%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW473+7 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n015.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 : Fri Sep  1 00:21:07 EDT 2023

% Result   : Theorem 28.33s 28.57s
% Output   : Proof 28.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.36/0.36  % Problem    : SWW473+7 : TPTP v8.1.2. Released v5.3.0.
% 0.36/0.37  % Command    : do_cvc5 %s %d
% 0.36/0.56  % Computer : n015.cluster.edu
% 0.36/0.56  % Model    : x86_64 x86_64
% 0.36/0.56  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.36/0.56  % Memory   : 8042.1875MB
% 0.36/0.56  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.36/0.56  % CPULimit   : 300
% 0.36/0.56  % WCLimit    : 300
% 0.36/0.56  % DateTime   : Sun Aug 27 22:30:25 EDT 2023
% 0.36/0.56  % CPUTime    : 
% 0.42/0.81  %----Proving TF0_NAR, FOF, or CNF
% 28.33/28.57  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Fq6qSXS0LB/cvc5---1.0.5_12613.p...
% 28.33/28.57  ------- get file name : TPTP file name is SWW473+7
% 28.33/28.57  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12613.smt2...
% 28.33/28.57  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 28.33/28.57  --- Run --no-e-matching --full-saturate-quant at 5...
% 28.33/28.57  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 28.33/28.57  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 28.33/28.57  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 28.33/28.57  % SZS status Theorem for SWW473+7
% 28.33/28.57  % SZS output start Proof for SWW473+7
% 28.33/28.57  (
% 28.33/28.57  (let ((_let_1 (tptp.fun tptp.x_a tptp.bool))) (let ((_let_2 (tptp.fun tptp.pname tptp.bool))) (let ((_let_3 (tptp.fun tptp.pname tptp.x_a))) (let ((_let_4 (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (let ((_let_5 (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn))) (let ((_let_6 (tptp.ord_less_eq _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.x_a (tptp.fun _let_1 _let_1) (tptp.insert tptp.x_a) _let_5) tptp.g)) _let_4)))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.hAPP tptp.x_a _let_7 (tptp.member tptp.x_a) _let_5))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.pname (tptp.fun _let_2 tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u)))) (let ((_let_12 (tptp.hAPP tptp.nat tptp.nat tptp.suc tptp.na))) (let ((_let_13 (tptp.finite_card tptp.x_a))) (let ((_let_14 (tptp.hAPP _let_1 tptp.nat _let_13 _let_4))) (let ((_let_15 (tptp.fun tptp.nat tptp.nat))) (let ((_let_16 (tptp.fun tptp.nat tptp.bool))) (let ((_let_17 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 tptp.g) _let_4)))) (let ((_let_18 (tptp.ord_less tptp.int))) (let ((_let_19 (tptp.fun tptp.int tptp.bool))) (let ((_let_20 (tptp.ord_less_eq tptp.int))) (let ((_let_21 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (let ((_let_22 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_21))) (let ((_let_23 (tptp.number_number_of tptp.int))) (let ((_let_24 (tptp.hAPP tptp.int tptp.int _let_23 _let_22))) (let ((_let_25 (tptp.zero_zero tptp.int))) (let ((_let_26 (tptp.hAPP tptp.int _let_19 _let_20 _let_25))) (let ((_let_27 (tptp.number_number_of tptp.nat))) (let ((_let_28 (tptp.hAPP tptp.int tptp.nat _let_27 tptp.pls))) (let ((_let_29 (tptp.zero_zero tptp.nat))) (let ((_let_30 (tptp.hAPP tptp.int tptp.int _let_23 tptp.pls))) (let ((_let_31 (tptp.one_one tptp.int))) (let ((_let_32 (tptp.one_one tptp.nat))) (let ((_let_33 (tptp.hAPP tptp.int tptp.nat _let_27 _let_21))) (let ((_let_34 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_29))) (let ((_let_35 (tptp.hAPP tptp.int tptp.nat _let_27 _let_22))) (let ((_let_36 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_37 (tptp.hAPP tptp.nat tptp.int _let_36 _let_29))) (let ((_let_38 (tptp.hAPP tptp.nat tptp.int _let_36 _let_32))) (let ((_let_39 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)) B_1)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.member X_b) X_1) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_1)))))))))) (let ((_let_40 (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (= (tptp.ti X_b B_3) (tptp.hAPP X_c X_b F X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_c (tptp.fun _let_2 tptp.bool) (tptp.member X_c) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_3) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3)))))))))) (let ((_let_41 (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= (tptp.ti X_c _let_1) _let_1))))) (let ((_let_42 (tptp.fun tptp.bool tptp.bool))) (let ((_let_43 (tptp.fun tptp.bool _let_42))) (let ((_let_44 (tptp.the_1 tptp.com))) (let ((_let_45 (tptp.option tptp.com))) (let ((_let_46 (tptp.fun tptp.int tptp.int))) (let ((_let_47 (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (or (not (= (tptp.ti X_b B_3) (tptp.hAPP X_c X_b F X_1))) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_c (tptp.fun _let_2 tptp.bool) (tptp.member X_c) X_1) A_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_3) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3))))))))) (let ((_let_48 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_10 _let_4)))) (let ((_let_49 (not _let_11))) (let ((_let_50 (= _let_5 (tptp.ti tptp.x_a _let_5)))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49 _let_48))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= _let_1 (tptp.ti X_c _let_1)))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (and _let_48 _let_17))) (let ((_let_58 (not _let_48))) (let ((_let_59 (= _let_8 _let_57))) (let ((_let_60 (not _let_57))) (let ((_let_61 (_let_39))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (tptp.fun X_b tptp.bool))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.x_a tptp.pname tptp.u _let_5 tptp.mgt_call tptp.pn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_49 _let_48 _let_51 _let_54))) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_57)) :args ((or (not _let_17) _let_57 _let_58))) (ASSUME :args (_let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_59)) :args ((or _let_8 _let_60 (not _let_59)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.x_a _let_5 tptp.g _let_4 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP _let_63 tptp.bool (tptp.hAPP _let_63 (tptp.fun _let_63 tptp.bool) (tptp.ord_less_eq _let_63) (tptp.hAPP _let_63 _let_63 (tptp.hAPP X_b (tptp.fun _let_63 _let_63) (tptp.insert X_b) X_1) A_3)) B_1)))) :args _let_61)) _let_62 :args (_let_59 false _let_39)) :args (_let_60 true _let_8 false _let_59)) :args (_let_58 false _let_17 true _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.x_a tptp.pname tptp.mgt_call tptp.pn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP X_a X_c B_1_1 B_2_1)))) :args (_let_55))) _let_56 :args (_let_50 false _let_55)) :args (_let_54 false _let_11 true _let_48 false _let_50)) _let_53 :args (false true _let_52 false _let_47)) :args ((forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.combb X_b X_c X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combc X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun X_b (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.combi X_a))) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.combk X_a X_b))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_b X_a)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combs X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (= (tptp.ti (tptp.fun tptp.pname _let_45) tptp.body) tptp.body) (forall ((X_c $$unsorted)) (let ((_let_1 (tptp.finite_card X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_c tptp.bool) tptp.nat) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite_comp_fun_idem X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_c)) tptp.bool) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite_fold_image X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun X_c X_b) (tptp.fun X_b (tptp.fun (tptp.fun X_c tptp.bool) X_b)))) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite1357897459simple X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool)))) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.finite908156982e_idem X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool)))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite_folding_one X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool)) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.finite2073411215e_idem X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (=> (tptp.ordere142940540dd_abs X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((X_c $$unsorted)) (let ((_let_1 (tptp.minus_minus X_c))) (=> (tptp.minus X_c) (= (tptp.ti (tptp.fun X_c (tptp.fun X_c X_c)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.one_one X_b))) (=> (tptp.one X_b) (= (tptp.ti X_b _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.monoid_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.plus_plus X_b))) (=> (tptp.cancel_semigroup_add X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b X_b)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.ab_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.ab_semigroup_mult X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.monoid_mult X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.semiring X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.no_zero_divisors X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.mult_zero X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (=> (tptp.zero X_b) (= (tptp.ti X_b _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.the X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) X_b) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.undefined X_a))) (= (tptp.ti X_a _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.if X_a))) (= (tptp.ti (tptp.fun tptp.bool (tptp.fun X_a (tptp.fun X_a X_a))) _let_1) _let_1))) (= (tptp.ti _let_46 tptp.bit1) tptp.bit1) (= (tptp.ti tptp.int tptp.pls) tptp.pls) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b))) (=> (tptp.number X_b) (= (tptp.ti (tptp.fun tptp.int X_b) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_b))) (=> (tptp.ring_1 X_b) (= (tptp.ti (tptp.fun X_b tptp.bool) _let_1) _let_1)))) (= (tptp.ti _let_46 tptp.succ) tptp.succ) (= (tptp.ti _let_15 tptp.suc) tptp.suc) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.nat_case X_b))) (let ((_let_2 (tptp.fun tptp.nat X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.ti (tptp.fun tptp.nat X_a) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.semiri532925092at_aux X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (=> (tptp.semiring_1 X_b) (= (tptp.ti (tptp.fun _let_2 (tptp.fun tptp.nat _let_2)) _let_1) _let_1))))) (= (tptp.ti _let_19 tptp.nat_neg) tptp.nat_neg) (= (tptp.ti (tptp.fun tptp.int _let_46) tptp.nat_tsub) tptp.nat_tsub) (= (tptp.ti (tptp.fun _let_45 tptp.com) _let_44) _let_44) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.bot_bot X_b))) (=> (tptp.bot X_b) (= (tptp.ti X_b _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.partial_flat_lub X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) X_b)) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.image X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool))) _let_1) _let_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.insert X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun X_b (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.the_elem X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) X_b) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.sum_Plus X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool))) _let_1) _let_1))) (= (tptp.ti tptp.bool tptp.fFalse) tptp.fFalse) (= (tptp.ti _let_42 tptp.fNot) tptp.fNot) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (= (tptp.ti _let_43 tptp.fconj) tptp.fconj) (= (tptp.ti _let_43 tptp.fdisj) tptp.fdisj) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fequal X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_43 tptp.fimplies) tptp.fimplies) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.ti (tptp.fun X_a X_c) B_1_1) B_2_1) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a X_c B_1_1 B_2_1))) _let_41 (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.member X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_1 tptp.g) tptp.g) (= (tptp.ti (tptp.fun _let_1 _let_7) tptp.p) tptp.p) (= (tptp.ti _let_2 tptp.u) tptp.u) (= (tptp.ti (tptp.fun tptp.com tptp.x_a) tptp.mgt) tptp.mgt) (= (tptp.ti _let_3 tptp.mgt_call) tptp.mgt_call) (= (tptp.ti tptp.nat tptp.na) tptp.na) (= (tptp.ti tptp.pname tptp.pn) tptp.pn) (= (tptp.ti (tptp.fun tptp.com tptp.bool) tptp.wt) tptp.wt) (forall ((Ts $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.x_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) Ts) G_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 tptp.p G_1) Ts)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite _let_1) (tptp.hAPP _let_2 _let_2 (tptp.collect _let_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc _let_1 _let_1 tptp.bool) (tptp.ord_less_eq _let_1)) A_3))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (H $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) F_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) H) F_1))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_finite X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_3))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_c) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_1 _let_2) (tptp.image X_b X_c) F) A_3))) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.hAPP _let_2 tptp.nat _let_1 B_1)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 B_1)) (tptp.hAPP _let_1 tptp.nat _let_2 A_3))) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_1)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 A_3)) (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 tptp.nat _let_1 A_3))) (let ((_let_4 (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (and (=> _let_5 (= _let_4 _let_3)) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_3))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP _let_2 tptp.nat _let_1 A_3)))))))) (forall ((X_b $$unsorted) (Q_3 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.collect X_b))) (let ((_let_5 (tptp.finite_finite X_b))) (=> (or (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Pa))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Q_3)))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.bool _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.bool _let_1 X_b) tptp.fconj) Pa)) Q_3))))))))))) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) K))))))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) Na))) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))))) (forall ((X_b $$unsorted)) (=> (tptp.finite_finite_1 X_b) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3))))) (forall ((X_b $$unsorted)) (=> (tptp.finite_finite_1 X_b) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat tptp.suc X) (tptp.hAPP tptp.nat tptp.nat tptp.suc Y)) (= X Y))) (forall ((Nat_3 $$unsorted) (Nat_4 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_3) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_4)) (= Nat_3 Nat_4))) (forall ((N $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) N))) (forall ((N $$unsorted)) (not (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M_1)) (= M_1 N)))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 K_1)))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (=> (= M_1 N) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) N)))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M_1)))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) N))) (forall ((I_2 $$unsorted) (J $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I_2))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J)) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K_1)) J)))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.finite_finite X_b))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) Pa)) Q_3)))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Pa))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Q_3))))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_2) A_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N))) (= M_1 _let_1)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((Na $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) M)))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 Na)) (= M _let_1)))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) M)))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) N)))) (forall ((M_1 $$unsorted) (N $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)) K_1))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N))))) (forall ((Na $$unsorted) (K $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 _let_1 K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Na) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na))))))))))) (forall ((N $$unsorted) (K_1 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M_1))) (let ((_let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 M_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_1)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))))))))) (forall ((Na $$unsorted) (K $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Na)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Na) K)) (= M Na)))))))) (forall ((I_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) N)) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 I_2)) I_2)))) (forall ((L_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 M_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) L_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) L_1))))))))) (forall ((L_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L_1))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (tptp.hAPP tptp.nat tptp.nat _let_1 M_1)))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) N)) M_1))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) B_1))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3))) (exists ((C_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) C_3) A_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_c) C_3)) (= (tptp.ti _let_1 B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) C_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP tptp.nat X_b F N_1)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Na) N_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP tptp.nat X_b F Na)) (tptp.hAPP tptp.nat X_b F N_3)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.member X_b))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_7 _let_5 X_2) A_3)) (not (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite X_b) (tptp.hAPP _let_4 _let_4 (tptp.collect X_b) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.bool _let_8 X_b) tptp.fconj) (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun X_b _let_7) _let_6 (tptp.combc X_b _let_4 tptp.bool) _let_5) A_3))) (tptp.hAPP X_c _let_4 (tptp.hAPP _let_2 (tptp.fun X_c _let_4) (tptp.combc X_b X_c tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_c _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_c _let_1 X_b) (tptp.fequal X_c)) F)) (tptp.hAPP X_b X_c F X_2))))))))))))))))))))))) _let_40 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) A_3)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_1)))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_b $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1))) (= (tptp.ti X_b A_2) (tptp.ti X_b B_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_3) B_1))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_3) A_3))) (=> (not (= (tptp.ti X_b A_2) (tptp.ti X_b B_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((I_1 $$unsorted) (Pa $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K)) (=> (forall ((N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_1)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) K) I_1)))))) (forall ((N $$unsorted) (M_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) M_4)) (exists ((M_2 $$unsorted)) (= M_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) X))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= X Y) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= A_1 B) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (= B C) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) B_1))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2) B_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) B_1)))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.collect X_b))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) A_2) (tptp.hAPP _let_1 _let_1 _let_6 Pa)) (tptp.hAPP _let_1 _let_1 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_3 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fimplies) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_3 (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2)))) Pa)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (=> (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_b X_c F X_2) (tptp.hAPP X_b X_c G X_2))) (= (tptp.ti _let_1 F) (tptp.ti _let_1 G))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_3 X_1))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa) (tptp.ti _let_1 Pa)))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 _let_2 A_3))) (= (tptp.hAPP _let_1 _let_1 _let_2 _let_3) _let_3))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.insert X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP X_b _let_3 _let_1 X_1))) (let ((_let_5 (tptp.hAPP X_b _let_3 _let_1 Y_2))) (= (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 _let_5 A_3)) (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP _let_2 _let_2 _let_4 A_3))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_3) A_3))) (or (= (tptp.ti X_b A_2) (tptp.ti X_b B_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((X_b $$unsorted) (Y_2 $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Y_2) A_3) X_1)) (or (= (tptp.ti X_b Y_2) (tptp.ti X_b X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_3 X_1)))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1))) (= (= (tptp.hAPP _let_1 _let_1 _let_2 A_3) (tptp.hAPP _let_1 _let_1 _let_2 B_1)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_1))))))))) (forall ((X_b $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_3) B_1))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_3) (tptp.ti _let_1 A_3))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) A_3)))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_1)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) A_3)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_1))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_1) A_3))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_2))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_1)) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) A_3)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Z_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) A_3)) (= (tptp.ti X_b Z_2) (tptp.hAPP X_c X_b F X_2))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (=> (= (tptp.ti X_c B_3) (tptp.hAPP X_b X_c F X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) B_3) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3)))))))) (forall ((X_b $$unsorted) (X_2 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_2) Xa) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) X_2))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) Xa)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_d $$unsorted) (F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_d X_b))) (let ((_let_2 (tptp.fun X_d X_c))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.fun X_d tptp.bool))) (let ((_let_6 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_6 _let_4) (tptp.image X_c X_b) F) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_6) (tptp.image X_d X_c) G) A_3)) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_5 _let_4) (tptp.image X_d X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb X_c X_b X_d) F) G)) A_3))))))))) (forall ((X_b $$unsorted) (Y_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) (tptp.combi X_b)) Y_3) (tptp.ti _let_1 Y_3)))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c G X_2))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP X_b X_c G X_1)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP X_b X_c G X_1)))))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) B_1))))) _let_39 (forall ((X_b $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1) A_3))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_b $$unsorted) (B_3 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_3) B_1))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (C_2 $$unsorted) (D_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2))) (let ((_let_3 (tptp.ord_less_eq _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 C_2) D_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 C_2)) (tptp.hAPP _let_1 _let_1 _let_2 D_3))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F))) (= (tptp.hAPP _let_2 _let_1 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_c (tptp.fun _let_2 _let_2) (tptp.insert X_c) A_2) B_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) (tptp.hAPP X_c X_b F A_2)) (tptp.hAPP _let_2 _let_1 _let_3 B_1))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) (tptp.hAPP X_b X_c F X_1)) _let_3) _let_3)))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3))) (exists ((AA $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) AA) A_3)) (= (tptp.ti _let_1 B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) AA)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_1)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (B_3 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_3) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3))) (not (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (= (tptp.ti X_b B_3) (tptp.hAPP X_c X_b F X_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) A_3))))))))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_1))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_2)) B_1)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3)) B_1)))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c G X_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G))))))) (forall ((N_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) N_2)) (exists ((M_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X_2) M_2)))))))) (forall ((G_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.x_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.x_a tptp.bool))) (let ((_let_2 (tptp.fun tptp.pname tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.pname (tptp.fun _let_2 tptp.bool) (tptp.member tptp.pname) X_2) tptp.u)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) tptp.p G_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.x_a (tptp.fun _let_1 _let_1) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call X_2)) (tptp.bot_bot _let_1)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) tptp.p G_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.x_a (tptp.fun _let_1 _let_1) (tptp.insert tptp.x_a) (tptp.hAPP tptp.com tptp.x_a tptp.mgt C_1)) (tptp.bot_bot _let_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.minus_minus X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (=> (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 A_2) B_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 C_1) D_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 C_1) D_1))))))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.bool (tptp.fun _let_2 _let_2) (tptp.nat_case tptp.bool) tptp.fFalse) (tptp.hAPP tptp.nat _let_2 _let_1 M)) Na)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_1 A_3))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_c X_b))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_b _let_7 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun X_b _let_7) (tptp.finite908156982e_idem X_b X_c) F) Z_2) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_1) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP _let_1 X_b F_1 B_1)) _let_2) _let_2)))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_c X_b))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_5 _let_4 (tptp.hAPP X_b _let_6 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_6) (tptp.finite908156982e_idem X_b X_c) F) Z_2) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) A_3)) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_1 A_3)))))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_finite X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1))))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.bot_bot _let_1)) A_3)))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa) (tptp.bot_bot _let_1)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) A_3) (tptp.bot_bot _let_1)))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) (tptp.bot_bot _let_1)) (tptp.ti _let_1 A_3)))) (forall ((X_b $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) C_1) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) _let_2) A_3) _let_2)))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_3)))) (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_3))))) (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((X_1 $$unsorted)) (= (tptp.hAPP X_c X_b (tptp.bot_bot (tptp.fun X_c X_b)) X_1) (tptp.bot_bot X_b))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP tptp.bool _let_1 (tptp.combk tptp.bool X_b) tptp.fFalse))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.bot X_c) (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_b X_c (tptp.bot_bot (tptp.fun X_b X_c)) X_2) (tptp.bot_bot X_c))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2) A_3)) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) (tptp.ti _let_1 A_3))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) (tptp.hAPP _let_1 _let_1 _let_3 A_3)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1))) (tptp.ti _let_1 A_3))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2))) (= (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) (tptp.hAPP _let_1 _let_1 _let_3 A_3)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2))) (let ((_let_4 (tptp.minus_minus _let_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_2 _let_4 A_3))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 B_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) B_1)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2))) (let ((_let_4 (tptp.minus_minus _let_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_2 _let_4 A_3))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 B_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 B_1)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun (tptp.fun X_c tptp.bool) X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun X_b _let_5) (tptp.finite908156982e_idem X_b X_c) F) Z_2) G) F_1)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F X_1) X_1) (tptp.ti X_b X_1))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_5 (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_3) (tptp.hAPP _let_1 _let_1 _let_3 B_1))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_3))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.member X_b) X_1) A_3)))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.hAPP X_b _let_6 (tptp.insert X_b) X_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 (tptp.hAPP _let_1 _let_1 _let_7 B_1))) (and (=> _let_5 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_6 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_7 (tptp.bot_bot _let_1)))) B_1))) (=> (not _let_5) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_1))))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B_1)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) A_3) B_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) B_1)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) A_3)) B_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_1))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_1))) (let ((_let_5 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1))) (let ((_let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_5 A_3)) B_1))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) B_1)))) (and (=> _let_7 (= _let_6 _let_4)) (=> (not _let_7) (= _let_6 (tptp.hAPP _let_1 _let_1 _let_5 _let_4)))))))))))) (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 B_1) C_2)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C_2) A_3)) (tptp.ti _let_1 A_3)))))))))) (forall ((X_b $$unsorted) (D_3 $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_3) C_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 D_3) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C_2) D_3))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1)) A_3)))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.insert X_b))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (=> (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_4 _let_3 A_2) _let_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_4 _let_3 B_3) _let_2)) (= (tptp.ti X_b A_2) (tptp.ti X_b B_3)))))))) (forall ((X_b $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))) (= (tptp.ti X_b B_3) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ti X_b C_1))) (let ((_let_2 (tptp.ti X_b B_3))) (let ((_let_3 (tptp.ti X_b D_1))) (let ((_let_4 (tptp.ti X_b A_2))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (let ((_let_6 (tptp.bot_bot _let_5))) (let ((_let_7 (tptp.insert X_b))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (= (= (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 A_2) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 B_3) _let_6)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 C_1) (tptp.hAPP _let_5 _let_5 (tptp.hAPP X_b _let_8 _let_7 D_1) _let_6))) (or (and (= _let_4 _let_1) (= _let_2 _let_3)) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))))) (forall ((X_b $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))) (= (tptp.ti X_b B_3) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_3) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (= (tptp.bot_bot _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) A_3))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) _let_2)) (= (tptp.ti _let_1 A_3) _let_2))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 _let_2) (tptp.image X_c X_b) F) A_3) (tptp.bot_bot _let_2)) (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) (tptp.bot_bot _let_2)) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (= (tptp.bot_bot _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 _let_2) (tptp.image X_c X_b) F) A_3)) (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) _let_1)) (= (tptp.ti X_a A_1) _let_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) _let_1)) (= (tptp.ti X_b A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.bot_bot X_a)) A_1))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2))) Pa)))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)))) (and (=> _let_8 (= _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_6 (tptp.insert X_b) A_2) _let_2))) (=> (not _let_8) (= _let_7 _let_2)))))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_5 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 X_b) tptp.fconj) (tptp.hAPP X_b _let_1 (tptp.fequal X_b) A_2))) Pa)))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)))) (and (=> _let_7 (= _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_5 (tptp.insert X_b) A_2) _let_2))) (=> (not _let_7) (= _let_6 _let_2))))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP X_b _let_1 (tptp.fequal X_b) A_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.minus_minus _let_2) A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) (tptp.bot_bot _let_2))))) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1))) (let ((_let_4 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (= (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 _let_3 A_3)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.minus_minus _let_2) A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) (tptp.bot_bot _let_2))))) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3))) (let ((_let_4 (tptp.finite_finite X_b))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2) B_1)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B_1))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 _let_2) (tptp.image X_c X_b) F))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) (tptp.hAPP _let_1 _let_2 _let_3 A_3)) (tptp.hAPP _let_1 _let_2 _let_3 B_1))) (tptp.hAPP _let_1 _let_2 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) _let_2))) (let ((_let_4 (tptp.ti _let_1 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) _let_3)) (or (= _let_4 _let_2) (= _let_4 _let_3)))))))) (forall ((X_b $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Nat_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_b))) (= (tptp.hAPP tptp.nat X_b (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.nat_case X_b) F1) F2) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_3)) (tptp.hAPP tptp.nat X_b F2 Nat_3)))) (forall ((X_c $$unsorted) (X_b $$unsorted) (C_1 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b X_c))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP _let_3 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_1) (tptp.image X_b X_c) (tptp.hAPP X_c _let_2 (tptp.combk X_c X_b) C_1)) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) C_1) (tptp.bot_bot _let_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.hAPP _let_4 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_1) (tptp.image X_b X_c) (tptp.hAPP X_c _let_3 (tptp.combk X_c X_b) C_1)) A_3))) (let ((_let_6 (= (tptp.ti _let_4 A_3) (tptp.bot_bot _let_4)))) (and (=> _let_6 (= _let_5 _let_2)) (=> (not _let_6) (= _let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) C_1) _let_2))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_1 A_3))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_c X_b))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_b _let_7 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun X_b _let_7) (tptp.finite908156982e_idem X_b X_c) F) Z_2) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_1) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP X_c X_b G X_1)) _let_2) _let_2)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (=> (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_2) B_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 C_1) D_1)) (= (= (tptp.ti X_b A_2) (tptp.ti X_b B_3)) (= (tptp.ti X_b C_1) (tptp.ti X_b D_1))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) B_1) A_3)) (= (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) A_3) B_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.hAPP _let_2 tptp.nat _let_1 B_1)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) B_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 A_3)) (tptp.hAPP _let_1 tptp.nat _let_2 B_1))) (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1)))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F_1) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1))) (=> (forall ((A_4 $$unsorted) (F_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) F_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 F_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) F_3)))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_1)))))))) (forall ((Pn $$unsorted) (G_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.x_a tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.insert tptp.x_a))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.hAPP tptp.x_a _let_4 _let_3 (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call Pn)))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.option tptp.com))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_6 tptp.p (tptp.hAPP _let_1 _let_1 _let_5 G_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.x_a _let_4 _let_3 (tptp.hAPP tptp.com tptp.x_a tptp.mgt (tptp.hAPP _let_7 tptp.com (tptp.the_1 tptp.com) (tptp.hAPP tptp.pname _let_7 tptp.body Pn)))) _let_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_6 tptp.p G_1) (tptp.hAPP _let_1 _let_1 _let_5 _let_2)))))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_3)) (=> (forall ((A_4 $$unsorted) (A_5 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_5)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_4) A_5)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_5)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_5) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_4) (tptp.bot_bot _let_1))))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1)))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (F_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) F_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) F_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) F_3)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_1))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_2)) (or (= (tptp.ti _let_1 A_2) (tptp.bot_bot _let_1)) (exists ((A_5 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_4) A_5)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_5))))))))) (forall ((U $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat F N_1)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat _let_1 tptp.nat) (tptp.ord_less_eq tptp.nat)) F)) U))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.the_elem X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (exists ((X_2 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) B_4)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) B_4))))))))) (forall ((Pn $$unsorted)) (let ((_let_1 (tptp.option tptp.com))) (let ((_let_2 (tptp.fun tptp.pname tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.pname (tptp.fun _let_2 tptp.bool) (tptp.member tptp.pname) Pn) tptp.u)) (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt (tptp.hAPP _let_1 tptp.com (tptp.the_1 tptp.com) (tptp.hAPP tptp.pname _let_1 tptp.body Pn)))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1)))))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1)))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 _let_4) B_1) _let_4)))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) C_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_1)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) B_1) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP _let_1 _let_1 _let_3 A_3))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_2 (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP _let_1 _let_1 _let_3 B_1))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_4 _let_2)))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 _let_4 A_3)))) (let ((_let_8 (= _let_5 _let_2))) (let ((_let_9 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_9 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (and (=> _let_8 (= _let_7 (tptp.ti X_b X_1))) (=> (not _let_8) (= _let_7 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 F X_1) (tptp.hAPP _let_1 X_b F_1 _let_5))))))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) _let_2)))) (let ((_let_5 (tptp.fun X_b X_b))) (let ((_let_6 (tptp.hAPP _let_1 X_b F_1 A_3))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP (tptp.fun X_b _let_5) (tptp.fun _let_8 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (and (=> _let_7 (= _let_6 (tptp.ti X_b X_1))) (=> (not _let_7) (= _let_6 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 F X_1) (tptp.hAPP _let_1 X_b F_1 _let_4))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_c _let_2 (tptp.insert X_c) X_1))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun _let_1 X_b))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_c X_b))) (let ((_let_8 (tptp.fun _let_7 _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_7 _let_6 (tptp.hAPP X_b _let_8 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun X_b _let_8) (tptp.finite1357897459simple X_b X_c) F) Z_2) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) A_3)) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 _let_3 A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_c X_b))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_6 _let_5 (tptp.hAPP X_b _let_7 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun X_b _let_7) (tptp.finite1357897459simple X_b X_c) F) Z_2) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_1) A_3)) (= (tptp.hAPP _let_1 X_b F_1 A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c _let_2 (tptp.insert X_c) X_1) (tptp.bot_bot _let_1))))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.minus X_c) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (= (tptp.hAPP X_b X_c (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1) X_2) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.minus_minus X_c) (tptp.hAPP X_b X_c A_3 X_2)) (tptp.hAPP X_b X_c B_1 X_2))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.minus X_b) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_b))) (= (tptp.hAPP X_c X_b (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_1) X_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) (tptp.hAPP X_c X_b A_3 X_1)) (tptp.hAPP X_c X_b B_1 X_1))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 tptp.nat _let_1 A_3))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 (tptp.minus_minus _let_2) A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_4 (tptp.insert X_b) X_1) (tptp.bot_bot _let_2)))))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (and (=> _let_6 (= _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_3) (tptp.one_one tptp.nat)))) (=> (not _let_6) (= _let_5 _let_3))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.minus_minus _let_2) A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) (tptp.bot_bot _let_2)))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.one_one tptp.nat))))))))) (forall ((X_b $$unsorted)) (=> (tptp.one X_b) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_b))) (let ((_let_2 (tptp.ti X_b X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_5) (tptp.finite1357897459simple X_b X_c) F) Z_2) G) F_1)) (= (tptp.hAPP _let_1 X_b F_1 (tptp.bot_bot _let_1)) (tptp.ti X_b Z_2))))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.one_one tptp.nat)) N)) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M_1))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.one_one tptp.nat))) N)))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun X_c X_b))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_5 _let_4 (tptp.hAPP X_b _let_6 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun X_b _let_6) (tptp.finite1357897459simple X_b X_c) F) Z_2) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_1) A_3))) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_c (tptp.fun _let_1 _let_1) (tptp.insert X_c) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP _let_1 X_b F_1 A_3))))))))))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3))) (let ((_let_4 (tptp.finite_card X_b))) (let ((_let_5 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_5 A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_5 B_1))) (= (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2) B_1))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B_1))) (tptp.one_one tptp.nat)))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3))) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F X_1) (tptp.hAPP _let_1 X_b F_1 A_3))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_2) Y_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Y_1) (tptp.bot_bot _let_1))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP _let_1 X_b F_1 A_3)) A_3))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_5) (tptp.finite1357897459simple X_b X_c) F) Z_2) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) A_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) A_3)) (= (tptp.hAPP X_c X_b G X_2) (tptp.ti X_b Z_2))))) (= (tptp.hAPP _let_1 X_b F_1 A_3) (tptp.ti X_b Z_2))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP _let_1 tptp.nat _let_3 A_3) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP _let_1 tptp.nat _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1) (tptp.bot_bot _let_1)))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) X_1))) (let ((_let_4 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (= (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 _let_3 A_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))))) (forall ((X_b $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_1 A_3))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_4 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (= (tptp.ti _let_1 B_1) (tptp.bot_bot _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_1) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP _let_1 X_b F_1 B_1)) _let_2) _let_2)))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F X_1) (tptp.hAPP _let_1 X_b F_1 A_3)))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) F_1)) (=> (not (= (tptp.ti _let_1 F_1) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) (tptp.bot_bot _let_1)))))) (=> (forall ((X_2 $$unsorted) (F_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) F_3)) (=> (not (= (tptp.ti _let_1 F_3) (tptp.bot_bot _let_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) F_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) F_3))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_1)))))))) (forall ((X_b $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.the_elem X_b) X_3) (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb _let_1 tptp.bool X_b) (tptp.hAPP _let_1 _let_3 (tptp.fequal _let_1) X_3)) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 _let_1)) (tptp.fun _let_1 _let_2) (tptp.combc X_b _let_1 _let_1) (tptp.insert X_b)) (tptp.bot_bot _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_b $$unsorted)) (=> (tptp.cancel_semigroup_add X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2))) (= (= (tptp.hAPP X_b X_b _let_1 B_3) (tptp.hAPP X_b X_b _let_1 C_1)) (= (tptp.ti X_b B_3) (tptp.ti X_b C_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.cancel_semigroup_add X_b) (forall ((B_3 $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 B_3) A_2) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 C_1) A_2)) (= (tptp.ti X_b B_3) (tptp.ti X_b C_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1))) (=> (= (tptp.hAPP X_a X_a _let_1 B) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel146912293up_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1))) (=> (= (tptp.hAPP X_a X_a _let_1 B) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_1)) (= (tptp.ti X_a B) (tptp.ti X_a C)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun (tptp.fun X_b tptp.bool) X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F X_1) X_1) (tptp.ti X_b X_1)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) M_1))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat _let_4 Z)) (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 Z)))))))) (forall ((M_1 $$unsorted) (N $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 N)) K_1) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_1))))))) (forall ((K $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 M) (tptp.hAPP tptp.nat tptp.nat _let_1 Na)) (= M Na)))) (forall ((M $$unsorted) (K $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Na) K)) (= M Na))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 A_2) C_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 B_3) C_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) C_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 B_3))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_1) B)) B) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) B)) B) (tptp.ti X_a A_1)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat _let_1 N))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((N $$unsorted) (M_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) N)))) (forall ((N $$unsorted) (M_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M_1)))) (forall ((M $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) Na)) (exists ((K_2 $$unsorted)) (= Na (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K_2))))) (forall ((K $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na))))))) (forall ((M_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J) M_1)))))) (forall ((M_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) J)))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K_1))))))))) (forall ((K_1 $$unsorted) (L_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K_1) L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) L_1)))))))))) (forall ((M_1 $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) K_1)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) N)))))) (forall ((M_1 $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) K_1)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)))))) (forall ((M_1 $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) K_1)) N)) (not (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) N))))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M_1) N)) N) M_1))) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M_1)) N) M_1))) (forall ((I_2 $$unsorted) (J $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 _let_2 I_2))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_3 J)) K_1) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) J) K_1))))))) (forall ((K_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) K_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M_1)) (tptp.hAPP tptp.nat tptp.nat _let_3 N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)))))) (forall ((M_1 $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 N) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)))))) (forall ((I_2 $$unsorted) (K_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_2) K_1)) J)))))) (forall ((J_1 $$unsorted) (K $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) K)) I_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 J_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K)))))))) (forall ((M_1 $$unsorted) (K_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 K_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M_1)) K_1)))))))) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M_1) N)) M_1)))) (forall ((I_2 $$unsorted) (K_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_2))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J)) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 J) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 J)) K_1))))))) (forall ((I_1 $$unsorted) (K $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 K) J_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K)) J_1)))))))) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M_1) N)) N) M_1)))) (forall ((K $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_1)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) I_1) K) (= J_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) K) I_1)))))) (forall ((I_2 $$unsorted) (K_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J)) K_1) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K_1)))))))) (forall ((I_2 $$unsorted) (K_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) K_1)) I_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) I_2)) K_1))))))) (forall ((I_2 $$unsorted) (K_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) I_2)) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K_1)) I_2))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) N))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat)))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_1 A_3))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_4 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F X_1) _let_2) _let_2))))))))) (forall ((M_1 $$unsorted) (K_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) K_1))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M_1) K_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc J))))))) (forall ((M_1 $$unsorted) (K_1 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) K_1))) M_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc J)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) K_1) M_1))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)))))))) (forall ((X_b $$unsorted) (N_2 $$unsorted) (H $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_1)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (= (tptp.hAPP X_b X_b H (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F X_2) Y_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F (tptp.hAPP X_b X_b H X_2)) (tptp.hAPP X_b X_b H Y_1))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) N_2)) (=> (not (= (tptp.ti _let_1 N_2) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b F_1 N_2)) (tptp.hAPP _let_1 X_b F_1 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) H) N_2))))))))))) (forall ((Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) B_3) (tptp.bot_bot _let_1)))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.hAPP _let_1 X_b (tptp.hAPP X_b (tptp.fun _let_1 X_b) (tptp.partial_flat_lub X_b) B_3) A_3))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 (tptp.ord_less_eq _let_1) A_3) _let_3)))) (and (=> _let_6 (= _let_5 (tptp.ti X_b B_3))) (=> (not _let_6) (= _let_5 (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b _let_4) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) _let_3))))))))))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_comp_fun_idem X_b _let_1) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_4) (tptp.combb _let_1 _let_3 X_b) (tptp.hAPP _let_5 _let_5 (tptp.combc _let_1 _let_1 _let_1) (tptp.minus_minus _let_1))) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_2) (tptp.combc X_b _let_1 _let_1) (tptp.insert X_b)) (tptp.bot_bot _let_1))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.combb tptp.bool tptp.bool X_b))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun X_b _let_4))) (let ((_let_8 (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_7 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_7 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_7) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP tptp.bool _let_4 tptp.fimplies Pa)) (tptp.hAPP X_b _let_1 _let_3 X_1)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP tptp.bool _let_4 tptp.fimplies (tptp.hAPP tptp.bool tptp.bool tptp.fNot Pa))) (tptp.hAPP X_b _let_1 _let_3 Y_2)))))) (let ((_let_9 (tptp.hBOOL Pa))) (and (=> _let_9 (= (tptp.ti X_b X_1) _let_8)) (=> (not _let_9) (= (tptp.ti X_b Y_2) _let_8))))))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (= (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2)) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_c X_c))) (let ((_let_2 (tptp.hAPP X_b _let_1 F X_1))) (let ((_let_3 (tptp.hAPP X_c X_c _let_2 Z_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b _let_1) tptp.bool (tptp.finite_comp_fun_idem X_b X_c) F)) (= (tptp.hAPP X_c X_c _let_2 _let_3) _let_3)))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 _let_1)) tptp.bool (tptp.finite_comp_fun_idem X_b _let_1) (tptp.insert X_b))))) (forall ((X_b $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 X_b (tptp.the X_b) (tptp.hAPP X_b _let_1 (tptp.fequal X_b) X_1)) (tptp.ti X_b X_1)))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (= (tptp.ti X_b X_2) (tptp.ti X_b A_2)))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_1)) (= (tptp.ti X_b Y_1) (tptp.ti X_b X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_1)) (= (tptp.ti X_b Y_1) (tptp.ti X_b X_2)))))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (= (tptp.ti X_b X_2) (tptp.ti X_b A_2)))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa)))))) (forall ((X_b $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.bot_bot _let_2))) (let ((_let_4 (tptp.insert X_b))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.minus_minus _let_2))) (let ((_let_7 (tptp.member X_b))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_8 _let_7 X_1) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_8 _let_7 Y_2) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_5 _let_6 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_5 _let_6 A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_5 _let_4 X_1) _let_3))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_5 _let_4 Y_2) _let_3)))) (tptp.hAPP _let_2 tptp.nat _let_1 A_3))))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.minus_minus _let_2) A_3) (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) (tptp.bot_bot _let_2))))) (tptp.hAPP _let_2 tptp.nat _let_1 A_3))))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) K))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N)))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (= M Na)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) M))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N)))) (forall ((N $$unsorted) (M_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) M_1)) (not (= M_1 N)))) (forall ((S_1 $$unsorted) (T_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) S_1) T_4)) (not (= S_1 T_4)))) (forall ((Pa $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 Pa Na) M)))) (let ((_let_3 (tptp.ord_less tptp.nat))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 M) Na)) _let_2) (=> (=> (= M Na) _let_2) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 Na) M)) _let_2) _let_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) X)))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (not (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2))) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2))) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a X) (tptp.ti X_a Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun 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(tptp.hAPP X_a _let_2 _let_1 B) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= A_1 B) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (= B C) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) Y_2) X_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) Y_2) X_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Y) X))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_2)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_2)) (not (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2))))))))) (forall ((X_b $$unsorted)) (=> (tptp.preorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 (tptp.ord_less X_b) X_1) Y_2)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_2) X_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_2)) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_2)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 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(=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_2)) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_2))) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) A_1) B)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B) A_1)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) Z) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Z) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 A_2) C_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 B_3) C_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) C_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 B_3))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.bot_bot X_a))))))) (forall ((X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.bot_bot X_b))) (= (not (= (tptp.ti X_b A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) _let_1) A_2))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.minus_minus X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (=> (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 A_2) B_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 C_1) D_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 C_1) D_1))))))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc M))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na)) (= M Na))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na)))))) (forall ((Na $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (= Na M))))) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))) (= M_1 N))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M_1) N)) (=> (not (= _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) N)))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2)) K_1))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N))) (= M_1 N))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)))))) (forall ((I_2 $$unsorted) (J $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) J)) I_2)))) (forall ((J $$unsorted) (I_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J) I_2)) I_2)))) (forall ((K $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na))))))) (forall ((M_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J) M_1)))))) (forall ((M_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) J)))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K_1))))))))) (forall ((K_1 $$unsorted) (L_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K_1) L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) L_1)))))))))) (forall ((M_1 $$unsorted) (N $$unsorted) (K_1 $$unsorted) (L_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) L_1)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M_1) L_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 K_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N))))))))) (forall ((I_2 $$unsorted) (J $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) J)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K_1)))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)))))) (forall ((Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) Na)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) Na)) (not (= M Na)))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) Na)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) Na)) (= M Na))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) N))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) N)) (=> (not (= M_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) N)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) N)) (= M_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) N))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X) Y))))) (forall ((N $$unsorted) (J $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J) N)) K_1)))))) (forall ((L_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L_1))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 M_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (tptp.hAPP tptp.nat tptp.nat _let_1 M_1)))))))))) (forall ((N_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) N_2)) (exists ((M_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) M_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (=> (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat X_b) F) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) Na)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3))))))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) Na))) Na)))) (forall ((Pa $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 tptp.nat) tptp.fconj) Pa)) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) I_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((I_2 $$unsorted) (M_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) M_1))))) (forall ((I_2 $$unsorted) (M_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) I_2))))) (forall ((M $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) Na)) (exists ((K_2 $$unsorted)) (= Na (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K_2)))))) (forall ((Na $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Na) M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) M))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) Na))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) Na))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) N))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (= Na M))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) N))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)))) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K)) J_1))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) N))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M_1) N)) M_1)))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 (tptp.ord_less_eq tptp.nat) C) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B) C)))))))))) (forall ((Na $$unsorted) (K $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Na) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na))))))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc X_2))))) (forall ((M $$unsorted) (K $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M_2)) (tptp.hAPP tptp.nat tptp.nat F N_1))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M)) K)) (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) K)))))))) (forall ((Pa $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa J_1)) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc I))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I_1)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) N)) (exists ((K_2 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) K_2)))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Na $$unsorted) (M $$unsorted) (F $$unsorted)) (=> (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b F N_1)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b F Na)) (tptp.hAPP tptp.nat X_b F M))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) M))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b F N_1)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) N_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b F Na)) (tptp.hAPP tptp.nat X_b F N_3)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.one_one X_a))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.ord_less _let_1) F) G)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 F) G)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 G) F))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) A_3) (tptp.bot_bot _let_1)))))) (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.ord_less_eq _let_1) A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) C_2)))))))) (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) B_1) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 C_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_1)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_1)) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_1)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_1))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_1)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_1)) (not (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_1)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less _let_2) A_3) B_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.hAPP _let_2 tptp.nat _let_1 B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.hAPP X_b _let_5 (tptp.insert X_b) X_1))) (let ((_let_7 (tptp.ord_less _let_1))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))) (let ((_let_9 (tptp.hAPP _let_1 _let_2 _let_7 A_3))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_9 (tptp.hAPP _let_1 _let_1 _let_6 B_1))) (and (=> _let_8 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_9 B_1))) (=> (not _let_8) (and (=> _let_4 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 _let_7 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_5 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_6 (tptp.bot_bot _let_1)))) B_1))) (=> (not _let_4) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_1))))))))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_3 A_3)) (tptp.hAPP _let_1 tptp.nat _let_3 B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_1))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (exists ((N_1 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.ti _let_3 A_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun _let_1 _let_3) (tptp.image tptp.nat X_b) F_2) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) N_1)))))))))) (forall ((Na $$unsorted) (N_2 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) Na))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) N_2)))) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (forall ((I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F I)) (tptp.hAPP tptp.nat tptp.nat F J_2))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F I_1)) (tptp.hAPP tptp.nat tptp.nat F J_1)))))))) (forall ((I_2 $$unsorted) (K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) K_1)) (=> (not (= K_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2))) (not (forall ((J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J_2)) (not (= K_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc J_2))))))))) (forall ((I_2 $$unsorted) (K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2)) K_1)) (not (forall ((J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J_2)) (not (= K_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc J_2)))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_1)))))))) (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_1) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_2))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) A_3) B_1)) (exists ((B_5 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_5) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) B_1) A_3)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.ord X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F B_3)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) C_1) B_3)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) Y_1) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_c X_b F Y_1)) (tptp.hAPP X_c X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) (tptp.hAPP X_c X_b F C_1)) A_2))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_c X_b F B_3)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) C_1) B_3)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) Y_1) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F Y_1)) (tptp.hAPP X_c X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_c X_b F C_1)) A_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (F $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) A_2) (tptp.hAPP X_c X_b F B_3))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) B_3) C_1)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) X_2) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_c X_b F X_2)) (tptp.hAPP X_c X_b F Y_1))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) A_2) (tptp.hAPP X_c X_b F C_1)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (F $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_c X_b F B_3))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) B_3) C_1)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) X_2) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F X_2)) (tptp.hAPP X_c X_b F Y_1))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_c X_b F C_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z $$unsorted) (Y $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) Z))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) Z)))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (=> (forall ((W_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 X) W_3)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 W_3) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) W_3) Z))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) Z)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) B_3) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less_eq X_c) C_1) (tptp.hAPP X_b X_c F B_3))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_1) X_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F Y_1)) (tptp.hAPP X_b X_c F X_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less X_c) C_1) (tptp.hAPP X_b X_c F A_2)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) B_3) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool _let_1 (tptp.hAPP X_b X_c F B_3))) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_1) X_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F Y_1)) (tptp.hAPP X_b X_c F X_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool _let_1 (tptp.hAPP X_b X_c F A_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((F $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.ord_less X_c))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) B_3)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_2 _let_1 (tptp.hAPP X_b X_c F B_3)) C_1)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_2) Y_1)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c F Y_1))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_2 _let_1 (tptp.hAPP X_b X_c F A_2)) C_1)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((F $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2) B_3)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F B_3)) C_1)) (=> (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_2) Y_1)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c F Y_1))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less X_c) (tptp.hAPP X_b X_c F A_2)) C_1))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.sum_sum X_b X_c))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) B_1)) (= (tptp.hAPP _let_4 tptp.nat (tptp.finite_card _let_3) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_4) (tptp.sum_Plus X_b X_c) A_3) B_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_c) B_1)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted) (M_3 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.image X_b X_c))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun X_b X_c))) (=> (= (tptp.ti _let_3 M_3) (tptp.ti _let_3 N_2)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) N_2)) (= (tptp.hAPP X_b X_c F X_2) (tptp.hAPP X_b X_c G X_2))))) (= (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 F) M_3) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_5 _let_4 _let_1 G) N_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.sum_sum X_b X_c))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite _let_2) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun _let_1 _let_3) (tptp.sum_Plus X_b X_c) A_3) B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) B_1))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.sum_sum X_b X_c))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite _let_2) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_4 _let_3) (tptp.sum_Plus X_b X_c) A_3) B_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.sum_sum X_b X_c))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite X_c) B_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite _let_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.sum_Plus X_b X_c) A_3) B_1)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.sum_sum X_b X_c))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite _let_3) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_4) (tptp.sum_Plus X_b X_c) A_3) B_1))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) B_1))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool))) (= (= (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_3) (tptp.sum_Plus X_b X_c) A_3) B_1) (tptp.bot_bot _let_3)) (and (= (tptp.ti _let_2 A_3) (tptp.bot_bot _let_2)) (= (tptp.ti _let_1 B_1) (tptp.bot_bot _let_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.sum_sum X_b X_c))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.hAPP _let_2 tptp.nat (tptp.finite_card _let_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.sum_Plus X_b X_c) A_3) B_1)))) (let ((_let_6 (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite X_c) B_1))))) (and (=> _let_6 (= _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_4 tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP _let_3 tptp.nat (tptp.finite_card X_c) B_1)))) (=> (not _let_6) (= _let_5 (tptp.zero_zero tptp.nat))))))))))) (forall ((X_b $$unsorted) (R_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_1 _let_1) (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 R_1)) (tptp.hAPP _let_1 _let_1 _let_4 S))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 R_1) S)))))))) (forall ((X_b $$unsorted) (Q_3 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.collect X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_3 X_2)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_2 _let_2 _let_1 Pa)) (tptp.hAPP _let_2 _let_2 _let_1 Q_3))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.zero_zero tptp.nat))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Na) _let_1)) (= Na _let_1)))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 M_1) N) _let_1) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 N) M_1) _let_1) (= M_1 N))))))) (forall ((M_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) M_1) (tptp.zero_zero tptp.nat))) (forall ((M_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) (tptp.zero_zero tptp.nat)) M_1)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_1) N) _let_1))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.one_one X_a) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.zero_zero X_a) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (= (= _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2)) (= (tptp.ti X_b A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_b $$unsorted)) (=> (tptp.group_add X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted)) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B_3) (tptp.zero_zero X_b)) (= (tptp.ti X_b A_2) (tptp.ti X_b B_3)))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted)) (= (= (tptp.ti X_b A_2) (tptp.ti X_b B_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B_3) (tptp.zero_zero X_b)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) A_1) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_b $$unsorted)) (=> (tptp.zero X_b) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.ti X_b X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (= (tptp.bot_bot tptp.nat) _let_29) (forall ((M_1 $$unsorted) (N $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) N) M_1) (= N (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) Na) _let_1) (and (= M _let_1) (= Na _let_1))))) (forall ((M_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) (tptp.zero_zero tptp.nat)) M_1)) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.zero_zero tptp.nat)) N) N)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (not (= N _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) N)) (not (= N (tptp.zero_zero tptp.nat))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.zero_zero tptp.nat))))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (not (= Na _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) Na))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.zero_zero tptp.nat))))) (forall ((M_1 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1) (tptp.zero_zero tptp.nat)))) (forall ((M_1 $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)))) (forall ((Nat_2 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_2) (tptp.zero_zero tptp.nat)))) (forall ((M_1 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1) (tptp.zero_zero tptp.nat)))) (forall ((Nat_1 $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_1)))) (forall ((M_1 $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)))) (forall ((X_b $$unsorted) (F1 $$unsorted) (F2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_b))) (= (tptp.hAPP tptp.nat X_b (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.nat_case X_b) F1) F2) (tptp.zero_zero tptp.nat)) (tptp.ti X_b F1)))) (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 A_2))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.ord_less_eq X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere216010020id_add X_b) (forall ((Y_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_2 X_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_2 Y_2)) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) X_1) Y_2) _let_1) (and (= (tptp.ti X_b X_1) _let_1) (= (tptp.ti X_b Y_2) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.zero_zero X_b)))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 A_2))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.ord_less X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B_3)) (tptp.zero_zero X_b))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B_3)) (tptp.zero_zero X_b))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Na)) (exists ((M_2 $$unsorted)) (= Na (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= Na _let_1)))) (forall ((M $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (or (= M (tptp.zero_zero tptp.nat)) (exists ((J_2 $$unsorted)) (and (= M (tptp.hAPP tptp.nat tptp.nat tptp.suc J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J_2) Na))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) Na)) (or (and (= M _let_2) (= Na _let_1)) (and (= M _let_1) (= Na _let_2))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) Na) _let_2) (or (and (= M _let_2) (= Na _let_1)) (and (= M _let_1) (= Na _let_2))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) Na))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na)))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) (tptp.bot_bot _let_1)) (tptp.zero_zero tptp.nat)))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_3) (tptp.zero_zero tptp.nat))))) (forall ((Na $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) Na) M))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) N)) M_1)))))))) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M_1)) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted) (Na $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) Na) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) Na)))) (forall ((M_1 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) N) (tptp.zero_zero tptp.nat)))) (= _let_32 _let_34) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.nat_case tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.combi tptp.nat)) (tptp.hAPP tptp.nat tptp.nat _let_2 Na)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) _let_1) _let_1)))))) (forall ((X_b $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_2 X_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) _let_2)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_3) (tptp.zero_zero tptp.nat)) (or (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) N)))) (forall ((I_2 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2))) N)))))) (forall ((X_b $$unsorted) (Q_3 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) Pa) Q_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_3 X_1)))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Pa $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) Pa) Q_3)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_3 X_1)))))) (forall ((Pa $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) A_2) B_3))) (and (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) A_2) B_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat)))) (forall ((D_2 $$unsorted)) (=> (= A_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) B_3) D_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa D_2))))))) (forall ((Pa $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) A_2) B_3))) (not (or (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) A_2) B_3)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat))))) (exists ((D_2 $$unsorted)) (and (= A_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) B_3) D_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa D_2))))))))) (forall ((I_1 $$unsorted) (M_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)))) (let ((_let_4 (tptp.member tptp.nat))) (let ((_let_5 (tptp.combc tptp.nat _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (let ((_let_11 (tptp.hAPP (tptp.fun tptp.bool _let_9) (tptp.fun _let_1 _let_10) (tptp.combb tptp.bool _let_9 tptp.nat) tptp.fconj))) (let ((_let_12 (tptp.combs tptp.nat tptp.bool tptp.bool))) (let ((_let_13 (tptp.collect tptp.nat))) (let ((_let_14 (tptp.finite_card tptp.nat))) (let ((_let_15 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_7 _let_4 (tptp.zero_zero tptp.nat)) M_3)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 (tptp.hAPP _let_15 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_15 _let_8) (tptp.combb tptp.nat _let_7 tptp.nat) _let_4) tptp.suc)) M_3))) (tptp.hAPP tptp.nat _let_1 _let_3 I_1))))) (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 _let_4) M_3))) (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1))))))))))))))))))))))) (forall ((I_1 $$unsorted) (M_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.member tptp.nat))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.nat _let_6 _let_4 _let_1) M_3)) (not (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.nat) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_8 _let_5 (tptp.combs tptp.nat tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_8 (tptp.hAPP (tptp.fun tptp.bool _let_7) (tptp.fun _let_2 _let_8) (tptp.combb tptp.bool _let_7 tptp.nat) tptp.fconj) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.nat _let_6) _let_5 (tptp.combc tptp.nat _let_2 tptp.bool) _let_4) M_3))) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1))))) _let_1)))))))))))) (forall ((I_1 $$unsorted) (M_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)))) (let ((_let_4 (tptp.member tptp.nat))) (let ((_let_5 (tptp.combc tptp.nat _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (let ((_let_11 (tptp.hAPP (tptp.fun tptp.bool _let_9) (tptp.fun _let_1 _let_10) (tptp.combb tptp.bool _let_9 tptp.nat) tptp.fconj))) (let ((_let_12 (tptp.combs tptp.nat tptp.bool tptp.bool))) (let ((_let_13 (tptp.collect tptp.nat))) (let ((_let_14 (tptp.finite_card tptp.nat))) (let ((_let_15 (tptp.fun tptp.nat tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_7 _let_4 (tptp.zero_zero tptp.nat)) M_3))) (= (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 (tptp.hAPP _let_15 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_15 _let_8) (tptp.combb tptp.nat _let_7 tptp.nat) _let_4) tptp.suc)) M_3))) (tptp.hAPP tptp.nat _let_1 _let_3 I_1)))) (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 _let_4) M_3))) (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1))))))))))))))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_3))) (and (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)))))) (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))) N))) (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat)))))) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M_1) N))) (let ((_let_4 (= M_1 (tptp.zero_zero tptp.nat)))) (and (=> _let_4 (= _let_3 N)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M_1) (tptp.one_one tptp.nat))) N)))))))))) (forall ((Na $$unsorted) (Pa $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa Na)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) K_2) Na)) (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) K_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2) (tptp.one_one tptp.nat))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (K $$unsorted)) (= (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)) (exists ((B_5 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_5) B_4)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_5) B_4))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) B_4) K) (=> (= K (tptp.zero_zero tptp.nat)) (= (tptp.ti _let_1 B_4) (tptp.bot_bot _let_1)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (=> (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_3)))) (= (tptp.one_one tptp.nat) _let_1)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_b) A_3) _let_1)))))) (forall ((Na $$unsorted) (Pa $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa Na)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) Na)) (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) K_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K_2))))))) (forall ((I_2 $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) K_2) J))))) (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (exists ((M_2 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_idom X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.ord_less X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2) _let_1) (= (tptp.ti X_b A_2) _let_1)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (K $$unsorted)) (=> (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)) (exists ((B_5 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B_5) B_4)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_5) B_4))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) B_4) K) (=> (= K (tptp.zero_zero tptp.nat)) (= (tptp.ti _let_1 B_4) (tptp.bot_bot _let_1)))))))) (forall ((Y $$unsorted)) (=> (not (= Y (tptp.zero_zero tptp.nat))) (not (forall ((Nat $$unsorted)) (not (= Y (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat))))))) (forall ((Pa $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K)) (=> (forall ((N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_1)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat)))))) (forall ((N $$unsorted)) (=> (not (= N (tptp.zero_zero tptp.nat))) (exists ((M_2 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))) (forall ((Na $$unsorted) (Pa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.zero_zero tptp.nat))) (=> (forall ((N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa Na))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) D)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 C))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 D)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 D)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.semiri456707255roduct X_b) (forall ((B_3 $$unsorted) (A_2 $$unsorted)) (= (= (tptp.ti X_b B_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) B_3) A_2)) (= (tptp.ti X_b A_2) (tptp.zero_zero X_b)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (forall ((E_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) (tptp.zero_zero X_a)) E_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Y) E_2)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.nat))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_b) A_3) (tptp.hAPP _let_2 tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.nat)) (tptp.fun _let_1 _let_4) (tptp.finite_fold_image tptp.nat X_b) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_1 (tptp.combk tptp.nat X_b) (tptp.one_one tptp.nat))) (tptp.zero_zero tptp.nat)) A_3)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_b) A_3))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)))) (let ((_let_5 (tptp.fun X_b tptp.nat))) (let ((_let_6 (tptp.fun _let_2 tptp.nat))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (and (=> _let_4 (= _let_3 (tptp.hAPP _let_2 tptp.nat (tptp.hAPP tptp.nat _let_6 (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.nat)) (tptp.fun _let_5 _let_7) (tptp.finite_fold_image tptp.nat X_b) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_5 (tptp.combk tptp.nat X_b) (tptp.one_one tptp.nat))) _let_1) A_3))) (=> (not _let_4) (= _let_3 _let_1))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_c X_b))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_4 _let_3) (tptp.finite_fold_image X_b X_c) F) G) Z_2) (tptp.bot_bot _let_1)) (tptp.ti X_b Z_2))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_2 $$unsorted) (G $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun X_b (tptp.fun X_b X_b)))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_4 _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_6 (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 (tptp.fun X_b _let_7) (tptp.finite1357897459simple X_b X_c) F) Z_2) G) F_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) A_3)) (= (tptp.hAPP _let_1 X_b F_1 A_3) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.finite_fold_image X_b X_c) F) G) Z_2) A_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_idom X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.ord_less X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.plus_plus X_b))) (let ((_let_5 (tptp.fun X_b X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) A_2) (tptp.ring_1_Ints X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 _let_4 (tptp.one_one X_b)) A_2)) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 A_2) _let_1)))))))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) _let_1)) (= _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_1) (tptp.one_one tptp.nat))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord626643107strict X_a) (forall ((V $$unsorted) (U_1 $$unsorted) (Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.ord_less X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.hAPP X_a _let_5 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 X) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 Y) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_6 U_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_6 V)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 U_1) V) (tptp.one_one X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 U_1) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 V) Y))) A_1)))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ring_1 X_b) (forall ((B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_b))) (let ((_let_2 (tptp.member X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 _let_2 B_3) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B_3)) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.mult_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) _let_1) A_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.mult_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) _let_1) _let_1))))) (forall ((X_b $$unsorted)) (=> (tptp.ring_n68954251visors X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) A_2) B_3) _let_1) (or (= (tptp.ti X_b A_2) _let_1) (= (tptp.ti X_b B_3) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (=> (not (= (tptp.ti X_a B) _let_1)) (not (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B) _let_1) (or (= (tptp.ti X_a A_1) _let_1) (= (tptp.ti X_a B) _let_1))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) _let_1) N) _let_1))) (forall ((M_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1) _let_1) _let_1))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) Na) _let_1) (or (= M _let_1) (= Na _let_1))))) (forall ((K $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 M) (tptp.hAPP tptp.nat tptp.nat _let_1 Na)) (or (= M Na) (= K (tptp.zero_zero tptp.nat)))))) (forall ((M $$unsorted) (K $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Na) K)) (or (= M Na) (= K (tptp.zero_zero tptp.nat))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_b) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) tptp.bool (tptp.finite_comp_fun_idem X_b X_b) (tptp.times_times X_b))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring X_a) (forall ((A_1 $$unsorted) (E_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) E_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) E_1)) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) E_1)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((K $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 M) (tptp.hAPP tptp.nat tptp.nat _let_1 Na)) (= M Na)))) (forall ((M_1 $$unsorted) (N $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M_1) N)) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_1))))))) (forall ((K_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K_1))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 M_1) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 M_1)) (tptp.hAPP tptp.nat tptp.nat _let_2 N))))))) (forall ((K_1 $$unsorted) (L_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K_1) L_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) L_1)))))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K_1))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_2) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 I_2)) (tptp.hAPP tptp.nat tptp.nat _let_1 J)))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K_1))))))))) (forall ((M_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 M_1)))))) (forall ((M_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1) M_1)))) (forall ((M_1 $$unsorted) (N $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M_1) N)) K_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_1))))))) (forall ((K_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K_1))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 M_1) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 M_1)) (tptp.hAPP tptp.nat tptp.nat _let_2 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) X) (tptp.ti X_a X))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_mult X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) Na) _let_1) (and (= M _let_1) (= Na _let_1))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) N) (tptp.one_one tptp.nat)) N)) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) Na)) (and (= M _let_1) (= Na _let_1))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.one_one tptp.nat)) N) N)) (forall ((X_b $$unsorted)) (=> (and (tptp.number_ring X_b) (tptp.linordered_idom X_b)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.int X_b _let_1 X_1)) (tptp.hAPP tptp.int X_b _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X_1) Y_2))))))) (forall ((X_b $$unsorted)) (=> (tptp.number_ring X_b) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) W_1)) (tptp.ring_1_Ints X_b))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) V) W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W))))))) (forall ((X_b $$unsorted)) (=> (tptp.number X_b) (forall ((W_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) W_1))) (let ((_let_2 (tptp.ti X_b X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) V) W))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number_ring X_b) (tptp.ring_char_0 X_b)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b))) (= (= (tptp.hAPP tptp.int X_b _let_1 X_1) (tptp.hAPP tptp.int X_b _let_1 Y_2)) (= X_1 Y_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 W)) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) V) W))) Z)))))))) (forall ((X_b $$unsorted)) (=> (tptp.ring_1 X_b) (forall ((B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_b))) (let ((_let_2 (tptp.member X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 _let_2 B_3) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) A_2) B_3)) _let_1))))))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number_ring X_b) (tptp.linordered_idom X_b)) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP tptp.int X_b _let_1 X_1)) (tptp.hAPP tptp.int X_b _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) X_1) Y_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) V) W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ring X_b)) (forall ((A_1 $$unsorted) (B $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) V))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.minus_minus X_b))) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_4 A_1) B)) _let_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 A_1) _let_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 B) _let_1)))))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ring X_b)) (forall ((V $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.hAPP X_b _let_1 (tptp.times_times X_b) (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) V)))) (let ((_let_3 (tptp.minus_minus X_b))) (= (tptp.hAPP X_b X_b _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 B) C)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b _let_2 B)) (tptp.hAPP X_b X_b _let_2 C))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ring_1 X_b) (forall ((B_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_b))) (let ((_let_2 (tptp.member X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 _let_2 B_3) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) B_3)) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) W))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((V $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.hAPP X_b _let_1 (tptp.times_times X_b) (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) V)))) (let ((_let_3 (tptp.plus_plus X_b))) (= (tptp.hAPP X_b X_b _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 B) C)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b _let_2 B)) (tptp.hAPP X_b X_b _let_2 C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 W)) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) W))) Z)))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((A_1 $$unsorted) (B $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) V))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.plus_plus X_b))) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_4 A_1) B)) _let_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 A_1) _let_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 B) _let_1)))))))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.ring_1 X_b) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.zero_zero X_b)) (tptp.ring_1_Ints X_b)))))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.ring_1 X_b) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.one_one X_b)) (tptp.ring_1_Ints X_b)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Rx))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Ry)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Ry)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Rx) Ry)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Rx)) Ry)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Ly)) Rx) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ly) Rx))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Ly)) Rx) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Rx)) Ly)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Rx) Ry))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_4 Ly)) _let_3) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ly) _let_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Lx) Ly)))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Rx))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Ry)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Ry)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Ly)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Rx) Ry)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Rx)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ly) Ry))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z))))))))) (forall ((X_b $$unsorted)) (=> (tptp.semiri456707255roduct X_b) (forall ((C_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.hAPP X_b _let_2 _let_1 B_3))) (let ((_let_4 (tptp.hAPP X_b _let_2 _let_1 A_2))) (let ((_let_5 (tptp.plus_plus X_b))) (= (and (not (= (tptp.ti X_b A_2) (tptp.ti X_b B_3))) (not (= (tptp.ti X_b C_1) (tptp.ti X_b D_1)))) (not (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_5 (tptp.hAPP X_b X_b _let_4 C_1)) (tptp.hAPP X_b X_b _let_3 D_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_5 (tptp.hAPP X_b X_b _let_4 D_1)) (tptp.hAPP X_b X_b _let_3 C_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) M_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) M_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) M_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.semiri456707255roduct X_b) (forall ((W_1 $$unsorted) (Y_2 $$unsorted) (X_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.hAPP X_b _let_2 _let_1 X_1))) (let ((_let_4 (tptp.hAPP X_b _let_2 _let_1 W_1))) (let ((_let_5 (tptp.plus_plus X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_5 (tptp.hAPP X_b X_b _let_4 Y_2)) (tptp.hAPP X_b X_b _let_3 Z_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_5 (tptp.hAPP X_b X_b _let_4 Z_2)) (tptp.hAPP X_b X_b _let_3 Y_2))) (or (= (tptp.ti X_b W_1) (tptp.ti X_b X_1)) (= (tptp.ti X_b Y_2) (tptp.ti X_b Z_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) _let_1) A_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) _let_1) _let_1))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.linorder X_b)) (forall ((V_3 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b))) (let ((_let_2 (tptp.hAPP tptp.int X_b _let_1 V_3))) (let ((_let_3 (tptp.hAPP tptp.int X_b _let_1 W_1))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_4 (tptp.ord_less_eq X_b) _let_2) _let_3)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_4 (tptp.ord_less X_b) _let_3) _let_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.minus_minus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 W)) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) W))) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (=> (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (=> (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere1490568538miring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) A_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.ord_less_eq X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.hAPP X_b _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) A_2) B_3)) _let_1)) (or (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_4 A_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 B_3) _let_1))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_4 B_3)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.ord_less_eq X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.hAPP X_b _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) A_2) B_3))) (or (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_4 A_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_4 B_3))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 B_3) _let_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) A_1)) (tptp.zero_zero X_a))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.zero_zero X_b))) (let ((_let_4 (tptp.times_times X_b))) (let ((_let_5 (tptp.fun X_b X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 _let_4 A_2) C_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 _let_4 B_3) C_1))) (or (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 _let_3) C_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 C_1) _let_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 B_3) A_2))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.zero_zero X_b))) (let ((_let_4 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) C_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_4 A_2)) (tptp.hAPP X_b X_b _let_4 B_3))) (or (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 _let_3) C_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3))) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 C_1) _let_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 B_3) A_2)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.zero_zero X_b)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 B_3))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) A_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 C_1) (tptp.zero_zero X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 B_3))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 B_3) A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord893533164strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) R_3))) (let ((_let_3 (tptp.plus_plus X_a))) (=> (not (= (tptp.ti X_a R_3) (tptp.zero_zero X_a))) (=> (and (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (not (= (tptp.ti X_a C) (tptp.ti X_a D)))) (not (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 A_1) (tptp.hAPP X_a X_a _let_2 C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 B) (tptp.hAPP X_a X_a _let_2 D)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.fun X_b X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 (tptp.plus_plus X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 X_1) X_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 Y_2) Y_2)) _let_1) (and (= (tptp.ti X_b X_1) _let_1) (= (tptp.ti X_b Y_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 M_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) M_1) N))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_3 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) C_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 B_3) E)) D_1)) (= (tptp.ti X_b C_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) B_3) A_2)) E)) D_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_3 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) C_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 B_3) E)) D_1)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) A_2) B_3)) E)) C_1) (tptp.ti X_b D_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) M_1)) M_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) (tptp.one_one X_a))) M_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 M_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) M_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) (tptp.one_one X_a))) M_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 M_1) M_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 _let_1) _let_1)) M_1)))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) Na) _let_1) (and (= M _let_1) (= Na _let_1))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K_1))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.zero_zero tptp.nat)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 I_2)) (tptp.hAPP tptp.nat tptp.nat _let_1 J))))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.zero_zero tptp.nat)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K_1)))))))))) (forall ((M $$unsorted) (K $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Na) K))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na))))))))) (forall ((K $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na)))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) Na))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na)))))) (forall ((K $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) M_1))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M_1) (tptp.hAPP tptp.nat tptp.nat _let_2 N)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N)))))) (forall ((K $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (=> (= M_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1) N)) (or (= N (tptp.one_one tptp.nat)) (= M_1 (tptp.zero_zero tptp.nat))))) (forall ((X_b $$unsorted)) (=> (tptp.ring_char_0 X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) A_2) (tptp.ring_1_Ints X_b))) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2) _let_1) (= (tptp.ti X_b A_2) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semiring X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.zero_zero X_a))) (let ((_let_6 (tptp.ord_less_eq X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_6 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_5) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_6 _let_5) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.zero_zero X_a))) (let ((_let_6 (tptp.ord_less_eq X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_6 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_6 _let_5) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_5) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_5) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) _let_5) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D))))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 (tptp.ord_less X_b) C_1) (tptp.zero_zero X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 B_3))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 B_3) A_2)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((A_2 $$unsorted) (B_3 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 (tptp.ord_less X_b) (tptp.zero_zero X_b)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 B_3))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B_3)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.fun X_b X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 (tptp.plus_plus X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 X_1) X_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 Y_2) Y_2))) _let_1)) (and (= (tptp.ti X_b X_1) _let_1) (= (tptp.ti X_b Y_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Y))) (tptp.zero_zero X_a))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linord581940658strict X_b) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.fun X_b X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) _let_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 (tptp.plus_plus X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 X_1) X_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 Y_2) Y_2)))) (or (not (= (tptp.ti X_b X_1) _let_1)) (not (= (tptp.ti X_b Y_2) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) Y) X)) X))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) Y)) X))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_3 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.ord_less_eq X_b))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) C_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 B_3) E)) D_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 C_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) B_3) A_2)) E)) D_1)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_3 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.ord_less_eq X_b))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) C_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 B_3) E)) D_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) A_2) B_3)) E)) C_1)) D_1))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_3 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.ord_less X_b))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) C_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 B_3) E)) D_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 C_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) B_3) A_2)) E)) D_1)))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ring X_b) (forall ((A_2 $$unsorted) (E $$unsorted) (C_1 $$unsorted) (B_3 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.ord_less X_b))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 A_2) E)) C_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 B_3) E)) D_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_5 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 (tptp.minus_minus X_b) A_2) B_3)) E)) C_1)) D_1))))))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1) N))))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) N) M_1))))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1) N))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) Na))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na)))))) (forall ((K $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na)))))))) (forall ((M $$unsorted) (K $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Na) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ab_semigroup_mult X_c) (forall ((G $$unsorted) (Z_2 $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.times_times X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_c _let_3))) (let ((_let_5 (tptp.fun X_b X_c))) (let ((_let_6 (tptp.fun X_c X_c))) (let ((_let_7 (tptp.hAPP X_c _let_3 (tptp.hAPP _let_5 _let_4 (tptp.hAPP (tptp.fun X_c _let_6) (tptp.fun _let_5 _let_4) (tptp.finite_fold_image X_c X_b) _let_1) G) Z_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) A_2) A_3))) (= (tptp.hAPP _let_2 X_c _let_7 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_b (tptp.fun _let_2 _let_2) (tptp.insert X_b) A_2) A_3)) (tptp.hAPP X_c X_c (tptp.hAPP X_c _let_6 _let_1 (tptp.hAPP X_b X_c G A_2)) (tptp.hAPP _let_2 X_c _let_7 A_3))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((G $$unsorted) (H $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.one_one X_c))) (let ((_let_2 (tptp.times_times X_c))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 X_c))) (let ((_let_5 (tptp.fun X_c _let_4))) (let ((_let_6 (tptp.fun X_b X_c))) (let ((_let_7 (tptp.fun X_c X_c))) (let ((_let_8 (tptp.fun X_c _let_7))) (let ((_let_9 (tptp.hAPP _let_8 (tptp.fun _let_6 _let_5) (tptp.finite_fold_image X_c X_b) _let_2))) (let ((_let_10 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite X_b) A_3)) (= (tptp.hAPP _let_3 X_c (tptp.hAPP X_c _let_4 (tptp.hAPP _let_6 _let_5 _let_9 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_10 (tptp.fun _let_6 _let_6) (tptp.combs X_b X_c X_c) (tptp.hAPP _let_6 _let_10 (tptp.hAPP _let_8 (tptp.fun _let_6 _let_10) (tptp.combb X_c _let_7 X_b) _let_2) G)) H)) _let_1) A_3) (tptp.hAPP X_c X_c (tptp.hAPP X_c _let_7 _let_2 (tptp.hAPP _let_3 X_c (tptp.hAPP X_c _let_4 (tptp.hAPP _let_6 _let_5 _let_9 G) _let_1) A_3)) (tptp.hAPP _let_3 X_c (tptp.hAPP X_c _let_4 (tptp.hAPP _let_6 _let_5 _let_9 H) _let_1) A_3))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1278240602ring_1 X_a) (forall ((V $$unsorted) (U_1 $$unsorted) (Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.ord_less_eq X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.hAPP X_a _let_5 _let_4 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 X) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 Y) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_6 U_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_6 V)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 U_1) V) (tptp.one_one X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 U_1) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 V) Y))) A_1)))))))))))))))) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M_1) N))) (let ((_let_4 (tptp.zero_zero tptp.nat))) (let ((_let_5 (= M_1 _let_4))) (and (=> _let_5 (= _let_3 _let_4)) (=> (not _let_5) (= _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M_1) (tptp.one_one tptp.nat))) N))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ring_char_0 X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) A_2) (tptp.ring_1_Ints X_b))) (not (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 (tptp.one_one X_b)) A_2)) A_2) (tptp.zero_zero X_b)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (forall ((Z_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 (tptp.zero_zero X_a)) Z_3)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 Z_3) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) Z_3) X)) Y))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_mult X_c) (forall ((F $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.one_one X_c))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_c _let_3))) (let ((_let_5 (tptp.fun X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) S)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) S)) (= (tptp.hAPP X_b X_c F X_2) (tptp.one_one X_c))))) (= (tptp.hAPP _let_2 X_c (tptp.hAPP X_c _let_3 (tptp.hAPP _let_5 _let_4 (tptp.hAPP (tptp.fun X_c (tptp.fun X_c X_c)) (tptp.fun _let_5 _let_4) (tptp.finite_fold_image X_c X_b) (tptp.times_times X_c)) F) _let_1) S) _let_1))))))))))) (forall ((U $$unsorted) (M $$unsorted) (Na $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 (tptp.ord_less_eq tptp.nat) I_1) J_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) I_1)) U)) Na))))))))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) M_1))))) (forall ((M_1 $$unsorted) (N $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 N)) K_1) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_1))))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.number_number_of tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 K)) (tptp.hAPP tptp.int tptp.int _let_3 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L))))))) (forall ((Z $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.one_one tptp.int)) Z) Z)) (forall ((Z $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) Z) (tptp.one_one tptp.int)) Z)) (forall ((Z $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z) W) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W) Z))))) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.number_number_of tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 V)) (tptp.hAPP tptp.int tptp.int _let_3 W)) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 V) W))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 Z1))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 Z2)) Z3) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) Z3))))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.number_number_of tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 K)) (tptp.hAPP tptp.int tptp.int _let_3 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.minus_minus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 Z1) Z2)) W) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z1) W)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) W))))))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) W))) (let ((_let_3 (tptp.minus_minus tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 Z1) Z2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 Z1)) (tptp.hAPP tptp.int tptp.int _let_2 Z2))))))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) W))) (let ((_let_3 (tptp.plus_plus tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 Z1) Z2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 Z1)) (tptp.hAPP tptp.int tptp.int _let_2 Z2))))))) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.number_number_of tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 V)) (tptp.hAPP tptp.int tptp.int _let_3 W)) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 V) W))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.plus_plus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 Z1) Z2)) W) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z1) W)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) W))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) K_1))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 I_2)) (tptp.hAPP tptp.int tptp.int _let_1 J))))))))) (forall ((Na $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) M)) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) M) Na) _let_1) (and (= M _let_1) (= Na _let_1)))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.one_one tptp.int)) Z)) Z) (tptp.zero_zero tptp.int)))))) (forall ((Z $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Z) (tptp.zero_zero tptp.int)) Z)) (forall ((Z $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.zero_zero tptp.int)) Z) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_19 _let_18 _let_25) _let_31)) (forall ((Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.one_one tptp.int)) Z_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Z_2))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) K) L)) (tptp.zero_zero tptp.int))))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.one_one tptp.int)) Z))))))) (forall ((Z_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.plus_plus tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 _let_4 (tptp.one_one tptp.int)) Z_2)) Z_2)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Z_2) _let_1))))))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K_1))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 I_2) J)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 I_2)) (tptp.hAPP tptp.int tptp.int _let_1 J)))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 Z1))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 Z2)) Z3) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) Z3))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 _let_1 Y))) (= (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_4 Z)) (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int _let_3 Z)))))))) (forall ((Z $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z) W) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W) Z))))) (forall ((W $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) W) W))) (forall ((Z $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z) W)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W) Z)))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 I_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 J)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 J) K_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 K_1)))))))) (forall ((Z $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W) Z)) (= Z W)))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) W_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Z_2) (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) Z_2))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X) Y)) (= X Y) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Y) X)))))) (forall ((Z_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Z_2) W_1)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) Z_2) W_1)) (not (= Z_2 W_1)))))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 I_2) J)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 I_2) K_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 J) K_1))))))))) (forall ((Z_4 $$unsorted) (Z $$unsorted) (W_2 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 W_2) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) Z_4) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W_2) Z_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W) Z)))))))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Z_2) (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) W_1) Z_2))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W_1) (tptp.one_one tptp.int))) Z_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) Z_2))))) (forall ((W $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W) (tptp.one_one tptp.int))) Z))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) W_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Z_2) (tptp.one_one tptp.int)))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z_2)) (= W_1 Z_2))))) (forall ((K $$unsorted) (M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 M) (tptp.hAPP tptp.nat tptp.nat _let_1 Na)) (or (= K (tptp.zero_zero tptp.nat)) (= M Na))))) (forall ((I_2 $$unsorted) (U_1 $$unsorted) (J $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.times_times tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 I_2) U_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) U_1)) K_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J)) U_1)) K_1)))))) (forall ((M $$unsorted) (Na $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 M) (tptp.hAPP tptp.nat tptp.nat _let_1 Na)) (= M Na))))) (forall ((M $$unsorted) (Na $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na)))))))) (forall ((M $$unsorted) (Na $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) Na)))))))) (forall ((U $$unsorted) (M $$unsorted) (Na $$unsorted) (J_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less_eq tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 J_1) I_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) I_1) J_1)) U)) M)) Na)))))))))) (forall ((U_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted) (J $$unsorted) (I_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J) I_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 I_2) U_1)) M_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) U_1)) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J)) U_1)) M_1)) N)))))))) (forall ((U $$unsorted) (M $$unsorted) (Na $$unsorted) (J_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J_1) I_1)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) Na)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) I_1) J_1)) U)) M) Na))))))) (forall ((U $$unsorted) (M $$unsorted) (Na $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less_eq tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 I_1) J_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) I_1)) U)) Na))))))))))) (forall ((U_1 $$unsorted) (M_1 $$unsorted) (N $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) J)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 I_2) U_1)) M_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J) U_1)) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) I_2)) U_1)) N))))))))) (forall ((U $$unsorted) (M $$unsorted) (Na $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_1)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) Na)) (= M (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) I_1)) U)) Na)))))))) (forall ((U $$unsorted) (M $$unsorted) (Na $$unsorted) (J_1 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 (tptp.ord_less_eq tptp.nat) J_1) I_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) U)) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_1) U)) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) I_1) J_1)) U)) M)) Na)))))))))) (forall ((B $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted) (B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.times_times tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.plus_plus tptp.int))) (let ((_let_8 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 B_2) Q_1)) R_2))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 B) Q_2)) R_3) _let_8) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_8) _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_3) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_3) R_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_2) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_1) Q_2))))))))))))))))) (forall ((B $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) B))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 (tptp.times_times tptp.int) B))) (let ((_let_6 (tptp.plus_plus tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int _let_5 Q_1)) R_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int _let_5 Q_2)) R_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 R_3) (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 R_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 R_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_2) Q_1))))))))))))) (forall ((K_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) K_1) K_1)) (not (= _let_25 _let_31)) (forall ((R_3 $$unsorted) (Q_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 (tptp.zero_zero tptp.int)) A_1)) (=> (= A_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.plus_plus tptp.int) R_3) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) A_1) Q_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 R_3) A_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.one_one tptp.int)) Q_2))))))))) (forall ((R_3 $$unsorted) (Q_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_3) A_1)) (=> (= A_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.plus_plus tptp.int) R_3) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.times_times tptp.int) A_1) Q_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_3) R_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_2) (tptp.one_one tptp.int))))))))))) (forall ((B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.times_times tptp.int) B_2) Q_1)) R_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_2) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_1) B_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 Q_1))))))))))) (forall ((B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.times_times tptp.int) B_2) Q_1)) R_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) R_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 _let_1) B_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Q_1) _let_1))))))))))) (forall ((B $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 (tptp.times_times tptp.int) B))) (let ((_let_6 (tptp.plus_plus tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int _let_5 Q_1)) R_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int _let_5 Q_2)) R_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) R_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 R_2) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 R_3) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_1) Q_2))))))))))))) (forall ((B $$unsorted) (Q_2 $$unsorted) (R_3 $$unsorted) (B_2 $$unsorted) (Q_1 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_2 _let_1 _let_3))) (let ((_let_6 (tptp.times_times tptp.int))) (let ((_let_7 (tptp.fun tptp.int tptp.int))) (let ((_let_8 (tptp.plus_plus tptp.int))) (let ((_let_9 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_8 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_6 B_2) Q_1)) R_2))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_8 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_6 B) Q_2)) R_3) _let_9) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_5 _let_9)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_2) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_5 R_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_2) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_2) Q_1)))))))))))))))))) (forall ((Pa $$unsorted) (I_1 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I_1) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) K) (tptp.one_one tptp.int)))) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) I) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_1)))))) (forall ((Pa $$unsorted) (I_1 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I_1) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa K)) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) I) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_1)))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ab_semigroup_mult X_c) (forall ((Z_2 $$unsorted) (G $$unsorted) (H $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_c))) (let ((_let_3 (tptp.fun X_c _let_2))) (let ((_let_4 (tptp.fun X_b X_c))) (let ((_let_5 (tptp.hAPP (tptp.fun X_c (tptp.fun X_c X_c)) (tptp.fun _let_4 _let_3) (tptp.finite_fold_image X_c X_b) (tptp.times_times X_c)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_3)) (= (tptp.hAPP X_b X_c G X_2) (tptp.hAPP X_b X_c H X_2))))) (= (tptp.hAPP _let_1 X_c (tptp.hAPP X_c _let_2 (tptp.hAPP _let_4 _let_3 _let_5 G) Z_2) A_3) (tptp.hAPP _let_1 X_c (tptp.hAPP X_c _let_2 (tptp.hAPP _let_4 _let_3 _let_5 H) Z_2) A_3)))))))))))) (forall ((Pa $$unsorted) (K $$unsorted) (I_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) K) I_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K) (tptp.one_one tptp.int)))) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) K) I)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_1)))))) (forall ((Pa $$unsorted) (K $$unsorted) (I_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) K) I_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa K)) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) K) I)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_1)))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_26 _let_25)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X) Y))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_26 _let_31)) (forall ((P_1 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.bool _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.bool _let_2 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))))) (let ((_let_5 (tptp.collect tptp.int))) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2))))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_4 Pa)) (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_4 P_1)))))))))) (forall ((K $$unsorted) (Pa $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) D_1)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_2) D_1))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) K)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K) D_1))))))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hBOOL P_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)))) (let ((_let_3 (tptp.hBOOL Pa))) (=> (=> _let_2 (= _let_3 _let_1)) (= (and _let_2 _let_3) (and _let_2 _let_1))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hBOOL P_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)))) (let ((_let_3 (tptp.hBOOL Pa))) (=> (=> _let_2 (= _let_3 _let_1)) (= (=> _let_2 _let_3) (=> _let_2 _let_1))))))) (forall ((K $$unsorted) (Pa $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) D_1)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_2) D_1))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) K)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K) D_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_4 $$unsorted)) (exists ((Z_3 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Z_3)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) T_4) X_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_4 $$unsorted)) (exists ((Z_3 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_3) X_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) T_4)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_4 $$unsorted)) (exists ((Z_3 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Z_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) T_4))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_4 $$unsorted)) (exists ((Z_3 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_3) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) T_4) X_2))))))))) (forall ((I_1 $$unsorted) (Pa $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa K)) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) K) I)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I) (tptp.one_one tptp.int))))))) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) I) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa I_1)))))) (forall ((Pa $$unsorted) (P1 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_1)) (=> (forall ((X_2 $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_2) D_1))))))) (=> (exists ((Z_3 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X_2) Z_3)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P1 X_2)))))) (=> (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P1 X1))) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X1)))))))) (forall ((Pa $$unsorted) (P_1 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_1)) (=> (forall ((X_2 $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_2) D_1))))))) (=> (exists ((Z_3 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Z_3) X_2)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)))))) (=> (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X1))) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X1)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.nat_tsub X) Y))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Y) X)))) (and (=> _let_3 (= _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X) Y))) (=> (not _let_3) (= _let_2 (tptp.zero_zero tptp.int)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (and (=> _let_2 (= _let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V))) (=> (not _let_2) (= _let_1 (tptp.zero_zero X_a))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)))) (forall ((K_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) K_1)) (tptp.zero_zero tptp.int))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) M_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) M_1)) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.zero_zero tptp.nat)) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.one_one tptp.nat)) (tptp.one_one X_a)))) (= _let_38 _let_31) (= _let_37 _let_25) (forall ((Na $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Na) (tptp.zero_zero tptp.int)) (= Na (tptp.zero_zero tptp.nat)))) (forall ((X_b $$unsorted)) (=> (tptp.ring_1 X_b) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP tptp.nat X_b (tptp.semiring_1_of_nat X_b) Na)) (tptp.ring_1_Ints X_b))))))) (forall ((X_b $$unsorted)) (=> (tptp.semiring_char_0 X_b) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_b))) (= (= (tptp.hAPP tptp.nat X_b _let_1 M) (tptp.hAPP tptp.nat X_b _let_1 Na)) (= M Na)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a _let_1 M_1)) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP tptp.nat X_b _let_1 M)) (tptp.hAPP tptp.nat X_b _let_1 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) Na))))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b _let_1 M)) (tptp.hAPP tptp.nat X_b _let_1 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) Na))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a _let_1 M_1)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a _let_1 M_1)) (tptp.hAPP tptp.nat X_a _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) N))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.nat tptp.int _let_1 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) Na))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.nat tptp.int _let_1 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) Na))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M_1)) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) N))))) (forall ((M_1 $$unsorted) (N $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 M_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 N)) Z)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) N))) Z)))))) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) W_1) Z_2)) (exists ((N_1 $$unsorted)) (= Z_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1)))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M_1)) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1) N))))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1) N)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M_1)) (tptp.hAPP tptp.nat tptp.int _let_1 N))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_1) N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_1 M_1)) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) X) Y))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP tptp.nat tptp.int _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X_1) Y_2))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP tptp.nat tptp.int _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X_1) Y_2))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.nat_tsub (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) X) Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) X) Y))))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.nat) A_3) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) A_3)))))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite tptp.nat) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite tptp.int) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) A_3))))))) (= _let_31 _let_38) (= _let_25 _let_37) (forall ((Pa $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (= (tptp.hAPP _let_4 _let_4 (tptp.collect tptp.int) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_6 (tptp.fun _let_4 _let_4) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_4 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_4 _let_6) (tptp.combb tptp.bool _let_5 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) Pa)) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_4) (tptp.image tptp.nat tptp.int) _let_1) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.nat) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.combb tptp.int tptp.bool tptp.nat) Pa) _let_1))))))))))) (forall ((Z $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Z)))) (forall ((Pa $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)))) (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) X_2)))))) (forall ((Pa $$unsorted)) (= (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa X_2)))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) X_2)))))) (forall ((Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Na)) (tptp.zero_zero tptp.int))) (= Na (tptp.zero_zero tptp.nat)))) (= (tptp.hAPP tptp.nat tptp.int _let_36 _let_34) _let_31) (forall ((W_1 $$unsorted) (Z_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) W_1) Z_2)) (exists ((N_1 $$unsorted)) (= Z_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))))) (forall ((M_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.one_one tptp.int)) (tptp.hAPP tptp.nat tptp.int _let_1 M_1))))) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M_1)) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.nat X_a _let_1 M_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((N $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M_1)) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.nat X_a _let_1 M_1)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))) (forall ((Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Na)))) (forall ((K_1 $$unsorted) (I_2 $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) K_1)))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 I_2)) (tptp.hAPP tptp.int tptp.int _let_1 J))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.zero_zero X_b)) (tptp.hAPP tptp.nat X_b (tptp.semiring_1_of_nat X_b) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Na)))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.nat_tsub X) Y))))))) (forall ((Pa $$unsorted) (X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) X_1) Y_2)))) (and (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Y_2) X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_2 X_1)) (tptp.hAPP tptp.nat tptp.int _let_2 Y_2))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_1) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool Pa (tptp.zero_zero tptp.int))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Y) X)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.nat_tsub X) Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X) Y))))) (forall ((K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) K_1)) (exists ((N_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= K_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.semiring_1 X_b) (forall ((Na $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (= (tptp.hAPP tptp.nat X_b (tptp.semiring_1_of_nat X_b) Na) (tptp.hAPP X_b X_b (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_1) (tptp.semiri532925092at_aux X_b) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_b X_b X_b) (tptp.plus_plus X_b)) (tptp.one_one X_b))) Na) (tptp.zero_zero X_b)))))))) (forall ((M $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (= (tptp.hAPP tptp.nat tptp.int _let_1 M) (tptp.hAPP tptp.nat tptp.int _let_1 Na)) (= M Na)))) (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less _let_2) A_3) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_1)))))))) (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_1)))))))) (= (tptp.bot_bot _let_19) (tptp.hAPP _let_16 _let_19 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_16 _let_19) (tptp.image tptp.nat tptp.int) _let_36) (tptp.bot_bot _let_16))) (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)))) (= (= A_3 B_1) (= (tptp.hAPP _let_2 _let_1 _let_3 A_3) (tptp.hAPP _let_2 _let_1 _let_3 B_1))))))) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_3 tptp.bool) (tptp.member tptp.nat) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_2 tptp.bool) (tptp.member tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_3 _let_2) (tptp.image tptp.nat tptp.int) _let_1) A_3)))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted) (Pa $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.bool (tptp.fun tptp.nat _let_1) (tptp.if tptp.nat) Pa) X_1) Y_2)))) (let ((_let_4 (tptp.hBOOL Pa))) (and (=> _let_4 (= (tptp.hAPP tptp.nat tptp.int _let_2 X_1) _let_3)) (=> (not _let_4) (= (tptp.hAPP tptp.nat tptp.int _let_2 Y_2) _let_3)))))))) (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (= (tptp.hAPP tptp.nat tptp.int _let_1 X_1) (tptp.hAPP tptp.nat tptp.int _let_1 Y_2)) (= X_1 Y_2)))) (forall ((X_b $$unsorted)) (=> (tptp.semiring_1 X_b) (forall ((Inc $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (= (tptp.hAPP X_b X_b (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_1) (tptp.semiri532925092at_aux X_b) Inc) (tptp.zero_zero tptp.nat)) I_1) (tptp.ti X_b I_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.semiring_1 X_b) (forall ((Inc $$unsorted) (Na $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_1) (tptp.semiri532925092at_aux X_b) Inc))) (= (tptp.hAPP X_b X_b (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) I_1) (tptp.hAPP X_b X_b (tptp.hAPP tptp.nat _let_1 _let_2 Na) (tptp.hAPP X_b X_b Inc I_1)))))))) (forall ((K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) K_1)) (not (forall ((N_1 $$unsorted)) (not (= K_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1))))))) (forall ((Z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z)) (not (forall ((M_2 $$unsorted)) (not (= Z (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) M_2))))))) (forall ((K_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) K_1)) (exists ((N_1 $$unsorted)) (= K_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1))))) (forall ((Z $$unsorted)) (not (forall ((M_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (not (= Z (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M_2)) (tptp.hAPP tptp.nat tptp.int _let_1 N_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((H $$unsorted) (G $$unsorted) (S $$unsorted) (R_1 $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_4 _let_3) (tptp.finite_fold_image X_b X_c) (tptp.times_times X_b)))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_6 R_1 E) E)) (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 R_1 X1) X2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 R_1 Y1) Y2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 R_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 X1) Y1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 X2) Y2)))))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) S)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) S)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) R_1 (tptp.hAPP X_c X_b H X_2)) (tptp.hAPP X_c X_b G X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_6 R_1 (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_4 _let_3 _let_5 H) E) S)) (tptp.hAPP _let_1 X_b (tptp.hAPP X_b _let_2 (tptp.hAPP _let_4 _let_3 _let_5 G) E) S)))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_d $$unsorted)) (=> (tptp.comm_monoid_mult X_d) (forall ((E $$unsorted) (G $$unsorted) (F $$unsorted) (H $$unsorted) (K $$unsorted) (T_3 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.times_times X_d))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_d))) (let ((_let_4 (tptp.fun X_d _let_3))) (let ((_let_5 (tptp.fun X_c X_d))) (let ((_let_6 (tptp.fun X_d (tptp.fun X_d X_d)))) (let ((_let_7 (tptp.fun X_b tptp.bool))) (let ((_let_8 (tptp.fun _let_7 X_d))) (let ((_let_9 (tptp.fun X_d _let_8))) (let ((_let_10 (tptp.fun X_b X_d))) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.finite_finite X_b) S)) (=> (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_c X_b K Y_1))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_c (tptp.fun _let_3 tptp.bool) (tptp.member X_c) Y_1) T_3)) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) _let_1) S)) (= (tptp.hAPP X_b X_c H _let_1) (tptp.ti X_c Y_1)))))))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b X_c H X_2))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b (tptp.fun _let_3 tptp.bool) (tptp.member X_b) X_2) S)) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_c (tptp.fun _let_2 tptp.bool) (tptp.member X_c) _let_1) T_3)) (= (tptp.hAPP X_c X_b K _let_1) (tptp.ti X_b X_2)) (= (tptp.hAPP X_c X_d G _let_1) (tptp.hAPP X_b X_d F X_2)))))))) (= (tptp.hAPP _let_7 X_d (tptp.hAPP X_d _let_8 (tptp.hAPP _let_10 _let_9 (tptp.hAPP _let_6 (tptp.fun _let_10 _let_9) (tptp.finite_fold_image X_d X_b) _let_1) F) E) S) (tptp.hAPP _let_2 X_d (tptp.hAPP X_d _let_3 (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_6 (tptp.fun _let_5 _let_4) (tptp.finite_fold_image X_d X_c) _let_1) G) E) T_3)))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (and (=> _let_2 (= _let_1 (tptp.zero_zero X_a))) (=> (not _let_2) (= _let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V))))))))) (forall ((X $$unsorted) (Z $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.zero_zero tptp.int)) D)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 Z))) (tptp.one_one tptp.int))) D))) Z)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.minus_minus X_a) A_1) B))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (let ((_let_4 (tptp.plus_plus X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 C) D)))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((Z_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) Z_2)) (tptp.one_one tptp.int))) (= Z_2 (tptp.zero_zero tptp.int)))) (forall ((Z_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Z_1) (tptp.zero_zero tptp.int))))) (forall ((X_1 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg X_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1) (tptp.ti X_a A_1)))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere142940540dd_abs X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_b X_b (tptp.abs_abs X_b) A_2)) _let_1)) (= (tptp.ti X_b A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)) (tptp.zero_zero X_a))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere142940540dd_abs X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) _let_1) (tptp.hAPP X_b X_b (tptp.abs_abs X_b) A_2))) (not (= (tptp.ti X_b A_2) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) A_1)) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((B $$unsorted) (D $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (let ((_let_4 (tptp.hAPP X_a X_a _let_3 B))) (let ((_let_5 (tptp.hAPP X_a X_a _let_3 A_1))) (let ((_let_6 (tptp.ord_less X_a))) (let ((_let_7 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 _let_6 _let_5) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 _let_6 _let_4) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 _let_6 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 _let_5) _let_4)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring_abs X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.zero_zero X_a))) (let ((_let_5 (tptp.ord_less_eq X_a))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (let ((_let_7 (tptp.hAPP X_a _let_6 _let_5 _let_4))) (=> (and (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_7 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_6 _let_5 A_1) _let_4))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_7 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_6 _let_5 B) _let_4)))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) X)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) X) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 _let_3) _let_3) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_31))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.linordered_idom X_a) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) _let_1) _let_1)))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_25))) (forall ((X_b $$unsorted)) (=> (tptp.ordere142940540dd_abs X_b) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (= (= (tptp.hAPP X_b X_b (tptp.abs_abs X_b) A_2) _let_1) (= (tptp.ti X_b A_2) _let_1)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ordere142940540dd_abs X_a) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) _let_1) _let_1)))) (forall ((M_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.abs_abs tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) M_1) N)) _let_1) (= (tptp.hAPP tptp.int tptp.int _let_2 M_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N))) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) _let_1) _let_1))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N))))) (forall ((M_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) M_1))) (= (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) _let_1) _let_1))) (forall ((V $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))) (= (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V) (tptp.zero_zero tptp.nat)))) (forall ((V_3 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 V_2))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_2)))) (let ((_let_4 (tptp.zero_zero tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int tptp.int _let_1 V_3))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_5)))) (let ((_let_7 (tptp.number_number_of tptp.nat))) (= (= (tptp.hAPP tptp.int tptp.nat _let_7 V_3) (tptp.hAPP tptp.int tptp.nat _let_7 V_2)) (and (=> _let_6 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) _let_2) _let_4))) (=> (not _let_6) (and (=> _let_3 (= _let_5 _let_4)) (=> (not _let_3) (= V_3 V_2)))))))))))))) (forall ((V_1 $$unsorted) (K_1 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V_1)) K_1))) (let ((_let_5 (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V)))) (let ((_let_6 (tptp.hAPP tptp.nat tptp.nat _let_5 _let_4))) (let ((_let_7 (tptp.number_number_of tptp.int))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int _let_7 V_1))))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int _let_7 V))))) (and (=> _let_9 (= _let_6 _let_4)) (=> (not _let_9) (and (=> _let_8 (= _let_6 (tptp.hAPP tptp.nat tptp.nat _let_5 K_1))) (=> (not _let_8) (= _let_6 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) V_1))) K_1)))))))))))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)))) (and (=> _let_3 (= _let_2 (tptp.zero_zero tptp.int))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((Z $$unsorted) (X $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.zero_zero tptp.int)) D)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 Z) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 X) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X) Z))) (tptp.one_one tptp.int))) D)))))))))) (forall ((K $$unsorted) (F $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) Na)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) (tptp.one_one tptp.nat)))) (tptp.hAPP tptp.nat tptp.int F I)))) (tptp.one_one tptp.int))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int F (tptp.zero_zero tptp.nat))) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) (tptp.hAPP tptp.nat tptp.int F Na))) (exists ((I $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) Na)) (= (tptp.hAPP tptp.nat tptp.int F I) K))))))))) (forall ((K $$unsorted) (F $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) Na)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) (tptp.one_one tptp.nat)))) (tptp.hAPP tptp.nat tptp.int F I)))) (tptp.one_one tptp.int))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int F (tptp.zero_zero tptp.nat))) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) (tptp.hAPP tptp.nat tptp.int F Na))) (exists ((I $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) Na)) (= (tptp.hAPP tptp.nat tptp.int F I) K))))))))) (forall ((K $$unsorted) (F $$unsorted) (Na $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) I)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) I) Na))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) (tptp.one_one tptp.nat)))) (tptp.hAPP tptp.nat tptp.int F I)))) (tptp.one_one tptp.int)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) Na)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int F M)) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) (tptp.hAPP tptp.nat tptp.int F Na))) (exists ((I $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) I)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I) Na)) (= (tptp.hAPP tptp.nat tptp.int F I) K)))))))))))) (forall ((N $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V)) N)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (and (=> _let_5 (= _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.one_one tptp.nat)) N))) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ V))) N)))))))))) (forall ((K_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int tptp.succ K_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K_1) (tptp.one_one tptp.int)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((K_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ K_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a _let_1 K_1))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.int tptp.nat _let_1 V)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (and (=> _let_3 (= _let_2 (tptp.one_one tptp.nat))) (=> (not _let_3) (= _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ V))))))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat _let_1 W))) (let ((_let_3 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 W)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W))))) (and (=> _let_4 (= _let_3 (tptp.zero_zero tptp.nat))) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) _let_2) _let_2)))))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.one_one tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) _let_2) (tptp.hAPP tptp.int tptp.nat _let_1 V)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V) tptp.pls)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ V)))))))))) (= (tptp.hAPP tptp.int tptp.int tptp.succ tptp.pls) _let_21) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 W_1)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int _let_1 W_1)))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_30))) (= _let_24 (tptp.hAPP tptp.nat tptp.int _let_36 _let_35)) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.hAPP tptp.int X_a _let_1 W))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.one_one X_a)) _let_2)) _let_2))))))))) (= _let_33 _let_34) (= _let_35 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_34))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.one_one X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (= _let_32 _let_33) (= _let_33 _let_32) (= _let_31 (tptp.hAPP tptp.int tptp.int _let_23 _let_21)) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)) W))))))) (= _let_25 _let_30) (forall ((K_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int tptp.bit1 K_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.one_one tptp.int)) K_1)) K_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.zero_zero X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls)) (tptp.ti X_a A_1))))) (= _let_28 _let_29) (= _let_29 _let_28) (= tptp.pls _let_25) (forall ((K $$unsorted) (L $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.int tptp.bit1 K) (tptp.hAPP tptp.int tptp.int tptp.bit1 L)) (= K L))) (forall ((K_1 $$unsorted)) (not (= (tptp.hAPP tptp.int tptp.int tptp.bit1 K_1) tptp.pls))) (forall ((L_1 $$unsorted)) (not (= tptp.pls (tptp.hAPP tptp.int tptp.int tptp.bit1 L_1)))) (forall ((K_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) K_1) tptp.pls) K_1)) (forall ((K_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) tptp.pls) K_1) K_1)) (forall ((K_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K_1) tptp.pls) K_1)) (forall ((W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) tptp.pls) W) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_26 _let_24)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_19 _let_20 tptp.pls) tptp.pls)) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) (tptp.hAPP tptp.int tptp.int tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K1)) (tptp.hAPP tptp.int tptp.int tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_19 _let_18 tptp.pls) tptp.pls))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.pls)))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) (tptp.hAPP tptp.int tptp.int tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K1)) (tptp.hAPP tptp.int tptp.int tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) K) tptp.pls))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) tptp.pls) (tptp.hAPP tptp.int tptp.int tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) tptp.pls) K))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.preorder T_1) (tptp.preorder (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite_1 T_1) (tptp.finite_finite_1 T_2)) (tptp.finite_finite_1 (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.order T_1) (tptp.order (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.ord T_1) (tptp.ord (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.bot T_1) (tptp.bot (tptp.fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.minus T_1) (tptp.minus (tptp.fun T_2 T_1)))) (tptp.semiri456707255roduct tptp.int) (tptp.ordere223160158up_add tptp.int) (tptp.ordere236663937imp_le tptp.int) (tptp.linord893533164strict tptp.int) (tptp.linord626643107strict tptp.int) (tptp.linord20386208strict tptp.int) (tptp.ordere779506340up_add tptp.int) (tptp.ordere142940540dd_abs tptp.int) (tptp.ordere216010020id_add tptp.int) (tptp.linord219039673up_add tptp.int) (tptp.cancel146912293up_add tptp.int) (tptp.ordere453448008miring tptp.int) (tptp.linord581940658strict tptp.int) (tptp.ring_n68954251visors tptp.int) (tptp.ordere1490568538miring tptp.int) (tptp.linord1278240602ring_1 tptp.int) (tptp.ordered_ab_group_add tptp.int) (tptp.cancel_semigroup_add tptp.int) (tptp.linordered_semiring tptp.int) (tptp.linordered_semidom tptp.int) (tptp.ab_semigroup_mult tptp.int) (tptp.comm_monoid_mult tptp.int) (tptp.ab_semigroup_add tptp.int) (tptp.ordered_semiring tptp.int) (tptp.ordered_ring_abs tptp.int) (tptp.no_zero_divisors tptp.int) (tptp.comm_monoid_add tptp.int) (tptp.linordered_ring tptp.int) (tptp.linordered_idom tptp.int) (tptp.comm_semiring_1 tptp.int) (tptp.comm_semiring tptp.int) (tptp.semiring_char_0 tptp.int) (tptp.number_semiring tptp.int) (tptp.ab_group_add tptp.int) (tptp.zero_neq_one tptp.int) (tptp.ordered_ring tptp.int) (tptp.preorder tptp.int) (tptp.linorder tptp.int) (tptp.monoid_mult tptp.int) (tptp.monoid_add tptp.int) (tptp.semiring_1 tptp.int) (tptp.group_add tptp.int) (tptp.mult_zero tptp.int) (tptp.order tptp.int) (tptp.ring_char_0 tptp.int) (tptp.number_ring tptp.int) (tptp.semiring tptp.int) (tptp.ord tptp.int) (tptp.ring_1 tptp.int) (tptp.minus tptp.int) (tptp.zero tptp.int) (tptp.ring tptp.int) (tptp.number tptp.int) (tptp.one tptp.int) (tptp.semiri456707255roduct tptp.nat) (tptp.ordere223160158up_add tptp.nat) (tptp.ordere236663937imp_le tptp.nat) (tptp.linord893533164strict tptp.nat) (tptp.linord20386208strict tptp.nat) (tptp.ordere779506340up_add tptp.nat) (tptp.ordere216010020id_add tptp.nat) (tptp.cancel146912293up_add tptp.nat) (tptp.ordere453448008miring tptp.nat) (tptp.ordere1490568538miring tptp.nat) (tptp.cancel_semigroup_add tptp.nat) (tptp.linordered_semiring tptp.nat) (tptp.linordered_semidom tptp.nat) (tptp.ab_semigroup_mult tptp.nat) (tptp.comm_monoid_mult tptp.nat) (tptp.ab_semigroup_add tptp.nat) (tptp.ordered_semiring tptp.nat) (tptp.no_zero_divisors tptp.nat) (tptp.comm_monoid_add tptp.nat) (tptp.comm_semiring_1 tptp.nat) (tptp.comm_semiring tptp.nat) (tptp.semiring_char_0 tptp.nat) (tptp.number_semiring tptp.nat) (tptp.zero_neq_one tptp.nat) (tptp.preorder tptp.nat) (tptp.linorder tptp.nat) (tptp.monoid_mult tptp.nat) (tptp.monoid_add tptp.nat) (tptp.semiring_1 tptp.nat) (tptp.mult_zero tptp.nat) (tptp.order tptp.nat) (tptp.semiring tptp.nat) (tptp.ord tptp.nat) (tptp.bot tptp.nat) (tptp.minus tptp.nat) (tptp.zero tptp.nat) (tptp.number tptp.nat) (tptp.one tptp.nat) (tptp.preorder tptp.bool) (tptp.finite_finite_1 tptp.bool) (tptp.order tptp.bool) (tptp.ord tptp.bool) (tptp.bot tptp.bool) (tptp.minus tptp.bool) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite_1 T_1) (tptp.finite_finite_1 T_2)) (tptp.finite_finite_1 (tptp.sum_sum T_2 T_1)))) (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.ti T A))) (= (tptp.ti T _let_1) _let_1))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.bool (tptp.fun X_a _let_1) (tptp.if X_a) tptp.fTrue) X) Y) (tptp.ti X_a X)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.bool (tptp.fun X_a _let_1) (tptp.if X_a) tptp.fFalse) X) Y) (tptp.ti X_a Y)))) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P)))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_a X_c))) (let ((_let_2 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.combb X_b X_c X_a) P) Q) R) (tptp.hAPP X_b X_c P (tptp.hAPP X_a X_b Q R)))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (= (tptp.hAPP X_a X_c (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_b _let_2) (tptp.combc X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) Q))))) (forall ((X_a $$unsorted) (P $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.combi X_a) P) (tptp.ti X_a P))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) (tptp.combk X_a X_b) P) Q) (tptp.ti X_a P))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (let ((_let_3 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combs X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) (tptp.hAPP X_a X_b Q R))))))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y))) (= (tptp.ti X_a X) (tptp.ti X_a Y)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite tptp.pname) tptp.u)) _let_17 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_16 (tptp.ord_less_eq tptp.nat) _let_12) _let_14)) (= (tptp.hAPP _let_1 tptp.nat _let_13 tptp.g) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_15 (tptp.minus_minus tptp.nat) _let_14) _let_12)) _let_11 (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_10 tptp.g))) _let_9 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 28.39/28.58  )
% 28.39/28.58  % SZS output end Proof for SWW473+7
% 28.39/28.58  % cvc5---1.0.5 exiting
% 28.39/28.58  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------