TSTP Solution File: ITP385_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP385_1 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.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 : 300s
% DateTime : Mon May 20 23:10:14 EDT 2024
% Result : CounterSatisfiable 28.54s 4.51s
% Output : FiniteModel 28.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP385_1 : TPTP v8.2.0. Released v8.0.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35 % Computer : n016.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat May 18 17:32:52 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % (18153)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (18156)WARNING: value z3 for option sas not known
% 0.20/0.42 % (18155)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.42 % (18160)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.42 % (18158)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.42 % (18154)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.42 % (18157)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.42 % (18159)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.42 % (18156)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 3.89/0.99 TRYING [1]
% 4.84/1.07 TRYING [2]
% 10.19/1.87 TRYING [3]
% 10.78/1.96 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 10.78/1.98 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1]
% 11.18/2.00 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1]
% 11.18/2.02 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,2,1,1,1,1]
% 11.18/2.05 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,2,2,1,1,1,1]
% 11.80/2.08 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,2,1,1,1,2,2,1,1,1,1]
% 11.80/2.11 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,2,1,1,1,2,2,1,1,1,1]
% 12.31/2.14 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,4,2,1,1,1,2,2,1,1,1,1]
% 12.31/2.18 TRYING [1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,4,2,1,1,1,2,2,1,1,1,1]
% 12.31/2.22 TRYING [1,1,1,1,1,1,1,1,1,2,2,1,1,2,1,1,4,2,1,1,1,2,2,1,1,1,1]
% 12.88/2.26 TRYING [1,1,1,1,1,1,1,1,1,3,2,1,1,2,1,1,4,2,1,1,1,2,2,1,1,1,1]
% 13.36/2.30 TRYING [1,1,1,1,1,1,1,1,1,2,2,1,1,2,1,2,4,2,1,1,1,2,2,1,1,1,1]
% 13.36/2.35 TRYING [1,1,1,1,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,1,1,2,2,1,1,1,1]
% 14.01/2.40 TRYING [1,1,1,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,1,1,2,2,1,1,1,1]
% 14.28/2.44 TRYING [1,1,2,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,1,1,2,2,1,1,1,1]
% 14.28/2.49 TRYING [1,1,3,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,1,1,2,2,1,1,1,1]
% 14.85/2.54 TRYING [1,1,4,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,1,1,2,2,1,1,1,1]
% 15.36/2.59 TRYING [1,1,3,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,2,1,2,2,1,1,1,1]
% 15.36/2.64 TRYING [1,2,3,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,2,1,2,2,1,1,1,1]
% 16.10/2.70 TRYING [1,1,5,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,1,1,2,2,1,1,1,1]
% 16.33/2.76 TRYING [1,1,4,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,2,1,2,2,1,1,1,1]
% 16.33/2.81 TRYING [1,2,4,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,2,1,2,2,1,1,1,1]
% 17.03/2.87 TRYING [1,1,6,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,1,1,2,2,1,1,1,1]
% 17.59/2.93 TRYING [1,1,5,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,2,1,2,2,1,1,1,1]
% 17.59/2.98 TRYING [1,2,5,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,2,1,2,2,1,1,1,1]
% 18.23/3.05 TRYING [1,2,3,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,3,1,2,2,1,1,1,1]
% 19.04/3.11 TRYING [1,2,4,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,3,1,2,2,1,1,1,1]
% 19.04/3.17 TRYING [2,2,4,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,3,1,2,2,1,1,1,1]
% 20.33/3.32 TRYING [3,2,4,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,3,1,2,2,1,1,1,1]
% 21.95/3.53 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 22.43/3.60 TRYING [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1]
% 22.43/3.60 TRYING [2,2,4,2,1,1,1,3,1,2,2,1,1,2,1,2,4,2,1,3,1,2,2,1,1,1,1]
% 23.21/3.72 TRYING [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,2,2,1,1,1,1]
% 23.37/3.75 TRYING [3,2,4,2,1,1,1,3,1,2,2,1,1,2,1,2,4,2,1,3,1,2,2,1,1,1,1]
% 24.02/3.86 TRYING [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,2,1,1,1,2,2,1,1,1,1]
% 25.22/4.00 TRYING [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,2,1,1,1,2,2,1,1,1,1]
% 25.45/4.04 TRYING [4,2,4,2,1,1,1,2,1,2,2,1,1,2,1,2,4,2,1,3,1,2,2,1,1,1,1]
% 26.13/4.15 TRYING [2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,4,2,1,1,1,2,2,1,1,1,1]
% 27.20/4.32 TRYING [2,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,4,2,1,1,1,2,2,1,1,1,1]
% 28.54/4.47 TRYING [2,1,1,1,1,1,1,1,1,2,1,2,1,2,1,1,4,2,1,1,1,2,2,1,1,1,1]
% 28.54/4.51 Finite Model Found!
% 28.54/4.51 % SZS status CounterSatisfiable for theBenchmark
% 28.54/4.53 % (18157)First to succeed.
% 28.54/4.54 % (18157)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18153"
% 28.54/4.54 % SZS output start FiniteModel for theBenchmark
% 28.54/4.54 tff(declare_$i,type,$i:$tType).
% 28.54/4.54 tff(declare_$i1,type,fmb_$i_1:$i).
% 28.54/4.54 tff(finite_domain,axiom,
% 28.54/4.54 ! [X:$i] : (
% 28.54/4.54 X = fmb_$i_1
% 28.54/4.54 ) ).
% 28.54/4.54
% 28.54/4.54 tff(declare_bool,type,$o:$tType).
% 28.54/4.54 tff(declare_bool1,type,fmb_bool_1:$o).
% 28.54/4.54 tff(finite_domain,axiom,
% 28.54/4.54 ! [X:$o] : (
% 28.54/4.54 X = fmb_bool_1
% 28.54/4.54 ) ).
% 28.54/4.54
% 28.54/4.54 tff('declare_B_b_option_fun_b_option_fun$',type,'B_b_option_fun_b_option_fun$':$tType).
% 28.54/4.54 tff('declare_B_b_option_fun_b_option_fun$1',type,fmb_'B_b_option_fun_b_option_fun$'_1:'B_b_option_fun_b_option_fun$').
% 28.54/4.54 tff('declare_B_b_option_fun_b_option_fun$2',type,fmb_'B_b_option_fun_b_option_fun$'_2:'B_b_option_fun_b_option_fun$').
% 28.54/4.54 tff('declare_B_b_option_fun_b_option_fun$3',type,fmb_'B_b_option_fun_b_option_fun$'_3:'B_b_option_fun_b_option_fun$').
% 28.54/4.54 tff('declare_B_b_option_fun_b_option_fun$4',type,fmb_'B_b_option_fun_b_option_fun$'_4:'B_b_option_fun_b_option_fun$').
% 28.54/4.54 tff(finite_domain,axiom,
% 28.54/4.54 ! [X:'B_b_option_fun_b_option_fun$'] : (
% 28.54/4.54 X = fmb_'B_b_option_fun_b_option_fun$'_1 | X = fmb_'B_b_option_fun_b_option_fun$'_2 | X = fmb_'B_b_option_fun_b_option_fun$'_3 | X = fmb_'B_b_option_fun_b_option_fun$'_4
% 28.54/4.54 ) ).
% 28.54/4.54
% 28.54/4.54 tff(distinct_domain,axiom,
% 28.54/4.54 fmb_'B_b_option_fun_b_option_fun$'_1 != fmb_'B_b_option_fun_b_option_fun$'_2 & fmb_'B_b_option_fun_b_option_fun$'_1 != fmb_'B_b_option_fun_b_option_fun$'_3 & fmb_'B_b_option_fun_b_option_fun$'_1 != fmb_'B_b_option_fun_b_option_fun$'_4 & fmb_'B_b_option_fun_b_option_fun$'_2 != fmb_'B_b_option_fun_b_option_fun$'_3 & fmb_'B_b_option_fun_b_option_fun$'_2 != fmb_'B_b_option_fun_b_option_fun$'_4 &
% 28.54/4.54 fmb_'B_b_option_fun_b_option_fun$'_3 != fmb_'B_b_option_fun_b_option_fun$'_4
% 28.54/4.54 ).
% 28.54/4.54
% 28.54/4.54 tff('declare_A_a_prod_set$',type,'A_a_prod_set$':$tType).
% 28.54/4.54 tff('declare_A_a_prod_set$1',type,'bot$f':'A_a_prod_set$').
% 28.54/4.54 tff('declare_A_a_prod_set$2',type,fmb_'A_a_prod_set$'_2:'A_a_prod_set$').
% 28.54/4.54 tff('declare_A_a_prod_set$3',type,fmb_'A_a_prod_set$'_3:'A_a_prod_set$').
% 28.54/4.54 tff('declare_A_a_prod_set$4',type,fmb_'A_a_prod_set$'_4:'A_a_prod_set$').
% 28.54/4.54 tff(finite_domain,axiom,
% 28.54/4.54 ! [X:'A_a_prod_set$'] : (
% 28.54/4.54 X = 'bot$f' | X = fmb_'A_a_prod_set$'_2 | X = fmb_'A_a_prod_set$'_3 | X = fmb_'A_a_prod_set$'_4
% 28.54/4.54 ) ).
% 28.54/4.54
% 28.54/4.54 tff(distinct_domain,axiom,
% 28.54/4.54 'bot$f' != fmb_'A_a_prod_set$'_2 & 'bot$f' != fmb_'A_a_prod_set$'_3 & 'bot$f' != fmb_'A_a_prod_set$'_4 & fmb_'A_a_prod_set$'_2 != fmb_'A_a_prod_set$'_3 & fmb_'A_a_prod_set$'_2 != fmb_'A_a_prod_set$'_4 &
% 28.54/4.54 fmb_'A_a_prod_set$'_3 != fmb_'A_a_prod_set$'_4
% 28.54/4.54 ).
% 28.54/4.54
% 28.54/4.54 tff('declare_B_d_prod$',type,'B_d_prod$':$tType).
% 28.54/4.54 tff('declare_B_d_prod$1',type,fmb_'B_d_prod$'_1:'B_d_prod$').
% 28.54/4.54 tff('declare_B_d_prod$2',type,fmb_'B_d_prod$'_2:'B_d_prod$').
% 28.54/4.54 tff('declare_B_d_prod$3',type,fmb_'B_d_prod$'_3:'B_d_prod$').
% 28.54/4.54 tff('declare_B_d_prod$4',type,fmb_'B_d_prod$'_4:'B_d_prod$').
% 28.54/4.54 tff(finite_domain,axiom,
% 28.54/4.54 ! [X:'B_d_prod$'] : (
% 28.54/4.54 X = fmb_'B_d_prod$'_1 | X = fmb_'B_d_prod$'_2 | X = fmb_'B_d_prod$'_3 | X = fmb_'B_d_prod$'_4
% 28.54/4.54 ) ).
% 28.54/4.54
% 28.54/4.54 tff(distinct_domain,axiom,
% 28.54/4.54 fmb_'B_d_prod$'_1 != fmb_'B_d_prod$'_2 & fmb_'B_d_prod$'_1 != fmb_'B_d_prod$'_3 & fmb_'B_d_prod$'_1 != fmb_'B_d_prod$'_4 & fmb_'B_d_prod$'_2 != fmb_'B_d_prod$'_3 & fmb_'B_d_prod$'_2 != fmb_'B_d_prod$'_4 &
% 28.54/4.54 fmb_'B_d_prod$'_3 != fmb_'B_d_prod$'_4
% 28.54/4.54 ).
% 28.54/4.54
% 28.54/4.54 tff('declare_D_bool_fun$',type,'D_bool_fun$':$tType).
% 28.54/4.54 tff('declare_D_bool_fun$1',type,'bot$p':'D_bool_fun$').
% 28.54/4.54 tff('declare_D_bool_fun$2',type,fmb_'D_bool_fun$'_2:'D_bool_fun$').
% 28.54/4.54 tff('declare_D_bool_fun$3',type,fmb_'D_bool_fun$'_3:'D_bool_fun$').
% 28.54/4.54 tff('declare_D_bool_fun$4',type,fmb_'D_bool_fun$'_4:'D_bool_fun$').
% 28.54/4.54 tff(finite_domain,axiom,
% 28.54/4.54 ! [X:'D_bool_fun$'] : (
% 28.54/4.54 X = 'bot$p' | X = fmb_'D_bool_fun$'_2 | X = fmb_'D_bool_fun$'_3 | X = fmb_'D_bool_fun$'_4
% 28.54/4.54 ) ).
% 28.54/4.54
% 28.54/4.54 tff(distinct_domain,axiom,
% 28.54/4.54 'bot$p' != fmb_'D_bool_fun$'_2 & 'bot$p' != fmb_'D_bool_fun$'_3 & 'bot$p' != fmb_'D_bool_fun$'_4 & fmb_'D_bool_fun$'_2 != fmb_'D_bool_fun$'_3 & fmb_'D_bool_fun$'_2 != fmb_'D_bool_fun$'_4 &
% 28.54/4.54 fmb_'D_bool_fun$'_3 != fmb_'D_bool_fun$'_4
% 28.54/4.54 ).
% 28.54/4.54
% 28.54/4.54 tff('declare_D_d_prod_set$',type,'D_d_prod_set$':$tType).
% 28.54/4.54 tff('declare_D_d_prod_set$1',type,fmb_'D_d_prod_set$'_1:'D_d_prod_set$').
% 28.54/4.54 tff('declare_D_d_prod_set$2',type,fmb_'D_d_prod_set$'_2:'D_d_prod_set$').
% 28.54/4.54 tff('declare_D_d_prod_set$3',type,fmb_'D_d_prod_set$'_3:'D_d_prod_set$').
% 28.54/4.54 tff('declare_D_d_prod_set$4',type,fmb_'D_d_prod_set$'_4:'D_d_prod_set$').
% 28.54/4.54 tff(finite_domain,axiom,
% 28.54/4.54 ! [X:'D_d_prod_set$'] : (
% 28.54/4.54 X = fmb_'D_d_prod_set$'_1 | X = fmb_'D_d_prod_set$'_2 | X = fmb_'D_d_prod_set$'_3 | X = fmb_'D_d_prod_set$'_4
% 28.54/4.54 ) ).
% 28.54/4.54
% 28.54/4.54 tff(distinct_domain,axiom,
% 28.54/4.54 fmb_'D_d_prod_set$'_1 != fmb_'D_d_prod_set$'_2 & fmb_'D_d_prod_set$'_1 != fmb_'D_d_prod_set$'_3 & fmb_'D_d_prod_set$'_1 != fmb_'D_d_prod_set$'_4 & fmb_'D_d_prod_set$'_2 != fmb_'D_d_prod_set$'_3 & fmb_'D_d_prod_set$'_2 != fmb_'D_d_prod_set$'_4 &
% 28.54/4.54 fmb_'D_d_prod_set$'_3 != fmb_'D_d_prod_set$'_4
% 28.54/4.54 ).
% 28.54/4.54
% 28.54/4.54 tff('declare_B_c_prod$',type,'B_c_prod$':$tType).
% 28.54/4.54 tff('declare_B_c_prod$1',type,fmb_'B_c_prod$'_1:'B_c_prod$').
% 28.54/4.54 tff('declare_B_c_prod$2',type,fmb_'B_c_prod$'_2:'B_c_prod$').
% 28.54/4.54 tff('declare_B_c_prod$3',type,fmb_'B_c_prod$'_3:'B_c_prod$').
% 28.54/4.55 tff('declare_B_c_prod$4',type,fmb_'B_c_prod$'_4:'B_c_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_c_prod$'] : (
% 28.54/4.55 X = fmb_'B_c_prod$'_1 | X = fmb_'B_c_prod$'_2 | X = fmb_'B_c_prod$'_3 | X = fmb_'B_c_prod$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_c_prod$'_1 != fmb_'B_c_prod$'_2 & fmb_'B_c_prod$'_1 != fmb_'B_c_prod$'_3 & fmb_'B_c_prod$'_1 != fmb_'B_c_prod$'_4 & fmb_'B_c_prod$'_2 != fmb_'B_c_prod$'_3 & fmb_'B_c_prod$'_2 != fmb_'B_c_prod$'_4 &
% 28.54/4.55 fmb_'B_c_prod$'_3 != fmb_'B_c_prod$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_a_prod$',type,'A_a_prod$':$tType).
% 28.54/4.55 tff('declare_A_a_prod$1',type,fmb_'A_a_prod$'_1:'A_a_prod$').
% 28.54/4.55 tff('declare_A_a_prod$2',type,fmb_'A_a_prod$'_2:'A_a_prod$').
% 28.54/4.55 tff('declare_A_a_prod$3',type,fmb_'A_a_prod$'_3:'A_a_prod$').
% 28.54/4.55 tff('declare_A_a_prod$4',type,fmb_'A_a_prod$'_4:'A_a_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_a_prod$'] : (
% 28.54/4.55 X = fmb_'A_a_prod$'_1 | X = fmb_'A_a_prod$'_2 | X = fmb_'A_a_prod$'_3 | X = fmb_'A_a_prod$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'A_a_prod$'_1 != fmb_'A_a_prod$'_2 & fmb_'A_a_prod$'_1 != fmb_'A_a_prod$'_3 & fmb_'A_a_prod$'_1 != fmb_'A_a_prod$'_4 & fmb_'A_a_prod$'_2 != fmb_'A_a_prod$'_3 & fmb_'A_a_prod$'_2 != fmb_'A_a_prod$'_4 &
% 28.54/4.55 fmb_'A_a_prod$'_3 != fmb_'A_a_prod$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_c_option_fun$',type,'C_c_option_fun$':$tType).
% 28.54/4.55 tff('declare_C_c_option_fun$1',type,'some$a':'C_c_option_fun$').
% 28.54/4.55 tff('declare_C_c_option_fun$2',type,fmb_'C_c_option_fun$'_2:'C_c_option_fun$').
% 28.54/4.55 tff('declare_C_c_option_fun$3',type,fmb_'C_c_option_fun$'_3:'C_c_option_fun$').
% 28.54/4.55 tff('declare_C_c_option_fun$4',type,fmb_'C_c_option_fun$'_4:'C_c_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_c_option_fun$'] : (
% 28.54/4.55 X = 'some$a' | X = fmb_'C_c_option_fun$'_2 | X = fmb_'C_c_option_fun$'_3 | X = fmb_'C_c_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'some$a' != fmb_'C_c_option_fun$'_2 & 'some$a' != fmb_'C_c_option_fun$'_3 & 'some$a' != fmb_'C_c_option_fun$'_4 & fmb_'C_c_option_fun$'_2 != fmb_'C_c_option_fun$'_3 & fmb_'C_c_option_fun$'_2 != fmb_'C_c_option_fun$'_4 &
% 28.54/4.55 fmb_'C_c_option_fun$'_3 != fmb_'C_c_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_option$',type,'C_option$':$tType).
% 28.54/4.55 tff('declare_C_option$1',type,'none$a':'C_option$').
% 28.54/4.55 tff('declare_C_option$2',type,fmb_'C_option$'_2:'C_option$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_option$'] : (
% 28.54/4.55 X = 'none$a' | X = fmb_'C_option$'_2
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'none$a' != fmb_'C_option$'_2
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_option$',type,'B_option$':$tType).
% 28.54/4.55 tff('declare_B_option$1',type,'none$c':'B_option$').
% 28.54/4.55 tff('declare_B_option$2',type,fmb_'B_option$'_2:'B_option$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_option$'] : (
% 28.54/4.55 X = 'none$c' | X = fmb_'B_option$'_2
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'none$c' != fmb_'B_option$'_2
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_d_fun$',type,'D_d_fun$':$tType).
% 28.54/4.55 tff('declare_D_d_fun$1',type,fmb_'D_d_fun$'_1:'D_d_fun$').
% 28.54/4.55 tff('declare_D_d_fun$2',type,fmb_'D_d_fun$'_2:'D_d_fun$').
% 28.54/4.55 tff('declare_D_d_fun$3',type,fmb_'D_d_fun$'_3:'D_d_fun$').
% 28.54/4.55 tff('declare_D_d_fun$4',type,fmb_'D_d_fun$'_4:'D_d_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_d_fun$'] : (
% 28.54/4.55 X = fmb_'D_d_fun$'_1 | X = fmb_'D_d_fun$'_2 | X = fmb_'D_d_fun$'_3 | X = fmb_'D_d_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_d_fun$'_1 != fmb_'D_d_fun$'_2 & fmb_'D_d_fun$'_1 != fmb_'D_d_fun$'_3 & fmb_'D_d_fun$'_1 != fmb_'D_d_fun$'_4 & fmb_'D_d_fun$'_2 != fmb_'D_d_fun$'_3 & fmb_'D_d_fun$'_2 != fmb_'D_d_fun$'_4 &
% 28.54/4.55 fmb_'D_d_fun$'_3 != fmb_'D_d_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_option_c_option_bool_fun_fun$',type,'B_option_c_option_bool_fun_fun$':$tType).
% 28.54/4.55 tff('declare_B_option_c_option_bool_fun_fun$1',type,fmb_'B_option_c_option_bool_fun_fun$'_1:'B_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_B_option_c_option_bool_fun_fun$2',type,fmb_'B_option_c_option_bool_fun_fun$'_2:'B_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_B_option_c_option_bool_fun_fun$3',type,fmb_'B_option_c_option_bool_fun_fun$'_3:'B_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_B_option_c_option_bool_fun_fun$4',type,fmb_'B_option_c_option_bool_fun_fun$'_4:'B_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_option_c_option_bool_fun_fun$'] : (
% 28.54/4.55 X = fmb_'B_option_c_option_bool_fun_fun$'_1 | X = fmb_'B_option_c_option_bool_fun_fun$'_2 | X = fmb_'B_option_c_option_bool_fun_fun$'_3 | X = fmb_'B_option_c_option_bool_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_option_c_option_bool_fun_fun$'_1 != fmb_'B_option_c_option_bool_fun_fun$'_2 & fmb_'B_option_c_option_bool_fun_fun$'_1 != fmb_'B_option_c_option_bool_fun_fun$'_3 & fmb_'B_option_c_option_bool_fun_fun$'_1 != fmb_'B_option_c_option_bool_fun_fun$'_4 & fmb_'B_option_c_option_bool_fun_fun$'_2 != fmb_'B_option_c_option_bool_fun_fun$'_3 & fmb_'B_option_c_option_bool_fun_fun$'_2 != fmb_'B_option_c_option_bool_fun_fun$'_4 &
% 28.54/4.55 fmb_'B_option_c_option_bool_fun_fun$'_3 != fmb_'B_option_c_option_bool_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_d_option_fun$',type,'B_d_option_fun$':$tType).
% 28.54/4.55 tff('declare_B_d_option_fun$1',type,fmb_'B_d_option_fun$'_1:'B_d_option_fun$').
% 28.54/4.55 tff('declare_B_d_option_fun$2',type,fmb_'B_d_option_fun$'_2:'B_d_option_fun$').
% 28.54/4.55 tff('declare_B_d_option_fun$3',type,fmb_'B_d_option_fun$'_3:'B_d_option_fun$').
% 28.54/4.55 tff('declare_B_d_option_fun$4',type,fmb_'B_d_option_fun$'_4:'B_d_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_d_option_fun$'] : (
% 28.54/4.55 X = fmb_'B_d_option_fun$'_1 | X = fmb_'B_d_option_fun$'_2 | X = fmb_'B_d_option_fun$'_3 | X = fmb_'B_d_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_d_option_fun$'_1 != fmb_'B_d_option_fun$'_2 & fmb_'B_d_option_fun$'_1 != fmb_'B_d_option_fun$'_3 & fmb_'B_d_option_fun$'_1 != fmb_'B_d_option_fun$'_4 & fmb_'B_d_option_fun$'_2 != fmb_'B_d_option_fun$'_3 & fmb_'B_d_option_fun$'_2 != fmb_'B_d_option_fun$'_4 &
% 28.54/4.55 fmb_'B_d_option_fun$'_3 != fmb_'B_d_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_c_prod$',type,'C_c_prod$':$tType).
% 28.54/4.55 tff('declare_C_c_prod$1',type,fmb_'C_c_prod$'_1:'C_c_prod$').
% 28.54/4.55 tff('declare_C_c_prod$2',type,fmb_'C_c_prod$'_2:'C_c_prod$').
% 28.54/4.55 tff('declare_C_c_prod$3',type,fmb_'C_c_prod$'_3:'C_c_prod$').
% 28.54/4.55 tff('declare_C_c_prod$4',type,fmb_'C_c_prod$'_4:'C_c_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_c_prod$'] : (
% 28.54/4.55 X = fmb_'C_c_prod$'_1 | X = fmb_'C_c_prod$'_2 | X = fmb_'C_c_prod$'_3 | X = fmb_'C_c_prod$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_c_prod$'_1 != fmb_'C_c_prod$'_2 & fmb_'C_c_prod$'_1 != fmb_'C_c_prod$'_3 & fmb_'C_c_prod$'_1 != fmb_'C_c_prod$'_4 & fmb_'C_c_prod$'_2 != fmb_'C_c_prod$'_3 & fmb_'C_c_prod$'_2 != fmb_'C_c_prod$'_4 &
% 28.54/4.55 fmb_'C_c_prod$'_3 != fmb_'C_c_prod$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_d_prod_set$',type,'A_d_prod_set$':$tType).
% 28.54/4.55 tff('declare_A_d_prod_set$1',type,'bot$g':'A_d_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_d_prod_set$'] : (
% 28.54/4.55 X = 'bot$g'
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_a_prod_set$',type,'C_a_prod_set$':$tType).
% 28.54/4.55 tff('declare_C_a_prod_set$1',type,fmb_'C_a_prod_set$'_1:'C_a_prod_set$').
% 28.54/4.55 tff('declare_C_a_prod_set$2',type,fmb_'C_a_prod_set$'_2:'C_a_prod_set$').
% 28.54/4.55 tff('declare_C_a_prod_set$3',type,fmb_'C_a_prod_set$'_3:'C_a_prod_set$').
% 28.54/4.55 tff('declare_C_a_prod_set$4',type,fmb_'C_a_prod_set$'_4:'C_a_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_a_prod_set$'] : (
% 28.54/4.55 X = fmb_'C_a_prod_set$'_1 | X = fmb_'C_a_prod_set$'_2 | X = fmb_'C_a_prod_set$'_3 | X = fmb_'C_a_prod_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_a_prod_set$'_1 != fmb_'C_a_prod_set$'_2 & fmb_'C_a_prod_set$'_1 != fmb_'C_a_prod_set$'_3 & fmb_'C_a_prod_set$'_1 != fmb_'C_a_prod_set$'_4 & fmb_'C_a_prod_set$'_2 != fmb_'C_a_prod_set$'_3 & fmb_'C_a_prod_set$'_2 != fmb_'C_a_prod_set$'_4 &
% 28.54/4.55 fmb_'C_a_prod_set$'_3 != fmb_'C_a_prod_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_b_fun$',type,'B_b_fun$':$tType).
% 28.54/4.55 tff('declare_B_b_fun$1',type,fmb_'B_b_fun$'_1:'B_b_fun$').
% 28.54/4.55 tff('declare_B_b_fun$2',type,fmb_'B_b_fun$'_2:'B_b_fun$').
% 28.54/4.55 tff('declare_B_b_fun$3',type,fmb_'B_b_fun$'_3:'B_b_fun$').
% 28.54/4.55 tff('declare_B_b_fun$4',type,fmb_'B_b_fun$'_4:'B_b_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_b_fun$'] : (
% 28.54/4.55 X = fmb_'B_b_fun$'_1 | X = fmb_'B_b_fun$'_2 | X = fmb_'B_b_fun$'_3 | X = fmb_'B_b_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_b_fun$'_1 != fmb_'B_b_fun$'_2 & fmb_'B_b_fun$'_1 != fmb_'B_b_fun$'_3 & fmb_'B_b_fun$'_1 != fmb_'B_b_fun$'_4 & fmb_'B_b_fun$'_2 != fmb_'B_b_fun$'_3 & fmb_'B_b_fun$'_2 != fmb_'B_b_fun$'_4 &
% 28.54/4.55 fmb_'B_b_fun$'_3 != fmb_'B_b_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_c_c_fun_fun$',type,'C_c_c_fun_fun$':$tType).
% 28.54/4.55 tff('declare_C_c_c_fun_fun$1',type,fmb_'C_c_c_fun_fun$'_1:'C_c_c_fun_fun$').
% 28.54/4.55 tff('declare_C_c_c_fun_fun$2',type,fmb_'C_c_c_fun_fun$'_2:'C_c_c_fun_fun$').
% 28.54/4.55 tff('declare_C_c_c_fun_fun$3',type,fmb_'C_c_c_fun_fun$'_3:'C_c_c_fun_fun$').
% 28.54/4.55 tff('declare_C_c_c_fun_fun$4',type,fmb_'C_c_c_fun_fun$'_4:'C_c_c_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_c_c_fun_fun$'] : (
% 28.54/4.55 X = fmb_'C_c_c_fun_fun$'_1 | X = fmb_'C_c_c_fun_fun$'_2 | X = fmb_'C_c_c_fun_fun$'_3 | X = fmb_'C_c_c_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_c_c_fun_fun$'_1 != fmb_'C_c_c_fun_fun$'_2 & fmb_'C_c_c_fun_fun$'_1 != fmb_'C_c_c_fun_fun$'_3 & fmb_'C_c_c_fun_fun$'_1 != fmb_'C_c_c_fun_fun$'_4 & fmb_'C_c_c_fun_fun$'_2 != fmb_'C_c_c_fun_fun$'_3 & fmb_'C_c_c_fun_fun$'_2 != fmb_'C_c_c_fun_fun$'_4 &
% 28.54/4.55 fmb_'C_c_c_fun_fun$'_3 != fmb_'C_c_c_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_c_fun$',type,'C_c_fun$':$tType).
% 28.54/4.55 tff('declare_C_c_fun$1',type,fmb_'C_c_fun$'_1:'C_c_fun$').
% 28.54/4.55 tff('declare_C_c_fun$2',type,fmb_'C_c_fun$'_2:'C_c_fun$').
% 28.54/4.55 tff('declare_C_c_fun$3',type,fmb_'C_c_fun$'_3:'C_c_fun$').
% 28.54/4.55 tff('declare_C_c_fun$4',type,fmb_'C_c_fun$'_4:'C_c_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_c_fun$'] : (
% 28.54/4.55 X = fmb_'C_c_fun$'_1 | X = fmb_'C_c_fun$'_2 | X = fmb_'C_c_fun$'_3 | X = fmb_'C_c_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_c_fun$'_1 != fmb_'C_c_fun$'_2 & fmb_'C_c_fun$'_1 != fmb_'C_c_fun$'_3 & fmb_'C_c_fun$'_1 != fmb_'C_c_fun$'_4 & fmb_'C_c_fun$'_2 != fmb_'C_c_fun$'_3 & fmb_'C_c_fun$'_2 != fmb_'C_c_fun$'_4 &
% 28.54/4.55 fmb_'C_c_fun$'_3 != fmb_'C_c_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_option_b_option_fun$',type,'B_option_b_option_fun$':$tType).
% 28.54/4.55 tff('declare_B_option_b_option_fun$1',type,fmb_'B_option_b_option_fun$'_1:'B_option_b_option_fun$').
% 28.54/4.55 tff('declare_B_option_b_option_fun$2',type,fmb_'B_option_b_option_fun$'_2:'B_option_b_option_fun$').
% 28.54/4.55 tff('declare_B_option_b_option_fun$3',type,fmb_'B_option_b_option_fun$'_3:'B_option_b_option_fun$').
% 28.54/4.55 tff('declare_B_option_b_option_fun$4',type,fmb_'B_option_b_option_fun$'_4:'B_option_b_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_option_b_option_fun$'] : (
% 28.54/4.55 X = fmb_'B_option_b_option_fun$'_1 | X = fmb_'B_option_b_option_fun$'_2 | X = fmb_'B_option_b_option_fun$'_3 | X = fmb_'B_option_b_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_option_b_option_fun$'_1 != fmb_'B_option_b_option_fun$'_2 & fmb_'B_option_b_option_fun$'_1 != fmb_'B_option_b_option_fun$'_3 & fmb_'B_option_b_option_fun$'_1 != fmb_'B_option_b_option_fun$'_4 & fmb_'B_option_b_option_fun$'_2 != fmb_'B_option_b_option_fun$'_3 & fmb_'B_option_b_option_fun$'_2 != fmb_'B_option_b_option_fun$'_4 &
% 28.54/4.55 fmb_'B_option_b_option_fun$'_3 != fmb_'B_option_b_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_c_option_fun$',type,'B_c_option_fun$':$tType).
% 28.54/4.55 tff('declare_B_c_option_fun$1',type,fmb_'B_c_option_fun$'_1:'B_c_option_fun$').
% 28.54/4.55 tff('declare_B_c_option_fun$2',type,fmb_'B_c_option_fun$'_2:'B_c_option_fun$').
% 28.54/4.55 tff('declare_B_c_option_fun$3',type,fmb_'B_c_option_fun$'_3:'B_c_option_fun$').
% 28.54/4.55 tff('declare_B_c_option_fun$4',type,fmb_'B_c_option_fun$'_4:'B_c_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_c_option_fun$'] : (
% 28.54/4.55 X = fmb_'B_c_option_fun$'_1 | X = fmb_'B_c_option_fun$'_2 | X = fmb_'B_c_option_fun$'_3 | X = fmb_'B_c_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_c_option_fun$'_1 != fmb_'B_c_option_fun$'_2 & fmb_'B_c_option_fun$'_1 != fmb_'B_c_option_fun$'_3 & fmb_'B_c_option_fun$'_1 != fmb_'B_c_option_fun$'_4 & fmb_'B_c_option_fun$'_2 != fmb_'B_c_option_fun$'_3 & fmb_'B_c_option_fun$'_2 != fmb_'B_c_option_fun$'_4 &
% 28.54/4.55 fmb_'B_c_option_fun$'_3 != fmb_'B_c_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_a_option_fun$',type,'C_a_option_fun$':$tType).
% 28.54/4.55 tff('declare_C_a_option_fun$1',type,fmb_'C_a_option_fun$'_1:'C_a_option_fun$').
% 28.54/4.55 tff('declare_C_a_option_fun$2',type,fmb_'C_a_option_fun$'_2:'C_a_option_fun$').
% 28.54/4.55 tff('declare_C_a_option_fun$3',type,fmb_'C_a_option_fun$'_3:'C_a_option_fun$').
% 28.54/4.55 tff('declare_C_a_option_fun$4',type,fmb_'C_a_option_fun$'_4:'C_a_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_a_option_fun$'] : (
% 28.54/4.55 X = fmb_'C_a_option_fun$'_1 | X = fmb_'C_a_option_fun$'_2 | X = fmb_'C_a_option_fun$'_3 | X = fmb_'C_a_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_a_option_fun$'_1 != fmb_'C_a_option_fun$'_2 & fmb_'C_a_option_fun$'_1 != fmb_'C_a_option_fun$'_3 & fmb_'C_a_option_fun$'_1 != fmb_'C_a_option_fun$'_4 & fmb_'C_a_option_fun$'_2 != fmb_'C_a_option_fun$'_3 & fmb_'C_a_option_fun$'_2 != fmb_'C_a_option_fun$'_4 &
% 28.54/4.55 fmb_'C_a_option_fun$'_3 != fmb_'C_a_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_a_prod$',type,'C_a_prod$':$tType).
% 28.54/4.55 tff('declare_C_a_prod$1',type,fmb_'C_a_prod$'_1:'C_a_prod$').
% 28.54/4.55 tff('declare_C_a_prod$2',type,fmb_'C_a_prod$'_2:'C_a_prod$').
% 28.54/4.55 tff('declare_C_a_prod$3',type,fmb_'C_a_prod$'_3:'C_a_prod$').
% 28.54/4.55 tff('declare_C_a_prod$4',type,fmb_'C_a_prod$'_4:'C_a_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_a_prod$'] : (
% 28.54/4.55 X = fmb_'C_a_prod$'_1 | X = fmb_'C_a_prod$'_2 | X = fmb_'C_a_prod$'_3 | X = fmb_'C_a_prod$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_a_prod$'_1 != fmb_'C_a_prod$'_2 & fmb_'C_a_prod$'_1 != fmb_'C_a_prod$'_3 & fmb_'C_a_prod$'_1 != fmb_'C_a_prod$'_4 & fmb_'C_a_prod$'_2 != fmb_'C_a_prod$'_3 & fmb_'C_a_prod$'_2 != fmb_'C_a_prod$'_4 &
% 28.54/4.55 fmb_'C_a_prod$'_3 != fmb_'C_a_prod$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_option_set$',type,'C_option_set$':$tType).
% 28.54/4.55 tff('declare_C_option_set$1',type,'bot$n':'C_option_set$').
% 28.54/4.55 tff('declare_C_option_set$2',type,fmb_'C_option_set$'_2:'C_option_set$').
% 28.54/4.55 tff('declare_C_option_set$3',type,fmb_'C_option_set$'_3:'C_option_set$').
% 28.54/4.55 tff('declare_C_option_set$4',type,fmb_'C_option_set$'_4:'C_option_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_option_set$'] : (
% 28.54/4.55 X = 'bot$n' | X = fmb_'C_option_set$'_2 | X = fmb_'C_option_set$'_3 | X = fmb_'C_option_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$n' != fmb_'C_option_set$'_2 & 'bot$n' != fmb_'C_option_set$'_3 & 'bot$n' != fmb_'C_option_set$'_4 & fmb_'C_option_set$'_2 != fmb_'C_option_set$'_3 & fmb_'C_option_set$'_2 != fmb_'C_option_set$'_4 &
% 28.54/4.55 fmb_'C_option_set$'_3 != fmb_'C_option_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_b_prod_set$',type,'D_b_prod_set$':$tType).
% 28.54/4.55 tff('declare_D_b_prod_set$1',type,'bot$l':'D_b_prod_set$').
% 28.54/4.55 tff('declare_D_b_prod_set$2',type,fmb_'D_b_prod_set$'_2:'D_b_prod_set$').
% 28.54/4.55 tff('declare_D_b_prod_set$3',type,fmb_'D_b_prod_set$'_3:'D_b_prod_set$').
% 28.54/4.55 tff('declare_D_b_prod_set$4',type,fmb_'D_b_prod_set$'_4:'D_b_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_b_prod_set$'] : (
% 28.54/4.55 X = 'bot$l' | X = fmb_'D_b_prod_set$'_2 | X = fmb_'D_b_prod_set$'_3 | X = fmb_'D_b_prod_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$l' != fmb_'D_b_prod_set$'_2 & 'bot$l' != fmb_'D_b_prod_set$'_3 & 'bot$l' != fmb_'D_b_prod_set$'_4 & fmb_'D_b_prod_set$'_2 != fmb_'D_b_prod_set$'_3 & fmb_'D_b_prod_set$'_2 != fmb_'D_b_prod_set$'_4 &
% 28.54/4.55 fmb_'D_b_prod_set$'_3 != fmb_'D_b_prod_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D$',type,'D$':$tType).
% 28.54/4.55 tff('declare_D$1',type,fmb_'D$'_1:'D$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D$'] : (
% 28.54/4.55 X = fmb_'D$'_1
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_b_option_fun$',type,'D_b_option_fun$':$tType).
% 28.54/4.55 tff('declare_D_b_option_fun$1',type,'a$':'D_b_option_fun$').
% 28.54/4.55 tff('declare_D_b_option_fun$2',type,fmb_'D_b_option_fun$'_2:'D_b_option_fun$').
% 28.54/4.55 tff('declare_D_b_option_fun$3',type,fmb_'D_b_option_fun$'_3:'D_b_option_fun$').
% 28.54/4.55 tff('declare_D_b_option_fun$4',type,fmb_'D_b_option_fun$'_4:'D_b_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_b_option_fun$'] : (
% 28.54/4.55 X = 'a$' | X = fmb_'D_b_option_fun$'_2 | X = fmb_'D_b_option_fun$'_3 | X = fmb_'D_b_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'a$' != fmb_'D_b_option_fun$'_2 & 'a$' != fmb_'D_b_option_fun$'_3 & 'a$' != fmb_'D_b_option_fun$'_4 & fmb_'D_b_option_fun$'_2 != fmb_'D_b_option_fun$'_3 & fmb_'D_b_option_fun$'_2 != fmb_'D_b_option_fun$'_4 &
% 28.54/4.55 fmb_'D_b_option_fun$'_3 != fmb_'D_b_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_d_d_fun_fun$',type,'D_d_d_fun_fun$':$tType).
% 28.54/4.55 tff('declare_D_d_d_fun_fun$1',type,fmb_'D_d_d_fun_fun$'_1:'D_d_d_fun_fun$').
% 28.54/4.55 tff('declare_D_d_d_fun_fun$2',type,fmb_'D_d_d_fun_fun$'_2:'D_d_d_fun_fun$').
% 28.54/4.55 tff('declare_D_d_d_fun_fun$3',type,fmb_'D_d_d_fun_fun$'_3:'D_d_d_fun_fun$').
% 28.54/4.55 tff('declare_D_d_d_fun_fun$4',type,fmb_'D_d_d_fun_fun$'_4:'D_d_d_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_d_d_fun_fun$'] : (
% 28.54/4.55 X = fmb_'D_d_d_fun_fun$'_1 | X = fmb_'D_d_d_fun_fun$'_2 | X = fmb_'D_d_d_fun_fun$'_3 | X = fmb_'D_d_d_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_d_d_fun_fun$'_1 != fmb_'D_d_d_fun_fun$'_2 & fmb_'D_d_d_fun_fun$'_1 != fmb_'D_d_d_fun_fun$'_3 & fmb_'D_d_d_fun_fun$'_1 != fmb_'D_d_d_fun_fun$'_4 & fmb_'D_d_d_fun_fun$'_2 != fmb_'D_d_d_fun_fun$'_3 & fmb_'D_d_d_fun_fun$'_2 != fmb_'D_d_d_fun_fun$'_4 &
% 28.54/4.55 fmb_'D_d_d_fun_fun$'_3 != fmb_'D_d_d_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_d_prod_set$',type,'B_d_prod_set$':$tType).
% 28.54/4.55 tff('declare_B_d_prod_set$1',type,fmb_'B_d_prod_set$'_1:'B_d_prod_set$').
% 28.54/4.55 tff('declare_B_d_prod_set$2',type,fmb_'B_d_prod_set$'_2:'B_d_prod_set$').
% 28.54/4.55 tff('declare_B_d_prod_set$3',type,fmb_'B_d_prod_set$'_3:'B_d_prod_set$').
% 28.54/4.55 tff('declare_B_d_prod_set$4',type,fmb_'B_d_prod_set$'_4:'B_d_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_d_prod_set$'] : (
% 28.54/4.55 X = fmb_'B_d_prod_set$'_1 | X = fmb_'B_d_prod_set$'_2 | X = fmb_'B_d_prod_set$'_3 | X = fmb_'B_d_prod_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_d_prod_set$'_1 != fmb_'B_d_prod_set$'_2 & fmb_'B_d_prod_set$'_1 != fmb_'B_d_prod_set$'_3 & fmb_'B_d_prod_set$'_1 != fmb_'B_d_prod_set$'_4 & fmb_'B_d_prod_set$'_2 != fmb_'B_d_prod_set$'_3 & fmb_'B_d_prod_set$'_2 != fmb_'B_d_prod_set$'_4 &
% 28.54/4.55 fmb_'B_d_prod_set$'_3 != fmb_'B_d_prod_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_option_c_option_bool_fun_fun$',type,'C_option_c_option_bool_fun_fun$':$tType).
% 28.54/4.55 tff('declare_C_option_c_option_bool_fun_fun$1',type,fmb_'C_option_c_option_bool_fun_fun$'_1:'C_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_C_option_c_option_bool_fun_fun$2',type,fmb_'C_option_c_option_bool_fun_fun$'_2:'C_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_C_option_c_option_bool_fun_fun$3',type,fmb_'C_option_c_option_bool_fun_fun$'_3:'C_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_C_option_c_option_bool_fun_fun$4',type,fmb_'C_option_c_option_bool_fun_fun$'_4:'C_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_option_c_option_bool_fun_fun$'] : (
% 28.54/4.55 X = fmb_'C_option_c_option_bool_fun_fun$'_1 | X = fmb_'C_option_c_option_bool_fun_fun$'_2 | X = fmb_'C_option_c_option_bool_fun_fun$'_3 | X = fmb_'C_option_c_option_bool_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_option_c_option_bool_fun_fun$'_1 != fmb_'C_option_c_option_bool_fun_fun$'_2 & fmb_'C_option_c_option_bool_fun_fun$'_1 != fmb_'C_option_c_option_bool_fun_fun$'_3 & fmb_'C_option_c_option_bool_fun_fun$'_1 != fmb_'C_option_c_option_bool_fun_fun$'_4 & fmb_'C_option_c_option_bool_fun_fun$'_2 != fmb_'C_option_c_option_bool_fun_fun$'_3 & fmb_'C_option_c_option_bool_fun_fun$'_2 != fmb_'C_option_c_option_bool_fun_fun$'_4 &
% 28.54/4.55 fmb_'C_option_c_option_bool_fun_fun$'_3 != fmb_'C_option_c_option_bool_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_b_prod$',type,'D_b_prod$':$tType).
% 28.54/4.55 tff('declare_D_b_prod$1',type,fmb_'D_b_prod$'_1:'D_b_prod$').
% 28.54/4.55 tff('declare_D_b_prod$2',type,fmb_'D_b_prod$'_2:'D_b_prod$').
% 28.54/4.55 tff('declare_D_b_prod$3',type,fmb_'D_b_prod$'_3:'D_b_prod$').
% 28.54/4.55 tff('declare_D_b_prod$4',type,fmb_'D_b_prod$'_4:'D_b_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_b_prod$'] : (
% 28.54/4.55 X = fmb_'D_b_prod$'_1 | X = fmb_'D_b_prod$'_2 | X = fmb_'D_b_prod$'_3 | X = fmb_'D_b_prod$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_b_prod$'_1 != fmb_'D_b_prod$'_2 & fmb_'D_b_prod$'_1 != fmb_'D_b_prod$'_3 & fmb_'D_b_prod$'_1 != fmb_'D_b_prod$'_4 & fmb_'D_b_prod$'_2 != fmb_'D_b_prod$'_3 & fmb_'D_b_prod$'_2 != fmb_'D_b_prod$'_4 &
% 28.54/4.55 fmb_'D_b_prod$'_3 != fmb_'D_b_prod$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_b_prod_set$',type,'A_b_prod_set$':$tType).
% 28.54/4.55 tff('declare_A_b_prod_set$1',type,'bot$d':'A_b_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_b_prod_set$'] : (
% 28.54/4.55 X = 'bot$d'
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_b_prod_set$',type,'B_b_prod_set$':$tType).
% 28.54/4.55 tff('declare_B_b_prod_set$1',type,'bot$k':'B_b_prod_set$').
% 28.54/4.55 tff('declare_B_b_prod_set$2',type,fmb_'B_b_prod_set$'_2:'B_b_prod_set$').
% 28.54/4.55 tff('declare_B_b_prod_set$3',type,fmb_'B_b_prod_set$'_3:'B_b_prod_set$').
% 28.54/4.55 tff('declare_B_b_prod_set$4',type,fmb_'B_b_prod_set$'_4:'B_b_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_b_prod_set$'] : (
% 28.54/4.55 X = 'bot$k' | X = fmb_'B_b_prod_set$'_2 | X = fmb_'B_b_prod_set$'_3 | X = fmb_'B_b_prod_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$k' != fmb_'B_b_prod_set$'_2 & 'bot$k' != fmb_'B_b_prod_set$'_3 & 'bot$k' != fmb_'B_b_prod_set$'_4 & fmb_'B_b_prod_set$'_2 != fmb_'B_b_prod_set$'_3 & fmb_'B_b_prod_set$'_2 != fmb_'B_b_prod_set$'_4 &
% 28.54/4.55 fmb_'B_b_prod_set$'_3 != fmb_'B_b_prod_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_b_option_fun$',type,'C_b_option_fun$':$tType).
% 28.54/4.55 tff('declare_C_b_option_fun$1',type,fmb_'C_b_option_fun$'_1:'C_b_option_fun$').
% 28.54/4.55 tff('declare_C_b_option_fun$2',type,fmb_'C_b_option_fun$'_2:'C_b_option_fun$').
% 28.54/4.55 tff('declare_C_b_option_fun$3',type,fmb_'C_b_option_fun$'_3:'C_b_option_fun$').
% 28.54/4.55 tff('declare_C_b_option_fun$4',type,fmb_'C_b_option_fun$'_4:'C_b_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_b_option_fun$'] : (
% 28.54/4.55 X = fmb_'C_b_option_fun$'_1 | X = fmb_'C_b_option_fun$'_2 | X = fmb_'C_b_option_fun$'_3 | X = fmb_'C_b_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_b_option_fun$'_1 != fmb_'C_b_option_fun$'_2 & fmb_'C_b_option_fun$'_1 != fmb_'C_b_option_fun$'_3 & fmb_'C_b_option_fun$'_1 != fmb_'C_b_option_fun$'_4 & fmb_'C_b_option_fun$'_2 != fmb_'C_b_option_fun$'_3 & fmb_'C_b_option_fun$'_2 != fmb_'C_b_option_fun$'_4 &
% 28.54/4.55 fmb_'C_b_option_fun$'_3 != fmb_'C_b_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B$',type,'B$':$tType).
% 28.54/4.55 tff('declare_B$1',type,fmb_'B$'_1:'B$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B$'] : (
% 28.54/4.55 X = fmb_'B$'_1
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_option_b_option_bool_fun_fun$',type,'C_option_b_option_bool_fun_fun$':$tType).
% 28.54/4.55 tff('declare_C_option_b_option_bool_fun_fun$1',type,fmb_'C_option_b_option_bool_fun_fun$'_1:'C_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_C_option_b_option_bool_fun_fun$2',type,fmb_'C_option_b_option_bool_fun_fun$'_2:'C_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_C_option_b_option_bool_fun_fun$3',type,fmb_'C_option_b_option_bool_fun_fun$'_3:'C_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_C_option_b_option_bool_fun_fun$4',type,fmb_'C_option_b_option_bool_fun_fun$'_4:'C_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_option_b_option_bool_fun_fun$'] : (
% 28.54/4.55 X = fmb_'C_option_b_option_bool_fun_fun$'_1 | X = fmb_'C_option_b_option_bool_fun_fun$'_2 | X = fmb_'C_option_b_option_bool_fun_fun$'_3 | X = fmb_'C_option_b_option_bool_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_option_b_option_bool_fun_fun$'_1 != fmb_'C_option_b_option_bool_fun_fun$'_2 & fmb_'C_option_b_option_bool_fun_fun$'_1 != fmb_'C_option_b_option_bool_fun_fun$'_3 & fmb_'C_option_b_option_bool_fun_fun$'_1 != fmb_'C_option_b_option_bool_fun_fun$'_4 & fmb_'C_option_b_option_bool_fun_fun$'_2 != fmb_'C_option_b_option_bool_fun_fun$'_3 & fmb_'C_option_b_option_bool_fun_fun$'_2 != fmb_'C_option_b_option_bool_fun_fun$'_4 &
% 28.54/4.55 fmb_'C_option_b_option_bool_fun_fun$'_3 != fmb_'C_option_b_option_bool_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_b_prod_bool_fun$',type,'C_b_prod_bool_fun$':$tType).
% 28.54/4.55 tff('declare_C_b_prod_bool_fun$1',type,fmb_'C_b_prod_bool_fun$'_1:'C_b_prod_bool_fun$').
% 28.54/4.55 tff('declare_C_b_prod_bool_fun$2',type,fmb_'C_b_prod_bool_fun$'_2:'C_b_prod_bool_fun$').
% 28.54/4.55 tff('declare_C_b_prod_bool_fun$3',type,fmb_'C_b_prod_bool_fun$'_3:'C_b_prod_bool_fun$').
% 28.54/4.55 tff('declare_C_b_prod_bool_fun$4',type,fmb_'C_b_prod_bool_fun$'_4:'C_b_prod_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_b_prod_bool_fun$'] : (
% 28.54/4.55 X = fmb_'C_b_prod_bool_fun$'_1 | X = fmb_'C_b_prod_bool_fun$'_2 | X = fmb_'C_b_prod_bool_fun$'_3 | X = fmb_'C_b_prod_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_b_prod_bool_fun$'_1 != fmb_'C_b_prod_bool_fun$'_2 & fmb_'C_b_prod_bool_fun$'_1 != fmb_'C_b_prod_bool_fun$'_3 & fmb_'C_b_prod_bool_fun$'_1 != fmb_'C_b_prod_bool_fun$'_4 & fmb_'C_b_prod_bool_fun$'_2 != fmb_'C_b_prod_bool_fun$'_3 & fmb_'C_b_prod_bool_fun$'_2 != fmb_'C_b_prod_bool_fun$'_4 &
% 28.54/4.55 fmb_'C_b_prod_bool_fun$'_3 != fmb_'C_b_prod_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C$',type,'C$':$tType).
% 28.54/4.55 tff('declare_C$1',type,fmb_'C$'_1:'C$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C$'] : (
% 28.54/4.55 X = fmb_'C$'_1
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_option_bool_fun$',type,'D_option_bool_fun$':$tType).
% 28.54/4.55 tff('declare_D_option_bool_fun$1',type,'is_none$a':'D_option_bool_fun$').
% 28.54/4.55 tff('declare_D_option_bool_fun$2',type,fmb_'D_option_bool_fun$'_2:'D_option_bool_fun$').
% 28.54/4.55 tff('declare_D_option_bool_fun$3',type,fmb_'D_option_bool_fun$'_3:'D_option_bool_fun$').
% 28.54/4.55 tff('declare_D_option_bool_fun$4',type,fmb_'D_option_bool_fun$'_4:'D_option_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_option_bool_fun$'] : (
% 28.54/4.55 X = 'is_none$a' | X = fmb_'D_option_bool_fun$'_2 | X = fmb_'D_option_bool_fun$'_3 | X = fmb_'D_option_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'is_none$a' != fmb_'D_option_bool_fun$'_2 & 'is_none$a' != fmb_'D_option_bool_fun$'_3 & 'is_none$a' != fmb_'D_option_bool_fun$'_4 & fmb_'D_option_bool_fun$'_2 != fmb_'D_option_bool_fun$'_3 & fmb_'D_option_bool_fun$'_2 != fmb_'D_option_bool_fun$'_4 &
% 28.54/4.55 fmb_'D_option_bool_fun$'_3 != fmb_'D_option_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_c_prod_set$',type,'C_c_prod_set$':$tType).
% 28.54/4.55 tff('declare_C_c_prod_set$1',type,fmb_'C_c_prod_set$'_1:'C_c_prod_set$').
% 28.54/4.55 tff('declare_C_c_prod_set$2',type,fmb_'C_c_prod_set$'_2:'C_c_prod_set$').
% 28.54/4.55 tff('declare_C_c_prod_set$3',type,fmb_'C_c_prod_set$'_3:'C_c_prod_set$').
% 28.54/4.55 tff('declare_C_c_prod_set$4',type,fmb_'C_c_prod_set$'_4:'C_c_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_c_prod_set$'] : (
% 28.54/4.55 X = fmb_'C_c_prod_set$'_1 | X = fmb_'C_c_prod_set$'_2 | X = fmb_'C_c_prod_set$'_3 | X = fmb_'C_c_prod_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_c_prod_set$'_1 != fmb_'C_c_prod_set$'_2 & fmb_'C_c_prod_set$'_1 != fmb_'C_c_prod_set$'_3 & fmb_'C_c_prod_set$'_1 != fmb_'C_c_prod_set$'_4 & fmb_'C_c_prod_set$'_2 != fmb_'C_c_prod_set$'_3 & fmb_'C_c_prod_set$'_2 != fmb_'C_c_prod_set$'_4 &
% 28.54/4.55 fmb_'C_c_prod_set$'_3 != fmb_'C_c_prod_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_c_prod_bool_fun$',type,'A_c_prod_bool_fun$':$tType).
% 28.54/4.55 tff('declare_A_c_prod_bool_fun$1',type,fmb_'A_c_prod_bool_fun$'_1:'A_c_prod_bool_fun$').
% 28.54/4.55 tff('declare_A_c_prod_bool_fun$2',type,fmb_'A_c_prod_bool_fun$'_2:'A_c_prod_bool_fun$').
% 28.54/4.55 tff('declare_A_c_prod_bool_fun$3',type,fmb_'A_c_prod_bool_fun$'_3:'A_c_prod_bool_fun$').
% 28.54/4.55 tff('declare_A_c_prod_bool_fun$4',type,fmb_'A_c_prod_bool_fun$'_4:'A_c_prod_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_c_prod_bool_fun$'] : (
% 28.54/4.55 X = fmb_'A_c_prod_bool_fun$'_1 | X = fmb_'A_c_prod_bool_fun$'_2 | X = fmb_'A_c_prod_bool_fun$'_3 | X = fmb_'A_c_prod_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'A_c_prod_bool_fun$'_1 != fmb_'A_c_prod_bool_fun$'_2 & fmb_'A_c_prod_bool_fun$'_1 != fmb_'A_c_prod_bool_fun$'_3 & fmb_'A_c_prod_bool_fun$'_1 != fmb_'A_c_prod_bool_fun$'_4 & fmb_'A_c_prod_bool_fun$'_2 != fmb_'A_c_prod_bool_fun$'_3 & fmb_'A_c_prod_bool_fun$'_2 != fmb_'A_c_prod_bool_fun$'_4 &
% 28.54/4.55 fmb_'A_c_prod_bool_fun$'_3 != fmb_'A_c_prod_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_option_d_option_bool_fun_fun$',type,'D_option_d_option_bool_fun_fun$':$tType).
% 28.54/4.55 tff('declare_D_option_d_option_bool_fun_fun$1',type,fmb_'D_option_d_option_bool_fun_fun$'_1:'D_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_D_option_d_option_bool_fun_fun$2',type,fmb_'D_option_d_option_bool_fun_fun$'_2:'D_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_D_option_d_option_bool_fun_fun$3',type,fmb_'D_option_d_option_bool_fun_fun$'_3:'D_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_D_option_d_option_bool_fun_fun$4',type,fmb_'D_option_d_option_bool_fun_fun$'_4:'D_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_option_d_option_bool_fun_fun$'] : (
% 28.54/4.55 X = fmb_'D_option_d_option_bool_fun_fun$'_1 | X = fmb_'D_option_d_option_bool_fun_fun$'_2 | X = fmb_'D_option_d_option_bool_fun_fun$'_3 | X = fmb_'D_option_d_option_bool_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_option_d_option_bool_fun_fun$'_1 != fmb_'D_option_d_option_bool_fun_fun$'_2 & fmb_'D_option_d_option_bool_fun_fun$'_1 != fmb_'D_option_d_option_bool_fun_fun$'_3 & fmb_'D_option_d_option_bool_fun_fun$'_1 != fmb_'D_option_d_option_bool_fun_fun$'_4 & fmb_'D_option_d_option_bool_fun_fun$'_2 != fmb_'D_option_d_option_bool_fun_fun$'_3 & fmb_'D_option_d_option_bool_fun_fun$'_2 != fmb_'D_option_d_option_bool_fun_fun$'_4 &
% 28.54/4.55 fmb_'D_option_d_option_bool_fun_fun$'_3 != fmb_'D_option_d_option_bool_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_option$',type,'A_option$':$tType).
% 28.54/4.55 tff('declare_A_option$1',type,'none$':'A_option$').
% 28.54/4.55 tff('declare_A_option$2',type,fmb_'A_option$'_2:'A_option$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_option$'] : (
% 28.54/4.55 X = 'none$' | X = fmb_'A_option$'_2
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'none$' != fmb_'A_option$'_2
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_a_option_fun$',type,'D_a_option_fun$':$tType).
% 28.54/4.55 tff('declare_D_a_option_fun$1',type,fmb_'D_a_option_fun$'_1:'D_a_option_fun$').
% 28.54/4.55 tff('declare_D_a_option_fun$2',type,fmb_'D_a_option_fun$'_2:'D_a_option_fun$').
% 28.54/4.55 tff('declare_D_a_option_fun$3',type,fmb_'D_a_option_fun$'_3:'D_a_option_fun$').
% 28.54/4.55 tff('declare_D_a_option_fun$4',type,fmb_'D_a_option_fun$'_4:'D_a_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_a_option_fun$'] : (
% 28.54/4.55 X = fmb_'D_a_option_fun$'_1 | X = fmb_'D_a_option_fun$'_2 | X = fmb_'D_a_option_fun$'_3 | X = fmb_'D_a_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_a_option_fun$'_1 != fmb_'D_a_option_fun$'_2 & fmb_'D_a_option_fun$'_1 != fmb_'D_a_option_fun$'_3 & fmb_'D_a_option_fun$'_1 != fmb_'D_a_option_fun$'_4 & fmb_'D_a_option_fun$'_2 != fmb_'D_a_option_fun$'_3 & fmb_'D_a_option_fun$'_2 != fmb_'D_a_option_fun$'_4 &
% 28.54/4.55 fmb_'D_a_option_fun$'_3 != fmb_'D_a_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_set$',type,'D_set$':$tType).
% 28.54/4.55 tff('declare_D_set$1',type,'bot$':'D_set$').
% 28.54/4.55 tff('declare_D_set$2',type,fmb_'D_set$'_2:'D_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_set$'] : (
% 28.54/4.55 X = 'bot$' | X = fmb_'D_set$'_2
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$' != fmb_'D_set$'_2
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_d_prod_set$',type,'C_d_prod_set$':$tType).
% 28.54/4.55 tff('declare_C_d_prod_set$1',type,'bot$h':'C_d_prod_set$').
% 28.54/4.55 tff('declare_C_d_prod_set$2',type,fmb_'C_d_prod_set$'_2:'C_d_prod_set$').
% 28.54/4.55 tff('declare_C_d_prod_set$3',type,fmb_'C_d_prod_set$'_3:'C_d_prod_set$').
% 28.54/4.55 tff('declare_C_d_prod_set$4',type,fmb_'C_d_prod_set$'_4:'C_d_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_d_prod_set$'] : (
% 28.54/4.55 X = 'bot$h' | X = fmb_'C_d_prod_set$'_2 | X = fmb_'C_d_prod_set$'_3 | X = fmb_'C_d_prod_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$h' != fmb_'C_d_prod_set$'_2 & 'bot$h' != fmb_'C_d_prod_set$'_3 & 'bot$h' != fmb_'C_d_prod_set$'_4 & fmb_'C_d_prod_set$'_2 != fmb_'C_d_prod_set$'_3 & fmb_'C_d_prod_set$'_2 != fmb_'C_d_prod_set$'_4 &
% 28.54/4.55 fmb_'C_d_prod_set$'_3 != fmb_'C_d_prod_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_option_d_option_bool_fun_fun$',type,'B_option_d_option_bool_fun_fun$':$tType).
% 28.54/4.55 tff('declare_B_option_d_option_bool_fun_fun$1',type,fmb_'B_option_d_option_bool_fun_fun$'_1:'B_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_B_option_d_option_bool_fun_fun$2',type,fmb_'B_option_d_option_bool_fun_fun$'_2:'B_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_B_option_d_option_bool_fun_fun$3',type,fmb_'B_option_d_option_bool_fun_fun$'_3:'B_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_B_option_d_option_bool_fun_fun$4',type,fmb_'B_option_d_option_bool_fun_fun$'_4:'B_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_option_d_option_bool_fun_fun$'] : (
% 28.54/4.55 X = fmb_'B_option_d_option_bool_fun_fun$'_1 | X = fmb_'B_option_d_option_bool_fun_fun$'_2 | X = fmb_'B_option_d_option_bool_fun_fun$'_3 | X = fmb_'B_option_d_option_bool_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_option_d_option_bool_fun_fun$'_1 != fmb_'B_option_d_option_bool_fun_fun$'_2 & fmb_'B_option_d_option_bool_fun_fun$'_1 != fmb_'B_option_d_option_bool_fun_fun$'_3 & fmb_'B_option_d_option_bool_fun_fun$'_1 != fmb_'B_option_d_option_bool_fun_fun$'_4 & fmb_'B_option_d_option_bool_fun_fun$'_2 != fmb_'B_option_d_option_bool_fun_fun$'_3 & fmb_'B_option_d_option_bool_fun_fun$'_2 != fmb_'B_option_d_option_bool_fun_fun$'_4 &
% 28.54/4.55 fmb_'B_option_d_option_bool_fun_fun$'_3 != fmb_'B_option_d_option_bool_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_a_option_fun_a_b_option_fun_fun$',type,'A_a_option_fun_a_b_option_fun_fun$':$tType).
% 28.54/4.55 tff('declare_A_a_option_fun_a_b_option_fun_fun$1',type,fmb_'A_a_option_fun_a_b_option_fun_fun$'_1:'A_a_option_fun_a_b_option_fun_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun_a_b_option_fun_fun$2',type,fmb_'A_a_option_fun_a_b_option_fun_fun$'_2:'A_a_option_fun_a_b_option_fun_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun_a_b_option_fun_fun$3',type,fmb_'A_a_option_fun_a_b_option_fun_fun$'_3:'A_a_option_fun_a_b_option_fun_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun_a_b_option_fun_fun$4',type,fmb_'A_a_option_fun_a_b_option_fun_fun$'_4:'A_a_option_fun_a_b_option_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_a_option_fun_a_b_option_fun_fun$'] : (
% 28.54/4.55 X = fmb_'A_a_option_fun_a_b_option_fun_fun$'_1 | X = fmb_'A_a_option_fun_a_b_option_fun_fun$'_2 | X = fmb_'A_a_option_fun_a_b_option_fun_fun$'_3 | X = fmb_'A_a_option_fun_a_b_option_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'A_a_option_fun_a_b_option_fun_fun$'_1 != fmb_'A_a_option_fun_a_b_option_fun_fun$'_2 & fmb_'A_a_option_fun_a_b_option_fun_fun$'_1 != fmb_'A_a_option_fun_a_b_option_fun_fun$'_3 & fmb_'A_a_option_fun_a_b_option_fun_fun$'_1 != fmb_'A_a_option_fun_a_b_option_fun_fun$'_4 & fmb_'A_a_option_fun_a_b_option_fun_fun$'_2 != fmb_'A_a_option_fun_a_b_option_fun_fun$'_3 & fmb_'A_a_option_fun_a_b_option_fun_fun$'_2 != fmb_'A_a_option_fun_a_b_option_fun_fun$'_4 &
% 28.54/4.55 fmb_'A_a_option_fun_a_b_option_fun_fun$'_3 != fmb_'A_a_option_fun_a_b_option_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_c_option_fun$',type,'D_c_option_fun$':$tType).
% 28.54/4.55 tff('declare_D_c_option_fun$1',type,fmb_'D_c_option_fun$'_1:'D_c_option_fun$').
% 28.54/4.55 tff('declare_D_c_option_fun$2',type,fmb_'D_c_option_fun$'_2:'D_c_option_fun$').
% 28.54/4.55 tff('declare_D_c_option_fun$3',type,fmb_'D_c_option_fun$'_3:'D_c_option_fun$').
% 28.54/4.55 tff('declare_D_c_option_fun$4',type,fmb_'D_c_option_fun$'_4:'D_c_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_c_option_fun$'] : (
% 28.54/4.55 X = fmb_'D_c_option_fun$'_1 | X = fmb_'D_c_option_fun$'_2 | X = fmb_'D_c_option_fun$'_3 | X = fmb_'D_c_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_c_option_fun$'_1 != fmb_'D_c_option_fun$'_2 & fmb_'D_c_option_fun$'_1 != fmb_'D_c_option_fun$'_3 & fmb_'D_c_option_fun$'_1 != fmb_'D_c_option_fun$'_4 & fmb_'D_c_option_fun$'_2 != fmb_'D_c_option_fun$'_3 & fmb_'D_c_option_fun$'_2 != fmb_'D_c_option_fun$'_4 &
% 28.54/4.55 fmb_'D_c_option_fun$'_3 != fmb_'D_c_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_c_prod_set$',type,'A_c_prod_set$':$tType).
% 28.54/4.55 tff('declare_A_c_prod_set$1',type,'bot$e':'A_c_prod_set$').
% 28.54/4.55 tff('declare_A_c_prod_set$2',type,fmb_'A_c_prod_set$'_2:'A_c_prod_set$').
% 28.54/4.55 tff('declare_A_c_prod_set$3',type,fmb_'A_c_prod_set$'_3:'A_c_prod_set$').
% 28.54/4.55 tff('declare_A_c_prod_set$4',type,fmb_'A_c_prod_set$'_4:'A_c_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_c_prod_set$'] : (
% 28.54/4.55 X = 'bot$e' | X = fmb_'A_c_prod_set$'_2 | X = fmb_'A_c_prod_set$'_3 | X = fmb_'A_c_prod_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$e' != fmb_'A_c_prod_set$'_2 & 'bot$e' != fmb_'A_c_prod_set$'_3 & 'bot$e' != fmb_'A_c_prod_set$'_4 & fmb_'A_c_prod_set$'_2 != fmb_'A_c_prod_set$'_3 & fmb_'A_c_prod_set$'_2 != fmb_'A_c_prod_set$'_4 &
% 28.54/4.55 fmb_'A_c_prod_set$'_3 != fmb_'A_c_prod_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_d_prod_bool_fun$',type,'C_d_prod_bool_fun$':$tType).
% 28.54/4.55 tff('declare_C_d_prod_bool_fun$1',type,fmb_'C_d_prod_bool_fun$'_1:'C_d_prod_bool_fun$').
% 28.54/4.55 tff('declare_C_d_prod_bool_fun$2',type,fmb_'C_d_prod_bool_fun$'_2:'C_d_prod_bool_fun$').
% 28.54/4.55 tff('declare_C_d_prod_bool_fun$3',type,fmb_'C_d_prod_bool_fun$'_3:'C_d_prod_bool_fun$').
% 28.54/4.55 tff('declare_C_d_prod_bool_fun$4',type,fmb_'C_d_prod_bool_fun$'_4:'C_d_prod_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_d_prod_bool_fun$'] : (
% 28.54/4.55 X = fmb_'C_d_prod_bool_fun$'_1 | X = fmb_'C_d_prod_bool_fun$'_2 | X = fmb_'C_d_prod_bool_fun$'_3 | X = fmb_'C_d_prod_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_d_prod_bool_fun$'_1 != fmb_'C_d_prod_bool_fun$'_2 & fmb_'C_d_prod_bool_fun$'_1 != fmb_'C_d_prod_bool_fun$'_3 & fmb_'C_d_prod_bool_fun$'_1 != fmb_'C_d_prod_bool_fun$'_4 & fmb_'C_d_prod_bool_fun$'_2 != fmb_'C_d_prod_bool_fun$'_3 & fmb_'C_d_prod_bool_fun$'_2 != fmb_'C_d_prod_bool_fun$'_4 &
% 28.54/4.55 fmb_'C_d_prod_bool_fun$'_3 != fmb_'C_d_prod_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_b_prod$',type,'B_b_prod$':$tType).
% 28.54/4.55 tff('declare_B_b_prod$1',type,fmb_'B_b_prod$'_1:'B_b_prod$').
% 28.54/4.55 tff('declare_B_b_prod$2',type,fmb_'B_b_prod$'_2:'B_b_prod$').
% 28.54/4.55 tff('declare_B_b_prod$3',type,fmb_'B_b_prod$'_3:'B_b_prod$').
% 28.54/4.55 tff('declare_B_b_prod$4',type,fmb_'B_b_prod$'_4:'B_b_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_b_prod$'] : (
% 28.54/4.55 X = fmb_'B_b_prod$'_1 | X = fmb_'B_b_prod$'_2 | X = fmb_'B_b_prod$'_3 | X = fmb_'B_b_prod$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_b_prod$'_1 != fmb_'B_b_prod$'_2 & fmb_'B_b_prod$'_1 != fmb_'B_b_prod$'_3 & fmb_'B_b_prod$'_1 != fmb_'B_b_prod$'_4 & fmb_'B_b_prod$'_2 != fmb_'B_b_prod$'_3 & fmb_'B_b_prod$'_2 != fmb_'B_b_prod$'_4 &
% 28.54/4.55 fmb_'B_b_prod$'_3 != fmb_'B_b_prod$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_option_b_option_bool_fun_fun$',type,'D_option_b_option_bool_fun_fun$':$tType).
% 28.54/4.55 tff('declare_D_option_b_option_bool_fun_fun$1',type,fmb_'D_option_b_option_bool_fun_fun$'_1:'D_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_D_option_b_option_bool_fun_fun$2',type,fmb_'D_option_b_option_bool_fun_fun$'_2:'D_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_D_option_b_option_bool_fun_fun$3',type,fmb_'D_option_b_option_bool_fun_fun$'_3:'D_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_D_option_b_option_bool_fun_fun$4',type,fmb_'D_option_b_option_bool_fun_fun$'_4:'D_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_option_b_option_bool_fun_fun$'] : (
% 28.54/4.55 X = fmb_'D_option_b_option_bool_fun_fun$'_1 | X = fmb_'D_option_b_option_bool_fun_fun$'_2 | X = fmb_'D_option_b_option_bool_fun_fun$'_3 | X = fmb_'D_option_b_option_bool_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_option_b_option_bool_fun_fun$'_1 != fmb_'D_option_b_option_bool_fun_fun$'_2 & fmb_'D_option_b_option_bool_fun_fun$'_1 != fmb_'D_option_b_option_bool_fun_fun$'_3 & fmb_'D_option_b_option_bool_fun_fun$'_1 != fmb_'D_option_b_option_bool_fun_fun$'_4 & fmb_'D_option_b_option_bool_fun_fun$'_2 != fmb_'D_option_b_option_bool_fun_fun$'_3 & fmb_'D_option_b_option_bool_fun_fun$'_2 != fmb_'D_option_b_option_bool_fun_fun$'_4 &
% 28.54/4.55 fmb_'D_option_b_option_bool_fun_fun$'_3 != fmb_'D_option_b_option_bool_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_d_option_fun$',type,'A_d_option_fun$':$tType).
% 28.54/4.55 tff('declare_A_d_option_fun$1',type,fmb_'A_d_option_fun$'_1:'A_d_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_d_option_fun$'] : (
% 28.54/4.55 X = fmb_'A_d_option_fun$'_1
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_c_prod_set$',type,'B_c_prod_set$':$tType).
% 28.54/4.55 tff('declare_B_c_prod_set$1',type,'bot$j':'B_c_prod_set$').
% 28.54/4.55 tff('declare_B_c_prod_set$2',type,fmb_'B_c_prod_set$'_2:'B_c_prod_set$').
% 28.54/4.55 tff('declare_B_c_prod_set$3',type,fmb_'B_c_prod_set$'_3:'B_c_prod_set$').
% 28.54/4.55 tff('declare_B_c_prod_set$4',type,fmb_'B_c_prod_set$'_4:'B_c_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_c_prod_set$'] : (
% 28.54/4.55 X = 'bot$j' | X = fmb_'B_c_prod_set$'_2 | X = fmb_'B_c_prod_set$'_3 | X = fmb_'B_c_prod_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$j' != fmb_'B_c_prod_set$'_2 & 'bot$j' != fmb_'B_c_prod_set$'_3 & 'bot$j' != fmb_'B_c_prod_set$'_4 & fmb_'B_c_prod_set$'_2 != fmb_'B_c_prod_set$'_3 & fmb_'B_c_prod_set$'_2 != fmb_'B_c_prod_set$'_4 &
% 28.54/4.55 fmb_'B_c_prod_set$'_3 != fmb_'B_c_prod_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_a_option_fun$',type,'A_a_option_fun$':$tType).
% 28.54/4.55 tff('declare_A_a_option_fun$1',type,'some$':'A_a_option_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun$2',type,fmb_'A_a_option_fun$'_2:'A_a_option_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun$3',type,fmb_'A_a_option_fun$'_3:'A_a_option_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun$4',type,fmb_'A_a_option_fun$'_4:'A_a_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_a_option_fun$'] : (
% 28.54/4.55 X = 'some$' | X = fmb_'A_a_option_fun$'_2 | X = fmb_'A_a_option_fun$'_3 | X = fmb_'A_a_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'some$' != fmb_'A_a_option_fun$'_2 & 'some$' != fmb_'A_a_option_fun$'_3 & 'some$' != fmb_'A_a_option_fun$'_4 & fmb_'A_a_option_fun$'_2 != fmb_'A_a_option_fun$'_3 & fmb_'A_a_option_fun$'_2 != fmb_'A_a_option_fun$'_4 &
% 28.54/4.55 fmb_'A_a_option_fun$'_3 != fmb_'A_a_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_d_prod$',type,'A_d_prod$':$tType).
% 28.54/4.55 tff('declare_A_d_prod$1',type,fmb_'A_d_prod$'_1:'A_d_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_d_prod$'] : (
% 28.54/4.55 X = fmb_'A_d_prod$'_1
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_bool_fun$',type,'A_bool_fun$':$tType).
% 28.54/4.55 tff('declare_A_bool_fun$1',type,'bot$s':'A_bool_fun$').
% 28.54/4.55 tff('declare_A_bool_fun$2',type,fmb_'A_bool_fun$'_2:'A_bool_fun$').
% 28.54/4.55 tff('declare_A_bool_fun$3',type,fmb_'A_bool_fun$'_3:'A_bool_fun$').
% 28.54/4.55 tff('declare_A_bool_fun$4',type,fmb_'A_bool_fun$'_4:'A_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_bool_fun$'] : (
% 28.54/4.55 X = 'bot$s' | X = fmb_'A_bool_fun$'_2 | X = fmb_'A_bool_fun$'_3 | X = fmb_'A_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$s' != fmb_'A_bool_fun$'_2 & 'bot$s' != fmb_'A_bool_fun$'_3 & 'bot$s' != fmb_'A_bool_fun$'_4 & fmb_'A_bool_fun$'_2 != fmb_'A_bool_fun$'_3 & fmb_'A_bool_fun$'_2 != fmb_'A_bool_fun$'_4 &
% 28.54/4.55 fmb_'A_bool_fun$'_3 != fmb_'A_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_b_prod$',type,'A_b_prod$':$tType).
% 28.54/4.55 tff('declare_A_b_prod$1',type,fmb_'A_b_prod$'_1:'A_b_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_b_prod$'] : (
% 28.54/4.55 X = fmb_'A_b_prod$'_1
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_set$',type,'A_set$':$tType).
% 28.54/4.55 tff('declare_A_set$1',type,'bot$c':'A_set$').
% 28.54/4.55 tff('declare_A_set$2',type,fmb_'A_set$'_2:'A_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_set$'] : (
% 28.54/4.55 X = 'bot$c' | X = fmb_'A_set$'_2
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$c' != fmb_'A_set$'_2
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_d_prod_bool_fun$',type,'A_d_prod_bool_fun$':$tType).
% 28.54/4.55 tff('declare_A_d_prod_bool_fun$1',type,fmb_'A_d_prod_bool_fun$'_1:'A_d_prod_bool_fun$').
% 28.54/4.55 tff('declare_A_d_prod_bool_fun$2',type,fmb_'A_d_prod_bool_fun$'_2:'A_d_prod_bool_fun$').
% 28.54/4.55 tff('declare_A_d_prod_bool_fun$3',type,fmb_'A_d_prod_bool_fun$'_3:'A_d_prod_bool_fun$').
% 28.54/4.55 tff('declare_A_d_prod_bool_fun$4',type,fmb_'A_d_prod_bool_fun$'_4:'A_d_prod_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_d_prod_bool_fun$'] : (
% 28.54/4.55 X = fmb_'A_d_prod_bool_fun$'_1 | X = fmb_'A_d_prod_bool_fun$'_2 | X = fmb_'A_d_prod_bool_fun$'_3 | X = fmb_'A_d_prod_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'A_d_prod_bool_fun$'_1 != fmb_'A_d_prod_bool_fun$'_2 & fmb_'A_d_prod_bool_fun$'_1 != fmb_'A_d_prod_bool_fun$'_3 & fmb_'A_d_prod_bool_fun$'_1 != fmb_'A_d_prod_bool_fun$'_4 & fmb_'A_d_prod_bool_fun$'_2 != fmb_'A_d_prod_bool_fun$'_3 & fmb_'A_d_prod_bool_fun$'_2 != fmb_'A_d_prod_bool_fun$'_4 &
% 28.54/4.55 fmb_'A_d_prod_bool_fun$'_3 != fmb_'A_d_prod_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_a_option_fun_a_d_option_fun_fun$',type,'A_a_option_fun_a_d_option_fun_fun$':$tType).
% 28.54/4.55 tff('declare_A_a_option_fun_a_d_option_fun_fun$1',type,fmb_'A_a_option_fun_a_d_option_fun_fun$'_1:'A_a_option_fun_a_d_option_fun_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun_a_d_option_fun_fun$2',type,fmb_'A_a_option_fun_a_d_option_fun_fun$'_2:'A_a_option_fun_a_d_option_fun_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun_a_d_option_fun_fun$3',type,fmb_'A_a_option_fun_a_d_option_fun_fun$'_3:'A_a_option_fun_a_d_option_fun_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun_a_d_option_fun_fun$4',type,fmb_'A_a_option_fun_a_d_option_fun_fun$'_4:'A_a_option_fun_a_d_option_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_a_option_fun_a_d_option_fun_fun$'] : (
% 28.54/4.55 X = fmb_'A_a_option_fun_a_d_option_fun_fun$'_1 | X = fmb_'A_a_option_fun_a_d_option_fun_fun$'_2 | X = fmb_'A_a_option_fun_a_d_option_fun_fun$'_3 | X = fmb_'A_a_option_fun_a_d_option_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'A_a_option_fun_a_d_option_fun_fun$'_1 != fmb_'A_a_option_fun_a_d_option_fun_fun$'_2 & fmb_'A_a_option_fun_a_d_option_fun_fun$'_1 != fmb_'A_a_option_fun_a_d_option_fun_fun$'_3 & fmb_'A_a_option_fun_a_d_option_fun_fun$'_1 != fmb_'A_a_option_fun_a_d_option_fun_fun$'_4 & fmb_'A_a_option_fun_a_d_option_fun_fun$'_2 != fmb_'A_a_option_fun_a_d_option_fun_fun$'_3 & fmb_'A_a_option_fun_a_d_option_fun_fun$'_2 != fmb_'A_a_option_fun_a_d_option_fun_fun$'_4 &
% 28.54/4.55 fmb_'A_a_option_fun_a_d_option_fun_fun$'_3 != fmb_'A_a_option_fun_a_d_option_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_bool_fun$',type,'C_bool_fun$':$tType).
% 28.54/4.55 tff('declare_C_bool_fun$1',type,'bot$q':'C_bool_fun$').
% 28.54/4.55 tff('declare_C_bool_fun$2',type,fmb_'C_bool_fun$'_2:'C_bool_fun$').
% 28.54/4.55 tff('declare_C_bool_fun$3',type,fmb_'C_bool_fun$'_3:'C_bool_fun$').
% 28.54/4.55 tff('declare_C_bool_fun$4',type,fmb_'C_bool_fun$'_4:'C_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_bool_fun$'] : (
% 28.54/4.55 X = 'bot$q' | X = fmb_'C_bool_fun$'_2 | X = fmb_'C_bool_fun$'_3 | X = fmb_'C_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$q' != fmb_'C_bool_fun$'_2 & 'bot$q' != fmb_'C_bool_fun$'_3 & 'bot$q' != fmb_'C_bool_fun$'_4 & fmb_'C_bool_fun$'_2 != fmb_'C_bool_fun$'_3 & fmb_'C_bool_fun$'_2 != fmb_'C_bool_fun$'_4 &
% 28.54/4.55 fmb_'C_bool_fun$'_3 != fmb_'C_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_set$',type,'B_set$':$tType).
% 28.54/4.55 tff('declare_B_set$1',type,'bot$b':'B_set$').
% 28.54/4.55 tff('declare_B_set$2',type,fmb_'B_set$'_2:'B_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_set$'] : (
% 28.54/4.55 X = 'bot$b' | X = fmb_'B_set$'_2
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$b' != fmb_'B_set$'_2
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_option_d_option_fun$',type,'D_option_d_option_fun$':$tType).
% 28.54/4.55 tff('declare_D_option_d_option_fun$1',type,fmb_'D_option_d_option_fun$'_1:'D_option_d_option_fun$').
% 28.54/4.55 tff('declare_D_option_d_option_fun$2',type,fmb_'D_option_d_option_fun$'_2:'D_option_d_option_fun$').
% 28.54/4.55 tff('declare_D_option_d_option_fun$3',type,fmb_'D_option_d_option_fun$'_3:'D_option_d_option_fun$').
% 28.54/4.55 tff('declare_D_option_d_option_fun$4',type,fmb_'D_option_d_option_fun$'_4:'D_option_d_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_option_d_option_fun$'] : (
% 28.54/4.55 X = fmb_'D_option_d_option_fun$'_1 | X = fmb_'D_option_d_option_fun$'_2 | X = fmb_'D_option_d_option_fun$'_3 | X = fmb_'D_option_d_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_option_d_option_fun$'_1 != fmb_'D_option_d_option_fun$'_2 & fmb_'D_option_d_option_fun$'_1 != fmb_'D_option_d_option_fun$'_3 & fmb_'D_option_d_option_fun$'_1 != fmb_'D_option_d_option_fun$'_4 & fmb_'D_option_d_option_fun$'_2 != fmb_'D_option_d_option_fun$'_3 & fmb_'D_option_d_option_fun$'_2 != fmb_'D_option_d_option_fun$'_4 &
% 28.54/4.55 fmb_'D_option_d_option_fun$'_3 != fmb_'D_option_d_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A$',type,'A$':$tType).
% 28.54/4.55 tff('declare_A$1',type,fmb_'A$'_1:'A$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A$'] : (
% 28.54/4.55 X = fmb_'A$'_1
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_c_prod$',type,'A_c_prod$':$tType).
% 28.54/4.55 tff('declare_A_c_prod$1',type,fmb_'A_c_prod$'_1:'A_c_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_c_prod$'] : (
% 28.54/4.55 X = fmb_'A_c_prod$'_1
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_option_option$',type,'B_option_option$':$tType).
% 28.54/4.55 tff('declare_B_option_option$1',type,'none$d':'B_option_option$').
% 28.54/4.55 tff('declare_B_option_option$2',type,fmb_'B_option_option$'_2:'B_option_option$').
% 28.54/4.55 tff('declare_B_option_option$3',type,fmb_'B_option_option$'_3:'B_option_option$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_option_option$'] : (
% 28.54/4.55 X = 'none$d' | X = fmb_'B_option_option$'_2 | X = fmb_'B_option_option$'_3
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'none$d' != fmb_'B_option_option$'_2 & 'none$d' != fmb_'B_option_option$'_3 & fmb_'B_option_option$'_2 != fmb_'B_option_option$'_3
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_b_option_fun$',type,'A_b_option_fun$':$tType).
% 28.54/4.55 tff('declare_A_b_option_fun$1',type,fmb_'A_b_option_fun$'_1:'A_b_option_fun$').
% 28.54/4.55 tff('declare_A_b_option_fun$2',type,fmb_'A_b_option_fun$'_2:'A_b_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_b_option_fun$'] : (
% 28.54/4.55 X = fmb_'A_b_option_fun$'_1 | X = fmb_'A_b_option_fun$'_2
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'A_b_option_fun$'_1 != fmb_'A_b_option_fun$'_2
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_option_set$',type,'D_option_set$':$tType).
% 28.54/4.55 tff('declare_D_option_set$1',type,'bot$t':'D_option_set$').
% 28.54/4.55 tff('declare_D_option_set$2',type,fmb_'D_option_set$'_2:'D_option_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_option_set$'] : (
% 28.54/4.55 X = 'bot$t' | X = fmb_'D_option_set$'_2
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$t' != fmb_'D_option_set$'_2
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_a_option_fun$',type,'B_a_option_fun$':$tType).
% 28.54/4.55 tff('declare_B_a_option_fun$1',type,fmb_'B_a_option_fun$'_1:'B_a_option_fun$').
% 28.54/4.55 tff('declare_B_a_option_fun$2',type,fmb_'B_a_option_fun$'_2:'B_a_option_fun$').
% 28.54/4.55 tff('declare_B_a_option_fun$3',type,fmb_'B_a_option_fun$'_3:'B_a_option_fun$').
% 28.54/4.55 tff('declare_B_a_option_fun$4',type,fmb_'B_a_option_fun$'_4:'B_a_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_a_option_fun$'] : (
% 28.54/4.55 X = fmb_'B_a_option_fun$'_1 | X = fmb_'B_a_option_fun$'_2 | X = fmb_'B_a_option_fun$'_3 | X = fmb_'B_a_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_a_option_fun$'_1 != fmb_'B_a_option_fun$'_2 & fmb_'B_a_option_fun$'_1 != fmb_'B_a_option_fun$'_3 & fmb_'B_a_option_fun$'_1 != fmb_'B_a_option_fun$'_4 & fmb_'B_a_option_fun$'_2 != fmb_'B_a_option_fun$'_3 & fmb_'B_a_option_fun$'_2 != fmb_'B_a_option_fun$'_4 &
% 28.54/4.55 fmb_'B_a_option_fun$'_3 != fmb_'B_a_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_option_c_option_fun$',type,'C_option_c_option_fun$':$tType).
% 28.54/4.55 tff('declare_C_option_c_option_fun$1',type,fmb_'C_option_c_option_fun$'_1:'C_option_c_option_fun$').
% 28.54/4.55 tff('declare_C_option_c_option_fun$2',type,fmb_'C_option_c_option_fun$'_2:'C_option_c_option_fun$').
% 28.54/4.55 tff('declare_C_option_c_option_fun$3',type,fmb_'C_option_c_option_fun$'_3:'C_option_c_option_fun$').
% 28.54/4.55 tff('declare_C_option_c_option_fun$4',type,fmb_'C_option_c_option_fun$'_4:'C_option_c_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_option_c_option_fun$'] : (
% 28.54/4.55 X = fmb_'C_option_c_option_fun$'_1 | X = fmb_'C_option_c_option_fun$'_2 | X = fmb_'C_option_c_option_fun$'_3 | X = fmb_'C_option_c_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_option_c_option_fun$'_1 != fmb_'C_option_c_option_fun$'_2 & fmb_'C_option_c_option_fun$'_1 != fmb_'C_option_c_option_fun$'_3 & fmb_'C_option_c_option_fun$'_1 != fmb_'C_option_c_option_fun$'_4 & fmb_'C_option_c_option_fun$'_2 != fmb_'C_option_c_option_fun$'_3 & fmb_'C_option_c_option_fun$'_2 != fmb_'C_option_c_option_fun$'_4 &
% 28.54/4.55 fmb_'C_option_c_option_fun$'_3 != fmb_'C_option_c_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_option_d_option_bool_fun_fun$',type,'C_option_d_option_bool_fun_fun$':$tType).
% 28.54/4.55 tff('declare_C_option_d_option_bool_fun_fun$1',type,fmb_'C_option_d_option_bool_fun_fun$'_1:'C_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_C_option_d_option_bool_fun_fun$2',type,fmb_'C_option_d_option_bool_fun_fun$'_2:'C_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_C_option_d_option_bool_fun_fun$3',type,fmb_'C_option_d_option_bool_fun_fun$'_3:'C_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_C_option_d_option_bool_fun_fun$4',type,fmb_'C_option_d_option_bool_fun_fun$'_4:'C_option_d_option_bool_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_option_d_option_bool_fun_fun$'] : (
% 28.54/4.55 X = fmb_'C_option_d_option_bool_fun_fun$'_1 | X = fmb_'C_option_d_option_bool_fun_fun$'_2 | X = fmb_'C_option_d_option_bool_fun_fun$'_3 | X = fmb_'C_option_d_option_bool_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_option_d_option_bool_fun_fun$'_1 != fmb_'C_option_d_option_bool_fun_fun$'_2 & fmb_'C_option_d_option_bool_fun_fun$'_1 != fmb_'C_option_d_option_bool_fun_fun$'_3 & fmb_'C_option_d_option_bool_fun_fun$'_1 != fmb_'C_option_d_option_bool_fun_fun$'_4 & fmb_'C_option_d_option_bool_fun_fun$'_2 != fmb_'C_option_d_option_bool_fun_fun$'_3 & fmb_'C_option_d_option_bool_fun_fun$'_2 != fmb_'C_option_d_option_bool_fun_fun$'_4 &
% 28.54/4.55 fmb_'C_option_d_option_bool_fun_fun$'_3 != fmb_'C_option_d_option_bool_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_d_option_fun_d_option_fun$',type,'D_d_option_fun_d_option_fun$':$tType).
% 28.54/4.55 tff('declare_D_d_option_fun_d_option_fun$1',type,fmb_'D_d_option_fun_d_option_fun$'_1:'D_d_option_fun_d_option_fun$').
% 28.54/4.55 tff('declare_D_d_option_fun_d_option_fun$2',type,fmb_'D_d_option_fun_d_option_fun$'_2:'D_d_option_fun_d_option_fun$').
% 28.54/4.55 tff('declare_D_d_option_fun_d_option_fun$3',type,fmb_'D_d_option_fun_d_option_fun$'_3:'D_d_option_fun_d_option_fun$').
% 28.54/4.55 tff('declare_D_d_option_fun_d_option_fun$4',type,fmb_'D_d_option_fun_d_option_fun$'_4:'D_d_option_fun_d_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_d_option_fun_d_option_fun$'] : (
% 28.54/4.55 X = fmb_'D_d_option_fun_d_option_fun$'_1 | X = fmb_'D_d_option_fun_d_option_fun$'_2 | X = fmb_'D_d_option_fun_d_option_fun$'_3 | X = fmb_'D_d_option_fun_d_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_d_option_fun_d_option_fun$'_1 != fmb_'D_d_option_fun_d_option_fun$'_2 & fmb_'D_d_option_fun_d_option_fun$'_1 != fmb_'D_d_option_fun_d_option_fun$'_3 & fmb_'D_d_option_fun_d_option_fun$'_1 != fmb_'D_d_option_fun_d_option_fun$'_4 & fmb_'D_d_option_fun_d_option_fun$'_2 != fmb_'D_d_option_fun_d_option_fun$'_3 & fmb_'D_d_option_fun_d_option_fun$'_2 != fmb_'D_d_option_fun_d_option_fun$'_4 &
% 28.54/4.55 fmb_'D_d_option_fun_d_option_fun$'_3 != fmb_'D_d_option_fun_d_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_b_b_fun_fun$',type,'B_b_b_fun_fun$':$tType).
% 28.54/4.55 tff('declare_B_b_b_fun_fun$1',type,fmb_'B_b_b_fun_fun$'_1:'B_b_b_fun_fun$').
% 28.54/4.55 tff('declare_B_b_b_fun_fun$2',type,fmb_'B_b_b_fun_fun$'_2:'B_b_b_fun_fun$').
% 28.54/4.55 tff('declare_B_b_b_fun_fun$3',type,fmb_'B_b_b_fun_fun$'_3:'B_b_b_fun_fun$').
% 28.54/4.55 tff('declare_B_b_b_fun_fun$4',type,fmb_'B_b_b_fun_fun$'_4:'B_b_b_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_b_b_fun_fun$'] : (
% 28.54/4.55 X = fmb_'B_b_b_fun_fun$'_1 | X = fmb_'B_b_b_fun_fun$'_2 | X = fmb_'B_b_b_fun_fun$'_3 | X = fmb_'B_b_b_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_b_b_fun_fun$'_1 != fmb_'B_b_b_fun_fun$'_2 & fmb_'B_b_b_fun_fun$'_1 != fmb_'B_b_b_fun_fun$'_3 & fmb_'B_b_b_fun_fun$'_1 != fmb_'B_b_b_fun_fun$'_4 & fmb_'B_b_b_fun_fun$'_2 != fmb_'B_b_b_fun_fun$'_3 & fmb_'B_b_b_fun_fun$'_2 != fmb_'B_b_b_fun_fun$'_4 &
% 28.54/4.55 fmb_'B_b_b_fun_fun$'_3 != fmb_'B_b_b_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_option_c_option_bool_fun_fun$',type,'D_option_c_option_bool_fun_fun$':$tType).
% 28.54/4.55 tff('declare_D_option_c_option_bool_fun_fun$1',type,fmb_'D_option_c_option_bool_fun_fun$'_1:'D_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_D_option_c_option_bool_fun_fun$2',type,fmb_'D_option_c_option_bool_fun_fun$'_2:'D_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_D_option_c_option_bool_fun_fun$3',type,fmb_'D_option_c_option_bool_fun_fun$'_3:'D_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_D_option_c_option_bool_fun_fun$4',type,fmb_'D_option_c_option_bool_fun_fun$'_4:'D_option_c_option_bool_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_option_c_option_bool_fun_fun$'] : (
% 28.54/4.55 X = fmb_'D_option_c_option_bool_fun_fun$'_1 | X = fmb_'D_option_c_option_bool_fun_fun$'_2 | X = fmb_'D_option_c_option_bool_fun_fun$'_3 | X = fmb_'D_option_c_option_bool_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_option_c_option_bool_fun_fun$'_1 != fmb_'D_option_c_option_bool_fun_fun$'_2 & fmb_'D_option_c_option_bool_fun_fun$'_1 != fmb_'D_option_c_option_bool_fun_fun$'_3 & fmb_'D_option_c_option_bool_fun_fun$'_1 != fmb_'D_option_c_option_bool_fun_fun$'_4 & fmb_'D_option_c_option_bool_fun_fun$'_2 != fmb_'D_option_c_option_bool_fun_fun$'_3 & fmb_'D_option_c_option_bool_fun_fun$'_2 != fmb_'D_option_c_option_bool_fun_fun$'_4 &
% 28.54/4.55 fmb_'D_option_c_option_bool_fun_fun$'_3 != fmb_'D_option_c_option_bool_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_b_option_fun$',type,'B_b_option_fun$':$tType).
% 28.54/4.55 tff('declare_B_b_option_fun$1',type,'some$c':'B_b_option_fun$').
% 28.54/4.55 tff('declare_B_b_option_fun$2',type,fmb_'B_b_option_fun$'_2:'B_b_option_fun$').
% 28.54/4.55 tff('declare_B_b_option_fun$3',type,fmb_'B_b_option_fun$'_3:'B_b_option_fun$').
% 28.54/4.55 tff('declare_B_b_option_fun$4',type,fmb_'B_b_option_fun$'_4:'B_b_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_b_option_fun$'] : (
% 28.54/4.55 X = 'some$c' | X = fmb_'B_b_option_fun$'_2 | X = fmb_'B_b_option_fun$'_3 | X = fmb_'B_b_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'some$c' != fmb_'B_b_option_fun$'_2 & 'some$c' != fmb_'B_b_option_fun$'_3 & 'some$c' != fmb_'B_b_option_fun$'_4 & fmb_'B_b_option_fun$'_2 != fmb_'B_b_option_fun$'_3 & fmb_'B_b_option_fun$'_2 != fmb_'B_b_option_fun$'_4 &
% 28.54/4.55 fmb_'B_b_option_fun$'_3 != fmb_'B_b_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_option_option$',type,'C_option_option$':$tType).
% 28.54/4.55 tff('declare_C_option_option$1',type,fmb_'C_option_option$'_1:'C_option_option$').
% 28.54/4.55 tff('declare_C_option_option$2',type,fmb_'C_option_option$'_2:'C_option_option$').
% 28.54/4.55 tff('declare_C_option_option$3',type,fmb_'C_option_option$'_3:'C_option_option$').
% 28.54/4.55 tff('declare_C_option_option$4',type,fmb_'C_option_option$'_4:'C_option_option$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_option_option$'] : (
% 28.54/4.55 X = fmb_'C_option_option$'_1 | X = fmb_'C_option_option$'_2 | X = fmb_'C_option_option$'_3 | X = fmb_'C_option_option$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_option_option$'_1 != fmb_'C_option_option$'_2 & fmb_'C_option_option$'_1 != fmb_'C_option_option$'_3 & fmb_'C_option_option$'_1 != fmb_'C_option_option$'_4 & fmb_'C_option_option$'_2 != fmb_'C_option_option$'_3 & fmb_'C_option_option$'_2 != fmb_'C_option_option$'_4 &
% 28.54/4.55 fmb_'C_option_option$'_3 != fmb_'C_option_option$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_b_prod_bool_fun$',type,'A_b_prod_bool_fun$':$tType).
% 28.54/4.55 tff('declare_A_b_prod_bool_fun$1',type,fmb_'A_b_prod_bool_fun$'_1:'A_b_prod_bool_fun$').
% 28.54/4.55 tff('declare_A_b_prod_bool_fun$2',type,fmb_'A_b_prod_bool_fun$'_2:'A_b_prod_bool_fun$').
% 28.54/4.55 tff('declare_A_b_prod_bool_fun$3',type,fmb_'A_b_prod_bool_fun$'_3:'A_b_prod_bool_fun$').
% 28.54/4.55 tff('declare_A_b_prod_bool_fun$4',type,fmb_'A_b_prod_bool_fun$'_4:'A_b_prod_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_b_prod_bool_fun$'] : (
% 28.54/4.55 X = fmb_'A_b_prod_bool_fun$'_1 | X = fmb_'A_b_prod_bool_fun$'_2 | X = fmb_'A_b_prod_bool_fun$'_3 | X = fmb_'A_b_prod_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'A_b_prod_bool_fun$'_1 != fmb_'A_b_prod_bool_fun$'_2 & fmb_'A_b_prod_bool_fun$'_1 != fmb_'A_b_prod_bool_fun$'_3 & fmb_'A_b_prod_bool_fun$'_1 != fmb_'A_b_prod_bool_fun$'_4 & fmb_'A_b_prod_bool_fun$'_2 != fmb_'A_b_prod_bool_fun$'_3 & fmb_'A_b_prod_bool_fun$'_2 != fmb_'A_b_prod_bool_fun$'_4 &
% 28.54/4.55 fmb_'A_b_prod_bool_fun$'_3 != fmb_'A_b_prod_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_option_bool_fun$',type,'C_option_bool_fun$':$tType).
% 28.54/4.55 tff('declare_C_option_bool_fun$1',type,'is_none$b':'C_option_bool_fun$').
% 28.54/4.55 tff('declare_C_option_bool_fun$2',type,fmb_'C_option_bool_fun$'_2:'C_option_bool_fun$').
% 28.54/4.55 tff('declare_C_option_bool_fun$3',type,fmb_'C_option_bool_fun$'_3:'C_option_bool_fun$').
% 28.54/4.55 tff('declare_C_option_bool_fun$4',type,fmb_'C_option_bool_fun$'_4:'C_option_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_option_bool_fun$'] : (
% 28.54/4.55 X = 'is_none$b' | X = fmb_'C_option_bool_fun$'_2 | X = fmb_'C_option_bool_fun$'_3 | X = fmb_'C_option_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'is_none$b' != fmb_'C_option_bool_fun$'_2 & 'is_none$b' != fmb_'C_option_bool_fun$'_3 & 'is_none$b' != fmb_'C_option_bool_fun$'_4 & fmb_'C_option_bool_fun$'_2 != fmb_'C_option_bool_fun$'_3 & fmb_'C_option_bool_fun$'_2 != fmb_'C_option_bool_fun$'_4 &
% 28.54/4.55 fmb_'C_option_bool_fun$'_3 != fmb_'C_option_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_option$',type,'D_option$':$tType).
% 28.54/4.55 tff('declare_D_option$1',type,'none$b':'D_option$').
% 28.54/4.55 tff('declare_D_option$2',type,fmb_'D_option$'_2:'D_option$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_option$'] : (
% 28.54/4.55 X = 'none$b' | X = fmb_'D_option$'_2
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'none$b' != fmb_'D_option$'_2
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_a_option_fun_a_c_option_fun_fun$',type,'A_a_option_fun_a_c_option_fun_fun$':$tType).
% 28.54/4.55 tff('declare_A_a_option_fun_a_c_option_fun_fun$1',type,fmb_'A_a_option_fun_a_c_option_fun_fun$'_1:'A_a_option_fun_a_c_option_fun_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun_a_c_option_fun_fun$2',type,fmb_'A_a_option_fun_a_c_option_fun_fun$'_2:'A_a_option_fun_a_c_option_fun_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun_a_c_option_fun_fun$3',type,fmb_'A_a_option_fun_a_c_option_fun_fun$'_3:'A_a_option_fun_a_c_option_fun_fun$').
% 28.54/4.55 tff('declare_A_a_option_fun_a_c_option_fun_fun$4',type,fmb_'A_a_option_fun_a_c_option_fun_fun$'_4:'A_a_option_fun_a_c_option_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_a_option_fun_a_c_option_fun_fun$'] : (
% 28.54/4.55 X = fmb_'A_a_option_fun_a_c_option_fun_fun$'_1 | X = fmb_'A_a_option_fun_a_c_option_fun_fun$'_2 | X = fmb_'A_a_option_fun_a_c_option_fun_fun$'_3 | X = fmb_'A_a_option_fun_a_c_option_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'A_a_option_fun_a_c_option_fun_fun$'_1 != fmb_'A_a_option_fun_a_c_option_fun_fun$'_2 & fmb_'A_a_option_fun_a_c_option_fun_fun$'_1 != fmb_'A_a_option_fun_a_c_option_fun_fun$'_3 & fmb_'A_a_option_fun_a_c_option_fun_fun$'_1 != fmb_'A_a_option_fun_a_c_option_fun_fun$'_4 & fmb_'A_a_option_fun_a_c_option_fun_fun$'_2 != fmb_'A_a_option_fun_a_c_option_fun_fun$'_3 & fmb_'A_a_option_fun_a_c_option_fun_fun$'_2 != fmb_'A_a_option_fun_a_c_option_fun_fun$'_4 &
% 28.54/4.55 fmb_'A_a_option_fun_a_c_option_fun_fun$'_3 != fmb_'A_a_option_fun_a_c_option_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_c_option_fun_c_option_fun$',type,'C_c_option_fun_c_option_fun$':$tType).
% 28.54/4.55 tff('declare_C_c_option_fun_c_option_fun$1',type,fmb_'C_c_option_fun_c_option_fun$'_1:'C_c_option_fun_c_option_fun$').
% 28.54/4.55 tff('declare_C_c_option_fun_c_option_fun$2',type,fmb_'C_c_option_fun_c_option_fun$'_2:'C_c_option_fun_c_option_fun$').
% 28.54/4.55 tff('declare_C_c_option_fun_c_option_fun$3',type,fmb_'C_c_option_fun_c_option_fun$'_3:'C_c_option_fun_c_option_fun$').
% 28.54/4.55 tff('declare_C_c_option_fun_c_option_fun$4',type,fmb_'C_c_option_fun_c_option_fun$'_4:'C_c_option_fun_c_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_c_option_fun_c_option_fun$'] : (
% 28.54/4.55 X = fmb_'C_c_option_fun_c_option_fun$'_1 | X = fmb_'C_c_option_fun_c_option_fun$'_2 | X = fmb_'C_c_option_fun_c_option_fun$'_3 | X = fmb_'C_c_option_fun_c_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'C_c_option_fun_c_option_fun$'_1 != fmb_'C_c_option_fun_c_option_fun$'_2 & fmb_'C_c_option_fun_c_option_fun$'_1 != fmb_'C_c_option_fun_c_option_fun$'_3 & fmb_'C_c_option_fun_c_option_fun$'_1 != fmb_'C_c_option_fun_c_option_fun$'_4 & fmb_'C_c_option_fun_c_option_fun$'_2 != fmb_'C_c_option_fun_c_option_fun$'_3 & fmb_'C_c_option_fun_c_option_fun$'_2 != fmb_'C_c_option_fun_c_option_fun$'_4 &
% 28.54/4.55 fmb_'C_c_option_fun_c_option_fun$'_3 != fmb_'C_c_option_fun_c_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_b_prod$',type,'C_b_prod$':$tType).
% 28.54/4.55 tff('declare_C_b_prod$1',type,fmb_'C_b_prod$'_1:'C_b_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_b_prod$'] : (
% 28.54/4.55 X = fmb_'C_b_prod$'_1
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_d_prod$',type,'C_d_prod$':$tType).
% 28.54/4.55 tff('declare_C_d_prod$1',type,fmb_'C_d_prod$'_1:'C_d_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_d_prod$'] : (
% 28.54/4.55 X = fmb_'C_d_prod$'_1
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_d_option_fun$',type,'C_d_option_fun$':$tType).
% 28.54/4.55 tff('declare_C_d_option_fun$1',type,'b$':'C_d_option_fun$').
% 28.54/4.55 tff('declare_C_d_option_fun$2',type,fmb_'C_d_option_fun$'_2:'C_d_option_fun$').
% 28.54/4.55 tff('declare_C_d_option_fun$3',type,fmb_'C_d_option_fun$'_3:'C_d_option_fun$').
% 28.54/4.55 tff('declare_C_d_option_fun$4',type,fmb_'C_d_option_fun$'_4:'C_d_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_d_option_fun$'] : (
% 28.54/4.55 X = 'b$' | X = fmb_'C_d_option_fun$'_2 | X = fmb_'C_d_option_fun$'_3 | X = fmb_'C_d_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'b$' != fmb_'C_d_option_fun$'_2 & 'b$' != fmb_'C_d_option_fun$'_3 & 'b$' != fmb_'C_d_option_fun$'_4 & fmb_'C_d_option_fun$'_2 != fmb_'C_d_option_fun$'_3 & fmb_'C_d_option_fun$'_2 != fmb_'C_d_option_fun$'_4 &
% 28.54/4.55 fmb_'C_d_option_fun$'_3 != fmb_'C_d_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_option_bool_fun$',type,'B_option_bool_fun$':$tType).
% 28.54/4.55 tff('declare_B_option_bool_fun$1',type,'is_none$':'B_option_bool_fun$').
% 28.54/4.55 tff('declare_B_option_bool_fun$2',type,'bot$o':'B_option_bool_fun$').
% 28.54/4.55 tff('declare_B_option_bool_fun$3',type,fmb_'B_option_bool_fun$'_3:'B_option_bool_fun$').
% 28.54/4.55 tff('declare_B_option_bool_fun$4',type,fmb_'B_option_bool_fun$'_4:'B_option_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_option_bool_fun$'] : (
% 28.54/4.55 X = 'is_none$' | X = 'bot$o' | X = fmb_'B_option_bool_fun$'_3 | X = fmb_'B_option_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'is_none$' != 'bot$o' & 'is_none$' != fmb_'B_option_bool_fun$'_3 & 'is_none$' != fmb_'B_option_bool_fun$'_4 & 'bot$o' != fmb_'B_option_bool_fun$'_3 & 'bot$o' != fmb_'B_option_bool_fun$'_4 &
% 28.54/4.55 fmb_'B_option_bool_fun$'_3 != fmb_'B_option_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_d_prod$',type,'D_d_prod$':$tType).
% 28.54/4.55 tff('declare_D_d_prod$1',type,fmb_'D_d_prod$'_1:'D_d_prod$').
% 28.54/4.55 tff('declare_D_d_prod$2',type,fmb_'D_d_prod$'_2:'D_d_prod$').
% 28.54/4.55 tff('declare_D_d_prod$3',type,fmb_'D_d_prod$'_3:'D_d_prod$').
% 28.54/4.55 tff('declare_D_d_prod$4',type,fmb_'D_d_prod$'_4:'D_d_prod$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_d_prod$'] : (
% 28.54/4.55 X = fmb_'D_d_prod$'_1 | X = fmb_'D_d_prod$'_2 | X = fmb_'D_d_prod$'_3 | X = fmb_'D_d_prod$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'D_d_prod$'_1 != fmb_'D_d_prod$'_2 & fmb_'D_d_prod$'_1 != fmb_'D_d_prod$'_3 & fmb_'D_d_prod$'_1 != fmb_'D_d_prod$'_4 & fmb_'D_d_prod$'_2 != fmb_'D_d_prod$'_3 & fmb_'D_d_prod$'_2 != fmb_'D_d_prod$'_4 &
% 28.54/4.55 fmb_'D_d_prod$'_3 != fmb_'D_d_prod$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_set$',type,'C_set$':$tType).
% 28.54/4.55 tff('declare_C_set$1',type,'bot$a':'C_set$').
% 28.54/4.55 tff('declare_C_set$2',type,fmb_'C_set$'_2:'C_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_set$'] : (
% 28.54/4.55 X = 'bot$a' | X = fmb_'C_set$'_2
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$a' != fmb_'C_set$'_2
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_option_b_option_bool_fun_fun$',type,'B_option_b_option_bool_fun_fun$':$tType).
% 28.54/4.55 tff('declare_B_option_b_option_bool_fun_fun$1',type,fmb_'B_option_b_option_bool_fun_fun$'_1:'B_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_B_option_b_option_bool_fun_fun$2',type,fmb_'B_option_b_option_bool_fun_fun$'_2:'B_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_B_option_b_option_bool_fun_fun$3',type,fmb_'B_option_b_option_bool_fun_fun$'_3:'B_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff('declare_B_option_b_option_bool_fun_fun$4',type,fmb_'B_option_b_option_bool_fun_fun$'_4:'B_option_b_option_bool_fun_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_option_b_option_bool_fun_fun$'] : (
% 28.54/4.55 X = fmb_'B_option_b_option_bool_fun_fun$'_1 | X = fmb_'B_option_b_option_bool_fun_fun$'_2 | X = fmb_'B_option_b_option_bool_fun_fun$'_3 | X = fmb_'B_option_b_option_bool_fun_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 fmb_'B_option_b_option_bool_fun_fun$'_1 != fmb_'B_option_b_option_bool_fun_fun$'_2 & fmb_'B_option_b_option_bool_fun_fun$'_1 != fmb_'B_option_b_option_bool_fun_fun$'_3 & fmb_'B_option_b_option_bool_fun_fun$'_1 != fmb_'B_option_b_option_bool_fun_fun$'_4 & fmb_'B_option_b_option_bool_fun_fun$'_2 != fmb_'B_option_b_option_bool_fun_fun$'_3 & fmb_'B_option_b_option_bool_fun_fun$'_2 != fmb_'B_option_b_option_bool_fun_fun$'_4 &
% 28.54/4.55 fmb_'B_option_b_option_bool_fun_fun$'_3 != fmb_'B_option_b_option_bool_fun_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_bool_fun$',type,'B_bool_fun$':$tType).
% 28.54/4.55 tff('declare_B_bool_fun$1',type,'bot$r':'B_bool_fun$').
% 28.54/4.55 tff('declare_B_bool_fun$2',type,fmb_'B_bool_fun$'_2:'B_bool_fun$').
% 28.54/4.55 tff('declare_B_bool_fun$3',type,fmb_'B_bool_fun$'_3:'B_bool_fun$').
% 28.54/4.55 tff('declare_B_bool_fun$4',type,fmb_'B_bool_fun$'_4:'B_bool_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_bool_fun$'] : (
% 28.54/4.55 X = 'bot$r' | X = fmb_'B_bool_fun$'_2 | X = fmb_'B_bool_fun$'_3 | X = fmb_'B_bool_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$r' != fmb_'B_bool_fun$'_2 & 'bot$r' != fmb_'B_bool_fun$'_3 & 'bot$r' != fmb_'B_bool_fun$'_4 & fmb_'B_bool_fun$'_2 != fmb_'B_bool_fun$'_3 & fmb_'B_bool_fun$'_2 != fmb_'B_bool_fun$'_4 &
% 28.54/4.55 fmb_'B_bool_fun$'_3 != fmb_'B_bool_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_D_d_option_fun$',type,'D_d_option_fun$':$tType).
% 28.54/4.55 tff('declare_D_d_option_fun$1',type,'some$b':'D_d_option_fun$').
% 28.54/4.55 tff('declare_D_d_option_fun$2',type,fmb_'D_d_option_fun$'_2:'D_d_option_fun$').
% 28.54/4.55 tff('declare_D_d_option_fun$3',type,fmb_'D_d_option_fun$'_3:'D_d_option_fun$').
% 28.54/4.55 tff('declare_D_d_option_fun$4',type,fmb_'D_d_option_fun$'_4:'D_d_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'D_d_option_fun$'] : (
% 28.54/4.55 X = 'some$b' | X = fmb_'D_d_option_fun$'_2 | X = fmb_'D_d_option_fun$'_3 | X = fmb_'D_d_option_fun$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'some$b' != fmb_'D_d_option_fun$'_2 & 'some$b' != fmb_'D_d_option_fun$'_3 & 'some$b' != fmb_'D_d_option_fun$'_4 & fmb_'D_d_option_fun$'_2 != fmb_'D_d_option_fun$'_3 & fmb_'D_d_option_fun$'_2 != fmb_'D_d_option_fun$'_4 &
% 28.54/4.55 fmb_'D_d_option_fun$'_3 != fmb_'D_d_option_fun$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_A_c_option_fun$',type,'A_c_option_fun$':$tType).
% 28.54/4.55 tff('declare_A_c_option_fun$1',type,'c$':'A_c_option_fun$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'A_c_option_fun$'] : (
% 28.54/4.55 X = 'c$'
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff('declare_B_option_set$',type,'B_option_set$':$tType).
% 28.54/4.55 tff('declare_B_option_set$1',type,'bot$m':'B_option_set$').
% 28.54/4.55 tff('declare_B_option_set$2',type,fmb_'B_option_set$'_2:'B_option_set$').
% 28.54/4.55 tff('declare_B_option_set$3',type,fmb_'B_option_set$'_3:'B_option_set$').
% 28.54/4.55 tff('declare_B_option_set$4',type,fmb_'B_option_set$'_4:'B_option_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'B_option_set$'] : (
% 28.54/4.55 X = 'bot$m' | X = fmb_'B_option_set$'_2 | X = fmb_'B_option_set$'_3 | X = fmb_'B_option_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$m' != fmb_'B_option_set$'_2 & 'bot$m' != fmb_'B_option_set$'_3 & 'bot$m' != fmb_'B_option_set$'_4 & fmb_'B_option_set$'_2 != fmb_'B_option_set$'_3 & fmb_'B_option_set$'_2 != fmb_'B_option_set$'_4 &
% 28.54/4.55 fmb_'B_option_set$'_3 != fmb_'B_option_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_C_b_prod_set$',type,'C_b_prod_set$':$tType).
% 28.54/4.55 tff('declare_C_b_prod_set$1',type,'bot$i':'C_b_prod_set$').
% 28.54/4.55 tff('declare_C_b_prod_set$2',type,fmb_'C_b_prod_set$'_2:'C_b_prod_set$').
% 28.54/4.55 tff('declare_C_b_prod_set$3',type,fmb_'C_b_prod_set$'_3:'C_b_prod_set$').
% 28.54/4.55 tff('declare_C_b_prod_set$4',type,fmb_'C_b_prod_set$'_4:'C_b_prod_set$').
% 28.54/4.55 tff(finite_domain,axiom,
% 28.54/4.55 ! [X:'C_b_prod_set$'] : (
% 28.54/4.55 X = 'bot$i' | X = fmb_'C_b_prod_set$'_2 | X = fmb_'C_b_prod_set$'_3 | X = fmb_'C_b_prod_set$'_4
% 28.54/4.55 ) ).
% 28.54/4.55
% 28.54/4.55 tff(distinct_domain,axiom,
% 28.54/4.55 'bot$i' != fmb_'C_b_prod_set$'_2 & 'bot$i' != fmb_'C_b_prod_set$'_3 & 'bot$i' != fmb_'C_b_prod_set$'_4 & fmb_'C_b_prod_set$'_2 != fmb_'C_b_prod_set$'_3 & fmb_'C_b_prod_set$'_2 != fmb_'C_b_prod_set$'_4 &
% 28.54/4.55 fmb_'C_b_prod_set$'_3 != fmb_'C_b_prod_set$'_4
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$a',type,'relcomp$a': 'C_d_prod_set$' * 'D_b_prod_set$' > 'C_b_prod_set$').
% 28.54/4.55 tff('function_relcomp$a',axiom,
% 28.54/4.55 'relcomp$a'('bot$h','bot$l') = 'bot$i'
% 28.54/4.55 & 'relcomp$a'('bot$h',fmb_'D_b_prod_set$'_2) = 'bot$i'
% 28.54/4.55 & 'relcomp$a'('bot$h',fmb_'D_b_prod_set$'_3) = 'bot$i'
% 28.54/4.55 & 'relcomp$a'('bot$h',fmb_'D_b_prod_set$'_4) = 'bot$i'
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_2,'bot$l') = 'bot$i'
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_2,fmb_'D_b_prod_set$'_2) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_2,fmb_'D_b_prod_set$'_3) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_2,fmb_'D_b_prod_set$'_4) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_3,'bot$l') = 'bot$i'
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_3,fmb_'D_b_prod_set$'_2) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_3,fmb_'D_b_prod_set$'_3) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_3,fmb_'D_b_prod_set$'_4) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_4,'bot$l') = 'bot$i'
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_4,fmb_'D_b_prod_set$'_2) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_4,fmb_'D_b_prod_set$'_3) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'relcomp$a'(fmb_'C_d_prod_set$'_4,fmb_'D_b_prod_set$'_4) = fmb_'C_b_prod_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_the_elem$',type,'the_elem$': 'B_option_set$' > 'B_option$').
% 28.54/4.55 tff('function_the_elem$',axiom,
% 28.54/4.55 'the_elem$'('bot$m') = 'none$c'
% 28.54/4.55 & 'the_elem$'(fmb_'B_option_set$'_2) = 'none$c'
% 28.54/4.55 & 'the_elem$'(fmb_'B_option_set$'_3) = fmb_'B_option$'_2
% 28.54/4.55 & 'the_elem$'(fmb_'B_option_set$'_4) = fmb_'B_option$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$g',type,'fun_app$g': 'A_a_option_fun_a_b_option_fun_fun$' * 'A_a_option_fun$' > 'A_b_option_fun$').
% 28.54/4.55 tff('function_fun_app$g',axiom,
% 28.54/4.55 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_1,'some$') = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_1,fmb_'A_a_option_fun$'_2) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_1,fmb_'A_a_option_fun$'_3) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_1,fmb_'A_a_option_fun$'_4) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_2,'some$') = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_2,fmb_'A_a_option_fun$'_2) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_2,fmb_'A_a_option_fun$'_3) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_2,fmb_'A_a_option_fun$'_4) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_3,'some$') = fmb_'A_b_option_fun$'_2
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_3,fmb_'A_a_option_fun$'_2) = fmb_'A_b_option_fun$'_2
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_3,fmb_'A_a_option_fun$'_3) = fmb_'A_b_option_fun$'_2
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_3,fmb_'A_a_option_fun$'_4) = fmb_'A_b_option_fun$'_2
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_4,'some$') = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_4,fmb_'A_a_option_fun$'_2) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_4,fmb_'A_a_option_fun$'_3) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'fun_app$g'(fmb_'A_a_option_fun_a_b_option_fun_fun$'_4,fmb_'A_a_option_fun$'_4) = fmb_'A_b_option_fun$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_pair$g',type,'pair$g': 'A$' * 'D$' > 'A_d_prod$').
% 28.54/4.55 tff('function_pair$g',axiom,
% 28.54/4.55 'pair$g'(fmb_'A$'_1,fmb_'D$'_1) = fmb_'A_d_prod$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_image$c',type,'image$c': 'A_b_prod_set$' * 'A_set$' > 'B_set$').
% 28.54/4.55 tff('function_image$c',axiom,
% 28.54/4.55 'image$c'('bot$d','bot$c') = fmb_'B_set$'_2
% 28.54/4.55 % 'image$c'('bot$d',fmb_'A_set$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_insert$c',type,'insert$c': 'C$' * 'C_set$' > 'C_set$').
% 28.54/4.55 tff('function_insert$c',axiom,
% 28.54/4.55 'insert$c'(fmb_'C$'_1,'bot$a') = fmb_'C_set$'_2
% 28.54/4.55 & 'insert$c'(fmb_'C$'_1,fmb_'C_set$'_2) = fmb_'C_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$r',type,'relcomp$r': 'A_a_prod_set$' * 'A_b_prod_set$' > 'A_b_prod_set$').
% 28.54/4.55 tff('function_relcomp$r',axiom,
% 28.54/4.55 'relcomp$r'('bot$f','bot$d') = 'bot$d'
% 28.54/4.55 & 'relcomp$r'(fmb_'A_a_prod_set$'_2,'bot$d') = 'bot$d'
% 28.54/4.55 & 'relcomp$r'(fmb_'A_a_prod_set$'_3,'bot$d') = 'bot$d'
% 28.54/4.55 & 'relcomp$r'(fmb_'A_a_prod_set$'_4,'bot$d') = 'bot$d'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_comp$g',type,'map_comp$g': 'A_d_option_fun$' * 'C_a_option_fun$' > 'C_d_option_fun$').
% 28.54/4.55 tff('function_map_comp$g',axiom,
% 28.54/4.55 'map_comp$g'(fmb_'A_d_option_fun$'_1,fmb_'C_a_option_fun$'_1) = 'b$'
% 28.54/4.55 & 'map_comp$g'(fmb_'A_d_option_fun$'_1,fmb_'C_a_option_fun$'_2) = fmb_'C_d_option_fun$'_3
% 28.54/4.55 & 'map_comp$g'(fmb_'A_d_option_fun$'_1,fmb_'C_a_option_fun$'_3) = fmb_'C_d_option_fun$'_3
% 28.54/4.55 & 'map_comp$g'(fmb_'A_d_option_fun$'_1,fmb_'C_a_option_fun$'_4) = 'b$'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_dom$d',type,'dom$d': 'A_b_option_fun$' > 'A_set$').
% 28.54/4.55 tff('function_dom$d',axiom,
% 28.54/4.55 'dom$d'(fmb_'A_b_option_fun$'_1) = 'bot$c'
% 28.54/4.55 & 'dom$d'(fmb_'A_b_option_fun$'_2) = fmb_'A_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_bind$h',type,'bind$h': 'B_option$' > 'B_b_option_fun_b_option_fun$').
% 28.54/4.55 tff('function_bind$h',axiom,
% 28.54/4.55 'bind$h'('none$c') = fmb_'B_b_option_fun_b_option_fun$'_1
% 28.54/4.55 & 'bind$h'(fmb_'B_option$'_2) = fmb_'B_b_option_fun_b_option_fun$'_3
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_upd$b',type,'fun_upd$b': 'A_d_option_fun$' * 'A$' * 'D_option$' > 'A_d_option_fun$').
% 28.54/4.55 tff('function_fun_upd$b',axiom,
% 28.54/4.55 'fun_upd$b'(fmb_'A_d_option_fun$'_1,fmb_'A$'_1,'none$b') = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_upd$b'(fmb_'A_d_option_fun$'_1,fmb_'A$'_1,fmb_'D_option$'_2) = fmb_'A_d_option_fun$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$i',type,'restrict_map$i': 'A_b_option_fun$' * 'A_set$' > 'A_b_option_fun$').
% 28.54/4.55 tff('function_restrict_map$i',axiom,
% 28.54/4.55 'restrict_map$i'(fmb_'A_b_option_fun$'_1,'bot$c') = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'restrict_map$i'(fmb_'A_b_option_fun$'_1,fmb_'A_set$'_2) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'restrict_map$i'(fmb_'A_b_option_fun$'_2,'bot$c') = fmb_'A_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$i'(fmb_'A_b_option_fun$'_2,fmb_'A_set$'_2) = fmb_'A_b_option_fun$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_collect$',type,'collect$': 'B_option_bool_fun$' > 'B_option_set$').
% 28.54/4.55 tff('function_collect$',axiom,
% 28.54/4.55 'collect$'('is_none$') = fmb_'B_option_set$'_2
% 28.54/4.55 & 'collect$'('bot$o') = 'bot$m'
% 28.54/4.55 & 'collect$'(fmb_'B_option_bool_fun$'_3) = fmb_'B_option_set$'_3
% 28.54/4.55 & 'collect$'(fmb_'B_option_bool_fun$'_4) = fmb_'B_option_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$y',type,'fun_app$y': 'D_option_d_option_bool_fun_fun$' * 'D_option$' > 'D_option_bool_fun$').
% 28.54/4.55 tff('function_fun_app$y',axiom,
% 28.54/4.55 'fun_app$y'(fmb_'D_option_d_option_bool_fun_fun$'_1,'none$b') = 'is_none$a'
% 28.54/4.55 & 'fun_app$y'(fmb_'D_option_d_option_bool_fun_fun$'_1,fmb_'D_option$'_2) = 'is_none$a'
% 28.54/4.55 % 'fun_app$y'(fmb_'D_option_d_option_bool_fun_fun$'_2,'none$b') undefined in model
% 28.54/4.55 % 'fun_app$y'(fmb_'D_option_d_option_bool_fun_fun$'_2,fmb_'D_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$y'(fmb_'D_option_d_option_bool_fun_fun$'_3,'none$b') undefined in model
% 28.54/4.55 % 'fun_app$y'(fmb_'D_option_d_option_bool_fun_fun$'_3,fmb_'D_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$y'(fmb_'D_option_d_option_bool_fun_fun$'_4,'none$b') undefined in model
% 28.54/4.55 % 'fun_app$y'(fmb_'D_option_d_option_bool_fun_fun$'_4,fmb_'D_option$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$af',type,'fun_app$af': 'D_d_option_fun_d_option_fun$' * 'D_d_option_fun$' > 'D_option$').
% 28.54/4.55 tff('function_fun_app$af',axiom,
% 28.54/4.55 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_1,'some$b') = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_1,fmb_'D_d_option_fun$'_2) = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_1,fmb_'D_d_option_fun$'_3) = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_1,fmb_'D_d_option_fun$'_4) = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_2,'some$b') = fmb_'D_option$'_2
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_2,fmb_'D_d_option_fun$'_2) = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_2,fmb_'D_d_option_fun$'_3) = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_2,fmb_'D_d_option_fun$'_4) = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_3,'some$b') = fmb_'D_option$'_2
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_3,fmb_'D_d_option_fun$'_2) = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_3,fmb_'D_d_option_fun$'_3) = fmb_'D_option$'_2
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_3,fmb_'D_d_option_fun$'_4) = fmb_'D_option$'_2
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_4,'some$b') = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_4,fmb_'D_d_option_fun$'_2) = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_4,fmb_'D_d_option_fun$'_3) = 'none$b'
% 28.54/4.55 & 'fun_app$af'(fmb_'D_d_option_fun_d_option_fun$'_4,fmb_'D_d_option_fun$'_4) = 'none$b'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$t',type,'relcomp$t': 'A_b_prod_set$' * 'B_c_prod_set$' > 'A_c_prod_set$').
% 28.54/4.55 tff('function_relcomp$t',axiom,
% 28.54/4.55 'relcomp$t'('bot$d','bot$j') = 'bot$e'
% 28.54/4.55 % 'relcomp$t'('bot$d',fmb_'B_c_prod_set$'_2) undefined in model
% 28.54/4.55 % 'relcomp$t'('bot$d',fmb_'B_c_prod_set$'_3) undefined in model
% 28.54/4.55 % 'relcomp$t'('bot$d',fmb_'B_c_prod_set$'_4) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_insert$e',type,'insert$e': 'B$' * 'B_set$' > 'B_set$').
% 28.54/4.55 tff('function_insert$e',axiom,
% 28.54/4.55 'insert$e'(fmb_'B$'_1,'bot$b') = fmb_'B_set$'_2
% 28.54/4.55 & 'insert$e'(fmb_'B$'_1,fmb_'B_set$'_2) = fmb_'B_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$ab',type,'fun_app$ab': 'B_option_d_option_bool_fun_fun$' * 'B_option$' > 'D_option_bool_fun$').
% 28.54/4.55 tff('function_fun_app$ab',axiom,
% 28.54/4.55 'fun_app$ab'(fmb_'B_option_d_option_bool_fun_fun$'_1,'none$c') = 'is_none$a'
% 28.54/4.55 & 'fun_app$ab'(fmb_'B_option_d_option_bool_fun_fun$'_1,fmb_'B_option$'_2) = 'is_none$a'
% 28.54/4.55 % 'fun_app$ab'(fmb_'B_option_d_option_bool_fun_fun$'_2,'none$c') undefined in model
% 28.54/4.55 % 'fun_app$ab'(fmb_'B_option_d_option_bool_fun_fun$'_2,fmb_'B_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$ab'(fmb_'B_option_d_option_bool_fun_fun$'_3,'none$c') undefined in model
% 28.54/4.55 % 'fun_app$ab'(fmb_'B_option_d_option_bool_fun_fun$'_3,fmb_'B_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$ab'(fmb_'B_option_d_option_bool_fun_fun$'_4,'none$c') undefined in model
% 28.54/4.55 % 'fun_app$ab'(fmb_'B_option_d_option_bool_fun_fun$'_4,fmb_'B_option$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$i',type,'graph$i': 'B_d_option_fun$' > 'B_d_prod_set$').
% 28.54/4.55 tff('function_graph$i',axiom,
% 28.54/4.55 'graph$i'(fmb_'B_d_option_fun$'_1) = fmb_'B_d_prod_set$'_1
% 28.54/4.55 & 'graph$i'(fmb_'B_d_option_fun$'_2) = fmb_'B_d_prod_set$'_2
% 28.54/4.55 & 'graph$i'(fmb_'B_d_option_fun$'_3) = fmb_'B_d_prod_set$'_2
% 28.54/4.55 & 'graph$i'(fmb_'B_d_option_fun$'_4) = fmb_'B_d_prod_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_add$d',type,'map_add$d': 'A_b_option_fun$' * 'A_b_option_fun$' > 'A_b_option_fun$').
% 28.54/4.55 tff('function_map_add$d',axiom,
% 28.54/4.55 'map_add$d'(fmb_'A_b_option_fun$'_1,fmb_'A_b_option_fun$'_1) = fmb_'A_b_option_fun$'_2
% 28.54/4.55 & 'map_add$d'(fmb_'A_b_option_fun$'_1,fmb_'A_b_option_fun$'_2) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'map_add$d'(fmb_'A_b_option_fun$'_2,fmb_'A_b_option_fun$'_1) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'map_add$d'(fmb_'A_b_option_fun$'_2,fmb_'A_b_option_fun$'_2) = fmb_'A_b_option_fun$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$ax',type,'fun_app$ax': 'D_a_option_fun$' * 'D$' > 'A_option$').
% 28.54/4.55 tff('function_fun_app$ax',axiom,
% 28.54/4.55 'fun_app$ax'(fmb_'D_a_option_fun$'_1,fmb_'D$'_1) = fmb_'A_option$'_2
% 28.54/4.55 % 'fun_app$ax'(fmb_'D_a_option_fun$'_2,fmb_'D$'_1) undefined in model
% 28.54/4.55 % 'fun_app$ax'(fmb_'D_a_option_fun$'_3,fmb_'D$'_1) undefined in model
% 28.54/4.55 % 'fun_app$ax'(fmb_'D_a_option_fun$'_4,fmb_'D$'_1) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_the$d',type,'the$d': 'A_option$' > 'A$').
% 28.54/4.55 tff('function_the$d',axiom,
% 28.54/4.55 'the$d'('none$') = fmb_'A$'_1
% 28.54/4.55 & 'the$d'(fmb_'A_option$'_2) = fmb_'A$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_image$f',type,'image$f': 'C_c_option_fun$' * 'C_set$' > 'C_option_set$').
% 28.54/4.55 tff('function_image$f',axiom,
% 28.54/4.55 'image$f'('some$a','bot$a') = 'bot$n'
% 28.54/4.55 & 'image$f'('some$a',fmb_'C_set$'_2) = fmb_'C_option_set$'_4
% 28.54/4.55 & 'image$f'(fmb_'C_c_option_fun$'_2,'bot$a') = 'bot$n'
% 28.54/4.55 & 'image$f'(fmb_'C_c_option_fun$'_2,fmb_'C_set$'_2) = fmb_'C_option_set$'_2
% 28.54/4.55 & 'image$f'(fmb_'C_c_option_fun$'_3,'bot$a') = fmb_'C_option_set$'_2
% 28.54/4.55 & 'image$f'(fmb_'C_c_option_fun$'_3,fmb_'C_set$'_2) = 'bot$n'
% 28.54/4.55 & 'image$f'(fmb_'C_c_option_fun$'_4,'bot$a') = fmb_'C_option_set$'_4
% 28.54/4.55 & 'image$f'(fmb_'C_c_option_fun$'_4,fmb_'C_set$'_2) = 'bot$n'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$ad',type,'fun_app$ad': 'C_c_option_fun_c_option_fun$' * 'C_c_option_fun$' > 'C_option$').
% 28.54/4.55 tff('function_fun_app$ad',axiom,
% 28.54/4.55 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_1,'some$a') = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_1,fmb_'C_c_option_fun$'_2) = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_1,fmb_'C_c_option_fun$'_3) = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_1,fmb_'C_c_option_fun$'_4) = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_2,'some$a') = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_2,fmb_'C_c_option_fun$'_2) = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_2,fmb_'C_c_option_fun$'_3) = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_2,fmb_'C_c_option_fun$'_4) = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_3,'some$a') = fmb_'C_option$'_2
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_3,fmb_'C_c_option_fun$'_2) = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_3,fmb_'C_c_option_fun$'_3) = fmb_'C_option$'_2
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_3,fmb_'C_c_option_fun$'_4) = fmb_'C_option$'_2
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_4,'some$a') = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_4,fmb_'C_c_option_fun$'_2) = 'none$a'
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_4,fmb_'C_c_option_fun$'_3) = fmb_'C_option$'_2
% 28.54/4.55 & 'fun_app$ad'(fmb_'C_c_option_fun_c_option_fun$'_4,fmb_'C_c_option_fun$'_4) = 'none$a'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$j',type,'fun_app$j': 'C_d_option_fun$' * 'C$' > 'D_option$').
% 28.54/4.55 tff('function_fun_app$j',axiom,
% 28.54/4.55 'fun_app$j'('b$',fmb_'C$'_1) = 'none$b'
% 28.54/4.55 & 'fun_app$j'(fmb_'C_d_option_fun$'_2,fmb_'C$'_1) = 'none$b'
% 28.54/4.55 & 'fun_app$j'(fmb_'C_d_option_fun$'_3,fmb_'C$'_1) = 'none$b'
% 28.54/4.55 & 'fun_app$j'(fmb_'C_d_option_fun$'_4,fmb_'C$'_1) = 'none$b'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_uub$',type,'uub$': 'C_set$' > 'C_bool_fun$').
% 28.54/4.55 tff('function_uub$',axiom,
% 28.54/4.55 'uub$'('bot$a') = 'bot$q'
% 28.54/4.55 & 'uub$'(fmb_'C_set$'_2) = fmb_'C_bool_fun$'_3
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$e',type,'fun_app$e': 'A_a_option_fun_a_d_option_fun_fun$' * 'A_a_option_fun$' > 'A_d_option_fun$').
% 28.54/4.55 tff('function_fun_app$e',axiom,
% 28.54/4.55 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_1,'some$') = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_1,fmb_'A_a_option_fun$'_2) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_1,fmb_'A_a_option_fun$'_3) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_1,fmb_'A_a_option_fun$'_4) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_2,'some$') = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_2,fmb_'A_a_option_fun$'_2) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_2,fmb_'A_a_option_fun$'_3) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_2,fmb_'A_a_option_fun$'_4) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_3,'some$') = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_3,fmb_'A_a_option_fun$'_2) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_3,fmb_'A_a_option_fun$'_3) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_3,fmb_'A_a_option_fun$'_4) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_4,'some$') = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_4,fmb_'A_a_option_fun$'_2) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_4,fmb_'A_a_option_fun$'_3) = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'fun_app$e'(fmb_'A_a_option_fun_a_d_option_fun_fun$'_4,fmb_'A_a_option_fun$'_4) = fmb_'A_d_option_fun$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_pair$i',type,'pair$i': 'A$' * 'B$' > 'A_b_prod$').
% 28.54/4.55 tff('function_pair$i',axiom,
% 28.54/4.55 'pair$i'(fmb_'A$'_1,fmb_'B$'_1) = fmb_'A_b_prod$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$',type,'restrict_map$': 'C_a_option_fun$' * 'C_set$' > 'C_a_option_fun$').
% 28.54/4.55 tff('function_restrict_map$',axiom,
% 28.54/4.55 'restrict_map$'(fmb_'C_a_option_fun$'_1,'bot$a') = fmb_'C_a_option_fun$'_1
% 28.54/4.55 & 'restrict_map$'(fmb_'C_a_option_fun$'_1,fmb_'C_set$'_2) = fmb_'C_a_option_fun$'_1
% 28.54/4.55 & 'restrict_map$'(fmb_'C_a_option_fun$'_2,'bot$a') = fmb_'C_a_option_fun$'_1
% 28.54/4.55 & 'restrict_map$'(fmb_'C_a_option_fun$'_2,fmb_'C_set$'_2) = fmb_'C_a_option_fun$'_3
% 28.54/4.55 & 'restrict_map$'(fmb_'C_a_option_fun$'_3,'bot$a') = fmb_'C_a_option_fun$'_1
% 28.54/4.55 & 'restrict_map$'(fmb_'C_a_option_fun$'_3,fmb_'C_set$'_2) = fmb_'C_a_option_fun$'_4
% 28.54/4.55 & 'restrict_map$'(fmb_'C_a_option_fun$'_4,'bot$a') = fmb_'C_a_option_fun$'_1
% 28.54/4.55 & 'restrict_map$'(fmb_'C_a_option_fun$'_4,fmb_'C_set$'_2) = fmb_'C_a_option_fun$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$i',type,'fun_app$i': 'A_a_option_fun$' * 'A$' > 'A_option$').
% 28.54/4.55 tff('function_fun_app$i',axiom,
% 28.54/4.55 'fun_app$i'('some$',fmb_'A$'_1) = fmb_'A_option$'_2
% 28.54/4.55 & 'fun_app$i'(fmb_'A_a_option_fun$'_2,fmb_'A$'_1) = 'none$'
% 28.54/4.55 & 'fun_app$i'(fmb_'A_a_option_fun$'_3,fmb_'A$'_1) = 'none$'
% 28.54/4.55 & 'fun_app$i'(fmb_'A_a_option_fun$'_4,fmb_'A$'_1) = 'none$'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_comp$c',type,'map_comp$c': 'C_d_option_fun$' * 'A_c_option_fun$' > 'A_d_option_fun$').
% 28.54/4.55 tff('function_map_comp$c',axiom,
% 28.54/4.55 'map_comp$c'('b$','c$') = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'map_comp$c'(fmb_'C_d_option_fun$'_2,'c$') = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'map_comp$c'(fmb_'C_d_option_fun$'_3,'c$') = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'map_comp$c'(fmb_'C_d_option_fun$'_4,'c$') = fmb_'A_d_option_fun$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$e',type,'restrict_map$e': 'A_c_option_fun$' * 'A_set$' > 'A_c_option_fun$').
% 28.54/4.55 tff('function_restrict_map$e',axiom,
% 28.54/4.55 'restrict_map$e'('c$','bot$c') = 'c$'
% 28.54/4.55 & 'restrict_map$e'('c$',fmb_'A_set$'_2) = 'c$'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$m',type,'relcomp$m': 'C_b_prod_set$' * 'B_b_prod_set$' > 'C_b_prod_set$').
% 28.54/4.55 tff('function_relcomp$m',axiom,
% 28.54/4.55 'relcomp$m'('bot$i','bot$k') = 'bot$i'
% 28.54/4.55 % 'relcomp$m'('bot$i',fmb_'B_b_prod_set$'_2) undefined in model
% 28.54/4.55 % 'relcomp$m'('bot$i',fmb_'B_b_prod_set$'_3) undefined in model
% 28.54/4.55 % 'relcomp$m'('bot$i',fmb_'B_b_prod_set$'_4) undefined in model
% 28.54/4.55 & 'relcomp$m'(fmb_'C_b_prod_set$'_2,'bot$k') = 'bot$i'
% 28.54/4.55 % 'relcomp$m'(fmb_'C_b_prod_set$'_2,fmb_'B_b_prod_set$'_2) undefined in model
% 28.54/4.55 % 'relcomp$m'(fmb_'C_b_prod_set$'_2,fmb_'B_b_prod_set$'_3) undefined in model
% 28.54/4.55 % 'relcomp$m'(fmb_'C_b_prod_set$'_2,fmb_'B_b_prod_set$'_4) undefined in model
% 28.54/4.55 & 'relcomp$m'(fmb_'C_b_prod_set$'_3,'bot$k') = fmb_'C_b_prod_set$'_4
% 28.54/4.55 % 'relcomp$m'(fmb_'C_b_prod_set$'_3,fmb_'B_b_prod_set$'_2) undefined in model
% 28.54/4.55 % 'relcomp$m'(fmb_'C_b_prod_set$'_3,fmb_'B_b_prod_set$'_3) undefined in model
% 28.54/4.55 % 'relcomp$m'(fmb_'C_b_prod_set$'_3,fmb_'B_b_prod_set$'_4) undefined in model
% 28.54/4.55 & 'relcomp$m'(fmb_'C_b_prod_set$'_4,'bot$k') = fmb_'C_b_prod_set$'_4
% 28.54/4.55 % 'relcomp$m'(fmb_'C_b_prod_set$'_4,fmb_'B_b_prod_set$'_2) undefined in model
% 28.54/4.55 % 'relcomp$m'(fmb_'C_b_prod_set$'_4,fmb_'B_b_prod_set$'_3) undefined in model
% 28.54/4.55 % 'relcomp$m'(fmb_'C_b_prod_set$'_4,fmb_'B_b_prod_set$'_4) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_inf$',type,'inf$': 'C_set$' * 'C_set$' > 'C_set$').
% 28.54/4.55 tff('function_inf$',axiom,
% 28.54/4.55 'inf$'('bot$a','bot$a') = fmb_'C_set$'_2
% 28.54/4.55 & 'inf$'('bot$a',fmb_'C_set$'_2) = fmb_'C_set$'_2
% 28.54/4.55 & 'inf$'(fmb_'C_set$'_2,'bot$a') = fmb_'C_set$'_2
% 28.54/4.55 & 'inf$'(fmb_'C_set$'_2,fmb_'C_set$'_2) = fmb_'C_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$d',type,'relcomp$d': 'C_c_prod_set$' * 'C_d_prod_set$' > 'C_d_prod_set$').
% 28.54/4.55 tff('function_relcomp$d',axiom,
% 28.54/4.55 'relcomp$d'(fmb_'C_c_prod_set$'_1,'bot$h') = 'bot$h'
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_1,fmb_'C_d_prod_set$'_2) = fmb_'C_d_prod_set$'_2
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_1,fmb_'C_d_prod_set$'_3) = fmb_'C_d_prod_set$'_3
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_1,fmb_'C_d_prod_set$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_2,'bot$h') = 'bot$h'
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_2,fmb_'C_d_prod_set$'_2) = fmb_'C_d_prod_set$'_2
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_2,fmb_'C_d_prod_set$'_3) = fmb_'C_d_prod_set$'_3
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_2,fmb_'C_d_prod_set$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_3,'bot$h') = 'bot$h'
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_3,fmb_'C_d_prod_set$'_2) = fmb_'C_d_prod_set$'_3
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_3,fmb_'C_d_prod_set$'_3) = fmb_'C_d_prod_set$'_3
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_3,fmb_'C_d_prod_set$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_4,'bot$h') = 'bot$h'
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_4,fmb_'C_d_prod_set$'_2) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_4,fmb_'C_d_prod_set$'_3) = fmb_'C_d_prod_set$'_3
% 28.54/4.55 & 'relcomp$d'(fmb_'C_c_prod_set$'_4,fmb_'C_d_prod_set$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_these$b',type,'these$b': 'B_option_set$' > 'B_set$').
% 28.54/4.55 tff('function_these$b',axiom,
% 28.54/4.55 'these$b'('bot$m') = 'bot$b'
% 28.54/4.55 & 'these$b'(fmb_'B_option_set$'_2) = 'bot$b'
% 28.54/4.55 & 'these$b'(fmb_'B_option_set$'_3) = fmb_'B_set$'_2
% 28.54/4.55 & 'these$b'(fmb_'B_option_set$'_4) = fmb_'B_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_these$a',type,'these$a': 'D_option_set$' > 'D_set$').
% 28.54/4.55 tff('function_these$a',axiom,
% 28.54/4.55 'these$a'('bot$t') = 'bot$'
% 28.54/4.55 & 'these$a'(fmb_'D_option_set$'_2) = fmb_'D_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_pair$a',type,'pair$a': 'A$' * 'A$' > 'A_a_prod$').
% 28.54/4.55 tff('function_pair$a',axiom,
% 28.54/4.55 'pair$a'(fmb_'A$'_1,fmb_'A$'_1) = fmb_'A_a_prod$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$a',type,'restrict_map$a': 'A_a_option_fun$' * 'A_set$' > 'A_a_option_fun$').
% 28.54/4.55 tff('function_restrict_map$a',axiom,
% 28.54/4.55 'restrict_map$a'('some$','bot$c') = fmb_'A_a_option_fun$'_2
% 28.54/4.55 & 'restrict_map$a'('some$',fmb_'A_set$'_2) = fmb_'A_a_option_fun$'_2
% 28.54/4.55 & 'restrict_map$a'(fmb_'A_a_option_fun$'_2,'bot$c') = fmb_'A_a_option_fun$'_4
% 28.54/4.55 & 'restrict_map$a'(fmb_'A_a_option_fun$'_2,fmb_'A_set$'_2) = fmb_'A_a_option_fun$'_2
% 28.54/4.55 & 'restrict_map$a'(fmb_'A_a_option_fun$'_3,'bot$c') = fmb_'A_a_option_fun$'_3
% 28.54/4.55 & 'restrict_map$a'(fmb_'A_a_option_fun$'_3,fmb_'A_set$'_2) = fmb_'A_a_option_fun$'_2
% 28.54/4.55 & 'restrict_map$a'(fmb_'A_a_option_fun$'_4,'bot$c') = fmb_'A_a_option_fun$'_2
% 28.54/4.55 & 'restrict_map$a'(fmb_'A_a_option_fun$'_4,fmb_'A_set$'_2) = fmb_'A_a_option_fun$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$h',type,'graph$h': 'D_d_option_fun$' > 'D_d_prod_set$').
% 28.54/4.55 tff('function_graph$h',axiom,
% 28.54/4.55 'graph$h'('some$b') = fmb_'D_d_prod_set$'_1
% 28.54/4.55 % 'graph$h'(fmb_'D_d_option_fun$'_2) undefined in model
% 28.54/4.55 % 'graph$h'(fmb_'D_d_option_fun$'_3) undefined in model
% 28.54/4.55 % 'graph$h'(fmb_'D_d_option_fun$'_4) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$ae',type,'fun_app$ae': 'D_c_option_fun$' * 'D$' > 'C_option$').
% 28.54/4.55 tff('function_fun_app$ae',axiom,
% 28.54/4.55 'fun_app$ae'(fmb_'D_c_option_fun$'_1,fmb_'D$'_1) = 'none$a'
% 28.54/4.55 & 'fun_app$ae'(fmb_'D_c_option_fun$'_2,fmb_'D$'_1) = 'none$a'
% 28.54/4.55 & 'fun_app$ae'(fmb_'D_c_option_fun$'_3,fmb_'D$'_1) = 'none$a'
% 28.54/4.55 & 'fun_app$ae'(fmb_'D_c_option_fun$'_4,fmb_'D$'_1) = 'none$a'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$l',type,'fun_app$l': 'A_d_option_fun$' * 'A$' > 'D_option$').
% 28.54/4.55 tff('function_fun_app$l',axiom,
% 28.54/4.55 'fun_app$l'(fmb_'A_d_option_fun$'_1,fmb_'A$'_1) = 'none$b'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$f',type,'restrict_map$f': 'C_d_option_fun$' * 'C_set$' > 'C_d_option_fun$').
% 28.54/4.55 tff('function_restrict_map$f',axiom,
% 28.54/4.55 'restrict_map$f'('b$','bot$a') = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$f'('b$',fmb_'C_set$'_2) = 'b$'
% 28.54/4.55 & 'restrict_map$f'(fmb_'C_d_option_fun$'_2,'bot$a') = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$f'(fmb_'C_d_option_fun$'_2,fmb_'C_set$'_2) = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$f'(fmb_'C_d_option_fun$'_3,'bot$a') = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$f'(fmb_'C_d_option_fun$'_3,fmb_'C_set$'_2) = fmb_'C_d_option_fun$'_3
% 28.54/4.55 & 'restrict_map$f'(fmb_'C_d_option_fun$'_4,'bot$a') = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$f'(fmb_'C_d_option_fun$'_4,fmb_'C_set$'_2) = fmb_'C_d_option_fun$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$c',type,'relcomp$c': 'A_c_prod_set$' * 'C_d_prod_set$' > 'A_d_prod_set$').
% 28.54/4.55 tff('function_relcomp$c',axiom,
% 28.54/4.55 'relcomp$c'('bot$e','bot$h') = 'bot$g'
% 28.54/4.55 & 'relcomp$c'('bot$e',fmb_'C_d_prod_set$'_2) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'('bot$e',fmb_'C_d_prod_set$'_3) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'('bot$e',fmb_'C_d_prod_set$'_4) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_2,'bot$h') = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_2,fmb_'C_d_prod_set$'_2) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_2,fmb_'C_d_prod_set$'_3) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_2,fmb_'C_d_prod_set$'_4) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_3,'bot$h') = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_3,fmb_'C_d_prod_set$'_2) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_3,fmb_'C_d_prod_set$'_3) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_3,fmb_'C_d_prod_set$'_4) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_4,'bot$h') = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_4,fmb_'C_d_prod_set$'_2) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_4,fmb_'C_d_prod_set$'_3) = 'bot$g'
% 28.54/4.55 & 'relcomp$c'(fmb_'A_c_prod_set$'_4,fmb_'C_d_prod_set$'_4) = 'bot$g'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$z',type,'fun_app$z': 'D_option_b_option_bool_fun_fun$' * 'D_option$' > 'B_option_bool_fun$').
% 28.54/4.55 tff('function_fun_app$z',axiom,
% 28.54/4.55 'fun_app$z'(fmb_'D_option_b_option_bool_fun_fun$'_1,'none$b') = 'is_none$'
% 28.54/4.55 & 'fun_app$z'(fmb_'D_option_b_option_bool_fun_fun$'_1,fmb_'D_option$'_2) = 'is_none$'
% 28.54/4.55 % 'fun_app$z'(fmb_'D_option_b_option_bool_fun_fun$'_2,'none$b') undefined in model
% 28.54/4.55 % 'fun_app$z'(fmb_'D_option_b_option_bool_fun_fun$'_2,fmb_'D_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$z'(fmb_'D_option_b_option_bool_fun_fun$'_3,'none$b') undefined in model
% 28.54/4.55 % 'fun_app$z'(fmb_'D_option_b_option_bool_fun_fun$'_3,fmb_'D_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$z'(fmb_'D_option_b_option_bool_fun_fun$'_4,'none$b') undefined in model
% 28.54/4.55 % 'fun_app$z'(fmb_'D_option_b_option_bool_fun_fun$'_4,fmb_'D_option$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_sup$a',type,'sup$a': 'A_d_prod_set$' * 'A_d_prod_set$' > 'A_d_prod_set$').
% 28.54/4.55 tff('function_sup$a',axiom,
% 28.54/4.55 'sup$a'('bot$g','bot$g') = 'bot$g'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_ran$h',type,'ran$h': 'D_d_option_fun$' > 'D_set$').
% 28.54/4.55 tff('function_ran$h',axiom,
% 28.54/4.55 'ran$h'('some$b') = 'bot$'
% 28.54/4.55 & 'ran$h'(fmb_'D_d_option_fun$'_2) = 'bot$'
% 28.54/4.55 & 'ran$h'(fmb_'D_d_option_fun$'_3) = 'bot$'
% 28.54/4.55 & 'ran$h'(fmb_'D_d_option_fun$'_4) = 'bot$'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$l',type,'restrict_map$l': 'D_d_option_fun$' * 'D_set$' > 'D_d_option_fun$').
% 28.54/4.55 tff('function_restrict_map$l',axiom,
% 28.54/4.55 'restrict_map$l'('some$b','bot$') = fmb_'D_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$l'('some$b',fmb_'D_set$'_2) = 'some$b'
% 28.54/4.55 & 'restrict_map$l'(fmb_'D_d_option_fun$'_2,'bot$') = fmb_'D_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$l'(fmb_'D_d_option_fun$'_2,fmb_'D_set$'_2) = fmb_'D_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$l'(fmb_'D_d_option_fun$'_3,'bot$') = fmb_'D_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$l'(fmb_'D_d_option_fun$'_3,fmb_'D_set$'_2) = fmb_'D_d_option_fun$'_3
% 28.54/4.55 & 'restrict_map$l'(fmb_'D_d_option_fun$'_4,'bot$') = fmb_'D_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$l'(fmb_'D_d_option_fun$'_4,fmb_'D_set$'_2) = fmb_'D_d_option_fun$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$h',type,'fun_app$h': 'A_c_option_fun$' * 'A$' > 'C_option$').
% 28.54/4.55 tff('function_fun_app$h',axiom,
% 28.54/4.55 'fun_app$h'('c$',fmb_'A$'_1) = 'none$a'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_ran$g',type,'ran$g': 'A_c_option_fun$' > 'C_set$').
% 28.54/4.55 tff('function_ran$g',axiom,
% 28.54/4.55 'ran$g'('c$') = 'bot$a'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_pair$l',type,'pair$l': 'D$' * 'D$' > 'D_d_prod$').
% 28.54/4.55 tff('function_pair$l',axiom,
% 28.54/4.55 'pair$l'(fmb_'D$'_1,fmb_'D$'_1) = fmb_'D_d_prod$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_set_option$a',type,'set_option$a': 'A_option$' > 'A_set$').
% 28.54/4.55 tff('function_set_option$a',axiom,
% 28.54/4.55 'set_option$a'('none$') = 'bot$c'
% 28.54/4.55 & 'set_option$a'(fmb_'A_option$'_2) = fmb_'A_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$u',type,'fun_app$u': 'C_option_c_option_bool_fun_fun$' * 'C_option$' > 'C_option_bool_fun$').
% 28.54/4.55 tff('function_fun_app$u',axiom,
% 28.54/4.55 'fun_app$u'(fmb_'C_option_c_option_bool_fun_fun$'_1,'none$a') = 'is_none$b'
% 28.54/4.55 & 'fun_app$u'(fmb_'C_option_c_option_bool_fun_fun$'_1,fmb_'C_option$'_2) = 'is_none$b'
% 28.54/4.55 % 'fun_app$u'(fmb_'C_option_c_option_bool_fun_fun$'_2,'none$a') undefined in model
% 28.54/4.55 % 'fun_app$u'(fmb_'C_option_c_option_bool_fun_fun$'_2,fmb_'C_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$u'(fmb_'C_option_c_option_bool_fun_fun$'_3,'none$a') undefined in model
% 28.54/4.55 % 'fun_app$u'(fmb_'C_option_c_option_bool_fun_fun$'_3,fmb_'C_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$u'(fmb_'C_option_c_option_bool_fun_fun$'_4,'none$a') undefined in model
% 28.54/4.55 % 'fun_app$u'(fmb_'C_option_c_option_bool_fun_fun$'_4,fmb_'C_option$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_insert$d',type,'insert$d': 'D$' * 'D_set$' > 'D_set$').
% 28.54/4.55 tff('function_insert$d',axiom,
% 28.54/4.55 'insert$d'(fmb_'D$'_1,'bot$') = fmb_'D_set$'_2
% 28.54/4.55 & 'insert$d'(fmb_'D$'_1,fmb_'D_set$'_2) = fmb_'D_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_add$a',type,'map_add$a': 'C_b_option_fun$' * 'C_b_option_fun$' > 'C_b_option_fun$').
% 28.54/4.55 tff('function_map_add$a',axiom,
% 28.54/4.55 'map_add$a'(fmb_'C_b_option_fun$'_1,fmb_'C_b_option_fun$'_1) = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_1,fmb_'C_b_option_fun$'_2) = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_1,fmb_'C_b_option_fun$'_3) = fmb_'C_b_option_fun$'_2
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_1,fmb_'C_b_option_fun$'_4) = fmb_'C_b_option_fun$'_2
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_2,fmb_'C_b_option_fun$'_1) = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_2,fmb_'C_b_option_fun$'_2) = fmb_'C_b_option_fun$'_2
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_2,fmb_'C_b_option_fun$'_3) = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_2,fmb_'C_b_option_fun$'_4) = fmb_'C_b_option_fun$'_3
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_3,fmb_'C_b_option_fun$'_1) = fmb_'C_b_option_fun$'_3
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_3,fmb_'C_b_option_fun$'_2) = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_3,fmb_'C_b_option_fun$'_3) = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_3,fmb_'C_b_option_fun$'_4) = fmb_'C_b_option_fun$'_4
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_4,fmb_'C_b_option_fun$'_1) = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_4,fmb_'C_b_option_fun$'_2) = fmb_'C_b_option_fun$'_4
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_4,fmb_'C_b_option_fun$'_3) = fmb_'C_b_option_fun$'_4
% 28.54/4.55 & 'map_add$a'(fmb_'C_b_option_fun$'_4,fmb_'C_b_option_fun$'_4) = fmb_'C_b_option_fun$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_insert$a',type,'insert$a': 'B_option$' * 'B_option_set$' > 'B_option_set$').
% 28.54/4.55 tff('function_insert$a',axiom,
% 28.54/4.55 'insert$a'('none$c','bot$m') = fmb_'B_option_set$'_2
% 28.54/4.55 & 'insert$a'('none$c',fmb_'B_option_set$'_2) = fmb_'B_option_set$'_2
% 28.54/4.55 & 'insert$a'('none$c',fmb_'B_option_set$'_3) = fmb_'B_option_set$'_3
% 28.54/4.55 & 'insert$a'('none$c',fmb_'B_option_set$'_4) = fmb_'B_option_set$'_4
% 28.54/4.55 & 'insert$a'(fmb_'B_option$'_2,'bot$m') = fmb_'B_option_set$'_3
% 28.54/4.55 & 'insert$a'(fmb_'B_option$'_2,fmb_'B_option_set$'_2) = fmb_'B_option_set$'_3
% 28.54/4.55 & 'insert$a'(fmb_'B_option$'_2,fmb_'B_option_set$'_3) = fmb_'B_option_set$'_4
% 28.54/4.55 & 'insert$a'(fmb_'B_option$'_2,fmb_'B_option_set$'_4) = fmb_'B_option_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_the$a',type,'the$a': 'D_option$' > 'D$').
% 28.54/4.55 tff('function_the$a',axiom,
% 28.54/4.55 'the$a'('none$b') = fmb_'D$'_1
% 28.54/4.55 & 'the$a'(fmb_'D_option$'_2) = fmb_'D$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_image$e',type,'image$e': 'C_b_prod_set$' * 'C_set$' > 'B_set$').
% 28.54/4.55 tff('function_image$e',axiom,
% 28.54/4.55 'image$e'('bot$i','bot$a') = fmb_'B_set$'_2
% 28.54/4.55 & 'image$e'('bot$i',fmb_'C_set$'_2) = fmb_'B_set$'_2
% 28.54/4.55 & 'image$e'(fmb_'C_b_prod_set$'_2,'bot$a') = fmb_'B_set$'_2
% 28.54/4.55 & 'image$e'(fmb_'C_b_prod_set$'_2,fmb_'C_set$'_2) = fmb_'B_set$'_2
% 28.54/4.55 & 'image$e'(fmb_'C_b_prod_set$'_3,'bot$a') = 'bot$b'
% 28.54/4.55 & 'image$e'(fmb_'C_b_prod_set$'_3,fmb_'C_set$'_2) = fmb_'B_set$'_2
% 28.54/4.55 & 'image$e'(fmb_'C_b_prod_set$'_4,'bot$a') = fmb_'B_set$'_2
% 28.54/4.55 & 'image$e'(fmb_'C_b_prod_set$'_4,fmb_'C_set$'_2) = fmb_'B_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$n',type,'fun_app$n': 'A_b_option_fun$' * 'A$' > 'B_option$').
% 28.54/4.55 tff('function_fun_app$n',axiom,
% 28.54/4.55 'fun_app$n'(fmb_'A_b_option_fun$'_1,fmb_'A$'_1) = 'none$c'
% 28.54/4.55 & 'fun_app$n'(fmb_'A_b_option_fun$'_2,fmb_'A$'_1) = 'none$c'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$w',type,'fun_app$w': 'C_option_b_option_bool_fun_fun$' * 'C_option$' > 'B_option_bool_fun$').
% 28.54/4.55 tff('function_fun_app$w',axiom,
% 28.54/4.55 'fun_app$w'(fmb_'C_option_b_option_bool_fun_fun$'_1,'none$a') = 'is_none$'
% 28.54/4.55 & 'fun_app$w'(fmb_'C_option_b_option_bool_fun_fun$'_1,fmb_'C_option$'_2) = 'is_none$'
% 28.54/4.55 % 'fun_app$w'(fmb_'C_option_b_option_bool_fun_fun$'_2,'none$a') undefined in model
% 28.54/4.55 % 'fun_app$w'(fmb_'C_option_b_option_bool_fun_fun$'_2,fmb_'C_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$w'(fmb_'C_option_b_option_bool_fun_fun$'_3,'none$a') undefined in model
% 28.54/4.55 % 'fun_app$w'(fmb_'C_option_b_option_bool_fun_fun$'_3,fmb_'C_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$w'(fmb_'C_option_b_option_bool_fun_fun$'_4,'none$a') undefined in model
% 28.54/4.55 % 'fun_app$w'(fmb_'C_option_b_option_bool_fun_fun$'_4,fmb_'C_option$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$l',type,'graph$l': 'B_b_option_fun$' > 'B_b_prod_set$').
% 28.54/4.55 tff('function_graph$l',axiom,
% 28.54/4.55 'graph$l'('some$c') = 'bot$k'
% 28.54/4.55 & 'graph$l'(fmb_'B_b_option_fun$'_2) = fmb_'B_b_prod_set$'_2
% 28.54/4.55 & 'graph$l'(fmb_'B_b_option_fun$'_3) = fmb_'B_b_prod_set$'_2
% 28.54/4.55 & 'graph$l'(fmb_'B_b_option_fun$'_4) = fmb_'B_b_prod_set$'_3
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$f',type,'relcomp$f': 'C_d_prod_set$' * 'D_d_prod_set$' > 'C_d_prod_set$').
% 28.54/4.55 tff('function_relcomp$f',axiom,
% 28.54/4.55 'relcomp$f'('bot$h',fmb_'D_d_prod_set$'_1) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$f'('bot$h',fmb_'D_d_prod_set$'_2) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$f'('bot$h',fmb_'D_d_prod_set$'_3) = 'bot$h'
% 28.54/4.55 & 'relcomp$f'('bot$h',fmb_'D_d_prod_set$'_4) = 'bot$h'
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_2,fmb_'D_d_prod_set$'_1) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_2,fmb_'D_d_prod_set$'_2) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_2,fmb_'D_d_prod_set$'_3) = fmb_'C_d_prod_set$'_2
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_2,fmb_'D_d_prod_set$'_4) = fmb_'C_d_prod_set$'_2
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_3,fmb_'D_d_prod_set$'_1) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_3,fmb_'D_d_prod_set$'_2) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_3,fmb_'D_d_prod_set$'_3) = fmb_'C_d_prod_set$'_3
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_3,fmb_'D_d_prod_set$'_4) = fmb_'C_d_prod_set$'_3
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_4,fmb_'D_d_prod_set$'_1) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_4,fmb_'D_d_prod_set$'_2) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_4,fmb_'D_d_prod_set$'_3) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$f'(fmb_'C_d_prod_set$'_4,fmb_'D_d_prod_set$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$o',type,'restrict_map$o': 'B_a_option_fun$' * 'B_set$' > 'B_a_option_fun$').
% 28.54/4.55 tff('function_restrict_map$o',axiom,
% 28.54/4.55 'restrict_map$o'(fmb_'B_a_option_fun$'_1,'bot$b') = fmb_'B_a_option_fun$'_1
% 28.54/4.55 & 'restrict_map$o'(fmb_'B_a_option_fun$'_1,fmb_'B_set$'_2) = fmb_'B_a_option_fun$'_3
% 28.54/4.55 % 'restrict_map$o'(fmb_'B_a_option_fun$'_2,'bot$b') undefined in model
% 28.54/4.55 % 'restrict_map$o'(fmb_'B_a_option_fun$'_2,fmb_'B_set$'_2) undefined in model
% 28.54/4.55 % 'restrict_map$o'(fmb_'B_a_option_fun$'_3,'bot$b') undefined in model
% 28.54/4.55 % 'restrict_map$o'(fmb_'B_a_option_fun$'_3,fmb_'B_set$'_2) undefined in model
% 28.54/4.55 % 'restrict_map$o'(fmb_'B_a_option_fun$'_4,'bot$b') undefined in model
% 28.54/4.55 % 'restrict_map$o'(fmb_'B_a_option_fun$'_4,fmb_'B_set$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$ay',type,'fun_app$ay': 'B_a_option_fun$' * 'B$' > 'A_option$').
% 28.54/4.55 tff('function_fun_app$ay',axiom,
% 28.54/4.55 'fun_app$ay'(fmb_'B_a_option_fun$'_1,fmb_'B$'_1) = 'none$'
% 28.54/4.55 % 'fun_app$ay'(fmb_'B_a_option_fun$'_2,fmb_'B$'_1) undefined in model
% 28.54/4.55 % 'fun_app$ay'(fmb_'B_a_option_fun$'_3,fmb_'B$'_1) undefined in model
% 28.54/4.55 % 'fun_app$ay'(fmb_'B_a_option_fun$'_4,fmb_'B$'_1) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_the$c',type,'the$c': 'B_option_option$' > 'B_option$').
% 28.54/4.55 tff('function_the$c',axiom,
% 28.54/4.55 'the$c'('none$d') = 'none$c'
% 28.54/4.55 & 'the$c'(fmb_'B_option_option$'_2) = 'none$c'
% 28.54/4.55 & 'the$c'(fmb_'B_option_option$'_3) = fmb_'B_option$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_comp$k',type,'map_comp$k': 'B_d_option_fun$' * 'C_b_option_fun$' > 'C_d_option_fun$').
% 28.54/4.55 tff('function_map_comp$k',axiom,
% 28.54/4.55 'map_comp$k'(fmb_'B_d_option_fun$'_1,fmb_'C_b_option_fun$'_1) = 'b$'
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_1,fmb_'C_b_option_fun$'_2) = 'b$'
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_1,fmb_'C_b_option_fun$'_3) = 'b$'
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_1,fmb_'C_b_option_fun$'_4) = 'b$'
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_2,fmb_'C_b_option_fun$'_1) = 'b$'
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_2,fmb_'C_b_option_fun$'_2) = fmb_'C_d_option_fun$'_3
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_2,fmb_'C_b_option_fun$'_3) = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_2,fmb_'C_b_option_fun$'_4) = 'b$'
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_3,fmb_'C_b_option_fun$'_1) = 'b$'
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_3,fmb_'C_b_option_fun$'_2) = fmb_'C_d_option_fun$'_3
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_3,fmb_'C_b_option_fun$'_3) = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_3,fmb_'C_b_option_fun$'_4) = 'b$'
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_4,fmb_'C_b_option_fun$'_1) = 'b$'
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_4,fmb_'C_b_option_fun$'_2) = fmb_'C_d_option_fun$'_3
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_4,fmb_'C_b_option_fun$'_3) = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'map_comp$k'(fmb_'B_d_option_fun$'_4,fmb_'C_b_option_fun$'_4) = 'b$'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_ran$i',type,'ran$i': 'B_d_option_fun$' > 'D_set$').
% 28.54/4.55 tff('function_ran$i',axiom,
% 28.54/4.55 'ran$i'(fmb_'B_d_option_fun$'_1) = 'bot$'
% 28.54/4.55 & 'ran$i'(fmb_'B_d_option_fun$'_2) = 'bot$'
% 28.54/4.55 & 'ran$i'(fmb_'B_d_option_fun$'_3) = 'bot$'
% 28.54/4.55 & 'ran$i'(fmb_'B_d_option_fun$'_4) = 'bot$'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$m',type,'restrict_map$m': 'D_b_option_fun$' * 'D_set$' > 'D_b_option_fun$').
% 28.54/4.55 tff('function_restrict_map$m',axiom,
% 28.54/4.55 'restrict_map$m'('a$','bot$') = fmb_'D_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$m'('a$',fmb_'D_set$'_2) = 'a$'
% 28.54/4.55 & 'restrict_map$m'(fmb_'D_b_option_fun$'_2,'bot$') = 'a$'
% 28.54/4.55 & 'restrict_map$m'(fmb_'D_b_option_fun$'_2,fmb_'D_set$'_2) = fmb_'D_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$m'(fmb_'D_b_option_fun$'_3,'bot$') = fmb_'D_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$m'(fmb_'D_b_option_fun$'_3,fmb_'D_set$'_2) = fmb_'D_b_option_fun$'_3
% 28.54/4.55 & 'restrict_map$m'(fmb_'D_b_option_fun$'_4,'bot$') = fmb_'D_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$m'(fmb_'D_b_option_fun$'_4,fmb_'D_set$'_2) = fmb_'D_b_option_fun$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_comp$f',type,'map_comp$f': 'A_b_option_fun$' > 'A_a_option_fun_a_b_option_fun_fun$').
% 28.54/4.55 tff('function_map_comp$f',axiom,
% 28.54/4.55 'map_comp$f'(fmb_'A_b_option_fun$'_1) = fmb_'A_a_option_fun_a_b_option_fun_fun$'_1
% 28.54/4.55 & 'map_comp$f'(fmb_'A_b_option_fun$'_2) = fmb_'A_a_option_fun_a_b_option_fun_fun$'_3
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_bind$b',type,'bind$b': 'C_option$' * 'C_b_option_fun$' > 'B_option$').
% 28.54/4.55 tff('function_bind$b',axiom,
% 28.54/4.55 'bind$b'('none$a',fmb_'C_b_option_fun$'_1) = 'none$c'
% 28.54/4.55 & 'bind$b'('none$a',fmb_'C_b_option_fun$'_2) = 'none$c'
% 28.54/4.55 & 'bind$b'('none$a',fmb_'C_b_option_fun$'_3) = 'none$c'
% 28.54/4.55 & 'bind$b'('none$a',fmb_'C_b_option_fun$'_4) = 'none$c'
% 28.54/4.55 & 'bind$b'(fmb_'C_option$'_2,fmb_'C_b_option_fun$'_1) = 'none$c'
% 28.54/4.55 & 'bind$b'(fmb_'C_option$'_2,fmb_'C_b_option_fun$'_2) = 'none$c'
% 28.54/4.55 & 'bind$b'(fmb_'C_option$'_2,fmb_'C_b_option_fun$'_3) = 'none$c'
% 28.54/4.55 & 'bind$b'(fmb_'C_option$'_2,fmb_'C_b_option_fun$'_4) = 'none$c'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_combine_options$a',type,'combine_options$a': 'D_d_d_fun_fun$' * 'D_option$' > 'D_option_d_option_fun$').
% 28.54/4.55 tff('function_combine_options$a',axiom,
% 28.54/4.55 'combine_options$a'(fmb_'D_d_d_fun_fun$'_1,'none$b') = fmb_'D_option_d_option_fun$'_1
% 28.54/4.55 & 'combine_options$a'(fmb_'D_d_d_fun_fun$'_1,fmb_'D_option$'_2) = fmb_'D_option_d_option_fun$'_2
% 28.54/4.55 % 'combine_options$a'(fmb_'D_d_d_fun_fun$'_2,'none$b') undefined in model
% 28.54/4.55 % 'combine_options$a'(fmb_'D_d_d_fun_fun$'_2,fmb_'D_option$'_2) undefined in model
% 28.54/4.55 % 'combine_options$a'(fmb_'D_d_d_fun_fun$'_3,'none$b') undefined in model
% 28.54/4.55 % 'combine_options$a'(fmb_'D_d_d_fun_fun$'_3,fmb_'D_option$'_2) undefined in model
% 28.54/4.55 % 'combine_options$a'(fmb_'D_d_d_fun_fun$'_4,'none$b') undefined in model
% 28.54/4.55 % 'combine_options$a'(fmb_'D_d_d_fun_fun$'_4,fmb_'D_option$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_add$',type,'map_add$': 'C_d_option_fun$' * 'C_d_option_fun$' > 'C_d_option_fun$').
% 28.54/4.55 tff('function_map_add$',axiom,
% 28.54/4.55 'map_add$'('b$','b$') = 'b$'
% 28.54/4.55 & 'map_add$'('b$',fmb_'C_d_option_fun$'_2) = fmb_'C_d_option_fun$'_3
% 28.54/4.55 & 'map_add$'('b$',fmb_'C_d_option_fun$'_3) = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'map_add$'('b$',fmb_'C_d_option_fun$'_4) = fmb_'C_d_option_fun$'_4
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_2,'b$') = fmb_'C_d_option_fun$'_4
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_2,fmb_'C_d_option_fun$'_2) = fmb_'C_d_option_fun$'_4
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_2,fmb_'C_d_option_fun$'_3) = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_2,fmb_'C_d_option_fun$'_4) = 'b$'
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_3,'b$') = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_3,fmb_'C_d_option_fun$'_2) = fmb_'C_d_option_fun$'_2
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_3,fmb_'C_d_option_fun$'_3) = fmb_'C_d_option_fun$'_3
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_3,fmb_'C_d_option_fun$'_4) = fmb_'C_d_option_fun$'_3
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_4,'b$') = 'b$'
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_4,fmb_'C_d_option_fun$'_2) = fmb_'C_d_option_fun$'_3
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_4,fmb_'C_d_option_fun$'_3) = 'b$'
% 28.54/4.55 & 'map_add$'(fmb_'C_d_option_fun$'_4,fmb_'C_d_option_fun$'_4) = fmb_'C_d_option_fun$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$ao',type,'fun_app$ao': 'D_d_d_fun_fun$' * 'D$' > 'D_d_fun$').
% 28.54/4.55 tff('function_fun_app$ao',axiom,
% 28.54/4.55 'fun_app$ao'(fmb_'D_d_d_fun_fun$'_1,fmb_'D$'_1) = fmb_'D_d_fun$'_2
% 28.54/4.55 % 'fun_app$ao'(fmb_'D_d_d_fun_fun$'_2,fmb_'D$'_1) undefined in model
% 28.54/4.55 % 'fun_app$ao'(fmb_'D_d_d_fun_fun$'_3,fmb_'D$'_1) undefined in model
% 28.54/4.55 % 'fun_app$ao'(fmb_'D_d_d_fun_fun$'_4,fmb_'D$'_1) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_uua$',type,'uua$': 'D_set$' > 'D_bool_fun$').
% 28.54/4.55 tff('function_uua$',axiom,
% 28.54/4.55 'uua$'('bot$') = 'bot$p'
% 28.54/4.55 & 'uua$'(fmb_'D_set$'_2) = fmb_'D_bool_fun$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$g',type,'graph$g': 'C_a_option_fun$' > 'C_a_prod_set$').
% 28.54/4.55 tff('function_graph$g',axiom,
% 28.54/4.55 'graph$g'(fmb_'C_a_option_fun$'_1) = fmb_'C_a_prod_set$'_2
% 28.54/4.55 & 'graph$g'(fmb_'C_a_option_fun$'_2) = fmb_'C_a_prod_set$'_3
% 28.54/4.55 & 'graph$g'(fmb_'C_a_option_fun$'_3) = fmb_'C_a_prod_set$'_3
% 28.54/4.55 & 'graph$g'(fmb_'C_a_option_fun$'_4) = fmb_'C_a_prod_set$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_inf$a',type,'inf$a': 'A_set$' * 'A_set$' > 'A_set$').
% 28.54/4.55 tff('function_inf$a',axiom,
% 28.54/4.55 'inf$a'('bot$c','bot$c') = fmb_'A_set$'_2
% 28.54/4.55 & 'inf$a'('bot$c',fmb_'A_set$'_2) = fmb_'A_set$'_2
% 28.54/4.55 & 'inf$a'(fmb_'A_set$'_2,'bot$c') = fmb_'A_set$'_2
% 28.54/4.55 & 'inf$a'(fmb_'A_set$'_2,fmb_'A_set$'_2) = fmb_'A_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_sup$c',type,'sup$c': 'A_b_prod_set$' * 'A_b_prod_set$' > 'A_b_prod_set$').
% 28.54/4.55 tff('function_sup$c',axiom,
% 28.54/4.55 'sup$c'('bot$d','bot$d') = 'bot$d'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_comp$i',type,'map_comp$i': 'C_d_option_fun$' * 'C_c_option_fun$' > 'C_d_option_fun$').
% 28.54/4.55 tff('function_map_comp$i',axiom,
% 28.54/4.55 'map_comp$i'('b$','some$a') = 'b$'
% 28.54/4.55 % 'map_comp$i'('b$',fmb_'C_c_option_fun$'_2) undefined in model
% 28.54/4.55 % 'map_comp$i'('b$',fmb_'C_c_option_fun$'_3) undefined in model
% 28.54/4.55 % 'map_comp$i'('b$',fmb_'C_c_option_fun$'_4) undefined in model
% 28.54/4.55 & 'map_comp$i'(fmb_'C_d_option_fun$'_2,'some$a') = 'b$'
% 28.54/4.55 % 'map_comp$i'(fmb_'C_d_option_fun$'_2,fmb_'C_c_option_fun$'_2) undefined in model
% 28.54/4.55 % 'map_comp$i'(fmb_'C_d_option_fun$'_2,fmb_'C_c_option_fun$'_3) undefined in model
% 28.54/4.55 % 'map_comp$i'(fmb_'C_d_option_fun$'_2,fmb_'C_c_option_fun$'_4) undefined in model
% 28.54/4.55 & 'map_comp$i'(fmb_'C_d_option_fun$'_3,'some$a') = 'b$'
% 28.54/4.55 % 'map_comp$i'(fmb_'C_d_option_fun$'_3,fmb_'C_c_option_fun$'_2) undefined in model
% 28.54/4.55 % 'map_comp$i'(fmb_'C_d_option_fun$'_3,fmb_'C_c_option_fun$'_3) undefined in model
% 28.54/4.55 % 'map_comp$i'(fmb_'C_d_option_fun$'_3,fmb_'C_c_option_fun$'_4) undefined in model
% 28.54/4.55 & 'map_comp$i'(fmb_'C_d_option_fun$'_4,'some$a') = 'b$'
% 28.54/4.55 % 'map_comp$i'(fmb_'C_d_option_fun$'_4,fmb_'C_c_option_fun$'_2) undefined in model
% 28.54/4.55 % 'map_comp$i'(fmb_'C_d_option_fun$'_4,fmb_'C_c_option_fun$'_3) undefined in model
% 28.54/4.55 % 'map_comp$i'(fmb_'C_d_option_fun$'_4,fmb_'C_c_option_fun$'_4) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$g',type,'restrict_map$g': 'A_d_option_fun$' * 'A_set$' > 'A_d_option_fun$').
% 28.54/4.55 tff('function_restrict_map$g',axiom,
% 28.54/4.55 'restrict_map$g'(fmb_'A_d_option_fun$'_1,'bot$c') = fmb_'A_d_option_fun$'_1
% 28.54/4.55 & 'restrict_map$g'(fmb_'A_d_option_fun$'_1,fmb_'A_set$'_2) = fmb_'A_d_option_fun$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_these$',type,'these$': 'C_option_set$' > 'C_set$').
% 28.54/4.55 tff('function_these$',axiom,
% 28.54/4.55 'these$'('bot$n') = 'bot$a'
% 28.54/4.55 & 'these$'(fmb_'C_option_set$'_2) = 'bot$a'
% 28.54/4.55 & 'these$'(fmb_'C_option_set$'_3) = fmb_'C_set$'_2
% 28.54/4.55 & 'these$'(fmb_'C_option_set$'_4) = fmb_'C_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$k',type,'restrict_map$k': 'C_c_option_fun$' * 'C_set$' > 'C_c_option_fun$').
% 28.54/4.55 tff('function_restrict_map$k',axiom,
% 28.54/4.55 'restrict_map$k'('some$a','bot$a') = fmb_'C_c_option_fun$'_2
% 28.54/4.55 & 'restrict_map$k'('some$a',fmb_'C_set$'_2) = 'some$a'
% 28.54/4.55 & 'restrict_map$k'(fmb_'C_c_option_fun$'_2,'bot$a') = fmb_'C_c_option_fun$'_2
% 28.54/4.55 & 'restrict_map$k'(fmb_'C_c_option_fun$'_2,fmb_'C_set$'_2) = fmb_'C_c_option_fun$'_2
% 28.54/4.55 & 'restrict_map$k'(fmb_'C_c_option_fun$'_3,'bot$a') = fmb_'C_c_option_fun$'_2
% 28.54/4.55 & 'restrict_map$k'(fmb_'C_c_option_fun$'_3,fmb_'C_set$'_2) = 'some$a'
% 28.54/4.55 & 'restrict_map$k'(fmb_'C_c_option_fun$'_4,'bot$a') = fmb_'C_c_option_fun$'_2
% 28.54/4.55 & 'restrict_map$k'(fmb_'C_c_option_fun$'_4,fmb_'C_set$'_2) = 'some$a'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_ran$a',type,'ran$a': 'C_a_option_fun$' > 'A_set$').
% 28.54/4.55 tff('function_ran$a',axiom,
% 28.54/4.55 'ran$a'(fmb_'C_a_option_fun$'_1) = 'bot$c'
% 28.54/4.55 & 'ran$a'(fmb_'C_a_option_fun$'_2) = 'bot$c'
% 28.54/4.55 & 'ran$a'(fmb_'C_a_option_fun$'_3) = 'bot$c'
% 28.54/4.55 & 'ran$a'(fmb_'C_a_option_fun$'_4) = 'bot$c'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_set_option$b',type,'set_option$b': 'C_option$' > 'C_set$').
% 28.54/4.55 tff('function_set_option$b',axiom,
% 28.54/4.55 'set_option$b'('none$a') = 'bot$a'
% 28.54/4.55 & 'set_option$b'(fmb_'C_option$'_2) = fmb_'C_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_pair$b',type,'pair$b': 'B$' * 'C$' > 'B_c_prod$').
% 28.54/4.55 tff('function_pair$b',axiom,
% 28.54/4.55 'pair$b'(fmb_'B$'_1,fmb_'C$'_1) = fmb_'B_c_prod$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_the_elem$a',type,'the_elem$a': 'D_set$' > 'D$').
% 28.54/4.55 tff('function_the_elem$a',axiom,
% 28.54/4.55 'the_elem$a'('bot$') = fmb_'D$'_1
% 28.54/4.55 & 'the_elem$a'(fmb_'D_set$'_2) = fmb_'D$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_the$b',type,'the$b': 'B_option$' > 'B$').
% 28.54/4.55 tff('function_the$b',axiom,
% 28.54/4.55 'the$b'('none$c') = fmb_'B$'_1
% 28.54/4.55 & 'the$b'(fmb_'B_option$'_2) = fmb_'B$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$aj',type,'fun_app$aj': 'C_option_c_option_fun$' * 'C_option$' > 'C_option$').
% 28.54/4.55 tff('function_fun_app$aj',axiom,
% 28.54/4.55 'fun_app$aj'(fmb_'C_option_c_option_fun$'_1,'none$a') = 'none$a'
% 28.54/4.55 & 'fun_app$aj'(fmb_'C_option_c_option_fun$'_1,fmb_'C_option$'_2) = fmb_'C_option$'_2
% 28.54/4.55 & 'fun_app$aj'(fmb_'C_option_c_option_fun$'_2,'none$a') = fmb_'C_option$'_2
% 28.54/4.55 & 'fun_app$aj'(fmb_'C_option_c_option_fun$'_2,fmb_'C_option$'_2) = 'none$a'
% 28.54/4.55 & 'fun_app$aj'(fmb_'C_option_c_option_fun$'_3,'none$a') = fmb_'C_option$'_2
% 28.54/4.55 & 'fun_app$aj'(fmb_'C_option_c_option_fun$'_3,fmb_'C_option$'_2) = fmb_'C_option$'_2
% 28.54/4.55 & 'fun_app$aj'(fmb_'C_option_c_option_fun$'_4,'none$a') = fmb_'C_option$'_2
% 28.54/4.55 & 'fun_app$aj'(fmb_'C_option_c_option_fun$'_4,fmb_'C_option$'_2) = fmb_'C_option$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$k',type,'relcomp$k': 'A_b_prod_set$' * 'B_b_prod_set$' > 'A_b_prod_set$').
% 28.54/4.55 tff('function_relcomp$k',axiom,
% 28.54/4.55 'relcomp$k'('bot$d','bot$k') = 'bot$d'
% 28.54/4.55 % 'relcomp$k'('bot$d',fmb_'B_b_prod_set$'_2) undefined in model
% 28.54/4.55 % 'relcomp$k'('bot$d',fmb_'B_b_prod_set$'_3) undefined in model
% 28.54/4.55 % 'relcomp$k'('bot$d',fmb_'B_b_prod_set$'_4) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$e',type,'relcomp$e': 'C_a_prod_set$' * 'A_d_prod_set$' > 'C_d_prod_set$').
% 28.54/4.55 tff('function_relcomp$e',axiom,
% 28.54/4.55 'relcomp$e'(fmb_'C_a_prod_set$'_1,'bot$g') = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$e'(fmb_'C_a_prod_set$'_2,'bot$g') = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$e'(fmb_'C_a_prod_set$'_3,'bot$g') = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$e'(fmb_'C_a_prod_set$'_4,'bot$g') = fmb_'C_d_prod_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_collect$a',type,'collect$a': 'D_bool_fun$' > 'D_set$').
% 28.54/4.55 tff('function_collect$a',axiom,
% 28.54/4.55 'collect$a'('bot$p') = 'bot$'
% 28.54/4.55 & 'collect$a'(fmb_'D_bool_fun$'_2) = fmb_'D_set$'_2
% 28.54/4.55 & 'collect$a'(fmb_'D_bool_fun$'_3) = 'bot$'
% 28.54/4.55 & 'collect$a'(fmb_'D_bool_fun$'_4) = fmb_'D_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_uud$',type,'uud$': 'A_set$' > 'A_bool_fun$').
% 28.54/4.55 tff('function_uud$',axiom,
% 28.54/4.55 'uud$'('bot$c') = 'bot$s'
% 28.54/4.55 & 'uud$'(fmb_'A_set$'_2) = fmb_'A_bool_fun$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$b',type,'relcomp$b': 'A_d_prod_set$' * 'D_b_prod_set$' > 'A_b_prod_set$').
% 28.54/4.55 tff('function_relcomp$b',axiom,
% 28.54/4.55 'relcomp$b'('bot$g','bot$l') = 'bot$d'
% 28.54/4.55 & 'relcomp$b'('bot$g',fmb_'D_b_prod_set$'_2) = 'bot$d'
% 28.54/4.55 & 'relcomp$b'('bot$g',fmb_'D_b_prod_set$'_3) = 'bot$d'
% 28.54/4.55 & 'relcomp$b'('bot$g',fmb_'D_b_prod_set$'_4) = 'bot$d'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_dom$',type,'dom$': 'C_d_option_fun$' > 'C_set$').
% 28.54/4.55 tff('function_dom$',axiom,
% 28.54/4.55 'dom$'('b$') = 'bot$a'
% 28.54/4.55 & 'dom$'(fmb_'C_d_option_fun$'_2) = fmb_'C_set$'_2
% 28.54/4.55 & 'dom$'(fmb_'C_d_option_fun$'_3) = fmb_'C_set$'_2
% 28.54/4.55 & 'dom$'(fmb_'C_d_option_fun$'_4) = 'bot$a'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$n',type,'restrict_map$n': 'D_a_option_fun$' * 'D_set$' > 'D_a_option_fun$').
% 28.54/4.55 tff('function_restrict_map$n',axiom,
% 28.54/4.55 'restrict_map$n'(fmb_'D_a_option_fun$'_1,'bot$') = fmb_'D_a_option_fun$'_2
% 28.54/4.55 & 'restrict_map$n'(fmb_'D_a_option_fun$'_1,fmb_'D_set$'_2) = fmb_'D_a_option_fun$'_2
% 28.54/4.55 % 'restrict_map$n'(fmb_'D_a_option_fun$'_2,'bot$') undefined in model
% 28.54/4.55 % 'restrict_map$n'(fmb_'D_a_option_fun$'_2,fmb_'D_set$'_2) undefined in model
% 28.54/4.55 % 'restrict_map$n'(fmb_'D_a_option_fun$'_3,'bot$') undefined in model
% 28.54/4.55 % 'restrict_map$n'(fmb_'D_a_option_fun$'_3,fmb_'D_set$'_2) undefined in model
% 28.54/4.55 % 'restrict_map$n'(fmb_'D_a_option_fun$'_4,'bot$') undefined in model
% 28.54/4.55 % 'restrict_map$n'(fmb_'D_a_option_fun$'_4,fmb_'D_set$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_ran$c',type,'ran$c': 'A_a_option_fun$' > 'A_set$').
% 28.54/4.55 tff('function_ran$c',axiom,
% 28.54/4.55 'ran$c'('some$') = 'bot$c'
% 28.54/4.55 & 'ran$c'(fmb_'A_a_option_fun$'_2) = 'bot$c'
% 28.54/4.55 & 'ran$c'(fmb_'A_a_option_fun$'_3) = 'bot$c'
% 28.54/4.55 & 'ran$c'(fmb_'A_a_option_fun$'_4) = 'bot$c'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$e',type,'graph$e': 'A_d_option_fun$' > 'A_d_prod_set$').
% 28.54/4.55 tff('function_graph$e',axiom,
% 28.54/4.55 'graph$e'(fmb_'A_d_option_fun$'_1) = 'bot$g'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_insert$',type,'insert$': 'C_option$' * 'C_option_set$' > 'C_option_set$').
% 28.54/4.55 tff('function_insert$',axiom,
% 28.54/4.55 'insert$'('none$a','bot$n') = fmb_'C_option_set$'_2
% 28.54/4.55 & 'insert$'('none$a',fmb_'C_option_set$'_2) = fmb_'C_option_set$'_2
% 28.54/4.55 & 'insert$'('none$a',fmb_'C_option_set$'_3) = fmb_'C_option_set$'_3
% 28.54/4.55 & 'insert$'('none$a',fmb_'C_option_set$'_4) = fmb_'C_option_set$'_3
% 28.54/4.55 & 'insert$'(fmb_'C_option$'_2,'bot$n') = fmb_'C_option_set$'_3
% 28.54/4.55 & 'insert$'(fmb_'C_option$'_2,fmb_'C_option_set$'_2) = fmb_'C_option_set$'_3
% 28.54/4.55 & 'insert$'(fmb_'C_option$'_2,fmb_'C_option_set$'_3) = fmb_'C_option_set$'_4
% 28.54/4.55 & 'insert$'(fmb_'C_option$'_2,fmb_'C_option_set$'_4) = fmb_'C_option_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_pair$j',type,'pair$j': 'D$' * 'B$' > 'D_b_prod$').
% 28.54/4.55 tff('function_pair$j',axiom,
% 28.54/4.55 'pair$j'(fmb_'D$'_1,fmb_'B$'_1) = fmb_'D_b_prod$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_collect$d',type,'collect$d': 'A_bool_fun$' > 'A_set$').
% 28.54/4.55 tff('function_collect$d',axiom,
% 28.54/4.55 'collect$d'('bot$s') = 'bot$c'
% 28.54/4.55 & 'collect$d'(fmb_'A_bool_fun$'_2) = fmb_'A_set$'_2
% 28.54/4.55 & 'collect$d'(fmb_'A_bool_fun$'_3) = 'bot$c'
% 28.54/4.55 & 'collect$d'(fmb_'A_bool_fun$'_4) = 'bot$c'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_insert$g',type,'insert$g': 'A_c_prod$' * 'A_c_prod_set$' > 'A_c_prod_set$').
% 28.54/4.55 tff('function_insert$g',axiom,
% 28.54/4.55 'insert$g'(fmb_'A_c_prod$'_1,'bot$e') = fmb_'A_c_prod_set$'_2
% 28.54/4.55 & 'insert$g'(fmb_'A_c_prod$'_1,fmb_'A_c_prod_set$'_2) = fmb_'A_c_prod_set$'_2
% 28.54/4.55 & 'insert$g'(fmb_'A_c_prod$'_1,fmb_'A_c_prod_set$'_3) = 'bot$e'
% 28.54/4.55 & 'insert$g'(fmb_'A_c_prod$'_1,fmb_'A_c_prod_set$'_4) = fmb_'A_c_prod_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$q',type,'relcomp$q': 'A_c_prod_set$' * 'C_c_prod_set$' > 'A_c_prod_set$').
% 28.54/4.55 tff('function_relcomp$q',axiom,
% 28.54/4.55 'relcomp$q'('bot$e',fmb_'C_c_prod_set$'_1) = 'bot$e'
% 28.54/4.55 & 'relcomp$q'('bot$e',fmb_'C_c_prod_set$'_2) = 'bot$e'
% 28.54/4.55 & 'relcomp$q'('bot$e',fmb_'C_c_prod_set$'_3) = fmb_'A_c_prod_set$'_2
% 28.54/4.55 & 'relcomp$q'('bot$e',fmb_'C_c_prod_set$'_4) = fmb_'A_c_prod_set$'_4
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_2,fmb_'C_c_prod_set$'_1) = fmb_'A_c_prod_set$'_3
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_2,fmb_'C_c_prod_set$'_2) = fmb_'A_c_prod_set$'_3
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_2,fmb_'C_c_prod_set$'_3) = 'bot$e'
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_2,fmb_'C_c_prod_set$'_4) = fmb_'A_c_prod_set$'_2
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_3,fmb_'C_c_prod_set$'_1) = fmb_'A_c_prod_set$'_2
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_3,fmb_'C_c_prod_set$'_2) = fmb_'A_c_prod_set$'_2
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_3,fmb_'C_c_prod_set$'_3) = fmb_'A_c_prod_set$'_4
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_3,fmb_'C_c_prod_set$'_4) = fmb_'A_c_prod_set$'_4
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_4,fmb_'C_c_prod_set$'_1) = fmb_'A_c_prod_set$'_3
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_4,fmb_'C_c_prod_set$'_2) = fmb_'A_c_prod_set$'_3
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_4,fmb_'C_c_prod_set$'_3) = 'bot$e'
% 28.54/4.55 & 'relcomp$q'(fmb_'A_c_prod_set$'_4,fmb_'C_c_prod_set$'_4) = 'bot$e'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_upd$a',type,'fun_upd$a': 'C_d_option_fun$' * 'C$' * 'D_option$' > 'C_d_option_fun$').
% 28.54/4.55 tff('function_fun_upd$a',axiom,
% 28.54/4.55 'fun_upd$a'('b$',fmb_'C$'_1,'none$b') = fmb_'C_d_option_fun$'_4
% 28.54/4.55 & 'fun_upd$a'('b$',fmb_'C$'_1,fmb_'D_option$'_2) = 'b$'
% 28.54/4.55 % 'fun_upd$a'(fmb_'C_d_option_fun$'_2,fmb_'C$'_1,'none$b') undefined in model
% 28.54/4.55 % 'fun_upd$a'(fmb_'C_d_option_fun$'_2,fmb_'C$'_1,fmb_'D_option$'_2) undefined in model
% 28.54/4.55 % 'fun_upd$a'(fmb_'C_d_option_fun$'_3,fmb_'C$'_1,'none$b') undefined in model
% 28.54/4.55 % 'fun_upd$a'(fmb_'C_d_option_fun$'_3,fmb_'C$'_1,fmb_'D_option$'_2) undefined in model
% 28.54/4.55 % 'fun_upd$a'(fmb_'C_d_option_fun$'_4,fmb_'C$'_1,'none$b') undefined in model
% 28.54/4.55 % 'fun_upd$a'(fmb_'C_d_option_fun$'_4,fmb_'C$'_1,fmb_'D_option$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_pair$',type,'pair$': 'C$' * 'A$' > 'C_a_prod$').
% 28.54/4.55 tff('function_pair$',axiom,
% 28.54/4.55 'pair$'(fmb_'C$'_1,fmb_'A$'_1) = fmb_'C_a_prod$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$g',type,'relcomp$g': 'C_b_prod_set$' * 'B_d_prod_set$' > 'C_d_prod_set$').
% 28.54/4.55 tff('function_relcomp$g',axiom,
% 28.54/4.55 'relcomp$g'('bot$i',fmb_'B_d_prod_set$'_1) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'('bot$i',fmb_'B_d_prod_set$'_2) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'('bot$i',fmb_'B_d_prod_set$'_3) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'('bot$i',fmb_'B_d_prod_set$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_2,fmb_'B_d_prod_set$'_1) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_2,fmb_'B_d_prod_set$'_2) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_2,fmb_'B_d_prod_set$'_3) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_2,fmb_'B_d_prod_set$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_3,fmb_'B_d_prod_set$'_1) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_3,fmb_'B_d_prod_set$'_2) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_3,fmb_'B_d_prod_set$'_3) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_3,fmb_'B_d_prod_set$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_4,fmb_'B_d_prod_set$'_1) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_4,fmb_'B_d_prod_set$'_2) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_4,fmb_'B_d_prod_set$'_3) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'relcomp$g'(fmb_'C_b_prod_set$'_4,fmb_'B_d_prod_set$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$',type,'relcomp$': 'A_c_prod_set$' * 'C_b_prod_set$' > 'A_b_prod_set$').
% 28.54/4.55 tff('function_relcomp$',axiom,
% 28.54/4.55 'relcomp$'('bot$e','bot$i') = 'bot$d'
% 28.54/4.55 & 'relcomp$'('bot$e',fmb_'C_b_prod_set$'_2) = 'bot$d'
% 28.54/4.55 & 'relcomp$'('bot$e',fmb_'C_b_prod_set$'_3) = 'bot$d'
% 28.54/4.55 & 'relcomp$'('bot$e',fmb_'C_b_prod_set$'_4) = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_2,'bot$i') = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_2,fmb_'C_b_prod_set$'_2) = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_2,fmb_'C_b_prod_set$'_3) = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_2,fmb_'C_b_prod_set$'_4) = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_3,'bot$i') = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_3,fmb_'C_b_prod_set$'_2) = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_3,fmb_'C_b_prod_set$'_3) = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_3,fmb_'C_b_prod_set$'_4) = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_4,'bot$i') = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_4,fmb_'C_b_prod_set$'_2) = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_4,fmb_'C_b_prod_set$'_3) = 'bot$d'
% 28.54/4.55 & 'relcomp$'(fmb_'A_c_prod_set$'_4,fmb_'C_b_prod_set$'_4) = 'bot$d'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_set_option$d',type,'set_option$d': 'B_option$' > 'B_set$').
% 28.54/4.55 tff('function_set_option$d',axiom,
% 28.54/4.55 'set_option$d'('none$c') = 'bot$b'
% 28.54/4.55 & 'set_option$d'(fmb_'B_option$'_2) = fmb_'B_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_image$h',type,'image$h': 'B_b_option_fun$' * 'B_set$' > 'B_option_set$').
% 28.54/4.55 tff('function_image$h',axiom,
% 28.54/4.55 'image$h'('some$c','bot$b') = 'bot$m'
% 28.54/4.55 & 'image$h'('some$c',fmb_'B_set$'_2) = fmb_'B_option_set$'_4
% 28.54/4.55 & 'image$h'(fmb_'B_b_option_fun$'_2,'bot$b') = 'bot$m'
% 28.54/4.55 & 'image$h'(fmb_'B_b_option_fun$'_2,fmb_'B_set$'_2) = 'bot$m'
% 28.54/4.55 & 'image$h'(fmb_'B_b_option_fun$'_3,'bot$b') = 'bot$m'
% 28.54/4.55 & 'image$h'(fmb_'B_b_option_fun$'_3,fmb_'B_set$'_2) = fmb_'B_option_set$'_4
% 28.54/4.55 & 'image$h'(fmb_'B_b_option_fun$'_4,'bot$b') = 'bot$m'
% 28.54/4.55 & 'image$h'(fmb_'B_b_option_fun$'_4,fmb_'B_set$'_2) = 'bot$m'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_pair$d',type,'pair$d': 'B$' * 'B$' > 'B_b_prod$').
% 28.54/4.55 tff('function_pair$d',axiom,
% 28.54/4.55 'pair$d'(fmb_'B$'_1,fmb_'B$'_1) = fmb_'B_b_prod$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_uu$',type,'uu$': 'B_option_set$' > 'B_option_bool_fun$').
% 28.54/4.55 tff('function_uu$',axiom,
% 28.54/4.55 'uu$'('bot$m') = 'bot$o'
% 28.54/4.55 & 'uu$'(fmb_'B_option_set$'_2) = 'is_none$'
% 28.54/4.55 & 'uu$'(fmb_'B_option_set$'_3) = fmb_'B_option_bool_fun$'_3
% 28.54/4.55 & 'uu$'(fmb_'B_option_set$'_4) = fmb_'B_option_bool_fun$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_bind$f',type,'bind$f': 'B_option$' * 'B_c_option_fun$' > 'C_option$').
% 28.54/4.55 tff('function_bind$f',axiom,
% 28.54/4.55 'bind$f'('none$c',fmb_'B_c_option_fun$'_1) = 'none$a'
% 28.54/4.55 & 'bind$f'('none$c',fmb_'B_c_option_fun$'_2) = 'none$a'
% 28.54/4.55 & 'bind$f'('none$c',fmb_'B_c_option_fun$'_3) = 'none$a'
% 28.54/4.55 & 'bind$f'('none$c',fmb_'B_c_option_fun$'_4) = 'none$a'
% 28.54/4.55 & 'bind$f'(fmb_'B_option$'_2,fmb_'B_c_option_fun$'_1) = 'none$a'
% 28.54/4.55 & 'bind$f'(fmb_'B_option$'_2,fmb_'B_c_option_fun$'_2) = 'none$a'
% 28.54/4.55 & 'bind$f'(fmb_'B_option$'_2,fmb_'B_c_option_fun$'_3) = 'none$a'
% 28.54/4.55 & 'bind$f'(fmb_'B_option$'_2,fmb_'B_c_option_fun$'_4) = 'none$a'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_some$d',type,'some$d': 'B_option$' > 'B_option_option$').
% 28.54/4.55 tff('function_some$d',axiom,
% 28.54/4.55 'some$d'('none$c') = fmb_'B_option_option$'_2
% 28.54/4.55 & 'some$d'(fmb_'B_option$'_2) = fmb_'B_option_option$'_3
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$k',type,'graph$k': 'B_c_option_fun$' > 'B_c_prod_set$').
% 28.54/4.55 tff('function_graph$k',axiom,
% 28.54/4.55 'graph$k'(fmb_'B_c_option_fun$'_1) = fmb_'B_c_prod_set$'_2
% 28.54/4.55 & 'graph$k'(fmb_'B_c_option_fun$'_2) = fmb_'B_c_prod_set$'_3
% 28.54/4.55 & 'graph$k'(fmb_'B_c_option_fun$'_3) = fmb_'B_c_prod_set$'_4
% 28.54/4.55 & 'graph$k'(fmb_'B_c_option_fun$'_4) = fmb_'B_c_prod_set$'_3
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_combine_options$',type,'combine_options$': 'C_c_c_fun_fun$' * 'C_option$' > 'C_option_c_option_fun$').
% 28.54/4.55 tff('function_combine_options$',axiom,
% 28.54/4.55 'combine_options$'(fmb_'C_c_c_fun_fun$'_1,'none$a') = fmb_'C_option_c_option_fun$'_1
% 28.54/4.55 & 'combine_options$'(fmb_'C_c_c_fun_fun$'_1,fmb_'C_option$'_2) = fmb_'C_option_c_option_fun$'_3
% 28.54/4.55 % 'combine_options$'(fmb_'C_c_c_fun_fun$'_2,'none$a') undefined in model
% 28.54/4.55 % 'combine_options$'(fmb_'C_c_c_fun_fun$'_2,fmb_'C_option$'_2) undefined in model
% 28.54/4.55 % 'combine_options$'(fmb_'C_c_c_fun_fun$'_3,'none$a') undefined in model
% 28.54/4.55 % 'combine_options$'(fmb_'C_c_c_fun_fun$'_3,fmb_'C_option$'_2) undefined in model
% 28.54/4.55 % 'combine_options$'(fmb_'C_c_c_fun_fun$'_4,'none$a') undefined in model
% 28.54/4.55 % 'combine_options$'(fmb_'C_c_c_fun_fun$'_4,fmb_'C_option$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_image$a',type,'image$a': 'C_d_prod_set$' * 'C_set$' > 'D_set$').
% 28.54/4.55 tff('function_image$a',axiom,
% 28.54/4.55 'image$a'('bot$h','bot$a') = 'bot$'
% 28.54/4.55 & 'image$a'('bot$h',fmb_'C_set$'_2) = 'bot$'
% 28.54/4.55 & 'image$a'(fmb_'C_d_prod_set$'_2,'bot$a') = fmb_'D_set$'_2
% 28.54/4.55 & 'image$a'(fmb_'C_d_prod_set$'_2,fmb_'C_set$'_2) = 'bot$'
% 28.54/4.55 & 'image$a'(fmb_'C_d_prod_set$'_3,'bot$a') = 'bot$'
% 28.54/4.55 & 'image$a'(fmb_'C_d_prod_set$'_3,fmb_'C_set$'_2) = 'bot$'
% 28.54/4.55 & 'image$a'(fmb_'C_d_prod_set$'_4,'bot$a') = 'bot$'
% 28.54/4.55 & 'image$a'(fmb_'C_d_prod_set$'_4,fmb_'C_set$'_2) = 'bot$'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$aa',type,'fun_app$aa': 'B_option_c_option_bool_fun_fun$' * 'B_option$' > 'C_option_bool_fun$').
% 28.54/4.55 tff('function_fun_app$aa',axiom,
% 28.54/4.55 'fun_app$aa'(fmb_'B_option_c_option_bool_fun_fun$'_1,'none$c') = 'is_none$b'
% 28.54/4.55 & 'fun_app$aa'(fmb_'B_option_c_option_bool_fun_fun$'_1,fmb_'B_option$'_2) = 'is_none$b'
% 28.54/4.55 % 'fun_app$aa'(fmb_'B_option_c_option_bool_fun_fun$'_2,'none$c') undefined in model
% 28.54/4.55 % 'fun_app$aa'(fmb_'B_option_c_option_bool_fun_fun$'_2,fmb_'B_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$aa'(fmb_'B_option_c_option_bool_fun_fun$'_3,'none$c') undefined in model
% 28.54/4.55 % 'fun_app$aa'(fmb_'B_option_c_option_bool_fun_fun$'_3,fmb_'B_option$'_2) undefined in model
% 28.54/4.55 % 'fun_app$aa'(fmb_'B_option_c_option_bool_fun_fun$'_4,'none$c') undefined in model
% 28.54/4.55 % 'fun_app$aa'(fmb_'B_option_c_option_bool_fun_fun$'_4,fmb_'B_option$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$an',type,'fun_app$an': 'D_d_fun$' * 'D$' > 'D$').
% 28.54/4.55 tff('function_fun_app$an',axiom,
% 28.54/4.55 'fun_app$an'(fmb_'D_d_fun$'_1,fmb_'D$'_1) = fmb_'D$'_1
% 28.54/4.55 & 'fun_app$an'(fmb_'D_d_fun$'_2,fmb_'D$'_1) = fmb_'D$'_1
% 28.54/4.55 & 'fun_app$an'(fmb_'D_d_fun$'_3,fmb_'D$'_1) = fmb_'D$'_1
% 28.54/4.55 & 'fun_app$an'(fmb_'D_d_fun$'_4,fmb_'D$'_1) = fmb_'D$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_insert$j',type,'insert$j': 'C_b_prod$' * 'C_b_prod_set$' > 'C_b_prod_set$').
% 28.54/4.55 tff('function_insert$j',axiom,
% 28.54/4.55 'insert$j'(fmb_'C_b_prod$'_1,'bot$i') = fmb_'C_b_prod_set$'_4
% 28.54/4.55 & 'insert$j'(fmb_'C_b_prod$'_1,fmb_'C_b_prod_set$'_2) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'insert$j'(fmb_'C_b_prod$'_1,fmb_'C_b_prod_set$'_3) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'insert$j'(fmb_'C_b_prod$'_1,fmb_'C_b_prod_set$'_4) = 'bot$i'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_collect$b',type,'collect$b': 'C_bool_fun$' > 'C_set$').
% 28.54/4.55 tff('function_collect$b',axiom,
% 28.54/4.55 'collect$b'('bot$q') = 'bot$a'
% 28.54/4.55 & 'collect$b'(fmb_'C_bool_fun$'_2) = 'bot$a'
% 28.54/4.55 & 'collect$b'(fmb_'C_bool_fun$'_3) = fmb_'C_set$'_2
% 28.54/4.55 & 'collect$b'(fmb_'C_bool_fun$'_4) = 'bot$a'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$b',type,'restrict_map$b': 'B_c_option_fun$' * 'B_set$' > 'B_c_option_fun$').
% 28.54/4.55 tff('function_restrict_map$b',axiom,
% 28.54/4.55 'restrict_map$b'(fmb_'B_c_option_fun$'_1,'bot$b') = fmb_'B_c_option_fun$'_1
% 28.54/4.55 & 'restrict_map$b'(fmb_'B_c_option_fun$'_1,fmb_'B_set$'_2) = fmb_'B_c_option_fun$'_1
% 28.54/4.55 & 'restrict_map$b'(fmb_'B_c_option_fun$'_2,'bot$b') = fmb_'B_c_option_fun$'_1
% 28.54/4.55 & 'restrict_map$b'(fmb_'B_c_option_fun$'_2,fmb_'B_set$'_2) = fmb_'B_c_option_fun$'_2
% 28.54/4.55 & 'restrict_map$b'(fmb_'B_c_option_fun$'_3,'bot$b') = fmb_'B_c_option_fun$'_1
% 28.54/4.55 & 'restrict_map$b'(fmb_'B_c_option_fun$'_3,fmb_'B_set$'_2) = fmb_'B_c_option_fun$'_3
% 28.54/4.55 & 'restrict_map$b'(fmb_'B_c_option_fun$'_4,'bot$b') = fmb_'B_c_option_fun$'_1
% 28.54/4.55 & 'restrict_map$b'(fmb_'B_c_option_fun$'_4,fmb_'B_set$'_2) = fmb_'B_c_option_fun$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$j',type,'graph$j': 'A_a_option_fun$' > 'A_a_prod_set$').
% 28.54/4.55 tff('function_graph$j',axiom,
% 28.54/4.55 'graph$j'('some$') = fmb_'A_a_prod_set$'_2
% 28.54/4.55 & 'graph$j'(fmb_'A_a_option_fun$'_2) = fmb_'A_a_prod_set$'_3
% 28.54/4.55 & 'graph$j'(fmb_'A_a_option_fun$'_3) = fmb_'A_a_prod_set$'_3
% 28.54/4.55 & 'graph$j'(fmb_'A_a_option_fun$'_4) = fmb_'A_a_prod_set$'_3
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_pair$c',type,'pair$c': 'B$' * 'D$' > 'B_d_prod$').
% 28.54/4.55 tff('function_pair$c',axiom,
% 28.54/4.55 'pair$c'(fmb_'B$'_1,fmb_'D$'_1) = fmb_'B_d_prod$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_uuc$',type,'uuc$': 'B_set$' > 'B_bool_fun$').
% 28.54/4.55 tff('function_uuc$',axiom,
% 28.54/4.55 'uuc$'('bot$b') = 'bot$r'
% 28.54/4.55 & 'uuc$'(fmb_'B_set$'_2) = fmb_'B_bool_fun$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_upd$c',type,'fun_upd$c': 'C_b_option_fun$' * 'C$' * 'B_option$' > 'C_b_option_fun$').
% 28.54/4.55 tff('function_fun_upd$c',axiom,
% 28.54/4.55 'fun_upd$c'(fmb_'C_b_option_fun$'_1,fmb_'C$'_1,'none$c') = fmb_'C_b_option_fun$'_4
% 28.54/4.55 & 'fun_upd$c'(fmb_'C_b_option_fun$'_1,fmb_'C$'_1,fmb_'B_option$'_2) = fmb_'C_b_option_fun$'_3
% 28.54/4.55 % 'fun_upd$c'(fmb_'C_b_option_fun$'_2,fmb_'C$'_1,'none$c') undefined in model
% 28.54/4.55 % 'fun_upd$c'(fmb_'C_b_option_fun$'_2,fmb_'C$'_1,fmb_'B_option$'_2) undefined in model
% 28.54/4.55 % 'fun_upd$c'(fmb_'C_b_option_fun$'_3,fmb_'C$'_1,'none$c') undefined in model
% 28.54/4.55 % 'fun_upd$c'(fmb_'C_b_option_fun$'_3,fmb_'C$'_1,fmb_'B_option$'_2) undefined in model
% 28.54/4.55 % 'fun_upd$c'(fmb_'C_b_option_fun$'_4,fmb_'C$'_1,'none$c') undefined in model
% 28.54/4.55 % 'fun_upd$c'(fmb_'C_b_option_fun$'_4,fmb_'C$'_1,fmb_'B_option$'_2) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$al',type,'fun_app$al': 'C_c_c_fun_fun$' * 'C$' > 'C_c_fun$').
% 28.54/4.55 tff('function_fun_app$al',axiom,
% 28.54/4.55 'fun_app$al'(fmb_'C_c_c_fun_fun$'_1,fmb_'C$'_1) = fmb_'C_c_fun$'_1
% 28.54/4.55 % 'fun_app$al'(fmb_'C_c_c_fun_fun$'_2,fmb_'C$'_1) undefined in model
% 28.54/4.55 % 'fun_app$al'(fmb_'C_c_c_fun_fun$'_3,fmb_'C$'_1) undefined in model
% 28.54/4.55 % 'fun_app$al'(fmb_'C_c_c_fun_fun$'_4,fmb_'C$'_1) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_ran$d',type,'ran$d': 'D_c_option_fun$' > 'C_set$').
% 28.54/4.55 tff('function_ran$d',axiom,
% 28.54/4.55 'ran$d'(fmb_'D_c_option_fun$'_1) = 'bot$a'
% 28.54/4.55 & 'ran$d'(fmb_'D_c_option_fun$'_2) = 'bot$a'
% 28.54/4.55 & 'ran$d'(fmb_'D_c_option_fun$'_3) = 'bot$a'
% 28.54/4.55 & 'ran$d'(fmb_'D_c_option_fun$'_4) = 'bot$a'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$h',type,'restrict_map$h': 'C_b_option_fun$' * 'C_set$' > 'C_b_option_fun$').
% 28.54/4.55 tff('function_restrict_map$h',axiom,
% 28.54/4.55 'restrict_map$h'(fmb_'C_b_option_fun$'_1,'bot$a') = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'restrict_map$h'(fmb_'C_b_option_fun$'_1,fmb_'C_set$'_2) = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'restrict_map$h'(fmb_'C_b_option_fun$'_2,'bot$a') = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'restrict_map$h'(fmb_'C_b_option_fun$'_2,fmb_'C_set$'_2) = fmb_'C_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$h'(fmb_'C_b_option_fun$'_3,'bot$a') = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'restrict_map$h'(fmb_'C_b_option_fun$'_3,fmb_'C_set$'_2) = fmb_'C_b_option_fun$'_3
% 28.54/4.55 & 'restrict_map$h'(fmb_'C_b_option_fun$'_4,'bot$a') = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'restrict_map$h'(fmb_'C_b_option_fun$'_4,fmb_'C_set$'_2) = fmb_'C_b_option_fun$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$ar',type,'fun_app$ar': 'B_b_b_fun_fun$' * 'B$' > 'B_b_fun$').
% 28.54/4.55 tff('function_fun_app$ar',axiom,
% 28.54/4.55 'fun_app$ar'(fmb_'B_b_b_fun_fun$'_1,fmb_'B$'_1) = fmb_'B_b_fun$'_1
% 28.54/4.55 % 'fun_app$ar'(fmb_'B_b_b_fun_fun$'_2,fmb_'B$'_1) undefined in model
% 28.54/4.55 % 'fun_app$ar'(fmb_'B_b_b_fun_fun$'_3,fmb_'B$'_1) undefined in model
% 28.54/4.55 % 'fun_app$ar'(fmb_'B_b_b_fun_fun$'_4,fmb_'B$'_1) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$l',type,'relcomp$l': 'D_b_prod_set$' * 'B_b_prod_set$' > 'D_b_prod_set$').
% 28.54/4.55 tff('function_relcomp$l',axiom,
% 28.54/4.55 'relcomp$l'('bot$l','bot$k') = 'bot$l'
% 28.54/4.55 % 'relcomp$l'('bot$l',fmb_'B_b_prod_set$'_2) undefined in model
% 28.54/4.55 % 'relcomp$l'('bot$l',fmb_'B_b_prod_set$'_3) undefined in model
% 28.54/4.55 % 'relcomp$l'('bot$l',fmb_'B_b_prod_set$'_4) undefined in model
% 28.54/4.55 & 'relcomp$l'(fmb_'D_b_prod_set$'_2,'bot$k') = 'bot$l'
% 28.54/4.55 % 'relcomp$l'(fmb_'D_b_prod_set$'_2,fmb_'B_b_prod_set$'_2) undefined in model
% 28.54/4.55 % 'relcomp$l'(fmb_'D_b_prod_set$'_2,fmb_'B_b_prod_set$'_3) undefined in model
% 28.54/4.55 % 'relcomp$l'(fmb_'D_b_prod_set$'_2,fmb_'B_b_prod_set$'_4) undefined in model
% 28.54/4.55 & 'relcomp$l'(fmb_'D_b_prod_set$'_3,'bot$k') = 'bot$l'
% 28.54/4.55 % 'relcomp$l'(fmb_'D_b_prod_set$'_3,fmb_'B_b_prod_set$'_2) undefined in model
% 28.54/4.55 % 'relcomp$l'(fmb_'D_b_prod_set$'_3,fmb_'B_b_prod_set$'_3) undefined in model
% 28.54/4.55 % 'relcomp$l'(fmb_'D_b_prod_set$'_3,fmb_'B_b_prod_set$'_4) undefined in model
% 28.54/4.55 & 'relcomp$l'(fmb_'D_b_prod_set$'_4,'bot$k') = 'bot$l'
% 28.54/4.55 % 'relcomp$l'(fmb_'D_b_prod_set$'_4,fmb_'B_b_prod_set$'_2) undefined in model
% 28.54/4.55 % 'relcomp$l'(fmb_'D_b_prod_set$'_4,fmb_'B_b_prod_set$'_3) undefined in model
% 28.54/4.55 % 'relcomp$l'(fmb_'D_b_prod_set$'_4,fmb_'B_b_prod_set$'_4) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_curry$c',type,'curry$c': 'A_c_prod_bool_fun$' * 'A$' > 'C_bool_fun$').
% 28.54/4.55 tff('function_curry$c',axiom,
% 28.54/4.55 'curry$c'(fmb_'A_c_prod_bool_fun$'_1,fmb_'A$'_1) = fmb_'C_bool_fun$'_4
% 28.54/4.55 % 'curry$c'(fmb_'A_c_prod_bool_fun$'_2,fmb_'A$'_1) undefined in model
% 28.54/4.55 % 'curry$c'(fmb_'A_c_prod_bool_fun$'_3,fmb_'A$'_1) undefined in model
% 28.54/4.55 % 'curry$c'(fmb_'A_c_prod_bool_fun$'_4,fmb_'A$'_1) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$f',type,'graph$f': 'C_c_option_fun$' > 'C_c_prod_set$').
% 28.54/4.55 tff('function_graph$f',axiom,
% 28.54/4.55 'graph$f'('some$a') = fmb_'C_c_prod_set$'_1
% 28.54/4.55 % 'graph$f'(fmb_'C_c_option_fun$'_2) undefined in model
% 28.54/4.55 % 'graph$f'(fmb_'C_c_option_fun$'_3) undefined in model
% 28.54/4.55 % 'graph$f'(fmb_'C_c_option_fun$'_4) undefined in model
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_image$g',type,'image$g': 'D_d_option_fun$' * 'D_set$' > 'D_option_set$').
% 28.54/4.55 tff('function_image$g',axiom,
% 28.54/4.55 'image$g'('some$b','bot$') = 'bot$t'
% 28.54/4.55 & 'image$g'('some$b',fmb_'D_set$'_2) = fmb_'D_option_set$'_2
% 28.54/4.55 & 'image$g'(fmb_'D_d_option_fun$'_2,'bot$') = 'bot$t'
% 28.54/4.55 & 'image$g'(fmb_'D_d_option_fun$'_2,fmb_'D_set$'_2) = 'bot$t'
% 28.54/4.55 & 'image$g'(fmb_'D_d_option_fun$'_3,'bot$') = 'bot$t'
% 28.54/4.55 & 'image$g'(fmb_'D_d_option_fun$'_3,fmb_'D_set$'_2) = fmb_'D_option_set$'_2
% 28.54/4.55 & 'image$g'(fmb_'D_d_option_fun$'_4,'bot$') = 'bot$t'
% 28.54/4.55 & 'image$g'(fmb_'D_d_option_fun$'_4,fmb_'D_set$'_2) = 'bot$t'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$c',type,'graph$c': 'C_d_option_fun$' > 'C_d_prod_set$').
% 28.54/4.55 tff('function_graph$c',axiom,
% 28.54/4.55 'graph$c'('b$') = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'graph$c'(fmb_'C_d_option_fun$'_2) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'graph$c'(fmb_'C_d_option_fun$'_3) = fmb_'C_d_prod_set$'_4
% 28.54/4.55 & 'graph$c'(fmb_'C_d_option_fun$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_comp$d',type,'map_comp$d': 'A_d_option_fun$' > 'A_a_option_fun_a_d_option_fun_fun$').
% 28.54/4.55 tff('function_map_comp$d',axiom,
% 28.54/4.55 'map_comp$d'(fmb_'A_d_option_fun$'_1) = fmb_'A_a_option_fun_a_d_option_fun_fun$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_insert$i',type,'insert$i': 'A_d_prod$' * 'A_d_prod_set$' > 'A_d_prod_set$').
% 28.54/4.55 tff('function_insert$i',axiom,
% 28.54/4.55 'insert$i'(fmb_'A_d_prod$'_1,'bot$g') = 'bot$g'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_sup$b',type,'sup$b': 'D_b_prod_set$' * 'D_b_prod_set$' > 'D_b_prod_set$').
% 28.54/4.55 tff('function_sup$b',axiom,
% 28.54/4.55 'sup$b'('bot$l','bot$l') = 'bot$l'
% 28.54/4.55 & 'sup$b'('bot$l',fmb_'D_b_prod_set$'_2) = 'bot$l'
% 28.54/4.55 & 'sup$b'('bot$l',fmb_'D_b_prod_set$'_3) = 'bot$l'
% 28.54/4.55 & 'sup$b'('bot$l',fmb_'D_b_prod_set$'_4) = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_2,'bot$l') = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_2,fmb_'D_b_prod_set$'_2) = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_2,fmb_'D_b_prod_set$'_3) = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_2,fmb_'D_b_prod_set$'_4) = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_3,'bot$l') = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_3,fmb_'D_b_prod_set$'_2) = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_3,fmb_'D_b_prod_set$'_3) = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_3,fmb_'D_b_prod_set$'_4) = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_4,'bot$l') = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_4,fmb_'D_b_prod_set$'_2) = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_4,fmb_'D_b_prod_set$'_3) = 'bot$l'
% 28.54/4.55 & 'sup$b'(fmb_'D_b_prod_set$'_4,fmb_'D_b_prod_set$'_4) = 'bot$l'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_the_elem$d',type,'the_elem$d': 'A_set$' > 'A$').
% 28.54/4.55 tff('function_the_elem$d',axiom,
% 28.54/4.55 'the_elem$d'('bot$c') = fmb_'A$'_1
% 28.54/4.55 & 'the_elem$d'(fmb_'A_set$'_2) = fmb_'A$'_1
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_set_option$e',type,'set_option$e': 'C_option_option$' > 'C_option_set$').
% 28.54/4.55 tff('function_set_option$e',axiom,
% 28.54/4.55 'set_option$e'(fmb_'C_option_option$'_1) = fmb_'C_option_set$'_3
% 28.54/4.55 & 'set_option$e'(fmb_'C_option_option$'_2) = fmb_'C_option_set$'_2
% 28.54/4.55 & 'set_option$e'(fmb_'C_option_option$'_3) = fmb_'C_option_set$'_3
% 28.54/4.55 & 'set_option$e'(fmb_'C_option_option$'_4) = fmb_'C_option_set$'_3
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$ai',type,'fun_app$ai': 'B_b_option_fun_b_option_fun$' * 'B_b_option_fun$' > 'B_option$').
% 28.54/4.55 tff('function_fun_app$ai',axiom,
% 28.54/4.55 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_1,'some$c') = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_1,fmb_'B_b_option_fun$'_2) = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_1,fmb_'B_b_option_fun$'_3) = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_1,fmb_'B_b_option_fun$'_4) = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_2,'some$c') = fmb_'B_option$'_2
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_2,fmb_'B_b_option_fun$'_2) = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_2,fmb_'B_b_option_fun$'_3) = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_2,fmb_'B_b_option_fun$'_4) = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_3,'some$c') = fmb_'B_option$'_2
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_3,fmb_'B_b_option_fun$'_2) = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_3,fmb_'B_b_option_fun$'_3) = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_3,fmb_'B_b_option_fun$'_4) = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_4,'some$c') = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_4,fmb_'B_b_option_fun$'_2) = fmb_'B_option$'_2
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_4,fmb_'B_b_option_fun$'_3) = 'none$c'
% 28.54/4.55 & 'fun_app$ai'(fmb_'B_b_option_fun_b_option_fun$'_4,fmb_'B_b_option_fun$'_4) = 'none$c'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_relcomp$o',type,'relcomp$o': 'A_a_prod_set$' * 'A_c_prod_set$' > 'A_c_prod_set$').
% 28.54/4.55 tff('function_relcomp$o',axiom,
% 28.54/4.55 'relcomp$o'('bot$f','bot$e') = 'bot$e'
% 28.54/4.55 & 'relcomp$o'('bot$f',fmb_'A_c_prod_set$'_2) = 'bot$e'
% 28.54/4.55 & 'relcomp$o'('bot$f',fmb_'A_c_prod_set$'_3) = 'bot$e'
% 28.54/4.55 & 'relcomp$o'('bot$f',fmb_'A_c_prod_set$'_4) = 'bot$e'
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_2,'bot$e') = 'bot$e'
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_2,fmb_'A_c_prod_set$'_2) = fmb_'A_c_prod_set$'_3
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_2,fmb_'A_c_prod_set$'_3) = fmb_'A_c_prod_set$'_4
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_2,fmb_'A_c_prod_set$'_4) = 'bot$e'
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_3,'bot$e') = 'bot$e'
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_3,fmb_'A_c_prod_set$'_2) = fmb_'A_c_prod_set$'_3
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_3,fmb_'A_c_prod_set$'_3) = fmb_'A_c_prod_set$'_3
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_3,fmb_'A_c_prod_set$'_4) = fmb_'A_c_prod_set$'_4
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_4,'bot$e') = 'bot$e'
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_4,fmb_'A_c_prod_set$'_2) = 'bot$e'
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_4,fmb_'A_c_prod_set$'_3) = fmb_'A_c_prod_set$'_2
% 28.54/4.55 & 'relcomp$o'(fmb_'A_a_prod_set$'_4,fmb_'A_c_prod_set$'_4) = fmb_'A_c_prod_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_comp$b',type,'map_comp$b': 'D_b_option_fun$' * 'A_d_option_fun$' > 'A_b_option_fun$').
% 28.54/4.55 tff('function_map_comp$b',axiom,
% 28.54/4.55 'map_comp$b'('a$',fmb_'A_d_option_fun$'_1) = fmb_'A_b_option_fun$'_2
% 28.54/4.55 & 'map_comp$b'(fmb_'D_b_option_fun$'_2,fmb_'A_d_option_fun$'_1) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'map_comp$b'(fmb_'D_b_option_fun$'_3,fmb_'A_d_option_fun$'_1) = fmb_'A_b_option_fun$'_1
% 28.54/4.55 & 'map_comp$b'(fmb_'D_b_option_fun$'_4,fmb_'A_d_option_fun$'_1) = fmb_'A_b_option_fun$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_insert$h',type,'insert$h': 'C_d_prod$' * 'C_d_prod_set$' > 'C_d_prod_set$').
% 28.54/4.55 tff('function_insert$h',axiom,
% 28.54/4.55 'insert$h'(fmb_'C_d_prod$'_1,'bot$h') = fmb_'C_d_prod_set$'_2
% 28.54/4.55 & 'insert$h'(fmb_'C_d_prod$'_1,fmb_'C_d_prod_set$'_2) = 'bot$h'
% 28.54/4.55 & 'insert$h'(fmb_'C_d_prod$'_1,fmb_'C_d_prod_set$'_3) = 'bot$h'
% 28.54/4.55 & 'insert$h'(fmb_'C_d_prod$'_1,fmb_'C_d_prod_set$'_4) = fmb_'C_d_prod_set$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$d',type,'restrict_map$d': 'B_b_option_fun$' * 'B_set$' > 'B_b_option_fun$').
% 28.54/4.55 tff('function_restrict_map$d',axiom,
% 28.54/4.55 'restrict_map$d'('some$c','bot$b') = fmb_'B_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$d'('some$c',fmb_'B_set$'_2) = 'some$c'
% 28.54/4.55 & 'restrict_map$d'(fmb_'B_b_option_fun$'_2,'bot$b') = fmb_'B_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$d'(fmb_'B_b_option_fun$'_2,fmb_'B_set$'_2) = fmb_'B_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$d'(fmb_'B_b_option_fun$'_3,'bot$b') = fmb_'B_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$d'(fmb_'B_b_option_fun$'_3,fmb_'B_set$'_2) = fmb_'B_b_option_fun$'_3
% 28.54/4.55 & 'restrict_map$d'(fmb_'B_b_option_fun$'_4,'bot$b') = fmb_'B_b_option_fun$'_2
% 28.54/4.55 & 'restrict_map$d'(fmb_'B_b_option_fun$'_4,fmb_'B_set$'_2) = fmb_'B_b_option_fun$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_bind$a',type,'bind$a': 'C_option$' * 'C_d_option_fun$' > 'D_option$').
% 28.54/4.55 tff('function_bind$a',axiom,
% 28.54/4.55 'bind$a'('none$a','b$') = 'none$b'
% 28.54/4.55 & 'bind$a'('none$a',fmb_'C_d_option_fun$'_2) = 'none$b'
% 28.54/4.55 & 'bind$a'('none$a',fmb_'C_d_option_fun$'_3) = 'none$b'
% 28.54/4.55 & 'bind$a'('none$a',fmb_'C_d_option_fun$'_4) = 'none$b'
% 28.54/4.55 & 'bind$a'(fmb_'C_option$'_2,'b$') = 'none$b'
% 28.54/4.55 & 'bind$a'(fmb_'C_option$'_2,fmb_'C_d_option_fun$'_2) = 'none$b'
% 28.54/4.55 & 'bind$a'(fmb_'C_option$'_2,fmb_'C_d_option_fun$'_3) = 'none$b'
% 28.54/4.55 & 'bind$a'(fmb_'C_option$'_2,fmb_'C_d_option_fun$'_4) = 'none$b'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_restrict_map$c',type,'restrict_map$c': 'B_d_option_fun$' * 'B_set$' > 'B_d_option_fun$').
% 28.54/4.55 tff('function_restrict_map$c',axiom,
% 28.54/4.55 'restrict_map$c'(fmb_'B_d_option_fun$'_1,'bot$b') = fmb_'B_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$c'(fmb_'B_d_option_fun$'_1,fmb_'B_set$'_2) = fmb_'B_d_option_fun$'_1
% 28.54/4.55 & 'restrict_map$c'(fmb_'B_d_option_fun$'_2,'bot$b') = fmb_'B_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$c'(fmb_'B_d_option_fun$'_2,fmb_'B_set$'_2) = fmb_'B_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$c'(fmb_'B_d_option_fun$'_3,'bot$b') = fmb_'B_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$c'(fmb_'B_d_option_fun$'_3,fmb_'B_set$'_2) = fmb_'B_d_option_fun$'_3
% 28.54/4.55 & 'restrict_map$c'(fmb_'B_d_option_fun$'_4,'bot$b') = fmb_'B_d_option_fun$'_2
% 28.54/4.55 & 'restrict_map$c'(fmb_'B_d_option_fun$'_4,fmb_'B_set$'_2) = fmb_'B_d_option_fun$'_4
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_fun_app$f',type,'fun_app$f': 'A_a_option_fun_a_c_option_fun_fun$' * 'A_a_option_fun$' > 'A_c_option_fun$').
% 28.54/4.55 tff('function_fun_app$f',axiom,
% 28.54/4.55 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_1,'some$') = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_1,fmb_'A_a_option_fun$'_2) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_1,fmb_'A_a_option_fun$'_3) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_1,fmb_'A_a_option_fun$'_4) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_2,'some$') = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_2,fmb_'A_a_option_fun$'_2) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_2,fmb_'A_a_option_fun$'_3) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_2,fmb_'A_a_option_fun$'_4) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_3,'some$') = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_3,fmb_'A_a_option_fun$'_2) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_3,fmb_'A_a_option_fun$'_3) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_3,fmb_'A_a_option_fun$'_4) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_4,'some$') = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_4,fmb_'A_a_option_fun$'_2) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_4,fmb_'A_a_option_fun$'_3) = 'c$'
% 28.54/4.55 & 'fun_app$f'(fmb_'A_a_option_fun_a_c_option_fun_fun$'_4,fmb_'A_a_option_fun$'_4) = 'c$'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_dom$b',type,'dom$b': 'A_d_option_fun$' > 'A_set$').
% 28.54/4.55 tff('function_dom$b',axiom,
% 28.54/4.55 'dom$b'(fmb_'A_d_option_fun$'_1) = fmb_'A_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_bind$e',type,'bind$e': 'D_option$' * 'D_b_option_fun$' > 'B_option$').
% 28.54/4.55 tff('function_bind$e',axiom,
% 28.54/4.55 'bind$e'('none$b','a$') = 'none$c'
% 28.54/4.55 & 'bind$e'('none$b',fmb_'D_b_option_fun$'_2) = 'none$c'
% 28.54/4.55 & 'bind$e'('none$b',fmb_'D_b_option_fun$'_3) = 'none$c'
% 28.54/4.55 & 'bind$e'('none$b',fmb_'D_b_option_fun$'_4) = 'none$c'
% 28.54/4.55 & 'bind$e'(fmb_'D_option$'_2,'a$') = 'none$c'
% 28.54/4.55 & 'bind$e'(fmb_'D_option$'_2,fmb_'D_b_option_fun$'_2) = 'none$c'
% 28.54/4.55 & 'bind$e'(fmb_'D_option$'_2,fmb_'D_b_option_fun$'_3) = 'none$c'
% 28.54/4.55 & 'bind$e'(fmb_'D_option$'_2,fmb_'D_b_option_fun$'_4) = 'none$c'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_sup$',type,'sup$': 'C_d_prod_set$' * 'C_d_prod_set$' > 'C_d_prod_set$').
% 28.54/4.55 tff('function_sup$',axiom,
% 28.54/4.55 'sup$'('bot$h','bot$h') = 'bot$h'
% 28.54/4.55 & 'sup$'('bot$h',fmb_'C_d_prod_set$'_2) = 'bot$h'
% 28.54/4.55 & 'sup$'('bot$h',fmb_'C_d_prod_set$'_3) = 'bot$h'
% 28.54/4.55 & 'sup$'('bot$h',fmb_'C_d_prod_set$'_4) = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_2,'bot$h') = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_2,fmb_'C_d_prod_set$'_2) = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_2,fmb_'C_d_prod_set$'_3) = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_2,fmb_'C_d_prod_set$'_4) = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_3,'bot$h') = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_3,fmb_'C_d_prod_set$'_2) = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_3,fmb_'C_d_prod_set$'_3) = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_3,fmb_'C_d_prod_set$'_4) = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_4,'bot$h') = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_4,fmb_'C_d_prod_set$'_2) = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_4,fmb_'C_d_prod_set$'_3) = 'bot$h'
% 28.54/4.55 & 'sup$'(fmb_'C_d_prod_set$'_4,fmb_'C_d_prod_set$'_4) = 'bot$h'
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$a',type,'graph$a': 'A_c_option_fun$' > 'A_c_prod_set$').
% 28.54/4.55 tff('function_graph$a',axiom,
% 28.54/4.55 'graph$a'('c$') = fmb_'A_c_prod_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_graph$b',type,'graph$b': 'C_b_option_fun$' > 'C_b_prod_set$').
% 28.54/4.55 tff('function_graph$b',axiom,
% 28.54/4.55 'graph$b'(fmb_'C_b_option_fun$'_1) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'graph$b'(fmb_'C_b_option_fun$'_2) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'graph$b'(fmb_'C_b_option_fun$'_3) = fmb_'C_b_prod_set$'_2
% 28.54/4.55 & 'graph$b'(fmb_'C_b_option_fun$'_4) = fmb_'C_b_prod_set$'_2
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_set_option$',type,'set_option$': 'B_option_option$' > 'B_option_set$').
% 28.54/4.55 tff('function_set_option$',axiom,
% 28.54/4.55 'set_option$'('none$d') = 'bot$m'
% 28.54/4.55 & 'set_option$'(fmb_'B_option_option$'_2) = fmb_'B_option_set$'_2
% 28.54/4.55 & 'set_option$'(fmb_'B_option_option$'_3) = fmb_'B_option_set$'_3
% 28.54/4.55
% 28.54/4.55 ).
% 28.54/4.55
% 28.54/4.55 tff('declare_map_comp$a',type,'map_comp$a': 'D_b_option_fun$' * 'C_d_option_fun$' > 'C_b_option_fun$').
% 28.54/4.55 tff('function_map_comp$a',axiom,
% 28.54/4.55 'map_comp$a'('a$','b$') = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'map_comp$a'('a$',fmb_'C_d_option_fun$'_2) = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'map_comp$a'('a$',fmb_'C_d_option_fun$'_3) = fmb_'C_b_option_fun$'_1
% 28.54/4.55 & 'map_comp$a'('a$',fmb_'C_d_option_fun$'_4) = fmb_'C_b_option_fun$'_3
% 28.54/4.55 & 'map_comp$a'(fmb_'D_b_option_fun$'_2,'b$') = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_2,fmb_'C_d_option_fun$'_2) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_2,fmb_'C_d_option_fun$'_3) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_2,fmb_'C_d_option_fun$'_4) = fmb_'C_b_option_fun$'_3
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_3,'b$') = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_3,fmb_'C_d_option_fun$'_2) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_3,fmb_'C_d_option_fun$'_3) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_3,fmb_'C_d_option_fun$'_4) = fmb_'C_b_option_fun$'_3
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_4,'b$') = fmb_'C_b_option_fun$'_4
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_4,fmb_'C_d_option_fun$'_2) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_4,fmb_'C_d_option_fun$'_3) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$a'(fmb_'D_b_option_fun$'_4,fmb_'C_d_option_fun$'_4) = fmb_'C_b_option_fun$'_3
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_map_comp$e',type,'map_comp$e': 'A_c_option_fun$' > 'A_a_option_fun_a_c_option_fun_fun$').
% 28.54/4.56 tff('function_map_comp$e',axiom,
% 28.54/4.56 'map_comp$e'('c$') = fmb_'A_a_option_fun_a_c_option_fun_fun$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_map_add$c',type,'map_add$c': 'A_c_option_fun$' * 'A_c_option_fun$' > 'A_c_option_fun$').
% 28.54/4.56 tff('function_map_add$c',axiom,
% 28.54/4.56 'map_add$c'('c$','c$') = 'c$'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_map_comp$j',type,'map_comp$j': 'D_d_option_fun$' * 'C_d_option_fun$' > 'C_d_option_fun$').
% 28.54/4.56 tff('function_map_comp$j',axiom,
% 28.54/4.56 'map_comp$j'('some$b','b$') = fmb_'C_d_option_fun$'_2
% 28.54/4.56 & 'map_comp$j'('some$b',fmb_'C_d_option_fun$'_2) = 'b$'
% 28.54/4.56 & 'map_comp$j'('some$b',fmb_'C_d_option_fun$'_3) = fmb_'C_d_option_fun$'_2
% 28.54/4.56 & 'map_comp$j'('some$b',fmb_'C_d_option_fun$'_4) = fmb_'C_d_option_fun$'_3
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_2,'b$') undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_2,fmb_'C_d_option_fun$'_2) undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_2,fmb_'C_d_option_fun$'_3) undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_2,fmb_'C_d_option_fun$'_4) undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_3,'b$') undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_3,fmb_'C_d_option_fun$'_2) undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_3,fmb_'C_d_option_fun$'_3) undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_3,fmb_'C_d_option_fun$'_4) undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_4,'b$') undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_4,fmb_'C_d_option_fun$'_2) undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_4,fmb_'C_d_option_fun$'_3) undefined in model
% 28.54/4.56 % 'map_comp$j'(fmb_'D_d_option_fun$'_4,fmb_'C_d_option_fun$'_4) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_ran$',type,'ran$': 'D_a_option_fun$' > 'A_set$').
% 28.54/4.56 tff('function_ran$',axiom,
% 28.54/4.56 'ran$'(fmb_'D_a_option_fun$'_1) = 'bot$c'
% 28.54/4.56 & 'ran$'(fmb_'D_a_option_fun$'_2) = 'bot$c'
% 28.54/4.56 & 'ran$'(fmb_'D_a_option_fun$'_3) = 'bot$c'
% 28.54/4.56 & 'ran$'(fmb_'D_a_option_fun$'_4) = 'bot$c'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_graph$',type,'graph$': 'A_b_option_fun$' > 'A_b_prod_set$').
% 28.54/4.56 tff('function_graph$',axiom,
% 28.54/4.56 'graph$'(fmb_'A_b_option_fun$'_1) = 'bot$d'
% 28.54/4.56 & 'graph$'(fmb_'A_b_option_fun$'_2) = 'bot$d'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_relcomp$h',type,'relcomp$h': 'C_c_prod_set$' * 'C_b_prod_set$' > 'C_b_prod_set$').
% 28.54/4.56 tff('function_relcomp$h',axiom,
% 28.54/4.56 'relcomp$h'(fmb_'C_c_prod_set$'_1,'bot$i') = 'bot$i'
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_1,fmb_'C_b_prod_set$'_2) = fmb_'C_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_1,fmb_'C_b_prod_set$'_3) = fmb_'C_b_prod_set$'_3
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_1,fmb_'C_b_prod_set$'_4) = fmb_'C_b_prod_set$'_4
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_2,'bot$i') = 'bot$i'
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_2,fmb_'C_b_prod_set$'_2) = fmb_'C_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_2,fmb_'C_b_prod_set$'_3) = fmb_'C_b_prod_set$'_3
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_2,fmb_'C_b_prod_set$'_4) = fmb_'C_b_prod_set$'_4
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_3,'bot$i') = 'bot$i'
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_3,fmb_'C_b_prod_set$'_2) = fmb_'C_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_3,fmb_'C_b_prod_set$'_3) = fmb_'C_b_prod_set$'_3
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_3,fmb_'C_b_prod_set$'_4) = fmb_'C_b_prod_set$'_4
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_4,'bot$i') = 'bot$i'
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_4,fmb_'C_b_prod_set$'_2) = fmb_'C_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_4,fmb_'C_b_prod_set$'_3) = fmb_'C_b_prod_set$'_3
% 28.54/4.56 & 'relcomp$h'(fmb_'C_c_prod_set$'_4,fmb_'C_b_prod_set$'_4) = fmb_'C_b_prod_set$'_4
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$am',type,'fun_app$am': 'D_option_d_option_fun$' * 'D_option$' > 'D_option$').
% 28.54/4.56 tff('function_fun_app$am',axiom,
% 28.54/4.56 'fun_app$am'(fmb_'D_option_d_option_fun$'_1,'none$b') = 'none$b'
% 28.54/4.56 & 'fun_app$am'(fmb_'D_option_d_option_fun$'_1,fmb_'D_option$'_2) = fmb_'D_option$'_2
% 28.54/4.56 & 'fun_app$am'(fmb_'D_option_d_option_fun$'_2,'none$b') = fmb_'D_option$'_2
% 28.54/4.56 & 'fun_app$am'(fmb_'D_option_d_option_fun$'_2,fmb_'D_option$'_2) = fmb_'D_option$'_2
% 28.54/4.56 & 'fun_app$am'(fmb_'D_option_d_option_fun$'_3,'none$b') = fmb_'D_option$'_2
% 28.54/4.56 & 'fun_app$am'(fmb_'D_option_d_option_fun$'_3,fmb_'D_option$'_2) = fmb_'D_option$'_2
% 28.54/4.56 & 'fun_app$am'(fmb_'D_option_d_option_fun$'_4,'none$b') = fmb_'D_option$'_2
% 28.54/4.56 & 'fun_app$am'(fmb_'D_option_d_option_fun$'_4,fmb_'D_option$'_2) = fmb_'D_option$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_relcomp$p',type,'relcomp$p': 'A_a_prod_set$' * 'A_d_prod_set$' > 'A_d_prod_set$').
% 28.54/4.56 tff('function_relcomp$p',axiom,
% 28.54/4.56 'relcomp$p'('bot$f','bot$g') = 'bot$g'
% 28.54/4.56 & 'relcomp$p'(fmb_'A_a_prod_set$'_2,'bot$g') = 'bot$g'
% 28.54/4.56 & 'relcomp$p'(fmb_'A_a_prod_set$'_3,'bot$g') = 'bot$g'
% 28.54/4.56 & 'relcomp$p'(fmb_'A_a_prod_set$'_4,'bot$g') = 'bot$g'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_image$d',type,'image$d': 'D_b_prod_set$' * 'D_set$' > 'B_set$').
% 28.54/4.56 tff('function_image$d',axiom,
% 28.54/4.56 'image$d'('bot$l','bot$') = fmb_'B_set$'_2
% 28.54/4.56 & 'image$d'('bot$l',fmb_'D_set$'_2) = fmb_'B_set$'_2
% 28.54/4.56 & 'image$d'(fmb_'D_b_prod_set$'_2,'bot$') = fmb_'B_set$'_2
% 28.54/4.56 & 'image$d'(fmb_'D_b_prod_set$'_2,fmb_'D_set$'_2) = fmb_'B_set$'_2
% 28.54/4.56 & 'image$d'(fmb_'D_b_prod_set$'_3,'bot$') = fmb_'B_set$'_2
% 28.54/4.56 & 'image$d'(fmb_'D_b_prod_set$'_3,fmb_'D_set$'_2) = fmb_'B_set$'_2
% 28.54/4.56 & 'image$d'(fmb_'D_b_prod_set$'_4,'bot$') = fmb_'B_set$'_2
% 28.54/4.56 & 'image$d'(fmb_'D_b_prod_set$'_4,fmb_'D_set$'_2) = fmb_'B_set$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_map_comp$l',type,'map_comp$l': 'C_b_option_fun$' * 'C_c_option_fun$' > 'C_b_option_fun$').
% 28.54/4.56 tff('function_map_comp$l',axiom,
% 28.54/4.56 'map_comp$l'(fmb_'C_b_option_fun$'_1,'some$a') = fmb_'C_b_option_fun$'_3
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_1,fmb_'C_c_option_fun$'_2) undefined in model
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_1,fmb_'C_c_option_fun$'_3) undefined in model
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_1,fmb_'C_c_option_fun$'_4) undefined in model
% 28.54/4.56 & 'map_comp$l'(fmb_'C_b_option_fun$'_2,'some$a') = fmb_'C_b_option_fun$'_4
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_2,fmb_'C_c_option_fun$'_2) undefined in model
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_2,fmb_'C_c_option_fun$'_3) undefined in model
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_2,fmb_'C_c_option_fun$'_4) undefined in model
% 28.54/4.56 & 'map_comp$l'(fmb_'C_b_option_fun$'_3,'some$a') = fmb_'C_b_option_fun$'_3
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_3,fmb_'C_c_option_fun$'_2) undefined in model
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_3,fmb_'C_c_option_fun$'_3) undefined in model
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_3,fmb_'C_c_option_fun$'_4) undefined in model
% 28.54/4.56 & 'map_comp$l'(fmb_'C_b_option_fun$'_4,'some$a') = fmb_'C_b_option_fun$'_4
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_4,fmb_'C_c_option_fun$'_2) undefined in model
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_4,fmb_'C_c_option_fun$'_3) undefined in model
% 28.54/4.56 % 'map_comp$l'(fmb_'C_b_option_fun$'_4,fmb_'C_c_option_fun$'_4) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$k',type,'fun_app$k': 'C_a_option_fun$' * 'C$' > 'A_option$').
% 28.54/4.56 tff('function_fun_app$k',axiom,
% 28.54/4.56 'fun_app$k'(fmb_'C_a_option_fun$'_1,fmb_'C$'_1) = 'none$'
% 28.54/4.56 & 'fun_app$k'(fmb_'C_a_option_fun$'_2,fmb_'C$'_1) = 'none$'
% 28.54/4.56 & 'fun_app$k'(fmb_'C_a_option_fun$'_3,fmb_'C$'_1) = 'none$'
% 28.54/4.56 & 'fun_app$k'(fmb_'C_a_option_fun$'_4,fmb_'C$'_1) = 'none$'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$p',type,'fun_app$p': 'D_d_option_fun$' * 'D$' > 'D_option$').
% 28.54/4.56 tff('function_fun_app$p',axiom,
% 28.54/4.56 'fun_app$p'('some$b',fmb_'D$'_1) = fmb_'D_option$'_2
% 28.54/4.56 & 'fun_app$p'(fmb_'D_d_option_fun$'_2,fmb_'D$'_1) = 'none$b'
% 28.54/4.56 & 'fun_app$p'(fmb_'D_d_option_fun$'_3,fmb_'D$'_1) = fmb_'D_option$'_2
% 28.54/4.56 & 'fun_app$p'(fmb_'D_d_option_fun$'_4,fmb_'D$'_1) = fmb_'D_option$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_pair$e',type,'pair$e': 'A$' * 'C$' > 'A_c_prod$').
% 28.54/4.56 tff('function_pair$e',axiom,
% 28.54/4.56 'pair$e'(fmb_'A$'_1,fmb_'C$'_1) = fmb_'A_c_prod$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_sup$d',type,'sup$d': 'C_b_prod_set$' * 'C_b_prod_set$' > 'C_b_prod_set$').
% 28.54/4.56 tff('function_sup$d',axiom,
% 28.54/4.56 'sup$d'('bot$i','bot$i') = 'bot$i'
% 28.54/4.56 & 'sup$d'('bot$i',fmb_'C_b_prod_set$'_2) = 'bot$i'
% 28.54/4.56 & 'sup$d'('bot$i',fmb_'C_b_prod_set$'_3) = 'bot$i'
% 28.54/4.56 & 'sup$d'('bot$i',fmb_'C_b_prod_set$'_4) = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_2,'bot$i') = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_2,fmb_'C_b_prod_set$'_2) = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_2,fmb_'C_b_prod_set$'_3) = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_2,fmb_'C_b_prod_set$'_4) = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_3,'bot$i') = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_3,fmb_'C_b_prod_set$'_2) = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_3,fmb_'C_b_prod_set$'_3) = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_3,fmb_'C_b_prod_set$'_4) = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_4,'bot$i') = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_4,fmb_'C_b_prod_set$'_2) = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_4,fmb_'C_b_prod_set$'_3) = 'bot$i'
% 28.54/4.56 & 'sup$d'(fmb_'C_b_prod_set$'_4,fmb_'C_b_prod_set$'_4) = 'bot$i'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_curry$d',type,'curry$d': 'A_b_prod_bool_fun$' * 'A$' > 'B_bool_fun$').
% 28.54/4.56 tff('function_curry$d',axiom,
% 28.54/4.56 'curry$d'(fmb_'A_b_prod_bool_fun$'_1,fmb_'A$'_1) = fmb_'B_bool_fun$'_4
% 28.54/4.56 % 'curry$d'(fmb_'A_b_prod_bool_fun$'_2,fmb_'A$'_1) undefined in model
% 28.54/4.56 % 'curry$d'(fmb_'A_b_prod_bool_fun$'_3,fmb_'A$'_1) undefined in model
% 28.54/4.56 % 'curry$d'(fmb_'A_b_prod_bool_fun$'_4,fmb_'A$'_1) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_pair$f',type,'pair$f': 'C$' * 'D$' > 'C_d_prod$').
% 28.54/4.56 tff('function_pair$f',axiom,
% 28.54/4.56 'pair$f'(fmb_'C$'_1,fmb_'D$'_1) = fmb_'C_d_prod$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_bind$d',type,'bind$d': 'D_option$' > 'D_d_option_fun_d_option_fun$').
% 28.54/4.56 tff('function_bind$d',axiom,
% 28.54/4.56 'bind$d'('none$b') = fmb_'D_d_option_fun_d_option_fun$'_1
% 28.54/4.56 & 'bind$d'(fmb_'D_option$'_2) = fmb_'D_d_option_fun_d_option_fun$'_3
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_pair$h',type,'pair$h': 'C$' * 'B$' > 'C_b_prod$').
% 28.54/4.56 tff('function_pair$h',axiom,
% 28.54/4.56 'pair$h'(fmb_'C$'_1,fmb_'B$'_1) = fmb_'C_b_prod$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$aq',type,'fun_app$aq': 'B_b_fun$' * 'B$' > 'B$').
% 28.54/4.56 tff('function_fun_app$aq',axiom,
% 28.54/4.56 'fun_app$aq'(fmb_'B_b_fun$'_1,fmb_'B$'_1) = fmb_'B$'_1
% 28.54/4.56 & 'fun_app$aq'(fmb_'B_b_fun$'_2,fmb_'B$'_1) = fmb_'B$'_1
% 28.54/4.56 & 'fun_app$aq'(fmb_'B_b_fun$'_3,fmb_'B$'_1) = fmb_'B$'_1
% 28.54/4.56 & 'fun_app$aq'(fmb_'B_b_fun$'_4,fmb_'B$'_1) = fmb_'B$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_graph$d',type,'graph$d': 'D_b_option_fun$' > 'D_b_prod_set$').
% 28.54/4.56 tff('function_graph$d',axiom,
% 28.54/4.56 'graph$d'('a$') = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'graph$d'(fmb_'D_b_option_fun$'_2) = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'graph$d'(fmb_'D_b_option_fun$'_3) = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'graph$d'(fmb_'D_b_option_fun$'_4) = fmb_'D_b_prod_set$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$r',type,'fun_app$r': 'B_b_option_fun$' * 'B$' > 'B_option$').
% 28.54/4.56 tff('function_fun_app$r',axiom,
% 28.54/4.56 'fun_app$r'('some$c',fmb_'B$'_1) = fmb_'B_option$'_2
% 28.54/4.56 & 'fun_app$r'(fmb_'B_b_option_fun$'_2,fmb_'B$'_1) = 'none$c'
% 28.54/4.56 & 'fun_app$r'(fmb_'B_b_option_fun$'_3,fmb_'B$'_1) = 'none$c'
% 28.54/4.56 & 'fun_app$r'(fmb_'B_b_option_fun$'_4,fmb_'B$'_1) = 'none$c'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_map_comp$',type,'map_comp$': 'C_b_option_fun$' * 'A_c_option_fun$' > 'A_b_option_fun$').
% 28.54/4.56 tff('function_map_comp$',axiom,
% 28.54/4.56 'map_comp$'(fmb_'C_b_option_fun$'_1,'c$') = fmb_'A_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$'(fmb_'C_b_option_fun$'_2,'c$') = fmb_'A_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$'(fmb_'C_b_option_fun$'_3,'c$') = fmb_'A_b_option_fun$'_2
% 28.54/4.56 & 'map_comp$'(fmb_'C_b_option_fun$'_4,'c$') = fmb_'A_b_option_fun$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_collect$c',type,'collect$c': 'B_bool_fun$' > 'B_set$').
% 28.54/4.56 tff('function_collect$c',axiom,
% 28.54/4.56 'collect$c'('bot$r') = 'bot$b'
% 28.54/4.56 & 'collect$c'(fmb_'B_bool_fun$'_2) = fmb_'B_set$'_2
% 28.54/4.56 & 'collect$c'(fmb_'B_bool_fun$'_3) = 'bot$b'
% 28.54/4.56 & 'collect$c'(fmb_'B_bool_fun$'_4) = 'bot$b'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_bind$',type,'bind$': 'C_option$' > 'C_c_option_fun_c_option_fun$').
% 28.54/4.56 tff('function_bind$',axiom,
% 28.54/4.56 'bind$'('none$a') = fmb_'C_c_option_fun_c_option_fun$'_1
% 28.54/4.56 & 'bind$'(fmb_'C_option$'_2) = fmb_'C_c_option_fun_c_option_fun$'_3
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_insert$b',type,'insert$b': 'A$' * 'A_set$' > 'A_set$').
% 28.54/4.56 tff('function_insert$b',axiom,
% 28.54/4.56 'insert$b'(fmb_'A$'_1,'bot$c') = fmb_'A_set$'_2
% 28.54/4.56 & 'insert$b'(fmb_'A$'_1,fmb_'A_set$'_2) = fmb_'A_set$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_relcomp$n',type,'relcomp$n': 'A_b_prod_set$' * 'B_d_prod_set$' > 'A_d_prod_set$').
% 28.54/4.56 tff('function_relcomp$n',axiom,
% 28.54/4.56 'relcomp$n'('bot$d',fmb_'B_d_prod_set$'_1) = 'bot$g'
% 28.54/4.56 & 'relcomp$n'('bot$d',fmb_'B_d_prod_set$'_2) = 'bot$g'
% 28.54/4.56 & 'relcomp$n'('bot$d',fmb_'B_d_prod_set$'_3) = 'bot$g'
% 28.54/4.56 & 'relcomp$n'('bot$d',fmb_'B_d_prod_set$'_4) = 'bot$g'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_relcomp$s',type,'relcomp$s': 'D_d_prod_set$' * 'D_b_prod_set$' > 'D_b_prod_set$').
% 28.54/4.56 tff('function_relcomp$s',axiom,
% 28.54/4.56 'relcomp$s'(fmb_'D_d_prod_set$'_1,'bot$l') = fmb_'D_b_prod_set$'_3
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_1,fmb_'D_b_prod_set$'_2) = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_1,fmb_'D_b_prod_set$'_3) = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_1,fmb_'D_b_prod_set$'_4) = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_2,'bot$l') = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_2,fmb_'D_b_prod_set$'_2) = 'bot$l'
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_2,fmb_'D_b_prod_set$'_3) = fmb_'D_b_prod_set$'_3
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_2,fmb_'D_b_prod_set$'_4) = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_3,'bot$l') = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_3,fmb_'D_b_prod_set$'_2) = 'bot$l'
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_3,fmb_'D_b_prod_set$'_3) = 'bot$l'
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_3,fmb_'D_b_prod_set$'_4) = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_4,'bot$l') = fmb_'D_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_4,fmb_'D_b_prod_set$'_2) = 'bot$l'
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_4,fmb_'D_b_prod_set$'_3) = fmb_'D_b_prod_set$'_3
% 28.54/4.56 & 'relcomp$s'(fmb_'D_d_prod_set$'_4,fmb_'D_b_prod_set$'_4) = 'bot$l'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_curry$b',type,'curry$b': 'A_d_prod_bool_fun$' * 'A$' > 'D_bool_fun$').
% 28.54/4.56 tff('function_curry$b',axiom,
% 28.54/4.56 'curry$b'(fmb_'A_d_prod_bool_fun$'_1,fmb_'A$'_1) = fmb_'D_bool_fun$'_2
% 28.54/4.56 % 'curry$b'(fmb_'A_d_prod_bool_fun$'_2,fmb_'A$'_1) undefined in model
% 28.54/4.56 % 'curry$b'(fmb_'A_d_prod_bool_fun$'_3,fmb_'A$'_1) undefined in model
% 28.54/4.56 % 'curry$b'(fmb_'A_d_prod_bool_fun$'_4,fmb_'A$'_1) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_relcomp$j',type,'relcomp$j': 'A_d_prod_set$' * 'D_d_prod_set$' > 'A_d_prod_set$').
% 28.54/4.56 tff('function_relcomp$j',axiom,
% 28.54/4.56 'relcomp$j'('bot$g',fmb_'D_d_prod_set$'_1) = 'bot$g'
% 28.54/4.56 & 'relcomp$j'('bot$g',fmb_'D_d_prod_set$'_2) = 'bot$g'
% 28.54/4.56 & 'relcomp$j'('bot$g',fmb_'D_d_prod_set$'_3) = 'bot$g'
% 28.54/4.56 & 'relcomp$j'('bot$g',fmb_'D_d_prod_set$'_4) = 'bot$g'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_map_add$b',type,'map_add$b': 'A_d_option_fun$' * 'A_d_option_fun$' > 'A_d_option_fun$').
% 28.54/4.56 tff('function_map_add$b',axiom,
% 28.54/4.56 'map_add$b'(fmb_'A_d_option_fun$'_1,fmb_'A_d_option_fun$'_1) = fmb_'A_d_option_fun$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_the_elem$b',type,'the_elem$b': 'C_set$' > 'C$').
% 28.54/4.56 tff('function_the_elem$b',axiom,
% 28.54/4.56 'the_elem$b'('bot$a') = fmb_'C$'_1
% 28.54/4.56 & 'the_elem$b'(fmb_'C_set$'_2) = fmb_'C$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$ap',type,'fun_app$ap': 'B_option_b_option_fun$' * 'B_option$' > 'B_option$').
% 28.54/4.56 tff('function_fun_app$ap',axiom,
% 28.54/4.56 'fun_app$ap'(fmb_'B_option_b_option_fun$'_1,'none$c') = 'none$c'
% 28.54/4.56 & 'fun_app$ap'(fmb_'B_option_b_option_fun$'_1,fmb_'B_option$'_2) = fmb_'B_option$'_2
% 28.54/4.56 & 'fun_app$ap'(fmb_'B_option_b_option_fun$'_2,'none$c') = 'none$c'
% 28.54/4.56 & 'fun_app$ap'(fmb_'B_option_b_option_fun$'_2,fmb_'B_option$'_2) = 'none$c'
% 28.54/4.56 & 'fun_app$ap'(fmb_'B_option_b_option_fun$'_3,'none$c') = fmb_'B_option$'_2
% 28.54/4.56 & 'fun_app$ap'(fmb_'B_option_b_option_fun$'_3,fmb_'B_option$'_2) = fmb_'B_option$'_2
% 28.54/4.56 & 'fun_app$ap'(fmb_'B_option_b_option_fun$'_4,'none$c') = fmb_'B_option$'_2
% 28.54/4.56 & 'fun_app$ap'(fmb_'B_option_b_option_fun$'_4,fmb_'B_option$'_2) = fmb_'B_option$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_some$e',type,'some$e': 'C_option$' > 'C_option_option$').
% 28.54/4.56 tff('function_some$e',axiom,
% 28.54/4.56 'some$e'('none$a') = fmb_'C_option_option$'_2
% 28.54/4.56 & 'some$e'(fmb_'C_option$'_2) = fmb_'C_option_option$'_3
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_dom$a',type,'dom$a': 'C_b_option_fun$' > 'C_set$').
% 28.54/4.56 tff('function_dom$a',axiom,
% 28.54/4.56 'dom$a'(fmb_'C_b_option_fun$'_1) = 'bot$a'
% 28.54/4.56 & 'dom$a'(fmb_'C_b_option_fun$'_2) = fmb_'C_set$'_2
% 28.54/4.56 & 'dom$a'(fmb_'C_b_option_fun$'_3) = 'bot$a'
% 28.54/4.56 & 'dom$a'(fmb_'C_b_option_fun$'_4) = 'bot$a'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_insert$f',type,'insert$f': 'D_option$' * 'D_option_set$' > 'D_option_set$').
% 28.54/4.56 tff('function_insert$f',axiom,
% 28.54/4.56 'insert$f'('none$b','bot$t') = 'bot$t'
% 28.54/4.56 & 'insert$f'('none$b',fmb_'D_option_set$'_2) = fmb_'D_option_set$'_2
% 28.54/4.56 & 'insert$f'(fmb_'D_option$'_2,'bot$t') = fmb_'D_option_set$'_2
% 28.54/4.56 & 'insert$f'(fmb_'D_option$'_2,fmb_'D_option_set$'_2) = fmb_'D_option_set$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_upd$',type,'fun_upd$': 'A_c_option_fun$' * 'A$' * 'C_option$' > 'A_c_option_fun$').
% 28.54/4.56 tff('function_fun_upd$',axiom,
% 28.54/4.56 'fun_upd$'('c$',fmb_'A$'_1,'none$a') = 'c$'
% 28.54/4.56 & 'fun_upd$'('c$',fmb_'A$'_1,fmb_'C_option$'_2) = 'c$'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_sup$e',type,'sup$e': 'A_c_prod_set$' * 'A_c_prod_set$' > 'A_c_prod_set$').
% 28.54/4.56 tff('function_sup$e',axiom,
% 28.54/4.56 'sup$e'('bot$e','bot$e') = fmb_'A_c_prod_set$'_4
% 28.54/4.56 & 'sup$e'('bot$e',fmb_'A_c_prod_set$'_2) = fmb_'A_c_prod_set$'_3
% 28.54/4.56 & 'sup$e'('bot$e',fmb_'A_c_prod_set$'_3) = fmb_'A_c_prod_set$'_2
% 28.54/4.56 & 'sup$e'('bot$e',fmb_'A_c_prod_set$'_4) = fmb_'A_c_prod_set$'_3
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_2,'bot$e') = fmb_'A_c_prod_set$'_4
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_2,fmb_'A_c_prod_set$'_2) = fmb_'A_c_prod_set$'_3
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_2,fmb_'A_c_prod_set$'_3) = fmb_'A_c_prod_set$'_4
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_2,fmb_'A_c_prod_set$'_4) = 'bot$e'
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_3,'bot$e') = fmb_'A_c_prod_set$'_2
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_3,fmb_'A_c_prod_set$'_2) = fmb_'A_c_prod_set$'_4
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_3,fmb_'A_c_prod_set$'_3) = fmb_'A_c_prod_set$'_4
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_3,fmb_'A_c_prod_set$'_4) = fmb_'A_c_prod_set$'_4
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_4,'bot$e') = fmb_'A_c_prod_set$'_3
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_4,fmb_'A_c_prod_set$'_2) = 'bot$e'
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_4,fmb_'A_c_prod_set$'_3) = fmb_'A_c_prod_set$'_2
% 28.54/4.56 & 'sup$e'(fmb_'A_c_prod_set$'_4,fmb_'A_c_prod_set$'_4) = fmb_'A_c_prod_set$'_4
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_bind$c',type,'bind$c': 'D_option$' * 'D_c_option_fun$' > 'C_option$').
% 28.54/4.56 tff('function_bind$c',axiom,
% 28.54/4.56 'bind$c'('none$b',fmb_'D_c_option_fun$'_1) = 'none$a'
% 28.54/4.56 & 'bind$c'('none$b',fmb_'D_c_option_fun$'_2) = 'none$a'
% 28.54/4.56 & 'bind$c'('none$b',fmb_'D_c_option_fun$'_3) = 'none$a'
% 28.54/4.56 & 'bind$c'('none$b',fmb_'D_c_option_fun$'_4) = 'none$a'
% 28.54/4.56 & 'bind$c'(fmb_'D_option$'_2,fmb_'D_c_option_fun$'_1) = 'none$a'
% 28.54/4.56 & 'bind$c'(fmb_'D_option$'_2,fmb_'D_c_option_fun$'_2) = 'none$a'
% 28.54/4.56 & 'bind$c'(fmb_'D_option$'_2,fmb_'D_c_option_fun$'_3) = 'none$a'
% 28.54/4.56 & 'bind$c'(fmb_'D_option$'_2,fmb_'D_c_option_fun$'_4) = 'none$a'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_image$b',type,'image$b': 'A_c_prod_set$' * 'A_set$' > 'C_set$').
% 28.54/4.56 tff('function_image$b',axiom,
% 28.54/4.56 'image$b'('bot$e','bot$c') = fmb_'C_set$'_2
% 28.54/4.56 % 'image$b'('bot$e',fmb_'A_set$'_2) undefined in model
% 28.54/4.56 & 'image$b'(fmb_'A_c_prod_set$'_2,'bot$c') = fmb_'C_set$'_2
% 28.54/4.56 % 'image$b'(fmb_'A_c_prod_set$'_2,fmb_'A_set$'_2) undefined in model
% 28.54/4.56 & 'image$b'(fmb_'A_c_prod_set$'_3,'bot$c') = fmb_'C_set$'_2
% 28.54/4.56 % 'image$b'(fmb_'A_c_prod_set$'_3,fmb_'A_set$'_2) undefined in model
% 28.54/4.56 & 'image$b'(fmb_'A_c_prod_set$'_4,'bot$c') = fmb_'C_set$'_2
% 28.54/4.56 % 'image$b'(fmb_'A_c_prod_set$'_4,fmb_'A_set$'_2) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$ak',type,'fun_app$ak': 'C_c_fun$' * 'C$' > 'C$').
% 28.54/4.56 tff('function_fun_app$ak',axiom,
% 28.54/4.56 'fun_app$ak'(fmb_'C_c_fun$'_1,fmb_'C$'_1) = fmb_'C$'_1
% 28.54/4.56 & 'fun_app$ak'(fmb_'C_c_fun$'_2,fmb_'C$'_1) = fmb_'C$'_1
% 28.54/4.56 & 'fun_app$ak'(fmb_'C_c_fun$'_3,fmb_'C$'_1) = fmb_'C$'_1
% 28.54/4.56 & 'fun_app$ak'(fmb_'C_c_fun$'_4,fmb_'C$'_1) = fmb_'C$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_bind$g',type,'bind$g': 'B_option$' * 'B_d_option_fun$' > 'D_option$').
% 28.54/4.56 tff('function_bind$g',axiom,
% 28.54/4.56 'bind$g'('none$c',fmb_'B_d_option_fun$'_1) = 'none$b'
% 28.54/4.56 & 'bind$g'('none$c',fmb_'B_d_option_fun$'_2) = 'none$b'
% 28.54/4.56 & 'bind$g'('none$c',fmb_'B_d_option_fun$'_3) = 'none$b'
% 28.54/4.56 & 'bind$g'('none$c',fmb_'B_d_option_fun$'_4) = 'none$b'
% 28.54/4.56 & 'bind$g'(fmb_'B_option$'_2,fmb_'B_d_option_fun$'_1) = fmb_'D_option$'_2
% 28.54/4.56 & 'bind$g'(fmb_'B_option$'_2,fmb_'B_d_option_fun$'_2) = 'none$b'
% 28.54/4.56 & 'bind$g'(fmb_'B_option$'_2,fmb_'B_d_option_fun$'_3) = 'none$b'
% 28.54/4.56 & 'bind$g'(fmb_'B_option$'_2,fmb_'B_d_option_fun$'_4) = 'none$b'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_set_option$c',type,'set_option$c': 'D_option$' > 'D_set$').
% 28.54/4.56 tff('function_set_option$c',axiom,
% 28.54/4.56 'set_option$c'('none$b') = 'bot$'
% 28.54/4.56 & 'set_option$c'(fmb_'D_option$'_2) = fmb_'D_set$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_curry$a',type,'curry$a': 'C_b_prod_bool_fun$' * 'C$' > 'B_bool_fun$').
% 28.54/4.56 tff('function_curry$a',axiom,
% 28.54/4.56 'curry$a'(fmb_'C_b_prod_bool_fun$'_1,fmb_'C$'_1) = fmb_'B_bool_fun$'_2
% 28.54/4.56 % 'curry$a'(fmb_'C_b_prod_bool_fun$'_2,fmb_'C$'_1) undefined in model
% 28.54/4.56 % 'curry$a'(fmb_'C_b_prod_bool_fun$'_3,fmb_'C$'_1) undefined in model
% 28.54/4.56 % 'curry$a'(fmb_'C_b_prod_bool_fun$'_4,fmb_'C$'_1) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_relcomp$i',type,'relcomp$i': 'C_a_prod_set$' * 'A_b_prod_set$' > 'C_b_prod_set$').
% 28.54/4.56 tff('function_relcomp$i',axiom,
% 28.54/4.56 'relcomp$i'(fmb_'C_a_prod_set$'_1,'bot$d') = fmb_'C_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$i'(fmb_'C_a_prod_set$'_2,'bot$d') = fmb_'C_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$i'(fmb_'C_a_prod_set$'_3,'bot$d') = fmb_'C_b_prod_set$'_2
% 28.54/4.56 & 'relcomp$i'(fmb_'C_a_prod_set$'_4,'bot$d') = fmb_'C_b_prod_set$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_curry$',type,'curry$': 'C_d_prod_bool_fun$' * 'C$' > 'D_bool_fun$').
% 28.54/4.56 tff('function_curry$',axiom,
% 28.54/4.56 'curry$'(fmb_'C_d_prod_bool_fun$'_1,fmb_'C$'_1) = 'bot$p'
% 28.54/4.56 % 'curry$'(fmb_'C_d_prod_bool_fun$'_2,fmb_'C$'_1) undefined in model
% 28.54/4.56 % 'curry$'(fmb_'C_d_prod_bool_fun$'_3,fmb_'C$'_1) undefined in model
% 28.54/4.56 % 'curry$'(fmb_'C_d_prod_bool_fun$'_4,fmb_'C$'_1) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$o',type,'fun_app$o': 'C_c_option_fun$' * 'C$' > 'C_option$').
% 28.54/4.56 tff('function_fun_app$o',axiom,
% 28.54/4.56 'fun_app$o'('some$a',fmb_'C$'_1) = fmb_'C_option$'_2
% 28.54/4.56 & 'fun_app$o'(fmb_'C_c_option_fun$'_2,fmb_'C$'_1) = 'none$a'
% 28.54/4.56 & 'fun_app$o'(fmb_'C_c_option_fun$'_3,fmb_'C$'_1) = fmb_'C_option$'_2
% 28.54/4.56 & 'fun_app$o'(fmb_'C_c_option_fun$'_4,fmb_'C$'_1) = fmb_'C_option$'_2
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_image$',type,'image$': 'A_d_prod_set$' * 'A_set$' > 'D_set$').
% 28.54/4.56 tff('function_image$',axiom,
% 28.54/4.56 'image$'('bot$g','bot$c') = 'bot$'
% 28.54/4.56 % 'image$'('bot$g',fmb_'A_set$'_2) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_restrict_map$j',type,'restrict_map$j': 'D_c_option_fun$' * 'D_set$' > 'D_c_option_fun$').
% 28.54/4.56 tff('function_restrict_map$j',axiom,
% 28.54/4.56 'restrict_map$j'(fmb_'D_c_option_fun$'_1,'bot$') = fmb_'D_c_option_fun$'_2
% 28.54/4.56 & 'restrict_map$j'(fmb_'D_c_option_fun$'_1,fmb_'D_set$'_2) = fmb_'D_c_option_fun$'_1
% 28.54/4.56 & 'restrict_map$j'(fmb_'D_c_option_fun$'_2,'bot$') = fmb_'D_c_option_fun$'_1
% 28.54/4.56 & 'restrict_map$j'(fmb_'D_c_option_fun$'_2,fmb_'D_set$'_2) = fmb_'D_c_option_fun$'_2
% 28.54/4.56 & 'restrict_map$j'(fmb_'D_c_option_fun$'_3,'bot$') = fmb_'D_c_option_fun$'_4
% 28.54/4.56 & 'restrict_map$j'(fmb_'D_c_option_fun$'_3,fmb_'D_set$'_2) = fmb_'D_c_option_fun$'_3
% 28.54/4.56 & 'restrict_map$j'(fmb_'D_c_option_fun$'_4,'bot$') = fmb_'D_c_option_fun$'_1
% 28.54/4.56 & 'restrict_map$j'(fmb_'D_c_option_fun$'_4,fmb_'D_set$'_2) = fmb_'D_c_option_fun$'_4
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$q',type,'fun_app$q': 'D_b_option_fun$' * 'D$' > 'B_option$').
% 28.54/4.56 tff('function_fun_app$q',axiom,
% 28.54/4.56 'fun_app$q'('a$',fmb_'D$'_1) = 'none$c'
% 28.54/4.56 & 'fun_app$q'(fmb_'D_b_option_fun$'_2,fmb_'D$'_1) = 'none$c'
% 28.54/4.56 & 'fun_app$q'(fmb_'D_b_option_fun$'_3,fmb_'D$'_1) = 'none$c'
% 28.54/4.56 & 'fun_app$q'(fmb_'D_b_option_fun$'_4,fmb_'D$'_1) = 'none$c'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_pair$k',type,'pair$k': 'C$' * 'C$' > 'C_c_prod$').
% 28.54/4.56 tff('function_pair$k',axiom,
% 28.54/4.56 'pair$k'(fmb_'C$'_1,fmb_'C$'_1) = fmb_'C_c_prod$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$x',type,'fun_app$x': 'D_option_c_option_bool_fun_fun$' * 'D_option$' > 'C_option_bool_fun$').
% 28.54/4.56 tff('function_fun_app$x',axiom,
% 28.54/4.56 'fun_app$x'(fmb_'D_option_c_option_bool_fun_fun$'_1,'none$b') = 'is_none$b'
% 28.54/4.56 & 'fun_app$x'(fmb_'D_option_c_option_bool_fun_fun$'_1,fmb_'D_option$'_2) = 'is_none$b'
% 28.54/4.56 % 'fun_app$x'(fmb_'D_option_c_option_bool_fun_fun$'_2,'none$b') undefined in model
% 28.54/4.56 % 'fun_app$x'(fmb_'D_option_c_option_bool_fun_fun$'_2,fmb_'D_option$'_2) undefined in model
% 28.54/4.56 % 'fun_app$x'(fmb_'D_option_c_option_bool_fun_fun$'_3,'none$b') undefined in model
% 28.54/4.56 % 'fun_app$x'(fmb_'D_option_c_option_bool_fun_fun$'_3,fmb_'D_option$'_2) undefined in model
% 28.54/4.56 % 'fun_app$x'(fmb_'D_option_c_option_bool_fun_fun$'_4,'none$b') undefined in model
% 28.54/4.56 % 'fun_app$x'(fmb_'D_option_c_option_bool_fun_fun$'_4,fmb_'D_option$'_2) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$ac',type,'fun_app$ac': 'B_option_b_option_bool_fun_fun$' * 'B_option$' > 'B_option_bool_fun$').
% 28.54/4.56 tff('function_fun_app$ac',axiom,
% 28.54/4.56 'fun_app$ac'(fmb_'B_option_b_option_bool_fun_fun$'_1,'none$c') = 'is_none$'
% 28.54/4.56 & 'fun_app$ac'(fmb_'B_option_b_option_bool_fun_fun$'_1,fmb_'B_option$'_2) = 'is_none$'
% 28.54/4.56 % 'fun_app$ac'(fmb_'B_option_b_option_bool_fun_fun$'_2,'none$c') undefined in model
% 28.54/4.56 % 'fun_app$ac'(fmb_'B_option_b_option_bool_fun_fun$'_2,fmb_'B_option$'_2) undefined in model
% 28.54/4.56 % 'fun_app$ac'(fmb_'B_option_b_option_bool_fun_fun$'_3,'none$c') undefined in model
% 28.54/4.56 % 'fun_app$ac'(fmb_'B_option_b_option_bool_fun_fun$'_3,fmb_'B_option$'_2) undefined in model
% 28.54/4.56 % 'fun_app$ac'(fmb_'B_option_b_option_bool_fun_fun$'_4,'none$c') undefined in model
% 28.54/4.56 % 'fun_app$ac'(fmb_'B_option_b_option_bool_fun_fun$'_4,fmb_'B_option$'_2) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_dom$c',type,'dom$c': 'A_c_option_fun$' > 'A_set$').
% 28.54/4.56 tff('function_dom$c',axiom,
% 28.54/4.56 'dom$c'('c$') = 'bot$c'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_combine_options$b',type,'combine_options$b': 'B_b_b_fun_fun$' * 'B_option$' > 'B_option_b_option_fun$').
% 28.54/4.56 tff('function_combine_options$b',axiom,
% 28.54/4.56 'combine_options$b'(fmb_'B_b_b_fun_fun$'_1,'none$c') = fmb_'B_option_b_option_fun$'_1
% 28.54/4.56 & 'combine_options$b'(fmb_'B_b_b_fun_fun$'_1,fmb_'B_option$'_2) = fmb_'B_option_b_option_fun$'_3
% 28.54/4.56 % 'combine_options$b'(fmb_'B_b_b_fun_fun$'_2,'none$c') undefined in model
% 28.54/4.56 % 'combine_options$b'(fmb_'B_b_b_fun_fun$'_2,fmb_'B_option$'_2) undefined in model
% 28.54/4.56 % 'combine_options$b'(fmb_'B_b_b_fun_fun$'_3,'none$c') undefined in model
% 28.54/4.56 % 'combine_options$b'(fmb_'B_b_b_fun_fun$'_3,fmb_'B_option$'_2) undefined in model
% 28.54/4.56 % 'combine_options$b'(fmb_'B_b_b_fun_fun$'_4,'none$c') undefined in model
% 28.54/4.56 % 'combine_options$b'(fmb_'B_b_b_fun_fun$'_4,fmb_'B_option$'_2) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_the_elem$c',type,'the_elem$c': 'B_set$' > 'B$').
% 28.54/4.56 tff('function_the_elem$c',axiom,
% 28.54/4.56 'the_elem$c'('bot$b') = fmb_'B$'_1
% 28.54/4.56 & 'the_elem$c'(fmb_'B_set$'_2) = fmb_'B$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_the$',type,'the$': 'C_option$' > 'C$').
% 28.54/4.56 tff('function_the$',axiom,
% 28.54/4.56 'the$'('none$a') = fmb_'C$'_1
% 28.54/4.56 & 'the$'(fmb_'C_option$'_2) = fmb_'C$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_upd$d',type,'fun_upd$d': 'A_b_option_fun$' * 'A$' * 'B_option$' > 'A_b_option_fun$').
% 28.54/4.56 tff('function_fun_upd$d',axiom,
% 28.54/4.56 'fun_upd$d'(fmb_'A_b_option_fun$'_1,fmb_'A$'_1,'none$c') = fmb_'A_b_option_fun$'_2
% 28.54/4.56 & 'fun_upd$d'(fmb_'A_b_option_fun$'_1,fmb_'A$'_1,fmb_'B_option$'_2) = fmb_'A_b_option_fun$'_1
% 28.54/4.56 % 'fun_upd$d'(fmb_'A_b_option_fun$'_2,fmb_'A$'_1,'none$c') undefined in model
% 28.54/4.56 % 'fun_upd$d'(fmb_'A_b_option_fun$'_2,fmb_'A$'_1,fmb_'B_option$'_2) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_ran$e',type,'ran$e': 'C_c_option_fun$' > 'C_set$').
% 28.54/4.56 tff('function_ran$e',axiom,
% 28.54/4.56 'ran$e'('some$a') = 'bot$a'
% 28.54/4.56 & 'ran$e'(fmb_'C_c_option_fun$'_2) = 'bot$a'
% 28.54/4.56 & 'ran$e'(fmb_'C_c_option_fun$'_3) = 'bot$a'
% 28.54/4.56 & 'ran$e'(fmb_'C_c_option_fun$'_4) = 'bot$a'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$v',type,'fun_app$v': 'C_option_d_option_bool_fun_fun$' * 'C_option$' > 'D_option_bool_fun$').
% 28.54/4.56 tff('function_fun_app$v',axiom,
% 28.54/4.56 'fun_app$v'(fmb_'C_option_d_option_bool_fun_fun$'_1,'none$a') = 'is_none$a'
% 28.54/4.56 & 'fun_app$v'(fmb_'C_option_d_option_bool_fun_fun$'_1,fmb_'C_option$'_2) = 'is_none$a'
% 28.54/4.56 % 'fun_app$v'(fmb_'C_option_d_option_bool_fun_fun$'_2,'none$a') undefined in model
% 28.54/4.56 % 'fun_app$v'(fmb_'C_option_d_option_bool_fun_fun$'_2,fmb_'C_option$'_2) undefined in model
% 28.54/4.56 % 'fun_app$v'(fmb_'C_option_d_option_bool_fun_fun$'_3,'none$a') undefined in model
% 28.54/4.56 % 'fun_app$v'(fmb_'C_option_d_option_bool_fun_fun$'_3,fmb_'C_option$'_2) undefined in model
% 28.54/4.56 % 'fun_app$v'(fmb_'C_option_d_option_bool_fun_fun$'_4,'none$a') undefined in model
% 28.54/4.56 % 'fun_app$v'(fmb_'C_option_d_option_bool_fun_fun$'_4,fmb_'C_option$'_2) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_ran$b',type,'ran$b': 'B_a_option_fun$' > 'A_set$').
% 28.54/4.56 tff('function_ran$b',axiom,
% 28.54/4.56 'ran$b'(fmb_'B_a_option_fun$'_1) = 'bot$c'
% 28.54/4.56 & 'ran$b'(fmb_'B_a_option_fun$'_2) = 'bot$c'
% 28.54/4.56 & 'ran$b'(fmb_'B_a_option_fun$'_3) = 'bot$c'
% 28.54/4.56 & 'ran$b'(fmb_'B_a_option_fun$'_4) = 'bot$c'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_insert$k',type,'insert$k': 'A_b_prod$' * 'A_b_prod_set$' > 'A_b_prod_set$').
% 28.54/4.56 tff('function_insert$k',axiom,
% 28.54/4.56 'insert$k'(fmb_'A_b_prod$'_1,'bot$d') = 'bot$d'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_map_comp$h',type,'map_comp$h': 'A_b_option_fun$' * 'C_a_option_fun$' > 'C_b_option_fun$').
% 28.54/4.56 tff('function_map_comp$h',axiom,
% 28.54/4.56 'map_comp$h'(fmb_'A_b_option_fun$'_1,fmb_'C_a_option_fun$'_1) = fmb_'C_b_option_fun$'_3
% 28.54/4.56 & 'map_comp$h'(fmb_'A_b_option_fun$'_1,fmb_'C_a_option_fun$'_2) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$h'(fmb_'A_b_option_fun$'_1,fmb_'C_a_option_fun$'_3) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$h'(fmb_'A_b_option_fun$'_1,fmb_'C_a_option_fun$'_4) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$h'(fmb_'A_b_option_fun$'_2,fmb_'C_a_option_fun$'_1) = fmb_'C_b_option_fun$'_3
% 28.54/4.56 & 'map_comp$h'(fmb_'A_b_option_fun$'_2,fmb_'C_a_option_fun$'_2) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$h'(fmb_'A_b_option_fun$'_2,fmb_'C_a_option_fun$'_3) = fmb_'C_b_option_fun$'_1
% 28.54/4.56 & 'map_comp$h'(fmb_'A_b_option_fun$'_2,fmb_'C_a_option_fun$'_4) = fmb_'C_b_option_fun$'_1
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_ran$f',type,'ran$f': 'B_c_option_fun$' > 'C_set$').
% 28.54/4.56 tff('function_ran$f',axiom,
% 28.54/4.56 'ran$f'(fmb_'B_c_option_fun$'_1) = 'bot$a'
% 28.54/4.56 & 'ran$f'(fmb_'B_c_option_fun$'_2) = 'bot$a'
% 28.54/4.56 & 'ran$f'(fmb_'B_c_option_fun$'_3) = 'bot$a'
% 28.54/4.56 & 'ran$f'(fmb_'B_c_option_fun$'_4) = 'bot$a'
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$b',type,'member$b': 'C$' * 'C_set$' > $o ).
% 28.54/4.56 tff('predicate_member$b',axiom,
% 28.54/4.56 ~'member$b'(fmb_'C$'_1,'bot$a')
% 28.54/4.56 & 'member$b'(fmb_'C$'_1,fmb_'C_set$'_2)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_less_eq$a',type,'less_eq$a': 'C_d_prod_set$' * 'C_d_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_less_eq$a',axiom,
% 28.54/4.56 ~'less_eq$a'('bot$h','bot$h')
% 28.54/4.56 % 'less_eq$a'('bot$h',fmb_'C_d_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$a'('bot$h',fmb_'C_d_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$a'('bot$h',fmb_'C_d_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_2,'bot$h') undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_2,fmb_'C_d_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_2,fmb_'C_d_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_2,fmb_'C_d_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_3,'bot$h') undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_3,fmb_'C_d_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_3,fmb_'C_d_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_3,fmb_'C_d_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_4,'bot$h') undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_4,fmb_'C_d_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_4,fmb_'C_d_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$a'(fmb_'C_d_prod_set$'_4,fmb_'C_d_prod_set$'_4) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_less_eq$e',type,'less_eq$e': 'C_b_prod_set$' * 'C_b_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_less_eq$e',axiom,
% 28.54/4.56 % 'less_eq$e'('bot$i','bot$i') undefined in model
% 28.54/4.56 % 'less_eq$e'('bot$i',fmb_'C_b_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$e'('bot$i',fmb_'C_b_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$e'('bot$i',fmb_'C_b_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_2,'bot$i') undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_2,fmb_'C_b_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_2,fmb_'C_b_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_2,fmb_'C_b_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_3,'bot$i') undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_3,fmb_'C_b_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_3,fmb_'C_b_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_3,fmb_'C_b_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_4,'bot$i') undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_4,fmb_'C_b_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_4,fmb_'C_b_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$e'(fmb_'C_b_prod_set$'_4,fmb_'C_b_prod_set$'_4) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$m',type,'member$m': 'C_b_prod$' * 'C_b_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$m',axiom,
% 28.54/4.56 ~'member$m'(fmb_'C_b_prod$'_1,'bot$i')
% 28.54/4.56 & ~'member$m'(fmb_'C_b_prod$'_1,fmb_'C_b_prod_set$'_2)
% 28.54/4.56 & ~'member$m'(fmb_'C_b_prod$'_1,fmb_'C_b_prod_set$'_3)
% 28.54/4.56 & ~'member$m'(fmb_'C_b_prod$'_1,fmb_'C_b_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$c',type,'member$c': 'B$' * 'B_set$' > $o ).
% 28.54/4.56 tff('predicate_member$c',axiom,
% 28.54/4.56 ~'member$c'(fmb_'B$'_1,'bot$b')
% 28.54/4.56 & 'member$c'(fmb_'B$'_1,fmb_'B_set$'_2)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_inj_on$a',type,'inj_on$a': 'D_d_option_fun$' * 'D_set$' > $o ).
% 28.54/4.56 tff('predicate_inj_on$a',axiom,
% 28.54/4.56 % 'inj_on$a'('some$b','bot$') undefined in model
% 28.54/4.56 % 'inj_on$a'('some$b',fmb_'D_set$'_2) undefined in model
% 28.54/4.56 % 'inj_on$a'(fmb_'D_d_option_fun$'_2,'bot$') undefined in model
% 28.54/4.56 % 'inj_on$a'(fmb_'D_d_option_fun$'_2,fmb_'D_set$'_2) undefined in model
% 28.54/4.56 % 'inj_on$a'(fmb_'D_d_option_fun$'_3,'bot$') undefined in model
% 28.54/4.56 % 'inj_on$a'(fmb_'D_d_option_fun$'_3,fmb_'D_set$'_2) undefined in model
% 28.54/4.56 % 'inj_on$a'(fmb_'D_d_option_fun$'_4,'bot$') undefined in model
% 28.54/4.56 % 'inj_on$a'(fmb_'D_d_option_fun$'_4,fmb_'D_set$'_2) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$d',type,'member$d': 'A$' * 'A_set$' > $o ).
% 28.54/4.56 tff('predicate_member$d',axiom,
% 28.54/4.56 ~'member$d'(fmb_'A$'_1,'bot$c')
% 28.54/4.56 & 'member$d'(fmb_'A$'_1,fmb_'A_set$'_2)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$f',type,'member$f': 'A_a_prod$' * 'A_a_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$f',axiom,
% 28.54/4.56 ~'member$f'(fmb_'A_a_prod$'_1,'bot$f')
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_1,fmb_'A_a_prod_set$'_2)
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_1,fmb_'A_a_prod_set$'_3)
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_1,fmb_'A_a_prod_set$'_4)
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_2,'bot$f')
% 28.54/4.56 & 'member$f'(fmb_'A_a_prod$'_2,fmb_'A_a_prod_set$'_2)
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_2,fmb_'A_a_prod_set$'_3)
% 28.54/4.56 & 'member$f'(fmb_'A_a_prod$'_2,fmb_'A_a_prod_set$'_4)
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_3,'bot$f')
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_3,fmb_'A_a_prod_set$'_2)
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_3,fmb_'A_a_prod_set$'_3)
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_3,fmb_'A_a_prod_set$'_4)
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_4,'bot$f')
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_4,fmb_'A_a_prod_set$'_2)
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_4,fmb_'A_a_prod_set$'_3)
% 28.54/4.56 & ~'member$f'(fmb_'A_a_prod$'_4,fmb_'A_a_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$o',type,'member$o': 'D_b_prod$' * 'D_b_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$o',axiom,
% 28.54/4.56 'member$o'(fmb_'D_b_prod$'_1,'bot$l')
% 28.54/4.56 & 'member$o'(fmb_'D_b_prod$'_1,fmb_'D_b_prod_set$'_2)
% 28.54/4.56 & 'member$o'(fmb_'D_b_prod$'_1,fmb_'D_b_prod_set$'_3)
% 28.54/4.56 & 'member$o'(fmb_'D_b_prod$'_1,fmb_'D_b_prod_set$'_4)
% 28.54/4.56 & 'member$o'(fmb_'D_b_prod$'_2,'bot$l')
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_2,fmb_'D_b_prod_set$'_2)
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_2,fmb_'D_b_prod_set$'_3)
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_2,fmb_'D_b_prod_set$'_4)
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_3,'bot$l')
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_3,fmb_'D_b_prod_set$'_2)
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_3,fmb_'D_b_prod_set$'_3)
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_3,fmb_'D_b_prod_set$'_4)
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_4,'bot$l')
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_4,fmb_'D_b_prod_set$'_2)
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_4,fmb_'D_b_prod_set$'_3)
% 28.54/4.56 & ~'member$o'(fmb_'D_b_prod$'_4,fmb_'D_b_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_finite$',type,'finite$': 'C_d_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_finite$',axiom,
% 28.54/4.56 ~'finite$'('bot$h')
% 28.54/4.56 & ~'finite$'(fmb_'C_d_prod_set$'_2)
% 28.54/4.56 & ~'finite$'(fmb_'C_d_prod_set$'_3)
% 28.54/4.56 & ~'finite$'(fmb_'C_d_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$g',type,'member$g': 'B_c_prod$' * 'B_c_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$g',axiom,
% 28.54/4.56 ~'member$g'(fmb_'B_c_prod$'_1,'bot$j')
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_1,fmb_'B_c_prod_set$'_2)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_1,fmb_'B_c_prod_set$'_3)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_1,fmb_'B_c_prod_set$'_4)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_2,'bot$j')
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_2,fmb_'B_c_prod_set$'_2)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_2,fmb_'B_c_prod_set$'_3)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_2,fmb_'B_c_prod_set$'_4)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_3,'bot$j')
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_3,fmb_'B_c_prod_set$'_2)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_3,fmb_'B_c_prod_set$'_3)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_3,fmb_'B_c_prod_set$'_4)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_4,'bot$j')
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_4,fmb_'B_c_prod_set$'_2)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_4,fmb_'B_c_prod_set$'_3)
% 28.54/4.56 & ~'member$g'(fmb_'B_c_prod$'_4,fmb_'B_c_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$j',type,'member$j': 'A_c_prod$' * 'A_c_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$j',axiom,
% 28.54/4.56 ~'member$j'(fmb_'A_c_prod$'_1,'bot$e')
% 28.54/4.56 & ~'member$j'(fmb_'A_c_prod$'_1,fmb_'A_c_prod_set$'_2)
% 28.54/4.56 & ~'member$j'(fmb_'A_c_prod$'_1,fmb_'A_c_prod_set$'_3)
% 28.54/4.56 & ~'member$j'(fmb_'A_c_prod$'_1,fmb_'A_c_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_inj_on$',type,'inj_on$': 'C_c_option_fun$' * 'C_set$' > $o ).
% 28.54/4.56 tff('predicate_inj_on$',axiom,
% 28.54/4.56 % 'inj_on$'('some$a','bot$a') undefined in model
% 28.54/4.56 % 'inj_on$'('some$a',fmb_'C_set$'_2) undefined in model
% 28.54/4.56 % 'inj_on$'(fmb_'C_c_option_fun$'_2,'bot$a') undefined in model
% 28.54/4.56 % 'inj_on$'(fmb_'C_c_option_fun$'_2,fmb_'C_set$'_2) undefined in model
% 28.54/4.56 % 'inj_on$'(fmb_'C_c_option_fun$'_3,'bot$a') undefined in model
% 28.54/4.56 % 'inj_on$'(fmb_'C_c_option_fun$'_3,fmb_'C_set$'_2) undefined in model
% 28.54/4.56 % 'inj_on$'(fmb_'C_c_option_fun$'_4,'bot$a') undefined in model
% 28.54/4.56 % 'inj_on$'(fmb_'C_c_option_fun$'_4,fmb_'C_set$'_2) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_finite$a',type,'finite$a': 'C_set$' > $o ).
% 28.54/4.56 tff('predicate_finite$a',axiom,
% 28.54/4.56 ~'finite$a'('bot$a')
% 28.54/4.56 & ~'finite$a'(fmb_'C_set$'_2)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$i',type,'member$i': 'B_b_prod$' * 'B_b_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$i',axiom,
% 28.54/4.56 ~'member$i'(fmb_'B_b_prod$'_1,'bot$k')
% 28.54/4.56 & ~'member$i'(fmb_'B_b_prod$'_1,fmb_'B_b_prod_set$'_2)
% 28.54/4.56 & ~'member$i'(fmb_'B_b_prod$'_1,fmb_'B_b_prod_set$'_3)
% 28.54/4.56 & 'member$i'(fmb_'B_b_prod$'_1,fmb_'B_b_prod_set$'_4)
% 28.54/4.56 & 'member$i'(fmb_'B_b_prod$'_2,'bot$k')
% 28.54/4.56 & ~'member$i'(fmb_'B_b_prod$'_2,fmb_'B_b_prod_set$'_2)
% 28.54/4.56 & ~'member$i'(fmb_'B_b_prod$'_2,fmb_'B_b_prod_set$'_3)
% 28.54/4.56 & 'member$i'(fmb_'B_b_prod$'_2,fmb_'B_b_prod_set$'_4)
% 28.54/4.56 & ~'member$i'(fmb_'B_b_prod$'_3,'bot$k')
% 28.54/4.56 & ~'member$i'(fmb_'B_b_prod$'_3,fmb_'B_b_prod_set$'_2)
% 28.54/4.56 & 'member$i'(fmb_'B_b_prod$'_3,fmb_'B_b_prod_set$'_3)
% 28.54/4.56 & 'member$i'(fmb_'B_b_prod$'_3,fmb_'B_b_prod_set$'_4)
% 28.54/4.56 & ~'member$i'(fmb_'B_b_prod$'_4,'bot$k')
% 28.54/4.56 & ~'member$i'(fmb_'B_b_prod$'_4,fmb_'B_b_prod_set$'_2)
% 28.54/4.56 & ~'member$i'(fmb_'B_b_prod$'_4,fmb_'B_b_prod_set$'_3)
% 28.54/4.56 & ~'member$i'(fmb_'B_b_prod$'_4,fmb_'B_b_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$t',type,'fun_app$t': 'D_option_bool_fun$' * 'D_option$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$t',axiom,
% 28.54/4.56 'fun_app$t'('is_none$a','none$b')
% 28.54/4.56 & ~'fun_app$t'('is_none$a',fmb_'D_option$'_2)
% 28.54/4.56 & ~'fun_app$t'(fmb_'D_option_bool_fun$'_2,'none$b')
% 28.54/4.56 & ~'fun_app$t'(fmb_'D_option_bool_fun$'_2,fmb_'D_option$'_2)
% 28.54/4.56 & ~'fun_app$t'(fmb_'D_option_bool_fun$'_3,'none$b')
% 28.54/4.56 & ~'fun_app$t'(fmb_'D_option_bool_fun$'_3,fmb_'D_option$'_2)
% 28.54/4.56 & ~'fun_app$t'(fmb_'D_option_bool_fun$'_4,'none$b')
% 28.54/4.56 & ~'fun_app$t'(fmb_'D_option_bool_fun$'_4,fmb_'D_option$'_2)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_finite$e',type,'finite$e': 'A_c_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_finite$e',axiom,
% 28.54/4.56 ~'finite$e'('bot$e')
% 28.54/4.56 & ~'finite$e'(fmb_'A_c_prod_set$'_2)
% 28.54/4.56 & ~'finite$e'(fmb_'A_c_prod_set$'_3)
% 28.54/4.56 & ~'finite$e'(fmb_'A_c_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$r',type,'member$r': 'C_option$' * 'C_option_set$' > $o ).
% 28.54/4.56 tff('predicate_member$r',axiom,
% 28.54/4.56 ~'member$r'('none$a','bot$n')
% 28.54/4.56 & 'member$r'('none$a',fmb_'C_option_set$'_2)
% 28.54/4.56 & ~'member$r'('none$a',fmb_'C_option_set$'_3)
% 28.54/4.56 & ~'member$r'('none$a',fmb_'C_option_set$'_4)
% 28.54/4.56 & ~'member$r'(fmb_'C_option$'_2,'bot$n')
% 28.54/4.56 & ~'member$r'(fmb_'C_option$'_2,fmb_'C_option_set$'_2)
% 28.54/4.56 & 'member$r'(fmb_'C_option$'_2,fmb_'C_option_set$'_3)
% 28.54/4.56 & 'member$r'(fmb_'C_option$'_2,fmb_'C_option_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$q',type,'member$q': 'D_d_prod$' * 'D_d_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$q',axiom,
% 28.54/4.56 'member$q'(fmb_'D_d_prod$'_1,fmb_'D_d_prod_set$'_1)
% 28.54/4.56 & 'member$q'(fmb_'D_d_prod$'_1,fmb_'D_d_prod_set$'_2)
% 28.54/4.56 & 'member$q'(fmb_'D_d_prod$'_1,fmb_'D_d_prod_set$'_3)
% 28.54/4.56 & 'member$q'(fmb_'D_d_prod$'_1,fmb_'D_d_prod_set$'_4)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_2,fmb_'D_d_prod_set$'_1)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_2,fmb_'D_d_prod_set$'_2)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_2,fmb_'D_d_prod_set$'_3)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_2,fmb_'D_d_prod_set$'_4)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_3,fmb_'D_d_prod_set$'_1)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_3,fmb_'D_d_prod_set$'_2)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_3,fmb_'D_d_prod_set$'_3)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_3,fmb_'D_d_prod_set$'_4)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_4,fmb_'D_d_prod_set$'_1)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_4,fmb_'D_d_prod_set$'_2)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_4,fmb_'D_d_prod_set$'_3)
% 28.54/4.56 & ~'member$q'(fmb_'D_d_prod$'_4,fmb_'D_d_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_less_eq$d',type,'less_eq$d': 'A_b_prod_set$' * 'A_b_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_less_eq$d',axiom,
% 28.54/4.56 % 'less_eq$d'('bot$d','bot$d') undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$au',type,'fun_app$au': 'A_d_prod_bool_fun$' * 'A_d_prod$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$au',axiom,
% 28.54/4.56 'fun_app$au'(fmb_'A_d_prod_bool_fun$'_1,fmb_'A_d_prod$'_1)
% 28.54/4.56 % 'fun_app$au'(fmb_'A_d_prod_bool_fun$'_2,fmb_'A_d_prod$'_1) undefined in model
% 28.54/4.56 % 'fun_app$au'(fmb_'A_d_prod_bool_fun$'_3,fmb_'A_d_prod$'_1) undefined in model
% 28.54/4.56 % 'fun_app$au'(fmb_'A_d_prod_bool_fun$'_4,fmb_'A_d_prod$'_1) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$b',type,'fun_app$b': 'C_bool_fun$' * 'C$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$b',axiom,
% 28.54/4.56 ~'fun_app$b'('bot$q',fmb_'C$'_1)
% 28.54/4.56 & ~'fun_app$b'(fmb_'C_bool_fun$'_2,fmb_'C$'_1)
% 28.54/4.56 & 'fun_app$b'(fmb_'C_bool_fun$'_3,fmb_'C$'_1)
% 28.54/4.56 & ~'fun_app$b'(fmb_'C_bool_fun$'_4,fmb_'C$'_1)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_less_eq$',type,'less_eq$': 'A_c_prod_set$' * 'A_c_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_less_eq$',axiom,
% 28.54/4.56 % 'less_eq$'('bot$e','bot$e') undefined in model
% 28.54/4.56 % 'less_eq$'('bot$e',fmb_'A_c_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$'('bot$e',fmb_'A_c_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$'('bot$e',fmb_'A_c_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_2,'bot$e') undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_2,fmb_'A_c_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_2,fmb_'A_c_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_2,fmb_'A_c_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_3,'bot$e') undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_3,fmb_'A_c_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_3,fmb_'A_c_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_3,fmb_'A_c_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_4,'bot$e') undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_4,fmb_'A_c_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_4,fmb_'A_c_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$'(fmb_'A_c_prod_set$'_4,fmb_'A_c_prod_set$'_4) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_inj_on$b',type,'inj_on$b': 'B_b_option_fun$' * 'B_set$' > $o ).
% 28.54/4.56 tff('predicate_inj_on$b',axiom,
% 28.54/4.56 % 'inj_on$b'('some$c','bot$b') undefined in model
% 28.54/4.56 % 'inj_on$b'('some$c',fmb_'B_set$'_2) undefined in model
% 28.54/4.56 % 'inj_on$b'(fmb_'B_b_option_fun$'_2,'bot$b') undefined in model
% 28.54/4.56 % 'inj_on$b'(fmb_'B_b_option_fun$'_2,fmb_'B_set$'_2) undefined in model
% 28.54/4.56 % 'inj_on$b'(fmb_'B_b_option_fun$'_3,'bot$b') undefined in model
% 28.54/4.56 % 'inj_on$b'(fmb_'B_b_option_fun$'_3,fmb_'B_set$'_2) undefined in model
% 28.54/4.56 % 'inj_on$b'(fmb_'B_b_option_fun$'_4,'bot$b') undefined in model
% 28.54/4.56 % 'inj_on$b'(fmb_'B_b_option_fun$'_4,fmb_'B_set$'_2) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$',type,'member$': 'B_option$' * 'B_option_set$' > $o ).
% 28.54/4.56 tff('predicate_member$',axiom,
% 28.54/4.56 ~'member$'('none$c','bot$m')
% 28.54/4.56 & 'member$'('none$c',fmb_'B_option_set$'_2)
% 28.54/4.56 & ~'member$'('none$c',fmb_'B_option_set$'_3)
% 28.54/4.56 & ~'member$'('none$c',fmb_'B_option_set$'_4)
% 28.54/4.56 & ~'member$'(fmb_'B_option$'_2,'bot$m')
% 28.54/4.56 & ~'member$'(fmb_'B_option$'_2,fmb_'B_option_set$'_2)
% 28.54/4.56 & 'member$'(fmb_'B_option$'_2,fmb_'B_option_set$'_3)
% 28.54/4.56 & 'member$'(fmb_'B_option$'_2,fmb_'B_option_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$s',type,'fun_app$s': 'C_option_bool_fun$' * 'C_option$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$s',axiom,
% 28.54/4.56 'fun_app$s'('is_none$b','none$a')
% 28.54/4.56 & ~'fun_app$s'('is_none$b',fmb_'C_option$'_2)
% 28.54/4.56 & 'fun_app$s'(fmb_'C_option_bool_fun$'_2,'none$a')
% 28.54/4.56 & ~'fun_app$s'(fmb_'C_option_bool_fun$'_2,fmb_'C_option$'_2)
% 28.54/4.56 & 'fun_app$s'(fmb_'C_option_bool_fun$'_3,'none$a')
% 28.54/4.56 & ~'fun_app$s'(fmb_'C_option_bool_fun$'_3,fmb_'C_option$'_2)
% 28.54/4.56 & 'fun_app$s'(fmb_'C_option_bool_fun$'_4,'none$a')
% 28.54/4.56 & ~'fun_app$s'(fmb_'C_option_bool_fun$'_4,fmb_'C_option$'_2)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$at',type,'fun_app$at': 'C_b_prod_bool_fun$' * 'C_b_prod$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$at',axiom,
% 28.54/4.56 'fun_app$at'(fmb_'C_b_prod_bool_fun$'_1,fmb_'C_b_prod$'_1)
% 28.54/4.56 % 'fun_app$at'(fmb_'C_b_prod_bool_fun$'_2,fmb_'C_b_prod$'_1) undefined in model
% 28.54/4.56 % 'fun_app$at'(fmb_'C_b_prod_bool_fun$'_3,fmb_'C_b_prod$'_1) undefined in model
% 28.54/4.56 % 'fun_app$at'(fmb_'C_b_prod_bool_fun$'_4,fmb_'C_b_prod$'_1) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$',type,'fun_app$': 'B_option_bool_fun$' * 'B_option$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$',axiom,
% 28.54/4.56 'fun_app$'('is_none$','none$c')
% 28.54/4.56 & ~'fun_app$'('is_none$',fmb_'B_option$'_2)
% 28.54/4.56 & ~'fun_app$'('bot$o','none$c')
% 28.54/4.56 & ~'fun_app$'('bot$o',fmb_'B_option$'_2)
% 28.54/4.56 & ~'fun_app$'(fmb_'B_option_bool_fun$'_3,'none$c')
% 28.54/4.56 & 'fun_app$'(fmb_'B_option_bool_fun$'_3,fmb_'B_option$'_2)
% 28.54/4.56 & ~'fun_app$'(fmb_'B_option_bool_fun$'_4,'none$c')
% 28.54/4.56 & 'fun_app$'(fmb_'B_option_bool_fun$'_4,fmb_'B_option$'_2)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_finite$c',type,'finite$c': 'A_d_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_finite$c',axiom,
% 28.54/4.56 ~'finite$c'('bot$g')
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$e',type,'member$e': 'C_a_prod$' * 'C_a_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$e',axiom,
% 28.54/4.56 'member$e'(fmb_'C_a_prod$'_1,fmb_'C_a_prod_set$'_1)
% 28.54/4.56 & 'member$e'(fmb_'C_a_prod$'_1,fmb_'C_a_prod_set$'_2)
% 28.54/4.56 & 'member$e'(fmb_'C_a_prod$'_1,fmb_'C_a_prod_set$'_3)
% 28.54/4.56 & 'member$e'(fmb_'C_a_prod$'_1,fmb_'C_a_prod_set$'_4)
% 28.54/4.56 & ~'member$e'(fmb_'C_a_prod$'_2,fmb_'C_a_prod_set$'_1)
% 28.54/4.56 & ~'member$e'(fmb_'C_a_prod$'_2,fmb_'C_a_prod_set$'_2)
% 28.54/4.56 & ~'member$e'(fmb_'C_a_prod$'_2,fmb_'C_a_prod_set$'_3)
% 28.54/4.56 & ~'member$e'(fmb_'C_a_prod$'_2,fmb_'C_a_prod_set$'_4)
% 28.54/4.56 & ~'member$e'(fmb_'C_a_prod$'_3,fmb_'C_a_prod_set$'_1)
% 28.54/4.56 & ~'member$e'(fmb_'C_a_prod$'_3,fmb_'C_a_prod_set$'_2)
% 28.54/4.56 & 'member$e'(fmb_'C_a_prod$'_3,fmb_'C_a_prod_set$'_3)
% 28.54/4.56 & 'member$e'(fmb_'C_a_prod$'_3,fmb_'C_a_prod_set$'_4)
% 28.54/4.56 & ~'member$e'(fmb_'C_a_prod$'_4,fmb_'C_a_prod_set$'_1)
% 28.54/4.56 & ~'member$e'(fmb_'C_a_prod$'_4,fmb_'C_a_prod_set$'_2)
% 28.54/4.56 & ~'member$e'(fmb_'C_a_prod$'_4,fmb_'C_a_prod_set$'_3)
% 28.54/4.56 & ~'member$e'(fmb_'C_a_prod$'_4,fmb_'C_a_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_finite$d',type,'finite$d': 'A_set$' > $o ).
% 28.54/4.56 tff('predicate_finite$d',axiom,
% 28.54/4.56 ~'finite$d'('bot$c')
% 28.54/4.56 & ~'finite$d'(fmb_'A_set$'_2)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$av',type,'fun_app$av': 'A_c_prod_bool_fun$' * 'A_c_prod$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$av',axiom,
% 28.54/4.56 ~'fun_app$av'(fmb_'A_c_prod_bool_fun$'_1,fmb_'A_c_prod$'_1)
% 28.54/4.56 % 'fun_app$av'(fmb_'A_c_prod_bool_fun$'_2,fmb_'A_c_prod$'_1) undefined in model
% 28.54/4.56 % 'fun_app$av'(fmb_'A_c_prod_bool_fun$'_3,fmb_'A_c_prod$'_1) undefined in model
% 28.54/4.56 % 'fun_app$av'(fmb_'A_c_prod_bool_fun$'_4,fmb_'A_c_prod$'_1) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$c',type,'fun_app$c': 'B_bool_fun$' * 'B$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$c',axiom,
% 28.54/4.56 ~'fun_app$c'('bot$r',fmb_'B$'_1)
% 28.54/4.56 & 'fun_app$c'(fmb_'B_bool_fun$'_2,fmb_'B$'_1)
% 28.54/4.56 & ~'fun_app$c'(fmb_'B_bool_fun$'_3,fmb_'B$'_1)
% 28.54/4.56 & ~'fun_app$c'(fmb_'B_bool_fun$'_4,fmb_'B$'_1)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$as',type,'fun_app$as': 'C_d_prod_bool_fun$' * 'C_d_prod$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$as',axiom,
% 28.54/4.56 ~'fun_app$as'(fmb_'C_d_prod_bool_fun$'_1,fmb_'C_d_prod$'_1)
% 28.54/4.56 % 'fun_app$as'(fmb_'C_d_prod_bool_fun$'_2,fmb_'C_d_prod$'_1) undefined in model
% 28.54/4.56 % 'fun_app$as'(fmb_'C_d_prod_bool_fun$'_3,fmb_'C_d_prod$'_1) undefined in model
% 28.54/4.56 % 'fun_app$as'(fmb_'C_d_prod_bool_fun$'_4,fmb_'C_d_prod$'_1) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_less_eq$c',type,'less_eq$c': 'D_b_prod_set$' * 'D_b_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_less_eq$c',axiom,
% 28.54/4.56 % 'less_eq$c'('bot$l','bot$l') undefined in model
% 28.54/4.56 % 'less_eq$c'('bot$l',fmb_'D_b_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$c'('bot$l',fmb_'D_b_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$c'('bot$l',fmb_'D_b_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_2,'bot$l') undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_2,fmb_'D_b_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_2,fmb_'D_b_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_2,fmb_'D_b_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_3,'bot$l') undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_3,fmb_'D_b_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_3,fmb_'D_b_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_3,fmb_'D_b_prod_set$'_4) undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_4,'bot$l') undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_4,fmb_'D_b_prod_set$'_2) undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_4,fmb_'D_b_prod_set$'_3) undefined in model
% 28.54/4.56 % 'less_eq$c'(fmb_'D_b_prod_set$'_4,fmb_'D_b_prod_set$'_4) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$h',type,'member$h': 'B_d_prod$' * 'B_d_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$h',axiom,
% 28.54/4.56 'member$h'(fmb_'B_d_prod$'_1,fmb_'B_d_prod_set$'_1)
% 28.54/4.56 & ~'member$h'(fmb_'B_d_prod$'_1,fmb_'B_d_prod_set$'_2)
% 28.54/4.56 & 'member$h'(fmb_'B_d_prod$'_1,fmb_'B_d_prod_set$'_3)
% 28.54/4.56 & 'member$h'(fmb_'B_d_prod$'_1,fmb_'B_d_prod_set$'_4)
% 28.54/4.56 & 'member$h'(fmb_'B_d_prod$'_2,fmb_'B_d_prod_set$'_1)
% 28.54/4.56 & ~'member$h'(fmb_'B_d_prod$'_2,fmb_'B_d_prod_set$'_2)
% 28.54/4.56 & 'member$h'(fmb_'B_d_prod$'_2,fmb_'B_d_prod_set$'_3)
% 28.54/4.56 & 'member$h'(fmb_'B_d_prod$'_2,fmb_'B_d_prod_set$'_4)
% 28.54/4.56 & ~'member$h'(fmb_'B_d_prod$'_3,fmb_'B_d_prod_set$'_1)
% 28.54/4.56 & ~'member$h'(fmb_'B_d_prod$'_3,fmb_'B_d_prod_set$'_2)
% 28.54/4.56 & ~'member$h'(fmb_'B_d_prod$'_3,fmb_'B_d_prod_set$'_3)
% 28.54/4.56 & ~'member$h'(fmb_'B_d_prod$'_3,fmb_'B_d_prod_set$'_4)
% 28.54/4.56 & ~'member$h'(fmb_'B_d_prod$'_4,fmb_'B_d_prod_set$'_1)
% 28.54/4.56 & ~'member$h'(fmb_'B_d_prod$'_4,fmb_'B_d_prod_set$'_2)
% 28.54/4.56 & ~'member$h'(fmb_'B_d_prod$'_4,fmb_'B_d_prod_set$'_3)
% 28.54/4.56 & ~'member$h'(fmb_'B_d_prod$'_4,fmb_'B_d_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$p',type,'member$p': 'C_c_prod$' * 'C_c_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$p',axiom,
% 28.54/4.56 'member$p'(fmb_'C_c_prod$'_1,fmb_'C_c_prod_set$'_1)
% 28.54/4.56 & 'member$p'(fmb_'C_c_prod$'_1,fmb_'C_c_prod_set$'_2)
% 28.54/4.56 & 'member$p'(fmb_'C_c_prod$'_1,fmb_'C_c_prod_set$'_3)
% 28.54/4.56 & 'member$p'(fmb_'C_c_prod$'_1,fmb_'C_c_prod_set$'_4)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_2,fmb_'C_c_prod_set$'_1)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_2,fmb_'C_c_prod_set$'_2)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_2,fmb_'C_c_prod_set$'_3)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_2,fmb_'C_c_prod_set$'_4)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_3,fmb_'C_c_prod_set$'_1)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_3,fmb_'C_c_prod_set$'_2)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_3,fmb_'C_c_prod_set$'_3)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_3,fmb_'C_c_prod_set$'_4)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_4,fmb_'C_c_prod_set$'_1)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_4,fmb_'C_c_prod_set$'_2)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_4,fmb_'C_c_prod_set$'_3)
% 28.54/4.56 & ~'member$p'(fmb_'C_c_prod$'_4,fmb_'C_c_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_finite$b',type,'finite$b': 'C_b_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_finite$b',axiom,
% 28.54/4.56 ~'finite$b'('bot$i')
% 28.54/4.56 & ~'finite$b'(fmb_'C_b_prod_set$'_2)
% 28.54/4.56 & ~'finite$b'(fmb_'C_b_prod_set$'_3)
% 28.54/4.56 & ~'finite$b'(fmb_'C_b_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$a',type,'fun_app$a': 'D_bool_fun$' * 'D$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$a',axiom,
% 28.54/4.56 ~'fun_app$a'('bot$p',fmb_'D$'_1)
% 28.54/4.56 & 'fun_app$a'(fmb_'D_bool_fun$'_2,fmb_'D$'_1)
% 28.54/4.56 & ~'fun_app$a'(fmb_'D_bool_fun$'_3,fmb_'D$'_1)
% 28.54/4.56 & 'fun_app$a'(fmb_'D_bool_fun$'_4,fmb_'D$'_1)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_less_eq$b',type,'less_eq$b': 'A_d_prod_set$' * 'A_d_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_less_eq$b',axiom,
% 28.54/4.56 % 'less_eq$b'('bot$g','bot$g') undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$aw',type,'fun_app$aw': 'A_b_prod_bool_fun$' * 'A_b_prod$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$aw',axiom,
% 28.54/4.56 ~'fun_app$aw'(fmb_'A_b_prod_bool_fun$'_1,fmb_'A_b_prod$'_1)
% 28.54/4.56 % 'fun_app$aw'(fmb_'A_b_prod_bool_fun$'_2,fmb_'A_b_prod$'_1) undefined in model
% 28.54/4.56 % 'fun_app$aw'(fmb_'A_b_prod_bool_fun$'_3,fmb_'A_b_prod$'_1) undefined in model
% 28.54/4.56 % 'fun_app$aw'(fmb_'A_b_prod_bool_fun$'_4,fmb_'A_b_prod$'_1) undefined in model
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$k',type,'member$k': 'C_d_prod$' * 'C_d_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$k',axiom,
% 28.54/4.56 ~'member$k'(fmb_'C_d_prod$'_1,'bot$h')
% 28.54/4.56 & ~'member$k'(fmb_'C_d_prod$'_1,fmb_'C_d_prod_set$'_2)
% 28.54/4.56 & ~'member$k'(fmb_'C_d_prod$'_1,fmb_'C_d_prod_set$'_3)
% 28.54/4.56 & ~'member$k'(fmb_'C_d_prod$'_1,fmb_'C_d_prod_set$'_4)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_finite$f',type,'finite$f': 'A_b_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_finite$f',axiom,
% 28.54/4.56 ~'finite$f'('bot$d')
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$l',type,'member$l': 'A_d_prod$' * 'A_d_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$l',axiom,
% 28.54/4.56 ~'member$l'(fmb_'A_d_prod$'_1,'bot$g')
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$a',type,'member$a': 'D$' * 'D_set$' > $o ).
% 28.54/4.56 tff('predicate_member$a',axiom,
% 28.54/4.56 ~'member$a'(fmb_'D$'_1,'bot$')
% 28.54/4.56 & 'member$a'(fmb_'D$'_1,fmb_'D_set$'_2)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_fun_app$d',type,'fun_app$d': 'A_bool_fun$' * 'A$' > $o ).
% 28.54/4.56 tff('predicate_fun_app$d',axiom,
% 28.54/4.56 ~'fun_app$d'('bot$s',fmb_'A$'_1)
% 28.54/4.56 & 'fun_app$d'(fmb_'A_bool_fun$'_2,fmb_'A$'_1)
% 28.54/4.56 & ~'fun_app$d'(fmb_'A_bool_fun$'_3,fmb_'A$'_1)
% 28.54/4.56 & ~'fun_app$d'(fmb_'A_bool_fun$'_4,fmb_'A$'_1)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$s',type,'member$s': 'D_option$' * 'D_option_set$' > $o ).
% 28.54/4.56 tff('predicate_member$s',axiom,
% 28.54/4.56 ~'member$s'('none$b','bot$t')
% 28.54/4.56 & ~'member$s'('none$b',fmb_'D_option_set$'_2)
% 28.54/4.56 & ~'member$s'(fmb_'D_option$'_2,'bot$t')
% 28.54/4.56 & 'member$s'(fmb_'D_option$'_2,fmb_'D_option_set$'_2)
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 tff('declare_member$n',type,'member$n': 'A_b_prod$' * 'A_b_prod_set$' > $o ).
% 28.54/4.56 tff('predicate_member$n',axiom,
% 28.54/4.56 ~'member$n'(fmb_'A_b_prod$'_1,'bot$d')
% 28.54/4.56
% 28.54/4.56 ).
% 28.54/4.56
% 28.54/4.56 % SZS output end FiniteModel for theBenchmark
% 28.54/4.56 % (18157)------------------------------
% 28.54/4.56 % (18157)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 28.54/4.56 % (18157)Termination reason: Satisfiable
% 28.54/4.56
% 28.54/4.56 % (18157)Memory used [KB]: 26652
% 28.54/4.56 % (18157)Time elapsed: 4.106 s
% 28.54/4.56 % (18157)Instructions burned: 7531 (million)
% 28.54/4.56 % (18153)Success in time 4.155 s
%------------------------------------------------------------------------------