TSTP Solution File: SWW473+6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW473+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 00:21:06 EDT 2023
% Result : Theorem 10.35s 10.58s
% Output : Proof 10.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.22 % Problem : SWW473+6 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.23 % Command : do_cvc5 %s %d
% 0.22/0.44 % Computer : n027.cluster.edu
% 0.22/0.44 % Model : x86_64 x86_64
% 0.22/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.44 % Memory : 8042.1875MB
% 0.22/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.22/0.44 % CPULimit : 300
% 0.22/0.44 % WCLimit : 300
% 0.22/0.44 % DateTime : Sun Aug 27 18:47:06 EDT 2023
% 0.22/0.44 % CPUTime :
% 0.29/0.66 %----Proving TF0_NAR, FOF, or CNF
% 10.35/10.58 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.JIOY8GjuYv/cvc5---1.0.5_26950.p...
% 10.35/10.58 ------- get file name : TPTP file name is SWW473+6
% 10.35/10.58 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26950.smt2...
% 10.35/10.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.35/10.58 % SZS status Theorem for SWW473+6
% 10.35/10.58 % SZS output start Proof for SWW473+6
% 10.35/10.58 (
% 10.35/10.58 (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.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 tptp.g) _let_4)))) (let ((_let_17 (tptp.zero_zero tptp.nat))) (let ((_let_18 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$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_2)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)))))))))) (let ((_let_19 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3))))))))) (let ((_let_20 (tptp.fun tptp.bool tptp.bool))) (let ((_let_21 (tptp.fun tptp.bool _let_20))) (let ((_let_22 (tptp.the_1 tptp.com))) (let ((_let_23 (tptp.option tptp.com))) (let ((_let_24 (forall ((X_c $$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))) (or (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.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))))))))) (let ((_let_25 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_10 _let_4)))) (let ((_let_26 (not _let_11))) (let ((_let_27 (or _let_26 _let_25))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (and _let_25 _let_16))) (let ((_let_31 (not _let_25))) (let ((_let_32 (= _let_8 _let_30))) (let ((_let_33 (not _let_30))) (let ((_let_34 (_let_18))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (tptp.fun X_b tptp.bool))) (let ((_let_37 (tptp.fun X_c tptp.bool))) (let ((_let_38 (tptp.fun X_b tptp.bool))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.x_a tptp.pname tptp.mgt_call tptp.pn tptp.u QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP _let_37 tptp.bool (tptp.hAPP X_c (tptp.fun _let_37 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP _let_38 _let_37 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_38 _let_37) (tptp.image X_b X_c) F) A_3))))) :args (_let_24))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_26 _let_25 _let_29))) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_30)) :args ((or (not _let_16) _let_30 _let_31))) (ASSUME :args (_let_16)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_32)) :args ((or _let_8 _let_33 (not _let_32)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.x_a _let_5 tptp.g _let_4 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP _let_36 tptp.bool (tptp.hAPP _let_36 (tptp.fun _let_36 tptp.bool) (tptp.ord_less_eq _let_36) (tptp.hAPP _let_36 _let_36 (tptp.hAPP X_b (tptp.fun _let_36 _let_36) (tptp.insert X_b) X_1) A_3)) B_2)))) :args _let_34)) _let_35 :args (_let_32 false _let_18)) :args (_let_33 true _let_8 false _let_32)) :args (_let_31 false _let_16 true _let_30)) :args (_let_29 false _let_11 true _let_25)) _let_28 :args (false true _let_27 false _let_24)) :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_23) 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.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 $$unsorted)) (let ((_let_1 (tptp.finite_folding_one X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool)) _let_1) _let_1))) (forall ((X_b $$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_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 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.monoid_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$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 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.cancel_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.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))) (= (tptp.ti _let_15 tptp.suc) tptp.suc) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.nat_case X_b))) (let ((_let_2 (tptp.fun tptp.nat X_b))) (= (tptp.ti (tptp.fun X_b (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (= (tptp.ti (tptp.fun _let_23 tptp.com) _let_22) _let_22) (forall ((X_c $$unsorted)) (let ((_let_1 (tptp.bot_bot X_c))) (=> (tptp.bot X_c) (= (tptp.ti X_c _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_c $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_c))) (=> (tptp.ord X_c) (= (tptp.ti (tptp.fun X_c (tptp.fun X_c 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_20 tptp.fNot) tptp.fNot) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (= (tptp.ti _let_21 tptp.fconj) tptp.fconj) (= (tptp.ti _let_21 tptp.fdisj) tptp.fdisj) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fequal X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_21 tptp.fimplies) tptp.fimplies) (forall ((X_a $$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 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= (tptp.ti X_c _let_1) _let_1))) (forall ((B_1_1 $$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_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) F_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) H) F_2))))))) (forall ((X_b $$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_2 $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.hAPP _let_2 tptp.nat _let_1 B_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_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) A_3) B_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) (tptp.hAPP _let_1 tptp.nat _let_2 B_2)) (tptp.hAPP _let_1 tptp.nat _let_2 A_3))) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))))) (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_1 $$unsorted) (Pa $$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_1)))) (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_1))))))))))) (forall ((N $$unsorted) (M $$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)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))) (forall ((K_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) K_2))))))) (forall ((Na $$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_2 $$unsorted) (Nat_3 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_3)) (= Nat_2 Nat_3))) (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 $$unsorted) (N $$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) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)) (= M N)))))) (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 K)))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= M N) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)))))) (forall ((N $$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 $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J_2)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K)) J_2)))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (Q_1 $$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_1)))) (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_1))))))))))) (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 $$unsorted) (B_2 $$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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N))) (= M _let_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((Na $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) M_1)))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 Na)) (= M_1 _let_1)))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) M_1)))))) (forall ((N $$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 $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) K))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))) (forall ((Na $$unsorted) (K_2 $$unsorted) (M_1 $$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_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 M_1)) (=> (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_1) K_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Na) K_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) Na))))))))))) (forall ((N $$unsorted) (K $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (let ((_let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))))))))) (forall ((Na $$unsorted) (K_2 $$unsorted) (M_1 $$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 (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M_1)) (=> (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_1) K_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Na) K_2)) (= M_1 Na)))))))) (forall ((I $$unsorted) (N $$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) N)) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 I)) I)))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) L)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) L))))))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L))) (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) 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)))))))) (forall ((M $$unsorted) (N $$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) N)) M))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) B_2))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$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_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) B_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 ((C_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) C_3) A_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_c) C_3)) (= (tptp.ti _let_1 B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) C_3))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$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_2)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_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) 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 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.member X_b))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_7 _let_5 X_2) A_3)) (not (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite X_b) (tptp.hAPP _let_4 _let_4 (tptp.collect X_b) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_6 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.bool _let_8 X_b) tptp.fconj) (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun X_b _let_7) _let_6 (tptp.combc X_b _let_4 tptp.bool) _let_5) A_3))) (tptp.hAPP X_c _let_4 (tptp.hAPP _let_2 (tptp.fun X_c _let_4) (tptp.combc X_b X_c tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_c _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_c _let_1 X_b) (tptp.fequal X_c)) F)) (tptp.hAPP X_b X_c F X_2))))))))))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (= (tptp.ti X_b B) (tptp.hAPP X_c X_b F X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_c (tptp.fun _let_2 tptp.bool) (tptp.member X_c) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_2 $$unsorted) (B_2 $$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) A_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2))) (= (tptp.ti X_b A_2) (tptp.ti X_b B))) (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) B_2))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted) (A_3 $$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) A_3))) (=> (not (= (tptp.ti X_b A_2) (tptp.ti X_b B))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((I_1 $$unsorted) (Pa $$unsorted) (K_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K_2)) (=> (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_2)))) (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_2) I_1)))))) (forall ((N $$unsorted) (M_3 $$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_3)) (exists ((M_2 $$unsorted)) (= M_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_2 $$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) 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_2))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2) B_2) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fdisj) (tptp.hAPP X_b _let_1 (tptp.hAPP _let_3 _let_3 (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) B_2)))))))))) (forall ((X_b $$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 $$unsorted) (X_1 $$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 $$unsorted) (Y_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.insert X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP X_b _let_3 _let_1 X_1))) (let ((_let_5 (tptp.hAPP X_b _let_3 _let_1 Y_1))) (= (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_2 _let_2 _let_5 A_3)) (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP _let_2 _let_2 _let_4 A_3))))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B) A_3))) (or (= (tptp.ti X_b A_2) (tptp.ti X_b B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((X_b $$unsorted) (Y_1 $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) Y_1) A_3) X_1)) (or (= (tptp.ti X_b Y_1) (tptp.ti X_b X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_3 X_1)))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2))) (= (= (tptp.hAPP _let_1 _let_1 _let_2 A_3) (tptp.hAPP _let_1 _let_1 _let_2 B_2)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2))))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) B) B_2))))))) (forall ((X_b $$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_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_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) A_3) B_2))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) A_3))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.member X_b) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$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) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_2))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_2)) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) Z_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3))) (exists ((X_2 $$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_1) (tptp.hAPP X_c X_b F X_2))))))))) _let_19 (forall ((X_c $$unsorted) (X_b $$unsorted) (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.ti X_c B) (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) (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) (B_2 $$unsorted) (A_2 $$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_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) B_2))))) _let_18 (forall ((X_b $$unsorted) (B_2 $$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_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_3 $$unsorted) (B_2 $$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_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) B_2))))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (C_2 $$unsorted) (D_2 $$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_2)) (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_2))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F))) (= (tptp.hAPP _let_2 _let_1 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP X_c (tptp.fun _let_2 _let_2) (tptp.insert X_c) A_2) B_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) (tptp.hAPP X_c X_b F A_2)) (tptp.hAPP _let_2 _let_1 _let_3 B_2))))))) (forall ((X_c $$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))) (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_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.image X_c X_b) F) A_3))) (exists ((AA $$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_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) AA)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_2)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (B $$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.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B) (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 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (= (tptp.ti X_b B) (tptp.hAPP X_c X_b F X_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) X_2) A_3))))))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_2))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_2)) B_2)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.image X_b X_c) F) A_3)) B_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) X))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) N_1)) (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_1)) (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) (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 $$unsorted) (A_2 $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) (tptp.bot_bot _let_1))))) (forall ((X_b $$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) (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))) (= (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_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_c $$unsorted) (X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((X_1 $$unsorted)) (= (tptp.hAPP X_c X_b (tptp.bot_bot (tptp.fun X_c X_b)) X_1) (tptp.bot_bot X_b))))) (forall ((X_a $$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) (A_2 $$unsorted) (B $$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) _let_2)) (= (tptp.ti X_b A_2) (tptp.ti X_b B)))))))) (forall ((X_b $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))) (= (tptp.ti X_b B) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ti X_b C_1))) (let ((_let_2 (tptp.ti X_b B))) (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) _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 $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_2) (tptp.bot_bot _let_1)))) (= (tptp.ti X_b B) (tptp.ti X_b A_2))))) (forall ((X_b $$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_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 $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) _let_2))) (let ((_let_4 (tptp.ti _let_1 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) _let_3)) (or (= _let_4 _let_2) (= _let_4 _let_3)))))))) (forall ((X_c $$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_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_a $$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.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 $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$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 $$unsorted)) (=> (tptp.order X_a) (forall ((X $$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.order X_a) (forall ((C $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_1)) (=> (= (tptp.ti X_a B_1) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= A_1 B_1) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Y_1 $$unsorted) (X_1 $$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_1) X_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_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 ((X_1 $$unsorted) (Y_1 $$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_1)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_1) X_1))))))))) (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) (Pa $$unsorted) (A_3 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1))) (=> (forall ((A_5 $$unsorted) (F_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_5))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) F_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 F_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) A_5) F_3)))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa F_2)))))))) (forall ((Pn $$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 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) F_2)) (=> (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_2))))))) (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_4 $$unsorted) (A_5 $$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_5) A_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_4))))))))) (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_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_2) (tptp.hAPP tptp.nat tptp.nat F N_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat _let_1 tptp.nat) (tptp.ord_less_eq tptp.nat)) F)) U))))))))) (forall ((X_b $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_2) B_4)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) B_4))))))))) (forall ((X_b $$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 ((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)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (B $$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) (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)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 C_1) D_1))))))))))) (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_2 A_3))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_4 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (= (tptp.ti _let_1 B_2) (tptp.bot_bot _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 F (tptp.hAPP _let_1 X_b F_2 B_2)) _let_2) _let_2)))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$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_2)) (=> (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_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)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F X_1) (tptp.hAPP _let_1 X_b F_2 A_3)))))))))) (forall ((X_b $$unsorted) (Pa $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) F_2)) (=> (not (= (tptp.ti _let_1 F_2) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$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_2)))))))) (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_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) A_3))) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (= (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 F X_1) (tptp.hAPP _let_1 X_b F_2 A_3))))))))))) (forall ((X_b $$unsorted) (B_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 _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (F_2 $$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_2)) (= (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)) (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 $$unsorted) (A_3 $$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) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_finite X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B_2)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) A_3) B_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) B_2)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1) A_3)) B_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2))) (let ((_let_5 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1))) (let ((_let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_5 A_3)) B_2))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_1) B_2)))) (and (=> _let_7 (= _let_6 _let_4)) (=> (not _let_7) (= _let_6 (tptp.hAPP _let_1 _let_1 _let_5 _let_4)))))))))))) (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 B_2) C_2)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C_2) A_3)) (tptp.ti _let_1 A_3)))))))))) (forall ((X_b $$unsorted) (D_2 $$unsorted) (B_2 $$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_2) B_2)) (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_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C_2) D_2))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)) A_3)))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$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_2 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_2)) (=> (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_2 _let_4))))))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.bot_bot _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP X_b _let_3 (tptp.insert X_b) X_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 (tptp.minus_minus _let_1) A_3) (tptp.hAPP _let_1 _let_1 _let_4 _let_2)))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 _let_4 A_3)))) (let ((_let_8 (= _let_5 _let_2))) (let ((_let_9 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_9 tptp.bool (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_9 tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (and (=> _let_8 (= _let_7 (tptp.ti X_b X_1))) (=> (not _let_8) (= _let_7 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 F X_1) (tptp.hAPP _let_1 X_b F_2 _let_5))))))))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2))) (let ((_let_4 (tptp.minus_minus _let_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_2 _let_4 A_3))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 B_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 B_2)) (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2))) (let ((_let_4 (tptp.minus_minus _let_1))) (let ((_let_5 (tptp.hAPP _let_1 _let_2 _let_4 A_3))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 B_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 _let_4 (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.bot_bot _let_1)))) B_2)))))))) (forall ((X_b $$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 $$unsorted) (X_1 $$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.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 $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_2 $$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_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B_2))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 _let_2) (tptp.image X_c X_b) F))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) (tptp.hAPP _let_1 _let_2 _let_3 A_3)) (tptp.hAPP _let_1 _let_2 _let_3 B_2))) (tptp.hAPP _let_1 _let_2 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 X_b F_2 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_2)) (=> (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 ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$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_2)) (=> (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_2))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$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_2))) (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_2))) (=> (not _let_5) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_2))))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (=> (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_2) B) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 C_1) D_1)) (= (= (tptp.ti X_b A_2) (tptp.ti X_b B)) (= (tptp.ti X_b C_1) (tptp.ti X_b D_1))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (= (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.insert X_b) X_1) (tptp.bot_bot _let_1))) (tptp.ti X_b X_1)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_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) B_2) 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_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.hAPP _let_2 tptp.nat _let_1 B_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 A_3)) (tptp.hAPP _let_1 tptp.nat _let_2 B_2))) (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)))))))) (forall ((X_b $$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 $$unsorted) (N_1 $$unsorted) (H $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_3 tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_2)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (= (tptp.hAPP X_b X_b H (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F X_2) Y_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 F (tptp.hAPP X_b X_b H X_2)) (tptp.hAPP X_b X_b H Y_2))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) N_1)) (=> (not (= (tptp.ti _let_1 N_1) (tptp.bot_bot _let_1))) (= (tptp.hAPP X_b X_b H (tptp.hAPP _let_1 X_b F_2 N_1)) (tptp.hAPP _let_1 X_b F_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.image X_b X_b) H) N_1))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun _let_2 tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (= (tptp.ti _let_1 A_3) (tptp.bot_bot _let_1))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.insert X_b))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_2) Y_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_3 _let_2 Y_2) (tptp.bot_bot _let_1))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP _let_1 X_b F_2 A_3)) A_3))))))))) (forall ((X_b $$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_5 $$unsorted) (A_4 $$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_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_5) A_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa A_4)) (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_4) (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_5) (tptp.bot_bot _let_1))))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool Pa (tptp.bot_bot _let_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_2 $$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_1) G) F_2)) (=> (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_2 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_2 (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_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_2 $$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_1) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) A_3)) (= (tptp.hAPP _let_1 X_b F_2 (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_2 (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)) (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 $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$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) 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_2))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)))))))) (forall ((X_b $$unsorted) (B_2 $$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_2))) (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_2)))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$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) 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_2))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2))))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$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) 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_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 _let_4) B_2) _let_4)))))) (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) C_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_2) (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_2))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun _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_1) G) F_2)) (= (tptp.hAPP _let_1 X_b F_2 (tptp.bot_bot _let_1)) (tptp.ti X_b Z_1))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_2 $$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_1) G) F_2)) (=> (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_2 (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_2 A_3))))))))))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Pa $$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_1)))))) (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_1) _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 $$unsorted) (Pa $$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_c $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c X_b))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_4 _let_3 (tptp.hAPP X_b _let_5 (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b _let_5) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) A_3)) (=> (forall ((X_2 $$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_1))))) (= (tptp.hAPP _let_1 X_b F_2 A_3) (tptp.ti X_b Z_1))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.minus X_c) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (= (tptp.hAPP X_b X_c (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2) X_2) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.minus_minus X_c) (tptp.hAPP X_b X_c A_3 X_2)) (tptp.hAPP X_b X_c B_2 X_2))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.minus X_b) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X_1 $$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_2) 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_2 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.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 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_2)) (= (tptp.ti X_b Y_2) (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_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_2)) (= (tptp.ti X_b Y_2) (tptp.ti X_b X_2)))))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_2))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B $$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) (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) 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))) (=> (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 $$unsorted) (X_1 $$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) (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 $$unsorted)) (=> (tptp.one X_b) (forall ((X_1 $$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 ((M $$unsorted) (N $$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))) (= (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 ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.one_one tptp.nat)) N)) (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3))) (let ((_let_4 (tptp.finite_card X_b))) (let ((_let_5 (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_5 A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_5 B_2))) (= (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b _let_2 (tptp.insert X_b) A_2) B_2))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_4 (tptp.hAPP _let_1 _let_1 _let_3 B_2))) (tptp.one_one tptp.nat)))))))))))) (forall ((X_b $$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 $$unsorted) (X_1 $$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)) (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 ((M_1 $$unsorted) (Na $$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_1)) 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_1)) Na)))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B $$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) C_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B $$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))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$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_1)) (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_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$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_1)) (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_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B_1) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat _let_1 N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Z_1 $$unsorted) (F $$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_1))) (=> (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 ((M_1 $$unsorted) (K_2 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) K_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Na) K_2)) (= M_1 Na))))) (forall ((K_2 $$unsorted) (M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 M_1) (tptp.hAPP tptp.nat tptp.nat _let_1 Na)) (= M_1 Na)))) (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 N)) K) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K))))))) (forall ((X $$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 $$unsorted) (N $$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) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) M))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B_1 $$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_1) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_1)) (= (tptp.ti X_a B_1) (tptp.ti X_a C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel146912293up_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$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_1) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B_1) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$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_1) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B_1) (tptp.ti X_a C))))))) (forall ((X_b $$unsorted)) (=> (tptp.cancel_semigroup_add X_b) (forall ((B $$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) 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) (tptp.ti X_b C_1)))))))) (forall ((X_b $$unsorted)) (=> (tptp.cancel_semigroup_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$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) (tptp.hAPP X_b X_b _let_1 C_1)) (= (tptp.ti X_b B) (tptp.ti X_b C_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$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_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_1) C))))))))) (forall ((M $$unsorted) (N $$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) N)) N) M))) (forall ((N $$unsorted) (M $$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)) N) M))) (forall ((I $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 _let_2 I))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_3 J_2)) K) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) J_2) K))))))) (forall ((K $$unsorted) (M $$unsorted) (N $$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))) (= (tptp.hAPP tptp.nat tptp.nat (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 N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 N) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)) (exists ((K_1 $$unsorted)) (= Na (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))))) (forall ((K_2 $$unsorted) (M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M_1)) (tptp.hAPP tptp.nat tptp.nat _let_3 Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) Na))))))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (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_2) M)))))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) J_2)))))) (forall ((K $$unsorted) (I $$unsorted) (J_2 $$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) J_2)) (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) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K))))))))) (forall ((K $$unsorted) (L $$unsorted) (I $$unsorted) (J_2 $$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) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K) L)) (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) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) L)))))))))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K) N)))))) (forall ((M $$unsorted) (K $$unsorted) (N $$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) K)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N)) (not (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K) N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B_1 $$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_1)) B_1) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) B_1)) B_1) (tptp.ti X_a A_1)))))) (forall ((X_b $$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 ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J_2) I)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K)) I))))))) (forall ((I $$unsorted) (K $$unsorted) (J_2 $$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) J_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_3 J_2) K)) I) (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_2) I)) K))))))) (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J_2)) K) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K)))))))) (forall ((K_2 $$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_2) (= J_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) K_2) I_1)))))) (forall ((N $$unsorted) (M $$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)) (= (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) N)) N) M)))) (forall ((I_1 $$unsorted) (K_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 K_2) J_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) K_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K_2)) J_1)))))))) (forall ((I $$unsorted) (K $$unsorted) (J_2 $$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))) (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) J_2)) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 J_2) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 J_2)) K))))))) (forall ((N $$unsorted) (M $$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)) (= (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) N)) M)))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 K) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M)) K)))))))) (forall ((J_1 $$unsorted) (K_2 $$unsorted) (I_1 $$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_2)) 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_2)))))))) (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_2) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I) K)) J_2)))))) (forall ((N $$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) N) (tptp.one_one tptp.nat)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) N))) (forall ((X_b $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Nat_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_b))) (= (tptp.hAPP tptp.nat X_b (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.nat_case X_b) F1) F2) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_2)) (tptp.hAPP tptp.nat X_b F2 Nat_2)))) (forall ((M $$unsorted) (K $$unsorted) (J_2 $$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) J_2)) (= (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_2) K))) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc J_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) K) M))))))) (forall ((M $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_2) K))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M) K)) (tptp.hAPP tptp.nat tptp.nat tptp.suc J_2))))))) (forall ((X_b $$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 ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)))))) (forall ((Y $$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 ((X_b $$unsorted) (Y_1 $$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_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_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_1) _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 $$unsorted) (N $$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) 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)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))) (forall ((K_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) K_2))))))) (forall ((Z $$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 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)))))) (forall ((I $$unsorted) (J_2 $$unsorted) (K $$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) J_2)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I) K)))))) (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted) (L $$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) L)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M) L) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 K) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))))) (forall ((K $$unsorted) (L $$unsorted) (I $$unsorted) (J_2 $$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) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K) L)) (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) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) L)))))))))) (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K))))))))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (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) J_2)))))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) M)))))) (forall ((K_2 $$unsorted) (M_1 $$unsorted) (Na $$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_2))) (= (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_1)) (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_1) Na))))))) (forall ((J_2 $$unsorted) (I $$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_2) I)) I)))) (forall ((I $$unsorted) (J_2 $$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) I) J_2)) I)))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$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 (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_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B_1 $$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_1) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) C))))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) C_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b _let_3 A_2)) (tptp.hAPP X_b X_b _let_3 B))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.plus_plus X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 A_2) C_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 B) C_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (B $$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) (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)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 C_1) D_1))))))))))) (forall ((M $$unsorted) (N $$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)) (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) N)))))) (forall ((M $$unsorted) (N $$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)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$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 N))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N))) (= M N))))) (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I)) K))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) N)) (=> (not (= _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) N)))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (= M N))))) (forall ((Na $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))) (= Na M_1))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) Na)))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Na)) (= M_1 Na))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (= M N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N)) (=> (not (= M N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) Na)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) Na)) (= M_1 Na))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) Na)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_1) Na)) (not (= M_1 Na)))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L))) (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))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 L)) (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)))))))))) (forall ((N $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_2) N)) K)))))) (forall ((X_a $$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 $$unsorted) (Y_1 $$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_1))) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_1) X_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_1))) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_1) X_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))))))))) (forall ((X_a $$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 $$unsorted)) (=> (tptp.linorder X_b) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_1) X_1))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_1))) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))))))))) (forall ((X_a $$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 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 $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a Y) (tptp.ti X_a X))))))) (forall ((X_b $$unsorted)) (=> (tptp.preorder X_b) (forall ((Pa $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_1) X_1)) (tptp.hBOOL Pa)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((A_1 $$unsorted) (B_1 $$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 A_1) B_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= A_1 B_1) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_1)) (=> (= (tptp.ti X_a B_1) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))))) (forall ((X_a $$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 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X $$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)) (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_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (= M_1 Na)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Na) M_1))))))) (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) M)) (not (= M N)))) (forall ((S $$unsorted) (T_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) S) T_3)) (not (= S T_3)))) (forall ((Pa $$unsorted) (M_1 $$unsorted) (Na $$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_1)))) (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_1) Na)) _let_2) (=> (=> (= M_1 Na) _let_2) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 Na) M_1)) _let_2) _let_2))))))) (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 $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) Y_1) X_1))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$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_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) Y_1) 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 $$unsorted) (Y_1 $$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_1)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_1)) (not (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.preorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 (tptp.ord_less X_b) X_1) Y_1)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 X_1) Y_1)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 Y_1) X_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((X_1 $$unsorted) (Y_1 $$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_1)) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1)))))))) (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 (tptp.ord_less_eq X_a) Y) X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y))))))) (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) X_1) Y_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_1) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B_1) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B_1) A_1)))))))) (forall ((X_a $$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 $$unsorted) (Y_1 $$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_1)) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) X_1) Y_1))) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1)))))))) (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 $$unsorted) (B_1 $$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) A_1) B_1)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_1) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B_1) A_1)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B_1) A_1)))))))) (forall ((X_a $$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 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X))))))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) N_1)) (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_1)) (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 $$unsorted) (B_1 $$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_1)) (=> (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_1) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) D)))))))))))) (forall ((I $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) M))))) (forall ((I $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) I))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)) (exists ((K_1 $$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_1) K_1)))))) (forall ((Na $$unsorted) (M_1 $$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_1)) (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_1))))) (forall ((M_1 $$unsorted) (Na $$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_1) (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_1) Na))))) (forall ((M_1 $$unsorted) (Na $$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_1)) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_1) Na))))) (forall ((M $$unsorted) (N $$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) N)) (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 N)))))) (forall ((M $$unsorted) (N $$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) 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)) N))))) (forall ((M_1 $$unsorted) (Na $$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_1) 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_1))) (= Na M_1))))) (forall ((M $$unsorted) (N $$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)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N))))) (forall ((M $$unsorted) (N $$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) N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) (forall ((M $$unsorted) (N $$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) 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) N)) M)))) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (K_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J_1) K_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K_2)) J_1))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$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_1)) (=> (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_1) C)))))))))) (forall ((Na $$unsorted) (K_2 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) K_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 M_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M_1) K_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Na) K_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_1) Na))))))))))) (forall ((X_2 $$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_1 $$unsorted) (K_2 $$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_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M_2)) (tptp.hAPP tptp.nat tptp.nat F N_2))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M_1)) K_2)) (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M_1) K_2)))))))) (forall ((Pa $$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_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I_2))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (exists ((K_1 $$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) K_1)))))) (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) 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 $$unsorted) (B_2 $$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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) B_2) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 C_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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_2)) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (not (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))))) (forall ((X_b $$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) (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 $$unsorted) (B_2 $$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_2)) (=> (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_2)) (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_2)))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$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_2)))) (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_2))) (and (=> _let_8 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_9 B_2))) (=> (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_2))) (=> (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_2))))))))))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.finite_card X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_3 A_3)) (tptp.hAPP _let_1 tptp.nat _let_3 B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2))))))))) (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (exists ((N_2 $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.ti _let_3 A_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun _let_1 _let_3) (tptp.image tptp.nat X_b) F_1) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) N_2)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$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_2)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (=> (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_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$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_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_2))))))))) (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Na $$unsorted) (M_1 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b F N_2)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b F Na)) (tptp.hAPP tptp.nat X_b F M_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) M_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.one_one X_a))))))) (forall ((X_a $$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 ((Na $$unsorted) (N_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) Na))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) N_1)))) (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$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 _let_1) A_3) B_2)) (exists ((B_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) B_2) A_3)))))))) (forall ((I_1 $$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_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 (tptp.hAPP tptp.nat tptp.nat F I_2)) (tptp.hAPP tptp.nat tptp.nat F J))))))) (=> (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 $$unsorted) (K $$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)) K)) (not (forall ((J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J)) (not (= K (tptp.hAPP tptp.nat tptp.nat tptp.suc J)))))))) (forall ((I $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) K)) (=> (not (= K (tptp.hAPP tptp.nat tptp.nat tptp.suc I))) (not (forall ((J $$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) J)) (not (= K (tptp.hAPP tptp.nat tptp.nat tptp.suc J))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.ord X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B $$unsorted) (A_2 $$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)) 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)) (=> (forall ((X_2 $$unsorted) (Y_2 $$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_2) 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_2)) (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_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 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 X) W)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 W) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) W) Z))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) Z)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_c X_b F B)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) C_1) B)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F Y_2)) (tptp.hAPP X_c X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_c X_b F C_1)) A_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (F $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) A_2) (tptp.hAPP X_c X_b F B))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) B) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_c X_b F X_2)) (tptp.hAPP X_c X_b F Y_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) A_2) (tptp.hAPP X_c X_b F C_1)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) B) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less_eq X_c) C_1) (tptp.hAPP X_b X_c F B))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F Y_2)) (tptp.hAPP X_b X_c F X_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less X_c) C_1) (tptp.hAPP X_b X_c F A_2)))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) B) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool _let_1 (tptp.hAPP X_b X_c F B))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F Y_2)) (tptp.hAPP X_b X_c F X_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool _let_1 (tptp.hAPP X_b X_c F A_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (F $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_c X_b F B))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) B) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F X_2)) (tptp.hAPP X_c X_b F Y_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_c X_b F C_1)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((F $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_c))) (let ((_let_2 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) B)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_2 _let_1 (tptp.hAPP X_b X_c F B)) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c F Y_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_2 _let_1 (tptp.hAPP X_b X_c F A_2)) C_1)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((F $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2) B)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F B)) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c F Y_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c _let_1 (tptp.ord_less X_c) (tptp.hAPP X_b X_c F A_2)) C_1))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.sum_sum X_b X_c))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) B_2)) (= (tptp.hAPP _let_4 tptp.nat (tptp.finite_card _let_3) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_4) (tptp.sum_Plus X_b X_c) A_3) B_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_c) B_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.sum_sum X_b X_c))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite _let_3) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_4) (tptp.sum_Plus X_b X_c) A_3) B_2))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) B_2))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.sum_sum X_b X_c))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite X_c) B_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite _let_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.sum_Plus X_b X_c) A_3) B_2)))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.sum_sum X_b X_c))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_c tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite _let_2) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_4 _let_3) (tptp.sum_Plus X_b X_c) A_3) B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_b) A_3)))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.sum_sum X_b X_c))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite _let_2) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun _let_1 _let_3) (tptp.sum_Plus X_b X_c) A_3) B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite X_c) B_2))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool))) (= (= (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_3) (tptp.sum_Plus X_b X_c) A_3) B_2) (tptp.bot_bot _let_3)) (and (= (tptp.ti _let_2 A_3) (tptp.bot_bot _let_2)) (= (tptp.ti _let_1 B_2) (tptp.bot_bot _let_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.sum_sum X_b X_c))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_c tptp.bool))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.hAPP _let_2 tptp.nat (tptp.finite_card _let_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.sum_Plus X_b X_c) A_3) B_2)))) (let ((_let_6 (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite X_c) B_2))))) (and (=> _let_6 (= _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_4 tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP _let_3 tptp.nat (tptp.finite_card X_c) B_2)))) (=> (not _let_6) (= _let_5 (tptp.zero_zero tptp.nat))))))))))) (forall ((N $$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 ((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 ((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 ((X_b $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) (tptp.bot_bot _let_1)) (tptp.zero_zero tptp.nat)))) (forall ((X_a $$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 $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.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.zero_neq_one X_a) (not (= (tptp.one_one X_a) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.zero_zero X_a) (tptp.one_one X_a))))) (forall ((X_b $$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_1 $$unsorted) (A_1 $$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_1)) (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_1))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordere216010020id_add X_b) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_2 X_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_2 Y_1)) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) X_1) Y_1) _let_1) (and (= (tptp.ti X_b X_1) _let_1) (= (tptp.ti X_b Y_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$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_1) _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_1)) _let_1)))))))))) (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 A_2) B)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B)) (tptp.zero_zero X_b))))))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) Na) _let_2) (or (and (= M_1 _let_2) (= Na _let_1)) (and (= M_1 _let_1) (= Na _let_2))))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) Na)) (or (and (= M_1 _let_2) (= Na _let_1)) (and (= M_1 _let_1) (= Na _let_2))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M)) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N) (tptp.zero_zero tptp.nat)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) Na) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)))) (= (tptp.one_one tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_17)) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 M) N) _let_1) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 N) M) _let_1) (= M N))))))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) M) (tptp.zero_zero tptp.nat))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) (tptp.zero_zero tptp.nat)) M)) (forall ((N $$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 $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$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_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_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (= (tptp.ti X_b A_2) (tptp.ti X_b B)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B) (tptp.zero_zero X_b)))))) (forall ((X_b $$unsorted)) (=> (tptp.group_add X_b) (forall ((A_2 $$unsorted) (B $$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) (tptp.zero_zero X_b)) (= (tptp.ti X_b A_2) (tptp.ti X_b B)))))) (forall ((M $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) (forall ((Nat_1 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_1) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M) (tptp.zero_zero tptp.nat)))) (forall ((Nat $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat)))) (forall ((M $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) (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_17) (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 ((X_b $$unsorted) (F1 $$unsorted) (F2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_b))) (= (tptp.hAPP tptp.nat X_b (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_b (tptp.fun _let_1 _let_1) (tptp.nat_case X_b) F1) F2) (tptp.zero_zero tptp.nat)) (tptp.ti X_b F1)))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_b $$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.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.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((T_2 $$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 $$unsorted)) (=> (tptp.minus T_1) (tptp.minus (tptp.fun T_2 T_1)))) (tptp.ordere223160158up_add tptp.nat) (tptp.ordere236663937imp_le tptp.nat) (tptp.ordere779506340up_add tptp.nat) (tptp.ordere216010020id_add tptp.nat) (tptp.cancel146912293up_add tptp.nat) (tptp.cancel_semigroup_add tptp.nat) (tptp.linordered_semidom tptp.nat) (tptp.ab_semigroup_add tptp.nat) (tptp.comm_monoid_add tptp.nat) (tptp.zero_neq_one tptp.nat) (tptp.preorder tptp.nat) (tptp.linorder tptp.nat) (tptp.monoid_add tptp.nat) (tptp.order tptp.nat) (tptp.ord tptp.nat) (tptp.bot tptp.nat) (tptp.minus tptp.nat) (tptp.zero tptp.nat) (tptp.one tptp.nat) (tptp.preorder tptp.bool) (tptp.finite_finite_1 tptp.bool) (tptp.order tptp.bool) (tptp.ord tptp.bool) (tptp.bot tptp.bool) (tptp.minus tptp.bool) (forall ((T_2 $$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 $$unsorted)) (let ((_let_1 (tptp.ti T A))) (= (tptp.ti T _let_1) _let_1))) (forall ((P $$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_16 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (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)))))))))))))))))))))))))))))))))))))))))
% 10.35/10.59 )
% 10.35/10.59 % SZS output end Proof for SWW473+6
% 10.35/10.59 % cvc5---1.0.5 exiting
% 10.35/10.60 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------