TSTP Solution File: SWV414+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV414+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.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 16:24:47 EDT 2022
% Result : Theorem 0.48s 1.16s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV414+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n011.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 : Thu Jun 16 04:15:51 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.48/1.15 *** allocated 10000 integers for termspace/termends
% 0.48/1.15 *** allocated 10000 integers for clauses
% 0.48/1.15 *** allocated 10000 integers for justifications
% 0.48/1.15 Bliksem 1.12
% 0.48/1.15
% 0.48/1.15
% 0.48/1.15 Automatic Strategy Selection
% 0.48/1.15
% 0.48/1.15
% 0.48/1.15 Clauses:
% 0.48/1.15
% 0.48/1.15 { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.48/1.15 { less_than( X, Y ), less_than( Y, X ) }.
% 0.48/1.15 { less_than( X, X ) }.
% 0.48/1.15 { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.48/1.15 { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.48/1.15 { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.48/1.15 { less_than( bottom, X ) }.
% 0.48/1.15 { ! isnonempty_pq( create_pq ) }.
% 0.48/1.15 { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.48/1.15 { ! contains_pq( create_pq, X ) }.
% 0.48/1.15 { ! contains_pq( insert_pq( X, Y ), Z ), contains_pq( X, Z ), Y = Z }.
% 0.48/1.15 { ! contains_pq( X, Z ), contains_pq( insert_pq( X, Y ), Z ) }.
% 0.48/1.15 { ! Y = Z, contains_pq( insert_pq( X, Y ), Z ) }.
% 0.48/1.15 { ! issmallestelement_pq( X, Y ), ! contains_pq( X, Z ), less_than( Y, Z )
% 0.48/1.15 }.
% 0.48/1.15 { ! less_than( Y, skol1( Z, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.48/1.15 { contains_pq( X, skol1( X, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.48/1.15 { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 0.48/1.15 { ! contains_pq( X, Z ), Y = Z, remove_pq( insert_pq( X, Y ), Z ) =
% 0.48/1.15 insert_pq( remove_pq( X, Z ), Y ) }.
% 0.48/1.15 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_eff( X
% 0.48/1.15 , Y ) = X }.
% 0.48/1.15 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_res( X
% 0.48/1.15 , Y ) = Y }.
% 0.48/1.15 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_eff(
% 0.48/1.15 X, Y ) = remove_pq( X, Y ) }.
% 0.48/1.15 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_res(
% 0.48/1.15 X, Y ) = Y }.
% 0.48/1.15 { insert_pq( insert_pq( X, Y ), Z ) = insert_pq( insert_pq( X, Z ), Y ) }.
% 0.48/1.15 { ! isnonempty_slb( create_slb ) }.
% 0.48/1.15 { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) ) }.
% 0.48/1.15 { ! contains_slb( create_slb, X ) }.
% 0.48/1.15 { ! contains_slb( insert_slb( X, pair( Y, T ) ), Z ), contains_slb( X, Z )
% 0.48/1.15 , Y = Z }.
% 0.48/1.15 { ! contains_slb( X, Z ), contains_slb( insert_slb( X, pair( Y, T ) ), Z )
% 0.48/1.15 }.
% 0.48/1.15 { ! Y = Z, contains_slb( insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.48/1.15 { ! pair_in_list( create_slb, X, Y ) }.
% 0.48/1.15 { ! pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U ), pair_in_list( X, Z
% 0.48/1.15 , U ), alpha1( Y, Z, T, U ) }.
% 0.48/1.15 { ! pair_in_list( X, Z, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z
% 0.48/1.15 , U ) }.
% 0.48/1.15 { ! alpha1( Y, Z, T, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U
% 0.48/1.15 ) }.
% 0.48/1.15 { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.48/1.15 { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.48/1.15 { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.48/1.15 { remove_slb( insert_slb( X, pair( Y, Z ) ), Y ) = X }.
% 0.48/1.15 { Y = Z, ! contains_slb( X, Z ), remove_slb( insert_slb( X, pair( Y, T ) )
% 0.48/1.15 , Z ) = insert_slb( remove_slb( X, Z ), pair( Y, T ) ) }.
% 0.48/1.15 { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y ) = Z }.
% 0.48/1.15 { Y = Z, ! contains_slb( X, Z ), lookup_slb( insert_slb( X, pair( Y, T ) )
% 0.48/1.15 , Z ) = lookup_slb( X, Z ) }.
% 0.48/1.15 { update_slb( create_slb, X ) = create_slb }.
% 0.48/1.15 { ! strictly_less_than( Y, X ), update_slb( insert_slb( Z, pair( T, Y ) ),
% 0.48/1.15 X ) = insert_slb( update_slb( Z, X ), pair( T, X ) ) }.
% 0.48/1.15 { ! less_than( X, Y ), update_slb( insert_slb( Z, pair( T, Y ) ), X ) =
% 0.48/1.15 insert_slb( update_slb( Z, X ), pair( T, Y ) ) }.
% 0.48/1.15 { succ_cpq( X, X ) }.
% 0.48/1.15 { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y, Z ) ) }.
% 0.48/1.15 { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y, Z ) ) }.
% 0.48/1.15 { ! succ_cpq( X, Y ), succ_cpq( X, findmin_cpq_eff( Y ) ) }.
% 0.48/1.15 { ! succ_cpq( X, Y ), succ_cpq( X, removemin_cpq_eff( Y ) ) }.
% 0.48/1.15 { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.48/1.15 { ! less_than( Y, X ), ! check_cpq( triple( Z, insert_slb( T, pair( X, Y )
% 0.48/1.15 ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.48/1.15 { ! less_than( Y, X ), ! check_cpq( triple( Z, T, U ) ), check_cpq( triple
% 0.48/1.15 ( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.48/1.15 { ! strictly_less_than( X, Y ), ! check_cpq( triple( Z, insert_slb( T, pair
% 0.48/1.15 ( X, Y ) ), U ) ) }.
% 0.48/1.15 { ! strictly_less_than( X, Y ), ! ||, check_cpq( triple( Z, insert_slb( T,
% 0.48/1.15 pair( X, Y ) ), U ) ) }.
% 0.48/1.15 { ! contains_cpq( triple( X, Y, Z ), T ), contains_slb( Y, T ) }.
% 0.48/1.15 { ! contains_slb( Y, T ), contains_cpq( triple( X, Y, Z ), T ) }.
% 0.48/1.15 { ! ok( triple( X, Y, bad ) ) }.
% 0.48/1.15 { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.48/1.15 { ok( triple( Y, Z, X ) ), X = bad }.
% 0.48/1.16 { insert_cpq( triple( X, Y, Z ), T ) = triple( insert_pqp( X, T ),
% 0.48/1.16 insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.48/1.16 { contains_slb( X, Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( Z, X,
% 0.48/1.16 bad ) }.
% 0.48/1.16 { ! contains_slb( X, Y ), ! less_than( lookup_slb( X, Y ), Y ), remove_cpq
% 0.48/1.16 ( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y )
% 0.48/1.16 , T ) }.
% 0.48/1.16 { ! contains_slb( X, Y ), ! strictly_less_than( Y, lookup_slb( X, Y ) ),
% 0.48/1.16 remove_cpq( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ),
% 0.48/1.16 remove_slb( X, Y ), bad ) }.
% 0.48/1.16 { findmin_cpq_eff( triple( X, create_slb, Y ) ) = triple( X, create_slb,
% 0.48/1.16 bad ) }.
% 0.48/1.16 { Y = create_slb, contains_slb( Y, findmin_pqp_res( X ) ), findmin_cpq_eff
% 0.48/1.16 ( triple( X, Y, Z ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) )
% 0.48/1.16 , bad ) }.
% 0.48/1.16 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), !
% 0.48/1.16 strictly_less_than( findmin_pqp_res( X ), lookup_slb( Y, findmin_pqp_res
% 0.48/1.16 ( X ) ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb(
% 0.48/1.16 Y, findmin_pqp_res( X ) ), bad ) }.
% 0.48/1.16 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! less_than(
% 0.48/1.16 lookup_slb( Y, findmin_pqp_res( X ) ), findmin_pqp_res( X ) ),
% 0.48/1.16 findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( Y,
% 0.48/1.16 findmin_pqp_res( X ) ), Z ) }.
% 0.48/1.16 { findmin_cpq_res( triple( X, create_slb, Y ) ) = bottom }.
% 0.48/1.16 { X = create_slb, findmin_cpq_res( triple( Y, X, Z ) ) = findmin_pqp_res( Y
% 0.48/1.16 ) }.
% 0.48/1.16 { removemin_cpq_eff( X ) = remove_cpq( findmin_cpq_eff( X ),
% 0.48/1.16 findmin_cpq_res( X ) ) }.
% 0.48/1.16 { removemin_cpq_res( X ) = findmin_cpq_res( X ) }.
% 0.48/1.16 { i( triple( X, create_slb, Y ) ) = create_pq }.
% 0.48/1.16 { i( triple( X, insert_slb( Y, pair( T, U ) ), Z ) ) = insert_pq( i( triple
% 0.48/1.16 ( X, Y, Z ) ), T ) }.
% 0.48/1.16 { ! pi_sharp_remove( X, Y ), contains_pq( X, Y ) }.
% 0.48/1.16 { ! contains_pq( X, Y ), pi_sharp_remove( X, Y ) }.
% 0.48/1.16 { ! pi_remove( X, Y ), pi_sharp_remove( i( X ), Y ) }.
% 0.48/1.16 { ! pi_sharp_remove( i( X ), Y ), pi_remove( X, Y ) }.
% 0.48/1.16 { ! pi_sharp_find_min( X, Y ), contains_pq( X, Y ) }.
% 0.48/1.16 { ! pi_sharp_find_min( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.48/1.16 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_find_min
% 0.48/1.16 ( X, Y ) }.
% 0.48/1.16 { ! pi_find_min( X ), pi_sharp_find_min( i( X ), skol2( X ) ) }.
% 0.48/1.16 { ! pi_sharp_find_min( i( X ), Y ), pi_find_min( X ) }.
% 0.48/1.16 { ! pi_sharp_removemin( X, Y ), contains_pq( X, Y ) }.
% 0.48/1.16 { ! pi_sharp_removemin( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.48/1.16 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_removemin
% 0.48/1.16 ( X, Y ) }.
% 0.48/1.16 { ! pi_removemin( X ), pi_sharp_find_min( i( X ), skol3( X ) ) }.
% 0.48/1.16 { ! pi_sharp_find_min( i( X ), Y ), pi_removemin( X ) }.
% 0.48/1.16 { ! phi( X ), alpha2( skol4( Y ) ) }.
% 0.48/1.16 { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 0.48/1.16 { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X ) }.
% 0.48/1.16 { ! alpha2( X ), ok( X ) }.
% 0.48/1.16 { ! alpha2( X ), check_cpq( X ) }.
% 0.48/1.16 { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 0.48/1.16 { ! i( triple( create_pqp, create_slb, skol5 ) ) = create_pq }.
% 0.48/1.16
% 0.48/1.16 percentage equality = 0.238095, percentage horn = 0.838710
% 0.48/1.16 This is a problem with some equality
% 0.48/1.16
% 0.48/1.16
% 0.48/1.16
% 0.48/1.16 Options Used:
% 0.48/1.16
% 0.48/1.16 useres = 1
% 0.48/1.16 useparamod = 1
% 0.48/1.16 useeqrefl = 1
% 0.48/1.16 useeqfact = 1
% 0.48/1.16 usefactor = 1
% 0.48/1.16 usesimpsplitting = 0
% 0.48/1.16 usesimpdemod = 5
% 0.48/1.16 usesimpres = 3
% 0.48/1.16
% 0.48/1.16 resimpinuse = 1000
% 0.48/1.16 resimpclauses = 20000
% 0.48/1.16 substype = eqrewr
% 0.48/1.16 backwardsubs = 1
% 0.48/1.16 selectoldest = 5
% 0.48/1.16
% 0.48/1.16 litorderings [0] = split
% 0.48/1.16 litorderings [1] = extend the termordering, first sorting on arguments
% 0.48/1.16
% 0.48/1.16 termordering = kbo
% 0.48/1.16
% 0.48/1.16 litapriori = 0
% 0.48/1.16 termapriori = 1
% 0.48/1.16 litaposteriori = 0
% 0.48/1.16 termaposteriori = 0
% 0.48/1.16 demodaposteriori = 0
% 0.48/1.16 ordereqreflfact = 0
% 0.48/1.16
% 0.48/1.16 litselect = negord
% 0.48/1.16
% 0.48/1.16 maxweight = 15
% 0.48/1.16 maxdepth = 30000
% 0.48/1.16 maxlength = 115
% 0.48/1.16 maxnrvars = 195
% 0.48/1.16 excuselevel = 1
% 0.48/1.16 increasemaxweight = 1
% 0.48/1.16
% 0.48/1.16 maxselected = 10000000
% 0.48/1.16 maxnrclauses = 10000000
% 0.48/1.16
% 0.48/1.16 showgenerated = 0
% 0.48/1.16 showkept = 0
% 0.48/1.16 showselected = 0
% 0.48/1.16 showdeleted = 0
% 0.48/1.16 showresimp = 1
% 0.48/1.16 showstatus = 2000
% 0.48/1.16
% 0.48/1.16 prologoutput = 0
% 0.48/1.16 nrgoals = 5000000
% 0.48/1.16 totalproof = 1
% 0.48/1.16
% 0.48/1.16 Symbols occurring in the translation:
% 0.48/1.16
% 0.48/1.16 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.48/1.16 . [1, 2] (w:1, o:39, a:1, s:1, b:0),
% 0.48/1.16 || [2, 0] (w:1, o:3, a:1, s:1, b:0),
% 0.48/1.16 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 0.48/1.16 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.48/1.16 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.48/1.16 less_than [38, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.48/1.16 strictly_less_than [39, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.48/1.16 bottom [40, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.48/1.16 create_pq [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.48/1.16 isnonempty_pq [42, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.48/1.16 insert_pq [43, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.48/1.16 contains_pq [44, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.48/1.16 issmallestelement_pq [45, 2] (w:1, o:73, a:1, s:1, b:0),
% 0.48/1.16 remove_pq [46, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.48/1.16 findmin_pq_eff [47, 2] (w:1, o:74, a:1, s:1, b:0),
% 0.48/1.16 findmin_pq_res [48, 2] (w:1, o:75, a:1, s:1, b:0),
% 0.48/1.16 removemin_pq_eff [49, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.48/1.16 removemin_pq_res [50, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.48/1.16 create_slb [51, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.48/1.16 isnonempty_slb [52, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.48/1.16 pair [53, 2] (w:1, o:76, a:1, s:1, b:0),
% 0.48/1.16 insert_slb [54, 2] (w:1, o:77, a:1, s:1, b:0),
% 0.48/1.16 contains_slb [55, 2] (w:1, o:78, a:1, s:1, b:0),
% 0.48/1.16 pair_in_list [57, 3] (w:1, o:90, a:1, s:1, b:0),
% 0.48/1.16 remove_slb [59, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.48/1.16 lookup_slb [60, 2] (w:1, o:79, a:1, s:1, b:0),
% 0.48/1.16 update_slb [61, 2] (w:1, o:80, a:1, s:1, b:0),
% 0.48/1.16 succ_cpq [62, 2] (w:1, o:81, a:1, s:1, b:0),
% 0.48/1.16 insert_cpq [63, 2] (w:1, o:82, a:1, s:1, b:0),
% 0.48/1.16 remove_cpq [64, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.48/1.16 findmin_cpq_eff [65, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.48/1.16 removemin_cpq_eff [66, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.48/1.16 triple [67, 3] (w:1, o:91, a:1, s:1, b:0),
% 0.48/1.16 check_cpq [68, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.48/1.16 contains_cpq [69, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.48/1.16 bad [70, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.48/1.16 ok [71, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.48/1.16 insert_pqp [72, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.48/1.16 remove_pqp [73, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.48/1.16 findmin_pqp_res [74, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.48/1.16 findmin_cpq_res [75, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.48/1.16 removemin_cpq_res [76, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.48/1.16 i [77, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.48/1.16 pi_sharp_remove [78, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.48/1.16 pi_remove [79, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.48/1.16 pi_sharp_find_min [80, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.48/1.16 pi_find_min [81, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.48/1.16 pi_sharp_removemin [82, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.48/1.16 pi_removemin [83, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.48/1.16 phi [84, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.48/1.16 create_pqp [85, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.48/1.16 alpha1 [86, 4] (w:1, o:92, a:1, s:1, b:1),
% 0.48/1.16 alpha2 [87, 1] (w:1, o:35, a:1, s:1, b:1),
% 0.48/1.16 skol1 [88, 2] (w:1, o:89, a:1, s:1, b:1),
% 0.48/1.16 skol2 [89, 1] (w:1, o:36, a:1, s:1, b:1),
% 0.48/1.16 skol3 [90, 1] (w:1, o:37, a:1, s:1, b:1),
% 0.48/1.16 skol4 [91, 1] (w:1, o:38, a:1, s:1, b:1),
% 0.48/1.16 skol5 [92, 0] (w:1, o:16, a:1, s:1, b:1).
% 0.48/1.16
% 0.48/1.16
% 0.48/1.16 Starting Search:
% 0.48/1.16
% 0.48/1.16
% 0.48/1.16 Bliksems!, er is een bewijs:
% 0.48/1.16 % SZS status Theorem
% 0.48/1.16 % SZS output start Refutation
% 0.48/1.16
% 0.48/1.16 (70) {G0,W7,D4,L1,V2,M1} I { i( triple( X, create_slb, Y ) ) ==> create_pq
% 0.48/1.16 }.
% 0.48/1.16 (92) {G1,W0,D0,L0,V0,M0} I;d(70);q { }.
% 0.48/1.16
% 0.48/1.16
% 0.48/1.16 % SZS output end Refutation
% 0.48/1.16 found a proof!
% 0.48/1.16
% 0.48/1.16
% 0.48/1.16 Unprocessed initial clauses:
% 0.48/1.16
% 0.48/1.16 (94) {G0,W9,D2,L3,V3,M3} { ! less_than( X, Z ), ! less_than( Z, Y ),
% 0.48/1.16 less_than( X, Y ) }.
% 0.48/1.16 (95) {G0,W6,D2,L2,V2,M2} { less_than( X, Y ), less_than( Y, X ) }.
% 0.48/1.16 (96) {G0,W3,D2,L1,V1,M1} { less_than( X, X ) }.
% 0.48/1.16 (97) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), less_than( X, Y )
% 0.48/1.16 }.
% 0.48/1.16 (98) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), ! less_than( Y, X
% 0.48/1.16 ) }.
% 0.48/1.16 (99) {G0,W9,D2,L3,V2,M3} { ! less_than( X, Y ), less_than( Y, X ),
% 0.48/1.16 strictly_less_than( X, Y ) }.
% 0.48/1.16 (100) {G0,W3,D2,L1,V1,M1} { less_than( bottom, X ) }.
% 0.48/1.16 (101) {G0,W2,D2,L1,V0,M1} { ! isnonempty_pq( create_pq ) }.
% 0.48/1.16 (102) {G0,W4,D3,L1,V2,M1} { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.48/1.16 (103) {G0,W3,D2,L1,V1,M1} { ! contains_pq( create_pq, X ) }.
% 0.48/1.16 (104) {G0,W11,D3,L3,V3,M3} { ! contains_pq( insert_pq( X, Y ), Z ),
% 0.48/1.16 contains_pq( X, Z ), Y = Z }.
% 0.48/1.16 (105) {G0,W8,D3,L2,V3,M2} { ! contains_pq( X, Z ), contains_pq( insert_pq
% 0.48/1.16 ( X, Y ), Z ) }.
% 0.48/1.16 (106) {G0,W8,D3,L2,V3,M2} { ! Y = Z, contains_pq( insert_pq( X, Y ), Z )
% 0.48/1.16 }.
% 0.48/1.16 (107) {G0,W9,D2,L3,V3,M3} { ! issmallestelement_pq( X, Y ), ! contains_pq
% 0.48/1.16 ( X, Z ), less_than( Y, Z ) }.
% 0.48/1.16 (108) {G0,W8,D3,L2,V3,M2} { ! less_than( Y, skol1( Z, Y ) ),
% 0.48/1.16 issmallestelement_pq( X, Y ) }.
% 0.48/1.16 (109) {G0,W8,D3,L2,V2,M2} { contains_pq( X, skol1( X, Y ) ),
% 0.48/1.16 issmallestelement_pq( X, Y ) }.
% 0.48/1.16 (110) {G0,W7,D4,L1,V2,M1} { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 0.48/1.16 (111) {G0,W17,D4,L3,V3,M3} { ! contains_pq( X, Z ), Y = Z, remove_pq(
% 0.48/1.16 insert_pq( X, Y ), Z ) = insert_pq( remove_pq( X, Z ), Y ) }.
% 0.48/1.16 (112) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.48/1.16 ( X, Y ), findmin_pq_eff( X, Y ) = X }.
% 0.48/1.16 (113) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.48/1.16 ( X, Y ), findmin_pq_res( X, Y ) = Y }.
% 0.48/1.16 (114) {G0,W13,D3,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.48/1.16 ( X, Y ), removemin_pq_eff( X, Y ) = remove_pq( X, Y ) }.
% 0.48/1.16 (115) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.48/1.16 ( X, Y ), removemin_pq_res( X, Y ) = Y }.
% 0.48/1.16 (116) {G0,W11,D4,L1,V3,M1} { insert_pq( insert_pq( X, Y ), Z ) = insert_pq
% 0.48/1.16 ( insert_pq( X, Z ), Y ) }.
% 0.48/1.16 (117) {G0,W2,D2,L1,V0,M1} { ! isnonempty_slb( create_slb ) }.
% 0.48/1.16 (118) {G0,W6,D4,L1,V3,M1} { isnonempty_slb( insert_slb( X, pair( Y, Z ) )
% 0.48/1.16 ) }.
% 0.48/1.16 (119) {G0,W3,D2,L1,V1,M1} { ! contains_slb( create_slb, X ) }.
% 0.48/1.16 (120) {G0,W13,D4,L3,V4,M3} { ! contains_slb( insert_slb( X, pair( Y, T ) )
% 0.48/1.16 , Z ), contains_slb( X, Z ), Y = Z }.
% 0.48/1.16 (121) {G0,W10,D4,L2,V4,M2} { ! contains_slb( X, Z ), contains_slb(
% 0.48/1.16 insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.48/1.16 (122) {G0,W10,D4,L2,V4,M2} { ! Y = Z, contains_slb( insert_slb( X, pair( Y
% 0.48/1.16 , T ) ), Z ) }.
% 0.48/1.16 (123) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 0.48/1.16 (124) {G0,W17,D4,L3,V5,M3} { ! pair_in_list( insert_slb( X, pair( Y, T ) )
% 0.48/1.16 , Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 0.48/1.16 (125) {G0,W12,D4,L2,V5,M2} { ! pair_in_list( X, Z, U ), pair_in_list(
% 0.48/1.16 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.48/1.16 (126) {G0,W13,D4,L2,V5,M2} { ! alpha1( Y, Z, T, U ), pair_in_list(
% 0.48/1.16 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.48/1.16 (127) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.48/1.16 (128) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.48/1.16 (129) {G0,W11,D2,L3,V4,M3} { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.48/1.16 (130) {G0,W9,D5,L1,V3,M1} { remove_slb( insert_slb( X, pair( Y, Z ) ), Y )
% 0.48/1.16 = X }.
% 0.48/1.16 (131) {G0,W21,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), remove_slb(
% 0.48/1.16 insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 0.48/1.16 ( Y, T ) ) }.
% 0.48/1.16 (132) {G0,W9,D5,L1,V3,M1} { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y )
% 0.48/1.16 = Z }.
% 0.48/1.16 (133) {G0,W17,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), lookup_slb(
% 0.48/1.16 insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 0.48/1.16 (134) {G0,W5,D3,L1,V1,M1} { update_slb( create_slb, X ) = create_slb }.
% 0.48/1.16 (135) {G0,W18,D5,L2,V4,M2} { ! strictly_less_than( Y, X ), update_slb(
% 0.48/1.16 insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 0.48/1.16 ( T, X ) ) }.
% 0.48/1.16 (136) {G0,W18,D5,L2,V4,M2} { ! less_than( X, Y ), update_slb( insert_slb(
% 0.48/1.16 Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 0.48/1.16 }.
% 0.48/1.16 (137) {G0,W3,D2,L1,V1,M1} { succ_cpq( X, X ) }.
% 0.48/1.16 (138) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y
% 0.48/1.16 , Z ) ) }.
% 0.48/1.16 (139) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y
% 0.48/1.16 , Z ) ) }.
% 0.48/1.16 (140) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.48/1.16 findmin_cpq_eff( Y ) ) }.
% 0.48/1.16 (141) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.48/1.16 removemin_cpq_eff( Y ) ) }.
% 0.48/1.16 (142) {G0,W5,D3,L1,V2,M1} { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.48/1.16 (143) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z,
% 0.48/1.16 insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.48/1.16 (144) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z,
% 0.48/1.16 T, U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.48/1.16 (145) {G0,W12,D5,L2,V5,M2} { ! strictly_less_than( X, Y ), ! check_cpq(
% 0.48/1.16 triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.48/1.16 (146) {G0,W13,D5,L3,V5,M3} { ! strictly_less_than( X, Y ), ! ||, check_cpq
% 0.48/1.16 ( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.48/1.16 (147) {G0,W9,D3,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z ), T ),
% 0.48/1.16 contains_slb( Y, T ) }.
% 0.48/1.16 (148) {G0,W9,D3,L2,V4,M2} { ! contains_slb( Y, T ), contains_cpq( triple(
% 0.48/1.16 X, Y, Z ), T ) }.
% 0.48/1.16 (149) {G0,W5,D3,L1,V2,M1} { ! ok( triple( X, Y, bad ) ) }.
% 0.48/1.16 (150) {G0,W6,D3,L2,V2,M2} { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.48/1.16 (151) {G0,W8,D3,L2,V3,M2} { ok( triple( Y, Z, X ) ), X = bad }.
% 0.48/1.16 (152) {G0,W17,D5,L1,V4,M1} { insert_cpq( triple( X, Y, Z ), T ) = triple(
% 0.48/1.16 insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.48/1.16 (153) {G0,W14,D4,L2,V4,M2} { contains_slb( X, Y ), remove_cpq( triple( Z,
% 0.48/1.16 X, T ), Y ) = triple( Z, X, bad ) }.
% 0.48/1.16 (154) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! less_than(
% 0.48/1.16 lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.48/1.16 remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 0.48/1.16 (155) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! strictly_less_than
% 0.48/1.16 ( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.48/1.16 remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 0.48/1.16 (156) {G0,W10,D4,L1,V2,M1} { findmin_cpq_eff( triple( X, create_slb, Y ) )
% 0.48/1.16 = triple( X, create_slb, bad ) }.
% 0.48/1.16 (157) {G0,W20,D5,L3,V3,M3} { Y = create_slb, contains_slb( Y,
% 0.48/1.16 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 0.48/1.16 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.48/1.16 (158) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.48/1.16 findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ),
% 0.48/1.16 lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 0.48/1.16 ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.48/1.16 (159) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.48/1.16 findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 0.48/1.16 ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 0.48/1.16 ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 0.48/1.16 (160) {G0,W7,D4,L1,V2,M1} { findmin_cpq_res( triple( X, create_slb, Y ) )
% 0.48/1.16 = bottom }.
% 0.48/1.16 (161) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res( triple( Y, X
% 0.48/1.16 , Z ) ) = findmin_pqp_res( Y ) }.
% 0.48/1.16 (162) {G0,W8,D4,L1,V1,M1} { removemin_cpq_eff( X ) = remove_cpq(
% 0.48/1.16 findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 0.48/1.16 (163) {G0,W5,D3,L1,V1,M1} { removemin_cpq_res( X ) = findmin_cpq_res( X )
% 0.48/1.16 }.
% 0.48/1.16 (164) {G0,W7,D4,L1,V2,M1} { i( triple( X, create_slb, Y ) ) = create_pq
% 0.48/1.16 }.
% 0.48/1.16 (165) {G0,W17,D6,L1,V5,M1} { i( triple( X, insert_slb( Y, pair( T, U ) ),
% 0.48/1.16 Z ) ) = insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 0.48/1.16 (166) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_remove( X, Y ), contains_pq( X, Y )
% 0.48/1.16 }.
% 0.48/1.16 (167) {G0,W6,D2,L2,V2,M2} { ! contains_pq( X, Y ), pi_sharp_remove( X, Y )
% 0.48/1.16 }.
% 0.48/1.16 (168) {G0,W7,D3,L2,V2,M2} { ! pi_remove( X, Y ), pi_sharp_remove( i( X ),
% 0.48/1.16 Y ) }.
% 0.48/1.16 (169) {G0,W7,D3,L2,V2,M2} { ! pi_sharp_remove( i( X ), Y ), pi_remove( X,
% 0.48/1.16 Y ) }.
% 0.48/1.16 (170) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ), contains_pq( X, Y
% 0.48/1.16 ) }.
% 0.48/1.16 (171) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ),
% 0.48/1.16 issmallestelement_pq( X, Y ) }.
% 0.48/1.16 (172) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.48/1.16 ( X, Y ), pi_sharp_find_min( X, Y ) }.
% 0.48/1.16 (173) {G0,W7,D3,L2,V1,M2} { ! pi_find_min( X ), pi_sharp_find_min( i( X )
% 0.48/1.16 , skol2( X ) ) }.
% 0.48/1.16 (174) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ), pi_find_min
% 0.48/1.16 ( X ) }.
% 0.48/1.16 (175) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ), contains_pq( X,
% 0.48/1.16 Y ) }.
% 0.48/1.16 (176) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ),
% 0.48/1.16 issmallestelement_pq( X, Y ) }.
% 0.48/1.16 (177) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.48/1.16 ( X, Y ), pi_sharp_removemin( X, Y ) }.
% 0.48/1.16 (178) {G0,W7,D3,L2,V1,M2} { ! pi_removemin( X ), pi_sharp_find_min( i( X )
% 0.48/1.16 , skol3( X ) ) }.
% 0.48/1.16 (179) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ), pi_removemin
% 0.48/1.16 ( X ) }.
% 0.48/1.16 (180) {G0,W5,D3,L2,V2,M2} { ! phi( X ), alpha2( skol4( Y ) ) }.
% 0.48/1.16 (181) {G0,W6,D3,L2,V1,M2} { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 0.48/1.16 (182) {G0,W7,D2,L3,V2,M3} { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X )
% 0.48/1.16 }.
% 0.48/1.16 (183) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ok( X ) }.
% 0.48/1.16 (184) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), check_cpq( X ) }.
% 0.48/1.16 (185) {G0,W6,D2,L3,V1,M3} { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 0.48/1.16 (186) {G0,W7,D4,L1,V0,M1} { ! i( triple( create_pqp, create_slb, skol5 ) )
% 0.48/1.16 = create_pq }.
% 0.48/1.16
% 0.48/1.16
% 0.48/1.16 Total Proof:
% 0.48/1.16
% 0.48/1.16 *** allocated 15000 integers for clauses
% 0.48/1.16 subsumption: (70) {G0,W7,D4,L1,V2,M1} I { i( triple( X, create_slb, Y ) )
% 0.48/1.16 ==> create_pq }.
% 0.48/1.16 parent0: (164) {G0,W7,D4,L1,V2,M1} { i( triple( X, create_slb, Y ) ) =
% 0.48/1.16 create_pq }.
% 0.48/1.16 substitution0:
% 0.48/1.16 X := X
% 0.48/1.16 Y := Y
% 0.48/1.16 end
% 0.48/1.16 permutation0:
% 0.48/1.16 0 ==> 0
% 0.48/1.16 end
% 0.48/1.16
% 0.48/1.16 paramod: (396) {G1,W3,D2,L1,V0,M1} { ! create_pq = create_pq }.
% 0.48/1.16 parent0[0]: (70) {G0,W7,D4,L1,V2,M1} I { i( triple( X, create_slb, Y ) )
% 0.48/1.16 ==> create_pq }.
% 0.48/1.16 parent1[0; 2]: (186) {G0,W7,D4,L1,V0,M1} { ! i( triple( create_pqp,
% 0.48/1.16 create_slb, skol5 ) ) = create_pq }.
% 0.48/1.16 substitution0:
% 0.48/1.16 X := create_pqp
% 0.48/1.16 Y := skol5
% 0.48/1.16 end
% 0.48/1.16 substitution1:
% 0.48/1.16 end
% 0.48/1.16
% 0.48/1.16 eqrefl: (397) {G0,W0,D0,L0,V0,M0} { }.
% 0.48/1.16 parent0[0]: (396) {G1,W3,D2,L1,V0,M1} { ! create_pq = create_pq }.
% 0.48/1.16 substitution0:
% 0.48/1.16 end
% 0.48/1.16
% 0.48/1.16 subsumption: (92) {G1,W0,D0,L0,V0,M0} I;d(70);q { }.
% 0.48/1.16 parent0: (397) {G0,W0,D0,L0,V0,M0} { }.
% 0.48/1.16 substitution0:
% 0.48/1.16 end
% 0.48/1.16 permutation0:
% 0.48/1.16 end
% 0.48/1.16
% 0.48/1.16 Proof check complete!
% 0.48/1.16
% 0.48/1.16 Memory use:
% 0.48/1.16
% 0.48/1.16 space for terms: 3257
% 0.48/1.16 space for clauses: 7666
% 0.48/1.16
% 0.48/1.16
% 0.48/1.16 clauses generated: 93
% 0.48/1.16 clauses kept: 93
% 0.48/1.16 clauses selected: 0
% 0.48/1.16 clauses deleted: 0
% 0.48/1.16 clauses inuse deleted: 0
% 0.48/1.16
% 0.48/1.16 subsentry: 996
% 0.48/1.16 literals s-matched: 470
% 0.48/1.16 literals matched: 462
% 0.48/1.16 full subsumption: 127
% 0.48/1.16
% 0.48/1.16 checksum: -110769468
% 0.48/1.16
% 0.48/1.16
% 0.48/1.16 Bliksem ended
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