include('Axioms/SET010^0.ax').
thf(v2_struct_0_type, type, v2_struct_0: $i > $o).
thf(l1_graph_1_type, type, l1_graph_1: $i > $o).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(u1_struct_0_type, type, u1_struct_0: $i > $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(u1_graph_1_type, type, u1_graph_1: $i > $i).
thf(u2_graph_1_type, type, u2_graph_1: $i > $i).
thf(r1_graph_2_type, type, r1_graph_2: $i > $i > $i > $o).
thf(k2_finseq_4_type, type, k2_finseq_4: $i > $i > $i > $i).
thf(k9_finseq_1_type, type, k9_finseq_1: $i > $i).
thf(v1_relat_1_type, type, v1_relat_1: $i > $o).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v1_finseq_1_type, type, v1_finseq_1: $i > $o).
thf(k10_finseq_1_type, type, k10_finseq_1: $i > $i > $i).
thf(k3_finseq_1_type, type, k3_finseq_1: $i > $i).
thf(n2_type, type, 2: $i).
thf(n1_type, type, 1: $i).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(r1_xxreal_0_type, type, r1_xxreal_0: $i > $i > $o).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(k7_partfun1_type, type, k7_partfun1: $i > $i > $i > $i).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(m2_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k2_xcmplx_0_type, type, k2_xcmplx_0: $i > $i > $i).
thf(k5_finseq_1_type, type, k5_finseq_1: $i > $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(k2_nat_1_type, type, k2_nat_1: $i > $i > $i).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(l1_struct_0_type, type, l1_struct_0: $i > $o).
thf(v3_xxreal_2_type, type, v3_xxreal_2: $i > $o).
thf(v4_xxreal_2_type, type, v4_xxreal_2: $i > $o).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(l5_struct_0_type, type, l5_struct_0: $i > $o).
thf(m2_finseq_1_type, type, m2_finseq_1: $i > $i > $o).
thf(r2_graph_1_type, type, r2_graph_1: $i > $i > $i > $i > $o).
thf(v6_membered_type, type, v6_membered: $i > $o).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(t44_finseq_1, axiom,   (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  (v1_finseq_1 @ C) ) )  =>  ( ( (= @ C)  @  ( (k10_finseq_1 @ A)  @ B) )  <=>  ( ( (= @  (k3_finseq_1 @ C) )  @ 2)  &  ( ( (= @  ( (k1_funct_1 @ C)  @ 1) )  @ A)  &  ( (= @  ( (k1_funct_1 @ C)  @ 2) )  @ B) ) ) ) ) ) ) ) , file(finseq_1, t44_finseq_1)).
thf(t40_finseq_1, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  ( ( (= @ B)  @  (k9_finseq_1 @ A) )  <=>  ( ( (= @  (k3_finseq_1 @ B) )  @ 1)  &  ( (= @  ( (k1_funct_1 @ B)  @ 1) )  @ A) ) ) ) ) ) , file(finseq_1, t40_finseq_1)).
thf(t1_xxreal_0, axiom,   (! [A: $i] :  ( (v1_xxreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xxreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( (r1_xxreal_0 @ B)  @ A) )  =>  ( (= @ A)  @ B) ) ) ) ) ) , file(xxreal_0, t1_xxreal_0)).
thf(t17_finseq_4, axiom,   (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ A)  =>  ( ( (= @  ( ( (k7_partfun1 @ A)  @  ( ( (k2_finseq_4 @ A)  @ B)  @ C) )  @ 1) )  @ B)  &  ( (= @  ( ( (k7_partfun1 @ A)  @  ( ( (k2_finseq_4 @ A)  @ B)  @ C) )  @ 2) )  @ C) ) ) ) ) ) ) ) , file(finseq_4, t17_finseq_4)).
thf(spc1_numerals, axiom,   ( ( (v2_xxreal_0 @ 1)  &  ( ( (m2_subset_1 @ 1)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ 1)  @ k5_numbers)  &  ( (m1_subset_1 @ 1)  @ k1_numbers) ) ) , file(numerals, spc1_numerals)).
thf(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom,   ( (= @  ( (k2_xcmplx_0 @ 1)  @ 1) )  @ 2) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r1_r2)).
thf(redefinition_k9_finseq_1, axiom,   (! [A: $i] :  ( (= @  (k9_finseq_1 @ A) )  @  (k5_finseq_1 @ A) ) ) , file(finseq_1, k9_finseq_1)).
thf(redefinition_k5_numbers, axiom,   ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k2_nat_1, axiom,   (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  (v7_ordinal1 @ B) )  =>  ( (= @  ( (k2_nat_1 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, k2_nat_1)).
thf(redefinition_k2_finseq_4, axiom,   (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( (= @  ( ( (k2_finseq_4 @ A)  @ B)  @ C) )  @  ( (k10_finseq_1 @ B)  @ C) ) ) ) , file(finseq_4, k2_finseq_4)).
thf(fc8_finseq_1, axiom,   (! [A: $i, B: $i] :  ( (v1_relat_1 @  ( (k10_finseq_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k10_finseq_1 @ A)  @ B) ) ) ) , file(finseq_1, fc8_finseq_1)).
thf(fc7_finseq_1, axiom,   (! [A: $i] :  (v1_finseq_1 @  (k5_finseq_1 @ A) ) ) , file(finseq_1, fc7_finseq_1)).
thf(fc6_ordinal1, axiom,   ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc6_finseq_1, axiom,   (! [A: $i] :  ( (v1_relat_1 @  (k5_finseq_1 @ A) )  &  (v1_funct_1 @  (k5_finseq_1 @ A) ) ) ) , file(finseq_1, fc6_finseq_1)).
thf(fc2_struct_0, axiom,   (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_xboole_0 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc2_struct_0)).
thf(fc11_xxreal_2, axiom,   ( ~ ( (v3_xxreal_2 @ k1_numbers) )  &  ~ ( (v4_xxreal_2 @ k1_numbers) ) ) , file(xxreal_2, fc11_xxreal_2)).
thf(fc10_finseq_1, axiom,   (! [A: $i, B: $i] :  (v1_finseq_1 @  ( (k10_finseq_1 @ A)  @ B) ) ) , file(finseq_1, fc10_finseq_1)).
thf(dt_m2_subset_1, axiom,   (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ A)  @ B)  =>  ( (m1_subset_1 @ C)  @ A) ) ) ) ) , file(subset_1, m2_subset_1)).
thf(dt_l5_struct_0, axiom,   (! [A: $i] :  ( (l5_struct_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(struct_0, l5_struct_0)).
thf(dt_l1_graph_1, axiom,   (! [A: $i] :  ( (l1_graph_1 @ A)  =>  (l5_struct_0 @ A) ) ) , file(graph_1, l1_graph_1)).
thf(dt_k5_numbers, axiom,   ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(dt_k2_finseq_4, axiom,   (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( (m2_finseq_1 @  ( ( (k2_finseq_4 @ A)  @ B)  @ C) )  @ A) ) ) , file(finseq_4, k2_finseq_4)).
thf(d6_graph_2, axiom,   (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_graph_1 @ A) )  =>  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  (v1_finseq_1 @ C) ) )  =>  ( ( ( (r1_graph_2 @ A)  @ B)  @ C)  <=>  ( ( (= @  (k3_finseq_1 @ B) )  @  ( (k2_nat_1 @  (k3_finseq_1 @ C) )  @ 1) )  &  (! [D: $i] :  ( ( ( (m2_subset_1 @ D)  @ k1_numbers)  @ k5_numbers)  =>  ( ( ( (r1_xxreal_0 @ 1)  @ D)  &  ( (r1_xxreal_0 @ D)  @  (k3_finseq_1 @ C) ) )  =>  ( ( ( (r2_graph_1 @ A)  @  ( ( (k7_partfun1 @  (u1_struct_0 @ A) )  @ B)  @ D) )  @  ( ( (k7_partfun1 @  (u1_struct_0 @ A) )  @ B)  @  ( (k2_nat_1 @ D)  @ 1) ) )  @  ( (k1_funct_1 @ C)  @ D) ) ) ) ) ) ) ) ) ) ) ) ) , file(graph_2, d6_graph_2)).
thf(d12_graph_1, axiom,   (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_graph_1 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  (! [D: $i] :  ( ( ( ( (r2_graph_1 @ A)  @ B)  @ C)  @ D)  <=>  ( ( ( (= @  ( (k1_funct_1 @  (u1_graph_1 @ A) )  @ D) )  @ B)  &  ( (= @  ( (k1_funct_1 @  (u2_graph_1 @ A) )  @ D) )  @ C) )  |  ( ( (= @  ( (k1_funct_1 @  (u1_graph_1 @ A) )  @ D) )  @ C)  &  ( (= @  ( (k1_funct_1 @  (u2_graph_1 @ A) )  @ D) )  @ B) ) ) ) ) ) ) ) ) ) ) , file(graph_1, d12_graph_1)).
thf(cc9_xxreal_2, axiom,   (! [A: $i] :  ( (v6_membered @ A)  =>  ( (v6_membered @ A)  &  (v3_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc9_xxreal_2)).
thf(cc8_ordinal1, axiom,   (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(cc4_xreal_0, axiom,   (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)).
thf(cc1_xreal_0, axiom,   (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0)).
thf(cc18_membered, axiom,   (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_membered @ A) ) ) , file(membered, cc18_membered)).
thf(t11_graph_3, conjecture,   (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_graph_1 @ A) )  =>  (! [B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) )  =>  ( ( ( (= @ C)  @  ( (k1_funct_1 @  (u1_graph_1 @ A) )  @ B) )  &  ( (= @ D)  @  ( (k1_funct_1 @  (u2_graph_1 @ A) )  @ B) ) )  =>  ( ( (r1_graph_2 @ A)  @  ( ( (k2_finseq_4 @  (u1_struct_0 @ A) )  @ D)  @ C) )  @  (k9_finseq_1 @ B) ) ) ) ) ) ) ) ) ) , file(graph_3, t11_graph_3)).