
% 0.89/1.30 ) = Z }.
% 0.89/1.30 (5989) {G0,W17,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), lookup_slb(
% 0.89/1.30 insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 0.89/1.30 (5990) {G0,W5,D3,L1,V1,M1} { update_slb( create_slb, X ) = create_slb }.
% 0.89/1.30 (5991) {G0,W18,D5,L2,V4,M2} { ! strictly_less_than( Y, X ), update_slb(
% 0.89/1.30 insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 0.89/1.30 ( T, X ) ) }.
% 0.89/1.30 (5992) {G0,W18,D5,L2,V4,M2} { ! less_than( X, Y ), update_slb( insert_slb
% 0.89/1.30 ( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 0.89/1.30 }.
% 0.89/1.30 (5993) {G0,W3,D2,L1,V1,M1} { succ_cpq( X, X ) }.
% 0.89/1.30 (5994) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq(
% 0.89/1.30 Y, Z ) ) }.
% 0.89/1.30 (5995) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq(
% 0.89/1.30 Y, Z ) ) }.
% 0.89/1.30 (5996) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.89/1.30 findmin_cpq_eff( Y ) ) }.
% 0.89/1.30 (5997) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.89/1.30 removemin_cpq_eff( Y ) ) }.
% 0.89/1.30 (5998) {G0,W5,D3,L1,V2,M1} { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.89/1.30 (5999) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z
% 0.89/1.30 , insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) )
% 0.89/1.30 }.
% 0.89/1.30 (6000) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z
% 0.89/1.30 , T, U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) )
% 0.89/1.30 }.
% 0.89/1.30 (6001) {G0,W12,D5,L2,V5,M2} { ! strictly_less_than( X, Y ), ! check_cpq(
% 0.89/1.30 triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.89/1.30 (6002) {G0,W13,D5,L3,V5,M3} { ! strictly_less_than( X, Y ), ! ||,
% 0.89/1.30 check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.89/1.30 (6003) {G0,W9,D3,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z ), T ),
% 0.89/1.30 contains_slb( Y, T ) }.
% 0.89/1.30 (6004) {G0,W9,D3,L2,V4,M2} { ! contains_slb( Y, T ), contains_cpq( triple
% 0.89/1.30 ( X, Y, Z ), T ) }.
% 0.89/1.30 (6005) {G0,W5,D3,L1,V2,M1} { ! ok( triple( X, Y, bad ) ) }.
% 0.89/1.30 (6006) {G0,W6,D3,L2,V2,M2} { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.89/1.30 (6007) {G0,W8,D3,L2,V3,M2} { ok( triple( Y, Z, X ) ), X = bad }.
% 0.89/1.30 (6008) {G0,W17,D5,L1,V4,M1} { insert_cpq( triple( X, Y, Z ), T ) = triple
% 0.89/1.30 ( insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.89/1.30 (6009) {G0,W14,D4,L2,V4,M2} { contains_slb( X, Y ), remove_cpq( triple( Z
% 0.89/1.30 , X, T ), Y ) = triple( Z, X, bad ) }.
% 0.89/1.30 (6010) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! less_than(
% 0.89/1.30 lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.89/1.30 remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 0.89/1.30 (6011) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! strictly_less_than
% 0.89/1.30 ( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.89/1.30 remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 0.89/1.30 (6012) {G0,W10,D4,L1,V2,M1} { findmin_cpq_eff( triple( X, create_slb, Y )
% 0.89/1.30 ) = triple( X, create_slb, bad ) }.
% 0.89/1.30 (6013) {G0,W20,D5,L3,V3,M3} { Y = create_slb, contains_slb( Y,
% 0.89/1.30 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 0.89/1.30 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.89/1.30 (6014) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.89/1.30 findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ),
% 0.89/1.30 lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 0.89/1.30 ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.89/1.30 (6015) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.89/1.30 findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 0.89/1.30 ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 0.89/1.30 ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 0.89/1.30 (6016) {G0,W7,D4,L1,V2,M1} { findmin_cpq_res( triple( X, create_slb, Y ) )
% 0.89/1.30 = bottom }.
% 0.89/1.30 (6017) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res( triple( Y,
% 0.89/1.30 X, Z ) ) = findmin_pqp_res( Y ) }.
% 0.89/1.30 (6018) {G0,W8,D4,L1,V1,M1} { removemin_cpq_eff( X ) = remove_cpq(
% 0.89/1.30 findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 0.89/1.30 (6019) {G0,W5,D3,L1,V1,M1} { removemin_cpq_res( X ) = findmin_cpq_res( X )
% 0.89/1.30 }.
% 0.89/1.30 (6020) {G0,W7,D4,L1,V2,M1} { i( triple( X, create_slb, Y ) ) = create_pq
% 0.89/1.30 }.
% 0.89/1.30 (6021) {G0,W17,D6,L1,V5,M1} { i( triple( X, insert_slb( Y, pair( T, U ) )
% 0.89/1.30 , Z ) ) = insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 0.89/1.30 (6022) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_remove( X, Y ), contains_pq( X, Y
% 0.89/1.30 ) }.
% 0.89/1.30 (6023) {G0,W6,D2,L2,V2,M2} { ! contains_pq( X, Y ), pi_sharp_remove( X, Y
% 0.89/1.30 ) }.
% 0.89/1.30 (6024) {G0,W7,D3,L2,V2,M2} { ! pi_remove( X, Y ), pi_sharp_remove( i( X )
% 0.89/1.30 , Y ) }.
% 0.89/1.30 (6025) {G0,W7,D3,L2,V2,M2} { ! pi_sharp_remove( i( X ), Y ), pi_remove( X
% 0.89/1.30 , Y ) }.
% 0.89/1.30 (6026) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ), contains_pq( X,
% 0.89/1.30 Y ) }.
% 0.89/1.30 (6027) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ),
% 0.89/1.30 issmallestelement_pq( X, Y ) }.
% 0.89/1.30 (6028) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.89/1.30 ( X, Y ), pi_sharp_find_min( X, Y ) }.
% 0.89/1.30 (6029) {G0,W7,D3,L2,V1,M2} { ! pi_find_min( X ), pi_sharp_find_min( i( X )
% 0.89/1.30 , skol2( X ) ) }.
% 0.89/1.30 (6030) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ), pi_find_min
% 0.89/1.30 ( X ) }.
% 0.89/1.30 (6031) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ), contains_pq( X
% 0.89/1.30 , Y ) }.
% 0.89/1.30 (6032) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ),
% 0.89/1.30 issmallestelement_pq( X, Y ) }.
% 0.89/1.30 (6033) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.89/1.30 ( X, Y ), pi_sharp_removemin( X, Y ) }.
% 0.89/1.30 (6034) {G0,W7,D3,L2,V1,M2} { ! pi_removemin( X ), pi_sharp_find_min( i( X
% 0.89/1.30 ), skol3( X ) ) }.
% 0.89/1.30 (6035) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ),
% 0.89/1.30 pi_removemin( X ) }.
% 0.89/1.30 (6036) {G0,W5,D3,L2,V2,M2} { ! phi( X ), alpha2( skol4( Y ) ) }.
% 0.89/1.30 (6037) {G0,W6,D3,L2,V1,M2} { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 0.89/1.30 (6038) {G0,W7,D2,L3,V2,M3} { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X )
% 0.89/1.30 }.
% 0.89/1.30 (6039) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ok( X ) }.
% 0.89/1.30 (6040) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), check_cpq( X ) }.
% 0.89/1.30 (6041) {G0,W6,D2,L3,V1,M3} { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 0.89/1.30 (6042) {G0,W17,D4,L2,V3,M2} { ! phi( findmin_cpq_eff( triple( X, Y, Z ) )
% 0.89/1.30 ), pi_sharp_find_min( i( triple( X, Y, Z ) ), findmin_cpq_res( triple( X
% 0.89/1.30 , Y, Z ) ) ) }.
% 0.89/1.30 (6043) {G0,W5,D3,L1,V0,M1} { pi_find_min( triple( skol5, skol6, skol7 ) )
% 0.89/1.30 }.
% 0.89/1.30 (6044) {G0,W6,D4,L1,V0,M1} { phi( findmin_cpq_eff( triple( skol5, skol6,
% 0.89/1.30 skol7 ) ) ) }.
% 0.89/1.30 (6045) {G0,W20,D5,L2,V1,M2} { ! pi_sharp_find_min( i( triple( skol5, skol6
% 0.89/1.30 , skol7 ) ), X ), ! findmin_cpq_res( triple( skol5, skol6, skol7 ) ) =
% 0.89/1.30 findmin_pq_res( i( triple( skol5, skol6, skol7 ) ), X ) }.
% 0.89/1.30
% 0.89/1.30
% 0.89/1.30 Total Proof:
% 0.89/1.30
% 0.89/1.30 subsumption: (9) {G0,W3,D2,L1,V1,M1} I { ! contains_pq( create_pq, X ) }.
% 0.89/1.30 parent0: (5959) {G0,W3,D2,L1,V1,M1} { ! contains_pq( create_pq, X ) }.
% 0.89/1.30 substitution0:
% 0.89/1.30 X := X
% 0.89/1.30 end
% 0.89/1.30 permutation0:
% 0.89/1.30 0 ==> 0
% 0.89/1.30 end
% 0.89/1.30
% 0.89/1.30 subsumption: (19) {G0,W11,D3,L3,V2,M3} I { ! contains_pq( X, Y ), !
% 0.89/1.30 issmallestelement_pq( X, Y ), findmin_pq_res( X, Y ) ==> Y }.
% 0.89/1.30 parent0: (5969) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 0.89/1.30 issmallestelement_pq( X, Y ), findmin_pq_res( X, Y ) = Y }.
% 0.89/1.30 substitution0:
% 0.89/1.30 X := X
% 0.89/1.30 Y := Y
% 0.89/1.30 end
% 0.89/1.30 permutation0:
% 0.89/1.30 0 ==> 0
% 0.89/1.30 1 ==> 1
% 0.89/1.30 2 ==> 2
% 0.89/1.30 end
% 0.89/1.30
% 0.89/1.30 subsumption: (67) {G0,W11,D4,L2,V3,M2} I { X = create_slb, findmin_cpq_res
% 0.89/1.30 ( triple( Y, X, Z ) ) ==> findmin_pqp_res( Y ) }.
% 0.89/1.30 parent0: (6017) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res(
% 0.89/1.30 triple( Y, X, Z ) ) = findmin_pqp_res( Y ) }.
% 0.89/1.30 substitution0:
% 0.89/1.30 X := X
% 0.89/1.30 Y := Y
% 0.89/1.30 Z := Z
% 0.89/1.30 end
% 0.89/1.30 permutation0:
% 0.89/1.30 0 ==> 0
% 0.89/1.30 1 ==> 1
% 0.89/1.30 end
% 0.89/1.30
% 0.89/1.30 subsumption: (70) {G0,W7,D4,L1,V2,M1} I { i( triple( X, create_slb, Y ) )
% 0.89/1.30 ==> create_pq }.
% 0.89/1.30 parent0: (6020) {G0,W7,D4,L1,V2,M1} { i( triple( X, create_slb, Y ) ) =
% 0.89/1.30 create_pq }.
% 0.89/1.30 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 Y := Y
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (76) {G0,W6,D2,L2,V2,M2} I { ! pi_sharp_find_min( X, Y ),
% 0.89/1.31 contains_pq( X, Y ) }.
% 0.89/1.31 parent0: (6026) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ),
% 0.89/1.31 contains_pq( X, Y ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 Y := Y
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 1 ==> 1
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (77) {G0,W6,D2,L2,V2,M2} I { ! pi_sharp_find_min( X, Y ),
% 0.89/1.31 issmallestelement_pq( X, Y ) }.
% 0.89/1.31 parent0: (6027) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ),
% 0.89/1.31 issmallestelement_pq( X, Y ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 Y := Y
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 1 ==> 1
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (79) {G0,W7,D3,L2,V1,M2} I { ! pi_find_min( X ),
% 0.89/1.31 pi_sharp_find_min( i( X ), skol2( X ) ) }.
% 0.89/1.31 parent0: (6029) {G0,W7,D3,L2,V1,M2} { ! pi_find_min( X ),
% 0.89/1.31 pi_sharp_find_min( i( X ), skol2( X ) ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 1 ==> 1
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (80) {G0,W6,D3,L2,V2,M2} I { ! pi_sharp_find_min( i( X ), Y )
% 0.89/1.31 , pi_find_min( X ) }.
% 0.89/1.31 parent0: (6030) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ),
% 0.89/1.31 pi_find_min( X ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 Y := Y
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 1 ==> 1
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (84) {G0,W7,D3,L2,V1,M2} I { ! pi_removemin( X ),
% 0.89/1.31 pi_sharp_find_min( i( X ), skol3( X ) ) }.
% 0.89/1.31 parent0: (6034) {G0,W7,D3,L2,V1,M2} { ! pi_removemin( X ),
% 0.89/1.31 pi_sharp_find_min( i( X ), skol3( X ) ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 1 ==> 1
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (85) {G0,W6,D3,L2,V2,M2} I { ! pi_sharp_find_min( i( X ), Y )
% 0.89/1.31 , pi_removemin( X ) }.
% 0.89/1.31 parent0: (6035) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ),
% 0.89/1.31 pi_removemin( X ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 Y := Y
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 1 ==> 1
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (92) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple(
% 0.89/1.31 X, Y, Z ) ) ), pi_sharp_find_min( i( triple( X, Y, Z ) ), findmin_cpq_res
% 0.89/1.31 ( triple( X, Y, Z ) ) ) }.
% 0.89/1.31 parent0: (6042) {G0,W17,D4,L2,V3,M2} { ! phi( findmin_cpq_eff( triple( X,
% 0.89/1.31 Y, Z ) ) ), pi_sharp_find_min( i( triple( X, Y, Z ) ), findmin_cpq_res(
% 0.89/1.31 triple( X, Y, Z ) ) ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 Y := Y
% 0.89/1.31 Z := Z
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 1 ==> 1
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (93) {G0,W5,D3,L1,V0,M1} I { pi_find_min( triple( skol5, skol6
% 0.89/1.31 , skol7 ) ) }.
% 0.89/1.31 parent0: (6043) {G0,W5,D3,L1,V0,M1} { pi_find_min( triple( skol5, skol6,
% 0.89/1.31 skol7 ) ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (94) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple(
% 0.89/1.31 skol5, skol6, skol7 ) ) ) }.
% 0.89/1.31 parent0: (6044) {G0,W6,D4,L1,V0,M1} { phi( findmin_cpq_eff( triple( skol5
% 0.89/1.31 , skol6, skol7 ) ) ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 eqswap: (6737) {G0,W20,D5,L2,V1,M2} { ! findmin_pq_res( i( triple( skol5,
% 0.89/1.31 skol6, skol7 ) ), X ) = findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 0.89/1.31 , ! pi_sharp_find_min( i( triple( skol5, skol6, skol7 ) ), X ) }.
% 0.89/1.31 parent0[1]: (6045) {G0,W20,D5,L2,V1,M2} { ! pi_sharp_find_min( i( triple(
% 0.89/1.31 skol5, skol6, skol7 ) ), X ), ! findmin_cpq_res( triple( skol5, skol6,
% 0.89/1.31 skol7 ) ) = findmin_pq_res( i( triple( skol5, skol6, skol7 ) ), X ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (95) {G0,W20,D5,L2,V1,M2} I { ! pi_sharp_find_min( i( triple(
% 0.89/1.31 skol5, skol6, skol7 ) ), X ), ! findmin_pq_res( i( triple( skol5, skol6,
% 0.89/1.31 skol7 ) ), X ) ==> findmin_cpq_res( triple( skol5, skol6, skol7 ) ) }.
% 0.89/1.31 parent0: (6737) {G0,W20,D5,L2,V1,M2} { ! findmin_pq_res( i( triple( skol5
% 0.89/1.31 , skol6, skol7 ) ), X ) = findmin_cpq_res( triple( skol5, skol6, skol7 )
% 0.89/1.31 ), ! pi_sharp_find_min( i( triple( skol5, skol6, skol7 ) ), X ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 1
% 0.89/1.31 1 ==> 0
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 resolution: (6738) {G1,W3,D2,L1,V1,M1} { ! pi_sharp_find_min( create_pq, X
% 0.89/1.31 ) }.
% 0.89/1.31 parent0[0]: (9) {G0,W3,D2,L1,V1,M1} I { ! contains_pq( create_pq, X ) }.
% 0.89/1.31 parent1[1]: (76) {G0,W6,D2,L2,V2,M2} I { ! pi_sharp_find_min( X, Y ),
% 0.89/1.31 contains_pq( X, Y ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 end
% 0.89/1.31 substitution1:
% 0.89/1.31 X := create_pq
% 0.89/1.31 Y := X
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (197) {G1,W3,D2,L1,V1,M1} R(76,9) { ! pi_sharp_find_min(
% 0.89/1.31 create_pq, X ) }.
% 0.89/1.31 parent0: (6738) {G1,W3,D2,L1,V1,M1} { ! pi_sharp_find_min( create_pq, X )
% 0.89/1.31 }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 end
% 0.89/1.31 permutation0:
% 0.89/1.31 0 ==> 0
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 eqswap: (6739) {G0,W11,D3,L3,V2,M3} { Y ==> findmin_pq_res( X, Y ), !
% 0.89/1.31 contains_pq( X, Y ), ! issmallestelement_pq( X, Y ) }.
% 0.89/1.31 parent0[2]: (19) {G0,W11,D3,L3,V2,M3} I { ! contains_pq( X, Y ), !
% 0.89/1.31 issmallestelement_pq( X, Y ), findmin_pq_res( X, Y ) ==> Y }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 Y := Y
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 resolution: (6740) {G1,W11,D3,L3,V2,M3} { X ==> findmin_pq_res( Y, X ), !
% 0.89/1.31 issmallestelement_pq( Y, X ), ! pi_sharp_find_min( Y, X ) }.
% 0.89/1.31 parent0[1]: (6739) {G0,W11,D3,L3,V2,M3} { Y ==> findmin_pq_res( X, Y ), !
% 0.89/1.31 contains_pq( X, Y ), ! issmallestelement_pq( X, Y ) }.
% 0.89/1.31 parent1[1]: (76) {G0,W6,D2,L2,V2,M2} I { ! pi_sharp_find_min( X, Y ),
% 0.89/1.31 contains_pq( X, Y ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := Y
% 0.89/1.31 Y := X
% 0.89/1.31 end
% 0.89/1.31 substitution1:
% 0.89/1.31 X := Y
% 0.89/1.31 Y := X
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 resolution: (6741) {G1,W11,D3,L3,V2,M3} { X ==> findmin_pq_res( Y, X ), !
% 0.89/1.31 pi_sharp_find_min( Y, X ), ! pi_sharp_find_min( Y, X ) }.
% 0.89/1.31 parent0[1]: (6740) {G1,W11,D3,L3,V2,M3} { X ==> findmin_pq_res( Y, X ), !
% 0.89/1.31 issmallestelement_pq( Y, X ), ! pi_sharp_find_min( Y, X ) }.
% 0.89/1.31 parent1[1]: (77) {G0,W6,D2,L2,V2,M2} I { ! pi_sharp_find_min( X, Y ),
% 0.89/1.31 issmallestelement_pq( X, Y ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 Y := Y
% 0.89/1.31 end
% 0.89/1.31 substitution1:
% 0.89/1.31 X := Y
% 0.89/1.31 Y := X
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 eqswap: (6742) {G1,W11,D3,L3,V2,M3} { findmin_pq_res( Y, X ) ==> X, !
% 0.89/1.31 pi_sharp_find_min( Y, X ), ! pi_sharp_find_min( Y, X ) }.
% 0.89/1.31 parent0[0]: (6741) {G1,W11,D3,L3,V2,M3} { X ==> findmin_pq_res( Y, X ), !
% 0.89/1.31 pi_sharp_find_min( Y, X ), ! pi_sharp_find_min( Y, X ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := X
% 0.89/1.31 Y := Y
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 factor: (6743) {G1,W8,D3,L2,V2,M2} { findmin_pq_res( X, Y ) ==> Y, !
% 0.89/1.31 pi_sharp_find_min( X, Y ) }.
% 0.89/1.31 parent0[1, 2]: (6742) {G1,W11,D3,L3,V2,M3} { findmin_pq_res( Y, X ) ==> X
% 0.89/1.31 , ! pi_sharp_find_min( Y, X ), ! pi_sharp_find_min( Y, X ) }.
% 0.89/1.31 substitution0:
% 0.89/1.31 X := Y
% 0.89/1.31 Y := X
% 0.89/1.31 end
% 0.89/1.31
% 0.89/1.31 subsumption: (410) {G1,W8,D3,L2,V2,M2} R(19,76);r(77) { findmin_pq_res( X,
% 0.89/1.31 Y ) ==> Y, ! pi_sharp_find_min( X, Y ) }.
% 0.89/1.31 parent0: (6743) {G1,W8,D3,L2,V2,M2} { findmin_pq_res( X, Y ) ==> Y, !
% 0.98/1.35 pi_sharp_find_min( X, Y ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := X
% 0.98/1.35 Y := Y
% 0.98/1.35 end
% 0.98/1.35 permutation0:
% 0.98/1.35 0 ==> 0
% 0.98/1.35 1 ==> 1
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 resolution: (6745) {G1,W4,D2,L2,V1,M2} { pi_find_min( X ), ! pi_removemin
% 0.98/1.35 ( X ) }.
% 0.98/1.35 parent0[0]: (80) {G0,W6,D3,L2,V2,M2} I { ! pi_sharp_find_min( i( X ), Y ),
% 0.98/1.35 pi_find_min( X ) }.
% 0.98/1.35 parent1[1]: (84) {G0,W7,D3,L2,V1,M2} I { ! pi_removemin( X ),
% 0.98/1.35 pi_sharp_find_min( i( X ), skol3( X ) ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := X
% 0.98/1.35 Y := skol3( X )
% 0.98/1.35 end
% 0.98/1.35 substitution1:
% 0.98/1.35 X := X
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 subsumption: (814) {G1,W4,D2,L2,V1,M2} R(84,80) { ! pi_removemin( X ),
% 0.98/1.35 pi_find_min( X ) }.
% 0.98/1.35 parent0: (6745) {G1,W4,D2,L2,V1,M2} { pi_find_min( X ), ! pi_removemin( X
% 0.98/1.35 ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := X
% 0.98/1.35 end
% 0.98/1.35 permutation0:
% 0.98/1.35 0 ==> 1
% 0.98/1.35 1 ==> 0
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 resolution: (6746) {G1,W7,D3,L2,V1,M2} { pi_sharp_find_min( i( X ), skol2
% 0.98/1.35 ( X ) ), ! pi_removemin( X ) }.
% 0.98/1.35 parent0[0]: (79) {G0,W7,D3,L2,V1,M2} I { ! pi_find_min( X ),
% 0.98/1.35 pi_sharp_find_min( i( X ), skol2( X ) ) }.
% 0.98/1.35 parent1[1]: (814) {G1,W4,D2,L2,V1,M2} R(84,80) { ! pi_removemin( X ),
% 0.98/1.35 pi_find_min( X ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := X
% 0.98/1.35 end
% 0.98/1.35 substitution1:
% 0.98/1.35 X := X
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 subsumption: (867) {G2,W7,D3,L2,V1,M2} R(79,814) { pi_sharp_find_min( i( X
% 0.98/1.35 ), skol2( X ) ), ! pi_removemin( X ) }.
% 0.98/1.35 parent0: (6746) {G1,W7,D3,L2,V1,M2} { pi_sharp_find_min( i( X ), skol2( X
% 0.98/1.35 ) ), ! pi_removemin( X ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := X
% 0.98/1.35 end
% 0.98/1.35 permutation0:
% 0.98/1.35 0 ==> 0
% 0.98/1.35 1 ==> 1
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 resolution: (6747) {G1,W4,D2,L2,V1,M2} { pi_removemin( X ), ! pi_find_min
% 0.98/1.35 ( X ) }.
% 0.98/1.35 parent0[0]: (85) {G0,W6,D3,L2,V2,M2} I { ! pi_sharp_find_min( i( X ), Y ),
% 0.98/1.35 pi_removemin( X ) }.
% 0.98/1.35 parent1[1]: (79) {G0,W7,D3,L2,V1,M2} I { ! pi_find_min( X ),
% 0.98/1.35 pi_sharp_find_min( i( X ), skol2( X ) ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := X
% 0.98/1.35 Y := skol2( X )
% 0.98/1.35 end
% 0.98/1.35 substitution1:
% 0.98/1.35 X := X
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 subsumption: (870) {G1,W4,D2,L2,V1,M2} R(79,85) { ! pi_find_min( X ),
% 0.98/1.35 pi_removemin( X ) }.
% 0.98/1.35 parent0: (6747) {G1,W4,D2,L2,V1,M2} { pi_removemin( X ), ! pi_find_min( X
% 0.98/1.35 ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := X
% 0.98/1.35 end
% 0.98/1.35 permutation0:
% 0.98/1.35 0 ==> 1
% 0.98/1.35 1 ==> 0
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 resolution: (6748) {G1,W5,D3,L1,V0,M1} { pi_removemin( triple( skol5,
% 0.98/1.35 skol6, skol7 ) ) }.
% 0.98/1.35 parent0[0]: (870) {G1,W4,D2,L2,V1,M2} R(79,85) { ! pi_find_min( X ),
% 0.98/1.35 pi_removemin( X ) }.
% 0.98/1.35 parent1[0]: (93) {G0,W5,D3,L1,V0,M1} I { pi_find_min( triple( skol5, skol6
% 0.98/1.35 , skol7 ) ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := triple( skol5, skol6, skol7 )
% 0.98/1.35 end
% 0.98/1.35 substitution1:
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 subsumption: (892) {G2,W5,D3,L1,V0,M1} R(870,93) { pi_removemin( triple(
% 0.98/1.35 skol5, skol6, skol7 ) ) }.
% 0.98/1.35 parent0: (6748) {G1,W5,D3,L1,V0,M1} { pi_removemin( triple( skol5, skol6,
% 0.98/1.35 skol7 ) ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 end
% 0.98/1.35 permutation0:
% 0.98/1.35 0 ==> 0
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 paramod: (6750) {G1,W12,D4,L2,V2,M2} { pi_sharp_find_min( create_pq, skol2
% 0.98/1.35 ( triple( X, create_slb, Y ) ) ), ! pi_removemin( triple( X, create_slb,
% 0.98/1.35 Y ) ) }.
% 0.98/1.35 parent0[0]: (70) {G0,W7,D4,L1,V2,M1} I { i( triple( X, create_slb, Y ) )
% 0.98/1.35 ==> create_pq }.
% 0.98/1.35 parent1[0; 1]: (867) {G2,W7,D3,L2,V1,M2} R(79,814) { pi_sharp_find_min( i(
% 0.98/1.35 X ), skol2( X ) ), ! pi_removemin( X ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := X
% 0.98/1.35 Y := Y
% 0.98/1.35 end
% 0.98/1.35 substitution1:
% 0.98/1.35 X := triple( X, create_slb, Y )
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 resolution: (6751) {G2,W5,D3,L1,V2,M1} { ! pi_removemin( triple( X,
% 0.98/1.35 create_slb, Y ) ) }.
% 0.98/1.35 parent0[0]: (197) {G1,W3,D2,L1,V1,M1} R(76,9) { ! pi_sharp_find_min(
% 0.98/1.35 create_pq, X ) }.
% 0.98/1.35 parent1[0]: (6750) {G1,W12,D4,L2,V2,M2} { pi_sharp_find_min( create_pq,
% 0.98/1.35 skol2( triple( X, create_slb, Y ) ) ), ! pi_removemin( triple( X,
% 0.98/1.35 create_slb, Y ) ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := skol2( triple( X, create_slb, Y ) )
% 0.98/1.35 end
% 0.98/1.35 substitution1:
% 0.98/1.35 X := X
% 0.98/1.35 Y := Y
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 subsumption: (2231) {G3,W5,D3,L1,V2,M1} P(70,867);r(197) { ! pi_removemin(
% 0.98/1.35 triple( X, create_slb, Y ) ) }.
% 0.98/1.35 parent0: (6751) {G2,W5,D3,L1,V2,M1} { ! pi_removemin( triple( X,
% 0.98/1.35 create_slb, Y ) ) }.
% 0.98/1.35 substitution0:
% 0.98/1.35 X := X
% 0.98/1.35 Y := Y
% 0.98/1.35 end
% 0.98/1.35 permutation0:
% 0.98/1.35 0 ==> 0
% 0.98/1.35 end
% 0.98/1.35
% 0.98/1.35 *** allocated 15000 integers for justifications
% 0.98/1.35 *** allocated 22500 integers for justifications
% 0.98/1.35 *** allocated 33750 integers for justifications
% 0.98/1.35 *** allocated 50625 integers for justifications
% 0.98/1.35 *** allocated 256285 integers for termspaCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------