TSTP Solution File: SWV371+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV371+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:24:37 EDT 2022
% Result : Theorem 1.63s 2.00s
% Output : Refutation 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV371+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n010.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 : Tue Jun 14 15:28:24 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.74/1.13 *** allocated 10000 integers for termspace/termends
% 0.74/1.13 *** allocated 10000 integers for clauses
% 0.74/1.13 *** allocated 10000 integers for justifications
% 0.74/1.13 Bliksem 1.12
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Automatic Strategy Selection
% 0.74/1.13
% 0.74/1.13
% 0.74/1.13 Clauses:
% 0.74/1.13
% 0.74/1.13 { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.74/1.13 { less_than( X, Y ), less_than( Y, X ) }.
% 0.74/1.13 { less_than( X, X ) }.
% 0.74/1.13 { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.74/1.13 { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.74/1.13 { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.74/1.13 { less_than( bottom, X ) }.
% 0.74/1.13 { ! isnonempty_pq( create_pq ) }.
% 0.74/1.13 { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.74/1.13 { ! contains_pq( create_pq, X ) }.
% 0.74/1.13 { ! contains_pq( insert_pq( X, Y ), Z ), contains_pq( X, Z ), Y = Z }.
% 0.74/1.13 { ! contains_pq( X, Z ), contains_pq( insert_pq( X, Y ), Z ) }.
% 0.74/1.13 { ! Y = Z, contains_pq( insert_pq( X, Y ), Z ) }.
% 0.74/1.13 { ! issmallestelement_pq( X, Y ), ! contains_pq( X, Z ), less_than( Y, Z )
% 0.74/1.13 }.
% 0.74/1.13 { ! less_than( Y, skol1( Z, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.74/1.13 { 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 }.
% 0.74/1.17 { insert_cpq( triple( X, Y, Z ), T ) = triple( insert_pqp( X, T ),
% 0.74/1.17 insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.74/1.17 { contains_slb( X, Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( Z, X,
% 0.74/1.17 bad ) }.
% 0.74/1.17 { ! contains_slb( X, Y ), ! less_than( lookup_slb( X, Y ), Y ), remove_cpq
% 0.74/1.17 ( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y )
% 0.74/1.17 , T ) }.
% 0.74/1.17 { ! contains_slb( X, Y ), ! strictly_less_than( Y, lookup_slb( X, Y ) ),
% 0.74/1.17 remove_cpq( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ),
% 0.74/1.17 remove_slb( X, Y ), bad ) }.
% 0.74/1.17 { findmin_cpq_eff( triple( X, create_slb, Y ) ) = triple( X, create_slb,
% 0.74/1.17 bad ) }.
% 0.74/1.17 { Y = create_slb, contains_slb( Y, findmin_pqp_res( X ) ), findmin_cpq_eff
% 0.74/1.17 ( triple( X, Y, Z ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) )
% 0.74/1.17 , bad ) }.
% 0.74/1.17 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), !
% 0.74/1.17 strictly_less_than( findmin_pqp_res( X ), lookup_slb( Y, findmin_pqp_res
% 0.74/1.17 ( X ) ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb(
% 0.74/1.17 Y, findmin_pqp_res( X ) ), bad ) }.
% 0.74/1.17 { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! less_than(
% 0.74/1.17 lookup_slb( Y, findmin_pqp_res( X ) ), findmin_pqp_res( X ) ),
% 0.74/1.17 findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( Y,
% 0.74/1.17 findmin_pqp_res( X ) ), Z ) }.
% 0.74/1.17 { findmin_cpq_res( triple( X, create_slb, Y ) ) = bottom }.
% 0.74/1.17 { X = create_slb, findmin_cpq_res( triple( Y, X, Z ) ) = findmin_pqp_res( Y
% 0.74/1.17 ) }.
% 0.74/1.17 { removemin_cpq_eff( X ) = remove_cpq( findmin_cpq_eff( X ),
% 0.74/1.17 findmin_cpq_res( X ) ) }.
% 0.74/1.17 { removemin_cpq_res( X ) = findmin_cpq_res( X ) }.
% 0.74/1.17 { i( triple( X, create_slb, Y ) ) = create_pq }.
% 0.74/1.17 { i( triple( X, insert_slb( Y, pair( T, U ) ), Z ) ) = insert_pq( i( triple
% 0.74/1.17 ( X, Y, Z ) ), T ) }.
% 0.74/1.17 { ! pi_sharp_remove( X, Y ), contains_pq( X, Y ) }.
% 0.74/1.17 { ! contains_pq( X, Y ), pi_sharp_remove( X, Y ) }.
% 0.74/1.17 { ! pi_remove( X, Y ), pi_sharp_remove( i( X ), Y ) }.
% 0.74/1.17 { ! pi_sharp_remove( i( X ), Y ), pi_remove( X, Y ) }.
% 0.74/1.17 { ! pi_sharp_find_min( X, Y ), contains_pq( X, Y ) }.
% 0.74/1.17 { ! pi_sharp_find_min( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.74/1.17 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_find_min
% 0.74/1.17 ( X, Y ) }.
% 0.74/1.17 { ! pi_find_min( X ), pi_sharp_find_min( i( X ), skol2( X ) ) }.
% 0.74/1.17 { ! pi_sharp_find_min( i( X ), Y ), pi_find_min( X ) }.
% 0.74/1.17 { ! pi_sharp_removemin( X, Y ), contains_pq( X, Y ) }.
% 0.74/1.17 { ! pi_sharp_removemin( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.74/1.17 { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_removemin
% 0.74/1.17 ( X, Y ) }.
% 0.74/1.17 { ! pi_removemin( X ), pi_sharp_find_min( i( X ), skol3( X ) ) }.
% 0.74/1.17 { ! pi_sharp_find_min( i( X ), Y ), pi_removemin( X ) }.
% 0.74/1.17 { ! phi( X ), alpha2( skol4( Y ) ) }.
% 0.74/1.17 { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 0.74/1.17 { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X ) }.
% 0.74/1.17 { ! alpha2( X ), ok( X ) }.
% 0.74/1.17 { ! alpha2( X ), check_cpq( X ) }.
% 0.74/1.17 { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 0.74/1.17 { ! phi( findmin_cpq_eff( triple( X, Y, Z ) ) ), contains_pq( i( triple( X
% 0.74/1.17 , Y, Z ) ), findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 0.74/1.17 { ! phi( findmin_cpq_eff( triple( X, Y, Z ) ) ), issmallestelement_pq( i(
% 0.74/1.17 triple( X, Y, Z ) ), findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 0.74/1.17 { phi( findmin_cpq_eff( triple( skol5, skol6, skol7 ) ) ) }.
% 0.74/1.17 { ! pi_sharp_find_min( i( triple( skol5, skol6, skol7 ) ), findmin_cpq_res
% 0.74/1.17 ( triple( skol5, skol6, skol7 ) ) ) }.
% 0.74/1.17
% 0.74/1.17 percentage equality = 0.226804, percentage horn = 0.843750
% 0.74/1.17 This is a problem with some equality
% 0.74/1.17
% 0.74/1.17
% 0.74/1.17
% 0.74/1.17 Options Used:
% 0.74/1.17
% 0.74/1.17 useres = 1
% 0.74/1.17 useparamod = 1
% 0.74/1.17 useeqrefl = 1
% 0.74/1.17 useeqfact = 1
% 0.74/1.17 usefactor = 1
% 0.74/1.17 usesimpsplitting = 0
% 0.74/1.17 usesimpdemod = 5
% 0.74/1.17 usesimpres = 3
% 0.74/1.17
% 0.74/1.17 resimpinuse = 1000
% 0.74/1.17 resimpclauses = 20000
% 0.74/1.17 substype = eqrewr
% 0.74/1.17 backwardsubs = 1
% 0.74/1.17 selectoldest = 5
% 0.74/1.17
% 0.74/1.17 litorderings [0] = split
% 0.74/1.17 litorderings [1] = extend the termordering, first sorting on arguments
% 0.74/1.17
% 0.74/1.17 termordering = kbo
% 0.74/1.17
% 0.74/1.17 litapriori = 0
% 0.74/1.17 termapriori = 1
% 0.74/1.17 litaposteriori = 0
% 0.74/1.17 termaposteriori = 0
% 0.74/1.17 demodaposteriori = 0
% 0.74/1.17 ordereqreflfact = 0
% 0.74/1.17
% 0.74/1.17 litselect = negord
% 0.74/1.17
% 0.74/1.17 maxweight = 15
% 0.74/1.17 maxdepth = 30000
% 0.74/1.17 maxlength = 115
% 0.74/1.17 maxnrvars = 195
% 0.74/1.17 excuselevel = 1
% 0.74/1.17 increasemaxweight = 1
% 1.63/2.00
% 1.63/2.00 maxselected = 10000000
% 1.63/2.00 maxnrclauses = 10000000
% 1.63/2.00
% 1.63/2.00 showgenerated = 0
% 1.63/2.00 showkept = 0
% 1.63/2.00 showselected = 0
% 1.63/2.00 showdeleted = 0
% 1.63/2.00 showresimp = 1
% 1.63/2.00 showstatus = 2000
% 1.63/2.00
% 1.63/2.00 prologoutput = 0
% 1.63/2.00 nrgoals = 5000000
% 1.63/2.00 totalproof = 1
% 1.63/2.00
% 1.63/2.00 Symbols occurring in the translation:
% 1.63/2.00
% 1.63/2.00 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.63/2.00 . [1, 2] (w:1, o:40, a:1, s:1, b:0),
% 1.63/2.00 || [2, 0] (w:1, o:3, a:1, s:1, b:0),
% 1.63/2.00 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 1.63/2.00 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.63/2.00 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.63/2.00 less_than [38, 2] (w:1, o:64, a:1, s:1, b:0),
% 1.63/2.00 strictly_less_than [39, 2] (w:1, o:71, a:1, s:1, b:0),
% 1.63/2.00 bottom [40, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.63/2.00 create_pq [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.63/2.00 isnonempty_pq [42, 1] (w:1, o:23, a:1, s:1, b:0),
% 1.63/2.00 insert_pq [43, 2] (w:1, o:72, a:1, s:1, b:0),
% 1.63/2.00 contains_pq [44, 2] (w:1, o:73, a:1, s:1, b:0),
% 1.63/2.00 issmallestelement_pq [45, 2] (w:1, o:74, a:1, s:1, b:0),
% 1.63/2.00 remove_pq [46, 2] (w:1, o:65, a:1, s:1, b:0),
% 1.63/2.00 findmin_pq_eff [47, 2] (w:1, o:75, a:1, s:1, b:0),
% 1.63/2.00 findmin_pq_res [48, 2] (w:1, o:76, a:1, s:1, b:0),
% 1.63/2.00 removemin_pq_eff [49, 2] (w:1, o:66, a:1, s:1, b:0),
% 1.63/2.00 removemin_pq_res [50, 2] (w:1, o:67, a:1, s:1, b:0),
% 1.63/2.00 create_slb [51, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.63/2.00 isnonempty_slb [52, 1] (w:1, o:24, a:1, s:1, b:0),
% 1.63/2.00 pair [53, 2] (w:1, o:77, a:1, s:1, b:0),
% 1.63/2.00 insert_slb [54, 2] (w:1, o:78, a:1, s:1, b:0),
% 1.63/2.00 contains_slb [55, 2] (w:1, o:79, a:1, s:1, b:0),
% 1.63/2.00 pair_in_list [57, 3] (w:1, o:91, a:1, s:1, b:0),
% 1.63/2.00 remove_slb [59, 2] (w:1, o:68, a:1, s:1, b:0),
% 1.63/2.00 lookup_slb [60, 2] (w:1, o:80, a:1, s:1, b:0),
% 1.63/2.00 update_slb [61, 2] (w:1, o:81, a:1, s:1, b:0),
% 1.63/2.00 succ_cpq [62, 2] (w:1, o:82, a:1, s:1, b:0),
% 1.63/2.00 insert_cpq [63, 2] (w:1, o:83, a:1, s:1, b:0),
% 1.63/2.00 remove_cpq [64, 2] (w:1, o:69, a:1, s:1, b:0),
% 1.63/2.00 findmin_cpq_eff [65, 1] (w:1, o:25, a:1, s:1, b:0),
% 1.63/2.00 removemin_cpq_eff [66, 1] (w:1, o:26, a:1, s:1, b:0),
% 1.63/2.00 triple [67, 3] (w:1, o:92, a:1, s:1, b:0),
% 1.63/2.00 check_cpq [68, 1] (w:1, o:27, a:1, s:1, b:0),
% 1.63/2.00 contains_cpq [69, 2] (w:1, o:84, a:1, s:1, b:0),
% 1.63/2.00 bad [70, 0] (w:1, o:10, a:1, s:1, b:0),
% 1.63/2.00 ok [71, 1] (w:1, o:28, a:1, s:1, b:0),
% 1.63/2.00 insert_pqp [72, 2] (w:1, o:85, a:1, s:1, b:0),
% 1.63/2.00 remove_pqp [73, 2] (w:1, o:70, a:1, s:1, b:0),
% 1.63/2.00 findmin_pqp_res [74, 1] (w:1, o:29, a:1, s:1, b:0),
% 1.63/2.00 findmin_cpq_res [75, 1] (w:1, o:30, a:1, s:1, b:0),
% 1.63/2.00 removemin_cpq_res [76, 1] (w:1, o:31, a:1, s:1, b:0),
% 1.63/2.00 i [77, 1] (w:1, o:32, a:1, s:1, b:0),
% 1.63/2.00 pi_sharp_remove [78, 2] (w:1, o:87, a:1, s:1, b:0),
% 1.63/2.00 pi_remove [79, 2] (w:1, o:86, a:1, s:1, b:0),
% 1.63/2.00 pi_sharp_find_min [80, 2] (w:1, o:88, a:1, s:1, b:0),
% 1.63/2.00 pi_find_min [81, 1] (w:1, o:34, a:1, s:1, b:0),
% 1.63/2.00 pi_sharp_removemin [82, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.63/2.00 pi_removemin [83, 1] (w:1, o:35, a:1, s:1, b:0),
% 1.63/2.00 phi [84, 1] (w:1, o:33, a:1, s:1, b:0),
% 1.63/2.00 alpha1 [85, 4] (w:1, o:93, a:1, s:1, b:1),
% 1.63/2.00 alpha2 [86, 1] (w:1, o:36, a:1, s:1, b:1),
% 1.63/2.00 skol1 [87, 2] (w:1, o:90, a:1, s:1, b:1),
% 1.63/2.00 skol2 [88, 1] (w:1, o:37, a:1, s:1, b:1),
% 1.63/2.00 skol3 [89, 1] (w:1, o:38, a:1, s:1, b:1),
% 1.63/2.00 skol4 [90, 1] (w:1, o:39, a:1, s:1, b:1),
% 1.63/2.00 skol5 [91, 0] (w:1, o:15, a:1, s:1, b:1),
% 1.63/2.00 skol6 [92, 0] (w:1, o:16, a:1, s:1, b:1),
% 1.63/2.00 skol7 [93, 0] (w:1, o:17, a:1, s:1, b:1).
% 1.63/2.00
% 1.63/2.00
% 1.63/2.00 Starting Search:
% 1.63/2.00
% 1.63/2.00 *** allocated 15000 integers for clauses
% 1.63/2.00 *** allocated 22500 integers for clauses
% 1.63/2.00 *** allocated 33750 integers for clauses
% 1.63/2.00 *** allocated 15000 integers for termspace/termends
% 1.63/2.00 *** allocated 50625 integers for clauses
% 1.63/2.00 *** allocated 22500 integers for termspace/termends
% 1.63/2.00 *** allocated 75937 integers for clauses
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 *** allocated 33750 integers for termspace/termends
% 1.63/2.00 *** allocated 113905 integers for clauses
% 1.63/2.00 *** allocated 50625 integers for termspace/termends
% 1.63/2.00
% 1.63/2.00 Intermediate Status:
% 1.63/2.00 Generated: 3989
% 1.63/2.00 Kept: 2056
% 1.63/2.00 Inuse: 160
% 1.63/2.00 Deleted: 4
% 1.63/2.00 Deletedinuse: 3
% 1.63/2.00
% 1.63/2.00 *** allocated 170857 integers for clauses
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 *** allocated 75937 integers for termspace/termends
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 *** allocated 256285 integers for clauses
% 1.63/2.00 *** allocated 113905 integers for termspace/termends
% 1.63/2.00
% 1.63/2.00 Intermediate Status:
% 1.63/2.00 Generated: 8173
% 1.63/2.00 Kept: 4192
% 1.63/2.00 Inuse: 235
% 1.63/2.00 Deleted: 4
% 1.63/2.00 Deletedinuse: 3
% 1.63/2.00
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 *** allocated 384427 integers for clauses
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 *** allocated 170857 integers for termspace/termends
% 1.63/2.00
% 1.63/2.00 Intermediate Status:
% 1.63/2.00 Generated: 13220
% 1.63/2.00 Kept: 6194
% 1.63/2.00 Inuse: 291
% 1.63/2.00 Deleted: 6
% 1.63/2.00 Deletedinuse: 5
% 1.63/2.00
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 *** allocated 576640 integers for clauses
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00
% 1.63/2.00 Intermediate Status:
% 1.63/2.00 Generated: 21439
% 1.63/2.00 Kept: 8610
% 1.63/2.00 Inuse: 345
% 1.63/2.00 Deleted: 6
% 1.63/2.00 Deletedinuse: 5
% 1.63/2.00
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 *** allocated 256285 integers for termspace/termends
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00
% 1.63/2.00 Intermediate Status:
% 1.63/2.00 Generated: 34985
% 1.63/2.00 Kept: 10627
% 1.63/2.00 Inuse: 484
% 1.63/2.00 Deleted: 13
% 1.63/2.00 Deletedinuse: 5
% 1.63/2.00
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 *** allocated 864960 integers for clauses
% 1.63/2.00
% 1.63/2.00 Intermediate Status:
% 1.63/2.00 Generated: 46305
% 1.63/2.00 Kept: 12633
% 1.63/2.00 Inuse: 563
% 1.63/2.00 Deleted: 15
% 1.63/2.00 Deletedinuse: 5
% 1.63/2.00
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00
% 1.63/2.00 Intermediate Status:
% 1.63/2.00 Generated: 53313
% 1.63/2.00 Kept: 14683
% 1.63/2.00 Inuse: 580
% 1.63/2.00 Deleted: 15
% 1.63/2.00 Deletedinuse: 5
% 1.63/2.00
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 *** allocated 384427 integers for termspace/termends
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00
% 1.63/2.00 Intermediate Status:
% 1.63/2.00 Generated: 65256
% 1.63/2.00 Kept: 18287
% 1.63/2.00 Inuse: 623
% 1.63/2.00 Deleted: 15
% 1.63/2.00 Deletedinuse: 5
% 1.63/2.00
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 *** allocated 1297440 integers for clauses
% 1.63/2.00 Resimplifying inuse:
% 1.63/2.00 Done
% 1.63/2.00
% 1.63/2.00 Resimplifying clauses:
% 1.63/2.00
% 1.63/2.00 Bliksems!, er is een bewijs:
% 1.63/2.00 % SZS status Theorem
% 1.63/2.00 % SZS output start Refutation
% 1.63/2.00
% 1.63/2.00 (78) {G0,W9,D2,L3,V2,M3} I { ! contains_pq( X, Y ), ! issmallestelement_pq
% 1.63/2.00 ( X, Y ), pi_sharp_find_min( X, Y ) }.
% 1.63/2.00 (92) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( X, Y, Z ) ) )
% 1.63/2.00 , contains_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( triple( X, Y, Z )
% 1.63/2.00 ) ) }.
% 1.63/2.00 (93) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( X, Y, Z ) ) )
% 1.63/2.00 , issmallestelement_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( triple(
% 1.63/2.00 X, Y, Z ) ) ) }.
% 1.63/2.00 (94) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple( skol5, skol6,
% 1.63/2.00 skol7 ) ) ) }.
% 1.63/2.00 (95) {G0,W11,D4,L1,V0,M1} I { ! pi_sharp_find_min( i( triple( skol5, skol6
% 1.63/2.00 , skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 (5678) {G1,W11,D4,L1,V0,M1} R(92,94) { contains_pq( i( triple( skol5, skol6
% 1.63/2.00 , skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 (5843) {G1,W11,D4,L1,V0,M1} R(93,94) { issmallestelement_pq( i( triple(
% 1.63/2.00 skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00 ) }.
% 1.63/2.00 (5994) {G2,W11,D4,L1,V0,M1} R(95,78);r(5678) { ! issmallestelement_pq( i(
% 1.63/2.00 triple( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6,
% 1.63/2.00 skol7 ) ) ) }.
% 1.63/2.00 (20006) {G3,W0,D0,L0,V0,M0} S(5994);r(5843) { }.
% 1.63/2.00
% 1.63/2.00
% 1.63/2.00 % SZS output end Refutation
% 1.63/2.00 found a proof!
% 1.63/2.00
% 1.63/2.00
% 1.63/2.00 Unprocessed initial clauses:
% 1.63/2.00
% 1.63/2.00 (20008) {G0,W9,D2,L3,V3,M3} { ! less_than( X, Z ), ! less_than( Z, Y ),
% 1.63/2.00 less_than( X, Y ) }.
% 1.63/2.00 (20009) {G0,W6,D2,L2,V2,M2} { less_than( X, Y ), less_than( Y, X ) }.
% 1.63/2.00 (20010) {G0,W3,D2,L1,V1,M1} { less_than( X, X ) }.
% 1.63/2.00 (20011) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), less_than( X,
% 1.63/2.00 Y ) }.
% 1.63/2.00 (20012) {G0,W6,D2,L2,V2,M2} { ! strictly_less_than( X, Y ), ! less_than( Y
% 1.63/2.00 , X ) }.
% 1.63/2.00 (20013) {G0,W9,D2,L3,V2,M3} { ! less_than( X, Y ), less_than( Y, X ),
% 1.63/2.00 strictly_less_than( X, Y ) }.
% 1.63/2.00 (20014) {G0,W3,D2,L1,V1,M1} { less_than( bottom, X ) }.
% 1.63/2.00 (20015) {G0,W2,D2,L1,V0,M1} { ! isnonempty_pq( create_pq ) }.
% 1.63/2.00 (20016) {G0,W4,D3,L1,V2,M1} { isnonempty_pq( insert_pq( X, Y ) ) }.
% 1.63/2.00 (20017) {G0,W3,D2,L1,V1,M1} { ! contains_pq( create_pq, X ) }.
% 1.63/2.00 (20018) {G0,W11,D3,L3,V3,M3} { ! contains_pq( insert_pq( X, Y ), Z ),
% 1.63/2.00 contains_pq( X, Z ), Y = Z }.
% 1.63/2.00 (20019) {G0,W8,D3,L2,V3,M2} { ! contains_pq( X, Z ), contains_pq(
% 1.63/2.00 insert_pq( X, Y ), Z ) }.
% 1.63/2.00 (20020) {G0,W8,D3,L2,V3,M2} { ! Y = Z, contains_pq( insert_pq( X, Y ), Z )
% 1.63/2.00 }.
% 1.63/2.00 (20021) {G0,W9,D2,L3,V3,M3} { ! issmallestelement_pq( X, Y ), !
% 1.63/2.00 contains_pq( X, Z ), less_than( Y, Z ) }.
% 1.63/2.00 (20022) {G0,W8,D3,L2,V3,M2} { ! less_than( Y, skol1( Z, Y ) ),
% 1.63/2.00 issmallestelement_pq( X, Y ) }.
% 1.63/2.00 (20023) {G0,W8,D3,L2,V2,M2} { contains_pq( X, skol1( X, Y ) ),
% 1.63/2.00 issmallestelement_pq( X, Y ) }.
% 1.63/2.00 (20024) {G0,W7,D4,L1,V2,M1} { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 1.63/2.00 (20025) {G0,W17,D4,L3,V3,M3} { ! contains_pq( X, Z ), Y = Z, remove_pq(
% 1.63/2.00 insert_pq( X, Y ), Z ) = insert_pq( remove_pq( X, Z ), Y ) }.
% 1.63/2.00 (20026) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 1.63/2.00 issmallestelement_pq( X, Y ), findmin_pq_eff( X, Y ) = X }.
% 1.63/2.00 (20027) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 1.63/2.00 issmallestelement_pq( X, Y ), findmin_pq_res( X, Y ) = Y }.
% 1.63/2.00 (20028) {G0,W13,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 1.63/2.00 issmallestelement_pq( X, Y ), removemin_pq_eff( X, Y ) = remove_pq( X, Y
% 1.63/2.00 ) }.
% 1.63/2.00 (20029) {G0,W11,D3,L3,V2,M3} { ! contains_pq( X, Y ), !
% 1.63/2.00 issmallestelement_pq( X, Y ), removemin_pq_res( X, Y ) = Y }.
% 1.63/2.00 (20030) {G0,W11,D4,L1,V3,M1} { insert_pq( insert_pq( X, Y ), Z ) =
% 1.63/2.00 insert_pq( insert_pq( X, Z ), Y ) }.
% 1.63/2.00 (20031) {G0,W2,D2,L1,V0,M1} { ! isnonempty_slb( create_slb ) }.
% 1.63/2.00 (20032) {G0,W6,D4,L1,V3,M1} { isnonempty_slb( insert_slb( X, pair( Y, Z )
% 1.63/2.00 ) ) }.
% 1.63/2.00 (20033) {G0,W3,D2,L1,V1,M1} { ! contains_slb( create_slb, X ) }.
% 1.63/2.00 (20034) {G0,W13,D4,L3,V4,M3} { ! contains_slb( insert_slb( X, pair( Y, T )
% 1.63/2.00 ), Z ), contains_slb( X, Z ), Y = Z }.
% 1.63/2.00 (20035) {G0,W10,D4,L2,V4,M2} { ! contains_slb( X, Z ), contains_slb(
% 1.63/2.00 insert_slb( X, pair( Y, T ) ), Z ) }.
% 1.63/2.00 (20036) {G0,W10,D4,L2,V4,M2} { ! Y = Z, contains_slb( insert_slb( X, pair
% 1.63/2.00 ( Y, T ) ), Z ) }.
% 1.63/2.00 (20037) {G0,W4,D2,L1,V2,M1} { ! pair_in_list( create_slb, X, Y ) }.
% 1.63/2.00 (20038) {G0,W17,D4,L3,V5,M3} { ! pair_in_list( insert_slb( X, pair( Y, T )
% 1.63/2.00 ), Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 1.63/2.00 (20039) {G0,W12,D4,L2,V5,M2} { ! pair_in_list( X, Z, U ), pair_in_list(
% 1.63/2.00 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 1.63/2.00 (20040) {G0,W13,D4,L2,V5,M2} { ! alpha1( Y, Z, T, U ), pair_in_list(
% 1.63/2.00 insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 1.63/2.00 (20041) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), X = Y }.
% 1.63/2.00 (20042) {G0,W8,D2,L2,V4,M2} { ! alpha1( X, Y, Z, T ), Z = T }.
% 1.63/2.00 (20043) {G0,W11,D2,L3,V4,M3} { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 1.63/2.00 (20044) {G0,W9,D5,L1,V3,M1} { remove_slb( insert_slb( X, pair( Y, Z ) ), Y
% 1.63/2.00 ) = X }.
% 1.63/2.00 (20045) {G0,W21,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), remove_slb(
% 1.63/2.00 insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 1.63/2.00 ( Y, T ) ) }.
% 1.63/2.00 (20046) {G0,W9,D5,L1,V3,M1} { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y
% 1.63/2.00 ) = Z }.
% 1.63/2.00 (20047) {G0,W17,D5,L3,V4,M3} { Y = Z, ! contains_slb( X, Z ), lookup_slb(
% 1.63/2.00 insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 1.63/2.00 (20048) {G0,W5,D3,L1,V1,M1} { update_slb( create_slb, X ) = create_slb }.
% 1.63/2.00 (20049) {G0,W18,D5,L2,V4,M2} { ! strictly_less_than( Y, X ), update_slb(
% 1.63/2.00 insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 1.63/2.00 ( T, X ) ) }.
% 1.63/2.00 (20050) {G0,W18,D5,L2,V4,M2} { ! less_than( X, Y ), update_slb( insert_slb
% 1.63/2.00 ( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 1.63/2.00 }.
% 1.63/2.00 (20051) {G0,W3,D2,L1,V1,M1} { succ_cpq( X, X ) }.
% 1.63/2.00 (20052) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq
% 1.63/2.00 ( Y, Z ) ) }.
% 1.63/2.00 (20053) {G0,W8,D3,L2,V3,M2} { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq
% 1.63/2.00 ( Y, Z ) ) }.
% 1.63/2.00 (20054) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 1.63/2.00 findmin_cpq_eff( Y ) ) }.
% 1.63/2.00 (20055) {G0,W7,D3,L2,V2,M2} { ! succ_cpq( X, Y ), succ_cpq( X,
% 1.63/2.00 removemin_cpq_eff( Y ) ) }.
% 1.63/2.00 (20056) {G0,W5,D3,L1,V2,M1} { check_cpq( triple( X, create_slb, Y ) ) }.
% 1.63/2.00 (20057) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z
% 1.63/2.00 , insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) )
% 1.63/2.00 }.
% 1.63/2.00 (20058) {G0,W17,D5,L3,V5,M3} { ! less_than( Y, X ), ! check_cpq( triple( Z
% 1.63/2.00 , T, U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) )
% 1.63/2.00 }.
% 1.63/2.00 (20059) {G0,W12,D5,L2,V5,M2} { ! strictly_less_than( X, Y ), ! check_cpq(
% 1.63/2.00 triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 1.63/2.00 (20060) {G0,W13,D5,L3,V5,M3} { ! strictly_less_than( X, Y ), ! ||,
% 1.63/2.00 check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 1.63/2.00 (20061) {G0,W9,D3,L2,V4,M2} { ! contains_cpq( triple( X, Y, Z ), T ),
% 1.63/2.00 contains_slb( Y, T ) }.
% 1.63/2.00 (20062) {G0,W9,D3,L2,V4,M2} { ! contains_slb( Y, T ), contains_cpq( triple
% 1.63/2.00 ( X, Y, Z ), T ) }.
% 1.63/2.00 (20063) {G0,W5,D3,L1,V2,M1} { ! ok( triple( X, Y, bad ) ) }.
% 1.63/2.00 (20064) {G0,W6,D3,L2,V2,M2} { ! ||, ok( triple( X, Y, bad ) ) }.
% 1.63/2.00 (20065) {G0,W8,D3,L2,V3,M2} { ok( triple( Y, Z, X ) ), X = bad }.
% 1.63/2.00 (20066) {G0,W17,D5,L1,V4,M1} { insert_cpq( triple( X, Y, Z ), T ) = triple
% 1.63/2.00 ( insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 1.63/2.00 (20067) {G0,W14,D4,L2,V4,M2} { contains_slb( X, Y ), remove_cpq( triple( Z
% 1.63/2.00 , X, T ), Y ) = triple( Z, X, bad ) }.
% 1.63/2.00 (20068) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), ! less_than(
% 1.63/2.00 lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple(
% 1.63/2.00 remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 1.63/2.00 (20069) {G0,W23,D4,L3,V4,M3} { ! contains_slb( X, Y ), !
% 1.63/2.00 strictly_less_than( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T
% 1.63/2.00 ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 1.63/2.00 (20070) {G0,W10,D4,L1,V2,M1} { findmin_cpq_eff( triple( X, create_slb, Y )
% 1.63/2.00 ) = triple( X, create_slb, bad ) }.
% 1.63/2.00 (20071) {G0,W20,D5,L3,V3,M3} { Y = create_slb, contains_slb( Y,
% 1.63/2.00 findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 1.63/2.00 , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 1.63/2.00 (20072) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 1.63/2.00 findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ),
% 1.63/2.00 lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 1.63/2.00 ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 1.63/2.00 (20073) {G0,W27,D5,L4,V3,M4} { Y = create_slb, ! contains_slb( Y,
% 1.63/2.00 findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 1.63/2.00 ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 1.63/2.00 ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 1.63/2.00 (20074) {G0,W7,D4,L1,V2,M1} { findmin_cpq_res( triple( X, create_slb, Y )
% 1.63/2.00 ) = bottom }.
% 1.63/2.00 (20075) {G0,W11,D4,L2,V3,M2} { X = create_slb, findmin_cpq_res( triple( Y
% 1.63/2.00 , X, Z ) ) = findmin_pqp_res( Y ) }.
% 1.63/2.00 (20076) {G0,W8,D4,L1,V1,M1} { removemin_cpq_eff( X ) = remove_cpq(
% 1.63/2.00 findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 1.63/2.00 (20077) {G0,W5,D3,L1,V1,M1} { removemin_cpq_res( X ) = findmin_cpq_res( X
% 1.63/2.00 ) }.
% 1.63/2.00 (20078) {G0,W7,D4,L1,V2,M1} { i( triple( X, create_slb, Y ) ) = create_pq
% 1.63/2.00 }.
% 1.63/2.00 (20079) {G0,W17,D6,L1,V5,M1} { i( triple( X, insert_slb( Y, pair( T, U ) )
% 1.63/2.00 , Z ) ) = insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 1.63/2.00 (20080) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_remove( X, Y ), contains_pq( X, Y
% 1.63/2.00 ) }.
% 1.63/2.00 (20081) {G0,W6,D2,L2,V2,M2} { ! contains_pq( X, Y ), pi_sharp_remove( X, Y
% 1.63/2.00 ) }.
% 1.63/2.00 (20082) {G0,W7,D3,L2,V2,M2} { ! pi_remove( X, Y ), pi_sharp_remove( i( X )
% 1.63/2.00 , Y ) }.
% 1.63/2.00 (20083) {G0,W7,D3,L2,V2,M2} { ! pi_sharp_remove( i( X ), Y ), pi_remove( X
% 1.63/2.00 , Y ) }.
% 1.63/2.00 (20084) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ), contains_pq( X
% 1.63/2.00 , Y ) }.
% 1.63/2.00 (20085) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_find_min( X, Y ),
% 1.63/2.00 issmallestelement_pq( X, Y ) }.
% 1.63/2.00 (20086) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), !
% 1.63/2.00 issmallestelement_pq( X, Y ), pi_sharp_find_min( X, Y ) }.
% 1.63/2.00 (20087) {G0,W7,D3,L2,V1,M2} { ! pi_find_min( X ), pi_sharp_find_min( i( X
% 1.63/2.00 ), skol2( X ) ) }.
% 1.63/2.00 (20088) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ),
% 1.63/2.00 pi_find_min( X ) }.
% 1.63/2.00 (20089) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ), contains_pq( X
% 1.63/2.00 , Y ) }.
% 1.63/2.00 (20090) {G0,W6,D2,L2,V2,M2} { ! pi_sharp_removemin( X, Y ),
% 1.63/2.00 issmallestelement_pq( X, Y ) }.
% 1.63/2.00 (20091) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), !
% 1.63/2.00 issmallestelement_pq( X, Y ), pi_sharp_removemin( X, Y ) }.
% 1.63/2.00 (20092) {G0,W7,D3,L2,V1,M2} { ! pi_removemin( X ), pi_sharp_find_min( i( X
% 1.63/2.00 ), skol3( X ) ) }.
% 1.63/2.00 (20093) {G0,W6,D3,L2,V2,M2} { ! pi_sharp_find_min( i( X ), Y ),
% 1.63/2.00 pi_removemin( X ) }.
% 1.63/2.00 (20094) {G0,W5,D3,L2,V2,M2} { ! phi( X ), alpha2( skol4( Y ) ) }.
% 1.63/2.00 (20095) {G0,W6,D3,L2,V1,M2} { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 1.63/2.00 (20096) {G0,W7,D2,L3,V2,M3} { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X )
% 1.63/2.00 }.
% 1.63/2.00 (20097) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ok( X ) }.
% 1.63/2.00 (20098) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), check_cpq( X ) }.
% 1.63/2.00 (20099) {G0,W6,D2,L3,V1,M3} { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 1.63/2.00 (20100) {G0,W17,D4,L2,V3,M2} { ! phi( findmin_cpq_eff( triple( X, Y, Z ) )
% 1.63/2.00 ), contains_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( triple( X, Y, Z
% 1.63/2.00 ) ) ) }.
% 1.63/2.00 (20101) {G0,W17,D4,L2,V3,M2} { ! phi( findmin_cpq_eff( triple( X, Y, Z ) )
% 1.63/2.00 ), issmallestelement_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( triple
% 1.63/2.00 ( X, Y, Z ) ) ) }.
% 1.63/2.00 (20102) {G0,W6,D4,L1,V0,M1} { phi( findmin_cpq_eff( triple( skol5, skol6,
% 1.63/2.00 skol7 ) ) ) }.
% 1.63/2.00 (20103) {G0,W11,D4,L1,V0,M1} { ! pi_sharp_find_min( i( triple( skol5,
% 1.63/2.00 skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00
% 1.63/2.00
% 1.63/2.00 Total Proof:
% 1.63/2.00
% 1.63/2.00 subsumption: (78) {G0,W9,D2,L3,V2,M3} I { ! contains_pq( X, Y ), !
% 1.63/2.00 issmallestelement_pq( X, Y ), pi_sharp_find_min( X, Y ) }.
% 1.63/2.00 parent0: (20086) {G0,W9,D2,L3,V2,M3} { ! contains_pq( X, Y ), !
% 1.63/2.00 issmallestelement_pq( X, Y ), pi_sharp_find_min( X, Y ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 X := X
% 1.63/2.00 Y := Y
% 1.63/2.00 end
% 1.63/2.00 permutation0:
% 1.63/2.00 0 ==> 0
% 1.63/2.00 1 ==> 1
% 1.63/2.00 2 ==> 2
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 subsumption: (92) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple(
% 1.63/2.00 X, Y, Z ) ) ), contains_pq( i( triple( X, Y, Z ) ), findmin_cpq_res(
% 1.63/2.00 triple( X, Y, Z ) ) ) }.
% 1.63/2.00 parent0: (20100) {G0,W17,D4,L2,V3,M2} { ! phi( findmin_cpq_eff( triple( X
% 1.63/2.00 , Y, Z ) ) ), contains_pq( i( triple( X, Y, Z ) ), findmin_cpq_res(
% 1.63/2.00 triple( X, Y, Z ) ) ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 X := X
% 1.63/2.00 Y := Y
% 1.63/2.00 Z := Z
% 1.63/2.00 end
% 1.63/2.00 permutation0:
% 1.63/2.00 0 ==> 0
% 1.63/2.00 1 ==> 1
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 subsumption: (93) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple(
% 1.63/2.00 X, Y, Z ) ) ), issmallestelement_pq( i( triple( X, Y, Z ) ),
% 1.63/2.00 findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 1.63/2.00 parent0: (20101) {G0,W17,D4,L2,V3,M2} { ! phi( findmin_cpq_eff( triple( X
% 1.63/2.00 , Y, Z ) ) ), issmallestelement_pq( i( triple( X, Y, Z ) ),
% 1.63/2.00 findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 X := X
% 1.63/2.00 Y := Y
% 1.63/2.00 Z := Z
% 1.63/2.00 end
% 1.63/2.00 permutation0:
% 1.63/2.00 0 ==> 0
% 1.63/2.00 1 ==> 1
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 subsumption: (94) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple(
% 1.63/2.00 skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 parent0: (20102) {G0,W6,D4,L1,V0,M1} { phi( findmin_cpq_eff( triple( skol5
% 1.63/2.00 , skol6, skol7 ) ) ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 end
% 1.63/2.00 permutation0:
% 1.63/2.00 0 ==> 0
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 subsumption: (95) {G0,W11,D4,L1,V0,M1} I { ! pi_sharp_find_min( i( triple(
% 1.63/2.00 skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00 ) }.
% 1.63/2.00 parent0: (20103) {G0,W11,D4,L1,V0,M1} { ! pi_sharp_find_min( i( triple(
% 1.63/2.00 skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00 ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 end
% 1.63/2.00 permutation0:
% 1.63/2.00 0 ==> 0
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 resolution: (20389) {G1,W11,D4,L1,V0,M1} { contains_pq( i( triple( skol5,
% 1.63/2.00 skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 parent0[0]: (92) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( X
% 1.63/2.00 , Y, Z ) ) ), contains_pq( i( triple( X, Y, Z ) ), findmin_cpq_res(
% 1.63/2.00 triple( X, Y, Z ) ) ) }.
% 1.63/2.00 parent1[0]: (94) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple(
% 1.63/2.00 skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 X := skol5
% 1.63/2.00 Y := skol6
% 1.63/2.00 Z := skol7
% 1.63/2.00 end
% 1.63/2.00 substitution1:
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 subsumption: (5678) {G1,W11,D4,L1,V0,M1} R(92,94) { contains_pq( i( triple
% 1.63/2.00 ( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 )
% 1.63/2.00 ) ) }.
% 1.63/2.00 parent0: (20389) {G1,W11,D4,L1,V0,M1} { contains_pq( i( triple( skol5,
% 1.63/2.00 skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 end
% 1.63/2.00 permutation0:
% 1.63/2.00 0 ==> 0
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 resolution: (20390) {G1,W11,D4,L1,V0,M1} { issmallestelement_pq( i( triple
% 1.63/2.00 ( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 )
% 1.63/2.00 ) ) }.
% 1.63/2.00 parent0[0]: (93) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( X
% 1.63/2.00 , Y, Z ) ) ), issmallestelement_pq( i( triple( X, Y, Z ) ),
% 1.63/2.00 findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 1.63/2.00 parent1[0]: (94) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple(
% 1.63/2.00 skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 X := skol5
% 1.63/2.00 Y := skol6
% 1.63/2.00 Z := skol7
% 1.63/2.00 end
% 1.63/2.00 substitution1:
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 subsumption: (5843) {G1,W11,D4,L1,V0,M1} R(93,94) { issmallestelement_pq( i
% 1.63/2.00 ( triple( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6
% 1.63/2.00 , skol7 ) ) ) }.
% 1.63/2.00 parent0: (20390) {G1,W11,D4,L1,V0,M1} { issmallestelement_pq( i( triple(
% 1.63/2.00 skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00 ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 end
% 1.63/2.00 permutation0:
% 1.63/2.00 0 ==> 0
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 resolution: (20391) {G1,W22,D4,L2,V0,M2} { ! contains_pq( i( triple( skol5
% 1.63/2.00 , skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ), !
% 1.63/2.00 issmallestelement_pq( i( triple( skol5, skol6, skol7 ) ),
% 1.63/2.00 findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 parent0[0]: (95) {G0,W11,D4,L1,V0,M1} I { ! pi_sharp_find_min( i( triple(
% 1.63/2.00 skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00 ) }.
% 1.63/2.00 parent1[2]: (78) {G0,W9,D2,L3,V2,M3} I { ! contains_pq( X, Y ), !
% 1.63/2.00 issmallestelement_pq( X, Y ), pi_sharp_find_min( X, Y ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 end
% 1.63/2.00 substitution1:
% 1.63/2.00 X := i( triple( skol5, skol6, skol7 ) )
% 1.63/2.00 Y := findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 resolution: (20392) {G2,W11,D4,L1,V0,M1} { ! issmallestelement_pq( i(
% 1.63/2.00 triple( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6,
% 1.63/2.00 skol7 ) ) ) }.
% 1.63/2.00 parent0[0]: (20391) {G1,W22,D4,L2,V0,M2} { ! contains_pq( i( triple( skol5
% 1.63/2.00 , skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ), !
% 1.63/2.00 issmallestelement_pq( i( triple( skol5, skol6, skol7 ) ),
% 1.63/2.00 findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 parent1[0]: (5678) {G1,W11,D4,L1,V0,M1} R(92,94) { contains_pq( i( triple(
% 1.63/2.00 skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00 ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 end
% 1.63/2.00 substitution1:
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 subsumption: (5994) {G2,W11,D4,L1,V0,M1} R(95,78);r(5678) { !
% 1.63/2.00 issmallestelement_pq( i( triple( skol5, skol6, skol7 ) ), findmin_cpq_res
% 1.63/2.00 ( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 parent0: (20392) {G2,W11,D4,L1,V0,M1} { ! issmallestelement_pq( i( triple
% 1.63/2.00 ( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 )
% 1.63/2.00 ) ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 end
% 1.63/2.00 permutation0:
% 1.63/2.00 0 ==> 0
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 resolution: (20393) {G2,W0,D0,L0,V0,M0} { }.
% 1.63/2.00 parent0[0]: (5994) {G2,W11,D4,L1,V0,M1} R(95,78);r(5678) { !
% 1.63/2.00 issmallestelement_pq( i( triple( skol5, skol6, skol7 ) ), findmin_cpq_res
% 1.63/2.00 ( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00 parent1[0]: (5843) {G1,W11,D4,L1,V0,M1} R(93,94) { issmallestelement_pq( i
% 1.63/2.00 ( triple( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6
% 1.63/2.00 , skol7 ) ) ) }.
% 1.63/2.00 substitution0:
% 1.63/2.00 end
% 1.63/2.00 substitution1:
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 subsumption: (20006) {G3,W0,D0,L0,V0,M0} S(5994);r(5843) { }.
% 1.63/2.00 parent0: (20393) {G2,W0,D0,L0,V0,M0} { }.
% 1.63/2.00 substitution0:
% 1.63/2.00 end
% 1.63/2.00 permutation0:
% 1.63/2.00 end
% 1.63/2.00
% 1.63/2.00 Proof check complete!
% 1.63/2.00
% 1.63/2.00 Memory use:
% 1.63/2.00
% 1.63/2.00 space for terms: 325158
% 1.63/2.00 space for clauses: 885375
% 1.63/2.00
% 1.63/2.00
% 1.63/2.00 clauses generated: 68128
% 1.63/2.00 clauses kept: 20007
% 1.63/2.00 clauses selected: 625
% 1.63/2.00 clauses deleted: 85
% 1.63/2.00 clauses inuse deleted: 5
% 1.63/2.00
% 1.63/2.00 subsentry: 173354
% 1.63/2.00 literals s-matched: 103983
% 1.63/2.00 literals matched: 96845
% 1.63/2.00 full subsumption: 19232
% 1.63/2.00
% 1.63/2.00 checksum: -515230415
% 1.63/2.00
% 1.63/2.00
% 1.63/2.00 Bliksem ended
%------------------------------------------------------------------------------