TSTP Solution File: SCT159+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SCT159+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 : Mon Jul 18 21:01:35 EDT 2022
% Result : Timeout 300.03s 300.48s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT159+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Fri Jul 1 21:13:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.83/1.35 *** allocated 10000 integers for termspace/termends
% 0.83/1.35 *** allocated 10000 integers for clauses
% 0.83/1.35 *** allocated 10000 integers for justifications
% 0.83/1.35 *** allocated 15000 integers for termspace/termends
% 0.83/1.35 Bliksem 1.12
% 0.83/1.35
% 0.83/1.35
% 0.83/1.35 Automatic Strategy Selection
% 0.83/1.35
% 0.83/1.35 *** allocated 22500 integers for termspace/termends
% 0.83/1.35 *** allocated 33750 integers for termspace/termends
% 0.83/1.35 *** allocated 50625 integers for termspace/termends
% 0.83/1.35
% 0.83/1.35 Clauses:
% 0.83/1.35
% 0.83/1.35 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.83/1.35 { ! c_Fun_Oinj__on( T, Z, Y, X ), c_Finite__Set_Ocard( Z, c_Set_Oimage( T,
% 0.83/1.35 Z, Y, X ) ) = c_Finite__Set_Ocard( T, X ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_Set_Oimage( Z, Y, X, U ) = c_Set_Oimage( Z, Y, X
% 0.83/1.35 , T ), U = T }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! U = T, c_Set_Oimage( Z, Y, X, U ) = c_Set_Oimage( Z
% 0.83/1.35 , Y, X, T ) }.
% 0.83/1.35 { hBOOL( hAPP( c_Orderings_Otop__class_Otop( tc_fun( Y, tc_HOL_Obool ) ), X
% 0.83/1.35 ) ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! hAPP( X, U ) = hAPP( X, T ), U = T }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! U = T, hAPP( X, U ) = hAPP( X, T ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! hAPP( X, U ) = hAPP( X, T ), U = T }.
% 0.83/1.35 { ! class_Orderings_Otop( X ), hAPP( c_Orderings_Otop__class_Otop( tc_fun(
% 0.83/1.35 Z, X ) ), Y ) = c_Orderings_Otop__class_Otop( X ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( T, Z, Y, X ), ! c_member( T, U, X ), alpha16( X, Y, T,
% 0.83/1.35 U ) }.
% 0.83/1.35 { c_member( T, skol2( X, U, T ), X ), c_Fun_Oinj__on( T, Z, Y, X ) }.
% 0.83/1.35 { ! alpha16( X, Y, T, skol2( X, Y, T ) ), c_Fun_Oinj__on( T, Z, Y, X ) }.
% 0.83/1.35 { ! alpha16( X, Y, Z, T ), ! c_member( Z, U, X ), alpha1( Y, T, U ) }.
% 0.83/1.35 { ! alpha1( Y, T, skol3( U, Y, W, T ) ), alpha16( X, Y, Z, T ) }.
% 0.83/1.35 { c_member( Z, skol3( X, Y, Z, T ), X ), alpha16( X, Y, Z, T ) }.
% 0.83/1.35 { ! alpha1( X, Y, Z ), ! hAPP( X, Y ) = hAPP( X, Z ), Y = Z }.
% 0.83/1.35 { hAPP( X, Y ) = hAPP( X, Z ), alpha1( X, Y, Z ) }.
% 0.83/1.35 { ! Y = Z, alpha1( X, Y, Z ) }.
% 0.83/1.35 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.83/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.35 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.83/1.35 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.83/1.35 { c_Arrow__Order__Mirabelle_OIIA( v_F ) }.
% 0.83/1.35 { c_Arrow__Order__Mirabelle_Ounanimity( v_F ) }.
% 0.83/1.35 { c_Finite__Set_Ofinite( tc_Arrow__Order__Mirabelle_Oindi,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( tc_Arrow__Order__Mirabelle_Oindi,
% 0.83/1.35 tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( Y, X ), c_Finite__Set_Ofinite( T, c_Set_Oimage(
% 0.83/1.35 Y, T, Z, X ) ) }.
% 0.83/1.35 { ! class_Finite__Set_Ofinite( X ), c_Finite__Set_Ofinite( X, Y ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( tc_Option_Ooption( X ),
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( tc_Option_Ooption( X ),
% 0.83/1.35 tc_HOL_Obool ) ) ), c_Finite__Set_Ofinite( X,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( X, c_Orderings_Otop__class_Otop( tc_fun( X,
% 0.83/1.35 tc_HOL_Obool ) ) ), c_Finite__Set_Ofinite( tc_Option_Ooption( X ),
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( tc_Option_Ooption( X ),
% 0.83/1.35 tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( tc_sum( Y, X ), c_Orderings_Otop__class_Otop(
% 0.83/1.35 tc_fun( tc_sum( Y, X ), tc_HOL_Obool ) ) ), c_Finite__Set_Ofinite( Y,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( Y, tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( tc_sum( Y, X ), c_Orderings_Otop__class_Otop(
% 0.83/1.35 tc_fun( tc_sum( Y, X ), tc_HOL_Obool ) ) ), c_Finite__Set_Ofinite( X,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( Y, c_Orderings_Otop__class_Otop( tc_fun( Y,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_Finite__Set_Ofinite( X,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ),
% 0.83/1.35 c_Finite__Set_Ofinite( tc_sum( Y, X ), c_Orderings_Otop__class_Otop(
% 0.83/1.35 tc_fun( tc_sum( Y, X ), tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { ! class_Finite__Set_Ofinite( X ), c_Finite__Set_Ofinite( X, Y ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( tc_fun( Y, X ), c_Orderings_Otop__class_Otop(
% 0.83/1.35 tc_fun( tc_fun( Y, X ), tc_HOL_Obool ) ) ), c_Finite__Set_Ofinite( X,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( X, c_Orderings_Otop__class_Otop( tc_fun( X,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_Finite__Set_Ofinite( Y,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( Y, tc_HOL_Obool ) ) ),
% 0.83/1.35 c_Finite__Set_Ofinite( tc_prod( X, Y ), c_Orderings_Otop__class_Otop(
% 0.83/1.35 tc_fun( tc_prod( X, Y ), tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { ! class_Finite__Set_Ofinite( X ), c_Finite__Set_Ofinite( X,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { c_Finite__Set_Ofinite( Y, X ), c_Finite__Set_Ocard( Y, X ) =
% 0.83/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( T, c_Set_Oimage( Z, T, Y, X ) ), !
% 0.83/1.35 c_Fun_Oinj__on( Z, T, Y, X ), c_Finite__Set_Ofinite( Z, X ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( X, c_Orderings_Otop__class_Otop( tc_fun( X,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_Finite__Set_Ocard( X, Y ) = c_Finite__Set_Ocard(
% 0.83/1.35 X, c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ), Y =
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( X, c_Orderings_Otop__class_Otop( tc_fun( X,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_Set_Oimage( X, X, Y, c_Orderings_Otop__class_Otop
% 0.83/1.35 ( tc_fun( X, tc_HOL_Obool ) ) ) = c_Orderings_Otop__class_Otop( tc_fun( X
% 0.83/1.35 , tc_HOL_Obool ) ), c_Fun_Oinj__on( X, X, Y, c_Orderings_Otop__class_Otop
% 0.83/1.35 ( tc_fun( X, tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( X, c_Orderings_Otop__class_Otop( tc_fun( X,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_Fun_Oinj__on( X, X, Y,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ), c_Set_Oimage
% 0.83/1.35 ( X, X, Y, c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ) =
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Finite__Set_Ocard( T, c_Set_Oimage(
% 0.83/1.35 Y, T, Z, X ) ) = c_Finite__Set_Ocard( Y, X ), c_Fun_Oinj__on( Y, T, Z, X
% 0.83/1.35 ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Fun_Oinj__on( Y, T, Z, X ),
% 0.83/1.35 c_Finite__Set_Ocard( T, c_Set_Oimage( Y, T, Z, X ) ) =
% 0.83/1.35 c_Finite__Set_Ocard( Y, X ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Finite__Set_Ocard( T, c_Set_Oimage(
% 0.83/1.35 Y, T, Z, X ) ) = c_Finite__Set_Ocard( Y, X ), c_Fun_Oinj__on( Y, T, Z, X
% 0.83/1.35 ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( T, Z, Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.35 tc_fun( Z, tc_HOL_Obool ), c_Set_Oimage( T, Z, Y, X ), U ), !
% 0.83/1.35 c_Fun_Oinj__on( Z, T, W, U ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.83/1.35 ( T, tc_HOL_Obool ), c_Set_Oimage( Z, T, W, U ), X ), !
% 0.83/1.35 c_Finite__Set_Ofinite( T, X ), ! c_Finite__Set_Ofinite( Z, U ),
% 0.83/1.35 c_Finite__Set_Ocard( T, X ) = c_Finite__Set_Ocard( Z, U ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( X, c_Orderings_Otop__class_Otop( tc_fun( X,
% 0.83/1.35 tc_HOL_Obool ) ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.83/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Finite__Set_Ocard( X,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ) ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( T, Z, Y, X ), c_Set_Oimage( Z, T, c_Fun_Othe__inv__into
% 0.83/1.35 ( T, Z, X, Y ), c_Set_Oimage( T, Z, Y, X ) ) = X }.
% 0.83/1.35 { ! c_Fun_Oinj__on( T, Z, Y, X ), c_Fun_Oinj__on( Z, T,
% 0.83/1.35 c_Fun_Othe__inv__into( T, Z, X, Y ), c_Set_Oimage( T, Z, Y, X ) ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), hAPP( c_Fun_Othe__inv__into( Z, Y,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( Z, tc_HOL_Obool ) ), X ), hAPP( X,
% 0.83/1.35 T ) ) = T }.
% 0.83/1.35 { ! c_Finite__Set_Ocard( Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.83/1.35 ), X = c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ), !
% 0.83/1.35 c_Finite__Set_Ofinite( Y, X ) }.
% 0.83/1.35 { ! X = c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ),
% 0.83/1.35 c_Finite__Set_Ocard( Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.83/1.35 }.
% 0.83/1.35 { c_Finite__Set_Ofinite( Y, X ), c_Finite__Set_Ocard( Y, X ) =
% 0.83/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.35 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Finite__Set_Ocard( T,
% 0.83/1.35 c_Set_Oimage( Z, T, Y, X ) ), c_Finite__Set_Ocard( Z, X ) ), !
% 0.83/1.35 c_Fun_Oinj__on( Z, T, Y, X ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( Y,
% 0.83/1.35 tc_HOL_Obool ), c_Set_Oimage( Z, Y, X, U ), c_Set_Oimage( Z, Y, X, T ) )
% 0.83/1.35 , c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), U, T ) }
% 0.83/1.35 .
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ), U, T ), c_Orderings_Oord__class_Oless__eq( tc_fun( Y,
% 0.83/1.35 tc_HOL_Obool ), c_Set_Oimage( Z, Y, X, U ), c_Set_Oimage( Z, Y, X, T ) )
% 0.83/1.35 }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_member( Y, hAPP( X, U ), c_Set_Oimage( Z, Y, X, T
% 0.83/1.35 ) ), c_member( Z, U, T ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_member( Z, U, T ), c_member( Y, hAPP( X, U ),
% 0.83/1.35 c_Set_Oimage( Z, Y, X, T ) ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_member( Y, T, c_Set_Oimage( Z, Y, X,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( Z, tc_HOL_Obool ) ) ) ), T = hAPP(
% 0.83/1.35 X, skol4( X, T ) ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! c_member( Y, T, c_Set_Oimage( Z, Y, X,
% 0.83/1.35 c_Orderings_Otop__class_Otop( tc_fun( Z, tc_HOL_Obool ) ) ) ), alpha2( X
% 0.83/1.35 , T, skol4( X, T ) ) }.
% 0.83/1.35 { ! c_Fun_Oinj__on( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ), ! T = hAPP( X, U ), ! alpha2( X, T, U ), c_member( Y
% 0.83/1.35 , T, c_Set_Oimage( Z, Y, X, c_Orderings_Otop__class_Otop( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ) ) }.
% 0.83/1.35 { ! alpha2( X, Y, Z ), ! Y = hAPP( X, T ), T = Z }.
% 0.83/1.35 { ! skol5( T, U, Z ) = Z, alpha2( X, Y, Z ) }.
% 0.83/1.35 { Y = hAPP( X, skol5( X, Y, Z ) ), alpha2( X, Y, Z ) }.
% 0.83/1.35 { ! c_Finite__Set_Ofinite( Y, X ), c_Orderings_Oord__class_Oless__eq(
% 0.83/1.35 tc_Nat_Onat, c_Finite__Set_Ocard( T, c_Set_Oimage( Y, T, Z, X ) ),
% 0.83/1.35 c_Finite__Set_Ocard( Y, X ) ) }.
% 0.83/1.35 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.83/1.35 , Y ) }.
% 0.83/1.35 { c_Finite__Set_Ofinite( X, c_Orderings_Obot__class_Obot( tc_fun( X,
% 0.83/1.35 tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { c_Fun_Oinj__on( Z, Y, X, c_Orderings_Obot__class_Obot( tc_fun( Z,
% 0.83/1.35 tc_HOL_Obool ) ) ) }.
% 0.83/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.83/1.35 Y ) }.
% 0.83/1.35 { ! class_Orderings_Obot( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.83/1.35 c_Orderings_Obot__class_Obot( X ), Y ) }.
% 0.83/1.35 { ! class_Orderings_Obot( X ), hAPP( c_Orderings_Obot__class_Obot( tc_fun(
% 0.83/1.35 Z, X ) ), Y ) = c_Orderings_Obot__class_Obot( X ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.83/1.35 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.83/1.35 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.83/1.35 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.83/1.35 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.35 Y ), ! Z = Y }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.83/1.35 Z ), ! Z = Y }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.83/1.35 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.83/1.35 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.83/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.83/1.35 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.83/1.35 hAPP( Y, U ) ) }.
% 0.83/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.83/1.35 ( Z, skol6( X, Y, Z ) ), hAPP( Y, skol6( X, Y, Z ) ) ),
% 0.83/1.35 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.35 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.35 , ! Z = Y }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.35 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.35 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.83/1.35 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.83/1.35 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.83/1.35 ( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.83/1.35 ( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.35 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.83/1.35 ( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.83/1.35 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! c_member( Z, Y, c_fequal( X ) ), Y = X }.
% 0.83/1.35 { ! Y = X, c_member( Z, Y, c_fequal( X ) ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.83/1.35 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.83/1.35 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.83/1.35 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.83/1.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.83/1.35 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.83/1.35 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.83/1.35 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.83/1.35 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! hBOOL( hAPP( Y, X ) ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T,
% 0.83/1.35 tc_HOL_Obool ), Y, Z ), hBOOL( hAPP( Z, X ) ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.35 , ! Z = Y }.
% 0.83/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.35 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.83/1.35 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.83/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.35 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.35 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.83/1.35 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.83/1.35 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.83/1.35 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.83/1.35 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.83/1.35 hAPP( Y, U ) ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.35 , ! Z = Y }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.35 , ! Y = Z }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.35 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.35 hBOOL( hAPP( Y, T ) ), hBOOL( hAPP( X, T ) ) }.
% 0.83/1.35 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.35 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.35 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.35 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.83/1.35 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.83/1.35 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.83/1.35 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.83/1.35 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.83/1.35 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.83/1.35 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.83/1.36 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.83/1.36 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.36 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.83/1.36 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.36 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.83/1.36 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.36 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.36 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.36 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.83/1.36 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.83/1.36 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.36 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.83/1.36 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.83/1.36 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.36 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.83/1.36 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.83/1.36 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.36 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.36 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.36 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.83/1.36 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.36 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.36 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.83/1.36 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.83/1.36 hAPP( Y, U ) ) }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.36 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.83/1.36 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.36 { ! c_Fun_Oinj__on( T, Z, Y, X ), ! hAPP( Y, W ) = U, ! c_member( T, W, X )
% 0.83/1.36 , hAPP( c_Fun_Othe__inv__into( T, Z, X, Y ), U ) = W }.
% 0.83/1.36 { ! c_Fun_Oinj__on( T, Z, Y, X ), ! c_member( T, U, X ), hAPP(
% 0.83/1.36 c_Fun_Othe__inv__into( T, Z, X, Y ), hAPP( Y, U ) ) = U }.
% 0.83/1.36 { ! c_Fun_Oinj__on( T, Z, Y, X ), ! c_member( Z, U, c_Set_Oimage( T, Z, Y,
% 0.83/1.36 X ) ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, tc_HOL_Obool ), X
% 0.83/1.36 , W ), c_member( T, hAPP( c_Fun_Othe__inv__into( T, Z, X, Y ), U ), W ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( Y, tc_HOL_Obool ), Z, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_Nat_Onat, c_Finite__Set_Ocard( Y, X ), c_Finite__Set_Ocard( Y, Z ) ),
% 0.83/1.36 Z = X }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( Y, tc_HOL_Obool ), Z, X ), c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_Nat_Onat, c_Finite__Set_Ocard( Y, Z ), c_Finite__Set_Ocard( Y, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.36 c_Finite__Set_Ofinite( Z, X ), c_Finite__Set_Ofinite( Z, Y ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( Y, tc_HOL_Obool ), Z, X ), c_Finite__Set_Ofinite( Y, Z ) }.
% 0.83/1.36 { ! class_Orderings_Otop( X ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.83/1.36 c_Orderings_Otop__class_Otop( X ) ) }.
% 0.83/1.36 { c_Finite__Set_Ofinite( X, c_Orderings_Obot__class_Obot( tc_fun( X,
% 0.83/1.36 tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! c_Fun_Oinj__on( Z, T, Y, X ), W = U, ! c_member( Z, W, X ), ! c_member
% 0.83/1.36 ( Z, U, X ), ! hAPP( Y, W ) = hAPP( Y, U ) }.
% 0.83/1.36 { ! c_Fun_Oinj__on( Z, T, Y, X ), ! c_member( Z, U, X ), ! c_member( Z, W,
% 0.83/1.36 X ), ! hAPP( Y, U ) = hAPP( Y, W ), U = W }.
% 0.83/1.36 { ! c_Fun_Oinj__on( Z, T, Y, X ), ! c_member( Z, U, X ), ! c_member( Z, W,
% 0.83/1.36 X ), ! U = W, hAPP( Y, U ) = hAPP( Y, W ) }.
% 0.83/1.36 { ! c_Fun_Oinj__on( Z, T, Y, X ), ! hAPP( Y, W ) = hAPP( Y, U ), ! c_member
% 0.83/1.36 ( Z, W, X ), ! c_member( Z, U, X ), W = U }.
% 0.83/1.36 { ! c_Fun_Oinj__on( T, Z, Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( T, tc_HOL_Obool ), U, X ), c_Fun_Oinj__on( T, Z, Y, U ) }.
% 0.83/1.36 { ! c_Fun_Oinj__on( T, Z, Y, X ), ! c_member( Z, U, c_Set_Oimage( T, Z, Y,
% 0.83/1.36 X ) ), hAPP( Y, hAPP( c_Fun_Othe__inv__into( T, Z, X, Y ), U ) ) = U }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( tc_Nat_Onat ), c_Finite__Set_Ocard( Y, X ) ), ! X =
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( tc_Nat_Onat ), c_Finite__Set_Ocard( Y, X ) ), c_Finite__Set_Ofinite( Y
% 0.83/1.36 , X ) }.
% 0.83/1.36 { X = c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ), !
% 0.83/1.36 c_Finite__Set_Ofinite( Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Finite__Set_Ocard( Y, X )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! c_Fun_Oinj__on( T, Z, Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( Z, tc_HOL_Obool ), c_Set_Oimage( T, Z, Y, X ), U ), !
% 0.83/1.36 c_Finite__Set_Ofinite( Z, U ), c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_Nat_Onat, c_Finite__Set_Ocard( T, X ), c_Finite__Set_Ocard( Z, U ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( T, tc_HOL_Obool ), Z, c_Set_Oimage( Y, T, U, X ) ),
% 0.83/1.36 c_Finite__Set_Ofinite( T, Z ) }.
% 0.83/1.36 { c_Finite__Set_Ocard( X, c_Orderings_Obot__class_Obot( tc_fun( X,
% 0.83/1.36 tc_HOL_Obool ) ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( tc_Nat_Onat ), c_Finite__Set_Ocard( Y, X ) ), c_Finite__Set_Ofinite( Y
% 0.83/1.36 , X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( Y, tc_HOL_Obool ), X, c_Set_Oimage( Y, Y, Z, X ) ),
% 0.83/1.36 c_Fun_Oinj__on( Y, Y, Z, X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( Y, tc_HOL_Obool ), c_Set_Oimage( Y, Y, Z, X ), X ), !
% 0.83/1.36 c_Fun_Oinj__on( Y, Y, Z, X ), c_Set_Oimage( Y, Y, Z, X ) = X }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Finite__Set_Ofinite( T, Z ), !
% 0.83/1.36 c_Fun_Oinj__on( Y, T, U, X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.83/1.36 ( T, tc_HOL_Obool ), c_Set_Oimage( Y, T, U, X ), Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Finite__Set_Ocard( Y, X
% 0.83/1.36 ), c_Finite__Set_Ocard( T, Z ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Finite__Set_Ofinite( T, Z ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Finite__Set_Ocard( Y, X
% 0.83/1.36 ), c_Finite__Set_Ocard( T, Z ) ), c_Fun_Oinj__on( Y, T, skol7( X, Y, U,
% 0.83/1.36 T ), X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Finite__Set_Ofinite( T, Z ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Finite__Set_Ocard( Y, X
% 0.83/1.36 ), c_Finite__Set_Ocard( T, Z ) ), c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( T, tc_HOL_Obool ), c_Set_Oimage( Y, T, skol7( X, Y, Z, T ), X ),
% 0.83/1.36 Z ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_fun( Y, tc_HOL_Obool ),
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ), X ) }.
% 0.83/1.36 { ! Z = hAPP( Y, X ), ! c_member( U, X, T ), c_member( W, Z, c_Set_Oimage(
% 0.83/1.36 U, W, Y, T ) ) }.
% 0.83/1.36 { c_member( Y, X, c_Orderings_Otop__class_Otop( tc_fun( Y, tc_HOL_Obool ) )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.36 c_member( Z, T, Y ), c_member( Z, T, X ) }.
% 0.83/1.36 { ! c_member( Y, X, c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool )
% 0.83/1.36 ) ) }.
% 0.83/1.36 { Y = c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ), !
% 0.83/1.36 c_Fun_Oinj__on( X, T, U, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.83/1.36 ( T, tc_HOL_Obool ), c_Set_Oimage( X, T, U, Y ), Z ), c_Set_Oimage( T, X
% 0.83/1.36 , skol8( X, Y, Z, T ), Z ) = Y }.
% 0.83/1.36 { Y = c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ), !
% 0.83/1.36 c_Set_Oimage( T, X, U, Z ) = Y, c_Fun_Oinj__on( X, T, skol40( X, Y, W, T
% 0.83/1.36 ), Y ) }.
% 0.83/1.36 { Y = c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ), !
% 0.83/1.36 c_Set_Oimage( T, X, U, Z ) = Y, c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.83/1.36 ( T, tc_HOL_Obool ), c_Set_Oimage( X, T, skol40( X, Y, Z, T ), Y ), Z ) }
% 0.83/1.36 .
% 0.83/1.36 { ! alpha3( X, Y ), c_member( tc_Nat_Onat, skol9( Z, Y ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) ) }.
% 0.83/1.36 { ! alpha3( X, Y ), hBOOL( hAPP( X, skol9( X, Y ) ) ) }.
% 0.83/1.36 { ! c_member( tc_Nat_Onat, Z, c_SetInterval_Oord__class_OatLeastLessThan(
% 0.83/1.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) ), ! hBOOL(
% 0.83/1.36 hAPP( X, Z ) ), alpha3( X, Y ) }.
% 0.83/1.36 { ! alpha3( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol10( Z,
% 0.83/1.36 Y ), Y ) }.
% 0.83/1.36 { ! alpha3( X, Y ), hBOOL( hAPP( X, skol10( X, Y ) ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), ! hBOOL( hAPP( X, Z
% 0.83/1.36 ) ), alpha3( X, Y ) }.
% 0.83/1.36 { ! Y = X, alpha29( X, Y, Z, T ), ! c_member( T, Z, Y ) }.
% 0.83/1.36 { ! Y = X, alpha29( X, Y, Z, T ), ! c_member( T, Z, X ) }.
% 0.83/1.36 { ! alpha29( X, Y, Z, T ), c_member( T, Z, Y ) }.
% 0.83/1.36 { ! alpha29( X, Y, Z, T ), c_member( T, Z, X ) }.
% 0.83/1.36 { ! c_member( T, Z, Y ), ! c_member( T, Z, X ), alpha29( X, Y, Z, T ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), X, Y ), Y
% 0.83/1.36 = X }.
% 0.83/1.36 { c_Finite__Set_Ofinite( tc_Nat_Onat,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, Y, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.36 c_member( Z, T, Y ), c_member( Z, T, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_fun( Y, tc_HOL_Obool ), X,
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, X ), ! Y =
% 0.83/1.36 X }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ), Y
% 0.83/1.36 = X, c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, X ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, X ), Y = X }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ) }.
% 0.83/1.36 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y
% 0.83/1.36 , X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), X, T ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, T ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), X, T ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, T ) }.
% 0.83/1.36 { c_Orderings_Obot__class_Obot( tc_Nat_Onat ) = c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( tc_Nat_Onat ) }.
% 0.83/1.36 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.83/1.36 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.83/1.36 .
% 0.83/1.36 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.83/1.36 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.83/1.36 }.
% 0.83/1.36 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.83/1.36 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.83/1.36 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.83/1.36 { ! c_Fun_Oinj__on( T, Z, Y, X ), ! c_Orderings_Oord__class_Oless( tc_fun(
% 0.83/1.36 T, tc_HOL_Obool ), U, X ), c_Orderings_Oord__class_Oless( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ), c_Set_Oimage( T, Z, Y, U ), c_Set_Oimage( T, Z, Y, X ) )
% 0.83/1.36 }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Orderings_Oord__class_Oless( tc_fun
% 0.83/1.36 ( Y, tc_HOL_Obool ), Z, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.83/1.36 c_Finite__Set_Ocard( Y, Z ), c_Finite__Set_Ocard( Y, X ) ) }.
% 0.83/1.36 { ! c_member( Z, Y, X ), hBOOL( hAPP( X, Y ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( X, Y ) ), c_member( Z, Y, X ) }.
% 0.83/1.36 { ! Y = X, ! c_member( T, Z, Y ), c_member( T, Z, X ) }.
% 0.83/1.36 { ! Y = X, ! c_member( T, Z, X ), c_member( T, Z, Y ) }.
% 0.83/1.36 { ! Y = X, ! c_member( T, Y, Z ), c_member( T, X, Z ) }.
% 0.83/1.36 { ! Y = X, ! c_member( T, X, Z ), c_member( T, Y, Z ) }.
% 0.83/1.36 { ! Y = X, ! c_member( T, X, Z ), c_member( T, Y, Z ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.83/1.36 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.83/1.36 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.83/1.36 { alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.83/1.36 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.83/1.36 { alpha30( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.83/1.36 ( X, Y ), Z ) ) }.
% 0.83/1.36 { ! alpha30( X, Y, Z ), alpha31( X, Y, Z ), Z = Y }.
% 0.83/1.36 { ! alpha30( X, Y, Z ), alpha31( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! alpha31( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.83/1.36 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha30( X, Y, Z ) }.
% 0.83/1.36 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.83/1.36 }.
% 0.83/1.36 { ! alpha31( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.83/1.36 X, Y ), Z ) ), alpha31( X, Y, Z ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( tc_Nat_Onat, X ), ! c_member( tc_Nat_Onat, Y, X
% 0.83/1.36 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, skol11( X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol41( Z, Y ), Y ),
% 0.83/1.36 c_Finite__Set_Ofinite( tc_Nat_Onat, X ) }.
% 0.83/1.36 { c_member( tc_Nat_Onat, skol41( X, Y ), X ), c_Finite__Set_Ofinite(
% 0.83/1.36 tc_Nat_Onat, X ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_fun( Y, tc_HOL_Obool ), X, X ) }.
% 0.83/1.36 { ! Z = Y, c_Orderings_Oord__class_Oless__eq( tc_fun( X, tc_HOL_Obool ), Z
% 0.83/1.36 , Y ) }.
% 0.83/1.36 { ! Z = Y, c_Orderings_Oord__class_Oless__eq( tc_fun( X, tc_HOL_Obool ), Y
% 0.83/1.36 , Z ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( X, tc_HOL_Obool ), Z, Y ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( X, tc_HOL_Obool ), Y, Z ), Z
% 0.83/1.36 = Y }.
% 0.83/1.36 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y
% 0.83/1.36 , X ) }.
% 0.83/1.36 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), X
% 0.83/1.36 , Y ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), X, T ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, T ) }.
% 0.83/1.36 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y
% 0.83/1.36 , X ) }.
% 0.83/1.36 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), X
% 0.83/1.36 , Y ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.83/1.36 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( tc_Nat_Onat, X ), ! c_member( tc_Nat_Onat, Y, X
% 0.83/1.36 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, skol12( X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol42( Z, Y ), Y ),
% 0.83/1.36 c_Finite__Set_Ofinite( tc_Nat_Onat, X ) }.
% 0.83/1.36 { c_member( tc_Nat_Onat, skol42( X, Y ), X ), c_Finite__Set_Ofinite(
% 0.83/1.36 tc_Nat_Onat, X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( Y, tc_HOL_Obool ), Z, X ), ! c_Orderings_Oord__class_Oless(
% 0.83/1.36 tc_Nat_Onat, c_Finite__Set_Ocard( Y, Z ), c_Finite__Set_Ocard( Y, X ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_fun( Y, tc_HOL_Obool ), Z, X ) }.
% 0.83/1.36 { c_member( Y, skol13( X, Y ), X ), X = c_Orderings_Obot__class_Obot(
% 0.83/1.36 tc_fun( Y, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! X = c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ), !
% 0.83/1.36 c_member( Y, Z, X ) }.
% 0.83/1.36 { ! c_member( Y, Z, X ), ! X = c_Orderings_Obot__class_Obot( tc_fun( Y,
% 0.83/1.36 tc_HOL_Obool ) ) }.
% 0.83/1.36 { X = c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ), c_member(
% 0.83/1.36 Y, skol14( X, Y ), X ) }.
% 0.83/1.36 { ! c_member( Y, X, c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool )
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! Y = c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ), !
% 0.83/1.36 c_member( X, Z, Y ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.36 c_member( Z, T, Y ), c_member( Z, T, X ) }.
% 0.83/1.36 { ! c_member( Z, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ), X, T ), c_member( Z, Y, T ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.36 c_member( Z, T, Y ), c_member( Z, T, X ) }.
% 0.83/1.36 { ! c_member( Z, Y, X ), ! U = hAPP( T, Y ), c_member( W, U, c_Set_Oimage(
% 0.83/1.36 Z, W, T, X ) ) }.
% 0.83/1.36 { ! c_member( Z, Y, X ), c_member( U, hAPP( T, Y ), c_Set_Oimage( Z, U, T,
% 0.83/1.36 X ) ) }.
% 0.83/1.36 { ! c_member( U, T, c_Set_Oimage( Z, U, Y, X ) ), T = hAPP( Y, skol15( W, Y
% 0.83/1.36 , V0, T ) ) }.
% 0.83/1.36 { ! c_member( U, T, c_Set_Oimage( Z, U, Y, X ) ), c_member( Z, skol15( X, Y
% 0.83/1.36 , Z, T ), X ) }.
% 0.83/1.36 { ! c_member( Z, W, X ), ! T = hAPP( Y, W ), c_member( U, T, c_Set_Oimage(
% 0.83/1.36 Z, U, Y, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Y, tc_HOL_Obool ), X,
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ) ), X =
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! X = c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Y, tc_HOL_Obool ), X,
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) =
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! c_Set_Oimage( T, Z, Y, X ) = c_Orderings_Obot__class_Obot( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ) ), X = c_Orderings_Obot__class_Obot( tc_fun( T,
% 0.83/1.36 tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! X = c_Orderings_Obot__class_Obot( tc_fun( T, tc_HOL_Obool ) ),
% 0.83/1.36 c_Set_Oimage( T, Z, Y, X ) = c_Orderings_Obot__class_Obot( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ) ) }.
% 0.83/1.36 { c_Set_Oimage( Z, Y, X, c_Orderings_Obot__class_Obot( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ) ) ) = c_Orderings_Obot__class_Obot( tc_fun( Y,
% 0.83/1.36 tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! c_Orderings_Obot__class_Obot( tc_fun( T, tc_HOL_Obool ) ) =
% 0.83/1.36 c_Set_Oimage( Z, T, Y, X ), X = c_Orderings_Obot__class_Obot( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! X = c_Orderings_Obot__class_Obot( tc_fun( Z, tc_HOL_Obool ) ),
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( T, tc_HOL_Obool ) ) = c_Set_Oimage
% 0.83/1.36 ( Z, T, Y, X ) }.
% 0.83/1.36 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ), X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.83/1.36 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ), X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_fun( Y, tc_HOL_Obool ), X,
% 0.83/1.36 c_Orderings_Otop__class_Otop( tc_fun( Y, tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( U, tc_HOL_Obool ),
% 0.83/1.36 c_Set_Oimage( Z, U, T, Y ), c_Set_Oimage( Z, U, T, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( U, tc_HOL_Obool ), T,
% 0.83/1.36 c_Set_Oimage( Z, U, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_fun(
% 0.83/1.36 Z, tc_HOL_Obool ), skol16( X, W, Z, V0, V1 ), X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( U, tc_HOL_Obool ), T,
% 0.83/1.36 c_Set_Oimage( Z, U, Y, X ) ), T = c_Set_Oimage( Z, U, Y, skol16( X, Y, Z
% 0.83/1.36 , T, U ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), W, X ), !
% 0.83/1.36 T = c_Set_Oimage( Z, U, Y, W ), c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( U, tc_HOL_Obool ), T, c_Set_Oimage( Z, U, Y, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), !
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, U, T ) =
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.83/1.36 ( X, Z, Y ), T = Y }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), !
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, U, T ) =
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.83/1.36 ( X, Z, Y ), U = Z }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.36 Y ), ! c_Orderings_Oord__class_Oless( X, U, T ), !
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y ) =
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, U, T ), Z = U }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.36 Y ), ! c_Orderings_Oord__class_Oless( X, U, T ), !
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y ) =
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, U, T ), Y = T }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.83/1.36 Y ), ! c_Orderings_Oord__class_Oless( X, U, T ), ! Z = U, ! Y = T,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y ) =
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, U, T ) }.
% 0.83/1.36 { c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, X,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! Y = hAPP( X, Z ), c_member( U, Y, c_Set_Oimage( T, U, X,
% 0.83/1.36 c_Orderings_Otop__class_Otop( tc_fun( T, tc_HOL_Obool ) ) ) ) }.
% 0.83/1.36 { c_member( T, hAPP( Z, Y ), c_Set_Oimage( X, T, Z,
% 0.83/1.36 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ) ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.83/1.36 , Y ), c_SetInterval_Oord__class_OatLeastLessThan( X, Y, Z ) =
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Obot__class_Obot( tc_fun( X
% 0.83/1.36 , tc_HOL_Obool ) ) = c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ) =
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), !
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y ) =
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y ) =
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( X, tc_HOL_Obool ), c_SetInterval_Oord__class_OatLeastLessThan( X
% 0.83/1.36 , U, T ), c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, U ) }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( X, tc_HOL_Obool ), c_SetInterval_Oord__class_OatLeastLessThan( X
% 0.83/1.36 , U, T ), c_SetInterval_Oord__class_OatLeastLessThan( X, Z, Y ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.83/1.36 { ! alpha4( X, Y ), ! c_member( tc_Nat_Onat, Z,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) ), hBOOL( hAPP( X, Z ) )
% 0.83/1.36 }.
% 0.83/1.36 { c_member( tc_Nat_Onat, skol17( Z, Y ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) ), alpha4( X, Y ) }.
% 0.83/1.36 { ! hBOOL( hAPP( X, skol17( X, Y ) ) ), alpha4( X, Y ) }.
% 0.83/1.36 { ! alpha4( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 0.83/1.36 hBOOL( hAPP( X, Z ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol18( Z, Y ), Y ), alpha4(
% 0.83/1.36 X, Y ) }.
% 0.83/1.36 { ! hBOOL( hAPP( X, skol18( X, Y ) ) ), alpha4( X, Y ) }.
% 0.83/1.36 { ! c_member( T, Z, c_SetInterval_Oord_OatMost( T, Y, X ) ), hBOOL( hAPP(
% 0.83/1.36 hAPP( Y, Z ), X ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( hAPP( Y, Z ), X ) ), c_member( T, Z,
% 0.83/1.36 c_SetInterval_Oord_OatMost( T, Y, X ) ) }.
% 0.83/1.36 { ! c_member( T, Z, c_SetInterval_Oord_OatLeast( T, Y, X ) ), hBOOL( hAPP(
% 0.83/1.36 hAPP( Y, X ), Z ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( hAPP( Y, X ), Z ) ), c_member( T, Z,
% 0.83/1.36 c_SetInterval_Oord_OatLeast( T, Y, X ) ) }.
% 0.83/1.36 { ! c_member( T, Z, c_SetInterval_Oord_OlessThan( T, Y, X ) ), hBOOL( hAPP
% 0.83/1.36 ( hAPP( Y, Z ), X ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( hAPP( Y, Z ), X ) ), c_member( T, Z,
% 0.83/1.36 c_SetInterval_Oord_OlessThan( T, Y, X ) ) }.
% 0.83/1.36 { ! c_member( T, Z, c_SetInterval_Oord_OgreaterThan( T, Y, X ) ), hBOOL(
% 0.83/1.36 hAPP( hAPP( Y, X ), Z ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( hAPP( Y, X ), Z ) ), c_member( T, Z,
% 0.83/1.36 c_SetInterval_Oord_OgreaterThan( T, Y, X ) ) }.
% 0.83/1.36 { ! c_member( U, T, c_SetInterval_Oord_OatLeastAtMost( U, Z, Y, X ) ),
% 0.83/1.36 hBOOL( hAPP( hAPP( Z, Y ), T ) ) }.
% 0.83/1.36 { ! c_member( U, T, c_SetInterval_Oord_OatLeastAtMost( U, Z, Y, X ) ),
% 0.83/1.36 hBOOL( hAPP( hAPP( Z, T ), X ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( hAPP( Z, Y ), T ) ), ! hBOOL( hAPP( hAPP( Z, T ), X ) ),
% 0.83/1.36 c_member( U, T, c_SetInterval_Oord_OatLeastAtMost( U, Z, Y, X ) ) }.
% 0.83/1.36 { ! c_member( U, T, c_SetInterval_Oord_OgreaterThanLessThan( U, Z, Y, X ) )
% 0.83/1.36 , hBOOL( hAPP( hAPP( Z, Y ), T ) ) }.
% 0.83/1.36 { ! c_member( U, T, c_SetInterval_Oord_OgreaterThanLessThan( U, Z, Y, X ) )
% 0.83/1.36 , hBOOL( hAPP( hAPP( Z, T ), X ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( hAPP( Z, Y ), T ) ), ! hBOOL( hAPP( hAPP( Z, T ), X ) ),
% 0.83/1.36 c_member( U, T, c_SetInterval_Oord_OgreaterThanLessThan( U, Z, Y, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), X, T ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_fun( Z, tc_HOL_Obool ), Y, T ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( tc_Nat_Onat, c_Orderings_Otop__class_Otop(
% 0.83/1.36 tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! c_member( W, U, c_SetInterval_Oord_OgreaterThanAtMost( W, T, Z, Y, X )
% 0.83/1.36 ), hBOOL( hAPP( hAPP( Z, Y ), U ) ) }.
% 0.83/1.36 { ! c_member( W, U, c_SetInterval_Oord_OgreaterThanAtMost( W, T, Z, Y, X )
% 0.83/1.36 ), hBOOL( hAPP( hAPP( T, U ), X ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( hAPP( Z, Y ), U ) ), ! hBOOL( hAPP( hAPP( T, U ), X ) ),
% 0.83/1.36 c_member( W, U, c_SetInterval_Oord_OgreaterThanAtMost( W, T, Z, Y, X ) )
% 0.83/1.36 }.
% 0.83/1.36 { ! c_member( W, U, c_SetInterval_Oord_OatLeastLessThan( W, T, Z, Y, X ) )
% 0.83/1.36 , hBOOL( hAPP( hAPP( T, Y ), U ) ) }.
% 0.83/1.36 { ! c_member( W, U, c_SetInterval_Oord_OatLeastLessThan( W, T, Z, Y, X ) )
% 0.83/1.36 , hBOOL( hAPP( hAPP( Z, U ), X ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( hAPP( T, Y ), U ) ), ! hBOOL( hAPP( hAPP( Z, U ), X ) ),
% 0.83/1.36 c_member( W, U, c_SetInterval_Oord_OatLeastLessThan( W, T, Z, Y, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { c_member( Y, X, c_Orderings_Otop__class_Otop( tc_fun( Y, tc_HOL_Obool ) )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( tc_fun( Y, X ), c_Orderings_Otop__class_Otop(
% 0.83/1.36 tc_fun( tc_fun( Y, X ), tc_HOL_Obool ) ) ), c_Finite__Set_Ocard( X,
% 0.83/1.36 c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool ) ) ) = hAPP(
% 0.83/1.36 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.83/1.36 c_Finite__Set_Ofinite( Y, c_Orderings_Otop__class_Otop( tc_fun( Y,
% 0.83/1.36 tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofolding__one__idem( Z, Y, X ), ! c_Finite__Set_Ofinite(
% 0.83/1.36 Z, T ), U = c_Orderings_Obot__class_Obot( tc_fun( Z, tc_HOL_Obool ) ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), U, T ),
% 0.83/1.36 hAPP( hAPP( Y, hAPP( X, U ) ), hAPP( X, T ) ) = hAPP( X, T ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofolding__image__simple__idem( W, Z, Y, U, T, X ), !
% 0.83/1.36 c_Finite__Set_Ofinite( Z, V0 ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( Z, tc_HOL_Obool ), V1, V0 ), hAPP( hAPP( Y, hAPP( X, V1 ) ), hAPP
% 0.83/1.36 ( X, V0 ) ) = hAPP( X, V0 ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofolding__image__simple__idem( W, T, Z, U, Y, X ), !
% 0.83/1.36 c_Finite__Set_Ofinite( T, V0 ), ! c_member( T, V1, V0 ), hAPP( hAPP( Z,
% 0.83/1.36 hAPP( Y, V1 ) ), hAPP( X, V0 ) ) = hAPP( X, V0 ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP(
% 0.83/1.36 c_Nat_OSuc, X ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ), hAPP( c_Nat_OSuc, X ) ) }.
% 0.83/1.36 { ! X = hAPP( c_Nat_OSuc, X ) }.
% 0.83/1.36 { ! hAPP( c_Nat_OSuc, X ) = X }.
% 0.83/1.36 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 0.83/1.36 { ! Y = X, hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ) }.
% 0.83/1.36 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 0.83/1.36 { c_Fun_Oinj__on( tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofolding__one__idem( Z, X, Y ), hAPP( hAPP( X, T ), T ) =
% 0.83/1.36 T }.
% 0.83/1.36 { ! c_Finite__Set_Ofolding__image__simple__idem( W, U, X, T, Z, Y ), hAPP(
% 0.83/1.36 hAPP( X, V0 ), V0 ) = V0 }.
% 0.83/1.36 { c_Set_Oimage( tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, Y, X ) ) =
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.83/1.36 , Y ), hAPP( c_Nat_OSuc, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ),
% 0.83/1.36 X ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ), Y
% 0.83/1.36 ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ),
% 0.83/1.36 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X
% 0.83/1.36 ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = hAPP(
% 0.83/1.36 c_Nat_OSuc, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! Y = hAPP( c_Nat_OSuc, X ), c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ),
% 0.83/1.36 hAPP( c_Nat_OSuc, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ),
% 0.83/1.36 hAPP( c_Nat_OSuc, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X
% 0.83/1.36 ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = hAPP(
% 0.83/1.36 c_Nat_OSuc, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ),
% 0.83/1.36 X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, Y ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, Y ) )
% 0.83/1.36 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) )
% 0.83/1.36 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc
% 0.83/1.36 , X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP
% 0.83/1.36 ( c_Nat_OSuc, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP(
% 0.83/1.36 c_Nat_OSuc, X ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ), Y
% 0.83/1.36 = X }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ), X
% 0.83/1.36 = Y }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hAPP( c_Nat_OSuc, Y
% 0.83/1.36 ) = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y )
% 0.83/1.36 , X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), Z ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) )
% 0.83/1.36 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X )
% 0.83/1.36 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP
% 0.83/1.36 ( c_Nat_OSuc, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.83/1.36 .
% 0.83/1.36 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 0.83/1.36 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 0.83/1.36 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( tc_Nat_Onat ), X ), X = hAPP( c_Nat_OSuc, skol19( X ) ) }.
% 0.83/1.36 { ! X = hAPP( c_Nat_OSuc, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) )
% 0.83/1.36 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 0.83/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! alpha5( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP(
% 0.83/1.36 c_Nat_OSuc, X ) ) }.
% 0.83/1.36 { ! alpha5( X, Y ), Y = hAPP( c_Nat_OSuc, skol20( Z, Y ) ) }.
% 0.83/1.36 { ! alpha5( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol20( X,
% 0.83/1.36 Y ), X ) }.
% 0.83/1.36 { ! Y = hAPP( c_Nat_OSuc, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.83/1.36 , Z, X ), alpha5( X, Y ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ),
% 0.83/1.36 X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, Y ) ), X
% 0.83/1.36 = Y }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, Y ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X
% 0.83/1.36 ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ),
% 0.83/1.36 X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X
% 0.83/1.36 ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) )
% 0.83/1.36 , c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X
% 0.83/1.36 ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ),
% 0.83/1.36 X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofolding__one__idem( Z, Y, X ), ! c_Finite__Set_Ofinite(
% 0.83/1.36 Z, T ), ! c_member( Z, U, T ), hAPP( hAPP( Y, U ), hAPP( X, T ) ) = hAPP
% 0.83/1.36 ( X, T ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofolding__one__idem( Z, Y, X ), ! hAPP( T, hAPP( hAPP( Y
% 0.83/1.36 , skol21( Y, T ) ), skol43( Y, T ) ) ) = hAPP( hAPP( Y, hAPP( T, skol21(
% 0.83/1.36 Y, T ) ) ), hAPP( T, skol43( Y, T ) ) ), ! c_Finite__Set_Ofinite( Z, U )
% 0.83/1.36 , U = c_Orderings_Obot__class_Obot( tc_fun( Z, tc_HOL_Obool ) ), hAPP( T
% 0.83/1.36 , hAPP( X, U ) ) = hAPP( X, c_Set_Oimage( Z, Z, T, U ) ) }.
% 0.83/1.36 { c_SetInterval_Oord__class_OgreaterThan( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Set_Oimage( tc_Nat_Onat
% 0.83/1.36 , tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop( tc_fun(
% 0.83/1.36 tc_Nat_Onat, tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( tc_sum( T, Y ), c_Sum__Type_OPlus( T, Y, Z, X )
% 0.83/1.36 ), c_Finite__Set_Ofinite( Y, X ) }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), !
% 0.83/1.36 c_SetInterval_Oord__class_OgreaterThan( X, Z ) =
% 0.83/1.36 c_SetInterval_Oord__class_OgreaterThan( X, Y ), Z = Y }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), ! Z = Y,
% 0.83/1.36 c_SetInterval_Oord__class_OgreaterThan( X, Z ) =
% 0.83/1.36 c_SetInterval_Oord__class_OgreaterThan( X, Y ) }.
% 0.83/1.36 { ! class_Orderings_Oord( X ), ! c_member( X, Z,
% 0.83/1.36 c_SetInterval_Oord__class_OgreaterThan( X, Y ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.83/1.36 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Y, Z ),
% 0.83/1.36 c_member( X, Z, c_SetInterval_Oord__class_OgreaterThan( X, Y ) ) }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( X, tc_HOL_Obool ), c_SetInterval_Oord__class_OgreaterThan( X, Z )
% 0.83/1.36 , c_SetInterval_Oord__class_OgreaterThan( X, Y ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.83/1.36 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.83/1.36 , Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_fun( X, tc_HOL_Obool ),
% 0.83/1.36 c_SetInterval_Oord__class_OgreaterThan( X, Z ),
% 0.83/1.36 c_SetInterval_Oord__class_OgreaterThan( X, Y ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( tc_sum( T, Z ), c_Sum__Type_OPlus( T, Z, Y, X )
% 0.83/1.36 ), c_Finite__Set_Ofinite( T, Y ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( tc_sum( T, Z ), c_Sum__Type_OPlus( T, Z, Y, X )
% 0.83/1.36 ), c_Finite__Set_Ofinite( Z, X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( T, Y ), ! c_Finite__Set_Ofinite( Z, X ),
% 0.83/1.36 c_Finite__Set_Ofinite( tc_sum( T, Z ), c_Sum__Type_OPlus( T, Z, Y, X ) )
% 0.83/1.36 }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Finite__Set_Ofinite( T, Z ),
% 0.83/1.36 c_Finite__Set_Ofinite( tc_sum( Y, T ), c_Sum__Type_OPlus( Y, T, X, Z ) )
% 0.83/1.36 }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( tc_sum( Y, T ), c_Sum__Type_OPlus( Y, T, X, Z )
% 0.83/1.36 ), c_Finite__Set_Ofinite( Y, X ) }.
% 0.83/1.36 { c_Sum__Type_OPlus( Y, X, c_Orderings_Otop__class_Otop( tc_fun( Y,
% 0.83/1.36 tc_HOL_Obool ) ), c_Orderings_Otop__class_Otop( tc_fun( X, tc_HOL_Obool )
% 0.83/1.36 ) ) = c_Orderings_Otop__class_Otop( tc_fun( tc_sum( Y, X ), tc_HOL_Obool
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! c_Sum__Type_OPlus( T, Z, Y, X ) = c_Orderings_Obot__class_Obot( tc_fun
% 0.83/1.36 ( tc_sum( T, Z ), tc_HOL_Obool ) ), Y = c_Orderings_Obot__class_Obot(
% 0.83/1.36 tc_fun( T, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! c_Sum__Type_OPlus( T, Z, Y, X ) = c_Orderings_Obot__class_Obot( tc_fun
% 0.83/1.36 ( tc_sum( T, Z ), tc_HOL_Obool ) ), X = c_Orderings_Obot__class_Obot(
% 0.83/1.36 tc_fun( Z, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! Y = c_Orderings_Obot__class_Obot( tc_fun( T, tc_HOL_Obool ) ), ! X =
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( Z, tc_HOL_Obool ) ),
% 0.83/1.36 c_Sum__Type_OPlus( T, Z, Y, X ) = c_Orderings_Obot__class_Obot( tc_fun(
% 0.83/1.36 tc_sum( T, Z ), tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( T, Z ), ! c_Finite__Set_Ofinite( Y, X ),
% 0.83/1.36 c_Finite__Set_Ocard( tc_sum( T, Y ), c_Sum__Type_OPlus( T, Y, Z, X ) ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Finite__Set_Ocard( T, Z ),
% 0.83/1.36 c_Finite__Set_Ocard( Y, X ) ) }.
% 0.83/1.36 { c_Finite__Set_Ofinite( T, Z ), c_Finite__Set_Ocard( tc_sum( T, Y ),
% 0.83/1.36 c_Sum__Type_OPlus( T, Y, Z, X ) ) = c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) }.
% 0.83/1.36 { c_Finite__Set_Ofinite( Y, X ), c_Finite__Set_Ocard( tc_sum( T, Y ),
% 0.83/1.36 c_Sum__Type_OPlus( T, Y, Z, X ) ) = c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.83/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.83/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.83/1.36 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.83/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.83/1.36 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.83/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.83/1.36 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.83/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.83/1.36 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.83/1.36 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.83/1.36 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.83/1.36 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 T, Y ), Z = Y }.
% 0.83/1.36 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 T, Y ) }.
% 0.83/1.36 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 Y, Z ), T = Y }.
% 0.83/1.36 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 Y, Z ) }.
% 0.83/1.36 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 T, Y ), Z = Y }.
% 0.83/1.36 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 T, Y ), Z = Y }.
% 0.83/1.36 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 Y, T ), Z = Y }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( tc_Nat_Onat, tc_HOL_Obool )
% 0.83/1.36 , Y, c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, X,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Finite__Set_Ocard(
% 0.83/1.36 tc_Nat_Onat, Y ) ) ) ), Y = c_SetInterval_Oord__class_OatLeastLessThan(
% 0.83/1.36 tc_Nat_Onat, X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.83/1.36 c_Finite__Set_Ocard( tc_Nat_Onat, Y ) ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol22( X, Y ) ) }.
% 0.83/1.36 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.83/1.36 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.83/1.36 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.83/1.36 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.83/1.36 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.83/1.36 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.83/1.36 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.83/1.36 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.83/1.36 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.83/1.36 , X ) }.
% 0.83/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.83/1.36 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( tc_Nat_Onat ) ) = X }.
% 0.83/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ), X ) = X }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.83/1.36 ( X, Z, Y ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.83/1.36 ( X, Z, Y ) }.
% 0.83/1.36 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.83/1.36 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.83/1.36 , T ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.83/1.36 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.83/1.36 , T, Y ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.83/1.36 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.83/1.36 , Y, T ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.83/1.36 ( X, Z, Y ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.83/1.36 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.83/1.36 , T, Y ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.83/1.36 ( X, T, Y ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.83/1.36 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.83/1.36 , Y, Z ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.83/1.36 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.83/1.36 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.83/1.36 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.83/1.36 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.83/1.36 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.83/1.36 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.83/1.36 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.83/1.36 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.83/1.36 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.83/1.36 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.83/1.36 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.83/1.36 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.83/1.36 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.83/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }.
% 0.83/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 0.83/1.36 hAPP( c_Nat_OSuc, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.83/1.36 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) =
% 0.83/1.36 hAPP( c_Nat_OSuc, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 Z, Y ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 Y, Z ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.83/1.36 .
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.83/1.36 .
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.83/1.36 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.83/1.36 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.83/1.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.83/1.36 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.83/1.36 ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.83/1.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.83/1.36 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.83/1.36 , Y, T ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.83/1.36 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.83/1.36 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.83/1.36 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.83/1.36 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.83/1.36 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.83/1.36 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.83/1.36 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = hAPP( c_Nat_OSuc,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha6( X, Y ), alpha17( X
% 0.83/1.36 , Y ) }.
% 0.83/1.36 { ! alpha6( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = hAPP
% 0.83/1.36 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.83/1.36 { ! alpha17( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.83/1.36 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.83/1.36 { ! alpha17( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! alpha17( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) ) }.
% 0.83/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha17( X, Y ) }.
% 0.83/1.36 { ! alpha6( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) ) }.
% 0.83/1.36 { ! alpha6( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 0.83/1.36 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha6( X, Y ) }.
% 0.83/1.36 { ! hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha7( X, Y ), alpha18
% 0.83/1.36 ( X, Y ) }.
% 0.83/1.36 { ! alpha7( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! alpha18( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! alpha18( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! alpha18( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) ) }.
% 0.83/1.36 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha18( X, Y ) }.
% 0.83/1.36 { ! alpha7( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) ) }.
% 0.83/1.36 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 0.83/1.36 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.83/1.36 tc_Nat_Onat, Y, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.83/1.36 tc_Nat_Onat, Y, X ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = hAPP(
% 0.83/1.36 c_Nat_OSuc, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol23( X, Y ) )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! X = hAPP( c_Nat_OSuc, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z )
% 0.83/1.36 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.83/1.36 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.83/1.36 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.83/1.36 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.83/1.36 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.83/1.36 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.83/1.36 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.83/1.36 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.83/1.36 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.83/1.36 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Finite__Set_Ofinite( T, Z ),
% 0.83/1.36 c_Finite__Set_Ocard( tc_sum( Y, T ), c_Sum__Type_OPlus( Y, T, X, Z ) ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Finite__Set_Ocard( Y, X ),
% 0.83/1.36 c_Finite__Set_Ocard( T, Z ) ) }.
% 0.83/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.83/1.36 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.83/1.36 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.83/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.83/1.36 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.83/1.36 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.83/1.36 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.83/1.36 X, Y, Z ) }.
% 0.83/1.36 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.83/1.36 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.83/1.36 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.83/1.36 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.83/1.36 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.83/1.36 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.83/1.36 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.83/1.36 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.83/1.36 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.83/1.36 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.83/1.36 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.83/1.36 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.83/1.36 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.83/1.36 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.83/1.36 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.83/1.36 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.83/1.36 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.83/1.36 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.83/1.36 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.83/1.36 { c_Nat_Onat_Onat__size( hAPP( c_Nat_OSuc, X ) ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Onat_Onat__size( X ),
% 0.83/1.36 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.83/1.36 tc_Nat_Onat, T, Z ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(
% 0.83/1.36 tc_Nat_Onat, X, Y, c_SetInterval_Oord__class_OatLeastLessThan(
% 0.83/1.36 tc_Nat_Onat, Z, hAPP( c_Nat_OSuc, T ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.83/1.36 X ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), c_Orderings_Oord__class_Oless(
% 0.83/1.36 tc_Nat_Onat, T, Z ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(
% 0.83/1.36 tc_Nat_Onat, X, Y, c_SetInterval_Oord__class_OatLeastLessThan(
% 0.83/1.36 tc_Nat_Onat, Z, hAPP( c_Nat_OSuc, T ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.83/1.36 X, c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, Y
% 0.83/1.36 , c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, Z, T ) ), hAPP
% 0.83/1.36 ( Y, T ) ) }.
% 0.83/1.36 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, T ),
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, U,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, Z, Y ) ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, U,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, Y, T ) ) ) =
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, U,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, Z, T ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), ! hAPP( Y,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, Y,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ) =
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, Y,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.83/1.36 tc_Nat_Onat, Z, Y ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(
% 0.83/1.36 tc_Nat_Onat, X, T, c_SetInterval_Oord__class_OatLeastLessThan(
% 0.83/1.36 tc_Nat_Onat, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( T, Z ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, T,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.83/1.36 , Z ), Y ) ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), c_Finite__Set_Ofinite( Z, Y ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, X, T, Y ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), c_Finite__Set_Ofinite( Z, Y ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, X, T, Y ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), !
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Y, tc_Nat_Onat, Z, X
% 0.83/1.36 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! c_member( Y, T, X ),
% 0.83/1.36 hAPP( Z, T ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! hAPP( Z, skol24( T, U, Z ) ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Y, tc_Nat_Onat, Z, X
% 0.83/1.36 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), c_member( Y, skol24( X, Y, Z ), X ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Y, tc_Nat_Onat, Z, X
% 0.83/1.36 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), !
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Y, tc_Nat_Onat, Z, X
% 0.83/1.36 ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.83/1.36 c_member( Y, skol25( X, Y, T ), X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), !
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Y, tc_Nat_Onat, Z, X
% 0.83/1.36 ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.83/1.36 alpha19( X, Y, Z, skol25( X, Y, Z ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_member( Y, T, X ), ! alpha19( X, Y,
% 0.83/1.36 Z, T ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Y,
% 0.83/1.36 tc_Nat_Onat, Z, X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) ) }.
% 0.83/1.36 { ! alpha19( X, Y, Z, T ), hAPP( Z, T ) = hAPP( c_Nat_OSuc,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.83/1.36 { ! alpha19( X, Y, Z, T ), alpha25( X, Y, Z, T ) }.
% 0.83/1.36 { ! hAPP( Z, T ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) ), ! alpha25( X, Y, Z, T ), alpha19( X, Y, Z, T ) }.
% 0.83/1.36 { ! alpha25( X, Y, Z, T ), ! c_member( Y, U, X ), alpha8( Z, T, U ) }.
% 0.83/1.36 { ! alpha8( Z, T, skol26( U, W, Z, T ) ), alpha25( X, Y, Z, T ) }.
% 0.83/1.36 { c_member( Y, skol26( X, Y, Z, T ), X ), alpha25( X, Y, Z, T ) }.
% 0.83/1.36 { ! alpha8( X, Y, Z ), Y = Z, hAPP( X, Z ) = c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) }.
% 0.83/1.36 { ! Y = Z, alpha8( X, Y, Z ) }.
% 0.83/1.36 { ! hAPP( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y
% 0.83/1.36 , Z ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, X, Y,
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( Z, tc_HOL_Obool ) ) ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, X, Y,
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( Z, tc_HOL_Obool ) ) ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { c_Nat_Osize__class_Osize( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ) ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 0.83/1.36 tc_Nat_Onat, X ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.83/1.36 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.83/1.36 c_Finite__Set_Ofinite( Z, Y ), Y = c_Orderings_Obot__class_Obot( tc_fun(
% 0.83/1.36 Z, tc_HOL_Obool ) ), c_member( Z, skol27( W, Y, Z, V0, V1 ), Y ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X,
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, X, U, Y ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, X, T, Y ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.83/1.36 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.83/1.36 c_Finite__Set_Ofinite( Z, Y ), Y = c_Orderings_Obot__class_Obot( tc_fun(
% 0.83/1.36 Z, tc_HOL_Obool ) ), ! c_Orderings_Oord__class_Oless( X, hAPP( U, skol27
% 0.83/1.36 ( X, Y, Z, T, U ) ), hAPP( T, skol27( X, Y, Z, T, U ) ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X,
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, X, U, Y ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, X, T, Y ) ) }.
% 0.83/1.36 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 0.83/1.36 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, tc_Nat_Onat, Y,
% 0.83/1.36 X ) = hAPP( c_Nat_OSuc, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( Y, skol28( U, Y, W ) )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, tc_Nat_Onat, Y,
% 0.83/1.36 X ) = hAPP( c_Nat_OSuc, T ), c_member( Z, skol28( X, Y, Z ), X ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Fun_Oinj__on( U, T, Z, Y ), !
% 0.83/1.36 W = c_Set_Oimage( U, T, Z, Y ), c_member( U, skol29( Y, V2, U, V3, V4 )
% 0.83/1.36 , Y ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum( T, X, V0, W )
% 0.83/1.36 = c_Big__Operators_Ocomm__monoid__add__class_Osetsum( U, X, V1, Y ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Fun_Oinj__on( U, T, Z, Y ), !
% 0.83/1.36 W = c_Set_Oimage( U, T, Z, Y ), ! hAPP( V1, skol29( Y, Z, U, V0, V1 ) )
% 0.83/1.36 = hAPP( V0, hAPP( Z, skol29( Y, Z, U, V0, V1 ) ) ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( T, X, V0, W ) =
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( U, X, V1, Y ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( Y ), ! class_Orderings_Oord( X ), ! T
% 0.83/1.36 = Z, ! W = U, ! hAPP( V1, skol30( V2, V3, V4, V0, V1 ) ) = hAPP( V0,
% 0.83/1.36 skol30( V2, V3, V4, V0, V1 ) ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( X, Y, V1,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, T, W ) ) =
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( X, Y, V0,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, U ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( Y ), ! class_Orderings_Oord( X ), ! T
% 0.83/1.36 = Z, ! W = U, c_Orderings_Oord__class_Oless( X, skol30( X, V2, U, V0, V1
% 0.83/1.36 ), U ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum( X, Y, V1,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, T, W ) ) =
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( X, Y, V0,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, U ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( Y ), ! class_Orderings_Oord( X ), ! T
% 0.83/1.36 = Z, ! W = U, c_Orderings_Oord__class_Oless__eq( X, Z, skol30( X, Z, U,
% 0.83/1.36 V0, V1 ) ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum( X, Y, V1
% 0.83/1.36 , c_SetInterval_Oord__class_OatLeastLessThan( X, T, W ) ) =
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( X, Y, V0,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( X, Z, U ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.83/1.36 tc_Nat_Onat, hAPP( c_Nat_OSuc, T ), Z ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, Y,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, Z, hAPP(
% 0.83/1.36 c_Nat_OSuc, T ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), c_Orderings_Oord__class_Oless(
% 0.83/1.36 tc_Nat_Onat, hAPP( c_Nat_OSuc, T ), Z ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, Y,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, Z, hAPP(
% 0.83/1.36 c_Nat_OSuc, T ) ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, Y,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, Z, T ) ), hAPP( Y
% 0.83/1.36 , hAPP( c_Nat_OSuc, T ) ) ) }.
% 0.83/1.36 { c_Finite__Set_Ofinite( tc_Nat_Onat,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, Y, X ) ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_fun( X, tc_HOL_Obool ), c_SetInterval_Oord__class_OatLeastAtMost( X, U
% 0.83/1.36 , T ), c_SetInterval_Oord__class_OatLeastAtMost( X, Z, Y ) ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, U, T ), alpha9( X, Y, Z, T, U ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq( X, U, T
% 0.83/1.36 ), c_Orderings_Oord__class_Oless__eq( tc_fun( X, tc_HOL_Obool ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, U, T ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, Z, Y ) ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! alpha9( X, Y, Z, T, U ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( X, tc_HOL_Obool ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, U, T ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, Z, Y ) ) }.
% 0.83/1.36 { ! alpha9( X, Y, Z, T, U ), c_Orderings_Oord__class_Oless__eq( X, Z, U ) }
% 0.83/1.36 .
% 0.83/1.36 { ! alpha9( X, Y, Z, T, U ), c_Orderings_Oord__class_Oless__eq( X, T, Y ) }
% 0.83/1.36 .
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( X, Z, U ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ), alpha9( X, Y, Z, T, U ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.83/1.36 , c_SetInterval_Oord__class_OatLeastAtMost( X, Y, Z ) =
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_SetInterval_Oord__class_OatLeastAtMost
% 0.83/1.36 ( X, Z, Y ) = c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ),
% 0.83/1.36 ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.83/1.36 ), c_SetInterval_Oord__class_OatLeastAtMost( X, Z, Y ) =
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Obot__class_Obot( tc_fun( X
% 0.83/1.36 , tc_HOL_Obool ) ) = c_SetInterval_Oord__class_OatLeastAtMost( X, Z, Y )
% 0.83/1.36 , ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.83/1.36 ), c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ) =
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, Z, Y ) }.
% 0.83/1.36 { c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, Y, hAPP(
% 0.83/1.36 c_Nat_OSuc, X ) ) = c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat
% 0.83/1.36 , Y, X ) }.
% 0.83/1.36 { ! alpha10( X, Y ), c_member( tc_Nat_Onat, skol31( Z, Y ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) ) }.
% 0.83/1.36 { ! alpha10( X, Y ), hBOOL( hAPP( X, skol31( X, Y ) ) ) }.
% 0.83/1.36 { ! c_member( tc_Nat_Onat, Z, c_SetInterval_Oord__class_OatLeastAtMost(
% 0.83/1.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) ), ! hBOOL(
% 0.83/1.36 hAPP( X, Z ) ), alpha10( X, Y ) }.
% 0.83/1.36 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol32
% 0.83/1.36 ( Z, Y ), Y ) }.
% 0.83/1.36 { ! alpha10( X, Y ), hBOOL( hAPP( X, skol32( X, Y ) ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), ! hBOOL( hAPP(
% 0.83/1.36 X, Z ) ), alpha10( X, Y ) }.
% 0.83/1.36 { ! alpha11( X, Y ), ! c_member( tc_Nat_Onat, Z,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) ), hBOOL( hAPP( X, Z ) )
% 0.83/1.36 }.
% 0.83/1.36 { c_member( tc_Nat_Onat, skol33( Z, Y ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) ), alpha11( X, Y ) }.
% 0.83/1.36 { ! hBOOL( hAPP( X, skol33( X, Y ) ) ), alpha11( X, Y ) }.
% 0.83/1.36 { ! alpha11( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y
% 0.83/1.36 ), hBOOL( hAPP( X, Z ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol34( Z, Y ), Y ),
% 0.83/1.36 alpha11( X, Y ) }.
% 0.83/1.36 { ! hBOOL( hAPP( X, skol34( X, Y ) ) ), alpha11( X, Y ) }.
% 0.83/1.36 { c_Set_Oimage( tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, Y, X ) ) =
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 0.83/1.36 Y ), hAPP( c_Nat_OSuc, X ) ) }.
% 0.83/1.36 { ! hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat,
% 0.83/1.36 tc_Nat_Onat, X, c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat,
% 0.83/1.36 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ) =
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat,
% 0.83/1.36 tc_Nat_Onat, X, c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( tc_fun( X
% 0.83/1.36 , tc_HOL_Obool ), c_SetInterval_Oord__class_OatLeastAtMost( X, U, T ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, Z, Y ) ), alpha12( X, Y, Z,
% 0.83/1.36 T, U ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( tc_fun( X
% 0.83/1.36 , tc_HOL_Obool ), c_SetInterval_Oord__class_OatLeastAtMost( X, U, T ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, Z, Y ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! alpha12( X, Y, Z, T, U ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( tc_fun( X, tc_HOL_Obool ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, U, T ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, Z, Y ) ) }.
% 0.83/1.36 { ! alpha12( X, Y, Z, T, U ), ! c_Orderings_Oord__class_Oless__eq( X, U, T
% 0.83/1.36 ), alpha20( X, Y, Z, T, U ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( X, U, T ), alpha12( X, Y, Z, T, U ) }
% 0.83/1.36 .
% 0.83/1.36 { ! alpha20( X, Y, Z, T, U ), alpha12( X, Y, Z, T, U ) }.
% 0.83/1.36 { ! alpha20( X, Y, Z, T, U ), c_Orderings_Oord__class_Oless__eq( X, Z, U )
% 0.83/1.36 }.
% 0.83/1.36 { ! alpha20( X, Y, Z, T, U ), alpha26( X, Y, Z, T, U ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( X, Z, U ), ! alpha26( X, Y, Z, T, U
% 0.83/1.36 ), alpha20( X, Y, Z, T, U ) }.
% 0.83/1.36 { ! alpha26( X, Y, Z, T, U ), c_Orderings_Oord__class_Oless__eq( X, T, Y )
% 0.83/1.36 }.
% 0.83/1.36 { ! alpha26( X, Y, Z, T, U ), alpha28( X, Y, Z, T, U ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( X, T, Y ), ! alpha28( X, Y, Z, T, U
% 0.83/1.36 ), alpha26( X, Y, Z, T, U ) }.
% 0.83/1.36 { ! alpha28( X, Y, Z, T, U ), c_Orderings_Oord__class_Oless( X, Z, U ),
% 0.83/1.36 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( X, Z, U ), alpha28( X, Y, Z, T, U ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha28( X, Y, Z, T, U ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, T,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, Z, Y ) ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, hAPP( T, Z ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, T,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 0.83/1.36 Z ), Y ) ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.83/1.36 tc_Nat_Onat ) ) ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(
% 0.83/1.36 tc_Nat_Onat, X, U, c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat
% 0.83/1.36 , Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ) ) ) =
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, U,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, Z, Y ) ),
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( tc_Nat_Onat, X, U,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.83/1.36 tc_Nat_Onat ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ) ) ) ) }
% 0.83/1.36 .
% 0.83/1.36 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) }.
% 0.83/1.36 { c_Finite__Set_Ocard( tc_Product__Type_Ounit, c_Orderings_Otop__class_Otop
% 0.83/1.36 ( tc_fun( tc_Product__Type_Ounit, tc_HOL_Obool ) ) ) =
% 0.83/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.83/1.36 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.83/1.36 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! class_Rings_Olinordered__semidom( X ), !
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.83/1.36 { ! class_Rings_Olinordered__semidom( X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.83/1.36 c_Groups_Oone__class_Oone( X ) ) }.
% 0.83/1.36 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.83/1.36 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.83/1.36 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.83/1.36 c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.83/1.36 c_Groups_Oone__class_Oone( X ) }.
% 0.83/1.36 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Nat_OSuc,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.83/1.36 { hAPP( c_Nat_OSuc, X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.83/1.36 { hAPP( c_Nat_OSuc, X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.83/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.83/1.36 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.83/1.36 c_Groups_Oone__class_Oone( X ) }.
% 0.83/1.36 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.83/1.36 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.83/1.36 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), !
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Y, tc_Nat_Onat, Z, X
% 0.83/1.36 ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_member( Y, skol35( X, Y
% 0.83/1.36 , T ), X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), !
% 0.83/1.36 c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Y, tc_Nat_Onat, Z, X
% 0.83/1.36 ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ), alpha21( X, Y, Z, skol35(
% 0.83/1.36 X, Y, Z ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_member( Y, T, X ), ! alpha21( X, Y,
% 0.83/1.36 Z, T ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Y,
% 0.83/1.36 tc_Nat_Onat, Z, X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.83/1.36 { ! alpha21( X, Y, Z, T ), hAPP( Z, T ) = c_Groups_Oone__class_Oone(
% 0.83/1.36 tc_Nat_Onat ) }.
% 0.83/1.36 { ! alpha21( X, Y, Z, T ), alpha27( X, Y, Z, T ) }.
% 0.83/1.36 { ! hAPP( Z, T ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! alpha27( X,
% 0.83/1.36 Y, Z, T ), alpha21( X, Y, Z, T ) }.
% 0.83/1.36 { ! alpha27( X, Y, Z, T ), ! c_member( Y, U, X ), alpha13( Z, T, U ) }.
% 0.83/1.36 { ! alpha13( Z, T, skol36( U, W, Z, T ) ), alpha27( X, Y, Z, T ) }.
% 0.83/1.36 { c_member( Y, skol36( X, Y, Z, T ), X ), alpha27( X, Y, Z, T ) }.
% 0.83/1.36 { ! alpha13( X, Y, Z ), Y = Z, hAPP( X, Z ) = c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) }.
% 0.83/1.36 { ! Y = Z, alpha13( X, Y, Z ) }.
% 0.83/1.36 { ! hAPP( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha13( X,
% 0.83/1.36 Y, Z ) }.
% 0.83/1.36 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 0.83/1.36 tc_Nat_Onat ) }.
% 0.83/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_member( X, Y,
% 0.83/1.36 c_Int_Oring__1__class_OInts( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Oone__class_Oone( X ), Y ), Y ), c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! class_Rings_Olinordered__idom( X ), ! c_member( X, Y,
% 0.83/1.36 c_Int_Oring__1__class_OInts( X ) ), ! c_Orderings_Oord__class_Oless( X, Y
% 0.83/1.36 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Oone__class_Oone( X ), Y ), Y ), c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ) ) }.
% 0.83/1.36 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.83/1.36 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol37( Z, Y
% 0.83/1.36 ), Y ) }.
% 0.83/1.36 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.83/1.36 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.83/1.36 skol37( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.83/1.36 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.83/1.36 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.83/1.36 , skol37( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.83/1.36 { ! class_Rings_Oring__1( X ), c_member( X, c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ), c_Int_Oring__1__class_OInts( X ) ) }.
% 0.83/1.36 { ! class_Rings_Oring__1( X ), ! c_member( X, Y,
% 0.83/1.36 c_Int_Oring__1__class_OInts( X ) ), ! c_member( X, Z,
% 0.83/1.36 c_Int_Oring__1__class_OInts( X ) ), c_member( X,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Int_Oring__1__class_OInts( X )
% 0.83/1.36 ) }.
% 0.83/1.36 { ! class_Rings_Oring__1( X ), c_member( X, c_Groups_Oone__class_Oone( X )
% 0.83/1.36 , c_Int_Oring__1__class_OInts( X ) ) }.
% 0.83/1.36 { ! class_Int_Oring__char__0( X ), ! c_member( X, Y,
% 0.83/1.36 c_Int_Oring__1__class_OInts( X ) ), ! c_Groups_Oplus__class_Oplus( X, Y,
% 0.83/1.36 Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.83/1.36 X ) }.
% 0.83/1.36 { ! class_Int_Oring__char__0( X ), ! c_member( X, Y,
% 0.83/1.36 c_Int_Oring__1__class_OInts( X ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.83/1.36 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero
% 0.83/1.36 ( X ) }.
% 0.83/1.36 { ! class_Int_Oring__char__0( X ), ! c_member( X, Y,
% 0.83/1.36 c_Int_Oring__1__class_OInts( X ) ), ! c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ), Y ), Y )
% 0.83/1.36 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), c_member( Y, skol38( X, Y ), X ),
% 0.83/1.36 c_Finite__Set_Ocard( Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.83/1.36 }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_Groups_Oone__class_Oone( tc_Nat_Onat
% 0.83/1.36 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Finite__Set_Ocard( Y,
% 0.83/1.36 X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), c_member( Y, Z, X ), c_Finite__Set_Ocard
% 0.83/1.36 ( Y, c_Set_Oinsert( Y, Z, X ) ) = c_Groups_Oplus__class_Oplus(
% 0.83/1.36 tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.83/1.36 c_Finite__Set_Ocard( Y, X ) ) }.
% 0.83/1.36 { ! c_member( T, Z, c_Set_Oinsert( T, Y, X ) ), Z = Y, c_member( T, Z, X )
% 0.83/1.36 }.
% 0.83/1.36 { ! c_member( T, Z, Y ), c_member( T, Z, c_Set_Oinsert( T, X, Y ) ) }.
% 0.83/1.36 { ! Z = X, c_member( T, Z, c_Set_Oinsert( T, X, Y ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), c_Finite__Set_Ofinite( Y, c_Set_Oinsert
% 0.83/1.36 ( Y, Z, X ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofolding__image__simple__idem( W, T, Z, U, Y, X ), !
% 0.83/1.36 c_Finite__Set_Ofinite( T, V0 ), hAPP( X, c_Set_Oinsert( T, V1, V0 ) ) =
% 0.83/1.36 hAPP( hAPP( Z, hAPP( Y, V1 ) ), hAPP( X, V0 ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ),
% 0.83/1.36 c_Set_Oinsert( Z, T, Y ), c_Set_Oinsert( Z, T, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y, X ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y,
% 0.83/1.36 c_Set_Oinsert( Z, T, X ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y,
% 0.83/1.36 c_Set_Oinsert( Z, X, Y ) ) }.
% 0.83/1.36 { ! c_member( Z, Y, c_Set_Oinsert( Z, X, c_Orderings_Obot__class_Obot(
% 0.83/1.36 tc_fun( Z, tc_HOL_Obool ) ) ) ), Y = X }.
% 0.83/1.36 { ! Y = X, c_member( Z, Y, c_Set_Oinsert( Z, X,
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( Z, tc_HOL_Obool ) ) ) ) }.
% 0.83/1.36 { ! c_member( Z, Y, c_Set_Oinsert( Z, X, c_Orderings_Obot__class_Obot(
% 0.83/1.36 tc_fun( Z, tc_HOL_Obool ) ) ) ), Y = X }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, tc_HOL_Obool ),
% 0.83/1.36 c_Set_Oinsert( T, Z, Y ), X ), c_member( T, Z, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, tc_HOL_Obool ),
% 0.83/1.36 c_Set_Oinsert( T, Z, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.83/1.36 ( T, tc_HOL_Obool ), Y, X ) }.
% 0.83/1.36 { ! c_member( T, Z, X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T,
% 0.83/1.36 tc_HOL_Obool ), Y, X ), c_Orderings_Oord__class_Oless__eq( tc_fun( T,
% 0.83/1.36 tc_HOL_Obool ), c_Set_Oinsert( T, Z, Y ), X ) }.
% 0.83/1.36 { c_member( Z, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ), X, c_Set_Oinsert( Z, Y, T ) ),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), X, T ) }.
% 0.83/1.36 { c_member( Z, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ), X, T ), c_Orderings_Oord__class_Oless__eq( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ), X, c_Set_Oinsert( Z, Y, T ) ) }.
% 0.83/1.36 { ! c_member( Z, Y, X ), c_Set_Oinsert( U, hAPP( T, Y ), c_Set_Oimage( Z, U
% 0.83/1.36 , T, X ) ) = c_Set_Oimage( Z, U, T, X ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_fun( Z, tc_HOL_Obool ), Y,
% 0.83/1.36 c_Set_Oinsert( Z, X, c_Orderings_Obot__class_Obot( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ) ) ) ), Y = c_Orderings_Obot__class_Obot( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ) ), Y = c_Set_Oinsert( Z, X, c_Orderings_Obot__class_Obot(
% 0.83/1.36 tc_fun( Z, tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { c_Set_Oimage( U, T, Z, c_Set_Oinsert( U, Y, X ) ) = c_Set_Oinsert( T,
% 0.83/1.36 hAPP( Z, Y ), c_Set_Oimage( U, T, Z, X ) ) }.
% 0.83/1.36 { c_Set_Oinsert( Z, Y, c_Set_Oinsert( Z, Y, X ) ) = c_Set_Oinsert( Z, Y, X
% 0.83/1.36 ) }.
% 0.83/1.36 { c_Set_Oinsert( T, Z, c_Set_Oinsert( T, Y, X ) ) = c_Set_Oinsert( T, Y,
% 0.83/1.36 c_Set_Oinsert( T, Z, X ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( c_Set_Oinsert( T, Z, Y ), X ) ), Z = X, hBOOL( hAPP( Y, X
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! Z = X, hBOOL( hAPP( c_Set_Oinsert( T, Z, Y ), X ) ) }.
% 0.83/1.36 { ! hBOOL( hAPP( Y, X ) ), hBOOL( hAPP( c_Set_Oinsert( T, Z, Y ), X ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Z, c_Set_Oinsert( Z, Y, X ) ),
% 0.83/1.36 c_Finite__Set_Ofinite( Z, X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Z, X ), c_Finite__Set_Ofinite( Z, c_Set_Oinsert
% 0.83/1.36 ( Z, Y, X ) ) }.
% 0.83/1.36 { c_member( Z, Y, c_Set_Oinsert( Z, Y, X ) ) }.
% 0.83/1.36 { ! c_member( T, Z, c_Set_Oinsert( T, Y, X ) ), Z = Y, c_member( T, Z, X )
% 0.83/1.36 }.
% 0.83/1.36 { ! Z = Y, c_member( T, Z, c_Set_Oinsert( T, Y, X ) ) }.
% 0.83/1.36 { ! c_member( T, Z, X ), c_member( T, Z, c_Set_Oinsert( T, Y, X ) ) }.
% 0.83/1.36 { c_member( Z, Y, X ), c_member( Z, Y, T ), ! c_Set_Oinsert( Z, Y, X ) =
% 0.83/1.36 c_Set_Oinsert( Z, Y, T ), X = T }.
% 0.83/1.36 { c_member( Z, Y, X ), c_member( Z, Y, T ), ! X = T, c_Set_Oinsert( Z, Y, X
% 0.83/1.36 ) = c_Set_Oinsert( Z, Y, T ) }.
% 0.83/1.36 { ! c_member( Z, Y, X ), c_member( Z, Y, c_Set_Oinsert( Z, T, X ) ) }.
% 0.83/1.36 { ! c_member( Z, Y, X ), c_Set_Oinsert( Z, Y, X ) = X }.
% 0.83/1.36 { ! c_Set_Oinsert( Z, Y, c_Orderings_Obot__class_Obot( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ) ) ) = c_Set_Oinsert( Z, X, c_Orderings_Obot__class_Obot(
% 0.83/1.36 tc_fun( Z, tc_HOL_Obool ) ) ), Y = X }.
% 0.83/1.36 { ! c_Set_Oinsert( U, T, c_Set_Oinsert( U, Z, c_Orderings_Obot__class_Obot
% 0.83/1.36 ( tc_fun( U, tc_HOL_Obool ) ) ) ) = c_Set_Oinsert( U, Y, c_Set_Oinsert( U
% 0.83/1.36 , X, c_Orderings_Obot__class_Obot( tc_fun( U, tc_HOL_Obool ) ) ) ),
% 0.83/1.36 alpha14( X, Y, Z, T ), alpha22( X, Y, Z, T ) }.
% 0.83/1.36 { ! alpha14( X, Y, Z, T ), c_Set_Oinsert( U, T, c_Set_Oinsert( U, Z,
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( U, tc_HOL_Obool ) ) ) ) =
% 0.83/1.36 c_Set_Oinsert( U, Y, c_Set_Oinsert( U, X, c_Orderings_Obot__class_Obot(
% 0.83/1.36 tc_fun( U, tc_HOL_Obool ) ) ) ) }.
% 0.83/1.36 { ! alpha22( X, Y, Z, T ), c_Set_Oinsert( U, T, c_Set_Oinsert( U, Z,
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( U, tc_HOL_Obool ) ) ) ) =
% 0.83/1.36 c_Set_Oinsert( U, Y, c_Set_Oinsert( U, X, c_Orderings_Obot__class_Obot(
% 0.83/1.36 tc_fun( U, tc_HOL_Obool ) ) ) ) }.
% 0.83/1.36 { ! alpha22( X, Y, Z, T ), T = X }.
% 0.83/1.36 { ! alpha22( X, Y, Z, T ), Z = Y }.
% 0.83/1.36 { ! T = X, ! Z = Y, alpha22( X, Y, Z, T ) }.
% 0.83/1.36 { ! alpha14( X, Y, Z, T ), T = Y }.
% 0.83/1.36 { ! alpha14( X, Y, Z, T ), Z = X }.
% 0.83/1.36 { ! T = Y, ! Z = X, alpha14( X, Y, Z, T ) }.
% 0.83/1.36 { ! c_Set_Oinsert( Z, Y, X ) = c_Orderings_Obot__class_Obot( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ) ) }.
% 0.83/1.36 { ! c_Orderings_Obot__class_Obot( tc_fun( Z, tc_HOL_Obool ) ) =
% 0.83/1.36 c_Set_Oinsert( Z, Y, X ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! Z = Y,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, Z, Y ) = c_Set_Oinsert( X, Z
% 0.83/1.36 , c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_SetInterval_Oord__class_OatLeastAtMost
% 0.83/1.36 ( X, T, Z ) = c_Set_Oinsert( X, Y, c_Orderings_Obot__class_Obot( tc_fun(
% 0.83/1.36 X, tc_HOL_Obool ) ) ), T = Z }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! c_SetInterval_Oord__class_OatLeastAtMost
% 0.83/1.36 ( X, T, Z ) = c_Set_Oinsert( X, Y, c_Orderings_Obot__class_Obot( tc_fun(
% 0.83/1.36 X, tc_HOL_Obool ) ) ), Z = Y }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), ! T = Z, ! Z = Y,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( X, T, Z ) = c_Set_Oinsert( X, Y
% 0.83/1.36 , c_Orderings_Obot__class_Obot( tc_fun( X, tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), c_SetInterval_Oord__class_OatLeastAtMost(
% 0.83/1.36 X, Y, Y ) = c_Set_Oinsert( X, Y, c_Orderings_Obot__class_Obot( tc_fun( X
% 0.83/1.36 , tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), c_Orderings_Oord__class_Oless__eq(
% 0.83/1.36 tc_Nat_Onat, c_Finite__Set_Ocard( Y, X ), c_Finite__Set_Ocard( Y,
% 0.83/1.36 c_Set_Oinsert( Y, Z, X ) ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X
% 0.83/1.36 ) ), c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, Y, hAPP(
% 0.83/1.36 c_Nat_OSuc, X ) ) = c_Set_Oinsert( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastAtMost( tc_Nat_Onat, Y, X ) ) }.
% 0.83/1.36 { c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, X, hAPP(
% 0.83/1.36 c_Nat_OSuc, X ) ) = c_Set_Oinsert( tc_Nat_Onat, X,
% 0.83/1.36 c_Orderings_Obot__class_Obot( tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofolding__one__idem( Z, Y, X ), ! c_Finite__Set_Ofinite(
% 0.83/1.36 Z, T ), T = c_Orderings_Obot__class_Obot( tc_fun( Z, tc_HOL_Obool ) ),
% 0.83/1.36 hAPP( X, c_Set_Oinsert( Z, U, T ) ) = hAPP( hAPP( Y, U ), hAPP( X, T ) )
% 0.83/1.36 }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Finite__Set_Ofinite( Z, Y ),
% 0.83/1.36 c_member( Z, T, Y ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(
% 0.83/1.36 Z, X, U, c_Set_Oinsert( Z, T, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 hAPP( U, T ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, X, U
% 0.83/1.36 , Y ) ) }.
% 0.83/1.36 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Finite__Set_Ofinite( Z, Y ),
% 0.83/1.36 c_member( Z, T, Y ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(
% 0.83/1.36 Z, X, U, c_Set_Oinsert( Z, T, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.83/1.36 hAPP( U, T ), c_Big__Operators_Ocomm__monoid__add__class_Osetsum( Z, X, U
% 0.83/1.36 , Y ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), c_member( Y, Z, X ), c_Finite__Set_Ocard
% 0.83/1.36 ( Y, c_Set_Oinsert( Y, Z, X ) ) = hAPP( c_Nat_OSuc, c_Finite__Set_Ocard(
% 0.83/1.36 Y, X ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_member( Y, Z, X ),
% 0.83/1.36 c_Finite__Set_Ocard( Y, c_Set_Oinsert( Y, Z, X ) ) = c_Finite__Set_Ocard
% 0.83/1.36 ( Y, X ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), c_member( Y, Z, X ), c_Finite__Set_Ocard
% 0.83/1.36 ( Y, c_Set_Oinsert( Y, Z, X ) ) = hAPP( c_Nat_OSuc, c_Finite__Set_Ocard(
% 0.83/1.36 Y, X ) ) }.
% 0.83/1.36 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, Y, hAPP(
% 0.83/1.36 c_Nat_OSuc, X ) ) = c_Set_Oinsert( tc_Nat_Onat, X,
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, Y, X ) ) }.
% 0.83/1.36 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat, Y, hAPP(
% 0.83/1.36 c_Nat_OSuc, X ) ) = c_Orderings_Obot__class_Obot( tc_fun( tc_Nat_Onat,
% 0.83/1.36 tc_HOL_Obool ) ) }.
% 0.83/1.36 { c_Set_Othe__elem( Y, c_Set_Oinsert( Y, X, c_Orderings_Obot__class_Obot(
% 0.83/1.36 tc_fun( Y, tc_HOL_Obool ) ) ) ) = X }.
% 0.83/1.36 { ! c_Finite__Set_Ocard( Z, Y ) = hAPP( c_Nat_OSuc, X ), Y = c_Set_Oinsert
% 0.83/1.36 ( Z, skol39( X, Y, Z ), skol44( X, Y, Z ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ocard( Z, Y ) = hAPP( c_Nat_OSuc, X ), alpha23( X, Z,
% 0.83/1.36 skol39( X, Y, Z ), skol44( X, Y, Z ) ) }.
% 0.83/1.36 { ! Y = c_Set_Oinsert( Z, T, U ), ! alpha23( X, Z, T, U ),
% 0.83/1.36 c_Finite__Set_Ocard( Z, Y ) = hAPP( c_Nat_OSuc, X ) }.
% 0.83/1.36 { ! alpha23( X, Y, Z, T ), ! c_member( Y, Z, T ) }.
% 0.83/1.36 { ! alpha23( X, Y, Z, T ), alpha15( X, Y, T ) }.
% 0.83/1.36 { c_member( Y, Z, T ), ! alpha15( X, Y, T ), alpha23( X, Y, Z, T ) }.
% 0.83/1.36 { ! alpha15( X, Y, Z ), c_Finite__Set_Ocard( Y, Z ) = X }.
% 0.83/1.36 { ! alpha15( X, Y, Z ), alpha24( X, Y, Z ) }.
% 0.83/1.36 { ! c_Finite__Set_Ocard( Y, Z ) = X, ! alpha24( X, Y, Z ), alpha15( X, Y, Z
% 0.83/1.36 ) }.
% 0.83/1.36 { ! alpha24( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z
% 0.83/1.36 = c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ) }.
% 0.83/1.36 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha24( X, Y, Z ) }.
% 0.83/1.36 { ! Z = c_Orderings_Obot__class_Obot( tc_fun( Y, tc_HOL_Obool ) ), alpha24
% 0.83/1.36 ( X, Y, Z ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofolding__one( Z, Y, X ), ! c_Finite__Set_Ofinite( Z, T )
% 0.83/1.36 , c_member( Z, U, T ), T = c_Orderings_Obot__class_Obot( tc_fun( Z,
% 0.83/1.36 tc_HOL_Obool ) ), hAPP( X, c_Set_Oinsert( Z, U, T ) ) = hAPP( hAPP( Y, U
% 0.83/1.36 ), hAPP( X, T ) ) }.
% 0.83/1.36 { ! c_Finite__Set_Ofinite( Y, X ), ! c_member( Y, Z, X ),
% 0.83/1.36 c_Finite__Set_Ocard( Y, X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Finite__Set_Ocard( Y,
% 0.83/1.36 c_Groups_Ominus__class_Ominus( tc_fun( Y, tc_HOL_Obool ), X,
% 0.83/1.36 c_Set_Oinsert( Y, Z, c_Orderings_Obot__class_Obot( tc_fun( Y,
% 0.83/1.36 tc_HOL_Obool ) ) ) ) ) ) }.
% 0.83/1.36 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.83/1.36 ) ) }.
% 0.83/1.36 { ! class_Finite__Set_Ofinite( Y ), ! class_Finite__Set_Ofinite( X ),
% 0.83/1.36 class_Finite__Set_Ofinite( tc_fun( Y, X ) ) }.
% 0.83/1.36 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.83/1.36 .
% 0.83/1.36 { ! class_Orderings_Otop( X ), class_Orderings_Otop( tc_fun( Y, X ) ) }.
% 0.83/1.36 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.83/1.36 { ! class_Orderings_Obot( X ), class_Orderings_Obot( tc_fun( Y, X ) ) }.
% 0.83/1.36 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.83/1.36 tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Orderings_Obot( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.83/1.36 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.83/1.36 { class_Finite__Set_Ofinite( tc_HOL_Obool ) }.
% 0.83/1.36 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.83/1.36 { class_Orderings_Otop( tc_HOL_Obool ) }.
% 0.83/1.36 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.83/1.36 { class_Orderings_Obot( tc_HOL_Obool ) }.
% 0.83/1.36 { ! class_Finite__Set_Ofinite( Y ), ! class_Finite__Set_Ofinite( X ),
% 0.83/1.36 class_Finite__Set_Ofinite( tc_sum( Y, X ) ) }.
% 0.83/1.36 { ! class_Finite__Set_Ofinite( X ), class_Finite__Set_Ofinite(
% 0.83/1.36 tc_Option_Ooption( X ) ) }.
% 0.83/1.36 { ! class_Finite__Set_Ofinite( Y ), ! class_Finite__Set_Ofinite( X ),
% 0.83/1.36 class_Finite__Set_Ofinite( tc_prod( Y, X ) ) }.
% 0.83/1.36 { class_Finite__Set_Ofinite( tc_Product__Type_Ounit ) }.
% 0.83/1.36 { ! hBOOL( hAPP( c_fequal( Y ), X ) ), Y = X }.
% 0.83/1.36 { ! Y = X, hBOOL( hAPP( c_fequal( Y ), X ) ) }.
% 0.83/1.36 { ! hBOOL( c_fFalse ) }.
% 0.83/1.36 { hBOOL( c_fTrue ) }.
% 0.83/1.36 { ! c_Fun_Oinj__on( tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, X,
% 0.83/1.36 c_Orderings_Otop__class_Otop( tc_fun( tc_Arrow__Order__Mirabelle_Oindi,
% 0.83/1.36 tc_HOL_Obool ) ) ), ! c_Set_Oimage( tc_Arrow__Order__Mirabelle_Oindi,
% 0.83/1.36 tc_Nat_Onat, X, c_Orderings_Otop__class_Otop( tc_fun(
% 0.83/1.36 tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) ) ) =
% 0.83/1.36 c_SetInterval_Oord__class_OatLeastLessThan( tc_Nat_Onat,
% 0.83/1.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Finite__Set_Ocard(
% 0.83/1.36 tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop( tc_fun(
% 0.83/1.36 tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) ) ) ), v_thesis____ }.
% 0.83/1.36 { ! v_thesis____ }.
% 0.83/1.36
% 0.83/1.36 *** allocated 15000 integers for clauses
% 0.83/1.36 *** allocated 22500 integers for clauses
% 0.83/1.36 *** allocated 33750 integers for clauses
% 0.83/1.36 percentage equality = 0.255381, percentage horn = 0.867925
% 0.83/1.36 This is a problem with some equality
% 0.83/1.36
% 0.83/1.36
% 0.83/1.36
% 0.83/1.36 Options Used:
% 0.83/1.36
% 0.83/1.36 useres = 1
% 0.83/1.36 useparamod = 1
% 0.83/1.36 useeqrefl = 1
% 0.83/1.36 useeqfact = 1
% 0.83/1.36 usefactor = 1
% 0.83/1.36 usesimpsplitting = 0
% 0.83/1.36 usesimpdemod = 5
% 0.83/1.36 usesimpres = 3
% 0.83/1.36
% 0.83/1.36 resimpinuse = 1000
% 0.83/1.36 resimpclauses = 20000
% 0.83/1.36 substype = eqrewr
% 0.83/1.36 backwardsubs = 1
% 0.83/1.36 selectoldest = 5
% 0.83/1.36
% 0.83/1.36 litorderings [0] = split
% 0.83/1.36 litorderings [1] = extend the termordering, first sorting on arguments
% 0.83/1.36
% 0.83/1.36 termordering = kbo
% 0.83/1.36
% 0.83/1.36 litapriori = 0
% 0.83/1.36 termapriori = 1
% 0.83/1.36 litaposteriori = 0
% 0.83/1.36 termaposteriori = 0
% 0.83/1.36 demodaposteriori = 0
% 0.83/1.36 ordereqreflfact = 0
% 0.83/1.36
% 0.83/1.36 litselect = negord
% 0.83/1.36
% 0.83/1.36 maxweight = 15
% 0.83/1.36 maxdepth = 30000
% 0.83/1.36 maxlength = 115
% 0.83/1.36 maxnrvars = 195
% 0.83/1.36 excuselevel = 1
% 0.83/1.36 increasemaxweight = 1
% 0.83/1.36
% 0.83/1.36 maxselected = 10000000
% 0.83/1.36 maxnrclauses = 10000000
% 0.83/1.36
% 0.83/1.36 showgenerated = 0
% 0.83/1.36 showkept = 0
% 0.83/1.36 showselected = 0
% 0.83/1.36 showdeleted = 0
% 0.83/1.36 showresimp = 1
% 0.83/1.36 showstatus = 2000
% 0.83/1.36
% 0.83/1.36 prologoutput = 0
% 0.83/1.36 nrgoals = 5000000
% 0.83/1.36 totalproof = 1
% 0.83/1.36
% 0.83/1.36 Symbols occurring in the translation:
% 0.83/1.36
% 0.83/1.36 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.83/1.36 . [1, 2] (w:1, o:129, a:1, s:1, b:0),
% 0.83/1.36 ! [4, 1] (w:0, o:83, a:1, s:1, b:0),
% 0.83/1.36 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.83/1.36 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.83/1.36 hAPP [38, 2] (w:1, o:153, a:1, s:1, b:0),
% 0.83/1.36 c_Fun_Oinj__on [42, 4] (w:1, o:223, a:1, s:1, b:0),
% 0.83/1.36 c_Set_Oimage [43, 4] (w:1, o:224, a:1, s:1, b:0),
% 0.83/1.36 c_Finite__Set_Ocard [44, 2] (w:1, o:154, a:1, s:1, b:0),
% 0.83/1.36 tc_HOL_Obool [46, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.83/1.36 tc_fun [47, 2] (w:1, o:176, a:1, s:1, b:0),
% 0.83/1.36 c_Orderings_Otop__class_Otop [48, 1] (w:1, o:89, a:1, s:1, b:0),
% 0.83/1.36 hBOOL [50, 1] (w:1, o:90, a:1, s:1, b:0),
% 0.83/1.36 class_Orderings_Otop [52, 1] (w:1, o:91, a:1, s:1, b:0),
% 0.83/1.36 c_member [53, 3] (w:1, o:192, a:1, s:1, b:0),
% 0.83/1.36 class_Groups_Ozero [55, 1] (w:1, o:93, a:1, s:1, b:0),
% 0.83/1.36 c_Groups_Ozero__class_Ozero [56, 1] (w:1, o:94, a:1, s:1, b:0),
% 0.83/1.36 v_F [57, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.83/1.36 c_Arrow__Order__Mirabelle_OIIA [58, 1] (w:1, o:95, a:1, s:1, b:0),
% 0.83/1.36 c_Arrow__Order__Mirabelle_Ounanimity [59, 1] (w:1, o:96, a:1, s:1, b:
% 0.83/1.36 0),
% 0.83/1.36 tc_Arrow__Order__Mirabelle_Oindi [60, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.83/1.36
% 0.83/1.36 c_Finite__Set_Ofinite [61, 2] (w:1, o:177, a:1, s:1, b:0),
% 0.83/1.36 class_Finite__Set_Ofinite [64, 1] (w:1, o:92, a:1, s:1, b:0),
% 0.83/1.36 tc_Option_Ooption [65, 1] (w:1, o:100, a:1, s:1, b:0),
% 0.83/1.36 tc_sum [66, 2] (w:1, o:178, a:1, s:1, b:0),
% 0.83/1.36 tc_prod [67, 2] (w:1, o:179, a:1, s:1, b:0),
% 0.83/1.36 tc_Nat_Onat [68, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.83/1.36 c_Orderings_Oord__class_Oless__eq [69, 3] (w:1, o:193, a:1, s:1, b:0)
% 0.83/1.36 ,
% 0.83/1.36 c_Orderings_Oord__class_Oless [70, 3] (w:1, o:194, a:1, s:1, b:0),
% 0.83/1.36 c_Fun_Othe__inv__into [71, 4] (w:1, o:225, a:1, s:1, b:0),
% 0.83/1.36 c_Orderings_Obot__class_Obot [72, 1] (w:1, o:101, a:1, s:1, b:0),
% 0.83/1.36 class_Orderings_Opreorder [77, 1] (w:1, o:104, a:1, s:1, b:0),
% 0.83/1.36 class_Orderings_Obot [78, 1] (w:1, o:105, a:1, s:1, b:0),
% 0.83/1.36 class_Orderings_Olinorder [79, 1] (w:1, o:106, a:1, s:1, b:0),
% 0.83/1.36 class_Orderings_Oord [80, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.83/1.36 class_Orderings_Oorder [82, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.83/1.36 c_fequal [83, 1] (w:1, o:107, a:1, s:1, b:0),
% 0.83/1.46 c_SetInterval_Oord__class_OatLeastLessThan [97, 3] (w:1, o:195, a:1
% 0.83/1.46 , s:1, b:0),
% 0.83/1.46 c_SetInterval_Oord_OatMost [115, 3] (w:1, o:197, a:1, s:1, b:0),
% 0.83/1.46 c_SetInterval_Oord_OatLeast [116, 3] (w:1, o:196, a:1, s:1, b:0),
% 0.83/1.46 c_SetInterval_Oord_OlessThan [118, 3] (w:1, o:198, a:1, s:1, b:0),
% 0.83/1.46 c_SetInterval_Oord_OgreaterThan [119, 3] (w:1, o:199, a:1, s:1, b:0)
% 0.83/1.46 ,
% 0.83/1.46 c_SetInterval_Oord_OatLeastAtMost [120, 4] (w:1, o:226, a:1, s:1, b:0
% 0.83/1.46 ),
% 0.83/1.46 c_SetInterval_Oord_OgreaterThanLessThan [121, 4] (w:1, o:227, a:1, s:
% 0.83/1.46 1, b:0),
% 0.83/1.46 c_SetInterval_Oord_OgreaterThanAtMost [122, 5] (w:1, o:246, a:1, s:1
% 0.83/1.46 , b:0),
% 0.83/1.46 c_SetInterval_Oord_OatLeastLessThan [123, 5] (w:1, o:247, a:1, s:1
% 0.83/1.46 , b:0),
% 0.83/1.46 c_Nat_OSuc [124, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.83/1.46 c_Finite__Set_Ofolding__one__idem [125, 3] (w:1, o:200, a:1, s:1, b:0
% 0.83/1.46 ),
% 0.83/1.46 c_Finite__Set_Ofolding__image__simple__idem [126, 6] (w:1, o:257, a:1
% 0.83/1.46 , s:1, b:0),
% 0.83/1.46 c_SetInterval_Oord__class_OgreaterThan [133, 2] (w:1, o:180, a:1, s:1
% 0.83/1.46 , b:0),
% 0.83/1.46 c_Sum__Type_OPlus [134, 4] (w:1, o:228, a:1, s:1, b:0),
% 0.83/1.46 c_Groups_Oplus__class_Oplus [135, 3] (w:1, o:202, a:1, s:1, b:0),
% 0.83/1.46 class_Groups_Oab__semigroup__add [136, 1] (w:1, o:108, a:1, s:1, b:0)
% 0.83/1.46 ,
% 0.83/1.46 class_Groups_Ocancel__semigroup__add [137, 1] (w:1, o:109, a:1, s:1
% 0.83/1.46 , b:0),
% 0.83/1.46 class_Groups_Ocancel__ab__semigroup__add [138, 1] (w:1, o:110, a:1
% 0.83/1.46 , s:1, b:0),
% 0.83/1.46 class_Groups_Oordered__ab__semigroup__add__imp__le [141, 1] (w:1, o:
% 0.83/1.46 111, a:1, s:1, b:0),
% 0.83/1.46 class_Groups_Oordered__cancel__ab__semigroup__add [143, 1] (w:1, o:
% 0.83/1.46 112, a:1, s:1, b:0),
% 0.83/1.46 class_Groups_Ocomm__monoid__add [144, 1] (w:1, o:113, a:1, s:1, b:0)
% 0.83/1.46 ,
% 0.83/1.46 class_Groups_Omonoid__add [145, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.83/1.46 class_Groups_Olinordered__ab__group__add [146, 1] (w:1, o:114, a:1
% 0.83/1.46 , s:1, b:0),
% 0.83/1.46 class_Groups_Oordered__ab__semigroup__add [147, 1] (w:1, o:116, a:1
% 0.83/1.46 , s:1, b:0),
% 0.83/1.46 class_Groups_Oordered__comm__monoid__add [148, 1] (w:1, o:117, a:1
% 0.83/1.46 , s:1, b:0),
% 0.83/1.46 class_Rings_Olinordered__semidom [149, 1] (w:1, o:118, a:1, s:1, b:0)
% 0.83/1.46 ,
% 0.83/1.46 class_Rings_Olinordered__idom [150, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.83/1.46 class_Rings_Ocomm__semiring__1 [151, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.83/1.46
% 0.83/1.46 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.83/1.46 152, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.83/1.46 c_Nat_Onat_Onat__size [154, 1] (w:1, o:88, a:1, s:1, b:0),
% 0.83/1.46 c_Big__Operators_Ocomm__monoid__add__class_Osetsum [155, 4] (w:1, o:
% 0.83/1.46 229, a:1, s:1, b:0),
% 0.83/1.46 c_Nat_Osize__class_Osize [157, 2] (w:1, o:181, a:1, s:1, b:0),
% 0.83/1.46 c_SetInterval_Oord__class_OatLeastAtMost [160, 3] (w:1, o:203, a:1
% 0.83/1.46 , s:1, b:0),
% 0.83/1.46 c_Groups_Oone__class_Oone [161, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.83/1.46 c_fTrue [162, 0] (w:1, o:74, a:1, s:1, b:0),
% 0.83/1.46 c_HOL_Obool_Obool__size [163, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.83/1.46 tc_Product__Type_Ounit [164, 0] (w:1, o:75, a:1, s:1, b:0),
% 0.83/1.46 class_Rings_Ozero__neq__one [165, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.83/1.46 class_Groups_Oone [166, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.83/1.46 c_fFalse [167, 0] (w:1, o:76, a:1, s:1, b:0),
% 0.83/1.46 c_Int_Oring__1__class_OInts [168, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.83/1.46 class_Rings_Oring__1 [170, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.83/1.46 class_Int_Oring__char__0 [171, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.83/1.46 c_Set_Oinsert [172, 3] (w:1, o:204, a:1, s:1, b:0),
% 0.83/1.46 c_Set_Othe__elem [174, 2] (w:1, o:182, a:1, s:1, b:0),
% 0.83/1.46 c_Finite__Set_Ofolding__one [177, 3] (w:1, o:201, a:1, s:1, b:0),
% 0.83/1.46 c_Groups_Ominus__class_Ominus [178, 3] (w:1, o:205, a:1, s:1, b:0),
% 0.83/1.46 v_thesis____ [182, 0] (w:1, o:82, a:1, s:1, b:0),
% 0.83/1.46 alpha1 [183, 3] (w:1, o:206, a:1, s:1, b:1),
% 0.83/1.46 alpha2 [184, 3] (w:1, o:209, a:1, s:1, b:1),
% 0.83/1.46 alpha3 [185, 2] (w:1, o:183, a:1, s:1, b:1),
% 0.83/1.46 alpha4 [186, 2] (w:1, o:184, a:1, s:1, b:1),
% 0.83/1.46 alpha5 [187, 2] (w:1, o:185, a:1, s:1, b:1),
% 0.83/1.46 alpha6 [188, 2] (w:1, o:186, a:1, s:1, b:1),
% 0.83/1.46 alpha7 [189, 2] (w:1, o:187, a:1, s:1, b:1),
% 0.83/1.46 alpha8 [190, 3] (w:1, o:210, a:1, s:1, b:1),
% 5.09/5.51 alpha9 [191, 5] (w:1, o:248, a:1, s:1, b:1),
% 5.09/5.51 alpha10 [192, 2] (w:1, o:188, a:1, s:1, b:1),
% 5.09/5.51 alpha11 [193, 2] (w:1, o:189, a:1, s:1, b:1),
% 5.09/5.51 alpha12 [194, 5] (w:1, o:249, a:1, s:1, b:1),
% 5.09/5.51 alpha13 [195, 3] (w:1, o:207, a:1, s:1, b:1),
% 5.09/5.51 alpha14 [196, 4] (w:1, o:230, a:1, s:1, b:1),
% 5.09/5.51 alpha15 [197, 3] (w:1, o:208, a:1, s:1, b:1),
% 5.09/5.51 alpha16 [198, 4] (w:1, o:231, a:1, s:1, b:1),
% 5.09/5.51 alpha17 [199, 2] (w:1, o:190, a:1, s:1, b:1),
% 5.09/5.51 alpha18 [200, 2] (w:1, o:191, a:1, s:1, b:1),
% 5.09/5.51 alpha19 [201, 4] (w:1, o:232, a:1, s:1, b:1),
% 5.09/5.51 alpha20 [202, 5] (w:1, o:250, a:1, s:1, b:1),
% 5.09/5.51 alpha21 [203, 4] (w:1, o:233, a:1, s:1, b:1),
% 5.09/5.51 alpha22 [204, 4] (w:1, o:234, a:1, s:1, b:1),
% 5.09/5.51 alpha23 [205, 4] (w:1, o:235, a:1, s:1, b:1),
% 5.09/5.51 alpha24 [206, 3] (w:1, o:211, a:1, s:1, b:1),
% 5.09/5.51 alpha25 [207, 4] (w:1, o:236, a:1, s:1, b:1),
% 5.09/5.51 alpha26 [208, 5] (w:1, o:251, a:1, s:1, b:1),
% 5.09/5.51 alpha27 [209, 4] (w:1, o:237, a:1, s:1, b:1),
% 5.09/5.51 alpha28 [210, 5] (w:1, o:252, a:1, s:1, b:1),
% 5.09/5.51 alpha29 [211, 4] (w:1, o:238, a:1, s:1, b:1),
% 5.09/5.51 alpha30 [212, 3] (w:1, o:212, a:1, s:1, b:1),
% 5.09/5.51 alpha31 [213, 3] (w:1, o:213, a:1, s:1, b:1),
% 5.09/5.51 skol1 [214, 2] (w:1, o:155, a:1, s:1, b:1),
% 5.09/5.51 skol2 [215, 3] (w:1, o:214, a:1, s:1, b:1),
% 5.09/5.51 skol3 [216, 4] (w:1, o:240, a:1, s:1, b:1),
% 5.09/5.51 skol4 [217, 2] (w:1, o:162, a:1, s:1, b:1),
% 5.09/5.51 skol5 [218, 3] (w:1, o:216, a:1, s:1, b:1),
% 5.09/5.51 skol6 [219, 3] (w:1, o:217, a:1, s:1, b:1),
% 5.09/5.51 skol7 [220, 4] (w:1, o:241, a:1, s:1, b:1),
% 5.09/5.51 skol8 [221, 4] (w:1, o:242, a:1, s:1, b:1),
% 5.09/5.51 skol9 [222, 2] (w:1, o:163, a:1, s:1, b:1),
% 5.09/5.51 skol10 [223, 2] (w:1, o:164, a:1, s:1, b:1),
% 5.09/5.51 skol11 [224, 1] (w:1, o:97, a:1, s:1, b:1),
% 5.09/5.51 skol12 [225, 1] (w:1, o:98, a:1, s:1, b:1),
% 5.09/5.51 skol13 [226, 2] (w:1, o:165, a:1, s:1, b:1),
% 5.09/5.51 skol14 [227, 2] (w:1, o:166, a:1, s:1, b:1),
% 5.09/5.51 skol15 [228, 4] (w:1, o:243, a:1, s:1, b:1),
% 5.09/5.51 skol16 [229, 5] (w:1, o:253, a:1, s:1, b:1),
% 5.09/5.51 skol17 [230, 2] (w:1, o:167, a:1, s:1, b:1),
% 5.09/5.51 skol18 [231, 2] (w:1, o:168, a:1, s:1, b:1),
% 5.09/5.51 skol19 [232, 1] (w:1, o:99, a:1, s:1, b:1),
% 5.09/5.51 skol20 [233, 2] (w:1, o:169, a:1, s:1, b:1),
% 5.09/5.51 skol21 [234, 2] (w:1, o:170, a:1, s:1, b:1),
% 5.09/5.51 skol22 [235, 2] (w:1, o:171, a:1, s:1, b:1),
% 5.09/5.51 skol23 [236, 2] (w:1, o:172, a:1, s:1, b:1),
% 5.09/5.51 skol24 [237, 3] (w:1, o:218, a:1, s:1, b:1),
% 5.09/5.51 skol25 [238, 3] (w:1, o:219, a:1, s:1, b:1),
% 5.09/5.51 skol26 [239, 4] (w:1, o:239, a:1, s:1, b:1),
% 5.09/5.51 skol27 [240, 5] (w:1, o:254, a:1, s:1, b:1),
% 5.09/5.51 skol28 [241, 3] (w:1, o:220, a:1, s:1, b:1),
% 5.09/5.51 skol29 [242, 5] (w:1, o:255, a:1, s:1, b:1),
% 5.09/5.51 skol30 [243, 5] (w:1, o:256, a:1, s:1, b:1),
% 5.09/5.51 skol31 [244, 2] (w:1, o:156, a:1, s:1, b:1),
% 5.09/5.51 skol32 [245, 2] (w:1, o:157, a:1, s:1, b:1),
% 5.09/5.51 skol33 [246, 2] (w:1, o:158, a:1, s:1, b:1),
% 5.09/5.51 skol34 [247, 2] (w:1, o:159, a:1, s:1, b:1),
% 5.09/5.51 skol35 [248, 3] (w:1, o:221, a:1, s:1, b:1),
% 5.09/5.51 skol36 [249, 4] (w:1, o:244, a:1, s:1, b:1),
% 5.09/5.51 skol37 [250, 2] (w:1, o:160, a:1, s:1, b:1),
% 5.09/5.51 skol38 [251, 2] (w:1, o:161, a:1, s:1, b:1),
% 5.09/5.51 skol39 [252, 3] (w:1, o:222, a:1, s:1, b:1),
% 5.09/5.51 skol40 [253, 4] (w:1, o:245, a:1, s:1, b:1),
% 5.09/5.51 skol41 [254, 2] (w:1, o:173, a:1, s:1, b:1),
% 5.09/5.51 skol42 [255, 2] (w:1, o:174, a:1, s:1, b:1),
% 5.09/5.51 skol43 [256, 2] (w:1, o:175, a:1, s:1, b:1),
% 5.09/5.51 skol44 [257, 3] (w:1, o:215, a:1, s:1, b:1).
% 5.09/5.51
% 5.09/5.51
% 5.09/5.51 Starting Search:
% 5.09/5.51
% 5.09/5.51 *** allocated 50625 integers for clauses
% 5.09/5.51 *** allocated 75937 integers for clauses
% 5.09/5.51 Resimplifying inuse:
% 5.09/5.51 Done
% 5.09/5.51
% 5.09/5.51 *** allocated 113905 integers for clauses
% 5.09/5.51 *** allocated 75937 integers for termspace/termends
% 5.09/5.51 *** allocated 170857 integers for clauses
% 5.09/5.51
% 5.09/5.51 Intermediate Status:
% 5.09/5.51 Generated: 4828
% 5.09/5.51 Kept: 2041
% 5.09/5.51 Inuse: 126
% 5.09/5.51 Deleted: 0
% 5.09/5.51 Deletedinuse: 0
% 5.09/5.51
% 5.09/5.51 Resimplifying inuse:
% 5.09/5.51 Done
% 5.09/5.51
% 5.09/5.51 *** allocated 113905 integers for termspace/termends
% 5.09/5.51 *** allocated 256285 integers for clauses
% 5.09/5.51 Resimplifying inuse:
% 5.09/5.51 Done
% 5.09/5.51
% 5.09/5.51 *** allocated 170857 integers for termspace/termends
% 24.89/25.29 *** allocated 384427 integers for clauses
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 12306
% 24.89/25.29 Kept: 4410
% 24.89/25.29 Inuse: 218
% 24.89/25.29 Deleted: 3
% 24.89/25.29 Deletedinuse: 1
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 15814
% 24.89/25.29 Kept: 6442
% 24.89/25.29 Inuse: 242
% 24.89/25.29 Deleted: 5
% 24.89/25.29 Deletedinuse: 1
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 *** allocated 256285 integers for termspace/termends
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 *** allocated 576640 integers for clauses
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 21543
% 24.89/25.29 Kept: 8444
% 24.89/25.29 Inuse: 318
% 24.89/25.29 Deleted: 5
% 24.89/25.29 Deletedinuse: 1
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 *** allocated 384427 integers for termspace/termends
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 29395
% 24.89/25.29 Kept: 11793
% 24.89/25.29 Inuse: 357
% 24.89/25.29 Deleted: 5
% 24.89/25.29 Deletedinuse: 1
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 *** allocated 864960 integers for clauses
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 34960
% 24.89/25.29 Kept: 13802
% 24.89/25.29 Inuse: 418
% 24.89/25.29 Deleted: 5
% 24.89/25.29 Deletedinuse: 1
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 42582
% 24.89/25.29 Kept: 15813
% 24.89/25.29 Inuse: 485
% 24.89/25.29 Deleted: 5
% 24.89/25.29 Deletedinuse: 1
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 *** allocated 576640 integers for termspace/termends
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 51890
% 24.89/25.29 Kept: 17841
% 24.89/25.29 Inuse: 517
% 24.89/25.29 Deleted: 5
% 24.89/25.29 Deletedinuse: 1
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 59689
% 24.89/25.29 Kept: 19859
% 24.89/25.29 Inuse: 570
% 24.89/25.29 Deleted: 18
% 24.89/25.29 Deletedinuse: 12
% 24.89/25.29
% 24.89/25.29 *** allocated 1297440 integers for clauses
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying clauses:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 66855
% 24.89/25.29 Kept: 21861
% 24.89/25.29 Inuse: 601
% 24.89/25.29 Deleted: 1034
% 24.89/25.29 Deletedinuse: 13
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 *** allocated 864960 integers for termspace/termends
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 75834
% 24.89/25.29 Kept: 23872
% 24.89/25.29 Inuse: 627
% 24.89/25.29 Deleted: 1036
% 24.89/25.29 Deletedinuse: 14
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 85493
% 24.89/25.29 Kept: 26451
% 24.89/25.29 Inuse: 692
% 24.89/25.29 Deleted: 1036
% 24.89/25.29 Deletedinuse: 14
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 94798
% 24.89/25.29 Kept: 28617
% 24.89/25.29 Inuse: 739
% 24.89/25.29 Deleted: 1036
% 24.89/25.29 Deletedinuse: 14
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 *** allocated 1946160 integers for clauses
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 102092
% 24.89/25.29 Kept: 30788
% 24.89/25.29 Inuse: 764
% 24.89/25.29 Deleted: 1037
% 24.89/25.29 Deletedinuse: 15
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 107434
% 24.89/25.29 Kept: 33575
% 24.89/25.29 Inuse: 774
% 24.89/25.29 Deleted: 1037
% 24.89/25.29 Deletedinuse: 15
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 114091
% 24.89/25.29 Kept: 36190
% 24.89/25.29 Inuse: 812
% 24.89/25.29 Deleted: 1038
% 24.89/25.29 Deletedinuse: 15
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 122592
% 24.89/25.29 Kept: 38264
% 24.89/25.29 Inuse: 838
% 24.89/25.29 Deleted: 1039
% 24.89/25.29 Deletedinuse: 16
% 24.89/25.29
% 24.89/25.29 *** allocated 1297440 integers for termspace/termends
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying clauses:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 128353
% 24.89/25.29 Kept: 40324
% 24.89/25.29 Inuse: 865
% 24.89/25.29 Deleted: 2370
% 24.89/25.29 Deletedinuse: 17
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 134014
% 24.89/25.29 Kept: 42347
% 24.89/25.29 Inuse: 873
% 24.89/25.29 Deleted: 2390
% 24.89/25.29 Deletedinuse: 17
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 140424
% 24.89/25.29 Kept: 44798
% 24.89/25.29 Inuse: 891
% 24.89/25.29 Deleted: 2392
% 24.89/25.29 Deletedinuse: 17
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 *** allocated 2919240 integers for clauses
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 148649
% 24.89/25.29 Kept: 47855
% 24.89/25.29 Inuse: 924
% 24.89/25.29 Deleted: 2397
% 24.89/25.29 Deletedinuse: 20
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 156079
% 24.89/25.29 Kept: 51639
% 24.89/25.29 Inuse: 934
% 24.89/25.29 Deleted: 2397
% 24.89/25.29 Deletedinuse: 20
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29 Resimplifying inuse:
% 24.89/25.29 Done
% 24.89/25.29
% 24.89/25.29
% 24.89/25.29 Intermediate Status:
% 24.89/25.29 Generated: 171477
% 71.05/71.44 Kept: 53847
% 71.05/71.44 Inuse: 959
% 71.05/71.44 Deleted: 2397
% 71.05/71.44 Deletedinuse: 20
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 177374
% 71.05/71.44 Kept: 55988
% 71.05/71.44 Inuse: 989
% 71.05/71.44 Deleted: 2397
% 71.05/71.44 Deletedinuse: 20
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 *** allocated 1946160 integers for termspace/termends
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 182173
% 71.05/71.44 Kept: 58167
% 71.05/71.44 Inuse: 1013
% 71.05/71.44 Deleted: 2397
% 71.05/71.44 Deletedinuse: 20
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 187827
% 71.05/71.44 Kept: 60324
% 71.05/71.44 Inuse: 1054
% 71.05/71.44 Deleted: 2397
% 71.05/71.44 Deletedinuse: 20
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying clauses:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 193000
% 71.05/71.44 Kept: 62351
% 71.05/71.44 Inuse: 1092
% 71.05/71.44 Deleted: 2678
% 71.05/71.44 Deletedinuse: 20
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 203288
% 71.05/71.44 Kept: 65334
% 71.05/71.44 Inuse: 1129
% 71.05/71.44 Deleted: 2678
% 71.05/71.44 Deletedinuse: 20
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 215382
% 71.05/71.44 Kept: 68985
% 71.05/71.44 Inuse: 1149
% 71.05/71.44 Deleted: 2678
% 71.05/71.44 Deletedinuse: 20
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 *** allocated 4378860 integers for clauses
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 225720
% 71.05/71.44 Kept: 71143
% 71.05/71.44 Inuse: 1159
% 71.05/71.44 Deleted: 2702
% 71.05/71.44 Deletedinuse: 24
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 234662
% 71.05/71.44 Kept: 74126
% 71.05/71.44 Inuse: 1166
% 71.05/71.44 Deleted: 2730
% 71.05/71.44 Deletedinuse: 24
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 241201
% 71.05/71.44 Kept: 76169
% 71.05/71.44 Inuse: 1172
% 71.05/71.44 Deleted: 2754
% 71.05/71.44 Deletedinuse: 24
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 247160
% 71.05/71.44 Kept: 78208
% 71.05/71.44 Inuse: 1178
% 71.05/71.44 Deleted: 2773
% 71.05/71.44 Deletedinuse: 24
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 255282
% 71.05/71.44 Kept: 80923
% 71.05/71.44 Inuse: 1202
% 71.05/71.44 Deleted: 2776
% 71.05/71.44 Deletedinuse: 26
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying clauses:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 *** allocated 2919240 integers for termspace/termends
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 266059
% 71.05/71.44 Kept: 83882
% 71.05/71.44 Inuse: 1227
% 71.05/71.44 Deleted: 3169
% 71.05/71.44 Deletedinuse: 27
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 269579
% 71.05/71.44 Kept: 86041
% 71.05/71.44 Inuse: 1230
% 71.05/71.44 Deleted: 3169
% 71.05/71.44 Deletedinuse: 27
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 278005
% 71.05/71.44 Kept: 88444
% 71.05/71.44 Inuse: 1242
% 71.05/71.44 Deleted: 3169
% 71.05/71.44 Deletedinuse: 27
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 284007
% 71.05/71.44 Kept: 90476
% 71.05/71.44 Inuse: 1276
% 71.05/71.44 Deleted: 3169
% 71.05/71.44 Deletedinuse: 27
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 294234
% 71.05/71.44 Kept: 93646
% 71.05/71.44 Inuse: 1292
% 71.05/71.44 Deleted: 3169
% 71.05/71.44 Deletedinuse: 27
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 301837
% 71.05/71.44 Kept: 95677
% 71.05/71.44 Inuse: 1323
% 71.05/71.44 Deleted: 3169
% 71.05/71.44 Deletedinuse: 27
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 313595
% 71.05/71.44 Kept: 98984
% 71.05/71.44 Inuse: 1343
% 71.05/71.44 Deleted: 3175
% 71.05/71.44 Deletedinuse: 29
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 324069
% 71.05/71.44 Kept: 101963
% 71.05/71.44 Inuse: 1353
% 71.05/71.44 Deleted: 3175
% 71.05/71.44 Deletedinuse: 29
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying clauses:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 337039
% 71.05/71.44 Kept: 104155
% 71.05/71.44 Inuse: 1368
% 71.05/71.44 Deleted: 3862
% 71.05/71.44 Deletedinuse: 29
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 349427
% 71.05/71.44 Kept: 106255
% 71.05/71.44 Inuse: 1383
% 71.05/71.44 Deleted: 3862
% 71.05/71.44 Deletedinuse: 29
% 71.05/71.44
% 71.05/71.44 *** allocated 6568290 integers for clauses
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 360578
% 71.05/71.44 Kept: 108311
% 71.05/71.44 Inuse: 1403
% 71.05/71.44 Deleted: 3862
% 71.05/71.44 Deletedinuse: 29
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44 Resimplifying inuse:
% 71.05/71.44 Done
% 71.05/71.44
% 71.05/71.44
% 71.05/71.44 Intermediate Status:
% 71.05/71.44 Generated: 369729
% 71.05/71.44 Kept: 111431
% 191.52/191.96 Inuse: 1432
% 191.52/191.96 Deleted: 3862
% 191.52/191.96 Deletedinuse: 29
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 377800
% 191.52/191.96 Kept: 113465
% 191.52/191.96 Inuse: 1463
% 191.52/191.96 Deleted: 3862
% 191.52/191.96 Deletedinuse: 29
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 382657
% 191.52/191.96 Kept: 115713
% 191.52/191.96 Inuse: 1468
% 191.52/191.96 Deleted: 3862
% 191.52/191.96 Deletedinuse: 29
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 386849
% 191.52/191.96 Kept: 117986
% 191.52/191.96 Inuse: 1473
% 191.52/191.96 Deleted: 3865
% 191.52/191.96 Deletedinuse: 32
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 391786
% 191.52/191.96 Kept: 120435
% 191.52/191.96 Inuse: 1478
% 191.52/191.96 Deleted: 3865
% 191.52/191.96 Deletedinuse: 32
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying clauses:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 400022
% 191.52/191.96 Kept: 122493
% 191.52/191.96 Inuse: 1508
% 191.52/191.96 Deleted: 5105
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 *** allocated 4378860 integers for termspace/termends
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 408835
% 191.52/191.96 Kept: 125037
% 191.52/191.96 Inuse: 1543
% 191.52/191.96 Deleted: 5105
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 416194
% 191.52/191.96 Kept: 127237
% 191.52/191.96 Inuse: 1588
% 191.52/191.96 Deleted: 5105
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 427883
% 191.52/191.96 Kept: 129952
% 191.52/191.96 Inuse: 1618
% 191.52/191.96 Deleted: 5105
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 438273
% 191.52/191.96 Kept: 132060
% 191.52/191.96 Inuse: 1638
% 191.52/191.96 Deleted: 5105
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 445303
% 191.52/191.96 Kept: 134107
% 191.52/191.96 Inuse: 1668
% 191.52/191.96 Deleted: 5105
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 452352
% 191.52/191.96 Kept: 136368
% 191.52/191.96 Inuse: 1703
% 191.52/191.96 Deleted: 5105
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 459499
% 191.52/191.96 Kept: 138581
% 191.52/191.96 Inuse: 1738
% 191.52/191.96 Deleted: 5105
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 471329
% 191.52/191.96 Kept: 140597
% 191.52/191.96 Inuse: 1754
% 191.52/191.96 Deleted: 5105
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying clauses:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 486651
% 191.52/191.96 Kept: 144699
% 191.52/191.96 Inuse: 1783
% 191.52/191.96 Deleted: 5346
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 494923
% 191.52/191.96 Kept: 146790
% 191.52/191.96 Inuse: 1803
% 191.52/191.96 Deleted: 5346
% 191.52/191.96 Deletedinuse: 33
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 509548
% 191.52/191.96 Kept: 151100
% 191.52/191.96 Inuse: 1848
% 191.52/191.96 Deleted: 5347
% 191.52/191.96 Deletedinuse: 34
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 517348
% 191.52/191.96 Kept: 155887
% 191.52/191.96 Inuse: 1850
% 191.52/191.96 Deleted: 5347
% 191.52/191.96 Deletedinuse: 34
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 528992
% 191.52/191.96 Kept: 159517
% 191.52/191.96 Inuse: 1868
% 191.52/191.96 Deleted: 5347
% 191.52/191.96 Deletedinuse: 34
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 *** allocated 9852435 integers for clauses
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 535417
% 191.52/191.96 Kept: 161766
% 191.52/191.96 Inuse: 1888
% 191.52/191.96 Deleted: 5347
% 191.52/191.96 Deletedinuse: 34
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying clauses:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 549087
% 191.52/191.96 Kept: 164059
% 191.52/191.96 Inuse: 1903
% 191.52/191.96 Deleted: 5613
% 191.52/191.96 Deletedinuse: 34
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 553604
% 191.52/191.96 Kept: 166060
% 191.52/191.96 Inuse: 1929
% 191.52/191.96 Deleted: 5613
% 191.52/191.96 Deletedinuse: 34
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 558020
% 191.52/191.96 Kept: 168188
% 191.52/191.96 Inuse: 1958
% 191.52/191.96 Deleted: 5614
% 191.52/191.96 Deletedinuse: 35
% 191.52/191.96
% 191.52/191.96 *** allocated 6568290 integers for termspace/termends
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96 Resimplifying inuse:
% 191.52/191.96 Done
% 191.52/191.96
% 191.52/191.96
% 191.52/191.96 Intermediate Status:
% 191.52/191.96 Generated: 562838
% 191.52/191.96 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------