include('Axioms/SET010^0.ax').
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(u1_struct_0_type, type, u1_struct_0: $i > $i).
thf(k14_algstr_4_type, type, k14_algstr_4: $i > $i).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(k4_tarski_type, type, k4_tarski: $i > $i > $i).
thf(k1_xtuple_0_type, type, k1_xtuple_0: $i > $i).
thf(k2_xtuple_0_type, type, k2_xtuple_0: $i > $i).
thf(r1_xxreal_0_type, type, r1_xxreal_0: $i > $i > $o).
thf(n1_type, type, 1: $i).
thf(k15_algstr_4_type, type, k15_algstr_4: $i > $i > $i).
thf(v1_xtuple_0_type, type, v1_xtuple_0: $i > $o).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o).
thf(k12_algstr_4_type, type, k12_algstr_4: $i > $i).
thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i).
thf(k11_algstr_4_type, type, k11_algstr_4: $i > $i > $i).
thf(k1_tarski_type, type, k1_tarski: $i > $i).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(k1_nat_1_type, type, k1_nat_1: $i > $i > $i).
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(n0_type, type, 0: $i).
thf(k2_xcmplx_0_type, type, k2_xcmplx_0: $i > $i > $i).
thf(k9_setfam_1_type, type, k9_setfam_1: $i > $i).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v1_funct_2_type, type, v1_funct_2: $i > $i > $i > $o).
thf(g3_algstr_0_type, type, g3_algstr_0: $i > $i > $i).
thf(v15_algstr_0_type, type, v15_algstr_0: $i > $o).
thf(l3_algstr_0_type, type, l3_algstr_0: $i > $o).
thf(u2_algstr_0_type, type, u2_algstr_0: $i > $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k13_algstr_4_type, type, k13_algstr_4: $i > $i).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(t8_mcart_1, axiom,   (! [A: $i] :  ( (v1_xtuple_0 @ A)  =>  ( (= @  ( (k4_tarski @  (k1_xtuple_0 @ A) )  @  (k2_xtuple_0 @ A) ) )  @ A) ) ) , file(mcart_1, t8_mcart_1)).
thf(t6_real, axiom,   (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v1_xboole_0 @ A)  |  ( (v2_xxreal_0 @ B)  |  (v3_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t6_real)).
thf(t25_algstr_4, axiom,   (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k12_algstr_4 @ A) )  =>  ( (r2_hidden @ B)  @  ( (k2_zfmisc_1 @  ( (k11_algstr_4 @ A)  @  (k2_xtuple_0 @ B) ) )  @  (k1_tarski @  (k2_xtuple_0 @ B) ) ) ) ) ) ) ) , file(algstr_4, t25_algstr_4)).
thf(t13_nat_1, axiom,   (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( ~ ( ( (r1_xxreal_0 @  ( (k1_nat_1 @ B)  @ 1) )  @ A) )  <=>  ( (r1_xxreal_0 @ A)  @ B) ) ) ) ) ) , file(nat_1, t13_nat_1)).
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(spc0_numerals, axiom,   ( ( ( (m2_subset_1 @ 0)  @ k1_numbers)  @ k5_numbers)  &  ( ( (m1_subset_1 @ 0)  @ k5_numbers)  &  ( (m1_subset_1 @ 0)  @ k1_numbers) ) ) , file(numerals, spc0_numerals)).
thf(spc0_boole, axiom,   (v1_xboole_0 @ 0) , file(boole, spc0_boole)).
thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom,   ( (= @  ( (k2_xcmplx_0 @ 0)  @ 1) )  @ 1) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1)).
thf(redefinition_k9_setfam_1, axiom,   (! [A: $i] :  ( (= @  (k9_setfam_1 @ A) )  @  (k1_zfmisc_1 @ A) ) ) , file(setfam_1, k9_setfam_1)).
thf(redefinition_k5_numbers, axiom,   ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k1_nat_1, axiom,   (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k5_numbers) )  =>  ( (= @  ( (k1_nat_1 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, k1_nat_1)).
thf(free_g3_algstr_0, axiom,   (! [A: $i, B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  =>  (! [C: $i, D: $i] :  ( ( (= @  ( (g3_algstr_0 @ A)  @ B) )  @  ( (g3_algstr_0 @ C)  @ D) )  =>  ( ( (= @ A)  @ C)  &  ( (= @ B)  @ D) ) ) ) ) ) , file(algstr_0, g3_algstr_0)).
thf(fc1_xtuple_0, axiom,   (! [A: $i, B: $i] :  (v1_xtuple_0 @  ( (k4_tarski @ A)  @ B) ) ) , file(xtuple_0, fc1_xtuple_0)).
thf(fc17_algstr_4, axiom,   (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k14_algstr_4 @ A) ) ) )  =>  ( ~ ( (v1_xboole_0 @  (k2_xtuple_0 @ B) ) )  &  (v7_ordinal1 @  (k2_xtuple_0 @ B) ) ) ) ) , file(algstr_4, fc17_algstr_4)).
thf(fc14_algstr_4, axiom,   (! [A: $i] :  (v15_algstr_0 @  (k14_algstr_4 @ A) ) ) , file(algstr_4, fc14_algstr_4)).
thf(dt_u2_algstr_0, axiom,   (! [A: $i] :  ( (l3_algstr_0 @ A)  =>  ( (v1_funct_1 @  (u2_algstr_0 @ A) )  &  ( ( ( (v1_funct_2 @  (u2_algstr_0 @ A) )  @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @  (u2_algstr_0 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(algstr_0, u2_algstr_0)).
thf(dt_k14_algstr_4, axiom,   (! [A: $i] :  (l3_algstr_0 @  (k14_algstr_4 @ A) ) ) , file(algstr_4, k14_algstr_4)).
thf(d2_zfmisc_1, axiom,   (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (= @ C)  @  ( (k2_zfmisc_1 @ A)  @ B) )  <=>  (! [D: $i] :  ( ( (r2_hidden @ D)  @ C)  <=>  (? [E: $i] :  (? [F: $i] :  ( ( (r2_hidden @ E)  @ A)  &  ( ( (r2_hidden @ F)  @ B)  &  ( (= @ D)  @  ( (k4_tarski @ E)  @ F) ) ) ) ) ) ) ) ) ) ) ) , file(zfmisc_1, d2_zfmisc_1)).
thf(d18_algstr_4, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k14_algstr_4 @ A) ) )  =>  ( ( ~ ( (v1_xboole_0 @ A) )  =>  ( (= @  ( (k15_algstr_4 @ A)  @ B) )  @  (k2_xtuple_0 @ B) ) )  &  ( (v1_xboole_0 @ A)  =>  ( (= @  ( (k15_algstr_4 @ A)  @ B) )  @ k6_numbers) ) ) ) ) ) , file(algstr_4, d18_algstr_4)).
thf(d17_algstr_4, axiom,   (! [A: $i] :  ( (= @  (k14_algstr_4 @ A) )  @  ( (g3_algstr_0 @  (k12_algstr_4 @ A) )  @  (k13_algstr_4 @ A) ) ) ) , file(algstr_4, d17_algstr_4)).
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(cc3_xxreal_0, axiom,   (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc3_xxreal_0)).
thf(cc3_nat_1, axiom,   (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v7_ordinal1 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc3_nat_1)).
thf(cc2_xreal_0, axiom,   (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc2_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(abstractness_v15_algstr_0, axiom,   (! [A: $i] :  ( (l3_algstr_0 @ A)  =>  ( (v15_algstr_0 @ A)  =>  ( (= @ A)  @  ( (g3_algstr_0 @  (u1_struct_0 @ A) )  @  (u2_algstr_0 @ A) ) ) ) ) ) , file(algstr_0, v15_algstr_0)).
thf(t32_algstr_4, conjecture,   (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k14_algstr_4 @ A) ) )  =>  ( ~ ( (v1_xboole_0 @ A) )  =>  ( ( (= @ B)  @  ( (k4_tarski @  (k1_xtuple_0 @ B) )  @  (k2_xtuple_0 @ B) ) )  &  ( (r1_xxreal_0 @ 1)  @  ( (k15_algstr_4 @ A)  @ B) ) ) ) ) ) ) , file(algstr_4, t32_algstr_4)).