TSTP Solution File: LCL854-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LCL854-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 : Thu Aug 31 07:04:01 EDT 2023
% Result : Unsatisfiable 0.16s 0.50s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL854-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12 % Command : do_cvc5 %s %d
% 0.14/0.31 % Computer : n032.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Thu Aug 24 18:07:27 EDT 2023
% 0.14/0.31 % CPUTime :
% 0.16/0.42 %----Proving TF0_NAR, FOF, or CNF
% 0.16/0.42 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.COzfEJshTT/cvc5---1.0.5_31736.p...
% 0.16/0.45 ------- get file name : TPTP file name is LCL854-1
% 0.16/0.46 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31736.smt2...
% 0.16/0.46 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.16/0.50 % SZS status Unsatisfiable for LCL854-1
% 0.16/0.50 % SZS output start Proof for LCL854-1
% 0.16/0.51 (
% 0.16/0.51 (let ((_let_1 (tptp.c_Type_Otyping tptp.v_ea____ tptp.v_s____ (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun tptp.v_Ta____) tptp.v_U____)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_4 (tptp.c_Suc _let_3))) (let ((_let_5 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_6 (tptp.hAPP _let_5 _let_3))) (let ((_let_7 (tptp.hAPP _let_6 _let_4))) (let ((_let_8 (tptp.hAPP (tptp.hAPP _let_5 _let_4) _let_3))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (ASSUME :args (_let_2)) (ASSUME :args (_let_1)) :args (false false _let_1)) :args ((forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp (tptp.c_Predicate_Oconversep V_r T_a T_a) T_a) V_x) V_y))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp (tptp.c_Predicate_Oconversep V_r T_a T_a) T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_y) V_x))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x))) (or (not (= (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z))) (= V_y V_z)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (= V_m V_n)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z))) (= V_y V_z)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))) (= V_b V_c)))) (forall ((V_e $$unsorted) (V_us $$unsorted) (V_T $$unsorted) (V_U $$unsorted) (V_i $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (tptp.c_Type_Otypings V_e V_us (tptp.c_Type_Osko__Type__Xvar__app__types__1__1 V_T V_U V_e V_us)) (not (tptp.c_Type_Otyping V_e _let_1 V_U)) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_us tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_2)) (= V_n _let_2) (= V_n _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_2)) (= V_m _let_1) (= V_m _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((V_x $$unsorted)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n) V_n)) (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_m)) (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))))) (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))) (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))) (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))) (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))) (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))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.c_Suc V_n))))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_Suc V_m) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_m _let_1) (= V_m _let_2))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_n _let_2) (= V_n _let_1))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (= _let_4 _let_7) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Olist_ONil T_b) V_a T_b T_a) V_a)) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 V_T V_e V_t V_ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 V_u))) (= (tptp.hAPP _let_2 V_z) V_u)))))) (forall ((V_r $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep V_r T_a T_b) V_a) V_b))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep V_r T_a T_b) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_b) V_a))))) (forall ((V_r $$unsorted) (V_a2 $$unsorted) (V_a1 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a2) V_a1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep V_r T_a T_b) V_a1) V_a2))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep V_r T_a T_b) V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_c))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_d)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_m))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_n)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.c_lessequals _let_1 _let_1 T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1))))) (= (tptp.hAPP _let_6 _let_3) _let_3) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 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))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a))))) (= _let_8 _let_4) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_r $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Wellfounded_Oaccp V_r V_b T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_b) V_a))) (not (tptp.c_Wellfounded_Oaccp V_r V_a T_a)))) (forall ((V_r $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Wellfounded_Oaccp V_r V_b T_a) (not (tptp.c_Wellfounded_Oaccp V_r V_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_b) V_a))))) (forall ((V_t $$unsorted)) (or (tptp.c_Wellfounded_Oaccp (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_t tptp.tc_Lambda_OdB) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r)) (not (tptp.c_Wellfounded_Oaccp (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_r tptp.tc_Lambda_OdB)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m))) (= (tptp.hAPP _let_1 (tptp.c_Suc V_n)) (tptp.c_Suc (tptp.hAPP _let_1 V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n) (tptp.c_Suc (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (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)))) (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)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_OrderedGroup_Osemigroup__add T_a)) (= (tptp.c_List_Ofoldl _let_1 (tptp.hAPP _let_2 V_y) V_zs T_a T_a) (tptp.hAPP _let_2 (tptp.c_List_Ofoldl _let_1 V_y V_zs T_a T_a))))))) (forall ((T_a $$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)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) V_m)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (or (not (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) V_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (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) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (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) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.c_List_Ofoldr _let_1 V_xs V_a T_a T_a) (tptp.c_List_Ofoldl _let_1 V_a V_xs T_a T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_ONil T_a) V_xs T_a))) (forall ((V_r $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (not (tptp.c_ListOrder_Ostep1 V_r V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_Suc _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_m _let_1) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.c_List_Ofoldl _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) V_zs T_a T_a)) (tptp.c_List_Ofoldl _let_1 V_x V_zs T_a T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_ONil T_b) T_a T_b) V_a)) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_fequal T_a))) (= (tptp.c_Predicate_Oconversep _let_1 T_a T_a) _let_1))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (= _let_4 _let_8) (forall ((T_a $$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)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$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)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_t)))) (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)))) (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)))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 V_T V_e V_t V_ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Predicate_Oconversep (tptp.c_Predicate_Oconversep V_r T_a T_b) T_b T_a) V_r)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (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) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (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)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP _let_1 V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a (tptp.hAPP _let_1 V_c) T_a))))) (= _let_7 _let_4) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))))) (forall ((V_r $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) (tptp.c_Suc _let_1))) (= V_m _let_1) (= V_n _let_1)))) (forall ((V_r $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Wellfounded_Oaccp V_r V_y T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_a))) (not (tptp.c_Wellfounded_Oaccp V_r V_a T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_Wellfounded_Oaccp V_r V_a T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a) V_b))) (not (tptp.c_Wellfounded_Oaccp V_r V_b T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a) V_b)))))) (forall ((V_dB $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__size (tptp.c_Lambda_OdB_OAbs V_dB)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Lambda_OdB_OdB__size V_dB)) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_Lambda_OdB_OdB__size (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_OdB_OdB__size V_dB1)) (tptp.c_Lambda_OdB_OdB__size V_dB2))) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u) V_s V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_t V_s V_k)) (tptp.c_Lambda_Osubst V_u V_s V_k)))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_i $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xvar__app__typesE__1__1 V_T V_e V_i V_ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_Nat_Osize__class_Osize (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) tptp.tc_Type_Otype) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Nat_Osize__class_Osize V_type1 tptp.tc_Type_Otype)) (tptp.c_Nat_Osize__class_Osize V_type2 tptp.tc_Type_Otype))) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_k $$unsorted) (V_u $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_k) V_u V_k) V_u)) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_U $$unsorted) (V_T $$unsorted) (V_e $$unsorted) (V_us $$unsorted) (V_i $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (= V_U (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xvar__app__types__1__1 V_T V_U V_e V_us) V_T tptp.tc_Type_Otype tptp.tc_Type_Otype)) (not (tptp.c_Type_Otyping V_e _let_1 V_U)) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_us tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T))))) (forall ((V_r $$unsorted) (V_ss $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_s)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (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) _let_1)) (= V_a _let_1)))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_Type_Otype_Otype__size (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Type_Otype_Otype__size V_type1)) (tptp.c_Type_Otype_Otype__size V_type2))) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals 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_Power_Opower__class_Opower V_a _let_1 T_a) (tptp.c_Power_Opower__class_Opower V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Ofoldl _let_2 _let_1 V_xs T_a T_a) (tptp.c_List_Ofoldr _let_2 V_xs _let_1 T_a T_a)))))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_ss $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta V_rs V_ss tptp.tc_Lambda_OdB)))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_Olift V_r V_i)) (tptp.c_Lambda_Olift V_s V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_s)))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_r) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Olift V_t V_i))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_x) V_y))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_t $$unsorted) (V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_Osubst V_t V_r V_i)) (tptp.c_Lambda_Osubst V_t V_s V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_s)))))) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_Osubst V_r V_t V_i)) (tptp.c_Lambda_Osubst V_s V_t V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_s)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (= V_m V_n))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Olift (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t) V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Olift V_s V_k)) (tptp.c_Lambda_Olift V_t V_k)))) (forall ((V_t $$unsorted) (V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB) (tptp.c_Lambda_Osubst V_t V_r V_i)) (tptp.c_Lambda_Osubst V_t V_s V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_m $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_m)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_nat_H)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 (tptp.c_Suc V_n) T_a) _let_1)))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_ts $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 V_T V_e V_t V_ts) V_T tptp.tc_Type_Otype tptp.tc_Type_Otype)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_x) V_x))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_a) V_a))) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_Osubst V_r V_t V_i)) (tptp.c_Lambda_Osubst V_s V_t V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (not (tptp.c_Wellfounded_Oaccp _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_r V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB)) (not (tptp.c_Wellfounded_Oaccp _let_1 V_s tptp.tc_Lambda_OdB)) (tptp.c_Wellfounded_Oaccp _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r)) V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB)))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_Ts $$unsorted)) (or (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)) (not (tptp.c_Type_Otyping V_e V_t (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun V_Ts V_T tptp.tc_Type_Otype tptp.tc_Type_Otype))))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_Nat_Osize__class_Osize (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Nat_Osize__class_Osize V_dB1 tptp.tc_Lambda_OdB)) (tptp.c_Nat_Osize__class_Osize V_dB2 tptp.tc_Lambda_OdB))) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Ofoldl _let_1 V_a V_xs T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_List_Ofoldr _let_1 V_xs (tptp.c_HOL_Ozero__class_Ozero T_a) T_a T_a)))))) (forall ((V_s $$unsorted) (V_ss $$unsorted) (V_r $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_Lambda_OdB_OAbs V_r))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_r $$unsorted) (V_ts $$unsorted) (V_s $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r V_s))) (forall ((V_dB $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_Lambda_OdB_OAbs V_dB) tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Nat_Osize__class_Osize V_dB tptp.tc_Lambda_OdB)) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_t $$unsorted) (V_k $$unsorted) (V_s $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_Olift V_t V_k) V_s V_k) V_t)) (forall ((V_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) _let_1))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_Olift V_r V_i)) (tptp.c_Lambda_Olift V_s V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_m $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OVar V_m) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_ts $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 V_T V_e V_t V_ts) V_T tptp.tc_Type_Otype tptp.tc_Type_Otype)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (forall ((V_rs $$unsorted) (V_n $$unsorted) (V_v $$unsorted)) (or (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta V_rs (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 V_n V_rs V_v) tptp.tc_Lambda_OdB) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_v))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a _let_2 T_a) (tptp.c_Power_Opower__class_Opower V_b _let_2 T_a))) (= V_a V_b) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (= (tptp.c_Transitive__Closure_Ortranclp _let_1 T_a) _let_1))) (forall ((V_dB1_H $$unsorted) (V_dB2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_nat $$unsorted) (T_a $$unsorted)) (= (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.c_Type_Otype_OAtom V_nat) T_a) (tptp.hAPP V_f1 V_nat))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_s)) (tptp.c_Lambda_OdB_OAbs V_t))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_s) V_t))))) (forall ((V_s $$unsorted) (V_r $$unsorted)) (or (= V_s (tptp.c_Lambda_OdB_OAbs (tptp.c_Lambda_Osko__Lambda__Xbeta__cases__2__1 V_r V_s))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_r)) V_s))))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_e_H $$unsorted) (V_u $$unsorted) (V_U $$unsorted) (V_i $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (not (tptp.c_Type_Otyping V_e_H V_u V_U)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e_H V_i V_U tptp.tc_Type_Otype) V_t V_T)) (tptp.c_Type_Otyping V_e_H (tptp.c_Lambda_Osubst V_t V_u V_i) V_T))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) (tptp.c_Lambda_OdB_OVar V_i)))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_e $$unsorted) (V_t_H $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t_H V_T) (not (tptp.c_Type_Otyping V_e V_t V_T)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB) V_t) V_t_H))))) (forall ((V_nat $$unsorted)) (= (tptp.c_Type_Otype_Otype__size (tptp.c_Type_Otype_OAtom V_nat)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_s $$unsorted) (V_u $$unsorted) (V_t $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_u)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_s) V_t))))) (forall ((V_u $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Lambda_OdB_OApp V_u))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP _let_1 V_s)) (tptp.hAPP _let_1 V_t))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_s) V_t)))))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_s_H $$unsorted) (V_t_H $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s_H) V_t_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) V_t_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s) V_s_H)))))) (forall ((V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OAbs V_r))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_nat $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.c_Type_Otype_OAtom V_nat) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f1 V_nat))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_xc $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.c_Type_Otype_OAtom V_xc) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f1 V_xc))))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_s_H $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s_H) V_t))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s) V_s_H)))))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_t_H $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (let ((_let_2 (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_t)) (tptp.hAPP _let_2 V_t_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) V_t_H))))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_P $$unsorted) (V_T $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_T)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Type_Osko__Type__Xtype__induct__1__1 V_P)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((V_e $$unsorted) (V_u $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping V_e V_u (tptp.c_Type_Osko__Type__Xtyping__elims__2__1 V_T V_e V_t V_u)) (not (tptp.c_Type_Otyping V_e (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u) V_T)))) (forall ((V_e $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Type_Osko__Type__Xtyping__elims__3__1 V_T V_e V_t) tptp.tc_Type_Otype) V_t (tptp.c_Type_Osko__Type__Xtyping__elims__3__2 V_T V_e V_t)) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OAbs V_t) V_T)))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_ta____)) (forall ((V_v $$unsorted) (V_n $$unsorted) (V_rs $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_n))) (or (= V_v (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 V_n V_rs V_v) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_v)))))) (forall ((V_s $$unsorted) (V_s_H $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_OdB_OAbs V_s)) (tptp.c_Lambda_OdB_OAbs V_s_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s) V_s_H)))))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (tptp.c_Type_Otyping V_e _let_1 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xvar__app__typesE__1__1 V_T V_e V_i V_ts) V_T tptp.tc_Type_Otype tptp.tc_Type_Otype)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T))))) (forall ((V_nat $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__size (tptp.c_Lambda_OdB_OVar V_nat)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Type_Osko__Type__Xabs__typeE__1__1 V_e V_t) tptp.tc_Type_Otype) V_t (tptp.c_Type_Osko__Type__Xabs__typeE__1__2 V_e V_t)) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OAbs V_t) V_T)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Type_Otype_OAtom V_nat) (tptp.c_Type_Otype_OAtom V_nat_H))) (= V_nat V_nat_H))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar V_n)))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (T_a $$unsorted) (V_T $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Type_Oshift (tptp.c_Type_Oshift V_e V_i V_U T_a) _let_1 V_T T_a) (tptp.c_Type_Oshift (tptp.c_Type_Oshift V_e _let_1 V_T T_a) (tptp.c_Suc V_i) V_U T_a)))) (forall ((V_nat $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r)) V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_s))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_r V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))))) (forall ((V_e $$unsorted) (V_x $$unsorted) (V_T $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Type_Oshift V_e V_x V_T T_a) V_x) V_T)) (forall ((V_n $$unsorted) (V_ts $$unsorted) (V_r $$unsorted) (V_ss $$unsorted)) (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_dB $$unsorted) (V_dB_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_dB) (tptp.c_Lambda_OdB_OAbs V_dB_H))) (= V_dB V_dB_H))) (forall ((V_nat $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H)))) (forall ((V_m $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_nat $$unsorted) (T_a $$unsorted)) (= (tptp.c_Type_Otype_Otype__rec V_f1 V_f2 (tptp.c_Type_Otype_OAtom V_nat) T_a) (tptp.hAPP V_f1 V_nat))) (forall ((V_r $$unsorted) (V_ss $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t)) (tptp.c_Lambda_Osubst V_s V_t (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_T $$unsorted) (V_U $$unsorted) (V_e $$unsorted) (V_i $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (= V_T V_U) (not (tptp.c_Type_Otyping V_e _let_1 V_U)) (not (tptp.c_Type_Otyping V_e _let_1 V_T))))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB2 V_dB2_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB1 V_dB1_H))) (forall ((V_n $$unsorted) (V_rs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT V_rs tptp.tc_Lambda_OdB)))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_rs V_ss))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r V_s))) (forall ((V_s $$unsorted) (V_ss $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) _let_1)) (= V_s _let_1)))) (forall ((V_i $$unsorted) (V_t $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OVar V_i)) V_t)))) (forall ((V_r $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) (tptp.c_Lambda_Osko__Lambda__Xbeta__cases__2__1 V_r V_s))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_r)) V_s))))) (forall ((V_nat $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_Type_Otype_OAtom V_nat) tptp.tc_Type_Otype) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (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 _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_r (tptp.c_Lambda_OdB_OVar V_i) V_j))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((V_m $$unsorted) (V_rs $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_m) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_rs V_ss))) (forall ((V_m $$unsorted) (V_rs $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_m) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_m V_n))) (forall ((V_dB_H $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OVar V_nat_H))) (= V_nat V_nat_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((V_dB_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_nat $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_Lambda_OdB_OVar V_nat) tptp.tc_Lambda_OdB) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_U $$unsorted) (V_T $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_t V_u V_i))) (not (tptp.c_Type_Otyping V_e V_u V_U)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_U tptp.tc_Type_Otype) V_t V_T)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_U tptp.tc_Type_Otype) (tptp.c_Lambda_Olift V_t V_i) V_T) (not (tptp.c_Type_Otyping V_e V_t V_T)))) (forall ((V_type1_H $$unsorted) (V_type2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1_H) V_type2_H) (tptp.c_Type_Otype_OAtom V_nat)))) (forall ((V_T $$unsorted) (V_e $$unsorted) (V_t $$unsorted)) (or (= V_T (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xtyping__elims__3__1 V_T V_e V_t)) (tptp.c_Type_Osko__Type__Xtyping__elims__3__2 V_T V_e V_t))) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OAbs V_t) V_T)))) (forall ((V_e $$unsorted) (V_t_H $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t_H V_T) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_t) V_t_H))) (not (tptp.c_Type_Otyping V_e V_t V_T)))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1_H) V_type2_H))) (= V_type1 V_type1_H))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1_H) V_type2_H))) (= V_type2 V_type2_H))) (forall ((V_P $$unsorted) (V_T1 $$unsorted) (V_T2 $$unsorted) (V_T $$unsorted)) (or (not (= (tptp.c_Type_Osko__Type__Xtype__induct__1__1 V_P) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T1) V_T2))) (tptp.hBOOL (tptp.hAPP V_P V_T)) (tptp.hBOOL (tptp.hAPP V_P V_T2)))) (forall ((V_P $$unsorted) (V_T1a $$unsorted) (V_x $$unsorted) (V_T $$unsorted)) (or (not (= (tptp.c_Type_Osko__Type__Xtype__induct__1__1 V_P) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T1a) V_x))) (tptp.hBOOL (tptp.hAPP V_P V_T)) (tptp.hBOOL (tptp.hAPP V_P V_T1a)))) (forall ((V_env $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_U $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otyping V_env (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t) V_U) (not (tptp.c_Type_Otyping V_env V_t V_T)) (not (tptp.c_Type_Otyping V_env V_s (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T) V_U))))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_s____)) (forall ((V_env $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_U $$unsorted)) (or (tptp.c_Type_Otyping V_env (tptp.c_Lambda_OdB_OAbs V_t) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T) V_U)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_env (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_T tptp.tc_Type_Otype) V_t V_U)))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted)) (or (= (tptp.hAPP V_e V_i) V_T) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OVar V_i) V_T)))) (tptp.c_Type_Otyping tptp.v_ea____ tptp.v_ta____ tptp.v_Ta____) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_type1 $$unsorted) (V_type2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Type_Otype_Otype__rec V_f1 V_f2 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f2 V_type1) V_type2) (tptp.c_Type_Otype_Otype__rec V_f1 V_f2 V_type1 T_a)) (tptp.c_Type_Otype_Otype__rec V_f1 V_f2 V_type2 T_a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_type1 $$unsorted) (V_type2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) T_a) (tptp.hAPP (tptp.hAPP V_f2 V_type1) V_type2))) _let_1 (forall ((V_env $$unsorted) (V_x $$unsorted)) (tptp.c_Type_Otyping V_env (tptp.c_Lambda_OdB_OVar V_x) (tptp.hAPP V_env V_x))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_xa) V_xb) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_xa) V_xb))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_type1 $$unsorted) (V_type2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_type1) V_type2))))) (forall ((V_nat $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (not (= (tptp.c_Type_Otype_OAtom V_nat) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1_H) V_type2_H)))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_u $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xtyping__elims__2__1 V_T V_e V_t V_u)) V_T)) (not (tptp.c_Type_Otyping V_e (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u) V_T)))) _let_2 (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)))) (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)))) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_OrderedGroup_Osemigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (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))))))))))))))))
% 0.16/0.51 )
% 0.16/0.51 % SZS output end Proof for LCL854-1
% 0.16/0.51 % cvc5---1.0.5 exiting
% 0.16/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------