%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV367+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 16:24:36 EDT 2022
% Result : Theorem 0.74s 1.13s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV367+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Wed Jun 15 10:44:07 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.74/1.12 *** allocated 10000 integers for termspace/termends
% 0.74/1.12 *** allocated 10000 integers for clauses
% 0.74/1.12 *** allocated 10000 integers for justifications
% 0.74/1.12 Bliksem 1.12
% 0.74/1.12
% 0.74/1.12
% 0.74/1.12 Automatic Strategy Selection
% 0.74/1.12
% 0.74/1.12
% 0.74/1.12 Clauses:
% 0.74/1.12
% 0.74/1.12 { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.74/1.12 { less_than( X, Y ), less_than( Y, X ) }.
% 0.74/1.12 { less_than( X, X ) }.
% 0.74/1.12 { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.74/1.12 { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.74/1.12 { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.74/1.12 { less_than( bottom, X ) }.
% 0.74/1.12 { ! isnonempty_pq( create_pq ) }.
% 0.74/1.12 { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.74/1.12 { ! contains_pq( create_pq, X ) }.
% 0.74/1.12 { ! contains_pq( insert_pq( X, Y ), Z ), contains_pq( X, Z ), Y = Z }.
% 0.74/1.12 { ! contains_pq( X, Z ), contains_pq( insert_pq( X, Y ), Z ) }.
% 0.74/1.12 { ! Y = Z, contains_pq( insert_pq( X, Y ), Z ) }.
% 0.74/1.12 { ! issmallestelement_pq( X, Y ), ! contains_pq( X, Z ), less_than( Y, Z )
% 0.74/1.12 }.
% 0.74/1.12 { ! less_than( Y, skol1( Z, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.74/1.12 { contains_pq( X, skol1( X, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.74/1.13 { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 0.74/1.13 { ! contains_pq( X, Z ), Y = Z, remove_pq( insert_pq( X, Y ), Z ) =
% 0.74/1.13 insert_pq( remove_pq( X, Z ), Y ) }.
% 0.74/1.13 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_eff( X
% 0.74/1.13 , Y ) = X }.
% 0.74/1.13 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_res( X
% 0.74/1.13 , Y ) = Y }.
% 0.74/1.13 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_eff(
% 0.74/1.13 X, Y ) = remove_pq( X, Y ) }.
% 0.74/1.13 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_res(
% 0.74/1.13 X, Y ) = Y }.
% 0.74/1.13 { insert_pq( insert_pq( X, Y ), Z ) = insert_pq( insert_pq( X, Z ), Y ) }.
% 0.74/1.13 { ! isnonempty_slb( create_slb ) }.
% 0.74/1.13 { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) ) }.
% 0.74/1.13 { ! contains_slb( create_slb, X ) }.
% 0.74/1.13 { ! contains_slb( insert_slb( X, pair( Y, T ) ), Z ), contains_slb( X, Z )
% 0.74/1.13 , Y = Z }.
% 0.74/1.13 { ! contains_slb( X, Z ), contains_slb( insert_slb( X, pair( Y, T ) ), Z )
% 0.74/1.13 }.
% 0.74/1.13 { ! Y = Z, contains_slb( insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.74/1.13 { ! pair_in_list( create_slb, X, Y ) }.
% 0.74/1.13 { ! pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U ), pair_in_list( X, Z
% 0.74/1.13 , U ), alpha1( Y, Z, T, U ) }.
% 0.74/1.13 { ! pair_in_list( X, Z, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z
% 0.74/1.13 , U ) }.
% 0.74/1.13 { ! alpha1( Y, Z, T, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U
% 0.74/1.13 ) }.
% 0.74/1.13 { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.74/1.13 { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.74/1.13 { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.74/1.13 { remove_slb( insert_slb( X, pair( Y, Z ) ), Y ) = X }.
% 0.74/1.13 { Y = Z, ! contains_slb( X, Z ), remove_slb( insert_slb( X, pair( Y, T ) )
% 0.74/1.13 , Z ) = insert_slb( remove_slb( X, Z ), pair( Y, T ) ) }.
% 0.74/1.13 { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y ) = Z }.
% 0.74/1.13 { Y = Z, ! contains_slb( X, Z ), lookup_slb( insert_slb( X, pair( Y, T ) )
% 0.74/1.13 , Z ) = lookup_slb( X, Z ) }.
% 0.74/1.13 { update_slb( create_slb, X ) = create_slb }.
% 0.74/1.13 { ! strictly_less_than( Y, X ), update_slb( insert_slb( Z, pair( T, Y ) ),
% 0.74/1.13 X ) = insert_slb( update_slb( Z, X ), pair( T, X ) ) }.
% 0.74/1.13 { ! less_than( X, Y ), update_slb( insert_slb( Z, pair( T, Y ) ), X ) =
% 0.74/1.13 insert_slb( update_slb( Z, X ), pair( T, Y ) ) }.
% 0.74/1.13 { succ_cpq( X, X ) }.
% 0.74/1.13 { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y, Z ) ) }.
% 0.74/1.13 { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y, Z ) ) }.
% 0.74/1.13 { ! succ_cpq( X, Y ), succ_cpq( X, findmin_cpq_eff( Y ) ) }.
% 0.74/1.13 { ! succ_cpq( X, Y ), succ_cpq( X, removemin_cpq_eff( Y ) ) }.
% 0.74/1.13 { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.74/1.13 { ! less_than( Y, X ), ! check_cpq( triple( Z, insert_slb( T, pair( X, Y )
% 0.74/1.13 ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.74/1.13 { ! less_than( Y, X ), ! check_cpq( triple( Z, T, U ) ), check_cpq( triple
% 0.74/1.13 ( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.74/1.13 { ! strictly_less_than( X, Y ), ! check_cpq( triple( Z, insert_slb( T, pair
% 0.74/1.13 ( X, Y ) ), U ) ) }.
% 0.74/1.13 { ! strictly_less_than( X, Y ), ! ||, check_cpq( triple( Z, insert_slb( T,
% 0.74/1.13 pair( X, Y ) ), U ) ) }.
% 0.74/1.13 { ! contains_cpq( triple( X, Y, Z ), T ), contains_slb( Y, T ) }.
% 0.74/1.13 { ! contains_slb( Y, T ), contains_cpq( triple( X, Y, Z ), T ) }.
% 0.74/1.13 { ! ok( triple( X, Y, bad ) ) }.
% 0.74/1.13 { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.74/1.13 { ok( triple( Y, Z, X ) ), X = bad }.
% 0.74/1.13 { insert_cpq( triple( X, Y, Z ), T ) = triple( insert_pqp( X, T ),
% 0.74/1.13 insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.74/1.13 { contains_slb( X, Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( Z, X,
% 0.74/1.13 bad ) }.
% 0.74/1.13 { ! contains_slb( X, Y ), ! less_than( lookup_slb( X, Y ), Y ), remove_cpq
% 0.74/1.13 ( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y )
% 0.74/1.13 , T ) }.
% 0.74/1.13 { ! contains_slb( X, Y ), ! strictly_less_than( Y, lookup_slb( X, Y ) ),
% 0.74/1.13 remove_cpq( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ),
% 0.74/1.13 remove_slb( X, Y ), bad ) }.
% 0.74/1.13 { findmin_cpq_eff( triple( X, create_slb, Y ) ) = triple( X, create_slb,
% 0.74/1.13 bad ) }.
% 0.74/1.13 { Y = create_slb, contains_slb( Y, findmin_pqp_res( X ) ), findmin_cpq_eff
% 0.74/1.13 ( triple( X, Y, Z ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) )
% 0.74/1.13 , bad ) }.
% 0.74/1.13 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), !
% 0.74/1.13 strictly_less_than( findmin_pqp_res( X ), lookup_slb( Y, findmin_pqp_res
% 0.74/1.13 ( X ) ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb(
% 0.74/1.13 Y, findmin_pqp_res( X ) ), bad ) }.
% 0.74/1.13 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! less_than(
% 0.74/1.13 lookup_slb( Y, findmin_pqp_res( X ) ), findmin_pqp_res( X ) ),
% 0.74/1.13 findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( Y,
% 0.74/1.13 findmin_pqp_res( X ) ), Z ) }.
% 0.74/1.13 { findmin_cpq_res( triple( X, create_slb, Y ) ) = bottom }.
% 0.74/1.13 { X = create_slb, findmin_cpq_res( triple( Y, X, Z ) ) = findmin_pqp_res( Y
% 0.74/1.13 ) }.
% 0.74/1.13 { removemin_cpq_eff( X ) = remove_cpq( findmin_cpq_eff( X ),
% 0.74/1.13 findmin_cpq_res( X ) ) }.
% 0.74/1.13 { removemin_cpq_res( X ) = findmin_cpq_res( X ) }.
% 0.74/1.13 { i( triple( X, create_slb, Y ) ) = create_pq }.
% 0.74/1.13 { i( triple( X, insert_slb( Y, pair( T, U ) ), Z ) ) = insert_pq( i( triple
% 0.74/1.13 ( X, Y, Z ) ), T ) }.
% 0.74/1.13 { ! pi_sharp_remove( X, Y ), contains_pq( X, Y ) }.
% 0.74/1.13 { ! contains_pq( X, Y ), pi_sharp_remove( X, Y ) }.
% 0.74/1.13 { ! pi_remove( X, Y ), pi_sharp_remove( i( X ), Y ) }.
% 0.74/1.13 { ! pi_sharp_remove( i( X ), Y ), pi_remove( X, Y ) }.
% 0.74/1.13 { ! pi_sharp_find_min( X, Y ), contains_pq( X, Y ) }.
% 0.74/1.13 { ! pi_sharp_find_min( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.74/1.13 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_find_min
% 0.74/1.13 ( X, Y ) }.
% 0.74/1.13 { ! pi_find_min( X ), pi_sharp_find_min( i( X ), skol2( X ) ) }.
% 0.74/1.13 { ! pi_sharp_find_min( i( X ), Y ), pi_find_min( X ) }.
% 0.74/1.13 { ! pi_sharp_removemin( X, Y ), contains_pq( X, Y ) }.
% 0.74/1.13 { ! pi_sharp_removemin( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.74/1.13 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_removemin
% 0.74/1.13 ( X, Y ) }.
% 0.74/1.13 { ! pi_removemin( X ), pi_sharp_find_min( i( X ), skol3( X ) ) }.
% 0.74/1.13 { ! pi_sharp_find_min( i( X ), Y ), pi_removemin( X ) }.
% 0.74/1.13 { ! phi( X ), alpha2( skol4( Y ) ) }.
% 0.74/1.13 { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 0.74/1.13 { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X ) }.
% 0.74/1.13 { ! alpha2( X ), ok( X ) }.
% 0.74/1.13 { ! alpha2( X ), check_cpq( X ) }.
% 0.74/1.13 { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 0.74/1.13 { contains_pq( i( triple( skol5, create_slb, skol6 ) ), skol7 ) }.
% 0.74/1.13 { ! i( remove_cpq( triple( skol5, create_slb, skol6 ), skol7 ) ) =
% 0.74/1.13 remove_pq( i( triple( skol5, create_slb, skol6 ) ), skol7 ) }.
% 0.74/1.13
% 0.74/1.13 percentage equality = 0.236842, percentage horn = 0.840426
% 0.74/1.13 This is a problem with some equality
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Options Used:
% 0.74/1.13
% 0.74/1.13 useres = 1
% 0.74/1.13 useparamod = 1
% 0.74/1.13 useeqrefl = 1
% 0.74/1.13 useeqfact = 1
% 0.74/1.13 usefactor = 1
% 0.74/1.13 usesimpsplitting = 0
% 0.74/1.13 usesimpdemod = 5
% 0.74/1.13 usesimpres = 3
% 0.74/1.13
% 0.74/1.13 resimpinuse = 1000
% 0.74/1.13 resimpclauses = 20000
% 0.74/1.13 substype = eqrewr
% 0.74/1.13 backwardsubs = 1
% 0.74/1.13 selectoldest = 5
% 0.74/1.13
% 0.74/1.13 litorderings [0] = split
% 0.74/1.13 litorderings [1] = extend the termordering, first sorting on arguments
% 0.74/1.13
% 0.74/1.13 termordering = kbo
% 0.74/1.13
% 0.74/1.13 litapriori = 0
% 0.74/1.13 termapriori = 1
% 0.74/1.13 litaposteriori = 0
% 0.74/1.13 termaposteriori = 0
% 0.74/1.13 demodaposteriori = 0
% 0.74/1.13 ordereqreflfact = 0
% 0.74/1.13
% 0.74/1.13 litselect = negord
% 0.74/1.13
% 0.74/1.13 maxweight = 15
% 0.74/1.13 maxdepth = 30000
% 0.74/1.13 maxlength = 115
% 0.74/1.13 maxnrvars = 195
% 0.74/1.13 excuselevel = 1
% 0.74/1.13 increasemaxweight = 1
% 0.74/1.13
% 0.74/1.13 maxselected = 10000000
% 0.74/1.13 maxnrclauses = 10000000
% 0.74/1.13
% 0.74/1.13 showgenerated = 0
% 0.74/1.13 showkept = 0
% 0.74/1.13 showselected = 0
% 0.74/1.13 showdeleted = 0
% 0.74/1.13 showresimp = 1
% 0.74/1.13 showstatus = 2000
% 0.74/1.13
% 0.74/1.13 prologoutput = 0
% 0.74/1.13 nrgoals = 5000000
% 0.74/1.13 totalproof = 1
% 0.74/1.13
% 0.74/1.13 Symbols occurring in the translation:
% 0.74/1.13
% 0.74/1.13 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.74/1.13 . [1, 2] (w:1, o:40, a:1, s:1, b:0),
% 0.74/1.13 || [2, 0] (w:1, o:3, a:1, s:1, b:0),
% 0.74/1.13 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.74/1.13 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.13 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.13 less_than [38, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.74/1.13 strictly_less_than [39, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.74/1.13 bottom [40, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.74/1.13 create_pq [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.74/1.13 isnonempty_pq [42, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.74/1.13 insert_pq [43, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.74/1.13 contains_pq [44, 2] (w:1, o:73, a:1, s:1, b:0),
% 0.74/1.13 issmallestelement_pq [45, 2] (w:1, o:74, a:1, s:1, b:0),
% 0.74/1.13 remove_pq [46, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.74/1.13 findmin_pq_eff [47, 2] (w:1, o:75, a:1, s:1, b:0),
% 0.74/1.13 findmin_pq_res [48, 2] (w:1, o:76, a:1, s:1, b:0),
% 0.74/1.13 removemin_pq_eff [49, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.74/1.13 removemin_pq_res [50, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.74/1.13 create_slb [51, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.74/1.13 isnonempty_slb [52, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.74/1.13 pair [53, 2] (w:1, o:77, a:1, s:1, b:0),
% 0.74/1.13 insert_slb [54, 2] (w:1, o:78, a:1, s:1, b:0),
% 0.74/1.13 contains_slb [55, 2] (w:1, o:79, a:1, s:1, b:0),
% 0.74/1.13 pair_in_list [57, 3] (w:1, o:91, a:1, s:1, b:0),
% 0.74/1.13 remove_slb [59, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.74/1.13 lookup_slb [60, 2] (w:1, o:80, a:1, s:1, b:0),
% 0.74/1.13 update_slb [61, 2] (w:1, o:81, a:1, s:1, b:0),
% 0.74/1.13 succ_cpq [62, 2] (w:1, o:82, a:1, s:1, b:0),
% 0.74/1.13 insert_cpq [63, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.74/1.13 remove_cpq [64, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.74/1.13 findmin_cpq_eff [65, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.74/1.13 removemin_cpq_eff [66, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.74/1.13 triple [67, 3] (w:1, o:92, a:1, s:1, b:0),
% 0.74/1.13 check_cpq [68, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.74/1.13 contains_cpq [69, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.74/1.13 bad [70, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.74/1.13 ok [71, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.74/1.13 insert_pqp [72, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.74/1.13 remove_pqp [73, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.74/1.13 findmin_pqp_res [74, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.74/1.13 findmin_cpq_res [75, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.74/1.13 removemin_cpq_res [76, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.74/1.13 i [77, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.74/1.13 pi_sharp_remove [78, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.74/1.13 pi_remove [79, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.74/1.13 pi_sharp_find_min [80, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.74/1.13 pi_find_min [81, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.74/1.13 pi_sharp_removemin [82, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.74/1.13 pi_removemin [83, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.74/1.13 phi [84, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.74/1.13 alpha1 [85, 4] (w:1, o:93, a:1, s:1, b:1),
% 0.74/1.13 alpha2 [86, 1] (w:1, o:36, a:1, s:1, b:1),
% 0.74/1.13 skol1 [87, 2] (w:1, o:90, a:1, s:1, b:1),
% 0.74/1.13 skol2 [88, 1] (w:1, o:37, a:1, s:1, b:1),
% 0.74/1.13 skol3 [89, 1] (w:1, o:38, a:1, s:1, b:1),
% 0.74/1.13 skol4 [90, 1] (w:1, o:39, a:1, s:1, b:1),
% 0.74/1.13 skol5 [91, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.74/1.13 skol6 [92, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.74/1.13 skol7 [93, 0] (w:1, o:17, a:1, s:1, b:1).
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Starting Search:
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Bliksems!, er is een bewijs:
% 0.74/1.13 % SZS status Theorem
% 0.74/1.13 % SZS output start Refutation
% 0.74/1.13
% 0.74/1.13 (9) {G0,W3,D2,L1,V1,M1} I { ! contains_pq( create_pq, X ) }.
% 0.74/1.13 (70) {G0,W7,D4,L1,V2,M1} I { i( triple( X, create_slb, Y ) ) ==> create_pq
% 0.74/1.13 }.
% 0.74/1.13 (92) {G1,W0,D0,L0,V0,M0} I;d(70);r(9) { }.
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 % SZS output end Refutation
% 0.74/1.13 found a proof!
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Unprocessed initial clauses:
% 0.74/1.13
% 0.74/1.13 (94) {G0,W9,D2,L3,V3,M3} { ! less_than( X, Z ), ! less_than( Z, Y ),
% 0.74/1.13 less_than( X, Y ) }.
% 0.74/1.13 (95) {G0,W6,D2,L2,V2,M2} { less_than( X, Y ), less_than( Y, X ) }.
% 0.74/1.13 (96) {G0,W3,D2,L1,V1,M1} { less_than( X, X ) }.
% 0.74/1.13 (97) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), less_than( X, Y )
% 0.74/1.13 }.
% 0.74/1.13 (98) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), ! less_than( Y, X
% 0.74/1.13 ) }.
% 0.74/1.13 (99) {G0,W9,D2,L3,V2,M3} { ! less_than( X, Y ), less_than( Y, X ),
% 0.74/1.13 strictly_less_than( X, Y ) }.
% 0.74/1.13 (100) {G0,W3,D2,L1,V1,M1} { less_than( bottom, X ) }.
% 0.74/1.13 (101) {G0,W2,D2,L1,V0,M1} { ! isnonempty_pq( create_pq ) }.
% 0.74/1.13 (102) {G0,W4,D3,L1,V2,M1} { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.74/1.13 (103) {G0,W3,D2,L1,V1,M1} { ! contains_pq( create_pq, X ) }.
% 0.74/1.13 (104) {G0,W11,D3,L3,V3,M3} { ! contains_pq( insert_pq( X, Y ), Z ),
% 0.74/1.13 contains_pq( X, Z ), Y = Z }.
% 0.74/1.13 (105) {G0,W8,D3,L2,V3,M2} { ! contains_pq( X, Z ), contains_pq( insert_pq
% 0.74/1.13 ( X, Y ), Z ) }.
% 0.74/1.13 (106) {G0,W8,D3,L2,V3,M2} { ! Y = Z, contains_pq( insert_pq( X, Y ), Z )
% 0.74/1.13 }.
% 0.74/1.13 (107) {G0,W9,D2,L3,V3,M3} { ! issmallestelement_pq( X, Y ), ! contains_pq
% 0.74/1.13 ( X, Z ), less_than( Y, Z ) }.
% 0.74/1.13 (108) {G0,W8,D3,L2,V3,M2} { ! less_than( Y, skol1( Z, Y ) ),
% 0.74/1.13 issmallestelement_pq( X, Y ) }.
% 0.74/1.13 (109) {G0,W8,D3,L2,V2,M2} { contains_pq( X, skol1( X, Y ) ),
% 0.74/1.13 issmallestelement_pq( X, Y ) }.
% 0.74/1.13 (110) {G0,W7,D4,L1,V2,M1} { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 0.74/1.13 (111) {G0,W17,D4,L3,V3,M3} { ! contains_pq( X, Z ), Y = Z, remove_pq(
% 0.74/1.13 insert_pq( X, Y ), Z ) = insert_pq( remove_pq( X, Z ), Y ) }.
% 0.74/1.13 (112) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.74/1.13 ( X, Y ), findmin_pq_eff( X, Y ) = X }.
% 0.74/1.13 (113) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.74/1.13 ( X, Y ), findmin_pq_res( X, Y ) = Y }.
% 0.74/1.13 (114) {G0,W13,D3,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.74/1.13 ( X, Y ), removemin_pq_eff( X, Y ) = remove_pq( X, Y ) }.
% 0.74/1.13 (115) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.74/1.13 ( X, Y ), removemin_pq_res( X, Y ) = Y }.
% 0.74/1.13 (116) {G0,W11,D4,L1,V3,M1} { insert_pq( insert_pq( X, Y ), Z ) = insert_pq
% 0.74/1.13 ( insert_pq( X, Z ), Y ) }.
% 0.74/1.13 (117) {G0,W2,D2,L1,V0,M1} { ! isnonempty_slb( create_slb ) }.
% 0.74/1.13 (118) {G0,W6,D4,L1,V3,M1} { isnonempty_slb( insert_slb( X, pair( Y, Z ) )
% 0.74/1.13 ) }.
% 0.74/1.13 (119) {G0,W3,D2,L1,V1,M1} { ! contains_slb( create_slb, X ) }.
% 0.74/1.13 (120) {G0,W13,D4,L3,V4,M3} { ! contains_slb( insert_slb( X, pair( Y, T ) )
% 0.74/1.13 , Z ), contains_slb( X, Z ), Y = Z }.
% 0.74/1.13 (121) {G0,W10,D4,L2,V4,M2} { ! contains_slb( X, Z ), contains_slb(
% 0.74/1.13 insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.74/1.13 (122) {G0,W10,D4,L2,V4,M2} { ! Y = Z, contains_slb( insert_slb( X, pair( Y
% 0.74/1.13 , T ) ), Z ) }.
% 0.74/1.13 (123) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 0.74/1.13 (124) {G0,W17,D4,L3,V5,M3} { ! pair_in_list( insert_slb( X, pair( Y, T ) )
% 0.74/1.13 , Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 0.74/1.13 (125) {G0,W12,D4,L2,V5,M2} { ! pair_in_list( X, Z, U ), pair_in_list(
% 0.74/1.13 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.74/1.13 (126) {G0,W13,D4,L2,V5,M2} { ! alpha1( Y, Z, T, U ), pair_in_list(
% 0.74/1.13 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.74/1.13 (127) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.74/1.13 (128) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.74/1.13 (129) {G0,W11,D2,L3,V4,M3} { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.74/1.13 (130) {G0,W9,D5,L1,V3,M1} { remove_slb( insert_slb( X, pair( Y, Z ) ), Y )
% 0.74/1.13 = X }.
% 0.74/1.13 (131) {G0,W21,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), remove_slb(
% 0.74/1.13 insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 0.74/1.13 ( Y, T ) ) }.
% 0.74/1.13 (132) {G0,W9,D5,L1,V3,M1} { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y )
% 0.74/1.13 = Z }.
% 0.74/1.13 (133) {G0,W17,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), lookup_slb(
% 0.74/1.13 insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 0.74/1.13 (134) {G0,W5,D3,L1,V1,M1} { update_slb( create_slb, X ) = create_slb }.
% 0.74/1.13 (135) {G0,W18,D5,L2,V4,M2} { ! strictly_less_than( Y, X ), update_slb(
% 0.74/1.13 insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 0.74/1.13 ( T, X ) ) }.
% 0.74/1.13 (136) {G0,W18,D5,L2,V4,M2} { ! less_than( X, Y ), update_slb( insert_slb(
% 0.74/1.13 Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 0.74/1.13 }.
% 0.74/1.13 (137) {G0,W3,D2,L1,V1,M1} { succ_cpq( X, X ) }.
% 0.74/1.13 (138) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y
% 0.74/1.13 , Z ) ) }.
% 0.74/1.13 (139) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y
% 0.74/1.13 , Z ) ) }.
% 0.74/1.13 (140) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.74/1.13 findmin_cpq_eff( Y ) ) }.
% 0.74/1.13 (141) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.74/1.13 removemin_cpq_eff( Y ) ) }.
% 0.74/1.13 (142) {G0,W5,D3,L1,V2,M1} { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.74/1.13 (143) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z,
% 0.74/1.13 insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.74/1.13 (144) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z,
% 0.74/1.13 T, U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.74/1.13 (145) {G0,W12,D5,L2,V5,M2} { ! strictly_less_than( X, Y ), ! check_cpq(
% 0.74/1.13 triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.74/1.13 (146) {G0,W13,D5,L3,V5,M3} { ! strictly_less_than( X, Y ), ! ||, check_cpq
% 0.74/1.13 ( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.74/1.13 (147) {G0,W9,D3,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z ), T ),
% 0.74/1.13 contains_slb( Y, T ) }.
% 0.74/1.13 (148) {G0,W9,D3,L2,V4,M2} { ! contains_slb( Y, T ), contains_cpq( triple(
% 0.74/1.13 X, Y, Z ), T ) }.
% 0.74/1.13 (149) {G0,W5,D3,L1,V2,M1} { ! ok( triple( X, Y, bad ) ) }.
% 0.74/1.13 (150) {G0,W6,D3,L2,V2,M2} { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.74/1.13 (151) {G0,W8,D3,L2,V3,M2} { ok( triple( Y, Z, X ) ), X = bad }.
% 0.74/1.13 (152) {G0,W17,D5,L1,V4,M1} { insert_cpq( triple( X, Y, Z ), T ) = triple(
% 0.74/1.13 insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.74/1.13 (153) {G0,W14,D4,L2,V4,M2} { contains_slb( X, Y ), remove_cpq( triple( Z,
% 0.74/1.13 X, T ), Y ) = triple( Z, X, bad ) }.
% 0.74/1.13 (154) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! less_than(
% 0.74/1.13 lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.74/1.13 remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 0.74/1.13 (155) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! strictly_less_than
% 0.74/1.13 ( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.74/1.13 remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 0.74/1.13 (156) {G0,W10,D4,L1,V2,M1} { findmin_cpq_eff( triple( X, create_slb, Y ) )
% 0.74/1.13 = triple( X, create_slb, bad ) }.
% 0.74/1.13 (157) {G0,W20,D5,L3,V3,M3} { Y = create_slb, contains_slb( Y,
% 0.74/1.13 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 0.74/1.13 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.74/1.13 (158) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.74/1.13 findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ),
% 0.74/1.13 lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 0.74/1.13 ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.74/1.13 (159) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.74/1.13 findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 0.74/1.13 ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 0.74/1.13 ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 0.74/1.13 (160) {G0,W7,D4,L1,V2,M1} { findmin_cpq_res( triple( X, create_slb, Y ) )
% 0.74/1.13 = bottom }.
% 0.74/1.13 (161) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res( triple( Y, X
% 0.74/1.13 , Z ) ) = findmin_pqp_res( Y ) }.
% 0.74/1.13 (162) {G0,W8,D4,L1,V1,M1} { removemin_cpq_eff( X ) = remove_cpq(
% 0.74/1.13 findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 0.74/1.13 (163) {G0,W5,D3,L1,V1,M1} { removemin_cpq_res( X ) = findmin_cpq_res( X )
% 0.74/1.13 }.
% 0.74/1.13 (164) {G0,W7,D4,L1,V2,M1} { i( triple( X, create_slb, Y ) ) = create_pq
% 0.74/1.13 }.
% 0.74/1.13 (165) {G0,W17,D6,L1,V5,M1} { i( triple( X, insert_slb( Y, pair( T, U ) ),
% 0.74/1.13 Z ) ) = insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 0.74/1.13 (166) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_remove( X, Y ), contains_pq( X, Y )
% 0.74/1.13 }.
% 0.74/1.13 (167) {G0,W6,D2,L2,V2,M2} { ! contains_pq( X, Y ), pi_sharp_remove( X, Y )
% 0.74/1.13 }.
% 0.74/1.13 (168) {G0,W7,D3,L2,V2,M2} { ! pi_remove( X, Y ), pi_sharp_remove( i( X ),
% 0.74/1.13 Y ) }.
% 0.74/1.13 (169) {G0,W7,D3,L2,V2,M2} { ! pi_sharp_remove( i( X ), Y ), pi_remove( X,
% 0.74/1.13 Y ) }.
% 0.74/1.13 (170) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ), contains_pq( X, Y
% 0.74/1.13 ) }.
% 0.74/1.13 (171) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ),
% 0.74/1.13 issmallestelement_pq( X, Y ) }.
% 0.74/1.13 (172) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.74/1.13 ( X, Y ), pi_sharp_find_min( X, Y ) }.
% 0.74/1.13 (173) {G0,W7,D3,L2,V1,M2} { ! pi_find_min( X ), pi_sharp_find_min( i( X )
% 0.74/1.13 , skol2( X ) ) }.
% 0.74/1.13 (174) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ), pi_find_min
% 0.74/1.13 ( X ) }.
% 0.74/1.13 (175) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ), contains_pq( X,
% 0.74/1.13 Y ) }.
% 0.74/1.13 (176) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ),
% 0.74/1.13 issmallestelement_pq( X, Y ) }.
% 0.74/1.13 (177) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.74/1.13 ( X, Y ), pi_sharp_removemin( X, Y ) }.
% 0.74/1.13 (178) {G0,W7,D3,L2,V1,M2} { ! pi_removemin( X ), pi_sharp_find_min( i( X )
% 0.74/1.13 , skol3( X ) ) }.
% 0.74/1.13 (179) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ), pi_removemin
% 0.74/1.13 ( X ) }.
% 0.74/1.13 (180) {G0,W5,D3,L2,V2,M2} { ! phi( X ), alpha2( skol4( Y ) ) }.
% 0.74/1.13 (181) {G0,W6,D3,L2,V1,M2} { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 0.74/1.13 (182) {G0,W7,D2,L3,V2,M3} { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X )
% 0.74/1.13 }.
% 0.74/1.13 (183) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ok( X ) }.
% 0.74/1.13 (184) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), check_cpq( X ) }.
% 0.74/1.13 (185) {G0,W6,D2,L3,V1,M3} { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 0.74/1.13 (186) {G0,W7,D4,L1,V0,M1} { contains_pq( i( triple( skol5, create_slb,
% 0.74/1.13 skol6 ) ), skol7 ) }.
% 0.74/1.13 (187) {G0,W15,D5,L1,V0,M1} { ! i( remove_cpq( triple( skol5, create_slb,
% 0.74/1.13 skol6 ), skol7 ) ) = remove_pq( i( triple( skol5, create_slb, skol6 ) ),
% 0.74/1.13 skol7 ) }.
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Total Proof:
% 0.74/1.13
% 0.74/1.13 subsumption: (9) {G0,W3,D2,L1,V1,M1} I { ! contains_pq( create_pq, X ) }.
% 0.74/1.13 parent0: (103) {G0,W3,D2,L1,V1,M1} { ! contains_pq( create_pq, X ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 *** allocated 15000 integers for clauses
% 0.74/1.13 subsumption: (70) {G0,W7,D4,L1,V2,M1} I { i( triple( X, create_slb, Y ) )
% 0.74/1.13 ==> create_pq }.
% 0.74/1.13 parent0: (164) {G0,W7,D4,L1,V2,M1} { i( triple( X, create_slb, Y ) ) =
% 0.74/1.13 create_pq }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := X
% 0.74/1.13 Y := Y
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 0 ==> 0
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 paramod: (398) {G1,W3,D2,L1,V0,M1} { contains_pq( create_pq, skol7 ) }.
% 0.74/1.13 parent0[0]: (70) {G0,W7,D4,L1,V2,M1} I { i( triple( X, create_slb, Y ) )
% 0.74/1.13 ==> create_pq }.
% 0.74/1.13 parent1[0; 1]: (186) {G0,W7,D4,L1,V0,M1} { contains_pq( i( triple( skol5,
% 0.74/1.13 create_slb, skol6 ) ), skol7 ) }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := skol5
% 0.74/1.13 Y := skol6
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 resolution: (399) {G1,W0,D0,L0,V0,M0} { }.
% 0.74/1.13 parent0[0]: (9) {G0,W3,D2,L1,V1,M1} I { ! contains_pq( create_pq, X ) }.
% 0.74/1.13 parent1[0]: (398) {G1,W3,D2,L1,V0,M1} { contains_pq( create_pq, skol7 )
% 0.74/1.13 }.
% 0.74/1.13 substitution0:
% 0.74/1.13 X := skol7
% 0.74/1.13 end
% 0.74/1.13 substitution1:
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 subsumption: (92) {G1,W0,D0,L0,V0,M0} I;d(70);r(9) { }.
% 0.74/1.13 parent0: (399) {G1,W0,D0,L0,V0,M0} { }.
% 0.74/1.13 substitution0:
% 0.74/1.13 end
% 0.74/1.13 permutation0:
% 0.74/1.13 end
% 0.74/1.13
% 0.74/1.13 Proof check complete!
% 0.74/1.13
% 0.74/1.13 Memory use:
% 0.74/1.13
% 0.74/1.13 space for terms: 3294
% 0.74/1.13 space for clauses: 7667
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 clauses generated: 93
% 0.74/1.13 clauses kept: 93
% 0.74/1.13 clauses selected: 0
% 0.74/1.13 clauses deleted: 0
% 0.74/1.13 clauses inuse deleted: 0
% 0.74/1.13
% 0.74/1.13 subsentry: 993
% 0.74/1.13 literals s-matched: 469
% 0.74/1.13 literals matched: 461
% 0.74/1.13 full subsumption: 127
% 0.74/1.13
% 0.74/1.13 checksum: 144258682
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Bliksem ended
%------------------------------------------------------------------------------