TSTP Solution File: SWV372+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV372+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.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 16:24:37 EDT 2022
% Result : Theorem 5.58s 5.97s
% Output : Refutation 5.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV372+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Tue Jun 14 14:55:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.09 *** allocated 10000 integers for termspace/termends
% 0.71/1.09 *** allocated 10000 integers for clauses
% 0.71/1.09 *** allocated 10000 integers for justifications
% 0.71/1.09 Bliksem 1.12
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 Automatic Strategy Selection
% 0.71/1.09
% 0.71/1.09
% 0.71/1.09 Clauses:
% 0.71/1.09
% 0.71/1.09 { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.71/1.09 { less_than( X, Y ), less_than( Y, X ) }.
% 0.71/1.09 { less_than( X, X ) }.
% 0.71/1.09 { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.71/1.09 { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.71/1.09 { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.71/1.09 { less_than( bottom, X ) }.
% 0.71/1.09 { ! isnonempty_pq( create_pq ) }.
% 0.71/1.09 { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.71/1.09 { ! contains_pq( create_pq, X ) }.
% 0.71/1.09 { ! contains_pq( insert_pq( X, Y ), Z ), contains_pq( X, Z ), Y = Z }.
% 0.71/1.09 { ! contains_pq( X, Z ), contains_pq( insert_pq( X, Y ), Z ) }.
% 0.71/1.09 { ! Y = Z, contains_pq( insert_pq( X, Y ), Z ) }.
% 0.71/1.09 { ! issmallestelement_pq( X, Y ), ! contains_pq( X, Z ), less_than( Y, Z )
% 0.71/1.09 }.
% 0.71/1.09 { ! less_than( Y, skol1( Z, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.71/1.09 { contains_pq( X, skol1( X, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.71/1.09 { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 0.71/1.09 { ! contains_pq( X, Z ), Y = Z, remove_pq( insert_pq( X, Y ), Z ) =
% 0.71/1.09 insert_pq( remove_pq( X, Z ), Y ) }.
% 0.71/1.09 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_eff( X
% 0.71/1.09 , Y ) = X }.
% 0.71/1.09 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_res( X
% 0.71/1.09 , Y ) = Y }.
% 0.71/1.09 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_eff(
% 0.71/1.09 X, Y ) = remove_pq( X, Y ) }.
% 0.71/1.09 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_res(
% 0.71/1.09 X, Y ) = Y }.
% 0.71/1.09 { insert_pq( insert_pq( X, Y ), Z ) = insert_pq( insert_pq( X, Z ), Y ) }.
% 0.71/1.09 { ! isnonempty_slb( create_slb ) }.
% 0.71/1.09 { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) ) }.
% 0.71/1.09 { ! contains_slb( create_slb, X ) }.
% 0.71/1.09 { ! contains_slb( insert_slb( X, pair( Y, T ) ), Z ), contains_slb( X, Z )
% 0.71/1.09 , Y = Z }.
% 0.71/1.09 { ! contains_slb( X, Z ), contains_slb( insert_slb( X, pair( Y, T ) ), Z )
% 0.71/1.09 }.
% 0.71/1.09 { ! Y = Z, contains_slb( insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.71/1.09 { ! pair_in_list( create_slb, X, Y ) }.
% 0.71/1.09 { ! pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U ), pair_in_list( X, Z
% 0.71/1.09 , U ), alpha1( Y, Z, T, U ) }.
% 0.71/1.09 { ! pair_in_list( X, Z, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z
% 0.71/1.09 , U ) }.
% 0.71/1.09 { ! alpha1( Y, Z, T, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U
% 0.71/1.09 ) }.
% 0.71/1.09 { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.71/1.09 { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.71/1.09 { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.71/1.09 { remove_slb( insert_slb( X, pair( Y, Z ) ), Y ) = X }.
% 0.71/1.09 { Y = Z, ! contains_slb( X, Z ), remove_slb( insert_slb( X, pair( Y, T ) )
% 0.71/1.09 , Z ) = insert_slb( remove_slb( X, Z ), pair( Y, T ) ) }.
% 0.71/1.09 { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y ) = Z }.
% 0.71/1.09 { Y = Z, ! contains_slb( X, Z ), lookup_slb( insert_slb( X, pair( Y, T ) )
% 0.71/1.09 , Z ) = lookup_slb( X, Z ) }.
% 0.71/1.09 { update_slb( create_slb, X ) = create_slb }.
% 0.71/1.09 { ! strictly_less_than( Y, X ), update_slb( insert_slb( Z, pair( T, Y ) ),
% 0.71/1.09 X ) = insert_slb( update_slb( Z, X ), pair( T, X ) ) }.
% 0.71/1.09 { ! less_than( X, Y ), update_slb( insert_slb( Z, pair( T, Y ) ), X ) =
% 0.71/1.09 insert_slb( update_slb( Z, X ), pair( T, Y ) ) }.
% 0.71/1.09 { succ_cpq( X, X ) }.
% 0.71/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y, Z ) ) }.
% 0.71/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y, Z ) ) }.
% 0.71/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, findmin_cpq_eff( Y ) ) }.
% 0.71/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, removemin_cpq_eff( Y ) ) }.
% 0.71/1.09 { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.71/1.09 { ! less_than( Y, X ), ! check_cpq( triple( Z, insert_slb( T, pair( X, Y )
% 0.71/1.09 ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.71/1.09 { ! less_than( Y, X ), ! check_cpq( triple( Z, T, U ) ), check_cpq( triple
% 0.71/1.09 ( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.71/1.09 { ! strictly_less_than( X, Y ), ! check_cpq( triple( Z, insert_slb( T, pair
% 0.71/1.09 ( X, Y ) ), U ) ) }.
% 0.71/1.09 { ! strictly_less_than( X, Y ), ! ||, check_cpq( triple( Z, insert_slb( T,
% 0.71/1.09 pair( X, Y ) ), U ) ) }.
% 0.71/1.09 { ! contains_cpq( triple( X, Y, Z ), T ), contains_slb( Y, T ) }.
% 0.71/1.09 { ! contains_slb( Y, T ), contains_cpq( triple( X, Y, Z ), T ) }.
% 0.71/1.09 { ! ok( triple( X, Y, bad ) ) }.
% 0.71/1.09 { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.71/1.09 { ok( triple( Y, Z, X ) ), X = bad }.
% 0.71/1.13 { insert_cpq( triple( X, Y, Z ), T ) = triple( insert_pqp( X, T ),
% 0.71/1.13 insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.71/1.13 { contains_slb( X, Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( Z, X,
% 0.71/1.13 bad ) }.
% 0.71/1.13 { ! contains_slb( X, Y ), ! less_than( lookup_slb( X, Y ), Y ), remove_cpq
% 0.71/1.13 ( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y )
% 0.71/1.13 , T ) }.
% 0.71/1.13 { ! contains_slb( X, Y ), ! strictly_less_than( Y, lookup_slb( X, Y ) ),
% 0.71/1.13 remove_cpq( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ),
% 0.71/1.13 remove_slb( X, Y ), bad ) }.
% 0.71/1.13 { findmin_cpq_eff( triple( X, create_slb, Y ) ) = triple( X, create_slb,
% 0.71/1.13 bad ) }.
% 0.71/1.13 { Y = create_slb, contains_slb( Y, findmin_pqp_res( X ) ), findmin_cpq_eff
% 0.71/1.13 ( triple( X, Y, Z ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) )
% 0.71/1.13 , bad ) }.
% 0.71/1.13 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), !
% 0.71/1.13 strictly_less_than( findmin_pqp_res( X ), lookup_slb( Y, findmin_pqp_res
% 0.71/1.13 ( X ) ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb(
% 0.71/1.13 Y, findmin_pqp_res( X ) ), bad ) }.
% 0.71/1.13 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! less_than(
% 0.71/1.13 lookup_slb( Y, findmin_pqp_res( X ) ), findmin_pqp_res( X ) ),
% 0.71/1.13 findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( Y,
% 0.71/1.13 findmin_pqp_res( X ) ), Z ) }.
% 0.71/1.13 { findmin_cpq_res( triple( X, create_slb, Y ) ) = bottom }.
% 0.71/1.13 { X = create_slb, findmin_cpq_res( triple( Y, X, Z ) ) = findmin_pqp_res( Y
% 0.71/1.13 ) }.
% 0.71/1.13 { removemin_cpq_eff( X ) = remove_cpq( findmin_cpq_eff( X ),
% 0.71/1.13 findmin_cpq_res( X ) ) }.
% 0.71/1.13 { removemin_cpq_res( X ) = findmin_cpq_res( X ) }.
% 0.71/1.13 { i( triple( X, create_slb, Y ) ) = create_pq }.
% 0.71/1.13 { i( triple( X, insert_slb( Y, pair( T, U ) ), Z ) ) = insert_pq( i( triple
% 0.71/1.13 ( X, Y, Z ) ), T ) }.
% 0.71/1.13 { ! pi_sharp_remove( X, Y ), contains_pq( X, Y ) }.
% 0.71/1.13 { ! contains_pq( X, Y ), pi_sharp_remove( X, Y ) }.
% 0.71/1.13 { ! pi_remove( X, Y ), pi_sharp_remove( i( X ), Y ) }.
% 0.71/1.13 { ! pi_sharp_remove( i( X ), Y ), pi_remove( X, Y ) }.
% 0.71/1.13 { ! pi_sharp_find_min( X, Y ), contains_pq( X, Y ) }.
% 0.71/1.13 { ! pi_sharp_find_min( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.71/1.13 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_find_min
% 0.71/1.13 ( X, Y ) }.
% 0.71/1.13 { ! pi_find_min( X ), pi_sharp_find_min( i( X ), skol2( X ) ) }.
% 0.71/1.13 { ! pi_sharp_find_min( i( X ), Y ), pi_find_min( X ) }.
% 0.71/1.13 { ! pi_sharp_removemin( X, Y ), contains_pq( X, Y ) }.
% 0.71/1.13 { ! pi_sharp_removemin( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.71/1.13 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_removemin
% 0.71/1.13 ( X, Y ) }.
% 0.71/1.13 { ! pi_removemin( X ), pi_sharp_find_min( i( X ), skol3( X ) ) }.
% 0.71/1.13 { ! pi_sharp_find_min( i( X ), Y ), pi_removemin( X ) }.
% 0.71/1.13 { ! phi( X ), alpha2( skol4( Y ) ) }.
% 0.71/1.13 { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 0.71/1.13 { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X ) }.
% 0.71/1.13 { ! alpha2( X ), ok( X ) }.
% 0.71/1.13 { ! alpha2( X ), check_cpq( X ) }.
% 0.71/1.13 { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 0.71/1.13 { ! contains_cpq( triple( X, Y, Z ), T ), contains_pq( i( triple( X, Y, Z )
% 0.71/1.13 ), T ) }.
% 0.71/1.13 { ! contains_pq( i( triple( X, Y, Z ) ), T ), contains_cpq( triple( X, Y, Z
% 0.71/1.13 ), T ) }.
% 0.71/1.13 { contains_cpq( triple( X, Y, Z ), findmin_cpq_res( triple( X, Y, Z ) ) ),
% 0.71/1.13 ! ok( findmin_cpq_eff( triple( X, Y, Z ) ) ) }.
% 0.71/1.13 { ok( triple( X, Y, Z ) ), ! phi( triple( X, Y, Z ) ) }.
% 0.71/1.13 { phi( findmin_cpq_eff( triple( skol5, skol6, skol7 ) ) ) }.
% 0.71/1.13 { ! contains_pq( i( triple( skol5, skol6, skol7 ) ), findmin_cpq_res(
% 0.71/1.13 triple( skol5, skol6, skol7 ) ) ) }.
% 0.71/1.13
% 0.71/1.13 percentage equality = 0.222222, percentage horn = 0.846939
% 0.71/1.13 This is a problem with some equality
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13 Options Used:
% 0.71/1.13
% 0.71/1.13 useres = 1
% 0.71/1.13 useparamod = 1
% 0.71/1.13 useeqrefl = 1
% 0.71/1.13 useeqfact = 1
% 0.71/1.13 usefactor = 1
% 0.71/1.13 usesimpsplitting = 0
% 0.71/1.13 usesimpdemod = 5
% 0.71/1.13 usesimpres = 3
% 0.71/1.13
% 0.71/1.13 resimpinuse = 1000
% 0.71/1.13 resimpclauses = 20000
% 0.71/1.13 substype = eqrewr
% 0.71/1.13 backwardsubs = 1
% 0.71/1.13 selectoldest = 5
% 0.71/1.13
% 0.71/1.13 litorderings [0] = split
% 0.71/1.13 litorderings [1] = extend the termordering, first sorting on arguments
% 0.71/1.13
% 0.71/1.13 termordering = kbo
% 0.71/1.13
% 0.71/1.13 litapriori = 0
% 0.71/1.13 termapriori = 1
% 0.71/1.13 litaposteriori = 0
% 0.71/1.13 termaposteriori = 0
% 0.71/1.13 demodaposteriori = 0
% 0.71/1.13 ordereqreflfact = 0
% 0.71/1.13
% 0.71/1.13 litselect = negord
% 0.71/1.13
% 0.71/1.13 maxweight = 15
% 0.71/1.13 maxdepth = 30000
% 5.58/5.97 maxlength = 115
% 5.58/5.97 maxnrvars = 195
% 5.58/5.97 excuselevel = 1
% 5.58/5.97 increasemaxweight = 1
% 5.58/5.97
% 5.58/5.97 maxselected = 10000000
% 5.58/5.97 maxnrclauses = 10000000
% 5.58/5.97
% 5.58/5.97 showgenerated = 0
% 5.58/5.97 showkept = 0
% 5.58/5.97 showselected = 0
% 5.58/5.97 showdeleted = 0
% 5.58/5.97 showresimp = 1
% 5.58/5.97 showstatus = 2000
% 5.58/5.97
% 5.58/5.97 prologoutput = 0
% 5.58/5.97 nrgoals = 5000000
% 5.58/5.97 totalproof = 1
% 5.58/5.97
% 5.58/5.97 Symbols occurring in the translation:
% 5.58/5.97
% 5.58/5.97 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 5.58/5.97 . [1, 2] (w:1, o:40, a:1, s:1, b:0),
% 5.58/5.97 || [2, 0] (w:1, o:3, a:1, s:1, b:0),
% 5.58/5.97 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 5.58/5.97 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.58/5.97 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.58/5.97 less_than [38, 2] (w:1, o:64, a:1, s:1, b:0),
% 5.58/5.97 strictly_less_than [39, 2] (w:1, o:71, a:1, s:1, b:0),
% 5.58/5.97 bottom [40, 0] (w:1, o:9, a:1, s:1, b:0),
% 5.58/5.97 create_pq [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 5.58/5.97 isnonempty_pq [42, 1] (w:1, o:23, a:1, s:1, b:0),
% 5.58/5.97 insert_pq [43, 2] (w:1, o:72, a:1, s:1, b:0),
% 5.58/5.97 contains_pq [44, 2] (w:1, o:73, a:1, s:1, b:0),
% 5.58/5.97 issmallestelement_pq [45, 2] (w:1, o:74, a:1, s:1, b:0),
% 5.58/5.97 remove_pq [46, 2] (w:1, o:65, a:1, s:1, b:0),
% 5.58/5.97 findmin_pq_eff [47, 2] (w:1, o:75, a:1, s:1, b:0),
% 5.58/5.97 findmin_pq_res [48, 2] (w:1, o:76, a:1, s:1, b:0),
% 5.58/5.97 removemin_pq_eff [49, 2] (w:1, o:66, a:1, s:1, b:0),
% 5.58/5.97 removemin_pq_res [50, 2] (w:1, o:67, a:1, s:1, b:0),
% 5.58/5.97 create_slb [51, 0] (w:1, o:12, a:1, s:1, b:0),
% 5.58/5.97 isnonempty_slb [52, 1] (w:1, o:24, a:1, s:1, b:0),
% 5.58/5.97 pair [53, 2] (w:1, o:77, a:1, s:1, b:0),
% 5.58/5.97 insert_slb [54, 2] (w:1, o:78, a:1, s:1, b:0),
% 5.58/5.97 contains_slb [55, 2] (w:1, o:79, a:1, s:1, b:0),
% 5.58/5.97 pair_in_list [57, 3] (w:1, o:91, a:1, s:1, b:0),
% 5.58/5.97 remove_slb [59, 2] (w:1, o:68, a:1, s:1, b:0),
% 5.58/5.97 lookup_slb [60, 2] (w:1, o:80, a:1, s:1, b:0),
% 5.58/5.97 update_slb [61, 2] (w:1, o:81, a:1, s:1, b:0),
% 5.58/5.97 succ_cpq [62, 2] (w:1, o:82, a:1, s:1, b:0),
% 5.58/5.97 insert_cpq [63, 2] (w:1, o:83, a:1, s:1, b:0),
% 5.58/5.97 remove_cpq [64, 2] (w:1, o:69, a:1, s:1, b:0),
% 5.58/5.97 findmin_cpq_eff [65, 1] (w:1, o:25, a:1, s:1, b:0),
% 5.58/5.97 removemin_cpq_eff [66, 1] (w:1, o:26, a:1, s:1, b:0),
% 5.58/5.97 triple [67, 3] (w:1, o:92, a:1, s:1, b:0),
% 5.58/5.97 check_cpq [68, 1] (w:1, o:27, a:1, s:1, b:0),
% 5.58/5.97 contains_cpq [69, 2] (w:1, o:84, a:1, s:1, b:0),
% 5.58/5.97 bad [70, 0] (w:1, o:10, a:1, s:1, b:0),
% 5.58/5.97 ok [71, 1] (w:1, o:28, a:1, s:1, b:0),
% 5.58/5.97 insert_pqp [72, 2] (w:1, o:85, a:1, s:1, b:0),
% 5.58/5.97 remove_pqp [73, 2] (w:1, o:70, a:1, s:1, b:0),
% 5.58/5.97 findmin_pqp_res [74, 1] (w:1, o:29, a:1, s:1, b:0),
% 5.58/5.97 findmin_cpq_res [75, 1] (w:1, o:30, a:1, s:1, b:0),
% 5.58/5.97 removemin_cpq_res [76, 1] (w:1, o:31, a:1, s:1, b:0),
% 5.58/5.97 i [77, 1] (w:1, o:32, a:1, s:1, b:0),
% 5.58/5.97 pi_sharp_remove [78, 2] (w:1, o:87, a:1, s:1, b:0),
% 5.58/5.97 pi_remove [79, 2] (w:1, o:86, a:1, s:1, b:0),
% 5.58/5.97 pi_sharp_find_min [80, 2] (w:1, o:88, a:1, s:1, b:0),
% 5.58/5.97 pi_find_min [81, 1] (w:1, o:34, a:1, s:1, b:0),
% 5.58/5.97 pi_sharp_removemin [82, 2] (w:1, o:89, a:1, s:1, b:0),
% 5.58/5.97 pi_removemin [83, 1] (w:1, o:35, a:1, s:1, b:0),
% 5.58/5.97 phi [84, 1] (w:1, o:33, a:1, s:1, b:0),
% 5.58/5.97 alpha1 [85, 4] (w:1, o:93, a:1, s:1, b:1),
% 5.58/5.97 alpha2 [86, 1] (w:1, o:36, a:1, s:1, b:1),
% 5.58/5.97 skol1 [87, 2] (w:1, o:90, a:1, s:1, b:1),
% 5.58/5.97 skol2 [88, 1] (w:1, o:37, a:1, s:1, b:1),
% 5.58/5.97 skol3 [89, 1] (w:1, o:38, a:1, s:1, b:1),
% 5.58/5.97 skol4 [90, 1] (w:1, o:39, a:1, s:1, b:1),
% 5.58/5.97 skol5 [91, 0] (w:1, o:15, a:1, s:1, b:1),
% 5.58/5.97 skol6 [92, 0] (w:1, o:16, a:1, s:1, b:1),
% 5.58/5.97 skol7 [93, 0] (w:1, o:17, a:1, s:1, b:1).
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Starting Search:
% 5.58/5.97
% 5.58/5.97 *** allocated 15000 integers for clauses
% 5.58/5.97 *** allocated 22500 integers for clauses
% 5.58/5.97 *** allocated 33750 integers for clauses
% 5.58/5.97 *** allocated 15000 integers for termspace/termends
% 5.58/5.97 *** allocated 50625 integers for clauses
% 5.58/5.97 *** allocated 22500 integers for termspace/termends
% 5.58/5.97 *** allocated 75937 integers for clauses
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 33750 integers for termspace/termends
% 5.58/5.97 *** allocated 113905 integers for clauses
% 5.58/5.97 *** allocated 50625 integers for termspace/termends
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 3991
% 5.58/5.97 Kept: 2058
% 5.58/5.97 Inuse: 160
% 5.58/5.97 Deleted: 4
% 5.58/5.97 Deletedinuse: 3
% 5.58/5.97
% 5.58/5.97 *** allocated 170857 integers for clauses
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 75937 integers for termspace/termends
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 256285 integers for clauses
% 5.58/5.97 *** allocated 113905 integers for termspace/termends
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 8175
% 5.58/5.97 Kept: 4194
% 5.58/5.97 Inuse: 235
% 5.58/5.97 Deleted: 4
% 5.58/5.97 Deletedinuse: 3
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 384427 integers for clauses
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 170857 integers for termspace/termends
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 13234
% 5.58/5.97 Kept: 6271
% 5.58/5.97 Inuse: 295
% 5.58/5.97 Deleted: 6
% 5.58/5.97 Deletedinuse: 5
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 576640 integers for clauses
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 21526
% 5.58/5.97 Kept: 8736
% 5.58/5.97 Inuse: 355
% 5.58/5.97 Deleted: 7
% 5.58/5.97 Deletedinuse: 6
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 256285 integers for termspace/termends
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 34892
% 5.58/5.97 Kept: 10752
% 5.58/5.97 Inuse: 491
% 5.58/5.97 Deleted: 13
% 5.58/5.97 Deletedinuse: 6
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 864960 integers for clauses
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 45918
% 5.58/5.97 Kept: 12755
% 5.58/5.97 Inuse: 569
% 5.58/5.97 Deleted: 15
% 5.58/5.97 Deletedinuse: 6
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 54379
% 5.58/5.97 Kept: 14989
% 5.58/5.97 Inuse: 594
% 5.58/5.97 Deleted: 15
% 5.58/5.97 Deletedinuse: 6
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 384427 integers for termspace/termends
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 65994
% 5.58/5.97 Kept: 18613
% 5.58/5.97 Inuse: 636
% 5.58/5.97 Deleted: 15
% 5.58/5.97 Deletedinuse: 6
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 1297440 integers for clauses
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 Resimplifying clauses:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 70390
% 5.58/5.97 Kept: 20699
% 5.58/5.97 Inuse: 648
% 5.58/5.97 Deleted: 410
% 5.58/5.97 Deletedinuse: 6
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 77409
% 5.58/5.97 Kept: 22819
% 5.58/5.97 Inuse: 667
% 5.58/5.97 Deleted: 412
% 5.58/5.97 Deletedinuse: 8
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 576640 integers for termspace/termends
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 83868
% 5.58/5.97 Kept: 24819
% 5.58/5.97 Inuse: 696
% 5.58/5.97 Deleted: 412
% 5.58/5.97 Deletedinuse: 8
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 93748
% 5.58/5.97 Kept: 26873
% 5.58/5.97 Inuse: 743
% 5.58/5.97 Deleted: 412
% 5.58/5.97 Deletedinuse: 8
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 102301
% 5.58/5.97 Kept: 28874
% 5.58/5.97 Inuse: 767
% 5.58/5.97 Deleted: 412
% 5.58/5.97 Deletedinuse: 8
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 1946160 integers for clauses
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 114047
% 5.58/5.97 Kept: 30882
% 5.58/5.97 Inuse: 824
% 5.58/5.97 Deleted: 412
% 5.58/5.97 Deletedinuse: 8
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 126881
% 5.58/5.97 Kept: 32919
% 5.58/5.97 Inuse: 866
% 5.58/5.97 Deleted: 412
% 5.58/5.97 Deletedinuse: 8
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 141247
% 5.58/5.97 Kept: 36177
% 5.58/5.97 Inuse: 910
% 5.58/5.97 Deleted: 412
% 5.58/5.97 Deletedinuse: 8
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 *** allocated 864960 integers for termspace/termends
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 150303
% 5.58/5.97 Kept: 38209
% 5.58/5.97 Inuse: 929
% 5.58/5.97 Deleted: 413
% 5.58/5.97 Deletedinuse: 9
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97 Resimplifying inuse:
% 5.58/5.97 Done
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Intermediate Status:
% 5.58/5.97 Generated: 162074
% 5.58/5.97 Kept: 40230
% 5.58/5.97 Inuse: 973
% 5.58/5.97 Deleted: 417
% 5.58/5.97 Deletedinuse: 10
% 5.58/5.97
% 5.58/5.97 Resimplifying clauses:
% 5.58/5.97
% 5.58/5.97 Bliksems!, er is een bewijs:
% 5.58/5.97 % SZS status Theorem
% 5.58/5.97 % SZS output start Refutation
% 5.58/5.97
% 5.58/5.97 (54) {G0,W9,D3,L2,V4,M2} I { ! contains_slb( Y, T ), contains_cpq( triple(
% 5.58/5.97 X, Y, Z ), T ) }.
% 5.58/5.97 (55) {G0,W5,D3,L1,V2,M1} I { ! ok( triple( X, Y, bad ) ) }.
% 5.58/5.97 (62) {G0,W10,D4,L1,V2,M1} I { findmin_cpq_eff( triple( X, create_slb, Y ) )
% 5.58/5.97 ==> triple( X, create_slb, bad ) }.
% 5.58/5.97 (63) {G0,W20,D5,L3,V3,M3} I { Y = create_slb, contains_slb( Y,
% 5.58/5.97 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 5.58/5.97 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 5.58/5.97 (67) {G0,W11,D4,L2,V3,M2} I { X = create_slb, findmin_cpq_res( triple( Y, X
% 5.58/5.97 , Z ) ) ==> findmin_pqp_res( Y ) }.
% 5.58/5.97 (92) {G0,W13,D4,L2,V4,M2} I { ! contains_cpq( triple( X, Y, Z ), T ),
% 5.58/5.97 contains_pq( i( triple( X, Y, Z ) ), T ) }.
% 5.58/5.97 (95) {G0,W10,D3,L2,V3,M2} I { ok( triple( X, Y, Z ) ), ! phi( triple( X, Y
% 5.58/5.97 , Z ) ) }.
% 5.58/5.97 (96) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple( skol5, skol6,
% 5.58/5.97 skol7 ) ) ) }.
% 5.58/5.97 (97) {G0,W11,D4,L1,V0,M1} I { ! contains_pq( i( triple( skol5, skol6, skol7
% 5.58/5.97 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 5.58/5.97 (4155) {G1,W15,D5,L3,V0,M3} P(63,96) { phi( triple( skol5, update_slb(
% 5.58/5.97 skol6, findmin_pqp_res( skol5 ) ), bad ) ), skol6 ==> create_slb,
% 5.58/5.97 contains_slb( skol6, findmin_pqp_res( skol5 ) ) }.
% 5.58/5.97 (5221) {G1,W13,D4,L2,V2,M2} P(67,96);d(62) { findmin_cpq_res( triple( X,
% 5.58/5.97 skol6, Y ) ) ==> findmin_pqp_res( X ), phi( triple( skol5, create_slb,
% 5.58/5.97 bad ) ) }.
% 5.58/5.97 (6071) {G1,W5,D3,L1,V2,M1} R(95,55) { ! phi( triple( X, Y, bad ) ) }.
% 5.58/5.97 (20344) {G2,W8,D4,L1,V2,M1} S(5221);r(6071) { findmin_cpq_res( triple( X,
% 5.58/5.97 skol6, Y ) ) ==> findmin_pqp_res( X ) }.
% 5.58/5.97 (20345) {G2,W7,D3,L2,V0,M2} S(4155);r(6071) { skol6 ==> create_slb,
% 5.58/5.97 contains_slb( skol6, findmin_pqp_res( skol5 ) ) }.
% 5.58/5.97 (20397) {G3,W4,D3,L1,V0,M1} P(20345,96);d(62);r(6071) { contains_slb( skol6
% 5.58/5.97 , findmin_pqp_res( skol5 ) ) }.
% 5.58/5.97 (20416) {G4,W7,D3,L1,V2,M1} R(20397,54) { contains_cpq( triple( X, skol6, Y
% 5.58/5.97 ), findmin_pqp_res( skol5 ) ) }.
% 5.58/5.97 (21390) {G3,W8,D4,L1,V0,M1} S(97);d(20344) { ! contains_pq( i( triple(
% 5.58/5.97 skol5, skol6, skol7 ) ), findmin_pqp_res( skol5 ) ) }.
% 5.58/5.97 (21391) {G5,W8,D4,L1,V2,M1} R(20416,92) { contains_pq( i( triple( X, skol6
% 5.58/5.97 , Y ) ), findmin_pqp_res( skol5 ) ) }.
% 5.58/5.97 (40439) {G6,W0,D0,L0,V0,M0} S(21390);r(21391) { }.
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 % SZS output end Refutation
% 5.58/5.97 found a proof!
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Unprocessed initial clauses:
% 5.58/5.97
% 5.58/5.97 (40441) {G0,W9,D2,L3,V3,M3} { ! less_than( X, Z ), ! less_than( Z, Y ),
% 5.58/5.97 less_than( X, Y ) }.
% 5.58/5.97 (40442) {G0,W6,D2,L2,V2,M2} { less_than( X, Y ), less_than( Y, X ) }.
% 5.58/5.97 (40443) {G0,W3,D2,L1,V1,M1} { less_than( X, X ) }.
% 5.58/5.97 (40444) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), less_than( X,
% 5.58/5.97 Y ) }.
% 5.58/5.97 (40445) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), ! less_than( Y
% 5.58/5.97 , X ) }.
% 5.58/5.97 (40446) {G0,W9,D2,L3,V2,M3} { ! less_than( X, Y ), less_than( Y, X ),
% 5.58/5.97 strictly_less_than( X, Y ) }.
% 5.58/5.97 (40447) {G0,W3,D2,L1,V1,M1} { less_than( bottom, X ) }.
% 5.58/5.97 (40448) {G0,W2,D2,L1,V0,M1} { ! isnonempty_pq( create_pq ) }.
% 5.58/5.97 (40449) {G0,W4,D3,L1,V2,M1} { isnonempty_pq( insert_pq( X, Y ) ) }.
% 5.58/5.97 (40450) {G0,W3,D2,L1,V1,M1} { ! contains_pq( create_pq, X ) }.
% 5.58/5.97 (40451) {G0,W11,D3,L3,V3,M3} { ! contains_pq( insert_pq( X, Y ), Z ),
% 5.58/5.97 contains_pq( X, Z ), Y = Z }.
% 5.58/5.97 (40452) {G0,W8,D3,L2,V3,M2} { ! contains_pq( X, Z ), contains_pq(
% 5.58/5.97 insert_pq( X, Y ), Z ) }.
% 5.58/5.97 (40453) {G0,W8,D3,L2,V3,M2} { ! Y = Z, contains_pq( insert_pq( X, Y ), Z )
% 5.58/5.97 }.
% 5.58/5.97 (40454) {G0,W9,D2,L3,V3,M3} { ! issmallestelement_pq( X, Y ), !
% 5.58/5.97 contains_pq( X, Z ), less_than( Y, Z ) }.
% 5.58/5.97 (40455) {G0,W8,D3,L2,V3,M2} { ! less_than( Y, skol1( Z, Y ) ),
% 5.58/5.97 issmallestelement_pq( X, Y ) }.
% 5.58/5.97 (40456) {G0,W8,D3,L2,V2,M2} { contains_pq( X, skol1( X, Y ) ),
% 5.58/5.97 issmallestelement_pq( X, Y ) }.
% 5.58/5.97 (40457) {G0,W7,D4,L1,V2,M1} { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 5.58/5.97 (40458) {G0,W17,D4,L3,V3,M3} { ! contains_pq( X, Z ), Y = Z, remove_pq(
% 5.58/5.97 insert_pq( X, Y ), Z ) = insert_pq( remove_pq( X, Z ), Y ) }.
% 5.58/5.97 (40459) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 5.58/5.97 issmallestelement_pq( X, Y ), findmin_pq_eff( X, Y ) = X }.
% 5.58/5.97 (40460) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 5.58/5.97 issmallestelement_pq( X, Y ), findmin_pq_res( X, Y ) = Y }.
% 5.58/5.97 (40461) {G0,W13,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 5.58/5.97 issmallestelement_pq( X, Y ), removemin_pq_eff( X, Y ) = remove_pq( X, Y
% 5.58/5.97 ) }.
% 5.58/5.97 (40462) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 5.58/5.97 issmallestelement_pq( X, Y ), removemin_pq_res( X, Y ) = Y }.
% 5.58/5.97 (40463) {G0,W11,D4,L1,V3,M1} { insert_pq( insert_pq( X, Y ), Z ) =
% 5.58/5.97 insert_pq( insert_pq( X, Z ), Y ) }.
% 5.58/5.97 (40464) {G0,W2,D2,L1,V0,M1} { ! isnonempty_slb( create_slb ) }.
% 5.58/5.97 (40465) {G0,W6,D4,L1,V3,M1} { isnonempty_slb( insert_slb( X, pair( Y, Z )
% 5.58/5.97 ) ) }.
% 5.58/5.97 (40466) {G0,W3,D2,L1,V1,M1} { ! contains_slb( create_slb, X ) }.
% 5.58/5.97 (40467) {G0,W13,D4,L3,V4,M3} { ! contains_slb( insert_slb( X, pair( Y, T )
% 5.58/5.97 ), Z ), contains_slb( X, Z ), Y = Z }.
% 5.58/5.97 (40468) {G0,W10,D4,L2,V4,M2} { ! contains_slb( X, Z ), contains_slb(
% 5.58/5.97 insert_slb( X, pair( Y, T ) ), Z ) }.
% 5.58/5.97 (40469) {G0,W10,D4,L2,V4,M2} { ! Y = Z, contains_slb( insert_slb( X, pair
% 5.58/5.97 ( Y, T ) ), Z ) }.
% 5.58/5.97 (40470) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 5.58/5.97 (40471) {G0,W17,D4,L3,V5,M3} { ! pair_in_list( insert_slb( X, pair( Y, T )
% 5.58/5.97 ), Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 5.58/5.97 (40472) {G0,W12,D4,L2,V5,M2} { ! pair_in_list( X, Z, U ), pair_in_list(
% 5.58/5.97 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 5.58/5.97 (40473) {G0,W13,D4,L2,V5,M2} { ! alpha1( Y, Z, T, U ), pair_in_list(
% 5.58/5.97 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 5.58/5.97 (40474) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), X = Y }.
% 5.58/5.97 (40475) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), Z = T }.
% 5.58/5.97 (40476) {G0,W11,D2,L3,V4,M3} { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 5.58/5.97 (40477) {G0,W9,D5,L1,V3,M1} { remove_slb( insert_slb( X, pair( Y, Z ) ), Y
% 5.58/5.97 ) = X }.
% 5.58/5.97 (40478) {G0,W21,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), remove_slb(
% 5.58/5.97 insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 5.58/5.97 ( Y, T ) ) }.
% 5.58/5.97 (40479) {G0,W9,D5,L1,V3,M1} { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y
% 5.58/5.97 ) = Z }.
% 5.58/5.97 (40480) {G0,W17,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), lookup_slb(
% 5.58/5.97 insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 5.58/5.97 (40481) {G0,W5,D3,L1,V1,M1} { update_slb( create_slb, X ) = create_slb }.
% 5.58/5.97 (40482) {G0,W18,D5,L2,V4,M2} { ! strictly_less_than( Y, X ), update_slb(
% 5.58/5.97 insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 5.58/5.97 ( T, X ) ) }.
% 5.58/5.97 (40483) {G0,W18,D5,L2,V4,M2} { ! less_than( X, Y ), update_slb( insert_slb
% 5.58/5.97 ( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 5.58/5.97 }.
% 5.58/5.97 (40484) {G0,W3,D2,L1,V1,M1} { succ_cpq( X, X ) }.
% 5.58/5.97 (40485) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq
% 5.58/5.97 ( Y, Z ) ) }.
% 5.58/5.97 (40486) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq
% 5.58/5.97 ( Y, Z ) ) }.
% 5.58/5.97 (40487) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 5.58/5.97 findmin_cpq_eff( Y ) ) }.
% 5.58/5.97 (40488) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 5.58/5.97 removemin_cpq_eff( Y ) ) }.
% 5.58/5.97 (40489) {G0,W5,D3,L1,V2,M1} { check_cpq( triple( X, create_slb, Y ) ) }.
% 5.58/5.97 (40490) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z
% 5.58/5.97 , insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) )
% 5.58/5.97 }.
% 5.58/5.97 (40491) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z
% 5.58/5.97 , T, U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) )
% 5.58/5.97 }.
% 5.58/5.97 (40492) {G0,W12,D5,L2,V5,M2} { ! strictly_less_than( X, Y ), ! check_cpq(
% 5.58/5.97 triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 5.58/5.97 (40493) {G0,W13,D5,L3,V5,M3} { ! strictly_less_than( X, Y ), ! ||,
% 5.58/5.97 check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 5.58/5.97 (40494) {G0,W9,D3,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z ), T ),
% 5.58/5.97 contains_slb( Y, T ) }.
% 5.58/5.97 (40495) {G0,W9,D3,L2,V4,M2} { ! contains_slb( Y, T ), contains_cpq( triple
% 5.58/5.97 ( X, Y, Z ), T ) }.
% 5.58/5.97 (40496) {G0,W5,D3,L1,V2,M1} { ! ok( triple( X, Y, bad ) ) }.
% 5.58/5.97 (40497) {G0,W6,D3,L2,V2,M2} { ! ||, ok( triple( X, Y, bad ) ) }.
% 5.58/5.97 (40498) {G0,W8,D3,L2,V3,M2} { ok( triple( Y, Z, X ) ), X = bad }.
% 5.58/5.97 (40499) {G0,W17,D5,L1,V4,M1} { insert_cpq( triple( X, Y, Z ), T ) = triple
% 5.58/5.97 ( insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 5.58/5.97 (40500) {G0,W14,D4,L2,V4,M2} { contains_slb( X, Y ), remove_cpq( triple( Z
% 5.58/5.97 , X, T ), Y ) = triple( Z, X, bad ) }.
% 5.58/5.97 (40501) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! less_than(
% 5.58/5.97 lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 5.58/5.97 remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 5.58/5.97 (40502) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), !
% 5.58/5.97 strictly_less_than( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T
% 5.58/5.97 ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 5.58/5.97 (40503) {G0,W10,D4,L1,V2,M1} { findmin_cpq_eff( triple( X, create_slb, Y )
% 5.58/5.97 ) = triple( X, create_slb, bad ) }.
% 5.58/5.97 (40504) {G0,W20,D5,L3,V3,M3} { Y = create_slb, contains_slb( Y,
% 5.58/5.97 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 5.58/5.97 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 5.58/5.97 (40505) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 5.58/5.97 findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ),
% 5.58/5.97 lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 5.58/5.97 ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 5.58/5.97 (40506) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 5.58/5.97 findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 5.58/5.97 ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 5.58/5.97 ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 5.58/5.97 (40507) {G0,W7,D4,L1,V2,M1} { findmin_cpq_res( triple( X, create_slb, Y )
% 5.58/5.97 ) = bottom }.
% 5.58/5.97 (40508) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res( triple( Y
% 5.58/5.97 , X, Z ) ) = findmin_pqp_res( Y ) }.
% 5.58/5.97 (40509) {G0,W8,D4,L1,V1,M1} { removemin_cpq_eff( X ) = remove_cpq(
% 5.58/5.97 findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 5.58/5.97 (40510) {G0,W5,D3,L1,V1,M1} { removemin_cpq_res( X ) = findmin_cpq_res( X
% 5.58/5.97 ) }.
% 5.58/5.97 (40511) {G0,W7,D4,L1,V2,M1} { i( triple( X, create_slb, Y ) ) = create_pq
% 5.58/5.97 }.
% 5.58/5.97 (40512) {G0,W17,D6,L1,V5,M1} { i( triple( X, insert_slb( Y, pair( T, U ) )
% 5.58/5.97 , Z ) ) = insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 5.58/5.97 (40513) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_remove( X, Y ), contains_pq( X, Y
% 5.58/5.97 ) }.
% 5.58/5.97 (40514) {G0,W6,D2,L2,V2,M2} { ! contains_pq( X, Y ), pi_sharp_remove( X, Y
% 5.58/5.97 ) }.
% 5.58/5.97 (40515) {G0,W7,D3,L2,V2,M2} { ! pi_remove( X, Y ), pi_sharp_remove( i( X )
% 5.58/5.97 , Y ) }.
% 5.58/5.97 (40516) {G0,W7,D3,L2,V2,M2} { ! pi_sharp_remove( i( X ), Y ), pi_remove( X
% 5.58/5.97 , Y ) }.
% 5.58/5.97 (40517) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ), contains_pq( X
% 5.58/5.97 , Y ) }.
% 5.58/5.97 (40518) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ),
% 5.58/5.97 issmallestelement_pq( X, Y ) }.
% 5.58/5.97 (40519) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), !
% 5.58/5.97 issmallestelement_pq( X, Y ), pi_sharp_find_min( X, Y ) }.
% 5.58/5.97 (40520) {G0,W7,D3,L2,V1,M2} { ! pi_find_min( X ), pi_sharp_find_min( i( X
% 5.58/5.97 ), skol2( X ) ) }.
% 5.58/5.97 (40521) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ),
% 5.58/5.97 pi_find_min( X ) }.
% 5.58/5.97 (40522) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ), contains_pq( X
% 5.58/5.97 , Y ) }.
% 5.58/5.97 (40523) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ),
% 5.58/5.97 issmallestelement_pq( X, Y ) }.
% 5.58/5.97 (40524) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), !
% 5.58/5.97 issmallestelement_pq( X, Y ), pi_sharp_removemin( X, Y ) }.
% 5.58/5.97 (40525) {G0,W7,D3,L2,V1,M2} { ! pi_removemin( X ), pi_sharp_find_min( i( X
% 5.58/5.97 ), skol3( X ) ) }.
% 5.58/5.97 (40526) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ),
% 5.58/5.97 pi_removemin( X ) }.
% 5.58/5.97 (40527) {G0,W5,D3,L2,V2,M2} { ! phi( X ), alpha2( skol4( Y ) ) }.
% 5.58/5.97 (40528) {G0,W6,D3,L2,V1,M2} { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 5.58/5.97 (40529) {G0,W7,D2,L3,V2,M3} { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X )
% 5.58/5.97 }.
% 5.58/5.97 (40530) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ok( X ) }.
% 5.58/5.97 (40531) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), check_cpq( X ) }.
% 5.58/5.97 (40532) {G0,W6,D2,L3,V1,M3} { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 5.58/5.97 (40533) {G0,W13,D4,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z ), T ),
% 5.58/5.97 contains_pq( i( triple( X, Y, Z ) ), T ) }.
% 5.58/5.97 (40534) {G0,W13,D4,L2,V4,M2} { ! contains_pq( i( triple( X, Y, Z ) ), T )
% 5.58/5.97 , contains_cpq( triple( X, Y, Z ), T ) }.
% 5.58/5.97 (40535) {G0,W16,D4,L2,V3,M2} { contains_cpq( triple( X, Y, Z ),
% 5.58/5.97 findmin_cpq_res( triple( X, Y, Z ) ) ), ! ok( findmin_cpq_eff( triple( X
% 5.58/5.97 , Y, Z ) ) ) }.
% 5.58/5.97 (40536) {G0,W10,D3,L2,V3,M2} { ok( triple( X, Y, Z ) ), ! phi( triple( X,
% 5.58/5.97 Y, Z ) ) }.
% 5.58/5.97 (40537) {G0,W6,D4,L1,V0,M1} { phi( findmin_cpq_eff( triple( skol5, skol6,
% 5.58/5.97 skol7 ) ) ) }.
% 5.58/5.97 (40538) {G0,W11,D4,L1,V0,M1} { ! contains_pq( i( triple( skol5, skol6,
% 5.58/5.97 skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 5.58/5.97
% 5.58/5.97
% 5.58/5.97 Total Proof:
% 5.58/5.97
% 5.58/5.97 subsumption: (54) {G0,W9,D3,L2,V4,M2} I { ! contains_slb( Y, T ),
% 5.58/5.97 contains_cpq( triple( X, Y, Z ), T ) }.
% 5.58/5.97 parent0: (40495) {G0,W9,D3,L2,V4,M2} { ! contains_slb( Y, T ),
% 5.68/6.06 contains_cpq( triple( X, Y, Z ), T ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 X := X
% 5.68/6.06 Y := Y
% 5.68/6.06 Z := Z
% 5.68/6.06 T := T
% 5.68/6.06 end
% 5.68/6.06 permutation0:
% 5.68/6.06 0 ==> 0
% 5.68/6.06 1 ==> 1
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 subsumption: (55) {G0,W5,D3,L1,V2,M1} I { ! ok( triple( X, Y, bad ) ) }.
% 5.68/6.06 parent0: (40496) {G0,W5,D3,L1,V2,M1} { ! ok( triple( X, Y, bad ) ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 X := X
% 5.68/6.06 Y := Y
% 5.68/6.06 end
% 5.68/6.06 permutation0:
% 5.68/6.06 0 ==> 0
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 subsumption: (62) {G0,W10,D4,L1,V2,M1} I { findmin_cpq_eff( triple( X,
% 5.68/6.06 create_slb, Y ) ) ==> triple( X, create_slb, bad ) }.
% 5.68/6.06 parent0: (40503) {G0,W10,D4,L1,V2,M1} { findmin_cpq_eff( triple( X,
% 5.68/6.06 create_slb, Y ) ) = triple( X, create_slb, bad ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 X := X
% 5.68/6.06 Y := Y
% 5.68/6.06 end
% 5.68/6.06 permutation0:
% 5.68/6.06 0 ==> 0
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 subsumption: (63) {G0,W20,D5,L3,V3,M3} I { Y = create_slb, contains_slb( Y
% 5.68/6.06 , findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple(
% 5.68/6.06 X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 5.68/6.06 parent0: (40504) {G0,W20,D5,L3,V3,M3} { Y = create_slb, contains_slb( Y,
% 5.68/6.06 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 5.68/6.06 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 X := X
% 5.68/6.06 Y := Y
% 5.68/6.06 Z := Z
% 5.68/6.06 end
% 5.68/6.06 permutation0:
% 5.68/6.06 0 ==> 0
% 5.68/6.06 1 ==> 1
% 5.68/6.06 2 ==> 2
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 subsumption: (67) {G0,W11,D4,L2,V3,M2} I { X = create_slb, findmin_cpq_res
% 5.68/6.06 ( triple( Y, X, Z ) ) ==> findmin_pqp_res( Y ) }.
% 5.68/6.06 parent0: (40508) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res(
% 5.68/6.06 triple( Y, X, Z ) ) = findmin_pqp_res( Y ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 X := X
% 5.68/6.06 Y := Y
% 5.68/6.06 Z := Z
% 5.68/6.06 end
% 5.68/6.06 permutation0:
% 5.68/6.06 0 ==> 0
% 5.68/6.06 1 ==> 1
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 subsumption: (92) {G0,W13,D4,L2,V4,M2} I { ! contains_cpq( triple( X, Y, Z
% 5.68/6.06 ), T ), contains_pq( i( triple( X, Y, Z ) ), T ) }.
% 5.68/6.06 parent0: (40533) {G0,W13,D4,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z )
% 5.68/6.06 , T ), contains_pq( i( triple( X, Y, Z ) ), T ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 X := X
% 5.68/6.06 Y := Y
% 5.68/6.06 Z := Z
% 5.68/6.06 T := T
% 5.68/6.06 end
% 5.68/6.06 permutation0:
% 5.68/6.06 0 ==> 0
% 5.68/6.06 1 ==> 1
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 subsumption: (95) {G0,W10,D3,L2,V3,M2} I { ok( triple( X, Y, Z ) ), ! phi(
% 5.68/6.06 triple( X, Y, Z ) ) }.
% 5.68/6.06 parent0: (40536) {G0,W10,D3,L2,V3,M2} { ok( triple( X, Y, Z ) ), ! phi(
% 5.68/6.06 triple( X, Y, Z ) ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 X := X
% 5.68/6.06 Y := Y
% 5.68/6.06 Z := Z
% 5.68/6.06 end
% 5.68/6.06 permutation0:
% 5.68/6.06 0 ==> 0
% 5.68/6.06 1 ==> 1
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 subsumption: (96) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple(
% 5.68/6.06 skol5, skol6, skol7 ) ) ) }.
% 5.68/6.06 parent0: (40537) {G0,W6,D4,L1,V0,M1} { phi( findmin_cpq_eff( triple( skol5
% 5.68/6.06 , skol6, skol7 ) ) ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 end
% 5.68/6.06 permutation0:
% 5.68/6.06 0 ==> 0
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 subsumption: (97) {G0,W11,D4,L1,V0,M1} I { ! contains_pq( i( triple( skol5
% 5.68/6.06 , skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) )
% 5.68/6.06 }.
% 5.68/6.06 parent0: (40538) {G0,W11,D4,L1,V0,M1} { ! contains_pq( i( triple( skol5,
% 5.68/6.06 skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 end
% 5.68/6.06 permutation0:
% 5.68/6.06 0 ==> 0
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 *** allocated 15000 integers for justifications
% 5.68/6.06 *** allocated 22500 integers for justifications
% 5.68/6.06 *** allocated 33750 integers for justifications
% 5.68/6.06 eqswap: (40971) {G0,W20,D5,L3,V3,M3} { create_slb = X, contains_slb( X,
% 5.68/6.06 findmin_pqp_res( Y ) ), findmin_cpq_eff( triple( Y, X, Z ) ) = triple( Y
% 5.68/6.06 , update_slb( X, findmin_pqp_res( Y ) ), bad ) }.
% 5.68/6.06 parent0[0]: (63) {G0,W20,D5,L3,V3,M3} I { Y = create_slb, contains_slb( Y,
% 5.68/6.06 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 5.68/6.06 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 X := Y
% 5.68/6.06 Y := X
% 5.68/6.06 Z := Z
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 paramod: (40974) {G1,W15,D5,L3,V0,M3} { phi( triple( skol5, update_slb(
% 5.68/6.06 skol6, findmin_pqp_res( skol5 ) ), bad ) ), create_slb = skol6,
% 5.68/6.06 contains_slb( skol6, findmin_pqp_res( skol5 ) ) }.
% 5.68/6.06 parent0[2]: (40971) {G0,W20,D5,L3,V3,M3} { create_slb = X, contains_slb( X
% 5.68/6.06 , findmin_pqp_res( Y ) ), findmin_cpq_eff( triple( Y, X, Z ) ) = triple(
% 5.68/6.06 Y, update_slb( X, findmin_pqp_res( Y ) ), bad ) }.
% 5.68/6.06 parent1[0; 1]: (96) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple(
% 5.68/6.06 skol5, skol6, skol7 ) ) ) }.
% 5.68/6.06 substitution0:
% 5.68/6.06 X := skol6
% 5.68/6.06 Y := skol5
% 5.68/6.06 Z := skol7
% 5.68/6.06 end
% 5.68/6.06 substitution1:
% 5.68/6.06 end
% 5.68/6.06
% 5.68/6.06 eqswap: (41031) {G1,W15,D5,L3,V0,M3} { skol6 = create_slb, phi( tripleCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------