TSTP Solution File: SWW469+5 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 23:22:10 EDT 2022
% Result : Theorem 0.70s 1.12s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jun 4 21:24:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/1.11 *** allocated 10000 integers for termspace/termends
% 0.70/1.11 *** allocated 10000 integers for clauses
% 0.70/1.11 *** allocated 10000 integers for justifications
% 0.70/1.11 Bliksem 1.12
% 0.70/1.11
% 0.70/1.11
% 0.70/1.11 Automatic Strategy Selection
% 0.70/1.11
% 0.70/1.11 *** allocated 15000 integers for termspace/termends
% 0.70/1.11
% 0.70/1.11 Clauses:
% 0.70/1.11
% 0.70/1.11 { ! cl_HOL_Oequal( X ), ti( fun( X, fun( X, bool ) ), equal_equal( X ) ) =
% 0.70/1.11 equal_equal( X ) }.
% 0.70/1.11 { ti( fun( X, fun( X, bool ) ), induct_equal( X ) ) = induct_equal( X ) }.
% 0.70/1.11 { ti( bool, induct_false ) = induct_false }.
% 0.70/1.11 { ti( bool, induct_true ) = induct_true }.
% 0.70/1.11 { ti( X, undefined( X ) ) = undefined( X ) }.
% 0.70/1.11 { ti( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ), hoare_509422987triple( X ) ),
% 0.70/1.11 hoare_244953527triple( X ) ) = hoare_244953527triple( X ) }.
% 0.70/1.11 { ti( fun( hoare_509422987triple( X ), fun( node( sum_sum( com, fun( X, fun
% 0.70/1.11 ( state, bool ) ) ), sum_sum( state, X ) ), bool ) ),
% 0.70/1.11 hoare_2037801986triple( X ) ) = hoare_2037801986triple( X ) }.
% 0.70/1.11 { ti( bool, hoare_1883395792gleton ) = hoare_1883395792gleton }.
% 0.70/1.11 { ti( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ), bool ), hoare_1580379338ep_set( X ) ) =
% 0.70/1.11 hoare_1580379338ep_set( X ) }.
% 0.70/1.11 { ti( fun( fun( X, bool ), fun( X, bool ) ), collect( X ) ) = collect( X )
% 0.70/1.11 }.
% 0.70/1.11 { ti( fun( fun( X, Y ), fun( fun( Y, X ), fun( fun( Y, bool ), bool ) ) ),
% 0.70/1.11 type_definition( X, Y ) ) = type_definition( X, Y ) }.
% 0.70/1.11 { ti( fun( X, fun( X, bool ) ), fequal( X ) ) = fequal( X ) }.
% 0.70/1.11 { hAPP( X, Y, ti( fun( X, Y ), Z ), T ) = hAPP( X, Y, Z, T ) }.
% 0.70/1.11 { hAPP( X, Y, Z, ti( X, T ) ) = hAPP( X, Y, Z, T ) }.
% 0.70/1.11 { ti( X, hAPP( Y, X, Z, T ) ) = hAPP( Y, X, Z, T ) }.
% 0.70/1.11 { ! hBOOL( ti( bool, X ) ), hBOOL( X ) }.
% 0.70/1.11 { ! hBOOL( X ), hBOOL( ti( bool, X ) ) }.
% 0.70/1.11 { ti( fun( X, fun( fun( X, bool ), bool ) ), member( X ) ) = member( X ) }
% 0.70/1.11 .
% 0.70/1.11 { ! hBOOL( hoare_1883395792gleton ), ! ti( state, skol1 ) = ti( state,
% 0.70/1.11 skol12 ) }.
% 0.70/1.11 { ti( state, X ) = ti( state, Y ), hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.11 { ! hBOOL( hAPP( hoare_509422987triple( X ), bool, hAPP(
% 0.70/1.11 hoare_509422987triple( X ), fun( hoare_509422987triple( X ), bool ),
% 0.70/1.11 equal_equal( hoare_509422987triple( X ) ), Y ), Z ) ), Y = Z }.
% 0.70/1.11 { ! Y = Z, hBOOL( hAPP( hoare_509422987triple( X ), bool, hAPP(
% 0.70/1.11 hoare_509422987triple( X ), fun( hoare_509422987triple( X ), bool ),
% 0.70/1.11 equal_equal( hoare_509422987triple( X ) ), Y ), Z ) ) }.
% 0.70/1.11 { ! hAPP( hoare_509422987triple( X ), fun( node( sum_sum( com, fun( X, fun
% 0.70/1.11 ( state, bool ) ) ), sum_sum( state, X ) ), bool ),
% 0.70/1.11 hoare_2037801986triple( X ), Y ) = hAPP( hoare_509422987triple( X ), fun
% 0.70/1.11 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.11 ), bool ), hoare_2037801986triple( X ), Z ), Y = Z }.
% 0.70/1.11 { ! Y = Z, hAPP( hoare_509422987triple( X ), fun( node( sum_sum( com, fun(
% 0.70/1.11 X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ),
% 0.70/1.11 hoare_2037801986triple( X ), Y ) = hAPP( hoare_509422987triple( X ), fun
% 0.70/1.11 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.11 ), bool ), hoare_2037801986triple( X ), Z ) }.
% 0.70/1.11 { ! cl_HOL_Oequal( X ), equal_equal( X ) = fequal( X ) }.
% 0.70/1.11 { ! cl_HOL_Oequal( X ), hBOOL( hAPP( X, bool, hAPP( X, fun( X, bool ),
% 0.70/1.11 equal_equal( X ), Y ), Y ) ) }.
% 0.70/1.11 { ! cl_HOL_Oequal( X ), ! hBOOL( hAPP( X, bool, hAPP( X, fun( X, bool ),
% 0.70/1.11 equal_equal( X ), Y ), Z ) ), ti( X, Y ) = ti( X, Z ) }.
% 0.70/1.11 { ! cl_HOL_Oequal( X ), ! ti( X, Y ) = ti( X, Z ), hBOOL( hAPP( X, bool,
% 0.70/1.11 hAPP( X, fun( X, bool ), equal_equal( X ), Y ), Z ) ) }.
% 0.70/1.11 { ! cl_HOL_Oequal( X ), fequal( X ) = equal_equal( X ) }.
% 0.70/1.11 { hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), hoare_509422987triple( X ), hoare_244953527triple(
% 0.70/1.11 X ), hAPP( hoare_509422987triple( X ), fun( node( sum_sum( com, fun( X,
% 0.70/1.11 fun( state, bool ) ) ), sum_sum( state, X ) ), bool ),
% 0.70/1.11 hoare_2037801986triple( X ), Y ) ) = Y }.
% 0.70/1.11 { hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) )
% 0.70/1.11 , sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( node( sum_sum(
% 0.70/1.11 com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), fun(
% 0.70/1.11 fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), bool ), member( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), hAPP(
% 0.70/1.11 hoare_509422987triple( X ), fun( node( sum_sum( com, fun( X, fun( state,
% 0.70/1.11 bool ) ) ), sum_sum( state, X ) ), bool ), hoare_2037801986triple( X ), Y
% 0.70/1.11 ) ), hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) )
% 0.70/1.11 , sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.11 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) )
% 0.70/1.11 ), sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( node( sum_sum
% 0.70/1.11 ( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), fun
% 0.70/1.11 ( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), bool ), member( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), Y ),
% 0.70/1.11 hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.11 sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com, fun
% 0.70/1.11 ( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.11 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ), ! hBOOL(
% 0.70/1.11 hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool, Z, hAPP( hoare_509422987triple( X ), fun(
% 0.70/1.11 node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) )
% 0.70/1.11 , bool ), hoare_2037801986triple( X ), skol2( X, Z ) ) ) ), hBOOL( hAPP(
% 0.70/1.11 fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state,
% 0.70/1.11 X ) ), bool ), bool, Z, Y ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) )
% 0.70/1.11 ), sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( node( sum_sum
% 0.70/1.11 ( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), fun
% 0.70/1.11 ( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), bool ), member( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), Y ),
% 0.70/1.11 hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.11 sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com, fun
% 0.70/1.11 ( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.11 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ), Y = hAPP(
% 0.70/1.11 hoare_509422987triple( X ), fun( node( sum_sum( com, fun( X, fun( state,
% 0.70/1.11 bool ) ) ), sum_sum( state, X ) ), bool ), hoare_2037801986triple( X ),
% 0.70/1.11 skol3( X, Y ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) )
% 0.70/1.11 ), sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( node( sum_sum
% 0.70/1.11 ( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), fun
% 0.70/1.11 ( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), bool ), member( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), Y ),
% 0.70/1.11 hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.11 sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com, fun
% 0.70/1.11 ( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.11 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ), hAPP(
% 0.70/1.11 hoare_509422987triple( X ), fun( node( sum_sum( com, fun( X, fun( state,
% 0.70/1.11 bool ) ) ), sum_sum( state, X ) ), bool ), hoare_2037801986triple( X ),
% 0.70/1.11 hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), hoare_509422987triple( X ), hoare_244953527triple(
% 0.70/1.11 X ), Y ) ) = Y }.
% 0.70/1.11 { hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) )
% 0.70/1.11 , sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( fun( node(
% 0.70/1.11 sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool
% 0.70/1.11 ), hoare_509422987triple( X ) ), fun( fun( fun( node( sum_sum( com, fun
% 0.70/1.11 ( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool
% 0.70/1.11 ), hAPP( fun( hoare_509422987triple( X ), fun( node( sum_sum( com, fun(
% 0.70/1.11 X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), fun( fun( fun
% 0.70/1.11 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.11 ), bool ), hoare_509422987triple( X ) ), fun( fun( fun( node( sum_sum(
% 0.70/1.11 com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool
% 0.70/1.11 ), bool ) ), type_definition( hoare_509422987triple( X ), fun( node(
% 0.70/1.11 sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool
% 0.70/1.11 ) ), hoare_2037801986triple( X ) ), hoare_244953527triple( X ) ), hAPP(
% 0.70/1.11 fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com, fun( X, fun(
% 0.70/1.11 state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), collect( fun(
% 0.70/1.11 node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) )
% 0.70/1.11 , bool ) ), hoare_1580379338ep_set( X ) ) ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) )
% 0.70/1.11 ), sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( node( sum_sum
% 0.70/1.11 ( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), fun
% 0.70/1.11 ( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), bool ), member( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), Y ),
% 0.70/1.11 hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.11 sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com, fun
% 0.70/1.11 ( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.11 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ), ! hBOOL(
% 0.70/1.11 hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.11 sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( node( sum_sum(
% 0.70/1.11 com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), fun(
% 0.70/1.11 fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), bool ), member( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), Z ),
% 0.70/1.11 hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.11 sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com, fun
% 0.70/1.11 ( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.11 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ), ! hAPP( fun
% 0.70/1.11 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.11 ), bool ), hoare_509422987triple( X ), hoare_244953527triple( X ), Y ) =
% 0.70/1.11 hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), hoare_509422987triple( X ), hoare_244953527triple(
% 0.70/1.11 X ), Z ), Y = Z }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) )
% 0.70/1.11 ), sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( node( sum_sum
% 0.70/1.11 ( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), fun
% 0.70/1.11 ( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), bool ), member( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), Y ),
% 0.70/1.11 hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.11 sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com, fun
% 0.70/1.11 ( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.11 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ), ! hBOOL(
% 0.70/1.11 hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.11 sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( node( sum_sum(
% 0.70/1.11 com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), fun(
% 0.70/1.11 fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), bool ), member( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), Z ),
% 0.70/1.11 hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.11 sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com, fun
% 0.70/1.11 ( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.11 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ), ! Y = Z,
% 0.70/1.11 hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), hoare_509422987triple( X ), hoare_244953527triple(
% 0.70/1.11 X ), Y ) = hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) )
% 0.70/1.11 , sum_sum( state, X ) ), bool ), hoare_509422987triple( X ),
% 0.70/1.11 hoare_244953527triple( X ), Z ) }.
% 0.70/1.11 { hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) )
% 0.70/1.11 , sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( node( sum_sum(
% 0.70/1.11 com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), fun(
% 0.70/1.11 fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), bool ), member( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), skol4( X
% 0.70/1.11 , Z ) ), hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) )
% 0.70/1.11 ), sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.11 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ), hBOOL( hAPP
% 0.70/1.11 ( hoare_509422987triple( X ), bool, Y, T ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( hoare_509422987triple( X ), bool, Y, hAPP( fun( node(
% 0.70/1.11 sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool
% 0.70/1.11 ), hoare_509422987triple( X ), hoare_244953527triple( X ), skol4( X, Y )
% 0.70/1.11 ) ) ), hBOOL( hAPP( hoare_509422987triple( X ), bool, Y, Z ) ) }.
% 0.70/1.11 { hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) )
% 0.70/1.11 , sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun( node( sum_sum(
% 0.70/1.11 com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), fun(
% 0.70/1.11 fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.11 state, X ) ), bool ), bool ), bool ), member( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ), skol5( X
% 0.70/1.11 , Z ) ), hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) )
% 0.70/1.11 ), sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com,
% 0.70/1.11 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.11 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.11 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ) }.
% 0.70/1.11 { Y = hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.11 sum_sum( state, X ) ), bool ), hoare_509422987triple( X ),
% 0.70/1.11 hoare_244953527triple( X ), skol5( X, Y ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), U ), Z ), T ) ), ! hBOOL( hAPP( fun( X
% 0.70/1.11 , bool ), bool, hAPP( X, fun( fun( X, bool ), bool ), member( X ), W ), T
% 0.70/1.11 ) ), ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool ),
% 0.70/1.11 bool ), member( X ), V0 ), T ) ), ! hAPP( X, Y, Z, W ) = hAPP( X, Y, Z,
% 0.70/1.11 V0 ), ti( X, W ) = ti( X, V0 ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), U ), Z ), T ) ), ! hBOOL( hAPP( fun( X
% 0.70/1.11 , bool ), bool, hAPP( X, fun( fun( X, bool ), bool ), member( X ), W ), T
% 0.70/1.11 ) ), ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool ),
% 0.70/1.11 bool ), member( X ), V0 ), T ) ), ! ti( X, W ) = ti( X, V0 ), hAPP( X, Y
% 0.70/1.11 , Z, W ) = hAPP( X, Y, Z, V0 ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), Z ), T ), U ) ), ! hBOOL( hAPP( fun( X
% 0.70/1.11 , bool ), bool, hAPP( X, fun( fun( X, bool ), bool ), member( X ), W ), U
% 0.70/1.11 ) ), hAPP( Y, X, Z, hAPP( X, Y, T, W ) ) = ti( X, W ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), Z ), T ), U ) ), ! hAPP( Y, X, Z, W )
% 0.70/1.11 = hAPP( Y, X, Z, V0 ), ti( Y, W ) = ti( Y, V0 ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), Z ), T ), U ) ), ! ti( Y, W ) = ti( Y
% 0.70/1.11 , V0 ), hAPP( Y, X, Z, W ) = hAPP( Y, X, Z, V0 ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), Z ), T ), U ) ), hAPP( X, Y, T, hAPP(
% 0.70/1.11 Y, X, Z, W ) ) = ti( Y, W ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), Z ), U ), T ) ), hBOOL( hAPP( fun( X,
% 0.70/1.11 bool ), bool, hAPP( X, fun( fun( X, bool ), bool ), member( X ), hAPP( Y
% 0.70/1.11 , X, Z, W ) ), T ) ) }.
% 0.70/1.11 { ! hBOOL( induct_false ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), Z ), U ), T ) ), ! hBOOL( hAPP( fun( X
% 0.70/1.11 , bool ), bool, hAPP( X, fun( fun( X, bool ), bool ), member( X ), W ), T
% 0.70/1.11 ) ), ti( X, W ) = hAPP( Y, X, Z, skol6( X, Y, Z, W ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), U ), Z ), T ) ), hBOOL( hAPP( fun( X,
% 0.70/1.11 bool ), bool, hAPP( X, fun( fun( X, bool ), bool ), member( X ), skol7( X
% 0.70/1.11 , V0, V1, T, V2 ) ), T ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), U ), Z ), T ) ), ti( Y, W ) = hAPP( X
% 0.70/1.11 , Y, Z, skol7( X, Y, Z, T, W ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), U ), Z ), T ) ), hBOOL( hAPP( fun( X,
% 0.70/1.11 bool ), bool, hAPP( X, fun( fun( X, bool ), bool ), member( X ), skol8( X
% 0.70/1.11 , V0, V1, T, V2 ) ), T ) ), hBOOL( hAPP( Y, bool, W, V3 ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), U ), Z ), T ) ), ! hBOOL( hAPP( Y,
% 0.70/1.11 bool, W, hAPP( X, Y, Z, skol8( X, Y, Z, T, W ) ) ) ), hBOOL( hAPP( Y,
% 0.70/1.11 bool, W, V0 ) ) }.
% 0.70/1.11 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( fun( X, Y ), fun( fun( X, bool
% 0.70/1.11 ), bool ), hAPP( fun( Y, X ), fun( fun( X, Y ), fun( fun( X, bool ),
% 0.70/1.11 bool ) ), type_definition( Y, X ), Z ), U ), T ) ), ! hBOOL( hAPP( fun( X
% 0.70/1.11 , bool ), bool, hAPP( X, fun( fun( X, bool ), bool ), member( X ), W ), T
% 0.70/1.11 ) ), ! hBOOL( hAPP( X, bool, V0, hAPP( Y, X, Z, skol9( X, Y, Z, V0 ) ) )
% 0.70/1.11 ), hBOOL( hAPP( X, bool, V0, W ) ) }.
% 0.70/1.11 { hBOOL( induct_true ) }.
% 0.70/1.11 { hBOOL( induct_true ) }.
% 0.70/1.11 { ! hBOOL( hAPP( X, bool, hAPP( X, fun( X, bool ), induct_equal( X ), Y ),
% 0.70/1.11 Z ) ), ti( X, Y ) = ti( X, Z ) }.
% 0.70/1.11 { ! ti( X, Y ) = ti( X, Z ), hBOOL( hAPP( X, bool, hAPP( X, fun( X, bool )
% 0.70/1.11 , induct_equal( X ), Y ), Z ) ) }.
% 0.70/1.11 { ! hAPP( X, Y, Z, skol10( X, Y, Z, T ) ) = hAPP( X, Y, T, skol10( X, Y, Z
% 0.70/1.12 , T ) ), ti( fun( X, Y ), Z ) = ti( fun( X, Y ), T ) }.
% 0.70/1.12 { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool ), bool )
% 0.70/1.12 , member( X ), Y ), Z ) ), hBOOL( hAPP( X, bool, Z, Y ) ) }.
% 0.70/1.12 { ! hBOOL( hAPP( X, bool, Z, Y ) ), hBOOL( hAPP( fun( X, bool ), bool, hAPP
% 0.70/1.12 ( X, fun( fun( X, bool ), bool ), member( X ), Y ), Z ) ) }.
% 0.70/1.12 { hAPP( fun( X, bool ), fun( X, bool ), collect( X ), Y ) = ti( fun( X,
% 0.70/1.12 bool ), Y ) }.
% 0.70/1.12 { ! enum( Y ), ! enum( X ), enum( sum_sum( X, Y ) ) }.
% 0.70/1.12 { enum( bool ) }.
% 0.70/1.12 { ! enum( Y ), ! enum( X ), enum( fun( X, Y ) ) }.
% 0.70/1.12 { ! cl_HOL_Oequal( Y ), ! enum( X ), cl_HOL_Oequal( fun( X, Y ) ) }.
% 0.70/1.12 { cl_HOL_Oequal( com ) }.
% 0.70/1.12 { cl_HOL_Oequal( bool ) }.
% 0.70/1.12 { cl_HOL_Oequal( state ) }.
% 0.70/1.12 { cl_HOL_Oequal( sum_sum( X, Y ) ) }.
% 0.70/1.12 { cl_HOL_Oequal( hoare_509422987triple( X ) ) }.
% 0.70/1.12 { ti( X, ti( X, Y ) ) = ti( X, Y ) }.
% 0.70/1.12 { ! hBOOL( hAPP( X, bool, hAPP( X, fun( X, bool ), fequal( X ), Y ), Z ) )
% 0.70/1.12 , ti( X, Y ) = ti( X, Z ) }.
% 0.70/1.12 { ! ti( X, Y ) = ti( X, Z ), hBOOL( hAPP( X, bool, hAPP( X, fun( X, bool )
% 0.70/1.12 , fequal( X ), Y ), Z ) ) }.
% 0.70/1.12 { hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 { ti( state, X ) = ti( state, skol11 ) }.
% 0.70/1.12
% 0.70/1.12 percentage equality = 0.395833, percentage horn = 0.960526
% 0.70/1.12 This is a problem with some equality
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Options Used:
% 0.70/1.12
% 0.70/1.12 useres = 1
% 0.70/1.12 useparamod = 1
% 0.70/1.12 useeqrefl = 1
% 0.70/1.12 useeqfact = 1
% 0.70/1.12 usefactor = 1
% 0.70/1.12 usesimpsplitting = 0
% 0.70/1.12 usesimpdemod = 5
% 0.70/1.12 usesimpres = 3
% 0.70/1.12
% 0.70/1.12 resimpinuse = 1000
% 0.70/1.12 resimpclauses = 20000
% 0.70/1.12 substype = eqrewr
% 0.70/1.12 backwardsubs = 1
% 0.70/1.12 selectoldest = 5
% 0.70/1.12
% 0.70/1.12 litorderings [0] = split
% 0.70/1.12 litorderings [1] = extend the termordering, first sorting on arguments
% 0.70/1.12
% 0.70/1.12 termordering = kbo
% 0.70/1.12
% 0.70/1.12 litapriori = 0
% 0.70/1.12 termapriori = 1
% 0.70/1.12 litaposteriori = 0
% 0.70/1.12 termaposteriori = 0
% 0.70/1.12 demodaposteriori = 0
% 0.70/1.12 ordereqreflfact = 0
% 0.70/1.12
% 0.70/1.12 litselect = negord
% 0.70/1.12
% 0.70/1.12 maxweight = 15
% 0.70/1.12 maxdepth = 30000
% 0.70/1.12 maxlength = 115
% 0.70/1.12 maxnrvars = 195
% 0.70/1.12 excuselevel = 1
% 0.70/1.12 increasemaxweight = 1
% 0.70/1.12
% 0.70/1.12 maxselected = 10000000
% 0.70/1.12 maxnrclauses = 10000000
% 0.70/1.12
% 0.70/1.12 showgenerated = 0
% 0.70/1.12 showkept = 0
% 0.70/1.12 showselected = 0
% 0.70/1.12 showdeleted = 0
% 0.70/1.12 showresimp = 1
% 0.70/1.12 showstatus = 2000
% 0.70/1.12
% 0.70/1.12 prologoutput = 0
% 0.70/1.12 nrgoals = 5000000
% 0.70/1.12 totalproof = 1
% 0.70/1.12
% 0.70/1.12 Symbols occurring in the translation:
% 0.70/1.12
% 0.70/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.70/1.12 . [1, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.70/1.12 ! [4, 1] (w:0, o:37, a:1, s:1, b:0),
% 0.70/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.12 cl_HOL_Oequal [36, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.70/1.12 bool [37, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.70/1.12 fun [38, 2] (w:1, o:79, a:1, s:1, b:0),
% 0.70/1.12 equal_equal [39, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.70/1.12 ti [40, 2] (w:1, o:85, a:1, s:1, b:0),
% 0.70/1.12 induct_equal [41, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.70/1.12 induct_false [42, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.70/1.12 induct_true [43, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.70/1.12 undefined [44, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.70/1.12 com [45, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.70/1.12 state [46, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.70/1.12 sum_sum [47, 2] (w:1, o:80, a:1, s:1, b:0),
% 0.70/1.12 node [48, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.70/1.12 hoare_509422987triple [49, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.70/1.12 hoare_244953527triple [50, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.70/1.12 hoare_2037801986triple [51, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.70/1.12 hoare_1883395792gleton [52, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.70/1.12 hoare_1580379338ep_set [53, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.70/1.12 collect [54, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.70/1.12 type_definition [56, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.70/1.12 fequal [57, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.70/1.12 hAPP [60, 4] (w:1, o:88, a:1, s:1, b:0),
% 0.70/1.12 hBOOL [61, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.70/1.12 member [62, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.70/1.12 enum [78, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.70/1.12 skol1 [82, 0] (w:1, o:34, a:1, s:1, b:1),
% 0.70/1.12 skol2 [83, 2] (w:1, o:81, a:1, s:1, b:1),
% 0.70/1.12 skol3 [84, 2] (w:1, o:82, a:1, s:1, b:1),
% 0.70/1.12 skol4 [85, 2] (w:1, o:83, a:1, s:1, b:1),
% 0.70/1.12 skol5 [86, 2] (w:1, o:84, a:1, s:1, b:1),
% 0.70/1.12 skol6 [87, 4] (w:1, o:89, a:1, s:1, b:1),
% 0.70/1.12 skol7 [88, 5] (w:1, o:92, a:1, s:1, b:1),
% 0.70/1.12 skol8 [89, 5] (w:1, o:93, a:1, s:1, b:1),
% 0.70/1.12 skol9 [90, 4] (w:1, o:90, a:1, s:1, b:1),
% 0.70/1.12 skol10 [91, 4] (w:1, o:91, a:1, s:1, b:1),
% 0.70/1.12 skol11 [92, 0] (w:1, o:35, a:1, s:1, b:1),
% 0.70/1.12 skol12 [93, 0] (w:1, o:36, a:1, s:1, b:1).
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Starting Search:
% 0.70/1.12
% 0.70/1.12 *** allocated 15000 integers for clauses
% 0.70/1.12 *** allocated 22500 integers for clauses
% 0.70/1.12 *** allocated 33750 integers for clauses
% 0.70/1.12
% 0.70/1.12 Bliksems!, er is een bewijs:
% 0.70/1.12 % SZS status Theorem
% 0.70/1.12 % SZS output start Refutation
% 0.70/1.12
% 0.70/1.12 (4) {G0,W7,D4,L1,V1,M1} I { ti( X, undefined( X ) ) ==> undefined( X ) }.
% 0.70/1.12 (18) {G0,W9,D3,L2,V0,M2} I { ! hBOOL( hoare_1883395792gleton ), ! ti( state
% 0.70/1.12 , skol12 ) ==> ti( state, skol1 ) }.
% 0.70/1.12 (73) {G0,W2,D2,L1,V0,M1} I { hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 (74) {G0,W7,D3,L1,V1,M1} I { ti( state, X ) = ti( state, skol11 ) }.
% 0.70/1.12 (97) {G1,W6,D3,L1,V0,M1} P(74,4) { ti( state, skol11 ) ==> undefined( state
% 0.70/1.12 ) }.
% 0.70/1.12 (98) {G2,W6,D3,L1,V1,M1} P(97,74) { ti( state, X ) ==> undefined( state )
% 0.70/1.12 }.
% 0.70/1.12 (309) {G3,W0,D0,L0,V0,M0} S(18);d(98);d(98);q;r(73) { }.
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 % SZS output end Refutation
% 0.70/1.12 found a proof!
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Unprocessed initial clauses:
% 0.70/1.12
% 0.70/1.12 (311) {G0,W13,D5,L2,V1,M2} { ! cl_HOL_Oequal( X ), ti( fun( X, fun( X,
% 0.70/1.12 bool ) ), equal_equal( X ) ) = equal_equal( X ) }.
% 0.70/1.12 (312) {G0,W11,D5,L1,V1,M1} { ti( fun( X, fun( X, bool ) ), induct_equal( X
% 0.70/1.12 ) ) = induct_equal( X ) }.
% 0.70/1.12 (313) {G0,W5,D3,L1,V0,M1} { ti( bool, induct_false ) = induct_false }.
% 0.70/1.12 (314) {G0,W5,D3,L1,V0,M1} { ti( bool, induct_true ) = induct_true }.
% 0.70/1.12 (315) {G0,W7,D4,L1,V1,M1} { ti( X, undefined( X ) ) = undefined( X ) }.
% 0.70/1.12 (316) {G0,W22,D9,L1,V1,M1} { ti( fun( fun( node( sum_sum( com, fun( X, fun
% 0.70/1.12 ( state, bool ) ) ), sum_sum( state, X ) ), bool ), hoare_509422987triple
% 0.70/1.12 ( X ) ), hoare_244953527triple( X ) ) = hoare_244953527triple( X ) }.
% 0.70/1.12 (317) {G0,W22,D9,L1,V1,M1} { ti( fun( hoare_509422987triple( X ), fun(
% 0.70/1.12 node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) )
% 0.70/1.12 , bool ) ), hoare_2037801986triple( X ) ) = hoare_2037801986triple( X )
% 0.70/1.12 }.
% 0.70/1.12 (318) {G0,W5,D3,L1,V0,M1} { ti( bool, hoare_1883395792gleton ) =
% 0.70/1.12 hoare_1883395792gleton }.
% 0.70/1.12 (319) {G0,W21,D9,L1,V1,M1} { ti( fun( fun( node( sum_sum( com, fun( X, fun
% 0.70/1.12 ( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 hoare_1580379338ep_set( X ) ) = hoare_1580379338ep_set( X ) }.
% 0.70/1.12 (320) {G0,W13,D5,L1,V1,M1} { ti( fun( fun( X, bool ), fun( X, bool ) ),
% 0.70/1.12 collect( X ) ) = collect( X ) }.
% 0.70/1.12 (321) {G0,W21,D7,L1,V2,M1} { ti( fun( fun( X, Y ), fun( fun( Y, X ), fun(
% 0.70/1.12 fun( Y, bool ), bool ) ) ), type_definition( X, Y ) ) = type_definition(
% 0.70/1.12 X, Y ) }.
% 0.70/1.12 (322) {G0,W11,D5,L1,V1,M1} { ti( fun( X, fun( X, bool ) ), fequal( X ) ) =
% 0.70/1.12 fequal( X ) }.
% 0.70/1.12 (323) {G0,W15,D5,L1,V4,M1} { hAPP( X, Y, ti( fun( X, Y ), Z ), T ) = hAPP
% 0.70/1.12 ( X, Y, Z, T ) }.
% 0.70/1.12 (324) {G0,W13,D4,L1,V4,M1} { hAPP( X, Y, Z, ti( X, T ) ) = hAPP( X, Y, Z,
% 0.70/1.12 T ) }.
% 0.70/1.12 (325) {G0,W13,D4,L1,V4,M1} { ti( X, hAPP( Y, X, Z, T ) ) = hAPP( Y, X, Z,
% 0.70/1.12 T ) }.
% 0.70/1.12 (326) {G0,W6,D3,L2,V1,M2} { ! hBOOL( ti( bool, X ) ), hBOOL( X ) }.
% 0.70/1.12 (327) {G0,W6,D3,L2,V1,M2} { ! hBOOL( X ), hBOOL( ti( bool, X ) ) }.
% 0.70/1.12 (328) {G0,W13,D6,L1,V1,M1} { ti( fun( X, fun( fun( X, bool ), bool ) ),
% 0.70/1.12 member( X ) ) = member( X ) }.
% 0.70/1.12 (329) {G0,W9,D3,L2,V0,M2} { ! hBOOL( hoare_1883395792gleton ), ! ti( state
% 0.70/1.12 , skol1 ) = ti( state, skol12 ) }.
% 0.70/1.12 (330) {G0,W9,D3,L2,V2,M2} { ti( state, X ) = ti( state, Y ), hBOOL(
% 0.70/1.12 hoare_1883395792gleton ) }.
% 0.70/1.12 (331) {G0,W20,D6,L2,V3,M2} { ! hBOOL( hAPP( hoare_509422987triple( X ),
% 0.70/1.12 bool, hAPP( hoare_509422987triple( X ), fun( hoare_509422987triple( X ),
% 0.70/1.12 bool ), equal_equal( hoare_509422987triple( X ) ), Y ), Z ) ), Y = Z }.
% 0.70/1.12 (332) {G0,W20,D6,L2,V3,M2} { ! Y = Z, hBOOL( hAPP( hoare_509422987triple(
% 0.70/1.12 X ), bool, hAPP( hoare_509422987triple( X ), fun( hoare_509422987triple(
% 0.70/1.12 X ), bool ), equal_equal( hoare_509422987triple( X ) ), Y ), Z ) ) }.
% 0.70/1.12 (333) {G0,W42,D8,L2,V3,M2} { ! hAPP( hoare_509422987triple( X ), fun( node
% 0.70/1.12 ( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ),
% 0.70/1.12 bool ), hoare_2037801986triple( X ), Y ) = hAPP( hoare_509422987triple( X
% 0.70/1.12 ), fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.12 state, X ) ), bool ), hoare_2037801986triple( X ), Z ), Y = Z }.
% 0.70/1.12 (334) {G0,W42,D8,L2,V3,M2} { ! Y = Z, hAPP( hoare_509422987triple( X ),
% 0.70/1.12 fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state,
% 0.70/1.12 X ) ), bool ), hoare_2037801986triple( X ), Y ) = hAPP(
% 0.70/1.12 hoare_509422987triple( X ), fun( node( sum_sum( com, fun( X, fun( state,
% 0.70/1.12 bool ) ) ), sum_sum( state, X ) ), bool ), hoare_2037801986triple( X ), Z
% 0.70/1.12 ) }.
% 0.70/1.12 (335) {G0,W7,D3,L2,V1,M2} { ! cl_HOL_Oequal( X ), equal_equal( X ) =
% 0.70/1.12 fequal( X ) }.
% 0.70/1.12 (336) {G0,W15,D5,L2,V2,M2} { ! cl_HOL_Oequal( X ), hBOOL( hAPP( X, bool,
% 0.70/1.12 hAPP( X, fun( X, bool ), equal_equal( X ), Y ), Y ) ) }.
% 0.70/1.12 (337) {G0,W22,D5,L3,V3,M3} { ! cl_HOL_Oequal( X ), ! hBOOL( hAPP( X, bool
% 0.70/1.12 , hAPP( X, fun( X, bool ), equal_equal( X ), Y ), Z ) ), ti( X, Y ) = ti
% 0.70/1.12 ( X, Z ) }.
% 0.70/1.12 (338) {G0,W22,D5,L3,V3,M3} { ! cl_HOL_Oequal( X ), ! ti( X, Y ) = ti( X, Z
% 0.70/1.12 ), hBOOL( hAPP( X, bool, hAPP( X, fun( X, bool ), equal_equal( X ), Y )
% 0.70/1.12 , Z ) ) }.
% 0.70/1.12 (339) {G0,W7,D3,L2,V1,M2} { ! cl_HOL_Oequal( X ), fequal( X ) =
% 0.70/1.12 equal_equal( X ) }.
% 0.70/1.12 (340) {G0,W39,D9,L1,V2,M1} { hAPP( fun( node( sum_sum( com, fun( X, fun(
% 0.70/1.12 state, bool ) ) ), sum_sum( state, X ) ), bool ), hoare_509422987triple(
% 0.70/1.12 X ), hoare_244953527triple( X ), hAPP( hoare_509422987triple( X ), fun(
% 0.70/1.12 node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) )
% 0.70/1.12 , bool ), hoare_2037801986triple( X ), Y ) ) = Y }.
% 0.70/1.12 (341) {G0,W129,D11,L1,V2,M1} { hBOOL( hAPP( fun( fun( node( sum_sum( com,
% 0.70/1.12 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 bool, hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), fun( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool ),
% 0.70/1.12 member( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ) ), hAPP( hoare_509422987triple( X ), fun( node(
% 0.70/1.12 sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool
% 0.70/1.12 ), hoare_2037801986triple( X ), Y ) ), hAPP( fun( fun( node( sum_sum(
% 0.70/1.12 com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool
% 0.70/1.12 ), fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ), bool ), collect( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ),
% 0.70/1.12 hoare_1580379338ep_set( X ) ) ) ) }.
% 0.70/1.12 (342) {G0,W167,D11,L3,V3,M3} { ! hBOOL( hAPP( fun( fun( node( sum_sum( com
% 0.70/1.12 , fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 bool, hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), fun( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool ),
% 0.70/1.12 member( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ) ), Y ), hAPP( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), fun( fun
% 0.70/1.12 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.12 ), bool ), bool ), collect( fun( node( sum_sum( com, fun( X, fun( state
% 0.70/1.12 , bool ) ) ), sum_sum( state, X ) ), bool ) ), hoare_1580379338ep_set( X
% 0.70/1.12 ) ) ) ), ! hBOOL( hAPP( fun( node( sum_sum( com, fun( X, fun( state,
% 0.70/1.12 bool ) ) ), sum_sum( state, X ) ), bool ), bool, Z, hAPP(
% 0.70/1.12 hoare_509422987triple( X ), fun( node( sum_sum( com, fun( X, fun( state,
% 0.70/1.12 bool ) ) ), sum_sum( state, X ) ), bool ), hoare_2037801986triple( X ),
% 0.70/1.12 skol2( X, Z ) ) ) ), hBOOL( hAPP( fun( node( sum_sum( com, fun( X, fun(
% 0.70/1.12 state, bool ) ) ), sum_sum( state, X ) ), bool ), bool, Z, Y ) ) }.
% 0.70/1.12 (343) {G0,W134,D11,L2,V2,M2} { ! hBOOL( hAPP( fun( fun( node( sum_sum( com
% 0.70/1.12 , fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 bool, hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), fun( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool ),
% 0.70/1.12 member( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ) ), Y ), hAPP( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), fun( fun
% 0.70/1.12 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.12 ), bool ), bool ), collect( fun( node( sum_sum( com, fun( X, fun( state
% 0.70/1.12 , bool ) ) ), sum_sum( state, X ) ), bool ) ), hoare_1580379338ep_set( X
% 0.70/1.12 ) ) ) ), Y = hAPP( hoare_509422987triple( X ), fun( node( sum_sum( com,
% 0.70/1.12 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ),
% 0.70/1.12 hoare_2037801986triple( X ), skol3( X, Y ) ) }.
% 0.70/1.12 (344) {G0,W150,D11,L2,V2,M2} { ! hBOOL( hAPP( fun( fun( node( sum_sum( com
% 0.70/1.12 , fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 bool, hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), fun( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool ),
% 0.70/1.12 member( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ) ), Y ), hAPP( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), fun( fun
% 0.70/1.12 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.12 ), bool ), bool ), collect( fun( node( sum_sum( com, fun( X, fun( state
% 0.70/1.12 , bool ) ) ), sum_sum( state, X ) ), bool ) ), hoare_1580379338ep_set( X
% 0.70/1.12 ) ) ) ), hAPP( hoare_509422987triple( X ), fun( node( sum_sum( com, fun
% 0.70/1.12 ( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ),
% 0.70/1.12 hoare_2037801986triple( X ), hAPP( fun( node( sum_sum( com, fun( X, fun(
% 0.70/1.12 state, bool ) ) ), sum_sum( state, X ) ), bool ), hoare_509422987triple(
% 0.70/1.12 X ), hoare_244953527triple( X ), Y ) ) = Y }.
% 0.70/1.12 (345) {G0,W170,D13,L1,V1,M1} { hBOOL( hAPP( fun( fun( node( sum_sum( com,
% 0.70/1.12 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 bool, hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) )
% 0.70/1.12 , sum_sum( state, X ) ), bool ), hoare_509422987triple( X ) ), fun( fun(
% 0.70/1.12 fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state,
% 0.70/1.12 X ) ), bool ), bool ), bool ), hAPP( fun( hoare_509422987triple( X ), fun
% 0.70/1.12 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.12 ), bool ) ), fun( fun( fun( node( sum_sum( com, fun( X, fun( state, bool
% 0.70/1.12 ) ) ), sum_sum( state, X ) ), bool ), hoare_509422987triple( X ) ), fun
% 0.70/1.12 ( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.12 state, X ) ), bool ), bool ), bool ) ), type_definition(
% 0.70/1.12 hoare_509422987triple( X ), fun( node( sum_sum( com, fun( X, fun( state,
% 0.70/1.12 bool ) ) ), sum_sum( state, X ) ), bool ) ), hoare_2037801986triple( X )
% 0.70/1.12 ), hoare_244953527triple( X ) ), hAPP( fun( fun( node( sum_sum( com, fun
% 0.70/1.12 ( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), fun(
% 0.70/1.12 fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state,
% 0.70/1.12 X ) ), bool ), bool ), collect( fun( node( sum_sum( com, fun( X, fun(
% 0.70/1.12 state, bool ) ) ), sum_sum( state, X ) ), bool ) ),
% 0.70/1.12 hoare_1580379338ep_set( X ) ) ) ) }.
% 0.70/1.12 (346) {G0,W264,D11,L4,V3,M4} { ! hBOOL( hAPP( fun( fun( node( sum_sum( com
% 0.70/1.12 , fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 bool, hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), fun( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool ),
% 0.70/1.12 member( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ) ), Y ), hAPP( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), fun( fun
% 0.70/1.12 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.12 ), bool ), bool ), collect( fun( node( sum_sum( com, fun( X, fun( state
% 0.70/1.12 , bool ) ) ), sum_sum( state, X ) ), bool ) ), hoare_1580379338ep_set( X
% 0.70/1.12 ) ) ) ), ! hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state
% 0.70/1.12 , bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun(
% 0.70/1.12 node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) )
% 0.70/1.12 , bool ), fun( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) )
% 0.70/1.12 ), sum_sum( state, X ) ), bool ), bool ), bool ), member( fun( node(
% 0.70/1.12 sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool
% 0.70/1.12 ) ), Z ), hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool )
% 0.70/1.12 ) ), sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com
% 0.70/1.12 , fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ), ! hAPP( fun
% 0.70/1.12 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.12 ), bool ), hoare_509422987triple( X ), hoare_244953527triple( X ), Y ) =
% 0.70/1.12 hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.12 state, X ) ), bool ), hoare_509422987triple( X ), hoare_244953527triple(
% 0.70/1.12 X ), Z ), Y = Z }.
% 0.70/1.12 (347) {G0,W264,D11,L4,V3,M4} { ! hBOOL( hAPP( fun( fun( node( sum_sum( com
% 0.70/1.12 , fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 bool, hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), fun( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool ),
% 0.70/1.12 member( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ) ), Y ), hAPP( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), fun( fun
% 0.70/1.12 ( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X )
% 0.70/1.12 ), bool ), bool ), collect( fun( node( sum_sum( com, fun( X, fun( state
% 0.70/1.12 , bool ) ) ), sum_sum( state, X ) ), bool ) ), hoare_1580379338ep_set( X
% 0.70/1.12 ) ) ) ), ! hBOOL( hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state
% 0.70/1.12 , bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool, hAPP( fun(
% 0.70/1.12 node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) )
% 0.70/1.12 , bool ), fun( fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) )
% 0.70/1.12 ), sum_sum( state, X ) ), bool ), bool ), bool ), member( fun( node(
% 0.70/1.12 sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool
% 0.70/1.12 ) ), Z ), hAPP( fun( fun( node( sum_sum( com, fun( X, fun( state, bool )
% 0.70/1.12 ) ), sum_sum( state, X ) ), bool ), bool ), fun( fun( node( sum_sum( com
% 0.70/1.12 , fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 collect( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ) ), hoare_1580379338ep_set( X ) ) ) ), ! Y = Z,
% 0.70/1.12 hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum(
% 0.70/1.12 state, X ) ), bool ), hoare_509422987triple( X ), hoare_244953527triple(
% 0.70/1.12 X ), Y ) = hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) )
% 0.70/1.12 , sum_sum( state, X ) ), bool ), hoare_509422987triple( X ),
% 0.70/1.12 hoare_244953527triple( X ), Z ) }.
% 0.70/1.12 (348) {G0,W120,D11,L2,V4,M2} { hBOOL( hAPP( fun( fun( node( sum_sum( com,
% 0.70/1.12 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 bool, hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), fun( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool ),
% 0.70/1.12 member( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ) ), skol4( X, Z ) ), hAPP( fun( fun( node( sum_sum
% 0.70/1.12 ( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ),
% 0.70/1.12 bool ), fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), bool ), collect( fun( node( sum_sum( com,
% 0.70/1.12 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ),
% 0.70/1.12 hoare_1580379338ep_set( X ) ) ) ), hBOOL( hAPP( hoare_509422987triple( X
% 0.70/1.12 ), bool, Y, T ) ) }.
% 0.70/1.12 (349) {G0,W34,D9,L2,V3,M2} { ! hBOOL( hAPP( hoare_509422987triple( X ),
% 0.70/1.12 bool, Y, hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), hoare_509422987triple( X ),
% 0.70/1.12 hoare_244953527triple( X ), skol4( X, Y ) ) ) ), hBOOL( hAPP(
% 0.70/1.12 hoare_509422987triple( X ), bool, Y, Z ) ) }.
% 0.70/1.12 (350) {G0,W113,D11,L1,V2,M1} { hBOOL( hAPP( fun( fun( node( sum_sum( com,
% 0.70/1.12 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ),
% 0.70/1.12 bool, hAPP( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), fun( fun( fun( node( sum_sum( com, fun( X
% 0.70/1.12 , fun( state, bool ) ) ), sum_sum( state, X ) ), bool ), bool ), bool ),
% 0.70/1.12 member( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ), sum_sum
% 0.70/1.12 ( state, X ) ), bool ) ), skol5( X, Z ) ), hAPP( fun( fun( node( sum_sum
% 0.70/1.12 ( com, fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ),
% 0.70/1.12 bool ), fun( fun( node( sum_sum( com, fun( X, fun( state, bool ) ) ),
% 0.70/1.12 sum_sum( state, X ) ), bool ), bool ), collect( fun( node( sum_sum( com,
% 0.70/1.12 fun( X, fun( state, bool ) ) ), sum_sum( state, X ) ), bool ) ),
% 0.70/1.12 hoare_1580379338ep_set( X ) ) ) ) }.
% 0.70/1.12 (351) {G0,W23,D8,L1,V2,M1} { Y = hAPP( fun( node( sum_sum( com, fun( X,
% 0.70/1.12 fun( state, bool ) ) ), sum_sum( state, X ) ), bool ),
% 0.70/1.12 hoare_509422987triple( X ), hoare_244953527triple( X ), skol5( X, Y ) )
% 0.70/1.12 }.
% 0.70/1.12 (352) {G0,W86,D8,L5,V7,M5} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), U ), Z ),
% 0.70/1.12 T ) ), ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool )
% 0.70/1.12 , bool ), member( X ), W ), T ) ), ! hBOOL( hAPP( fun( X, bool ), bool,
% 0.70/1.12 hAPP( X, fun( fun( X, bool ), bool ), member( X ), V0 ), T ) ), ! hAPP( X
% 0.70/1.12 , Y, Z, W ) = hAPP( X, Y, Z, V0 ), ti( X, W ) = ti( X, V0 ) }.
% 0.70/1.12 (353) {G0,W86,D8,L5,V7,M5} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), U ), Z ),
% 0.70/1.12 T ) ), ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool )
% 0.70/1.12 , bool ), member( X ), W ), T ) ), ! hBOOL( hAPP( fun( X, bool ), bool,
% 0.70/1.12 hAPP( X, fun( fun( X, bool ), bool ), member( X ), V0 ), T ) ), ! ti( X,
% 0.70/1.12 W ) = ti( X, V0 ), hAPP( X, Y, Z, W ) = hAPP( X, Y, Z, V0 ) }.
% 0.70/1.12 (354) {G0,W64,D8,L3,V6,M3} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), Z ), T ),
% 0.70/1.12 U ) ), ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool )
% 0.70/1.12 , bool ), member( X ), W ), U ) ), hAPP( Y, X, Z, hAPP( X, Y, T, W ) ) =
% 0.70/1.12 ti( X, W ) }.
% 0.70/1.12 (355) {G0,W52,D8,L3,V7,M3} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), Z ), T ),
% 0.70/1.12 U ) ), ! hAPP( Y, X, Z, W ) = hAPP( Y, X, Z, V0 ), ti( Y, W ) = ti( Y, V0
% 0.70/1.12 ) }.
% 0.70/1.12 (356) {G0,W52,D8,L3,V7,M3} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), Z ), T ),
% 0.70/1.12 U ) ), ! ti( Y, W ) = ti( Y, V0 ), hAPP( Y, X, Z, W ) = hAPP( Y, X, Z, V0
% 0.70/1.12 ) }.
% 0.70/1.12 (357) {G0,W47,D8,L2,V6,M2} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), Z ), T ),
% 0.70/1.12 U ) ), hAPP( X, Y, T, hAPP( Y, X, Z, W ) ) = ti( Y, W ) }.
% 0.70/1.12 (358) {G0,W55,D8,L2,V6,M2} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), Z ), U ),
% 0.70/1.12 T ) ), hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool ),
% 0.70/1.12 bool ), member( X ), hAPP( Y, X, Z, W ) ), T ) ) }.
% 0.70/1.12 (359) {G0,W2,D2,L1,V0,M1} { ! hBOOL( induct_false ) }.
% 0.70/1.12 (360) {G0,W64,D8,L3,V6,M3} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), Z ), U ),
% 0.70/1.12 T ) ), ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool )
% 0.70/1.12 , bool ), member( X ), W ), T ) ), ti( X, W ) = hAPP( Y, X, Z, skol6( X,
% 0.70/1.12 Y, Z, W ) ) }.
% 0.70/1.12 (361) {G0,W56,D8,L2,V8,M2} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), U ), Z ),
% 0.70/1.12 T ) ), hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool ),
% 0.70/1.12 bool ), member( X ), skol7( X, V0, V1, T, V2 ) ), T ) ) }.
% 0.70/1.12 (362) {G0,W48,D8,L2,V6,M2} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), U ), Z ),
% 0.70/1.12 T ) ), ti( Y, W ) = hAPP( X, Y, Z, skol7( X, Y, Z, T, W ) ) }.
% 0.70/1.12 (363) {G0,W62,D8,L3,V10,M3} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), U ), Z ),
% 0.70/1.12 T ) ), hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool ),
% 0.70/1.12 bool ), member( X ), skol8( X, V0, V1, T, V2 ) ), T ) ), hBOOL( hAPP( Y,
% 0.70/1.12 bool, W, V3 ) ) }.
% 0.70/1.12 (364) {G0,W55,D8,L3,V7,M3} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), U ), Z ),
% 0.70/1.12 T ) ), ! hBOOL( hAPP( Y, bool, W, hAPP( X, Y, Z, skol8( X, Y, Z, T, W ) )
% 0.70/1.12 ) ), hBOOL( hAPP( Y, bool, W, V0 ) ) }.
% 0.70/1.12 (365) {G0,W71,D8,L4,V7,M4} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP(
% 0.70/1.12 fun( X, Y ), fun( fun( X, bool ), bool ), hAPP( fun( Y, X ), fun( fun( X
% 0.70/1.12 , Y ), fun( fun( X, bool ), bool ) ), type_definition( Y, X ), Z ), U ),
% 0.70/1.12 T ) ), ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool )
% 0.70/1.12 , bool ), member( X ), W ), T ) ), ! hBOOL( hAPP( X, bool, V0, hAPP( Y, X
% 0.70/1.12 , Z, skol9( X, Y, Z, V0 ) ) ) ), hBOOL( hAPP( X, bool, V0, W ) ) }.
% 0.70/1.12 (366) {G0,W2,D2,L1,V0,M1} { hBOOL( induct_true ) }.
% 0.70/1.12 (367) {G0,W2,D2,L1,V0,M1} { hBOOL( induct_true ) }.
% 0.70/1.12 (368) {G0,W20,D5,L2,V3,M2} { ! hBOOL( hAPP( X, bool, hAPP( X, fun( X, bool
% 0.70/1.12 ), induct_equal( X ), Y ), Z ) ), ti( X, Y ) = ti( X, Z ) }.
% 0.70/1.12 (369) {G0,W20,D5,L2,V3,M2} { ! ti( X, Y ) = ti( X, Z ), hBOOL( hAPP( X,
% 0.70/1.12 bool, hAPP( X, fun( X, bool ), induct_equal( X ), Y ), Z ) ) }.
% 0.70/1.12 (370) {G0,W30,D4,L2,V4,M2} { ! hAPP( X, Y, Z, skol10( X, Y, Z, T ) ) =
% 0.70/1.12 hAPP( X, Y, T, skol10( X, Y, Z, T ) ), ti( fun( X, Y ), Z ) = ti( fun( X
% 0.70/1.12 , Y ), T ) }.
% 0.70/1.12 (371) {G0,W23,D6,L2,V3,M2} { ! hBOOL( hAPP( fun( X, bool ), bool, hAPP( X
% 0.70/1.12 , fun( fun( X, bool ), bool ), member( X ), Y ), Z ) ), hBOOL( hAPP( X,
% 0.70/1.12 bool, Z, Y ) ) }.
% 0.70/1.12 (372) {G0,W23,D6,L2,V3,M2} { ! hBOOL( hAPP( X, bool, Z, Y ) ), hBOOL( hAPP
% 0.70/1.12 ( fun( X, bool ), bool, hAPP( X, fun( fun( X, bool ), bool ), member( X )
% 0.70/1.12 , Y ), Z ) ) }.
% 0.70/1.12 (373) {G0,W16,D4,L1,V2,M1} { hAPP( fun( X, bool ), fun( X, bool ), collect
% 0.70/1.12 ( X ), Y ) = ti( fun( X, bool ), Y ) }.
% 0.70/1.12 (374) {G0,W8,D3,L3,V2,M3} { ! enum( Y ), ! enum( X ), enum( sum_sum( X, Y
% 0.70/1.12 ) ) }.
% 0.70/1.12 (375) {G0,W2,D2,L1,V0,M1} { enum( bool ) }.
% 0.70/1.12 (376) {G0,W8,D3,L3,V2,M3} { ! enum( Y ), ! enum( X ), enum( fun( X, Y ) )
% 0.70/1.12 }.
% 0.70/1.12 (377) {G0,W8,D3,L3,V2,M3} { ! cl_HOL_Oequal( Y ), ! enum( X ),
% 0.70/1.12 cl_HOL_Oequal( fun( X, Y ) ) }.
% 0.70/1.12 (378) {G0,W2,D2,L1,V0,M1} { cl_HOL_Oequal( com ) }.
% 0.70/1.12 (379) {G0,W2,D2,L1,V0,M1} { cl_HOL_Oequal( bool ) }.
% 0.70/1.12 (380) {G0,W2,D2,L1,V0,M1} { cl_HOL_Oequal( state ) }.
% 0.70/1.12 (381) {G0,W4,D3,L1,V2,M1} { cl_HOL_Oequal( sum_sum( X, Y ) ) }.
% 0.70/1.12 (382) {G0,W3,D3,L1,V1,M1} { cl_HOL_Oequal( hoare_509422987triple( X ) )
% 0.70/1.12 }.
% 0.70/1.12 (383) {G0,W9,D4,L1,V2,M1} { ti( X, ti( X, Y ) ) = ti( X, Y ) }.
% 0.70/1.12 (384) {G0,W20,D5,L2,V3,M2} { ! hBOOL( hAPP( X, bool, hAPP( X, fun( X, bool
% 0.70/1.12 ), fequal( X ), Y ), Z ) ), ti( X, Y ) = ti( X, Z ) }.
% 0.70/1.12 (385) {G0,W20,D5,L2,V3,M2} { ! ti( X, Y ) = ti( X, Z ), hBOOL( hAPP( X,
% 0.70/1.12 bool, hAPP( X, fun( X, bool ), fequal( X ), Y ), Z ) ) }.
% 0.70/1.12 (386) {G0,W2,D2,L1,V0,M1} { hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 (387) {G0,W7,D3,L1,V1,M1} { ti( state, X ) = ti( state, skol11 ) }.
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Total Proof:
% 0.70/1.12
% 0.70/1.12 subsumption: (4) {G0,W7,D4,L1,V1,M1} I { ti( X, undefined( X ) ) ==>
% 0.70/1.12 undefined( X ) }.
% 0.70/1.12 parent0: (315) {G0,W7,D4,L1,V1,M1} { ti( X, undefined( X ) ) = undefined(
% 0.70/1.12 X ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 *** allocated 22500 integers for termspace/termends
% 0.70/1.12 eqswap: (409) {G0,W9,D3,L2,V0,M2} { ! ti( state, skol12 ) = ti( state,
% 0.70/1.12 skol1 ), ! hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 parent0[1]: (329) {G0,W9,D3,L2,V0,M2} { ! hBOOL( hoare_1883395792gleton )
% 0.70/1.12 , ! ti( state, skol1 ) = ti( state, skol12 ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (18) {G0,W9,D3,L2,V0,M2} I { ! hBOOL( hoare_1883395792gleton )
% 0.70/1.12 , ! ti( state, skol12 ) ==> ti( state, skol1 ) }.
% 0.70/1.12 parent0: (409) {G0,W9,D3,L2,V0,M2} { ! ti( state, skol12 ) = ti( state,
% 0.70/1.12 skol1 ), ! hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 1
% 0.70/1.12 1 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (73) {G0,W2,D2,L1,V0,M1} I { hBOOL( hoare_1883395792gleton )
% 0.70/1.12 }.
% 0.70/1.12 parent0: (386) {G0,W2,D2,L1,V0,M1} { hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (74) {G0,W7,D3,L1,V1,M1} I { ti( state, X ) = ti( state,
% 0.70/1.12 skol11 ) }.
% 0.70/1.12 parent0: (387) {G0,W7,D3,L1,V1,M1} { ti( state, X ) = ti( state, skol11 )
% 0.70/1.12 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqswap: (509) {G0,W7,D3,L1,V1,M1} { ti( state, skol11 ) = ti( state, X )
% 0.70/1.12 }.
% 0.70/1.12 parent0[0]: (74) {G0,W7,D3,L1,V1,M1} I { ti( state, X ) = ti( state, skol11
% 0.70/1.12 ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 paramod: (511) {G1,W6,D3,L1,V0,M1} { ti( state, skol11 ) = undefined(
% 0.70/1.12 state ) }.
% 0.70/1.12 parent0[0]: (4) {G0,W7,D4,L1,V1,M1} I { ti( X, undefined( X ) ) ==>
% 0.70/1.12 undefined( X ) }.
% 0.70/1.12 parent1[0; 4]: (509) {G0,W7,D3,L1,V1,M1} { ti( state, skol11 ) = ti( state
% 0.70/1.12 , X ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := state
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 X := undefined( state )
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (97) {G1,W6,D3,L1,V0,M1} P(74,4) { ti( state, skol11 ) ==>
% 0.70/1.12 undefined( state ) }.
% 0.70/1.12 parent0: (511) {G1,W6,D3,L1,V0,M1} { ti( state, skol11 ) = undefined(
% 0.70/1.12 state ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqswap: (513) {G1,W6,D3,L1,V0,M1} { undefined( state ) ==> ti( state,
% 0.70/1.12 skol11 ) }.
% 0.70/1.12 parent0[0]: (97) {G1,W6,D3,L1,V0,M1} P(74,4) { ti( state, skol11 ) ==>
% 0.70/1.12 undefined( state ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqswap: (514) {G0,W7,D3,L1,V1,M1} { ti( state, skol11 ) = ti( state, X )
% 0.70/1.12 }.
% 0.70/1.12 parent0[0]: (74) {G0,W7,D3,L1,V1,M1} I { ti( state, X ) = ti( state, skol11
% 0.70/1.12 ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 paramod: (515) {G1,W6,D3,L1,V1,M1} { undefined( state ) ==> ti( state, X )
% 0.70/1.12 }.
% 0.70/1.12 parent0[0]: (514) {G0,W7,D3,L1,V1,M1} { ti( state, skol11 ) = ti( state, X
% 0.70/1.12 ) }.
% 0.70/1.12 parent1[0; 3]: (513) {G1,W6,D3,L1,V0,M1} { undefined( state ) ==> ti(
% 0.70/1.12 state, skol11 ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqswap: (516) {G1,W6,D3,L1,V1,M1} { ti( state, X ) ==> undefined( state )
% 0.70/1.12 }.
% 0.70/1.12 parent0[0]: (515) {G1,W6,D3,L1,V1,M1} { undefined( state ) ==> ti( state,
% 0.70/1.12 X ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (98) {G2,W6,D3,L1,V1,M1} P(97,74) { ti( state, X ) ==>
% 0.70/1.12 undefined( state ) }.
% 0.70/1.12 parent0: (516) {G1,W6,D3,L1,V1,M1} { ti( state, X ) ==> undefined( state )
% 0.70/1.12 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 paramod: (521) {G1,W8,D3,L2,V0,M2} { ! ti( state, skol12 ) ==> undefined(
% 0.70/1.12 state ), ! hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 parent0[0]: (98) {G2,W6,D3,L1,V1,M1} P(97,74) { ti( state, X ) ==>
% 0.70/1.12 undefined( state ) }.
% 0.70/1.12 parent1[1; 5]: (18) {G0,W9,D3,L2,V0,M2} I { ! hBOOL( hoare_1883395792gleton
% 0.70/1.12 ), ! ti( state, skol12 ) ==> ti( state, skol1 ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := skol1
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 paramod: (523) {G2,W7,D3,L2,V0,M2} { ! undefined( state ) ==> undefined(
% 0.70/1.12 state ), ! hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 parent0[0]: (98) {G2,W6,D3,L1,V1,M1} P(97,74) { ti( state, X ) ==>
% 0.70/1.12 undefined( state ) }.
% 0.70/1.12 parent1[0; 2]: (521) {G1,W8,D3,L2,V0,M2} { ! ti( state, skol12 ) ==>
% 0.70/1.12 undefined( state ), ! hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := skol12
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqrefl: (524) {G0,W2,D2,L1,V0,M1} { ! hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 parent0[0]: (523) {G2,W7,D3,L2,V0,M2} { ! undefined( state ) ==> undefined
% 0.70/1.12 ( state ), ! hBOOL( hoare_1883395792gleton ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 resolution: (525) {G1,W0,D0,L0,V0,M0} { }.
% 0.70/1.12 parent0[0]: (524) {G0,W2,D2,L1,V0,M1} { ! hBOOL( hoare_1883395792gleton )
% 0.70/1.12 }.
% 0.70/1.12 parent1[0]: (73) {G0,W2,D2,L1,V0,M1} I { hBOOL( hoare_1883395792gleton )
% 0.70/1.12 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (309) {G3,W0,D0,L0,V0,M0} S(18);d(98);d(98);q;r(73) { }.
% 0.70/1.12 parent0: (525) {G1,W0,D0,L0,V0,M0} { }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 Proof check complete!
% 0.70/1.12
% 0.70/1.12 Memory use:
% 0.70/1.12
% 0.70/1.12 space for terms: 11653
% 0.70/1.12 space for clauses: 26336
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 clauses generated: 516
% 0.70/1.12 clauses kept: 310
% 0.70/1.12 clauses selected: 69
% 0.70/1.12 clauses deleted: 2
% 0.70/1.12 clauses inuse deleted: 0
% 0.70/1.12
% 0.70/1.12 subsentry: 1128
% 0.70/1.12 literals s-matched: 700
% 0.70/1.12 literals matched: 668
% 0.70/1.12 full subsumption: 86
% 0.70/1.12
% 0.70/1.12 checksum: 563768414
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Bliksem ended
%------------------------------------------------------------------------------