TSTP Solution File: SCT086-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT086-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 14:12:00 EDT 2023
% Result : Unsatisfiable 1.19s 1.53s
% Output : Proof 1.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.16/0.18 % Problem : SCT086-1 : TPTP v8.1.2. Released v4.1.0.
% 0.17/0.19 % Command : do_cvc5 %s %d
% 0.20/0.40 % Computer : n029.cluster.edu
% 0.20/0.40 % Model : x86_64 x86_64
% 0.20/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.40 % Memory : 8042.1875MB
% 0.20/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.40 % CPULimit : 300
% 0.20/0.40 % WCLimit : 300
% 0.20/0.40 % DateTime : Thu Aug 24 15:17:23 EDT 2023
% 0.20/0.40 % CPUTime :
% 0.26/0.60 %----Proving TF0_NAR, FOF, or CNF
% 0.26/0.60 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.tjv5vSnYzX/cvc5---1.0.5_32299.p...
% 0.26/0.72 ------- get file name : TPTP file name is SCT086-1
% 0.26/0.72 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32299.smt2...
% 0.26/0.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.19/1.53 % SZS status Unsatisfiable for SCT086-1
% 1.19/1.53 % SZS output start Proof for SCT086-1
% 1.37/1.55 (
% 1.37/1.55 (let ((_let_1 (not tptp.v_thesis____))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)))) (let ((_let_3 (tptp.v_sko__CHAINED__1 tptp.v_F tptp.v_Lab____ tptp.v_Lba____ tptp.v_a____ tptp.v_b____ tptp.v_h____))) (let ((_let_4 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 _let_3) (tptp.c_Finite__Set_Ocard _let_2 tptp.tc_Arrow__Order__Mirabelle_Oindi))))) (let ((_let_6 (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun _let_2 _let_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in _let_1) (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_2) (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 _let_2 _let_3) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_2 _let_3) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_2 _let_2) tptp.v_Lba____)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) (tptp.v_sko__CHAINED__1 tptp.v_F tptp.v_Lab____ tptp.v_Lba____ tptp.v_a____ tptp.v_b____ tptp.v_h____))))))))))) (let ((_let_7 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_8 (tptp.tc_fun _let_7 tptp.tc_bool))) (let ((_let_9 (tptp.tc_fun _let_8 _let_8))) (let ((_let_10 (tptp.tc_fun _let_8 _let_9))) (let ((_let_11 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (let ((_let_12 (tptp.c_COMBC (tptp.c_COMBB _let_4 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))) (let ((_let_13 (tptp.c_HOL_OIf _let_8))) (let ((_let_14 (tptp.c_in _let_7))) (let ((_let_15 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_14 (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_13 (tptp.hAPP _let_12 (tptp.c_HOL_Oplus__class_Oplus _let_3 _let_11 tptp.tc_nat)) tptp.tc_bool _let_10 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_8 _let_9) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_8 _let_8) tptp.v_Lba____)))))) (let ((_let_16 (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun _let_3 _let_3))) (or tptp.v_thesis____ (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in _let_2) (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_3) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_1 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.c_HOL_Oplus__class_Oplus V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) tptp.tc_bool (tptp.tc_fun _let_3 _let_4) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.v_sko__local__Xthat__1 tptp.v_F tptp.v_Lab____ tptp.v_Lba____ tptp.v_a____ tptp.v_b____ tptp.v_h____ V_n)) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi)))))))))))) (let ((_let_17 (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun _let_3 _let_3))) (let ((_let_5 (tptp.tc_fun _let_3 _let_4))) (let ((_let_6 (tptp.c_COMBC (tptp.c_COMBB _let_1 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))) (let ((_let_7 (tptp.c_HOL_OIf _let_3))) (let ((_let_8 (tptp.c_in _let_2))) (or tptp.v_thesis____ (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_7 (tptp.hAPP _let_6 (tptp.c_HOL_Oplus__class_Oplus V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) tptp.tc_bool _let_5 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_7 (tptp.hAPP _let_6 (tptp.v_sko__local__Xthat__1 tptp.v_F tptp.v_Lab____ tptp.v_Lba____ tptp.v_a____ tptp.v_b____ tptp.v_h____ V_n)) tptp.tc_bool _let_5 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi)))))))))))))))) (let ((_let_18 (tptp.c_lessequals tptp.tc_nat))) (let ((_let_19 (tptp.v_sko__local__Xthat__1 tptp.v_F tptp.v_Lab____ tptp.v_Lba____ tptp.v_a____ tptp.v_b____ tptp.v_h____ _let_3))) (let ((_let_20 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_18 _let_19) _let_3)))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_14 (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_13 (tptp.hAPP _let_12 _let_19) tptp.tc_bool _let_10 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_8 _let_9) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_8 _let_8) tptp.v_Lba____)))))) (let ((_let_23 (or _let_22 _let_21))) (let ((_let_24 (_let_6))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (not _let_23))) (let ((_let_27 (not _let_5))) (let ((_let_28 (not _let_15))) (let ((_let_29 (or _let_28 _let_20 _let_27))) (let ((_let_30 (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun _let_3 _let_3))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in _let_2) (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_3) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_1 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.c_HOL_Oplus__class_Oplus V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) tptp.tc_bool (tptp.tc_fun _let_3 _let_4) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.v_sko__local__Xthat__1 tptp.v_F tptp.v_Lab____ tptp.v_Lba____ tptp.v_a____ tptp.v_b____ tptp.v_h____ V_n)) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi)))))))))))) (let ((_let_31 (ASSUME :args (_let_1)))) (let ((_let_32 (_let_30))) (let ((_let_33 (ASSUME :args (_let_5)))) (let ((_let_34 (ASSUME :args (_let_15)))) (let ((_let_35 (not _let_22))) (let ((_let_36 (or _let_28 _let_35 _let_27))) (let ((_let_37 (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun _let_3 _let_3))) (let ((_let_5 (tptp.tc_fun _let_3 _let_4))) (let ((_let_6 (tptp.c_COMBC (tptp.c_COMBB _let_1 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))) (let ((_let_7 (tptp.c_HOL_OIf _let_3))) (let ((_let_8 (tptp.c_in _let_2))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_7 (tptp.hAPP _let_6 (tptp.c_HOL_Oplus__class_Oplus V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) tptp.tc_bool _let_5 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_7 (tptp.hAPP _let_6 (tptp.v_sko__local__Xthat__1 tptp.v_F tptp.v_Lab____ tptp.v_Lba____ tptp.v_a____ tptp.v_b____ tptp.v_h____ V_n)) tptp.tc_bool _let_5 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi)))))))))))))))) (let ((_let_38 (_let_37))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (_let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP _let_12 V_m)))) :args _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_21 _let_26))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_28 _let_27 _let_35 (not _let_36)))) _let_34 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_38) :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Oplus__class_Oplus V_n _let_11 tptp.tc_nat)))) :args _let_38)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) _let_31 :args (_let_37 true tptp.v_thesis____)) :args (_let_36 false _let_37)) :args (_let_35 false _let_15 false _let_5 false _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_27 _let_20 (not _let_29)))) _let_34 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Oplus__class_Oplus V_n _let_11 tptp.tc_nat)))) :args _let_32)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) _let_31 :args (_let_30 true tptp.v_thesis____)) :args (_let_29 false _let_30)) :args (_let_20 false _let_15 false _let_5 false _let_29)) :args (_let_26 true _let_22 false _let_20)) _let_25 :args (false true _let_23 false _let_6)) :args ((forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (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.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y)) (= V_x (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x)))) (forall ((V_P $$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))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP _let_1 V_A))))) (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)))))) (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)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Ouminus__class_Ouminus 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_Ogroup__add T_a)) (not (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (= _let_1 V_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((V_R $$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)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Otop__class_Otop T_a) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (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)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1))) (= V_A V_B)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) _let_1))))))) (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)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Obot__class_Obot T_a) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (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 _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (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 _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (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 _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (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 ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$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_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) V_n T_a))))) (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)) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a (tptp.c_Suc V_n) T_a)) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))) (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)) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (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.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (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.c_HOL_Oinverse__class_Odivide V_x V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (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 _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (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 _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (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 _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (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 _let_2 _let_1) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b T_b))) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a _let_2 tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b _let_3) T_a) T_a T_b _let_3) V_c) T_a T_b T_b) V_d) V_A T_a T_b) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_d) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_A))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b T_b))) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a _let_2 tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b _let_3) T_a) T_a T_b _let_3) V_c) T_a T_b T_b) V_d) V_A T_a T_b) (tptp.c_Orderings_Obot__class_Obot _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_d) V_A)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_A))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (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 _let_2 _let_1) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (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_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 ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)) (forall ((V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x)))) (forall ((V_A $$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)))) (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.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (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)))) (forall ((V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x)))) (forall ((V_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_b))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x)) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a))))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_less__eq $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a))))) (forall ((V_less__eq $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (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 _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Power_Opower__class_Opower V_a _let_1 T_a)) (tptp.c_Power_Opower__class_Opower V_b _let_1 T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$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_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (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)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (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 _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (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 _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (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 _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_A $$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))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (= V_x V_y) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (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 _let_1 V_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (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)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (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 _let_1 V_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) V_N)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_Orderings_Opreorder (tptp.c_lessequals T_a) (tptp.c_HOL_Oord__class_Oless T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) _let_1) _let_1))))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))) (= V_y _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))) (= V_x _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$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)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (= V_m V_n))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Relation_OId__on V_A T_a)))))) (forall ((V_i $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i) (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus V_i V_m tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i) (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus V_m V_i tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus V_m V_x tptp.tc_nat))))) (forall ((V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x) V_x))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) (tptp.c_Suc V_x))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) (tptp.c_Suc V_n)))))) (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) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Suc V_m)) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n))))) (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)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Suc V_m)) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Suc V_n)) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_m))))) (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)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Suc V_n)) V_m))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) (tptp.c_Suc V_m)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((V_n $$unsorted)) (= (tptp.c_Suc V_n) (tptp.c_HOL_Oplus__class_Oplus V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (= (tptp.c_Suc V_n) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) V_n tptp.tc_nat))) (forall ((V_P $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_List_Oall__from__to__nat V_P V_i V_j) (not (tptp.hBOOL (tptp.hAPP V_P V_i))) (not (tptp.c_List_Oall__from__to__nat V_P (tptp.c_HOL_Oplus__class_Oplus V_i (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_j)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_L)) (= V_x V_z) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (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 _let_3 V_b)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (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 _let_2 _let_1) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1))))))) (forall ((V_less $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))) (= V_a V_b) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_3) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 V_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.hAPP _let_1 _let_2))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) _let_2)) (tptp.hBOOL (tptp.hAPP _let_3 V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) V_a)))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (let ((_let_2 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a _let_2 T_a) (tptp.c_Power_Opower__class_Opower V_b _let_2 T_a))) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool))) (or (not (= (tptp.hAPP _let_1 V_R) (tptp.hAPP _let_1 V_S))) (= V_R V_S)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B))))) (forall ((T_b $$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))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_B))))) (forall ((T_b $$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)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_A T_a T_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_w) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 _let_1) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_x)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_w) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_w) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals T_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (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 _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (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 _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 _let_2) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.c_lessequals T_a))) (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 _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP 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_let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x V_a T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (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.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (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 _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not 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$$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a (tptp.c_Suc V_n) T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (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 _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (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 _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)) _let_1))))))) (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) (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)) (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)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n)))))) (forall ((V_P $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_List_Oall__from__to__nat V_P V_i V_j) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i) V_j)))) (forall ((V_P $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i) V_j))) (not (tptp.c_List_Oall__from__to__nat V_P V_i V_j)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_i)) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) (tptp.c_Suc V_x)))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) (tptp.c_Suc V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n))) (or (= V_n V_m) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_m)))) (tptp.hBOOL (tptp.hAPP _let_1 V_m))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n))) (or (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_m)))) (tptp.hBOOL (tptp.hAPP _let_1 V_m))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m))) (or (= V_m V_n) (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc V_m))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_n)) (= _let_2 V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_x)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.c_Suc V_m))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.c_Suc V_m))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_x)) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) (tptp.c_Suc V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (tptp.c_Orderings_Opreorder (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) T_a) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (tptp.c_Orderings_Olinorder (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) T_a) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (tptp.c_Orderings_Oorder (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) T_a) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_Suc V_n) tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_n)) (tptp.c_Suc V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_n)) (tptp.c_Suc V_m))))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_Suc V_n)) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_n)) V_m)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_n)) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) _let_1) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m))) (or (= V_m _let_1) (tptp.hBOOL (tptp.hAPP _let_2 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_x V_y))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_x))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (let ((_let_1 (= V_xa V_x))) (or _let_1 _let_1 (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.c_Arrow__Order__Mirabelle_Omktop V_L V_x)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (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)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_L))) (= V_x V_z) (= V_y V_z)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (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)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_L))) (= V_x V_y) (= V_y V_z)))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x))))) (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x))))) (forall ((V_x $$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.c_Arrow__Order__Mirabelle_Omkbot V_L V_x))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (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)))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_L)) (= V_y V_z) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x))))) (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_L))) (= V_y V_z) (= V_x V_z)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_L))) (= V_x V_y) (= V_x V_z)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_b))) (let ((_let_2 (tptp.tc_fun T_b T_b))) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b _let_2) T_a) T_a T_b _let_2) V_c) T_a T_b T_b) V_d) V_A T_a T_b) V_B) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_d) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_A))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_a T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((T_a $$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)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (let ((_let_2 (tptp.c_in (tptp.tc_prod T_a T_a)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Pair V_xa V_x T_a T_a)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Pair V_x V_xa T_a T_a)) V_r)) (= V_x V_xa) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))))) (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)))))) (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)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_ODomain V_r T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) V_r))))) (forall ((T_a $$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))))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.c_Relation_ORange V_r T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) V_r))))) (forall ((T_a $$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))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((T_a $$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)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) (tptp.c_Relation_OId__on V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Relation_OId__on V_A T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Relation_OImage V_r V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod 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(tptp.c_Wellfounded_Oacc V_r T_a))) (let ((_let_2 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (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_Oplus__class_Oplus _let_1 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a))) (let ((_let_2 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_Orderings_Opreorder (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_Orderings_Oorder (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Olinorder (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_b V_x T_a)) (tptp.c_Power_Opower__class_Opower V_b V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_b V_x T_a)) (tptp.c_Power_Opower__class_Opower V_b V_y T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_a V_N T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_N)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_m T_a)) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_a)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Wellfounded_Omeasure V_f T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_f $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Wellfounded_Omeasure V_f T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y)))))) (forall ((T_a $$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)))))) (tptp.c_Fun_Oinj__on tptp.v_h____ _let_2 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (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 _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) V_N)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_f $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Wellfounded_Omlex__prod V_f V_R T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_R))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))))))) (forall ((V_P $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_List_Oall__from__to__nat V_P (tptp.c_HOL_Oplus__class_Oplus V_i (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_j) (not (tptp.hBOOL (tptp.hAPP V_P V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i) V_j))) (not (tptp.c_List_Oall__from__to__nat V_P V_i V_j)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b T_b))) (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 _let_2 tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b _let_3) T_a) T_a T_b _let_3) V_c) T_a T_b T_b) V_d) V_A T_a T_b) (tptp.c_Orderings_Otop__class_Otop _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_d) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_A)))))))) (= (tptp.hAPP _let_4 tptp.v_n) (tptp.hAPP _let_18 (tptp.c_Suc tptp.v_n))) (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_lessequals 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_lessequals 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))))) (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_lessequals tptp.tc_nat) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals 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))))) (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_lessequals tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals 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))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1)) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_1) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_n) tptp.tc_bool (tptp.tc_fun _let_1 _let_2) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1 _let_2) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1 _let_1) tptp.v_Lba____)) tptp.c_Arrow__Order__Mirabelle_OProf))))) _let_17 _let_16 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_j V_k tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_z) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (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_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) V_n))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_i))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_j))))))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a)))))))) (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))) (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))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))) (= V_a V_b))) (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_j V_i tptp.tc_nat)) V_i)))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_i V_j tptp.tc_nat)) V_i)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_j V_k tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_j V_l tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_k) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (= V_m V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) (tptp.c_HOL_Oplus__class_Oplus V_m V_x tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) (tptp.c_HOL_Oplus__class_Oplus V_n V_m tptp.tc_nat)))) (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))) (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))))) (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))))) (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))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_n)))) (forall ((V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_x T_a)))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_l tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_k) V_l))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_n V_m tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_j tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_j V_m tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_i V_j tptp.tc_nat)) V_k)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_j V_l tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_k) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (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 ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (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.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Oplus__class_Oplus V_x V_z tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_HOL_Oplus__class_Oplus V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (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.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_d T_a)))) (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_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_b T_a)))) (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.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_HOL_Oplus__class_Oplus V_a V_d T_a) T_a)))) (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_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_u T_a))) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) V_u))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_i))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_j tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_i))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_j V_m tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_k) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat)) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat)) V_n)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$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))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S))))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))))) (forall ((T_a $$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_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_x V_z tptp.tc_nat))) (= V_y V_z))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_n V_k tptp.tc_nat))) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (= V_m V_n))) (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.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a))) (= V_y V_z))) (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.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (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.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (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.c_HOL_Oplus__class_Oplus V_b V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) _let_15 _let_6 _let_5 _let_1 (forall ((V_na $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun _let_3 _let_3))) (or tptp.v_thesis____ (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in _let_2) (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_3) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_1 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.c_HOL_Oplus__class_Oplus V_na (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) tptp.tc_bool (tptp.tc_fun _let_3 _let_4) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.hAPP tptp.v_n V_na)) V_na)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_na) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi)))))))))) (forall ((V_na $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun _let_3 _let_3))) (let ((_let_5 (tptp.tc_fun _let_3 _let_4))) (let ((_let_6 (tptp.c_COMBC (tptp.c_COMBB _let_1 tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool))) (let ((_let_7 (tptp.c_HOL_OIf _let_3))) (let ((_let_8 (tptp.c_in _let_2))) (or tptp.v_thesis____ (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_7 (tptp.hAPP _let_6 (tptp.c_HOL_Oplus__class_Oplus V_na (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) tptp.tc_bool _let_5 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_7 (tptp.hAPP _let_6 (tptp.hAPP tptp.v_n V_na)) tptp.tc_bool _let_5 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_na) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi)))))))))))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oboolean__algebra (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Oboolean__algebra T_1)))) (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_Lattices_Oboolean__algebra tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a)))))))))))))))))))))))))))))))))))))))))))))
% 1.37/1.55 )
% 1.37/1.55 % SZS output end Proof for SCT086-1
% 1.37/1.56 % cvc5---1.0.5 exiting
% 1.37/1.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------