TSTP Solution File: SWV366+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV366+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 1.23s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV366+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Wed Jun 15 04:49:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.74/1.09 *** allocated 10000 integers for termspace/termends
% 0.74/1.09 *** allocated 10000 integers for clauses
% 0.74/1.09 *** allocated 10000 integers for justifications
% 0.74/1.09 Bliksem 1.12
% 0.74/1.09
% 0.74/1.09
% 0.74/1.09 Automatic Strategy Selection
% 0.74/1.09
% 0.74/1.09
% 0.74/1.09 Clauses:
% 0.74/1.09
% 0.74/1.09 { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.74/1.09 { less_than( X, Y ), less_than( Y, X ) }.
% 0.74/1.09 { less_than( X, X ) }.
% 0.74/1.09 { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.74/1.09 { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.74/1.09 { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.74/1.09 { less_than( bottom, X ) }.
% 0.74/1.09 { ! isnonempty_pq( create_pq ) }.
% 0.74/1.09 { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.74/1.09 { ! contains_pq( create_pq, X ) }.
% 0.74/1.09 { ! contains_pq( insert_pq( X, Y ), Z ), contains_pq( X, Z ), Y = Z }.
% 0.74/1.09 { ! contains_pq( X, Z ), contains_pq( insert_pq( X, Y ), Z ) }.
% 0.74/1.09 { ! Y = Z, contains_pq( insert_pq( X, Y ), Z ) }.
% 0.74/1.09 { ! issmallestelement_pq( X, Y ), ! contains_pq( X, Z ), less_than( Y, Z )
% 0.74/1.09 }.
% 0.74/1.09 { ! less_than( Y, skol1( Z, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.74/1.09 { contains_pq( X, skol1( X, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.74/1.09 { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 0.74/1.09 { ! contains_pq( X, Z ), Y = Z, remove_pq( insert_pq( X, Y ), Z ) =
% 0.74/1.09 insert_pq( remove_pq( X, Z ), Y ) }.
% 0.74/1.09 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_eff( X
% 0.74/1.09 , Y ) = X }.
% 0.74/1.09 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_res( X
% 0.74/1.09 , Y ) = Y }.
% 0.74/1.09 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_eff(
% 0.74/1.09 X, Y ) = remove_pq( X, Y ) }.
% 0.74/1.09 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_res(
% 0.74/1.09 X, Y ) = Y }.
% 0.74/1.09 { insert_pq( insert_pq( X, Y ), Z ) = insert_pq( insert_pq( X, Z ), Y ) }.
% 0.74/1.09 { ! isnonempty_slb( create_slb ) }.
% 0.74/1.09 { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) ) }.
% 0.74/1.09 { ! contains_slb( create_slb, X ) }.
% 0.74/1.09 { ! contains_slb( insert_slb( X, pair( Y, T ) ), Z ), contains_slb( X, Z )
% 0.74/1.09 , Y = Z }.
% 0.74/1.09 { ! contains_slb( X, Z ), contains_slb( insert_slb( X, pair( Y, T ) ), Z )
% 0.74/1.09 }.
% 0.74/1.09 { ! Y = Z, contains_slb( insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.74/1.09 { ! pair_in_list( create_slb, X, Y ) }.
% 0.74/1.09 { ! pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U ), pair_in_list( X, Z
% 0.74/1.09 , U ), alpha1( Y, Z, T, U ) }.
% 0.74/1.09 { ! pair_in_list( X, Z, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z
% 0.74/1.09 , U ) }.
% 0.74/1.09 { ! alpha1( Y, Z, T, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U
% 0.74/1.09 ) }.
% 0.74/1.09 { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.74/1.09 { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.74/1.09 { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.74/1.09 { remove_slb( insert_slb( X, pair( Y, Z ) ), Y ) = X }.
% 0.74/1.09 { Y = Z, ! contains_slb( X, Z ), remove_slb( insert_slb( X, pair( Y, T ) )
% 0.74/1.09 , Z ) = insert_slb( remove_slb( X, Z ), pair( Y, T ) ) }.
% 0.74/1.09 { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y ) = Z }.
% 0.74/1.09 { Y = Z, ! contains_slb( X, Z ), lookup_slb( insert_slb( X, pair( Y, T ) )
% 0.74/1.09 , Z ) = lookup_slb( X, Z ) }.
% 0.74/1.09 { update_slb( create_slb, X ) = create_slb }.
% 0.74/1.09 { ! strictly_less_than( Y, X ), update_slb( insert_slb( Z, pair( T, Y ) ),
% 0.74/1.09 X ) = insert_slb( update_slb( Z, X ), pair( T, X ) ) }.
% 0.74/1.09 { ! less_than( X, Y ), update_slb( insert_slb( Z, pair( T, Y ) ), X ) =
% 0.74/1.09 insert_slb( update_slb( Z, X ), pair( T, Y ) ) }.
% 0.74/1.09 { succ_cpq( X, X ) }.
% 0.74/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y, Z ) ) }.
% 0.74/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y, Z ) ) }.
% 0.74/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, findmin_cpq_eff( Y ) ) }.
% 0.74/1.09 { ! succ_cpq( X, Y ), succ_cpq( X, removemin_cpq_eff( Y ) ) }.
% 0.74/1.09 { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.74/1.09 { ! less_than( Y, X ), ! check_cpq( triple( Z, insert_slb( T, pair( X, Y )
% 0.74/1.09 ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.74/1.09 { ! less_than( Y, X ), ! check_cpq( triple( Z, T, U ) ), check_cpq( triple
% 0.74/1.09 ( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.74/1.09 { ! strictly_less_than( X, Y ), ! check_cpq( triple( Z, insert_slb( T, pair
% 0.74/1.09 ( X, Y ) ), U ) ) }.
% 0.74/1.09 { ! strictly_less_than( X, Y ), ! ||, check_cpq( triple( Z, insert_slb( T,
% 0.74/1.09 pair( X, Y ) ), U ) ) }.
% 0.74/1.09 { ! contains_cpq( triple( X, Y, Z ), T ), contains_slb( Y, T ) }.
% 0.74/1.09 { ! contains_slb( Y, T ), contains_cpq( triple( X, Y, Z ), T ) }.
% 0.74/1.09 { ! ok( triple( X, Y, bad ) ) }.
% 0.74/1.09 { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.74/1.09 { 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 { i( triple( X, skol5, Z ) ) = i( triple( Y, skol5, T ) ) }.
% 0.74/1.13 { ! i( triple( skol6, insert_slb( skol5, pair( skol10, skol11 ) ), skol8 )
% 0.74/1.13 ) = i( triple( skol7, insert_slb( skol5, pair( skol10, skol11 ) ), skol9
% 0.74/1.13 ) ) }.
% 0.74/1.13
% 0.74/1.13 percentage equality = 0.242105, 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
% 0.74/1.23 nrgoals = 5000000
% 0.74/1.23 totalproof = 1
% 0.74/1.23
% 0.74/1.23 Symbols occurring in the translation:
% 0.74/1.23
% 0.74/1.23 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.74/1.23 . [1, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.74/1.23 || [2, 0] (w:1, o:3, a:1, s:1, b:0),
% 0.74/1.23 ! [4, 1] (w:0, o:28, a:1, s:1, b:0),
% 0.74/1.23 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.23 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.23 less_than [38, 2] (w:1, o:74, a:1, s:1, b:0),
% 0.74/1.23 strictly_less_than [39, 2] (w:1, o:81, a:1, s:1, b:0),
% 0.74/1.23 bottom [40, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.74/1.23 create_pq [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.74/1.23 isnonempty_pq [42, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.74/1.23 insert_pq [43, 2] (w:1, o:82, a:1, s:1, b:0),
% 0.74/1.23 contains_pq [44, 2] (w:1, o:83, a:1, s:1, b:0),
% 0.74/1.23 issmallestelement_pq [45, 2] (w:1, o:84, a:1, s:1, b:0),
% 0.74/1.23 remove_pq [46, 2] (w:1, o:75, a:1, s:1, b:0),
% 0.74/1.23 findmin_pq_eff [47, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.74/1.23 findmin_pq_res [48, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.74/1.23 removemin_pq_eff [49, 2] (w:1, o:76, a:1, s:1, b:0),
% 0.74/1.23 removemin_pq_res [50, 2] (w:1, o:77, a:1, s:1, b:0),
% 0.74/1.23 create_slb [51, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.74/1.23 isnonempty_slb [52, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.74/1.23 pair [53, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.74/1.23 insert_slb [54, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.74/1.23 contains_slb [55, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.74/1.23 pair_in_list [57, 3] (w:1, o:101, a:1, s:1, b:0),
% 0.74/1.23 remove_slb [59, 2] (w:1, o:78, a:1, s:1, b:0),
% 0.74/1.23 lookup_slb [60, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.74/1.23 update_slb [61, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.74/1.23 succ_cpq [62, 2] (w:1, o:92, a:1, s:1, b:0),
% 0.74/1.23 insert_cpq [63, 2] (w:1, o:93, a:1, s:1, b:0),
% 0.74/1.23 remove_cpq [64, 2] (w:1, o:79, a:1, s:1, b:0),
% 0.74/1.23 findmin_cpq_eff [65, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.74/1.23 removemin_cpq_eff [66, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.74/1.23 triple [67, 3] (w:1, o:102, a:1, s:1, b:0),
% 0.74/1.23 check_cpq [68, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.74/1.23 contains_cpq [69, 2] (w:1, o:94, a:1, s:1, b:0),
% 0.74/1.23 bad [70, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.74/1.23 ok [71, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.74/1.23 insert_pqp [72, 2] (w:1, o:95, a:1, s:1, b:0),
% 0.74/1.23 remove_pqp [73, 2] (w:1, o:80, a:1, s:1, b:0),
% 0.74/1.23 findmin_pqp_res [74, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.74/1.23 findmin_cpq_res [75, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.74/1.23 removemin_cpq_res [76, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.74/1.23 i [77, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.74/1.23 pi_sharp_remove [78, 2] (w:1, o:97, a:1, s:1, b:0),
% 0.74/1.23 pi_remove [79, 2] (w:1, o:96, a:1, s:1, b:0),
% 0.74/1.23 pi_sharp_find_min [80, 2] (w:1, o:98, a:1, s:1, b:0),
% 0.74/1.23 pi_find_min [81, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.74/1.23 pi_sharp_removemin [82, 2] (w:1, o:99, a:1, s:1, b:0),
% 0.74/1.23 pi_removemin [83, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.74/1.23 phi [84, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.74/1.23 alpha1 [91, 4] (w:1, o:103, a:1, s:1, b:1),
% 0.74/1.23 alpha2 [92, 1] (w:1, o:46, a:1, s:1, b:1),
% 0.74/1.23 skol1 [93, 2] (w:1, o:100, a:1, s:1, b:1),
% 0.74/1.23 skol2 [94, 1] (w:1, o:47, a:1, s:1, b:1),
% 0.74/1.23 skol3 [95, 1] (w:1, o:48, a:1, s:1, b:1),
% 0.74/1.23 skol4 [96, 1] (w:1, o:49, a:1, s:1, b:1),
% 0.74/1.23 skol5 [97, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.74/1.23 skol6 [98, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.74/1.23 skol7 [99, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.74/1.23 skol8 [100, 0] (w:1, o:24, a:1, s:1, b:1),
% 0.74/1.23 skol9 [101, 0] (w:1, o:25, a:1, s:1, b:1),
% 0.74/1.23 skol10 [102, 0] (w:1, o:26, a:1, s:1, b:1),
% 0.74/1.23 skol11 [103, 0] (w:1, o:27, a:1, s:1, b:1).
% 0.74/1.23
% 0.74/1.23
% 0.74/1.23 Starting Search:
% 0.74/1.23
% 0.74/1.23 *** allocated 15000 integers for clauses
% 0.74/1.23 *** allocated 22500 integers for clauses
% 0.74/1.23 *** allocated 33750 integers for clauses
% 0.74/1.23 *** allocated 15000 integers for termspace/termends
% 0.74/1.23 *** allocated 50625 integers for clauses
% 0.74/1.23 *** allocated 22500 integers for termspace/termends
% 0.74/1.23 *** allocated 75937 integers for clauses
% 0.74/1.23 Resimplifying inuse:
% 0.74/1.23 Done
% 0.74/1.23
% 0.74/1.23 *** allocated 33750 integers for termspace/termends
% 0.74/1.23 *** allocated 113905 integers for clauses
% 0.74/1.23 *** allocated 50625 integers for termspace/termends
% 0.74/1.23
% 0.74/1.23 Intermediate Status:
% 0.74/1.23 Generated: 3982
% 0.74/1.23 Kept: 2001
% 0.74/1.23 Inuse: 161
% 0.74/1.23 Deleted: 1
% 0.74/1.23 Deletedinuse: 0
% 0.74/1.23
% 0.74/1.23 Resimplifying inuse:
% 0.74/1.23 Done
% 0.74/1.23
% 0.74/1.23 *** allocated 170857 integers for clauses
% 0.74/1.23 *** allocated 75937 integers for termspace/termends
% 0.74/1.23 Resimplifying inuse:
% 0.74/1.23 Done
% 0.74/1.23
% 0.74/1.23 *** allocated 256285 integers for clauses
% 0.74/1.23 *** allocated 113905 integers for termspace/termends
% 0.74/1.23
% 0.74/1.23 Intermediate Status:
% 0.74/1.23 Generated: 8142
% 0.74/1.23 Kept: 4100
% 0.74/1.23 Inuse: 235
% 0.74/1.23 Deleted: 1
% 0.74/1.23 Deletedinuse: 0
% 0.74/1.23
% 0.74/1.23 Resimplifying inuse:
% 0.74/1.23 Done
% 0.74/1.23
% 0.74/1.23 *** allocated 384427 integers for clauses
% 0.74/1.23 Resimplifying inuse:
% 0.74/1.23 Done
% 0.74/1.23
% 0.74/1.23 *** allocated 170857 integers for termspace/termends
% 0.74/1.23
% 0.74/1.23 Bliksems!, er is een bewijs:
% 0.74/1.23 % SZS status Theorem
% 0.74/1.23 % SZS output start Refutation
% 0.74/1.23
% 0.74/1.23 (71) {G0,W17,D6,L1,V5,M1} I { i( triple( X, insert_slb( Y, pair( T, U ) ),
% 0.74/1.23 Z ) ) ==> insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 0.74/1.23 (92) {G0,W11,D4,L1,V4,M1} I { i( triple( X, skol5, Z ) ) = i( triple( Y,
% 0.74/1.23 skol5, T ) ) }.
% 0.74/1.23 (93) {G1,W15,D5,L1,V0,M1} I;d(71);d(71) { ! insert_pq( i( triple( skol7,
% 0.74/1.23 skol5, skol9 ) ), skol10 ) ==> insert_pq( i( triple( skol6, skol5, skol8
% 0.74/1.23 ) ), skol10 ) }.
% 0.74/1.23 (5702) {G2,W15,D5,L1,V2,M1} P(92,93) { ! insert_pq( i( triple( X, skol5, Y
% 0.74/1.23 ) ), skol10 ) = insert_pq( i( triple( skol6, skol5, skol8 ) ), skol10 )
% 0.74/1.23 }.
% 0.74/1.23 (5704) {G3,W0,D0,L0,V0,M0} Q(5702) { }.
% 0.74/1.23
% 0.74/1.23
% 0.74/1.23 % SZS output end Refutation
% 0.74/1.23 found a proof!
% 0.74/1.23
% 0.74/1.23
% 0.74/1.23 Unprocessed initial clauses:
% 0.74/1.23
% 0.74/1.23 (5706) {G0,W9,D2,L3,V3,M3} { ! less_than( X, Z ), ! less_than( Z, Y ),
% 0.74/1.23 less_than( X, Y ) }.
% 0.74/1.23 (5707) {G0,W6,D2,L2,V2,M2} { less_than( X, Y ), less_than( Y, X ) }.
% 0.74/1.23 (5708) {G0,W3,D2,L1,V1,M1} { less_than( X, X ) }.
% 0.74/1.23 (5709) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), less_than( X, Y
% 0.74/1.23 ) }.
% 0.74/1.23 (5710) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), ! less_than( Y
% 0.74/1.23 , X ) }.
% 0.74/1.23 (5711) {G0,W9,D2,L3,V2,M3} { ! less_than( X, Y ), less_than( Y, X ),
% 0.74/1.23 strictly_less_than( X, Y ) }.
% 0.74/1.23 (5712) {G0,W3,D2,L1,V1,M1} { less_than( bottom, X ) }.
% 0.74/1.23 (5713) {G0,W2,D2,L1,V0,M1} { ! isnonempty_pq( create_pq ) }.
% 0.74/1.23 (5714) {G0,W4,D3,L1,V2,M1} { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.74/1.23 (5715) {G0,W3,D2,L1,V1,M1} { ! contains_pq( create_pq, X ) }.
% 0.74/1.23 (5716) {G0,W11,D3,L3,V3,M3} { ! contains_pq( insert_pq( X, Y ), Z ),
% 0.74/1.23 contains_pq( X, Z ), Y = Z }.
% 0.74/1.23 (5717) {G0,W8,D3,L2,V3,M2} { ! contains_pq( X, Z ), contains_pq( insert_pq
% 0.74/1.23 ( X, Y ), Z ) }.
% 0.74/1.23 (5718) {G0,W8,D3,L2,V3,M2} { ! Y = Z, contains_pq( insert_pq( X, Y ), Z )
% 0.74/1.23 }.
% 0.74/1.23 (5719) {G0,W9,D2,L3,V3,M3} { ! issmallestelement_pq( X, Y ), ! contains_pq
% 0.74/1.23 ( X, Z ), less_than( Y, Z ) }.
% 0.74/1.23 (5720) {G0,W8,D3,L2,V3,M2} { ! less_than( Y, skol1( Z, Y ) ),
% 0.74/1.23 issmallestelement_pq( X, Y ) }.
% 0.74/1.23 (5721) {G0,W8,D3,L2,V2,M2} { contains_pq( X, skol1( X, Y ) ),
% 0.74/1.23 issmallestelement_pq( X, Y ) }.
% 0.74/1.23 (5722) {G0,W7,D4,L1,V2,M1} { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 0.74/1.23 (5723) {G0,W17,D4,L3,V3,M3} { ! contains_pq( X, Z ), Y = Z, remove_pq(
% 0.74/1.23 insert_pq( X, Y ), Z ) = insert_pq( remove_pq( X, Z ), Y ) }.
% 0.74/1.23 (5724) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 0.74/1.23 issmallestelement_pq( X, Y ), findmin_pq_eff( X, Y ) = X }.
% 0.74/1.23 (5725) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 0.74/1.23 issmallestelement_pq( X, Y ), findmin_pq_res( X, Y ) = Y }.
% 0.74/1.23 (5726) {G0,W13,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 0.74/1.23 issmallestelement_pq( X, Y ), removemin_pq_eff( X, Y ) = remove_pq( X, Y
% 0.74/1.23 ) }.
% 0.74/1.23 (5727) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 0.74/1.23 issmallestelement_pq( X, Y ), removemin_pq_res( X, Y ) = Y }.
% 0.74/1.23 (5728) {G0,W11,D4,L1,V3,M1} { insert_pq( insert_pq( X, Y ), Z ) =
% 0.74/1.23 insert_pq( insert_pq( X, Z ), Y ) }.
% 0.74/1.23 (5729) {G0,W2,D2,L1,V0,M1} { ! isnonempty_slb( create_slb ) }.
% 0.74/1.23 (5730) {G0,W6,D4,L1,V3,M1} { isnonempty_slb( insert_slb( X, pair( Y, Z ) )
% 0.74/1.23 ) }.
% 0.74/1.23 (5731) {G0,W3,D2,L1,V1,M1} { ! contains_slb( create_slb, X ) }.
% 0.74/1.23 (5732) {G0,W13,D4,L3,V4,M3} { ! contains_slb( insert_slb( X, pair( Y, T )
% 0.74/1.23 ), Z ), contains_slb( X, Z ), Y = Z }.
% 0.74/1.23 (5733) {G0,W10,D4,L2,V4,M2} { ! contains_slb( X, Z ), contains_slb(
% 0.74/1.23 insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.74/1.23 (5734) {G0,W10,D4,L2,V4,M2} { ! Y = Z, contains_slb( insert_slb( X, pair(
% 0.74/1.23 Y, T ) ), Z ) }.
% 0.74/1.23 (5735) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 0.74/1.23 (5736) {G0,W17,D4,L3,V5,M3} { ! pair_in_list( insert_slb( X, pair( Y, T )
% 0.74/1.23 ), Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 0.74/1.23 (5737) {G0,W12,D4,L2,V5,M2} { ! pair_in_list( X, Z, U ), pair_in_list(
% 0.74/1.23 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.74/1.23 (5738) {G0,W13,D4,L2,V5,M2} { ! alpha1( Y, Z, T, U ), pair_in_list(
% 0.74/1.23 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.74/1.23 (5739) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.74/1.23 (5740) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.74/1.23 (5741) {G0,W11,D2,L3,V4,M3} { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.74/1.23 (5742) {G0,W9,D5,L1,V3,M1} { remove_slb( insert_slb( X, pair( Y, Z ) ), Y
% 0.74/1.23 ) = X }.
% 0.74/1.23 (5743) {G0,W21,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), remove_slb(
% 0.74/1.23 insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 0.74/1.23 ( Y, T ) ) }.
% 0.74/1.23 (5744) {G0,W9,D5,L1,V3,M1} { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y
% 0.74/1.23 ) = Z }.
% 0.74/1.23 (5745) {G0,W17,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), lookup_slb(
% 0.74/1.23 insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 0.74/1.23 (5746) {G0,W5,D3,L1,V1,M1} { update_slb( create_slb, X ) = create_slb }.
% 0.74/1.23 (5747) {G0,W18,D5,L2,V4,M2} { ! strictly_less_than( Y, X ), update_slb(
% 0.74/1.23 insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 0.74/1.23 ( T, X ) ) }.
% 0.74/1.23 (5748) {G0,W18,D5,L2,V4,M2} { ! less_than( X, Y ), update_slb( insert_slb
% 0.74/1.23 ( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 0.74/1.23 }.
% 0.74/1.23 (5749) {G0,W3,D2,L1,V1,M1} { succ_cpq( X, X ) }.
% 0.74/1.23 (5750) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq(
% 0.74/1.23 Y, Z ) ) }.
% 0.74/1.23 (5751) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq(
% 0.74/1.23 Y, Z ) ) }.
% 0.74/1.23 (5752) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.74/1.23 findmin_cpq_eff( Y ) ) }.
% 0.74/1.23 (5753) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 0.74/1.23 removemin_cpq_eff( Y ) ) }.
% 0.74/1.23 (5754) {G0,W5,D3,L1,V2,M1} { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.74/1.23 (5755) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z
% 0.74/1.23 , insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) )
% 0.74/1.23 }.
% 0.74/1.23 (5756) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z
% 0.74/1.23 , T, U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) )
% 0.74/1.23 }.
% 0.74/1.23 (5757) {G0,W12,D5,L2,V5,M2} { ! strictly_less_than( X, Y ), ! check_cpq(
% 0.74/1.23 triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.74/1.23 (5758) {G0,W13,D5,L3,V5,M3} { ! strictly_less_than( X, Y ), ! ||,
% 0.74/1.23 check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.74/1.23 (5759) {G0,W9,D3,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z ), T ),
% 0.74/1.23 contains_slb( Y, T ) }.
% 0.74/1.23 (5760) {G0,W9,D3,L2,V4,M2} { ! contains_slb( Y, T ), contains_cpq( triple
% 0.74/1.23 ( X, Y, Z ), T ) }.
% 0.74/1.23 (5761) {G0,W5,D3,L1,V2,M1} { ! ok( triple( X, Y, bad ) ) }.
% 0.74/1.23 (5762) {G0,W6,D3,L2,V2,M2} { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.74/1.23 (5763) {G0,W8,D3,L2,V3,M2} { ok( triple( Y, Z, X ) ), X = bad }.
% 0.74/1.23 (5764) {G0,W17,D5,L1,V4,M1} { insert_cpq( triple( X, Y, Z ), T ) = triple
% 0.74/1.23 ( insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.74/1.23 (5765) {G0,W14,D4,L2,V4,M2} { contains_slb( X, Y ), remove_cpq( triple( Z
% 0.74/1.23 , X, T ), Y ) = triple( Z, X, bad ) }.
% 0.74/1.23 (5766) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! less_than(
% 0.74/1.23 lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.74/1.23 remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 0.74/1.23 (5767) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! strictly_less_than
% 0.74/1.23 ( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 0.74/1.23 remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 0.74/1.23 (5768) {G0,W10,D4,L1,V2,M1} { findmin_cpq_eff( triple( X, create_slb, Y )
% 0.74/1.23 ) = triple( X, create_slb, bad ) }.
% 0.74/1.23 (5769) {G0,W20,D5,L3,V3,M3} { Y = create_slb, contains_slb( Y,
% 0.74/1.23 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 0.74/1.23 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.74/1.23 (5770) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.74/1.23 findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ),
% 0.74/1.23 lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 0.74/1.23 ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.74/1.23 (5771) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 0.74/1.23 findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 0.74/1.23 ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 0.74/1.23 ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 0.74/1.23 (5772) {G0,W7,D4,L1,V2,M1} { findmin_cpq_res( triple( X, create_slb, Y ) )
% 0.74/1.23 = bottom }.
% 0.74/1.23 (5773) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res( triple( Y,
% 0.74/1.23 X, Z ) ) = findmin_pqp_res( Y ) }.
% 0.74/1.23 (5774) {G0,W8,D4,L1,V1,M1} { removemin_cpq_eff( X ) = remove_cpq(
% 0.74/1.23 findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 0.74/1.23 (5775) {G0,W5,D3,L1,V1,M1} { removemin_cpq_res( X ) = findmin_cpq_res( X )
% 0.74/1.23 }.
% 0.74/1.23 (5776) {G0,W7,D4,L1,V2,M1} { i( triple( X, create_slb, Y ) ) = create_pq
% 0.74/1.23 }.
% 0.74/1.23 (5777) {G0,W17,D6,L1,V5,M1} { i( triple( X, insert_slb( Y, pair( T, U ) )
% 0.74/1.23 , Z ) ) = insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 0.74/1.23 (5778) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_remove( X, Y ), contains_pq( X, Y
% 0.74/1.23 ) }.
% 0.74/1.23 (5779) {G0,W6,D2,L2,V2,M2} { ! contains_pq( X, Y ), pi_sharp_remove( X, Y
% 0.74/1.23 ) }.
% 0.74/1.23 (5780) {G0,W7,D3,L2,V2,M2} { ! pi_remove( X, Y ), pi_sharp_remove( i( X )
% 0.74/1.23 , Y ) }.
% 0.74/1.23 (5781) {G0,W7,D3,L2,V2,M2} { ! pi_sharp_remove( i( X ), Y ), pi_remove( X
% 0.74/1.23 , Y ) }.
% 0.74/1.23 (5782) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ), contains_pq( X,
% 0.74/1.23 Y ) }.
% 0.74/1.23 (5783) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ),
% 0.74/1.23 issmallestelement_pq( X, Y ) }.
% 0.74/1.23 (5784) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.74/1.23 ( X, Y ), pi_sharp_find_min( X, Y ) }.
% 0.74/1.23 (5785) {G0,W7,D3,L2,V1,M2} { ! pi_find_min( X ), pi_sharp_find_min( i( X )
% 0.74/1.23 , skol2( X ) ) }.
% 0.74/1.23 (5786) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ), pi_find_min
% 0.74/1.23 ( X ) }.
% 0.74/1.23 (5787) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ), contains_pq( X
% 0.74/1.23 , Y ) }.
% 0.74/1.23 (5788) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ),
% 0.74/1.23 issmallestelement_pq( X, Y ) }.
% 0.74/1.23 (5789) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), ! issmallestelement_pq
% 0.74/1.23 ( X, Y ), pi_sharp_removemin( X, Y ) }.
% 0.74/1.23 (5790) {G0,W7,D3,L2,V1,M2} { ! pi_removemin( X ), pi_sharp_find_min( i( X
% 0.74/1.23 ), skol3( X ) ) }.
% 0.74/1.23 (5791) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ),
% 0.74/1.23 pi_removemin( X ) }.
% 0.74/1.23 (5792) {G0,W5,D3,L2,V2,M2} { ! phi( X ), alpha2( skol4( Y ) ) }.
% 0.74/1.23 (5793) {G0,W6,D3,L2,V1,M2} { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 0.74/1.23 (5794) {G0,W7,D2,L3,V2,M3} { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X )
% 0.74/1.23 }.
% 0.74/1.23 (5795) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ok( X ) }.
% 0.74/1.23 (5796) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), check_cpq( X ) }.
% 0.74/1.23 (5797) {G0,W6,D2,L3,V1,M3} { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 0.74/1.23 (5798) {G0,W11,D4,L1,V4,M1} { i( triple( X, skol5, Z ) ) = i( triple( Y,
% 0.74/1.23 skol5, T ) ) }.
% 0.74/1.23 (5799) {G0,W19,D6,L1,V0,M1} { ! i( triple( skol6, insert_slb( skol5, pair
% 0.74/1.23 ( skol10, skol11 ) ), skol8 ) ) = i( triple( skol7, insert_slb( skol5,
% 0.74/1.23 pair( skol10, skol11 ) ), skol9 ) ) }.
% 0.74/1.23
% 0.74/1.23
% 0.74/1.23 Total Proof:
% 0.74/1.23
% 0.74/1.23 subsumption: (71) {G0,W17,D6,L1,V5,M1} I { i( triple( X, insert_slb( Y,
% 0.74/1.23 pair( T, U ) ), Z ) ) ==> insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 0.74/1.23 parent0: (5777) {G0,W17,D6,L1,V5,M1} { i( triple( X, insert_slb( Y, pair(
% 0.74/1.23 T, U ) ), Z ) ) = insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 X := X
% 0.74/1.23 Y := Y
% 0.74/1.23 Z := Z
% 0.74/1.23 T := T
% 0.74/1.23 U := U
% 0.74/1.23 end
% 0.74/1.23 permutation0:
% 0.74/1.23 0 ==> 0
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 subsumption: (92) {G0,W11,D4,L1,V4,M1} I { i( triple( X, skol5, Z ) ) = i(
% 0.74/1.23 triple( Y, skol5, T ) ) }.
% 0.74/1.23 parent0: (5798) {G0,W11,D4,L1,V4,M1} { i( triple( X, skol5, Z ) ) = i(
% 0.74/1.23 triple( Y, skol5, T ) ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 X := X
% 0.74/1.23 Y := Y
% 0.74/1.23 Z := Z
% 0.74/1.23 T := T
% 0.74/1.23 end
% 0.74/1.23 permutation0:
% 0.74/1.23 0 ==> 0
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 paramod: (6163) {G1,W17,D6,L1,V0,M1} { ! i( triple( skol6, insert_slb(
% 0.74/1.23 skol5, pair( skol10, skol11 ) ), skol8 ) ) = insert_pq( i( triple( skol7
% 0.74/1.23 , skol5, skol9 ) ), skol10 ) }.
% 0.74/1.23 parent0[0]: (71) {G0,W17,D6,L1,V5,M1} I { i( triple( X, insert_slb( Y, pair
% 0.74/1.23 ( T, U ) ), Z ) ) ==> insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 0.74/1.23 parent1[0; 11]: (5799) {G0,W19,D6,L1,V0,M1} { ! i( triple( skol6,
% 0.74/1.23 insert_slb( skol5, pair( skol10, skol11 ) ), skol8 ) ) = i( triple( skol7
% 0.74/1.23 , insert_slb( skol5, pair( skol10, skol11 ) ), skol9 ) ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 X := skol7
% 0.74/1.23 Y := skol5
% 0.74/1.23 Z := skol9
% 0.74/1.23 T := skol10
% 0.74/1.23 U := skol11
% 0.74/1.23 end
% 0.74/1.23 substitution1:
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 paramod: (6165) {G1,W15,D5,L1,V0,M1} { ! insert_pq( i( triple( skol6,
% 0.74/1.23 skol5, skol8 ) ), skol10 ) = insert_pq( i( triple( skol7, skol5, skol9 )
% 0.74/1.23 ), skol10 ) }.
% 0.74/1.23 parent0[0]: (71) {G0,W17,D6,L1,V5,M1} I { i( triple( X, insert_slb( Y, pair
% 0.74/1.23 ( T, U ) ), Z ) ) ==> insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 0.74/1.23 parent1[0; 2]: (6163) {G1,W17,D6,L1,V0,M1} { ! i( triple( skol6,
% 0.74/1.23 insert_slb( skol5, pair( skol10, skol11 ) ), skol8 ) ) = insert_pq( i(
% 0.74/1.23 triple( skol7, skol5, skol9 ) ), skol10 ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 X := skol6
% 0.74/1.23 Y := skol5
% 0.74/1.23 Z := skol8
% 0.74/1.23 T := skol10
% 0.74/1.23 U := skol11
% 0.74/1.23 end
% 0.74/1.23 substitution1:
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 eqswap: (6166) {G1,W15,D5,L1,V0,M1} { ! insert_pq( i( triple( skol7, skol5
% 0.74/1.23 , skol9 ) ), skol10 ) = insert_pq( i( triple( skol6, skol5, skol8 ) ),
% 0.74/1.23 skol10 ) }.
% 0.74/1.23 parent0[0]: (6165) {G1,W15,D5,L1,V0,M1} { ! insert_pq( i( triple( skol6,
% 0.74/1.23 skol5, skol8 ) ), skol10 ) = insert_pq( i( triple( skol7, skol5, skol9 )
% 0.74/1.23 ), skol10 ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 subsumption: (93) {G1,W15,D5,L1,V0,M1} I;d(71);d(71) { ! insert_pq( i(
% 0.74/1.23 triple( skol7, skol5, skol9 ) ), skol10 ) ==> insert_pq( i( triple( skol6
% 0.74/1.23 , skol5, skol8 ) ), skol10 ) }.
% 0.74/1.23 parent0: (6166) {G1,W15,D5,L1,V0,M1} { ! insert_pq( i( triple( skol7,
% 0.74/1.23 skol5, skol9 ) ), skol10 ) = insert_pq( i( triple( skol6, skol5, skol8 )
% 0.74/1.23 ), skol10 ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 end
% 0.74/1.23 permutation0:
% 0.74/1.23 0 ==> 0
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 eqswap: (6167) {G1,W15,D5,L1,V0,M1} { ! insert_pq( i( triple( skol6, skol5
% 0.74/1.23 , skol8 ) ), skol10 ) ==> insert_pq( i( triple( skol7, skol5, skol9 ) ),
% 0.74/1.23 skol10 ) }.
% 0.74/1.23 parent0[0]: (93) {G1,W15,D5,L1,V0,M1} I;d(71);d(71) { ! insert_pq( i(
% 0.74/1.23 triple( skol7, skol5, skol9 ) ), skol10 ) ==> insert_pq( i( triple( skol6
% 0.74/1.23 , skol5, skol8 ) ), skol10 ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 paramod: (6169) {G1,W15,D5,L1,V2,M1} { ! insert_pq( i( triple( skol6,
% 0.74/1.23 skol5, skol8 ) ), skol10 ) ==> insert_pq( i( triple( X, skol5, Y ) ),
% 0.74/1.23 skol10 ) }.
% 0.74/1.23 parent0[0]: (92) {G0,W11,D4,L1,V4,M1} I { i( triple( X, skol5, Z ) ) = i(
% 0.74/1.23 triple( Y, skol5, T ) ) }.
% 0.74/1.23 parent1[0; 10]: (6167) {G1,W15,D5,L1,V0,M1} { ! insert_pq( i( triple(
% 0.74/1.23 skol6, skol5, skol8 ) ), skol10 ) ==> insert_pq( i( triple( skol7, skol5
% 0.74/1.23 , skol9 ) ), skol10 ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 X := skol7
% 0.74/1.23 Y := X
% 0.74/1.23 Z := skol9
% 0.74/1.23 T := Y
% 0.74/1.23 end
% 0.74/1.23 substitution1:
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 paramod: (6170) {G1,W15,D5,L1,V4,M1} { ! insert_pq( i( triple( Z, skol5, T
% 0.74/1.23 ) ), skol10 ) ==> insert_pq( i( triple( X, skol5, Y ) ), skol10 ) }.
% 0.74/1.23 parent0[0]: (92) {G0,W11,D4,L1,V4,M1} I { i( triple( X, skol5, Z ) ) = i(
% 0.74/1.23 triple( Y, skol5, T ) ) }.
% 0.74/1.23 parent1[0; 3]: (6169) {G1,W15,D5,L1,V2,M1} { ! insert_pq( i( triple( skol6
% 0.74/1.23 , skol5, skol8 ) ), skol10 ) ==> insert_pq( i( triple( X, skol5, Y ) ),
% 0.74/1.23 skol10 ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 X := skol6
% 0.74/1.23 Y := Z
% 0.74/1.23 Z := skol8
% 0.74/1.23 T := T
% 0.74/1.23 end
% 0.74/1.23 substitution1:
% 0.74/1.23 X := X
% 0.74/1.23 Y := Y
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 subsumption: (5702) {G2,W15,D5,L1,V2,M1} P(92,93) { ! insert_pq( i( triple
% 0.74/1.23 ( X, skol5, Y ) ), skol10 ) = insert_pq( i( triple( skol6, skol5, skol8 )
% 0.74/1.23 ), skol10 ) }.
% 0.74/1.23 parent0: (6170) {G1,W15,D5,L1,V4,M1} { ! insert_pq( i( triple( Z, skol5, T
% 0.74/1.23 ) ), skol10 ) ==> insert_pq( i( triple( X, skol5, Y ) ), skol10 ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 X := skol6
% 0.74/1.23 Y := skol8
% 0.74/1.23 Z := X
% 0.74/1.23 T := Y
% 0.74/1.23 end
% 0.74/1.23 permutation0:
% 0.74/1.23 0 ==> 0
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 eqswap: (6171) {G2,W15,D5,L1,V2,M1} { ! insert_pq( i( triple( skol6, skol5
% 0.74/1.23 , skol8 ) ), skol10 ) = insert_pq( i( triple( X, skol5, Y ) ), skol10 )
% 0.74/1.23 }.
% 0.74/1.23 parent0[0]: (5702) {G2,W15,D5,L1,V2,M1} P(92,93) { ! insert_pq( i( triple(
% 0.74/1.23 X, skol5, Y ) ), skol10 ) = insert_pq( i( triple( skol6, skol5, skol8 ) )
% 0.74/1.23 , skol10 ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 X := X
% 0.74/1.23 Y := Y
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 eqrefl: (6172) {G0,W0,D0,L0,V0,M0} { }.
% 0.74/1.23 parent0[0]: (6171) {G2,W15,D5,L1,V2,M1} { ! insert_pq( i( triple( skol6,
% 0.74/1.23 skol5, skol8 ) ), skol10 ) = insert_pq( i( triple( X, skol5, Y ) ),
% 0.74/1.23 skol10 ) }.
% 0.74/1.23 substitution0:
% 0.74/1.23 X := skol6
% 0.74/1.23 Y := skol8
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 subsumption: (5704) {G3,W0,D0,L0,V0,M0} Q(5702) { }.
% 0.74/1.23 parent0: (6172) {G0,W0,D0,L0,V0,M0} { }.
% 0.74/1.23 substitution0:
% 0.74/1.23 end
% 0.74/1.23 permutation0:
% 0.74/1.23 end
% 0.74/1.23
% 0.74/1.23 Proof check complete!
% 0.74/1.23
% 0.74/1.23 Memory use:
% 0.74/1.23
% 0.74/1.23 space for terms: 118162
% 0.74/1.23 space for clauses: 296905
% 0.74/1.23
% 0.74/1.23
% 0.74/1.23 clauses generated: 12482
% 0.74/1.23 clauses kept: 5705
% 0.74/1.23 clauses selected: 280
% 0.74/1.23 clauses deleted: 3
% 0.74/1.23 clauses inuse deleted: 2
% 0.74/1.23
% 0.74/1.23 subsentry: 12242
% 0.74/1.23 literals s-matched: 9502
% 0.74/1.23 literals matched: 9191
% 0.74/1.23 full subsumption: 3074
% 0.74/1.23
% 0.74/1.23 checksum: 1874099217
% 0.74/1.23
% 0.74/1.23
% 0.74/1.23 Bliksem ended
%------------------------------------------------------------------------------