TSTP Solution File: SCT097-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT097-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n023.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 : Wed May 29 17:42:48 EDT 2024
% Result : Unsatisfiable 3.33s 3.60s
% Output : Proof 3.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.28 % Problem : SCT097-1 : TPTP v8.2.0. Released v4.1.0.
% 0.28/0.29 % Command : do_cvc5 %s %d
% 0.30/0.50 % Computer : n023.cluster.edu
% 0.30/0.50 % Model : x86_64 x86_64
% 0.30/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.30/0.50 % Memory : 8042.1875MB
% 0.30/0.50 % OS : Linux 3.10.0-693.el7.x86_64
% 0.30/0.50 % CPULimit : 300
% 0.30/0.50 % WCLimit : 300
% 0.30/0.50 % DateTime : Mon May 27 17:35:09 EDT 2024
% 0.30/0.50 % CPUTime :
% 0.64/1.17 %----Proving TF0_NAR, FOF, or CNF
% 0.64/1.17 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.33/3.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.YolkR8JEsv/cvc5---1.0.5_27159.smt2
% 3.33/3.60 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.YolkR8JEsv/cvc5---1.0.5_27159.smt2
% 3.51/3.69 (assume a0 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a) (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a1 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a2 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a3 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a4 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_y) V_x)))))
% 3.51/3.69 (assume a5 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_a)))))
% 3.51/3.69 (assume a6 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_a)))))
% 3.51/3.69 (assume a7 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a8 (forall ((T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a9 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 3.51/3.69 (assume a10 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 3.51/3.69 (assume a11 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_y)) T_a))))
% 3.51/3.69 (assume a12 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.c_Transitive__Closure_Ortrancl V_s T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 3.51/3.69 (assume a13 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)))))
% 3.51/3.69 (assume a14 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b) T_a)))))
% 3.51/3.69 (assume a15 (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Relation_Osym V_s T_a)) (not (tptp.c_Relation_Osym V_r T_a)))))
% 3.51/3.69 (assume a16 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Set_Oinsert (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)) T_a T_b) (tptp.c_Set_Oinsert V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a))))
% 3.51/3.69 (assume a17 (forall ((T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.69 (assume a18 (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))))
% 3.51/3.69 (assume a19 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c) V_d T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d) T_a)))))
% 3.51/3.69 (assume a20 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c) V_d T_a)))))
% 3.51/3.69 (assume a21 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals V_c (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d) T_a)))))
% 3.51/3.69 (assume a22 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d) T_a) (not (tptp.c_lessequals V_c (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d) T_a)))))
% 3.51/3.69 (assume a23 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a24 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a25 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_N T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_n V_N tptp.tc_nat)))))
% 3.51/3.69 (assume a26 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Set_Oinsert V_x V_A T_a))))
% 3.51/3.69 (assume a27 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a))))))
% 3.51/3.69 (assume a28 (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OImage V_R (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a29 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))))
% 3.51/3.69 (assume a30 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))))
% 3.51/3.69 (assume a31 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a32 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))
% 3.51/3.69 (assume a33 (forall ((T_aa $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_aa) V_a) (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_aa T_a)))))
% 3.51/3.69 (assume a34 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a35 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a36 (forall ((T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a37 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Otop__class_Otop T_a) V_x T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 3.51/3.69 (assume a38 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 3.51/3.69 (assume a39 (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a40 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))))
% 3.51/3.69 (assume a41 (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_A (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.69 (assume a42 (forall ((T_a $$unsorted) (V_f $$unsorted) (V_F $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a tptp.tc_nat) V_f) V_F) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.c_Finite__Set_Ofinite V_F T_a)) (= (tptp.hAPP V_f V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_F))))))
% 3.51/3.69 (assume a43 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c) V_d))))
% 3.51/3.69 (assume a44 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d))) (= V_c (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d)))))
% 3.51/3.69 (assume a45 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d)))))
% 3.51/3.69 (assume a46 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a47 (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_B V_A (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a48 (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a49 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a50 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a)))))
% 3.51/3.69 (assume a51 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_g) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_g) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_g) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_g) V_B))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.69 (assume a52 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))))
% 3.51/3.69 (assume a53 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_d))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.69 (assume a54 (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))
% 3.51/3.69 (assume a55 (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a V_B T_a) V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) T_a))))
% 3.51/3.69 (assume a56 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))))
% 3.51/3.69 (assume a57 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))))
% 3.51/3.69 (assume a58 (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.c_Transitive__Closure_Ortrancl V_S T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))
% 3.51/3.69 (assume a59 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c) V_b) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a60 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c) V_b) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_b V_a T_a)))))
% 3.51/3.69 (assume a61 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c))))))
% 3.51/3.69 (assume a62 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a)))))
% 3.51/3.69 (assume a63 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a64 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_a T_a)))))
% 3.51/3.69 (assume a65 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a66 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a)))))
% 3.51/3.69 (assume a67 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a68 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_a T_a)))))
% 3.51/3.69 (assume a69 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a70 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a71 (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.69 (assume a72 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_n T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Power_Opower__class_Opower (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_n T_a)) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))))))
% 3.51/3.69 (assume a73 (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oone__class_Oone T_a) V_n T_a) T_a))))
% 3.51/3.69 (assume a74 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a)))))
% 3.51/3.69 (assume a75 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.69 (assume a76 (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))
% 3.51/3.69 (assume a77 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a78 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) V_a T_a)))))
% 3.51/3.69 (assume a79 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) V_a T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)))))
% 3.51/3.69 (assume a80 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a)))))
% 3.51/3.69 (assume a81 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)))))
% 3.51/3.69 (assume a82 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) V_z T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_y))))))
% 3.51/3.69 (assume a83 (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_z (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y) V_x T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_y))))))
% 3.51/3.69 (assume a84 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 3.51/3.69 (assume a85 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 3.51/3.69 (assume a86 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 3.51/3.69 (assume a87 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 3.51/3.69 (assume a88 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_b))) (= V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (= V_a V_b))))
% 3.51/3.69 (assume a89 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a90 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a91 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))
% 3.51/3.69 (assume a92 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a93 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a94 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_y) V_z) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))))
% 3.51/3.69 (assume a95 (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))))
% 3.51/3.69 (assume a96 (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))))
% 3.51/3.69 (assume a97 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))))))
% 3.51/3.69 (assume a98 (forall ((V_R $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Relation_OImage V_R (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Relation_OImage V_R V_A T_b T_a) (tptp.c_Relation_OImage V_R V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.69 (assume a99 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.c_lessequals V_C V_A (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a100 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_C V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a101 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_b)) (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b) (tptp.c_Finite__Set_Osetprod V_f V_B T_a T_b) T_b) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))))
% 3.51/3.69 (assume a102 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_a))))))
% 3.51/3.69 (assume a103 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.69 (assume a104 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.69 (assume a105 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))))))
% 3.51/3.69 (assume a106 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)))))))
% 3.51/3.69 (assume a107 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.69 (assume a108 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.69 (assume a109 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_b))))))
% 3.51/3.69 (assume a110 (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_m) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_HOL_Oone__class_Oone T_a))) V_m)))))
% 3.51/3.69 (assume a111 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a112 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a113 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a114 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.69 (assume a115 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))))))
% 3.51/3.69 (assume a116 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d)))))))
% 3.51/3.69 (assume a117 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d)))))))
% 3.51/3.69 (assume a118 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c)) V_d))))))
% 3.51/3.69 (assume a119 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c)) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_d)))))))
% 3.51/3.69 (assume a120 (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_g) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_g) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_g) V_B))))))
% 3.51/3.69 (assume a121 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a122 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a123 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a124 (forall ((T_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) V_c)))))
% 3.51/3.69 (assume a125 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_b V_n T_a)))))))
% 3.51/3.69 (assume a126 (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_R V_S T_a T_a T_a) V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_Wellfounded_Owf V_S T_a)) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 3.51/3.69 (assume a127 (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))))
% 3.51/3.69 (assume a128 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))))
% 3.51/3.69 (assume a129 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))))
% 3.51/3.69 (assume a130 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Relation_ODomain V_r T_a T_a) (tptp.c_Relation_ORange V_s T_a T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.c_Wellfounded_Owf V_s T_a)) (not (tptp.c_Wellfounded_Owf V_r T_a)) (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a))))
% 3.51/3.69 (assume a131 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)))))
% 3.51/3.69 (assume a132 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_b))))
% 3.51/3.69 (assume a133 (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.c_Relation_Osingle__valued (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) T_a T_c) (not (tptp.c_Relation_Osingle__valued V_s T_b T_c)) (not (tptp.c_Relation_Osingle__valued V_r T_a T_b)))))
% 3.51/3.69 (assume a134 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Orefl__on (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Relation_Orefl__on V_B V_s T_a)) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 3.51/3.69 (assume a135 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))))
% 3.51/3.69 (assume a136 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))))
% 3.51/3.69 (assume a137 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))))
% 3.51/3.69 (assume a138 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))))
% 3.51/3.69 (assume a139 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a140 (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a141 (forall ((T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))
% 3.51/3.69 (assume a142 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_y))) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.69 (assume a143 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) V_a T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)))))
% 3.51/3.69 (assume a144 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)))))
% 3.51/3.69 (assume a145 (forall ((T_a $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_w) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_w) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y)))) (= V_y V_z) (= V_w V_x))))
% 3.51/3.69 (assume a146 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c)))) (= V_c V_d) (= V_a V_b))))
% 3.51/3.69 (assume a147 (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))
% 3.51/3.69 (assume a148 (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_G T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))
% 3.51/3.69 (assume a149 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x))))
% 3.51/3.69 (assume a150 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a) V_x))))
% 3.51/3.69 (assume a151 (forall ((T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool)) V_B)))
% 3.51/3.69 (assume a152 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) V_A)))
% 3.51/3.69 (assume a153 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a154 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.69 (assume a155 (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Orefl__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a)))
% 3.51/3.69 (assume a156 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))
% 3.51/3.69 (assume a157 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B T_a) (tptp.c_Orderings_Otop__class_Otop T_a))) (= V_B (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 3.51/3.69 (assume a158 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B T_a) (tptp.c_Orderings_Otop__class_Otop T_a))) (= V_A (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 3.51/3.69 (assume a159 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))
% 3.51/3.69 (assume a160 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a161 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a162 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_w) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_w) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_z))) (= V_z (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a163 (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) V_rx)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_ly) V_ry))))))
% 3.51/3.69 (assume a164 (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_ly) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_rx) V_ry)))))))
% 3.51/3.69 (assume a165 (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) V_ly)) V_ry))))))
% 3.51/3.69 (assume a166 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_c)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a167 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_c) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a168 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A (tptp.c_Relation_OImage V_R V_A T_a T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 3.51/3.69 (assume a169 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a170 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a171 (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a172 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a173 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) V_x T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 3.51/3.69 (assume a174 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 3.51/3.69 (assume a175 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_x) V_x))))
% 3.51/3.69 (assume a176 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a) V_a))))
% 3.51/3.69 (assume a177 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a) V_a))))
% 3.51/3.69 (assume a178 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))))
% 3.51/3.69 (assume a179 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))))
% 3.51/3.69 (assume a180 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a) V_a))))
% 3.51/3.69 (assume a181 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.69 (assume a182 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_k) T_a))))
% 3.51/3.69 (assume a183 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a))))
% 3.51/3.69 (assume a184 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a) T_a))))
% 3.51/3.69 (assume a185 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.69 (assume a186 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_y) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_w) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_w))) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x))))))
% 3.51/3.69 (assume a187 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a) V_n T_a)))))
% 3.51/3.69 (assume a188 (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n) T_a)))))
% 3.51/3.69 (assume a189 (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n) T_a) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))))
% 3.51/3.69 (assume a190 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a191 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))))
% 3.51/3.69 (assume a192 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_c))))))
% 3.51/3.69 (assume a193 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y))))))
% 3.51/3.69 (assume a194 (forall ((V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_b V_B T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a195 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a196 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a)))))
% 3.51/3.69 (assume a197 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a198 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a199 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.69 (assume a200 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_b) V_a))))
% 3.51/3.69 (assume a201 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))))
% 3.51/3.69 (assume a202 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a203 (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a204 (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a205 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))))
% 3.51/3.69 (assume a206 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_z V_x T_a) T_a)))))
% 3.51/3.69 (assume a207 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_x)))))
% 3.51/3.69 (assume a208 (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a209 (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a210 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a)))))
% 3.51/3.69 (assume a211 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__join T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_b V_c T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a)))))
% 3.51/3.69 (assume a212 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__join T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)) V_c) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c) T_a)))))
% 3.51/3.69 (assume a213 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_b V_c T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a)))))
% 3.51/3.69 (assume a214 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)) V_c) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c) T_a)))))
% 3.51/3.69 (assume a215 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a216 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)))
% 3.51/3.69 (assume a217 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))))
% 3.51/3.69 (assume a218 (forall ((V_r_H $$unsorted) (V_s_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_r_H V_s_H T_a T_b T_c) (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) (tptp.tc_fun (tptp.tc_prod T_a T_c) tptp.tc_bool)) (not (tptp.c_lessequals V_s_H V_s (tptp.tc_fun (tptp.tc_prod T_b T_c) tptp.tc_bool))) (not (tptp.c_lessequals V_r_H V_r (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))))
% 3.51/3.69 (assume a219 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osgn__if T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_x T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a220 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_y) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y)) V_z)))))
% 3.51/3.69 (assume a221 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_y) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_z))))))
% 3.51/3.69 (assume a222 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c))))))
% 3.51/3.69 (assume a223 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))))))
% 3.51/3.69 (assume a224 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c))))))
% 3.51/3.69 (assume a225 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c)) V_d)))))
% 3.51/3.69 (assume a226 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c)) V_b)))))
% 3.51/3.69 (assume a227 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_d))))))
% 3.51/3.69 (assume a228 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c))))))
% 3.51/3.69 (assume a229 (forall ((V_R $$unsorted) (V_S $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Relation_OImage (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) V_A T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_OImage V_R V_A T_b T_a) (tptp.c_Relation_OImage V_S V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a230 (forall ((V_R $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OImage V_R (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_OImage V_R V_A T_b T_a) (tptp.c_Relation_OImage V_R V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a231 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a))) (= (tptp.c_HOL_Ozero__class_Ozero T_a) V_a))))
% 3.51/3.69 (assume a232 (forall ((V_P $$unsorted) (V_Rb $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_Rb)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__Recdef__Xtfl__wf__induct__1__1 V_P V_R T_a)))) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 3.51/3.69 (assume a233 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))
% 3.51/3.69 (assume a234 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_y) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_y) V_u))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_z) V_u))))
% 3.51/3.69 (assume a235 (forall ((V_r $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_OImage V_r V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Relation_OImage (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a T_b)) (tptp.tc_fun T_b tptp.tc_bool))))))
% 3.51/3.69 (assume a236 (forall ((V_A $$unsorted) (T_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Relation_OImage (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a T_b)) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals (tptp.c_Relation_OImage V_r V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a237 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))))
% 3.51/3.69 (assume a238 (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oone__class_Oone T_a) V_n T_a) (tptp.c_HOL_Oone__class_Oone T_a)))))
% 3.51/3.69 (assume a239 (forall ((T_a $$unsorted)) (tptp.c_Relation_Osingle__valued (tptp.c_Relation_OId T_a) T_a T_a)))
% 3.51/3.69 (assume a240 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a)))))
% 3.51/3.69 (assume a241 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a242 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__meet T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_b V_c T_a)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a)))))
% 3.51/3.69 (assume a243 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__meet T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a)) V_c) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c) T_a)))))
% 3.51/3.69 (assume a244 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_b V_c T_a)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a)))))
% 3.51/3.69 (assume a245 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a)) V_c) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c) T_a)))))
% 3.51/3.69 (assume a246 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a)))))
% 3.51/3.69 (assume a247 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a)))))
% 3.51/3.69 (assume a248 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a)))))
% 3.51/3.69 (assume a249 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a)))))
% 3.51/3.69 (assume a250 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_c))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a251 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_a V_N T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (not (tptp.c_lessequals V_n V_N tptp.tc_nat)))))
% 3.51/3.69 (assume a252 (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_Finite__Set_Ocard V_A T_a)))))))
% 3.51/3.69 (assume a253 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a254 (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))))
% 3.51/3.69 (assume a255 (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_xa) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_x))) (= V_xa V_y))))
% 3.51/3.69 (assume a256 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x_H) V_y_H))) (= V_x_H V_y_H))))
% 3.51/3.69 (assume a257 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y) T_a)))))
% 3.51/3.69 (assume a258 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.69 (assume a259 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.69 (assume a260 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))
% 3.51/3.69 (assume a261 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))
% 3.51/3.69 (assume a262 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b) T_a)))))
% 3.51/3.69 (assume a263 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c) T_a)))))
% 3.51/3.69 (assume a264 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)))))
% 3.51/3.69 (assume a265 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.69 (assume a266 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)))))
% 3.51/3.69 (assume a267 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.69 (assume a268 (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a269 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a270 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))))
% 3.51/3.69 (assume a271 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a272 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a273 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a274 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a275 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a276 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= V_A V_B) (not (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_B T_a) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))))
% 3.51/3.69 (assume a277 (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 3.51/3.69 (assume a278 (forall ((T_a $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a279 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_m)) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a))) V_m)))))
% 3.51/3.69 (assume a280 (forall ((T_a $$unsorted) (V_m $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a))) V_m)))))
% 3.51/3.69 (assume a281 (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))))
% 3.51/3.69 (assume a282 (forall ((T_a $$unsorted)) (not (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a283 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))))
% 3.51/3.69 (assume a284 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a) V_x))))
% 3.51/3.69 (assume a285 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop T_a) V_x T_a) V_x))))
% 3.51/3.69 (assume a286 (forall ((T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool)) V_B)))
% 3.51/3.69 (assume a287 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) V_A)))
% 3.51/3.69 (assume a288 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a) T_a))))
% 3.51/3.69 (assume a289 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a290 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a291 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_x))))
% 3.51/3.69 (assume a292 (forall ((V_P $$unsorted) (V_xb $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xb)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.69 (assume a293 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_c)))))
% 3.51/3.69 (assume a294 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_c) V_a))))
% 3.51/3.69 (assume a295 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_c) V_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a296 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_c)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a297 (forall ((V_n $$unsorted)) (or (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_lessequals V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat)))))
% 3.51/3.69 (assume a298 (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))))
% 3.51/3.69 (assume a299 (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_Finite__Set_Ofinite V_A T_a))))
% 3.51/3.69 (assume a300 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y))) (= V_x V_y))))
% 3.51/3.69 (assume a301 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))) (= V_a V_b))))
% 3.51/3.69 (assume a302 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B))) (= V_A V_B))))
% 3.51/3.69 (assume a303 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) V_n T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))))))
% 3.51/3.69 (assume a304 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))))))
% 3.51/3.69 (assume a305 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Oacyclic (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 3.51/3.69 (assume a306 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))))
% 3.51/3.69 (assume a307 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a308 (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))))
% 3.51/3.69 (assume a309 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a310 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.69 (assume a311 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.69 (assume a312 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))))
% 3.51/3.69 (assume a313 (forall ((T_b $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) (tptp.c_Finite__Set_Osetprod V_g (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (tptp.c_Finite__Set_Osetprod V_g (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) (tptp.c_Finite__Set_Osetprod V_g V_A T_a T_b)) (tptp.c_Finite__Set_Osetprod V_g V_B T_a T_b))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.69 (assume a314 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a315 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a316 (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.c_Finite__Set_Osetprod V_g (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) (tptp.c_Finite__Set_Osetprod V_g V_A T_a T_b)) (tptp.c_Finite__Set_Osetprod V_g V_B T_a T_b))))))
% 3.51/3.69 (assume a317 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_x))))
% 3.51/3.69 (assume a318 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_x) (not (tptp.c_lessequals V_y V_x T_a)))))
% 3.51/3.69 (assume a319 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y)) (tptp.c_lessequals V_x V_y T_a))))
% 3.51/3.69 (assume a320 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.69 (assume a321 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_B) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a322 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A) (not (tptp.c_lessequals V_B V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a323 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_B)) (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a324 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_b))))
% 3.51/3.69 (assume a325 (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_y) V_z)) V_y))))
% 3.51/3.69 (assume a326 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))))
% 3.51/3.69 (assume a327 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_a T_a))))
% 3.51/3.69 (assume a328 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a329 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a330 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_y) V_w) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_w))) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)))))
% 3.51/3.69 (assume a331 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) V_B))) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.69 (assume a332 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))) (= V_a V_d) (= V_a V_c))))
% 3.51/3.69 (assume a333 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))) (= V_b V_c) (= V_a V_c))))
% 3.51/3.69 (assume a334 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))) (= V_a V_d) (= V_b V_d))))
% 3.51/3.69 (assume a335 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))) (= V_b V_c) (= V_b V_d))))
% 3.51/3.69 (assume a336 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)) T_a))))
% 3.51/3.69 (assume a337 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b) T_a))))
% 3.51/3.69 (assume a338 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c) T_a) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a339 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c) T_a)))))
% 3.51/3.69 (assume a340 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a341 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_b) T_a)))))
% 3.51/3.69 (assume a342 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c) T_a) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a343 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a344 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_z) V_w)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_w))))))
% 3.51/3.69 (assume a345 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))))))
% 3.51/3.69 (assume a346 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) V_b)))))
% 3.51/3.69 (assume a347 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.69 (assume a348 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.c_Transitive__Closure_Ortrancl V_s T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_lessequals V_r (tptp.c_Transitive__Closure_Ortrancl V_s T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 3.51/3.69 (assume a349 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a350 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) T_a)))))
% 3.51/3.69 (assume a351 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.69 (assume a352 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))))))
% 3.51/3.69 (assume a353 (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.69 (assume a354 (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.69 (assume a355 (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a356 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a357 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osgn__if T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a358 (forall ((T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.69 (assume a359 (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))
% 3.51/3.69 (assume a360 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y)))))
% 3.51/3.69 (assume a361 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))))
% 3.51/3.69 (assume a362 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a363 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a364 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a365 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a366 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.69 (assume a367 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_d))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) V_d))) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a368 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))))
% 3.51/3.69 (assume a369 (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_C))))))
% 3.51/3.69 (assume a370 (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))))
% 3.51/3.69 (assume a371 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))))
% 3.51/3.69 (assume a372 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))))
% 3.51/3.69 (assume a373 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))))
% 3.51/3.69 (assume a374 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))
% 3.51/3.69 (assume a375 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a376 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_B) (not (tptp.c_lessequals V_B V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a377 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.69 (assume a378 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x)) (tptp.c_lessequals V_x V_y T_a))))
% 3.51/3.69 (assume a379 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y) (not (tptp.c_lessequals V_y V_x T_a)))))
% 3.51/3.69 (assume a380 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_C (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a381 (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.69 (assume a382 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.69 (assume a383 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_C (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a384 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))))
% 3.51/3.69 (assume a385 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))))
% 3.51/3.69 (assume a386 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))))
% 3.51/3.69 (assume a387 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))))
% 3.51/3.69 (assume a388 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))))
% 3.51/3.69 (assume a389 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))))
% 3.51/3.69 (assume a390 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))))
% 3.51/3.69 (assume a391 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a392 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))))
% 3.51/3.69 (assume a393 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))))
% 3.51/3.69 (assume a394 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.69 (assume a395 (forall ((V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.69 (assume a396 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_e)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_e)) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_e)) V_c)))))
% 3.51/3.69 (assume a397 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) T_a))))
% 3.51/3.69 (assume a398 (forall ((V_S $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (= (tptp.c_Transitive__Closure_Ortrancl V_S T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a)) (not (tptp.c_lessequals V_S (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_lessequals V_R V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 3.51/3.69 (assume a399 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a400 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a401 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a402 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a403 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Orderings_Otop__class_Otop T_a))) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Orderings_Obot__class_Obot T_a))) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) V_y))))
% 3.51/3.69 (assume a404 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (= V_a V_b))))
% 3.51/3.69 (assume a405 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a406 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a407 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.69 (assume a408 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))))
% 3.51/3.69 (assume a409 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))))
% 3.51/3.69 (assume a410 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))))
% 3.51/3.69 (assume a411 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_y)) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a412 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_y)) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a413 (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a414 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a415 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) V_x T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 3.51/3.69 (assume a416 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 3.51/3.69 (assume a417 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a418 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a419 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a420 (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_xa)))))
% 3.51/3.69 (assume a421 (forall ((V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))
% 3.51/3.69 (assume a422 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a423 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.69 (assume a424 (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_b tptp.tc_bool)) V_A) T_a T_b) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_a T_b)))))
% 3.51/3.69 (assume a425 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a426 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a427 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a428 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a429 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a430 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a431 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.69 (assume a432 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a433 (forall ((V_I $$unsorted) (V_J $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_OSigma (tptp.c_Lattices_Oupper__semilattice__class_Osup V_I V_J (tptp.tc_fun T_a tptp.tc_bool)) V_C T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Product__Type_OSigma V_I V_C T_a T_b) (tptp.c_Product__Type_OSigma V_J V_C T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)))))
% 3.51/3.69 (assume a434 (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))))
% 3.51/3.69 (assume a435 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_z))) (= V_y V_z))))
% 3.51/3.69 (assume a436 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (= V_b V_c))))
% 3.51/3.69 (assume a437 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (= V_b V_c))))
% 3.51/3.69 (assume a438 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_a))) (= V_b V_c))))
% 3.51/3.69 (assume a439 (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))))
% 3.51/3.69 (assume a440 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a441 (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))))
% 3.51/3.69 (assume a442 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))))
% 3.51/3.69 (assume a443 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a444 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Ovimage V_f V_A T_b T_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a445 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))))
% 3.51/3.69 (assume a446 (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)))))
% 3.51/3.69 (assume a447 (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_C)))))
% 3.51/3.69 (assume a448 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)))))
% 3.51/3.69 (assume a449 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_x) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)))))
% 3.51/3.69 (assume a450 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a451 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_y))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)))))
% 3.51/3.69 (assume a452 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))))
% 3.51/3.69 (assume a453 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_B (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a454 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a455 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) (tptp.c_Orderings_Obot__class_Obot T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 3.51/3.69 (assume a456 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) (tptp.c_Orderings_Obot__class_Obot T_a))) (= V_B (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 3.51/3.69 (assume a457 (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (= V_A (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a458 (forall ((V_S $$unsorted) (V_T $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Lattices_Oupper__semilattice__class_Osup V_S V_T (tptp.tc_fun (tptp.tc_prod T_a T_c) tptp.tc_bool)) V_R T_a T_c T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_S V_R T_a T_c T_b) (tptp.c_Relation_Orel__comp V_T V_R T_a T_c T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)))))
% 3.51/3.69 (assume a459 (forall ((V_R $$unsorted) (V_S $$unsorted) (V_T $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp V_R (tptp.c_Lattices_Oupper__semilattice__class_Osup V_S V_T (tptp.tc_fun (tptp.tc_prod T_c T_b) tptp.tc_bool)) T_a T_c T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_S T_a T_c T_b) (tptp.c_Relation_Orel__comp V_R V_T T_a T_c T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)))))
% 3.51/3.69 (assume a460 (forall ((V_C $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals V_C V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a461 (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_C V_A (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a462 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))))
% 3.51/3.69 (assume a463 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))))
% 3.51/3.69 (assume a464 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))))
% 3.51/3.69 (assume a465 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))))
% 3.51/3.69 (assume a466 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))))
% 3.51/3.69 (assume a467 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))))
% 3.51/3.69 (assume a468 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y) T_a)))))
% 3.51/3.69 (assume a469 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))))
% 3.51/3.69 (assume a470 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) V_y T_a)))))
% 3.51/3.69 (assume a471 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))))
% 3.51/3.69 (assume a472 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))))
% 3.51/3.69 (assume a473 (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_r T_a)))
% 3.51/3.69 (assume a474 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_D (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_D (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a475 (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_f V_a) V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b)))))))
% 3.51/3.69 (assume a476 (forall ((V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r V_s (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.c_Relation_Oconverse V_s T_b T_a) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)))))
% 3.51/3.69 (assume a477 (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) V_n T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))
% 3.51/3.69 (assume a478 (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) V_n T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))
% 3.51/3.69 (assume a479 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))))
% 3.51/3.69 (assume a480 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))))
% 3.51/3.69 (assume a481 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.69 (assume a482 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.69 (assume a483 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)) (not (tptp.c_lessequals V_x V_a T_a)))))
% 3.51/3.69 (assume a484 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))))
% 3.51/3.69 (assume a485 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))))
% 3.51/3.69 (assume a486 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.69 (assume a487 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.69 (assume a488 (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_C V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_C V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a489 (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_C V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_C V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.69 (assume a490 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.69 (assume a491 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a))))
% 3.51/3.69 (assume a492 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))
% 3.51/3.69 (assume a493 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.69 (assume a494 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))))))
% 3.51/3.69 (assume a495 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_m T_a) T_a) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))))
% 3.51/3.69 (assume a496 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a) (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a497 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a498 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a499 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a500 (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a501 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) V_b)) V_b))))
% 3.51/3.69 (assume a502 (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a503 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z V_x T_a) T_a)))))
% 3.51/3.69 (assume a504 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))))
% 3.51/3.69 (assume a505 (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a506 (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a507 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))))
% 3.51/3.69 (assume a508 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))))))
% 3.51/3.69 (assume a509 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) V_c T_a)))))
% 3.51/3.69 (assume a510 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) V_c T_a)))))
% 3.51/3.69 (assume a511 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))))
% 3.51/3.69 (assume a512 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)))))
% 3.51/3.69 (assume a513 (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 3.51/3.69 (assume a514 (forall ((T_a $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a515 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a)))))
% 3.51/3.69 (assume a516 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a)))))
% 3.51/3.69 (assume a517 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.69 (assume a518 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a519 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.69 (assume a520 (forall ((V_R $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Relation_OImage V_R (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Relation_OImage V_R V_A T_b T_a) (tptp.c_Relation_OImage V_R V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Relation_Osingle__valued (tptp.c_Relation_Oconverse V_R T_b T_a) T_a T_b)))))
% 3.51/3.69 (assume a521 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) V_n T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.69 (assume a522 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))))))
% 3.51/3.69 (assume a523 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_d) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_c V_d T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))))
% 3.51/3.69 (assume a524 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))))
% 3.51/3.69 (assume a525 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))))
% 3.51/3.69 (assume a526 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a527 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.69 (assume a528 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.70 (assume a529 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) V_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))
% 3.51/3.70 (assume a530 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r) V_d)))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a531 (forall ((T_a $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))))
% 3.51/3.70 (assume a532 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_y)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a533 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_y)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a534 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_ORange V_A T_b T_a) (tptp.c_Relation_ORange V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a535 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))
% 3.51/3.70 (assume a536 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) V_a T_a)))))
% 3.51/3.70 (assume a537 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) V_a T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.70 (assume a538 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a)))))
% 3.51/3.70 (assume a539 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.70 (assume a540 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_x T_a) V_x))))
% 3.51/3.70 (assume a541 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)))
% 3.51/3.70 (assume a542 (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y)) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_y))))))
% 3.51/3.70 (assume a543 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_y))))))
% 3.51/3.70 (assume a544 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_a))))))
% 3.51/3.70 (assume a545 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))))))
% 3.51/3.70 (assume a546 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)))))))
% 3.51/3.70 (assume a547 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_b))))))
% 3.51/3.70 (assume a548 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))))
% 3.51/3.70 (assume a549 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))))
% 3.51/3.70 (assume a550 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)))))
% 3.51/3.70 (assume a551 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_a T_a)))))
% 3.51/3.70 (assume a552 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))))
% 3.51/3.70 (assume a553 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))))
% 3.51/3.70 (assume a554 (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a555 (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a556 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_Power_Opower__class_Opower V_x V_n T_a) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n))))))
% 3.51/3.70 (assume a557 (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))))
% 3.51/3.70 (assume a558 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.70 (assume a559 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_a V_m T_a) V_b T_a) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_a V_n T_a) V_b T_a)))))
% 3.51/3.70 (assume a560 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.70 (assume a561 (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)))
% 3.51/3.70 (assume a562 (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_nat) (not (tptp.c_lessequals V_j V_k tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))))
% 3.51/3.70 (assume a563 (forall ((V_x $$unsorted)) (tptp.c_lessequals V_x V_x tptp.tc_nat)))
% 3.51/3.70 (assume a564 (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.70 (assume a565 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))))
% 3.51/3.70 (assume a566 (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_C (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a567 (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a568 (forall ((V_p $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Wellfounded_Owf V_p T_a) (not (tptp.c_lessequals V_p V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a569 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))))
% 3.51/3.70 (assume a570 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))))
% 3.51/3.70 (assume a571 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))))
% 3.51/3.70 (assume a572 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a573 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y))))))
% 3.51/3.70 (assume a574 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y))))))
% 3.51/3.70 (assume a575 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))))))
% 3.51/3.70 (assume a576 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))))))
% 3.51/3.70 (assume a577 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_y)))) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a578 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_y)))) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a579 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_d))))))
% 3.51/3.70 (assume a580 (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y))) V_y)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a581 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y))) V_y)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a582 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) T_a))))))
% 3.51/3.70 (assume a583 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a584 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))))
% 3.51/3.70 (assume a585 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))))
% 3.51/3.70 (assume a586 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a587 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y) T_a)))))
% 3.51/3.70 (assume a588 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) T_a)))))
% 3.51/3.70 (assume a589 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_HOL_Oone__class_Oone T_a))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a590 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_HOL_Oone__class_Oone T_a)))) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a591 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)))))
% 3.51/3.70 (assume a592 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a593 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.70 (assume a594 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_ODomain V_A T_a T_b) (tptp.c_Relation_ODomain V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a595 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_y) V_z)) V_y)) (= V_x (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_z)))))
% 3.51/3.70 (assume a596 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a597 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a598 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) V_A (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a599 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))))
% 3.51/3.70 (assume a600 (forall ((V_R2 $$unsorted) (T_a $$unsorted) (V_R1 $$unsorted)) (or (tptp.c_lessequals (tptp.c_Wellfounded_Oacc V_R2 T_a) (tptp.c_Wellfounded_Oacc V_R1 T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_R1 V_R2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 3.51/3.70 (assume a601 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a602 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a)))))
% 3.51/3.70 (assume a603 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a)))))
% 3.51/3.70 (assume a604 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a605 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_y) T_a)))))
% 3.51/3.70 (assume a606 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) T_a)))))
% 3.51/3.70 (assume a607 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_a) tptp.tc_nat) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))))
% 3.51/3.70 (assume a608 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_z)) V_y)))))
% 3.51/3.70 (assume a609 (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a610 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a611 (forall ((T_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))))
% 3.51/3.70 (assume a612 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a613 (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.c_Transitive__Closure_Ortrancl V_S T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a))))
% 3.51/3.70 (assume a614 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_b))))))
% 3.51/3.70 (assume a615 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_b))))))
% 3.51/3.70 (assume a616 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))))))
% 3.51/3.70 (assume a617 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))))))
% 3.51/3.70 (assume a618 (forall ((T_a $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))
% 3.51/3.70 (assume a619 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.c_HOL_Osgn__class_Osgn V_a T_a) T_a) (tptp.c_HOL_Osgn__class_Osgn V_a T_a)))))
% 3.51/3.70 (assume a620 (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_Finite__Set_Ocard V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a621 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_d) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.70 (assume a622 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_d) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.70 (assume a623 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_b)))))
% 3.51/3.70 (assume a624 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))))
% 3.51/3.70 (assume a625 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)))))
% 3.51/3.70 (assume a626 (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))))
% 3.51/3.70 (assume a627 (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))))
% 3.51/3.70 (assume a628 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_w) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_w) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_z))) (= V_z (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a629 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_m)))))
% 3.51/3.70 (assume a630 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Set_Oinsert (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)) T_b T_a) (tptp.c_Set_Oinsert V_b (tptp.c_Relation_ORange V_r T_b T_a) T_a))))
% 3.51/3.70 (assume a631 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a632 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a633 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b) T_a)))))
% 3.51/3.70 (assume a634 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c) T_a)))))
% 3.51/3.70 (assume a635 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x) V_x))))
% 3.51/3.70 (assume a636 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))))
% 3.51/3.70 (assume a637 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a))))))
% 3.51/3.70 (assume a638 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))
% 3.51/3.70 (assume a639 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))))
% 3.51/3.70 (assume a640 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))
% 3.51/3.70 (assume a641 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))
% 3.51/3.70 (assume a642 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))))
% 3.51/3.70 (assume a643 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))))
% 3.51/3.70 (assume a644 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)))))
% 3.51/3.70 (assume a645 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.70 (assume a646 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a)))))
% 3.51/3.70 (assume a647 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)))))
% 3.51/3.70 (assume a648 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.70 (assume a649 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) V_a T_a)))))
% 3.51/3.70 (assume a650 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a651 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a)))))
% 3.51/3.70 (assume a652 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a)))))
% 3.51/3.70 (assume a653 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a)))))
% 3.51/3.70 (assume a654 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a)))))
% 3.51/3.70 (assume a655 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_b) V_a))))
% 3.51/3.70 (assume a656 (forall ((V_f $$unsorted) (V_g $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f (tptp.c_List_Osko__Recdef__Xcuts__eq__1__1 V_f V_g V_r V_x T_a T_b)) (tptp.hAPP V_g (tptp.c_List_Osko__Recdef__Xcuts__eq__1__1 V_f V_g V_r V_x T_a T_b)))) (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b)))))
% 3.51/3.70 (assume a657 (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))))))
% 3.51/3.70 (assume a658 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_x V_y tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))))))
% 3.51/3.70 (assume a659 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a) (not (tptp.c_lessequals V_x V_y tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))))))
% 3.51/3.70 (assume a660 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osingle__valued (tptp.c_Relation_OId__on V_A T_a) T_a T_a)))
% 3.51/3.70 (assume a661 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))))))
% 3.51/3.70 (assume a662 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) V_b)))))
% 3.51/3.70 (assume a663 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))))))
% 3.51/3.70 (assume a664 (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A)) V_A)))
% 3.51/3.70 (assume a665 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) V_a))))
% 3.51/3.70 (assume a666 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x)) V_x))))
% 3.51/3.70 (assume a667 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))))))
% 3.51/3.70 (assume a668 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a))))))
% 3.51/3.70 (assume a669 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) V_b))))
% 3.51/3.70 (assume a670 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Oacyclic (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a)))))
% 3.51/3.70 (assume a671 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym V_s T_a)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 3.51/3.70 (assume a672 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a673 (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))))
% 3.51/3.70 (assume a674 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_Wellfounded_Oacyclic V_s T_a)))))
% 3.51/3.70 (assume a675 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))))
% 3.51/3.70 (assume a676 (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Osingle__valued V_r T_a T_b) (not (tptp.c_Relation_Osingle__valued V_s T_a T_b)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))))
% 3.51/3.70 (assume a677 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c) T_a)))))
% 3.51/3.70 (assume a678 (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a679 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (or (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_D (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_D (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a680 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)))))
% 3.51/3.70 (assume a681 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_y))) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.70 (assume a682 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x) V_x))))
% 3.51/3.70 (assume a683 (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))
% 3.51/3.70 (assume a684 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_d))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a685 (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a686 (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_ODomain V_r T_a T_b) (tptp.c_Relation_ODomain V_s T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))))
% 3.51/3.70 (assume a687 (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a688 (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a689 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a690 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))))))
% 3.51/3.70 (assume a691 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))))
% 3.51/3.70 (assume a692 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) T_a))))))
% 3.51/3.70 (assume a693 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x_H) V_y_H))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))))
% 3.51/3.70 (assume a694 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x_H) V_y_H))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))))
% 3.51/3.70 (assume a695 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) V_n T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))))))
% 3.51/3.70 (assume a696 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y) V_q T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Power_Opower__class_Opower V_x V_q T_a)) (tptp.c_Power_Opower__class_Opower V_y V_q T_a))))))
% 3.51/3.70 (assume a697 (forall ((V_a $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_C V_D (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a698 (forall ((T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a699 (forall ((T_a $$unsorted) (V_d $$unsorted) (V_x $$unsorted) (V_t $$unsorted) (V_k $$unsorted) (V_D $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_t) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_k) V_D))) V_t) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d V_D T_a)))))
% 3.51/3.70 (assume a700 (forall ((T_a $$unsorted) (V_d $$unsorted) (V_x $$unsorted) (V_k $$unsorted) (V_D $$unsorted) (V_t $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_k) V_D))) V_t) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_t) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d V_D T_a)))))
% 3.51/3.70 (assume a701 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_w) V_y))) (= V_z (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_w) V_z)))))
% 3.51/3.70 (assume a702 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_w) V_z))) (= V_z (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_w) V_y)))))
% 3.51/3.70 (assume a703 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.70 (assume a704 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.70 (assume a705 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Osgn__class_Osgn V_a T_a)) (tptp.c_HOL_Osgn__class_Osgn V_b T_a))))))
% 3.51/3.70 (assume a706 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.70 (assume a707 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.70 (assume a708 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.70 (assume a709 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_a) T_a))))
% 3.51/3.70 (assume a710 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.70 (assume a711 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.70 (assume a712 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))))
% 3.51/3.70 (assume a713 (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a714 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.c_HOL_Oone__class_Oone T_a))) V_x)))))
% 3.51/3.70 (assume a715 (forall ((V_r_H $$unsorted) (V_A_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_OImage V_r_H V_A_H T_a T_b) (tptp.c_Relation_OImage V_r V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A_H V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_r_H V_r (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))))
% 3.51/3.70 (assume a716 (forall ((T_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a717 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c))))))
% 3.51/3.70 (assume a718 (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) V_ly)) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) V_rx)) V_ly)))))
% 3.51/3.70 (assume a719 (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) V_ly)) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_ly) V_rx))))))
% 3.51/3.70 (assume a720 (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) V_rx)) V_ry)))))
% 3.51/3.70 (assume a721 (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_lx) V_ry))))))
% 3.51/3.70 (assume a722 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y)) V_z)))))
% 3.51/3.70 (assume a723 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c))))))
% 3.51/3.70 (assume a724 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c))))))
% 3.51/3.70 (assume a725 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_y) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_z))))))
% 3.51/3.70 (assume a726 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))))))
% 3.51/3.70 (assume a727 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a))))))
% 3.51/3.70 (assume a728 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_y) V_w))) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)))))
% 3.51/3.70 (assume a729 (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))))
% 3.51/3.70 (assume a730 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))))
% 3.51/3.70 (assume a731 (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_Finite__Set_Osetprod V_f V_S T_a tptp.tc_nat)))) (not (tptp.c_Finite__Set_Ofinite V_S T_a)))))
% 3.51/3.70 (assume a732 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))))))
% 3.51/3.70 (assume a733 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_F $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) (tptp.c_Set_Oinsert V_a V_F T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.hAPP V_f V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) V_F))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_F)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))))
% 3.51/3.70 (assume a734 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.c_Finite__Set_Osetprod V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) (tptp.hAPP V_f V_a)) (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.70 (assume a735 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))))
% 3.51/3.70 (assume a736 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))) (not (tptp.c_Wellfounded_Oacyclic (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a)))))
% 3.51/3.70 (assume a737 (forall ((V_P $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 V_P V_b V_r T_a) (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 V_P V_b V_r T_a) T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP V_P V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a738 (forall ((V_P $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 V_P V_a V_r T_a) (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 V_P V_a V_r T_a) T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP V_P V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a739 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a740 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a741 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) V_A))) (not (tptp.c_lessequals (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a742 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a743 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)))))))
% 3.51/3.70 (assume a744 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_a))))))
% 3.51/3.70 (assume a745 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.70 (assume a746 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)))))))
% 3.51/3.70 (assume a747 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)))))
% 3.51/3.70 (assume a748 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a749 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a750 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))
% 3.51/3.70 (assume a751 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a752 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))))))
% 3.51/3.70 (assume a753 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a754 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))
% 3.51/3.70 (assume a755 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a756 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))))))
% 3.51/3.70 (assume a757 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))
% 3.51/3.70 (assume a758 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))
% 3.51/3.70 (assume a759 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a760 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a761 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 3.51/3.70 (assume a762 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 3.51/3.70 (assume a763 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a764 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x))))))
% 3.51/3.70 (assume a765 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a766 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a767 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a768 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a769 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a770 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a771 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)))))
% 3.51/3.70 (assume a772 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) V_d))) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.70 (assume a773 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_d))) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a774 (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a775 (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Olower__semilattice__class_Oinf V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)))))
% 3.51/3.70 (assume a776 (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Olower__semilattice__class_Oinf V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))))
% 3.51/3.70 (assume a777 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))))
% 3.51/3.70 (assume a778 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a) (not (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) T_a)))))
% 3.51/3.70 (assume a779 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) T_a) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) T_a)))))
% 3.51/3.70 (assume a780 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_b T_a)))))
% 3.51/3.70 (assume a781 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a) V_b T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b) V_a T_a)))))
% 3.51/3.70 (assume a782 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_A))))))
% 3.51/3.70 (assume a783 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_A))))))
% 3.51/3.70 (assume a784 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Oinsert V_b V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))))
% 3.51/3.70 (assume a785 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Oinsert V_b V_B T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_B))))))
% 3.51/3.70 (assume a786 (forall ((T_a $$unsorted) (V_t $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_t) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_t) V_A))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a787 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))))
% 3.51/3.70 (assume a788 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_A))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a789 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a790 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_A))))))
% 3.51/3.70 (assume a791 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_B))))))
% 3.51/3.70 (assume a792 (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))))
% 3.51/3.70 (assume a793 (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))))
% 3.51/3.70 (assume a794 (forall ((T_a $$unsorted) (V_c $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))))
% 3.51/3.70 (assume a795 (forall ((T_a $$unsorted) (V_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))))
% 3.51/3.70 (assume a796 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Oinsert V_b V_A T_a)))))))
% 3.51/3.70 (assume a797 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_B)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))))
% 3.51/3.70 (assume a798 (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a799 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_A)))))
% 3.51/3.70 (assume a800 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_A)))))))
% 3.51/3.70 (assume a801 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x V_A T_a)))))
% 3.51/3.70 (assume a802 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Oinsert V_a V_B T_a)))))
% 3.51/3.70 (assume a803 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x V_B T_a)))))
% 3.51/3.70 (assume a804 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))))
% 3.51/3.70 (assume a805 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))))
% 3.51/3.70 (assume a806 (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))))
% 3.51/3.70 (assume a807 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (= V_A V_B))))
% 3.51/3.70 (assume a808 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))))
% 3.51/3.70 (assume a809 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.70 (assume a810 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))))
% 3.51/3.70 (assume a811 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))))
% 3.51/3.70 (assume a812 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))))
% 3.51/3.70 (assume a813 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.70 (assume a814 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.70 (assume a815 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))))
% 3.51/3.70 (assume a816 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))))
% 3.51/3.70 (assume a817 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x_H) V_y_H))))))
% 3.51/3.70 (assume a818 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x_H) V_y_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))))
% 3.51/3.70 (assume a819 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_z)) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))))
% 3.51/3.70 (assume a820 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_z))) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.70 (assume a821 (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z) V_y))) (not (tptp.c_lessequals V_y V_x T_a)))))
% 3.51/3.70 (assume a822 (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z) V_x)) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))))))
% 3.51/3.70 (assume a823 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_b)))))))
% 3.51/3.70 (assume a824 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a825 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a826 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c)))))))
% 3.51/3.70 (assume a827 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a828 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a829 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))))
% 3.51/3.70 (assume a830 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))))
% 3.51/3.70 (assume a831 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_x))))))
% 3.51/3.70 (assume a832 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_x))))))
% 3.51/3.70 (assume a833 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a834 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))))
% 3.51/3.70 (assume a835 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)))))))
% 3.51/3.70 (assume a836 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a837 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.c_lessequals V_y V_x T_a))))
% 3.51/3.70 (assume a838 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))))
% 3.51/3.70 (assume a839 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x)) (tptp.c_lessequals V_x V_x T_a))))
% 3.51/3.70 (assume a840 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.c_lessequals V_y V_x T_a)))))
% 3.51/3.70 (assume a841 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))))
% 3.51/3.70 (assume a842 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))))))
% 3.51/3.70 (assume a843 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)) (tptp.c_lessequals V_x V_y T_a))))
% 3.51/3.70 (assume a844 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))))
% 3.51/3.70 (assume a845 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 3.51/3.70 (assume a846 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 3.51/3.70 (assume a847 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_a))))))
% 3.51/3.70 (assume a848 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_b))))))
% 3.51/3.70 (assume a849 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)))))))
% 3.51/3.70 (assume a850 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)))))))
% 3.51/3.70 (assume a851 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) V_b))))))
% 3.51/3.70 (assume a852 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_b)) V_a))))))
% 3.51/3.70 (assume a853 (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))))
% 3.51/3.70 (assume a854 (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))))
% 3.51/3.70 (assume a855 (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))))
% 3.51/3.70 (assume a856 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))
% 3.51/3.70 (assume a857 (forall ((V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))
% 3.51/3.70 (assume a858 (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n))))))
% 3.51/3.70 (assume a859 (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_nat) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y))))))
% 3.51/3.70 (assume a860 (forall ((V_m $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))))
% 3.51/3.70 (assume a861 (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))))
% 3.51/3.70 (assume a862 (forall ((V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) V_A))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a863 (forall ((V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_y (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))))
% 3.51/3.70 (assume a864 (forall ((V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_y (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a865 (forall ((V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_y (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r)))))
% 3.51/3.70 (assume a866 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_f T_a T_b (tptp.tc_fun T_b T_b)) V_g T_a T_b T_b)) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_g) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool))))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.70 (assume a867 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a868 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))
% 3.51/3.70 (assume a869 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b)))))))
% 3.51/3.70 (assume a870 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))))))
% 3.51/3.70 (assume a871 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Osgn__class_Osgn V_a T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a872 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Osgn__class_Osgn V_a T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a873 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))))))
% 3.51/3.70 (assume a874 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a875 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a876 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a877 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a878 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a879 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Osgn__class_Osgn V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a880 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Osgn__class_Osgn V_a T_a)))))))
% 3.51/3.70 (assume a881 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a882 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a883 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a884 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a885 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a)))))))
% 3.51/3.70 (assume a886 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 3.51/3.70 (assume a887 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a888 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a889 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a890 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a891 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a892 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a893 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a894 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a895 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a896 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a897 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a898 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x))))))
% 3.51/3.70 (assume a899 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))
% 3.51/3.70 (assume a900 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a901 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))
% 3.51/3.70 (assume a902 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))
% 3.51/3.70 (assume a903 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))
% 3.51/3.70 (assume a904 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))
% 3.51/3.70 (assume a905 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 3.51/3.70 (assume a906 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 3.51/3.70 (assume a907 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_c) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 3.51/3.70 (assume a908 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 3.51/3.70 (assume a909 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a910 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)))))))
% 3.51/3.70 (assume a911 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a)))))))
% 3.51/3.70 (assume a912 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a913 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_x) (tptp.c_HOL_Oone__class_Oone T_a)))))
% 3.51/3.70 (assume a914 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a915 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a916 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))))
% 3.51/3.70 (assume a917 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))
% 3.51/3.70 (assume a918 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))))
% 3.51/3.70 (assume a919 (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_m))))))
% 3.51/3.70 (assume a920 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)))))))
% 3.51/3.70 (assume a921 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (= V_m V_n))))
% 3.51/3.70 (assume a922 (forall ((V_y $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (= V_y V_z) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_x V_z T_a T_b)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_x V_y T_a T_b)) V_r))) (not (tptp.c_Relation_Osingle__valued V_r T_a T_b)))))
% 3.51/3.70 (assume a923 (forall ((V_f $$unsorted) (V_y1 $$unsorted) (V_y2 $$unsorted) (V_z1 $$unsorted) (V_z2 $$unsorted) (T_b $$unsorted) (V_r2 $$unsorted) (T_a $$unsorted) (V_r1 $$unsorted) (T_c $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_f V_y1) V_y2) (tptp.hAPP (tptp.hAPP V_f V_z1) V_z2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_b)) (tptp.c_Pair V_y2 V_z2 T_b T_b)) V_r2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y1 V_z1 T_a T_a)) V_r1))) (not (tptp.c_Equiv__Relations_Ocongruent2 V_r1 V_r2 V_f T_a T_b T_c)))))
% 3.51/3.70 (assume a924 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (not (= (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 V_A V_f T_a T_b)) (tptp.c_HOL_Ozero__class_Ozero T_b))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) V_A) (tptp.c_HOL_Ozero__class_Ozero T_b)))))
% 3.51/3.70 (assume a925 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_f) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a926 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) (tptp.c_COMBB (tptp.c_HOL_Ouminus__class_Ouminus T_a) V_f T_a T_a T_b)) V_A) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_f) V_A))))))
% 3.51/3.70 (assume a927 (forall ((T_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_f) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) (tptp.c_COMBB (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r) V_f T_a T_a T_b)) V_A)))))
% 3.51/3.70 (assume a928 (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m) T_a))))
% 3.51/3.70 (assume a929 (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n) T_a))))
% 3.51/3.70 (assume a930 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a931 (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_R V_S (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_R) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_S) (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a932 (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_R) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_S) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_R V_S (tptp.tc_fun T_a tptp.tc_bool))))))
% 3.51/3.70 (assume a933 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair V_a V_b T_b T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_b T_a)))))))
% 3.51/3.70 (assume a934 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair V_a V_b T_b T_a)) V_r))))))
% 3.51/3.70 (assume a935 (forall ((T_a $$unsorted) (V_Q $$unsorted) (V_r $$unsorted) (V_xa $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 V_Q V_r T_a)) V_Q)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) V_Q))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a936 (forall ((T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 V_Q V_R T_a)) V_Q)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_Q))) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 3.51/3.70 (assume a937 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a)))))
% 3.51/3.70 (assume a938 (forall ((T_b $$unsorted) (V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.c_ATP__Linkup_Osko__Relation__XImageE__1__1 V_A V_b V_r T_b T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Relation_OImage V_r V_A T_b T_a)))))))
% 3.51/3.70 (assume a939 (forall ((T_b $$unsorted) (V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 V_A V_b V_r T_b T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Relation_OImage V_r V_A T_b T_a)))))))
% 3.51/3.70 (assume a940 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_x) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_x) (tptp.c_Transitive__Closure_Ortrancl V_R T_a)))))))
% 3.51/3.70 (assume a941 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_x) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_x) (tptp.c_Transitive__Closure_Ortrancl V_S T_a)))))))
% 3.51/3.70 (assume a942 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_F $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (not (= (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1 V_F V_f T_a T_b)) (tptp.c_HOL_Oone__class_Oone T_b))) (= (tptp.c_Finite__Set_Osetprod V_f V_F T_a T_b) (tptp.c_HOL_Oone__class_Oone T_b)))))
% 3.51/3.70 (assume a943 (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_Finite__Set_Osetprod V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_HOL_Oone__class_Oone T_a)))))
% 3.51/3.70 (assume a944 (forall ((T_a $$unsorted) (V_p $$unsorted) (V_s $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_p) (tptp.c_Transitive__Closure_Otrancl V_s T_a))) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_p) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))))))
% 3.51/3.70 (assume a945 (forall ((V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a946 (forall ((V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_y (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a947 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a948 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) V_x) (tptp.c_Wellfounded_Oacc V_r tptp.t_a)))))))
% 3.51/3.70 (assume a949 (forall ((V_P $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a)) (tptp.c_Wellfounded_Oacc V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a950 (forall ((T_a $$unsorted) (V_R $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 V_R V_x T_a)) (tptp.c_Wellfounded_Oacc V_R T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Wellfounded_Oacc V_R T_a))))))
% 3.51/3.70 (assume a951 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a952 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) V_x) (tptp.c_Wellfounded_Oacc V_r tptp.t_a)))))))
% 3.51/3.70 (assume a953 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Wellfounded_Oacc V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 V_r V_x T_a)) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a954 (forall ((V_P $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a)) (tptp.c_Wellfounded_Oacc V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a955 (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) (tptp.c_Relation_Orel__comp V_S V_R T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a)))))
% 3.51/3.70 (assume a956 (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) (tptp.c_Relation_Orel__comp V_S V_R T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a)))))
% 3.51/3.70 (assume a957 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Otrancl V_r T_a) V_r T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)))))
% 3.51/3.70 (assume a958 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a959 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))
% 3.51/3.70 (assume a960 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))
% 3.51/3.70 (assume a961 (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Orefl__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a)))
% 3.51/3.70 (assume a962 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a963 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))))
% 3.51/3.70 (assume a964 (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_Oconverse V_r T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a)))
% 3.51/3.70 (assume a965 (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_OId T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a966 (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_OId T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a967 (forall ((T_a $$unsorted)) (tptp.c_Relation_Orefl__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Relation_OId T_a) T_a)))
% 3.51/3.70 (assume a968 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Relation_OImage (tptp.c_Relation_OId__on V_A T_a) V_B T_a T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))
% 3.51/3.70 (assume a969 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a)))))
% 3.51/3.70 (assume a970 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)))))
% 3.51/3.70 (assume a971 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osgn__if T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x))) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)))))
% 3.51/3.70 (assume a972 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a973 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a974 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_HOL_Oone__class_Oone T_a)))))))
% 3.51/3.70 (assume a975 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) V_A) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 V_A V_f T_a T_b)) V_A)))))
% 3.51/3.70 (assume a976 (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_Power_Opower__class_Opower V_a V_m T_a)) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))))))
% 3.51/3.70 (assume a977 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_a V_N T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_N))))))
% 3.51/3.70 (assume a978 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_Power_Opower__class_Opower V_b V_x T_a)) (tptp.c_Power_Opower__class_Opower V_b V_y T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))))))
% 3.51/3.70 (assume a979 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_Power_Opower__class_Opower V_b V_x T_a)) (tptp.c_Power_Opower__class_Opower V_b V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))))))
% 3.51/3.70 (assume a980 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_b) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_b) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1 V_A V_f T_a T_b))))))))
% 3.51/3.70 (assume a981 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_f) V_A)) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Otimes__class_Otimes T_a) V_f T_a (tptp.tc_fun T_a T_a) T_b) T_b T_a T_a) V_r)) V_A)))))
% 3.51/3.70 (assume a982 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_f) V_A)) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oinverse__class_Odivide T_a) V_f T_a (tptp.tc_fun T_a T_a) T_b) T_b T_a T_a) V_r)) V_A)))))
% 3.51/3.70 (assume a983 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_i $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_b)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP V_f V_i) (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b) T_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.70 (assume a984 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_Ominus__class_Ominus T_a) V_f T_a (tptp.tc_fun T_a T_a) T_b) V_g T_b T_a T_a)) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_f) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_g) V_A))))))
% 3.51/3.70 (assume a985 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_Oplus__class_Oplus T_a) V_f T_a (tptp.tc_fun T_a T_a) T_b) V_g T_b T_a T_a)) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_f) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_g) V_A))))))
% 3.51/3.70 (assume a986 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_F $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.c_Finite__Set_Osetprod V_f V_F T_a T_b) (tptp.c_HOL_Oone__class_Oone T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1 V_F V_f T_a T_b)) V_F)))))
% 3.51/3.70 (assume a987 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_b)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_b)) (not (= (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b) (tptp.c_HOL_Ozero__class_Ozero T_b))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1 V_A V_f T_a T_b)) (tptp.c_HOL_Ozero__class_Ozero T_b)))))
% 3.51/3.70 (assume a988 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 V_A V_B V_c T_a T_b)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) V_c) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b)))))))
% 3.51/3.70 (assume a989 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 V_a V_b V_r T_a) V_b T_a T_a)) V_r)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a990 (forall ((T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 V_r V_x V_z T_a) V_z T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (= V_x V_z) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_z T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a991 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 V_r V_x V_z T_a) T_a T_a)) V_r)) (= V_x V_z) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_z T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a992 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 V_P V_b V_r T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a993 (forall ((V_P $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 V_P V_b V_r T_a) V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a994 (forall ((V_P $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 V_P V_a V_r T_a) T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a995 (forall ((V_P $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_b)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 V_P V_a V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a996 (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_z V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y V_z T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_z T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))) (not (tptp.c_Relation_Osingle__valued V_r T_a T_a)))))
% 3.51/3.70 (assume a997 (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_a1 (tptp.v_sko__Transitive__Closure__Xrtrancl__Xcases__1 V_a1 V_a2 V_r) tptp.t_a tptp.t_a)) (tptp.c_Transitive__Closure_Ortrancl V_r tptp.t_a))) (= V_a2 V_a1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a)) (tptp.c_Transitive__Closure_Ortrancl V_r tptp.t_a)))))))
% 3.51/3.70 (assume a998 (forall ((V_P $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_b)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 V_P V_a V_r T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a999 (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair (tptp.v_sko__Transitive__Closure__Xrtrancl__Xcases__1 V_a1 V_a2 V_r) V_a2 tptp.t_a tptp.t_a)) V_r)) (= V_a2 V_a1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a)) (tptp.c_Transitive__Closure_Ortrancl V_r tptp.t_a)))))))
% 3.51/3.70 (assume a1000 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 V_P V_b V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP V_P V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a1001 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 V_a V_b V_r T_a) T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a1002 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 V_P V_r T_a) T_a T_a)) V_r))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a1003 (forall ((V_P $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xa)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 V_P V_r T_a) T_a T_a)) V_r))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a1004 (forall ((V_P $$unsorted) (V_Ra $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_Ra)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y (tptp.c_List_Osko__Recdef__Xtfl__wf__induct__1__1 V_P V_R T_a) T_a T_a)) V_R))) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 3.51/3.70 (assume a1005 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 V_P V_r T_a) T_a T_a)) V_r))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a1006 (forall ((T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_Finite__Set_Osetsum T_c T_a) V_f (tptp.tc_fun T_c T_a) (tptp.tc_fun (tptp.tc_fun T_c tptp.tc_bool) T_a) T_b) T_b (tptp.tc_fun T_c tptp.tc_bool) T_a) V_B)) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_c T_a) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_Finite__Set_Osetsum T_b T_a) (tptp.c_COMBC V_f T_b T_c T_a) (tptp.tc_fun T_b T_a) (tptp.tc_fun (tptp.tc_fun T_b tptp.tc_bool) T_a) T_c) T_c (tptp.tc_fun T_b tptp.tc_bool) T_a) V_A)) V_B)))))
% 3.51/3.70 (assume a1007 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) V_r))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 V_r T_a) T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))))))
% 3.51/3.70 (assume a1008 (forall ((T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 V_r V_x V_z T_a) V_z T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_z T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_z T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))))))
% 3.51/3.70 (assume a1009 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_R $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 V_R V_x V_y T_a) T_a T_a)) V_R)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_R T_a)))))))
% 3.51/3.70 (assume a1010 (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_a1 (tptp.v_sko__Transitive__Closure__Xtrancl__Xcases__1 V_a1 V_a2 V_r) tptp.t_a tptp.t_a)) (tptp.c_Transitive__Closure_Otrancl V_r tptp.t_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a)) (tptp.c_Transitive__Closure_Otrancl V_r tptp.t_a)))))))
% 3.51/3.70 (assume a1011 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))))
% 3.51/3.70 (assume a1012 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 V_a V_b V_r T_a) V_b T_a T_a)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))))))
% 3.51/3.70 (assume a1013 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 V_a V_b V_r T_a) T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))))))
% 3.51/3.70 (assume a1014 (forall ((T_a $$unsorted) (V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 V_R V_x V_y T_a) V_y T_a T_a)) V_R)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_R T_a)))))))
% 3.51/3.70 (assume a1015 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 V_r V_x V_z T_a) T_a T_a)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_z T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_z T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))))))
% 3.51/3.70 (assume a1016 (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair (tptp.v_sko__Transitive__Closure__Xtrancl__Xcases__1 V_a1 V_a2 V_r) V_a2 tptp.t_a tptp.t_a)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a)) (tptp.c_Transitive__Closure_Otrancl V_r tptp.t_a)))))))
% 3.51/3.70 (assume a1017 (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_Finite__Set_Osetprod (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_Otimes__class_Otimes T_a) V_f T_a (tptp.tc_fun T_a T_a) T_b) V_g T_b T_a T_a) V_A T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Finite__Set_Osetprod V_f V_A T_b T_a)) (tptp.c_Finite__Set_Osetprod V_g V_A T_b T_a))))))
% 3.51/3.70 (assume a1018 (forall ((T_c $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_c T_b)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 V_a V_c V_r V_s T_a T_b T_c) V_c T_c T_b)) V_s)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_c T_a T_b)) (tptp.c_Relation_Orel__comp V_r V_s T_a T_c T_b)))))))
% 3.51/3.70 (assume a1019 (forall ((T_a $$unsorted) (T_c $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_c)) (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 V_a V_c V_r V_s T_a T_b T_c) T_a T_c)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_c T_a T_b)) (tptp.c_Relation_Orel__comp V_r V_s T_a T_c T_b)))))))
% 3.51/3.70 (assume a1020 (forall ((V_p $$unsorted) (T_a $$unsorted)) (or (= V_p (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XIdE__1__1 V_p T_a) (tptp.c_ATP__Linkup_Osko__Relation__XIdE__1__1 V_p T_a) T_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_p) (tptp.c_Relation_OId T_a)))))))
% 3.51/3.70 (assume a1021 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b tptp.tc_nat) V_f) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) (tptp.c_COMBB (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_f tptp.tc_nat T_a T_b)) V_A)))))
% 3.51/3.70 (assume a1022 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 V_r T_a)) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a1023 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 V_r T_a)) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a1024 (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.c_Finite__Set_Osetprod V_f V_A T_b tptp.tc_nat)) (tptp.c_Finite__Set_Osetprod (tptp.c_COMBB (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_f tptp.tc_nat T_a T_b) V_A T_b T_a)))))
% 3.51/3.70 (assume a1025 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Relation__XId__onE__1__1 V_A V_c T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_c) (tptp.c_Relation_OId__on V_A T_a)))))))
% 3.51/3.70 (assume a1026 (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= V_c (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XId__onE__1__1 V_A V_c T_a) (tptp.c_ATP__Linkup_Osko__Relation__XId__onE__1__1 V_A V_c T_a) T_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_c) (tptp.c_Relation_OId__on V_A T_a)))))))
% 3.51/3.70 (assume a1027 (forall ((V_f $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted)) (or (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_List_Osko__Recdef__Xcuts__eq__1__1 V_f V_g V_r V_x T_a T_b) V_x T_a T_a)) V_r)))))
% 3.51/3.70 (assume a1028 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))))
% 3.51/3.70 (assume a1029 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))))
% 3.51/3.70 (assume a1030 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)))))
% 3.51/3.70 (assume a1031 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_OId T_a) (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Ortrancl V_r T_a) V_r T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)))))
% 3.51/3.70 (assume a1032 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals V_r (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 3.51/3.70 (assume a1033 (= (tptp.c_Relation_ORange tptp.v_r tptp.t_a tptp.t_b) (tptp.c_Relation_ODomain (tptp.c_Relation_Oconverse tptp.v_r tptp.t_a tptp.t_b) tptp.t_b tptp.t_a)))
% 3.51/3.70 (assume a1034 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oirrefl V_r T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 V_r T_a) T_a T_a)) V_r)))))
% 3.51/3.70 (assume a1035 (forall ((V_r2 $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_r1 $$unsorted)) (or (tptp.c_Equiv__Relations_Ocongruent V_r2 (tptp.hAPP V_f V_a) T_b T_c) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Equiv__Relations_Ocongruent2 V_r1 V_r2 V_f T_a T_b T_c)) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r1 T_a)))))
% 3.51/3.70 (assume a1036 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_f $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Wellfounded_Omlex__prod V_f V_R T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_R))) (not (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) tptp.tc_nat)))))
% 3.51/3.70 (assume a1037 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Nitpick_Orefl_H V_r T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 V_r T_a) (tptp.c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 V_r T_a) T_a T_a)) V_r))))))
% 3.51/3.70 (assume a1038 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_Power_Opower__class_Opower V_a V_N T_a)) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_N))))))
% 3.51/3.70 (assume a1039 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_b) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1 V_A V_f T_a T_b)) V_A)))))
% 3.51/3.70 (assume a1040 (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n)))))))
% 3.51/3.70 (assume a1041 (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n))))))
% 3.51/3.70 (assume a1042 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_b)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_b)) (not (= (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b) (tptp.c_HOL_Ozero__class_Ozero T_b))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1 V_A V_f T_a T_b)) V_A)))))
% 3.51/3.70 (assume a1043 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_Q $$unsorted) (V_R $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) V_Q))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 V_Q V_R T_a) T_a T_a)) V_R))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_Q))) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 3.51/3.70 (assume a1044 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_Q $$unsorted) (V_r $$unsorted) (V_xa $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) V_Q))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 V_Q V_r T_a) T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) V_Q))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a1045 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XImageE__1__1 V_A V_b V_r T_b T_a) V_b T_b T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Relation_OImage V_r V_A T_b T_a)))))))
% 3.51/3.70 (assume a1046 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 V_A V_b V_r T_b T_a) V_b T_b T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Relation_OImage V_r V_A T_b T_a)))))))
% 3.51/3.70 (assume a1047 (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (= (tptp.c_Finite__Set_Osetprod (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_Oinverse__class_Odivide T_b) V_f T_b (tptp.tc_fun T_b T_b) T_a) V_g T_a T_b T_b) V_A T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_b) (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b)) (tptp.c_Finite__Set_Osetprod V_g V_A T_a T_b))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.70 (assume a1048 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__XDomainE__1__1 V_a V_r T_a T_b) T_a T_b)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_ODomain V_r T_a T_b)))))))
% 3.51/3.70 (assume a1049 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 V_a V_r T_a T_b) T_a T_b)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_ODomain V_r T_a T_b)))))))
% 3.51/3.70 (assume a1050 (forall ((T_a $$unsorted) (V_R $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 V_R V_x T_a) V_x T_a T_a)) V_R)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Wellfounded_Oacc V_R T_a))))))
% 3.51/3.70 (assume a1051 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a) T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a1052 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_y (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r) tptp.t_a tptp.t_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) V_x) (tptp.c_Wellfounded_Oacc V_r tptp.t_a)))))))
% 3.51/3.70 (assume a1053 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Wellfounded_Oacc V_r T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 V_r V_x T_a) V_x T_a T_a)) V_r)))))
% 3.51/3.70 (assume a1054 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_ya $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) V_ya) (tptp.c_Wellfounded_Oacc V_r tptp.t_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_ya (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r) tptp.t_a tptp.t_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) V_x) (tptp.c_Wellfounded_Oacc V_r tptp.t_a)))))))
% 3.51/3.70 (assume a1055 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_y (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r) tptp.t_a tptp.t_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) V_x) (tptp.c_Wellfounded_Oacc V_r tptp.t_a)))))))
% 3.51/3.70 (assume a1056 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_ya $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) V_ya) (tptp.c_Wellfounded_Oacc V_r tptp.t_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.t_a tptp.t_a)) (tptp.c_Pair V_ya (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r) tptp.t_a tptp.t_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) V_x) (tptp.c_Wellfounded_Oacc V_r tptp.t_a)))))))
% 3.51/3.70 (assume a1057 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a) T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a1058 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))) (not (tptp.c_Wellfounded_Owf (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a)))))
% 3.51/3.70 (assume a1059 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a1060 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XRangeE__1__1 V_b V_r T_a T_b) V_b T_b T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Relation_ORange V_r T_b T_a)))))))
% 3.51/3.70 (assume a1061 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 V_a V_r T_a T_b) V_a T_b T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_ORange V_r T_b T_a)))))))
% 3.51/3.70 (assume a1062 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_R $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 V_R V_x V_y T_a) T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_R T_a)))))))
% 3.51/3.70 (assume a1063 (forall ((T_a $$unsorted) (V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 V_R V_x V_y T_a) V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_R T_a)))))))
% 3.51/3.70 (assume a1064 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_S $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.c_Finite__Set_Osetprod (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_b T_a T_b (tptp.tc_fun T_b T_b)) T_a T_b T_b) V_c) V_S T_a T_b) (tptp.c_Power_Opower__class_Opower V_c (tptp.c_Finite__Set_Ocard V_S T_a) T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_S)) (not (tptp.c_Finite__Set_Ofinite V_S T_a)))))
% 3.51/3.70 (assume a1065 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) T_a T_b (tptp.tc_fun T_b T_b)) V_c) T_a T_b T_b) V_d) V_A T_a T_b) (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus (tptp.tc_fun T_a tptp.tc_bool)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_d) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_c) V_A)))))
% 3.51/3.70 (assume a1066 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) T_a T_b (tptp.tc_fun T_b T_b)) V_c) T_a T_b T_b) V_d) V_A T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_d) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_c) V_A))))))
% 3.51/3.70 (assume a1067 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) T_a T_b (tptp.tc_fun T_b T_b)) V_c) T_a T_b T_b) V_d) V_A T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_d) V_A)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_c) V_A)))))
% 3.51/3.70 (assume a1068 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_f T_a T_b (tptp.tc_fun T_b T_b)) T_a T_b T_b) (tptp.c_HOL_Ozero__class_Ozero T_b))) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))
% 3.51/3.70 (assume a1069 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Relation_Oconverse V_r T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair V_b V_a T_b T_a)) V_r))))))
% 3.51/3.70 (assume a1070 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair V_b V_a T_b T_a)) (tptp.c_Relation_Oconverse V_r T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) V_r))))))
% 3.51/3.70 (assume a1071 (forall ((V_f $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Recdef_Ocut V_f V_r V_a T_a T_b) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_a T_a T_a)) V_r))))))
% 3.51/3.70 (assume a1072 (forall ((V_f $$unsorted) (V_R $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Recdef_Ocut V_f V_R V_a T_a T_b) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_a T_a T_a)) V_R))))))
% 3.51/3.70 (assume a1073 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_S $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.c_Finite__Set_Osetprod (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_fequal T_a) V_a) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_b T_a T_b (tptp.tc_fun T_b T_b)) T_a T_b T_b) (tptp.c_HOL_Oone__class_Oone T_b)) V_S T_a T_b) (tptp.c_HOL_Oone__class_Oone T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_S)) (not (tptp.c_Finite__Set_Ofinite V_S T_a)))))
% 3.51/3.70 (assume a1074 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_S $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_fequal T_a) V_a) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_b T_a T_b (tptp.tc_fun T_b T_b)) T_a T_b T_b) (tptp.c_HOL_Ozero__class_Ozero T_b))) V_S) (tptp.hAPP V_b V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_S))) (not (tptp.c_Finite__Set_Ofinite V_S T_a)))))
% 3.51/3.70 (assume a1075 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_S $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_fequal T_a) V_a) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_b T_a T_b (tptp.tc_fun T_b T_b)) T_a T_b T_b) (tptp.c_HOL_Ozero__class_Ozero T_b))) V_S) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_S)) (not (tptp.c_Finite__Set_Ofinite V_S T_a)))))
% 3.51/3.70 (assume a1076 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_S $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.c_Finite__Set_Osetprod (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_fequal T_a) V_a) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_b T_a T_b (tptp.tc_fun T_b T_b)) T_a T_b T_b) (tptp.c_HOL_Oone__class_Oone T_b)) V_S T_a T_b) (tptp.hAPP V_b V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_S))) (not (tptp.c_Finite__Set_Ofinite V_S T_a)))))
% 3.51/3.70 (assume a1077 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_R T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Relation_ODomain V_R T_a T_a))))))
% 3.51/3.70 (assume a1078 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Relation_ODomain V_R T_a T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))))
% 3.51/3.70 (assume a1079 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Wellfounded_Oacc V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_a T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a1080 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Wellfounded_Oacc V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Wellfounded_Oacc V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_a T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a1081 (forall ((T_a $$unsorted) (V_p $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_p) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_p) V_r))))))
% 3.51/3.70 (assume a1082 (forall ((T_a $$unsorted) (V_p $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_p) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) V_p) V_r))))))
% 3.51/3.70 (assume a1083 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_c T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_c T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))))))
% 3.51/3.70 (assume a1084 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_c T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_c T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a1085 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_R T_a)))) (= V_x V_y))))
% 3.51/3.70 (assume a1086 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_R T_a))) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_R T_a)))))))
% 3.51/3.70 (assume a1087 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_R T_a))) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_R T_a)))))))
% 3.51/3.70 (assume a1088 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y V_x T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a1089 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y V_x T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))))
% 3.51/3.70 (assume a1090 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))))))
% 3.51/3.70 (assume a1091 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_c T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_c T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))))))
% 3.51/3.70 (assume a1092 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_r $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_z T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y V_z T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a1093 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Otrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))))
% 3.51/3.70 (assume a1094 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Transitive__Closure_Otrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a)))))))
% 3.51/3.70 (assume a1095 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_A T_a T_b)))))))
% 3.51/3.70 (assume a1096 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))))))
% 3.51/3.70 (assume a1097 (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_B))))))
% 3.51/3.70 (assume a1098 (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_A))))))
% 3.51/3.70 (assume a1099 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B))))))
% 3.51/3.70 (assume a1100 (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_R) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_S))) (= V_R V_S))))
% 3.51/3.70 (assume a1101 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Wellfounded_Oacc V_r T_a))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a1102 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))))
% 3.51/3.70 (assume a1103 (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite V_A T_a))))
% 3.51/3.70 (assume a1104 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym V_r T_a) (not (tptp.c_Relation_Osym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 3.51/3.70 (assume a1105 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))))
% 3.51/3.70 (assume a1106 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.c_Relation_ODomain V_r T_a T_a))))
% 3.51/3.70 (assume a1107 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_b)) (not (= (tptp.hAPP V_f V_x) (tptp.c_HOL_Ozero__class_Ozero T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b) (tptp.c_HOL_Ozero__class_Ozero T_b)))))
% 3.51/3.70 (assume a1108 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_b)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_b)) (not (= (tptp.hAPP V_f V_x) (tptp.c_HOL_Ozero__class_Ozero T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b) (tptp.c_HOL_Ozero__class_Ozero T_b)))))
% 3.51/3.70 (assume a1109 (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a1110 (forall ((T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.c_Relation_OId T_a) T_a)))
% 3.51/3.70 (assume a1111 (forall ((T_a $$unsorted) (V_R $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_OId T_a) V_R T_a T_a T_b) V_R)))
% 3.51/3.70 (assume a1112 (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp V_R (tptp.c_Relation_OId T_b) T_a T_b T_b) V_R)))
% 3.51/3.70 (assume a1113 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oantisym (tptp.c_Relation_OId__on V_A T_a) T_a)))
% 3.51/3.70 (assume a1114 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 3.51/3.70 (assume a1115 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A V_r T_a) (not (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 3.51/3.70 (assume a1116 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 3.51/3.70 (assume a1117 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))))
% 3.51/3.70 (assume a1118 (forall ((V_R $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) T_a) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 3.51/3.70 (assume a1119 (forall ((V_R $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_R T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) T_a)))))
% 3.51/3.70 (assume a1120 (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Relation_OImage (tptp.c_Relation_OId T_a) V_A T_a T_a) V_A)))
% 3.51/3.70 (assume a1121 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))))
% 3.51/3.70 (assume a1122 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)))
% 3.51/3.70 (assume a1123 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Relation_Oconverse V_r T_a T_a) V_r) (not (tptp.c_Relation_Osym V_r T_a)))))
% 3.51/3.70 (assume a1124 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Relation_Oconverse V_r T_a T_a) V_r)) (tptp.c_Relation_Osym V_r T_a))))
% 3.51/3.70 (assume a1125 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.c_Relation_ORange V_r T_a T_a))))
% 3.51/3.70 (assume a1126 (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_Finite__Set_Osetprod V_f V_A T_b T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_Finite__Set_Ofinite V_A T_b))))
% 3.51/3.70 (assume a1127 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.c_Finite__Set_Osetprod V_f V_A T_a T_b) (tptp.c_HOL_Oone__class_Oone T_b)) (tptp.c_Finite__Set_Ofinite V_A T_a))))
% 3.51/3.70 (assume a1128 (forall ((V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Orel__comp V_r V_s T_b T_c T_a) T_b T_a) (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_s T_c T_a) (tptp.c_Relation_Oconverse V_r T_b T_c) T_a T_c T_b))))
% 3.51/3.70 (assume a1129 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.c_Relation_OId__on V_A T_a) T_a)))
% 3.51/3.70 (assume a1130 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_OId__on V_A T_a) T_a)))
% 3.51/3.70 (assume a1131 (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a1132 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp V_r (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a T_a T_a) (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Ortrancl V_r T_a) V_r T_a T_a T_a))))
% 3.51/3.70 (assume a1133 (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Relation_Osym V_r T_a)))))
% 3.51/3.70 (assume a1134 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))
% 3.51/3.70 (assume a1135 (forall ((T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_OId T_a) T_a T_a) (tptp.c_Relation_OId T_a))))
% 3.51/3.70 (assume a1136 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a1137 (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (V_T $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Orel__comp V_R V_S T_a T_d T_c) V_T T_a T_c T_b) (tptp.c_Relation_Orel__comp V_R (tptp.c_Relation_Orel__comp V_S V_T T_d T_c T_b) T_a T_d T_b))))
% 3.51/3.70 (assume a1138 (forall ((V_R $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oinv__image V_R V_f T_b T_a) T_a T_a) (tptp.c_Relation_Oinv__image (tptp.c_Relation_Oconverse V_R T_b T_b) V_f T_b T_a))))
% 3.51/3.70 (assume a1139 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a))))
% 3.51/3.70 (assume a1140 (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n))) (= V_m V_n))))
% 3.51/3.70 (assume a1141 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_OId__on V_A T_a) T_a T_a) (tptp.c_Relation_OId__on V_A T_a))))
% 3.51/3.70 (assume a1142 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) V_r)) (tptp.c_Equiv__Relations_Oequiv (tptp.c_Relation_ODomain V_r T_a T_a) V_r T_a))))
% 3.51/3.70 (assume a1143 (forall ((T_a $$unsorted)) (tptp.c_Relation_Oantisym (tptp.c_Relation_OId T_a) T_a)))
% 3.51/3.70 (assume a1144 (forall ((V_f $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Wellfounded_Omlex__prod V_f V_R T_a) T_a) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 3.51/3.70 (assume a1145 (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a) (tptp.c_Relation_ODomain V_r T_a T_b))))
% 3.51/3.70 (assume a1146 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)))
% 3.51/3.70 (assume a1147 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))))
% 3.51/3.70 (assume a1148 (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a) V_r)))
% 3.51/3.70 (assume a1149 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))
% 3.51/3.70 (assume a1150 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_f) V_A) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_Finite__Set_Ofinite V_A T_b))))
% 3.51/3.70 (assume a1151 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) V_A) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.c_Finite__Set_Ofinite V_A T_a))))
% 3.51/3.70 (assume a1152 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) V_r) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a1153 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))
% 3.51/3.70 (assume a1154 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 3.51/3.70 (assume a1155 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)))))
% 3.51/3.70 (assume a1156 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a1157 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Oone__class_Oone T_a))))))
% 3.51/3.70 (assume a1158 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a T_a))))
% 3.51/3.70 (assume a1159 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Osym V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a1160 (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_Oconverse V_r T_b T_a) T_a T_b) (tptp.c_Relation_ORange V_r T_b T_a))))
% 3.51/3.70 (assume a1161 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Ortrancl V_r T_a) V_r T_a T_a T_a))))
% 3.51/3.70 (assume a1162 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_Orel__comp V_r (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a T_a T_a))))
% 3.51/3.70 (assume a1163 (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange V_r T_b T_a) (tptp.c_Relation_ODomain (tptp.c_Relation_Oconverse V_r T_b T_a) T_a T_b))))
% 3.51/3.70 (assume a1164 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.c_Relation_Ototal__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 3.51/3.70 (assume a1165 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))))
% 3.51/3.70 (assume a1166 (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x))))))
% 3.51/3.70 (assume a1167 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))))
% 3.51/3.70 (assume a1168 (forall ((V_f $$unsorted) (T_a $$unsorted)) (tptp.c_Wellfounded_Owf (tptp.c_Wellfounded_Omeasure V_f T_a) T_a)))
% 3.51/3.70 (assume a1169 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Transitive__Closure_Otrancl V_R T_a) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))
% 3.51/3.70 (assume a1170 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))))
% 3.51/3.70 (assume a1171 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair V_b V_a T_b T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Relation_Oconverse V_r T_b T_a)))))))
% 3.51/3.70 (assume a1172 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) V_r))) (not (tptp.c_Relation_Oirrefl V_r T_a)))))
% 3.51/3.70 (assume a1173 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_c T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_c T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))))))
% 3.51/3.70 (assume a1174 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_c T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_c T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))))))
% 3.51/3.70 (assume a1175 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_c T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_c T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a1176 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_c T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_c T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))))))
% 3.51/3.70 (assume a1177 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))))))
% 3.51/3.70 (assume a1178 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_c T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_c T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))))
% 3.51/3.70 (assume a1179 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_a T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a)))))
% 3.51/3.70 (assume a1180 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_R $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_R T_a)))))
% 3.51/3.70 (assume a1181 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_a T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_x T_a T_a)) V_r))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a1182 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y V_x T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Relation_Oantisym V_r T_a)))))
% 3.51/3.70 (assume a1183 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_a T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))) (not (tptp.c_Relation_Oantisym V_r T_a)))))
% 3.51/3.70 (assume a1184 (forall ((V_f $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_f V_y) (tptp.hAPP V_f V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y V_z T_a T_a)) V_r))) (not (tptp.c_Equiv__Relations_Ocongruent V_r V_f T_a T_b)))))
% 3.51/3.70 (assume a1185 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Relation_OId__on V_A T_a)))))))
% 3.51/3.70 (assume a1186 (forall ((V_f $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b))) (= (tptp.hAPP V_f V_y) (tptp.hAPP V_g V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y V_x T_a T_a)) V_r))))))
% 3.51/3.70 (assume a1187 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Relation_OId T_a)))))))
% 3.51/3.70 (assume a1188 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) V_r)) (not (tptp.c_Nitpick_Orefl_H V_r T_a)))))
% 3.51/3.70 (assume a1189 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_a T_a T_a)) V_r))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 3.51/3.70 (assume a1190 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Relation_Oinv__image V_r V_f T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_b)) (tptp.c_Pair (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) T_b T_b)) V_r))))))
% 3.51/3.70 (assume a1191 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_b)) (tptp.c_Pair (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) T_b T_b)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Relation_Oinv__image V_r V_f T_b T_a)))))))
% 3.51/3.70 (assume a1192 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y V_x T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Relation_Osym V_r T_a)))))
% 3.51/3.70 (assume a1193 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_a T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))) (not (tptp.c_Relation_Osym V_r T_a)))))
% 3.51/3.70 (assume a1194 (forall ((T_a $$unsorted) (T_c $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_c)) (tptp.c_Pair V_a V_c T_a T_c)) (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_c)) (tptp.c_Pair V_b V_c T_b T_c)) V_s))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) V_r))))))
% 3.51/3.70 (assume a1195 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_R $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_c T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_R T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_c T_a T_a)) V_R))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_R))))))
% 3.51/3.70 (assume a1196 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_c T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_b V_c T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) (tptp.c_Transitive__Closure_Otrancl V_r T_a)))))))
% 3.51/3.70 (assume a1197 (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) (tptp.c_Relation_OId T_a)))))
% 3.51/3.70 (assume a1198 (forall ((T_a $$unsorted) (V_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_a T_a T_a)) (tptp.c_Relation_OId T_a)))))
% 3.51/3.70 (assume a1199 (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n)))))))
% 3.51/3.70 (assume a1200 (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n))))))
% 3.51/3.70 (assume a1201 (forall ((V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 V_a V_b))) (= V_a V_b))))
% 3.51/3.70 (assume a1202 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_S $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.c_Finite__Set_Osetprod (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_b T_a T_b (tptp.tc_fun T_b T_b)) T_a T_b T_b) (tptp.c_HOL_Oone__class_Oone T_b)) V_S T_a T_b) (tptp.c_HOL_Oone__class_Oone T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_S)) (not (tptp.c_Finite__Set_Ofinite V_S T_a)))))
% 3.51/3.70 (assume a1203 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_S $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_b T_a T_b (tptp.tc_fun T_b T_b)) T_a T_b T_b) (tptp.c_HOL_Ozero__class_Ozero T_b))) V_S) (tptp.hAPP V_b V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_S))) (not (tptp.c_Finite__Set_Ofinite V_S T_a)))))
% 3.51/3.70 (assume a1204 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_S $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_b)) (= (tptp.c_Finite__Set_Osetprod (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_b T_a T_b (tptp.tc_fun T_b T_b)) T_a T_b T_b) (tptp.c_HOL_Oone__class_Oone T_b)) V_S T_a T_b) (tptp.hAPP V_b V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_S))) (not (tptp.c_Finite__Set_Ofinite V_S T_a)))))
% 3.51/3.70 (assume a1205 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_S $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) V_b T_a T_b (tptp.tc_fun T_b T_b)) T_a T_b T_b) (tptp.c_HOL_Ozero__class_Ozero T_b))) V_S) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_S)) (not (tptp.c_Finite__Set_Ofinite V_S T_a)))))
% 3.51/3.70 (assume a1206 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b (tptp.tc_fun T_b T_b)) T_a) T_a T_b (tptp.tc_fun T_b T_b)) V_c) T_a T_b T_b) V_d) V_A T_a T_b) V_B) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_d) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_c) V_A))))))
% 3.51/3.70 (assume a1207 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))))
% 3.51/3.70 (assume a1208 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))))
% 3.51/3.70 (assume a1209 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Wellfounded_Oacc V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a1210 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) (tptp.c_Wellfounded_Oacc V_r T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y V_a T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Wellfounded_Oacc V_r T_a)))))))
% 3.51/3.70 (assume a1211 (forall ((T_b $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.c_Relation_OImage V_r V_A T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))))
% 3.51/3.70 (assume a1212 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Relation_OImage V_r V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair V_x V_b T_b T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))))
% 3.51/3.70 (assume a1213 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Relation_OId__on V_A T_a)))))))
% 3.51/3.70 (assume a1214 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) (tptp.c_Relation_OId__on V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))))
% 3.51/3.70 (assume a1215 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a1216 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 3.51/3.70 (assume a1217 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_ORange V_r T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair V_x V_a T_b T_a)) V_r))))))
% 3.51/3.70 (assume a1218 (forall ((T_b $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.c_Relation_ORange V_r T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) V_r))))))
% 3.51/3.70 (assume a1219 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_ODomain V_r T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_x T_a T_b)) V_r))))))
% 3.51/3.70 (assume a1220 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_ODomain V_r T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) V_r))))))
% 3.51/3.70 (assume a1221 (forall ((T_b $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b)))))))
% 3.51/3.70 (assume a1222 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b)))))))
% 3.51/3.70 (assume a1223 (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_xa V_x T_a T_a)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_xa T_a T_a)) V_r)) (= V_x V_xa) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))))
% 3.51/3.70 (assume a1224 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 3.51/3.70 (assume a1225 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 3.51/3.70 (assume a1226 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 3.51/3.70 (assume a1227 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_a T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 3.51/3.70 (assume a1228 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_f $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Wellfounded_Omlex__prod V_f V_R T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y)))))))
% 3.51/3.70 (assume a1229 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_f $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Wellfounded_Omeasure V_f T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y)))))))
% 3.51/3.70 (assume a1230 (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Wellfounded_Omeasure V_f T_a)))))))
% 3.51/3.70 (assume a1231 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))))))
% 3.51/3.70 (assume a1232 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))))
% 3.51/3.70 (assume a1233 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))))))
% 3.51/3.70 (assume a1234 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))))))
% 3.51/3.70 (assume a1235 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omktop V_L) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L))) (= V_x V_y) (= V_x V_z))))
% 3.51/3.70 (assume a1236 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omktop V_L) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L))) (= V_y V_z) (= V_x V_z))))
% 3.51/3.70 (assume a1237 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (or (not (= (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Pair V_a_H V_b_H T_a T_b))) (= V_b V_b_H))))
% 3.51/3.70 (assume a1238 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (or (not (= (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Pair V_a_H V_b_H T_a T_b))) (= V_a V_a_H))))
% 3.51/3.70 (assume a1239 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_c____ tptp.v_d____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F tptp.v_P____))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_c____ tptp.v_d____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omktop tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_fequal tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Oabove tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_c____) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omkbot tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))))))))
% 3.51/3.70 (assume a1240 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_c____ tptp.v_d____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omktop tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_fequal tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Oabove tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_c____) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omkbot tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_c____ tptp.v_d____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F tptp.v_P____))))))
% 3.51/3.70 (assume a1241 (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omktop V_L) V_x))))))
% 3.51/3.70 (assume a1242 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omktop V_L) V_x))))))
% 3.51/3.70 (assume a1243 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)))))
% 3.51/3.70 (assume a1244 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))))
% 3.51/3.70 (assume a1245 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y))))
% 3.51/3.70 (assume a1246 (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y)) (= V_x V_y))))
% 3.51/3.70 (assume a1247 (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_m)) (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)))))
% 3.51/3.70 (assume a1248 (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (= V_m V_n))))
% 3.51/3.70 (assume a1249 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))))
% 3.51/3.70 (assume a1250 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y))))
% 3.51/3.70 (assume a1251 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L)) (= V_y V_z) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omktop V_L) V_z)))))))
% 3.51/3.70 (assume a1252 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))))
% 3.51/3.70 (assume a1253 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))))
% 3.51/3.70 (assume a1254 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))))
% 3.51/3.70 (assume a1255 (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_n)))))
% 3.51/3.70 (assume a1256 (forall ((V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_x)))))
% 3.51/3.70 (assume a1257 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (or (= V_x V_y) (= V_y V_x) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omkbot V_L) V_x))))))
% 3.51/3.70 (assume a1258 (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omkbot V_L) V_x))))))
% 3.51/3.70 (assume a1259 (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omkbot V_L) V_x))))))
% 3.51/3.70 (assume a1260 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))))
% 3.51/3.70 (assume a1261 (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))))))
% 3.51/3.70 (assume a1262 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omkbot V_L) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L))) (= V_x V_y) (= V_y V_z))))
% 3.51/3.70 (assume a1263 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omkbot V_L) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L))) (= V_x V_z) (= V_y V_z))))
% 3.51/3.70 (assume a1264 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))))
% 3.51/3.70 (assume a1265 (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S))))))
% 3.51/3.70 (assume a1266 (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))))
% 3.51/3.70 (assume a1267 (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))))
% 3.51/3.70 (assume a1268 (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBS V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))))
% 3.51/3.70 (assume a1269 (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (or (= V_xa V_x) (= V_xa V_x) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omktop V_L) V_x))))))
% 3.51/3.70 (assume a1270 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L)) (= V_x V_z) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Omkbot V_L) V_z)))))))
% 3.51/3.70 (assume a1271 (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat)))))
% 3.51/3.70 (assume a1272 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_e____ tptp.v_d____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omktop tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_fequal tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Oabove tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_c____) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omkbot tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))))))
% 3.51/3.70 (assume a1273 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_e____ tptp.v_d____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omktop tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_fequal tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Oabove tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_c____) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omkbot tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))))))))
% 3.51/3.70 (assume a1274 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_e____ tptp.v_d____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omktop tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_fequal tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Oabove tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_c____) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omkbot tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)))))))
% 3.51/3.70 (assume a1275 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_prod T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))))
% 3.51/3.70 (assume a1276 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))))
% 3.51/3.70 (assume a1277 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))))
% 3.51/3.70 (assume a1278 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Odistrib__lattice T_1)))))
% 3.51/3.70 (assume a1279 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))))
% 3.51/3.70 (assume a1280 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oboolean__algebra (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Oboolean__algebra T_1)))))
% 3.51/3.70 (assume a1281 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))))
% 3.51/3.70 (assume a1282 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))))
% 3.51/3.70 (assume a1283 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))))
% 3.51/3.70 (assume a1284 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))))
% 3.51/3.70 (assume a1285 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))))
% 3.51/3.70 (assume a1286 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))))
% 3.51/3.70 (assume a1287 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))))
% 3.51/3.70 (assume a1288 (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat))
% 3.51/3.70 (assume a1289 (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat))
% 3.51/3.70 (assume a1290 (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat))
% 3.51/3.70 (assume a1291 (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat))
% 3.51/3.70 (assume a1292 (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat))
% 3.51/3.70 (assume a1293 (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat))
% 3.51/3.70 (assume a1294 (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat))
% 3.51/3.70 (assume a1295 (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat))
% 3.51/3.70 (assume a1296 (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat))
% 3.51/3.70 (assume a1297 (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat))
% 3.51/3.70 (assume a1298 (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_nat))
% 3.51/3.70 (assume a1299 (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat))
% 3.51/3.70 (assume a1300 (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat))
% 3.51/3.70 (assume a1301 (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat))
% 3.51/3.70 (assume a1302 (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat))
% 3.51/3.70 (assume a1303 (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat))
% 3.51/3.70 (assume a1304 (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat))
% 3.51/3.70 (assume a1305 (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat))
% 3.51/3.70 (assume a1306 (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat))
% 3.51/3.70 (assume a1307 (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat))
% 3.51/3.70 (assume a1308 (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat))
% 3.51/3.70 (assume a1309 (tptp.class_Lattices_Olower__semilattice tptp.tc_nat))
% 3.51/3.70 (assume a1310 (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat))
% 3.51/3.70 (assume a1311 (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat))
% 3.51/3.70 (assume a1312 (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_nat))
% 3.51/3.70 (assume a1313 (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat))
% 3.51/3.70 (assume a1314 (tptp.class_Ring__and__Field_Omult__mono tptp.tc_nat))
% 3.51/3.70 (assume a1315 (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat))
% 3.51/3.70 (assume a1316 (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat))
% 3.51/3.70 (assume a1317 (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat))
% 3.51/3.70 (assume a1318 (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat))
% 3.51/3.70 (assume a1319 (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat))
% 3.51/3.70 (assume a1320 (tptp.class_Ring__and__Field_Odvd tptp.tc_nat))
% 3.51/3.70 (assume a1321 (tptp.class_Orderings_Opreorder tptp.tc_nat))
% 3.51/3.70 (assume a1322 (tptp.class_Orderings_Olinorder tptp.tc_nat))
% 3.51/3.70 (assume a1323 (tptp.class_Lattices_Olattice tptp.tc_nat))
% 3.51/3.70 (assume a1324 (tptp.class_Orderings_Oorder tptp.tc_nat))
% 3.51/3.70 (assume a1325 (tptp.class_Orderings_Obot tptp.tc_nat))
% 3.51/3.70 (assume a1326 (tptp.class_Power_Opower tptp.tc_nat))
% 3.51/3.70 (assume a1327 (tptp.class_HOL_Oord tptp.tc_nat))
% 3.51/3.70 (assume a1328 (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool))
% 3.51/3.70 (assume a1329 (tptp.class_Lattices_Olower__semilattice tptp.tc_bool))
% 3.51/3.70 (assume a1330 (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool))
% 3.51/3.70 (assume a1331 (tptp.class_Lattices_Obounded__lattice tptp.tc_bool))
% 3.51/3.70 (assume a1332 (tptp.class_Lattices_Oboolean__algebra tptp.tc_bool))
% 3.51/3.70 (assume a1333 (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool))
% 3.51/3.70 (assume a1334 (tptp.class_Orderings_Opreorder tptp.tc_bool))
% 3.51/3.70 (assume a1335 (tptp.class_Lattices_Olattice tptp.tc_bool))
% 3.51/3.70 (assume a1336 (tptp.class_Orderings_Oorder tptp.tc_bool))
% 3.51/3.70 (assume a1337 (tptp.class_Orderings_Otop tptp.tc_bool))
% 3.51/3.70 (assume a1338 (tptp.class_Orderings_Obot tptp.tc_bool))
% 3.51/3.70 (assume a1339 (tptp.class_HOL_Oord tptp.tc_bool))
% 3.51/3.70 (assume a1340 (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBS V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))))
% 3.51/3.70 (assume a1341 (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))))
% 3.51/3.70 (assume a1342 (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))))
% 3.51/3.70 (assume a1343 (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))))
% 3.51/3.70 (assume a1344 (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y))))))
% 3.51/3.70 (step t1 (cl (=> (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)) (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat))) :rule implies_neg1)
% 3.51/3.70 (anchor :step t2)
% 3.51/3.70 (assume t2.a0 (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)))
% 3.51/3.70 (step t2.t1 (cl (or (not (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat))) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))) :rule forall_inst :args ((:= V_n tptp.v_n____)))
% 3.51/3.70 (step t2.t2 (cl (not (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat))) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)) :rule or :premises (t2.t1))
% 3.51/3.70 (step t2.t3 (cl (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)) :rule resolution :premises (t2.t2 t2.a0))
% 3.51/3.70 (step t2 (cl (not (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat))) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)) :rule subproof :discharge (t2.a0))
% 3.51/3.70 (step t3 (cl (=> (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)) :rule resolution :premises (t1 t2))
% 3.51/3.70 (step t4 (cl (=> (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))) :rule implies_neg2)
% 3.51/3.70 (step t5 (cl (=> (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)) (=> (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))) :rule resolution :premises (t3 t4))
% 3.51/3.70 (step t6 (cl (=> (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))) :rule contraction :premises (t5))
% 3.51/3.70 (step t7 (cl (not (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat))) (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)) :rule implies :premises (t6))
% 3.51/3.70 (step t8 (cl (not (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))) :rule or_pos)
% 3.51/3.70 (step t9 (cl (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)) (not (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))))) :rule reordering :premises (t8))
% 3.51/3.70 (step t10 (cl (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_e____ tptp.v_d____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omktop tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.c_COMBS (tptp.c_COMBS (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_fequal tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Oabove tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_c____) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB tptp.c_Arrow__Order__Mirabelle_Omkbot tptp.v_P____ (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_e____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))))) :rule or :premises (a1272))
% 3.51/3.70 (step t11 (cl (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))))) :rule resolution :premises (t10 a1274))
% 3.51/3.70 (step t12 (cl (=> (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat))))) :rule implies_neg1)
% 3.51/3.70 (anchor :step t13)
% 3.51/3.70 (assume t13.a0 (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat)))))
% 3.51/3.70 (step t13.t1 (cl (or (not (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat))))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))))) :rule forall_inst :args ((:= V_m tptp.v_n____)))
% 3.51/3.70 (step t13.t2 (cl (not (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat))))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) :rule or :premises (t13.t1))
% 3.51/3.70 (step t13.t3 (cl (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) :rule resolution :premises (t13.t2 t13.a0))
% 3.51/3.70 (step t13 (cl (not (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat))))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) :rule subproof :discharge (t13.a0))
% 3.51/3.70 (step t14 (cl (=> (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) :rule resolution :premises (t12 t13))
% 3.51/3.70 (step t15 (cl (=> (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) (not (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))))) :rule implies_neg2)
% 3.51/3.70 (step t16 (cl (=> (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) (=> (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))))) :rule resolution :premises (t14 t15))
% 3.51/3.70 (step t17 (cl (=> (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))))) :rule contraction :premises (t16))
% 3.51/3.70 (step t18 (cl (not (forall ((V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_m) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals V_m tptp.v_n____ tptp.tc_nat))))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) :rule implies :premises (t17))
% 3.51/3.70 (step t19 (cl (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) tptp.v_n____) tptp.tc_bool (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool) (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)) tptp.v_Lba____)))) (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat)))) :rule resolution :premises (t18 a1271))
% 3.51/3.70 (step t20 (cl (not (tptp.c_lessequals tptp.v_n____ tptp.v_n____ tptp.tc_nat))) :rule resolution :premises (t9 t11 t19))
% 3.51/3.70 (step t21 (cl) :rule resolution :premises (t7 t20 a561))
% 3.51/3.70
% 3.51/3.71 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.YolkR8JEsv/cvc5---1.0.5_27159.smt2
% 3.51/3.71 % cvc5---1.0.5 exiting
% 3.51/3.71 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------