include('Axioms/SET010^0.ax').
thf(v1_modelc_2_type, type, v1_modelc_2: $i > $o).
thf(m2_finseq_1_type, type, m2_finseq_1: $i > $i > $o).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(r1_modelc_2_type, type, r1_modelc_2: $i > $i > $o).
thf(k3_modelc_2_type, type, k3_modelc_2: $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(k7_finseq_1_type, type, k7_finseq_1: $i > $i > $i).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(n1_type, type, 1: $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k4_modelc_2_type, type, k4_modelc_2: $i > $i > $i).
thf(k5_modelc_2_type, type, k5_modelc_2: $i > $i > $i).
thf(n2_type, type, 2: $i).
thf(k6_modelc_2_type, type, k6_modelc_2: $i > $i).
thf(n3_type, type, 3: $i).
thf(k7_modelc_2_type, type, k7_modelc_2: $i > $i > $i).
thf(n4_type, type, 4: $i).
thf(k8_modelc_2_type, type, k8_modelc_2: $i > $i > $i).
thf(n5_type, type, 5: $i).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(m1_finseq_1_type, type, m1_finseq_1: $i > $i > $o).
thf(k8_finseq_1_type, type, k8_finseq_1: $i > $i > $i > $i).
thf(k12_finseq_1_type, type, k12_finseq_1: $i > $i > $i).
thf(k5_finseq_1_type, type, k5_finseq_1: $i > $i).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(t33_finseq_1, axiom,   (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  (v1_finseq_1 @ C) ) )  =>  ( ( ( (= @  ( (k7_finseq_1 @ A)  @ B) )  @  ( (k7_finseq_1 @ C)  @ B) )  |  ( (= @  ( (k7_finseq_1 @ B)  @ A) )  @  ( (k7_finseq_1 @ B)  @ C) ) )  =>  ( (= @ A)  @ C) ) ) ) ) ) ) ) , file(finseq_1, t33_finseq_1)).
thf(t1_numerals, axiom,   ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
thf(t12_modelc_2, axiom,   (! [A: $i] :  ( ( (v1_modelc_2 @ A)  &  ( (m2_finseq_1 @ A)  @ k5_numbers) )  =>  (! [B: $i] :  ( ( (v1_modelc_2 @ B)  &  ( (m2_finseq_1 @ B)  @ k5_numbers) )  =>  ( ( (= @  ( (k1_funct_1 @  (k3_modelc_2 @ A) )  @ 1) )  @ k6_numbers)  &  ( ( (= @  ( (k1_funct_1 @  ( (k4_modelc_2 @ A)  @ B) )  @ 1) )  @ 1)  &  ( ( (= @  ( (k1_funct_1 @  ( (k5_modelc_2 @ A)  @ B) )  @ 1) )  @ 2)  &  ( ( (= @  ( (k1_funct_1 @  (k6_modelc_2 @ A) )  @ 1) )  @ 3)  &  ( ( (= @  ( (k1_funct_1 @  ( (k7_modelc_2 @ A)  @ B) )  @ 1) )  @ 4)  &  ( (= @  ( (k1_funct_1 @  ( (k8_modelc_2 @ A)  @ B) )  @ 1) )  @ 5) ) ) ) ) ) ) ) ) ) , file(modelc_2, t12_modelc_2)).
thf(spc5_boole, axiom,   ~ ( (v1_xboole_0 @ 5) ) , file(boole, spc5_boole)).
thf(spc4_boole, axiom,   ~ ( (v1_xboole_0 @ 4) ) , file(boole, spc4_boole)).
thf(spc3_boole, axiom,   ~ ( (v1_xboole_0 @ 3) ) , file(boole, spc3_boole)).
thf(spc2_boole, axiom,   ~ ( (v1_xboole_0 @ 2) ) , file(boole, spc2_boole)).
thf(spc1_boole, axiom,   ~ ( (v1_xboole_0 @ 1) ) , file(boole, spc1_boole)).
thf(redefinition_m2_finseq_1, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  <=>  ( (m1_finseq_1 @ B)  @ A) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(redefinition_k8_finseq_1, axiom,   (! [A: $i, B: $i, C: $i] :  ( ( ( (m1_finseq_1 @ B)  @ A)  &  ( (m1_finseq_1 @ C)  @ A) )  =>  ( (= @  ( ( (k8_finseq_1 @ A)  @ B)  @ C) )  @  ( (k7_finseq_1 @ B)  @ C) ) ) ) , file(finseq_1, k8_finseq_1)).
thf(redefinition_k6_numbers, axiom,   ( (= @ k6_numbers)  @ k1_xboole_0) , file(numbers, k6_numbers)).
thf(redefinition_k5_numbers, axiom,   ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k12_finseq_1, axiom,   (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( (= @  ( (k12_finseq_1 @ A)  @ B) )  @  (k5_finseq_1 @ B) ) ) ) , file(finseq_1, k12_finseq_1)).
thf(fc6_ordinal1, axiom,   ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc2_modelc_2, axiom,   (! [A: $i] :  ( ( (v1_modelc_2 @ A)  &  ( (m1_finseq_1 @ A)  @ k5_numbers) )  =>  (v1_modelc_2 @  (k3_modelc_2 @ A) ) ) ) , file(modelc_2, fc2_modelc_2)).
thf(fc1_xboole_0, axiom,   (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(dt_m1_finseq_1, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) , file(finseq_1, m1_finseq_1)).
thf(dt_k3_modelc_2, axiom,   (! [A: $i] :  ( ( (m1_finseq_1 @ A)  @ k5_numbers)  =>  ( (m2_finseq_1 @  (k3_modelc_2 @ A) )  @ k5_numbers) ) ) , file(modelc_2, k3_modelc_2)).
thf(dt_k12_finseq_1, axiom,   (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( (m2_finseq_1 @  ( (k12_finseq_1 @ A)  @ B) )  @ A) ) ) , file(finseq_1, k12_finseq_1)).
thf(d3_modelc_2, axiom,   (! [A: $i] :  ( ( (m2_finseq_1 @ A)  @ k5_numbers)  =>  ( (= @  (k3_modelc_2 @ A) )  @  ( ( (k8_finseq_1 @ k5_numbers)  @  ( (k12_finseq_1 @ k5_numbers)  @ k6_numbers) )  @ A) ) ) ) , file(modelc_2, d3_modelc_2)).
thf(d21_modelc_2, axiom,   (! [A: $i] :  ( ( (v1_modelc_2 @ A)  &  ( (m2_finseq_1 @ A)  @ k5_numbers) )  =>  (! [B: $i] :  ( ( (v1_modelc_2 @ B)  &  ( (m2_finseq_1 @ B)  @ k5_numbers) )  =>  ( ( (r1_modelc_2 @ A)  @ B)  <=>  ~ ( ( ~ ( ( (= @ B)  @  (k3_modelc_2 @ A) ) )  &  ( ~ ( ( (= @ B)  @  (k6_modelc_2 @ A) ) )  &  (! [C: $i] :  ( ( (v1_modelc_2 @ C)  &  ( (m2_finseq_1 @ C)  @ k5_numbers) )  =>  ( ~ ( ( (= @ B)  @  ( (k4_modelc_2 @ A)  @ C) ) )  &  ( ~ ( ( (= @ B)  @  ( (k4_modelc_2 @ C)  @ A) ) )  &  ( ~ ( ( (= @ B)  @  ( (k5_modelc_2 @ A)  @ C) ) )  &  ( ~ ( ( (= @ B)  @  ( (k5_modelc_2 @ C)  @ A) ) )  &  ( ~ ( ( (= @ B)  @  ( (k7_modelc_2 @ A)  @ C) ) )  &  ( ~ ( ( (= @ B)  @  ( (k7_modelc_2 @ C)  @ A) ) )  &  ( ~ ( ( (= @ B)  @  ( (k8_modelc_2 @ A)  @ C) ) )  &  ~ ( ( (= @ B)  @  ( (k8_modelc_2 @ C)  @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(modelc_2, d21_modelc_2)).
thf(t13_modelc_2, conjecture,   (! [A: $i] :  ( ( (v1_modelc_2 @ A)  &  ( (m2_finseq_1 @ A)  @ k5_numbers) )  =>  (! [B: $i] :  ( ( (v1_modelc_2 @ B)  &  ( (m2_finseq_1 @ B)  @ k5_numbers) )  =>  ( ( (r1_modelc_2 @ A)  @  (k3_modelc_2 @ B) )  <=>  ( (= @ A)  @ B) ) ) ) ) ) , file(modelc_2, t13_modelc_2)).