TSTP Solution File: SWW473+2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 00:21:05 EDT 2023
% Result : Theorem 1.64s 1.84s
% Output : Proof 1.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.15/0.24 % Problem : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% 0.15/0.25 % Command : do_cvc5 %s %d
% 0.25/0.47 % Computer : n002.cluster.edu
% 0.25/0.47 % Model : x86_64 x86_64
% 0.25/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.47 % Memory : 8042.1875MB
% 0.25/0.47 % OS : Linux 3.10.0-693.el7.x86_64
% 0.25/0.47 % CPULimit : 300
% 0.25/0.47 % WCLimit : 300
% 0.25/0.47 % DateTime : Sun Aug 27 22:31:49 EDT 2023
% 0.25/0.47 % CPUTime :
% 0.33/0.71 %----Proving TF0_NAR, FOF, or CNF
% 1.64/1.84 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.c8WdhsEAgC/cvc5---1.0.5_28172.p...
% 1.64/1.84 ------- get file name : TPTP file name is SWW473+2
% 1.64/1.84 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28172.smt2...
% 1.64/1.84 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.64/1.84 % SZS status Theorem for SWW473+2
% 1.64/1.84 % SZS output start Proof for SWW473+2
% 1.64/1.84 (
% 1.64/1.84 (let ((_let_1 (tptp.image_pname_a tptp.mgt_call tptp.u))) (let ((_let_2 (tptp.hAPP_pname_a tptp.mgt_call tptp.pn))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.insert_a _let_2 tptp.g)) _let_1)))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.hAPP_a85458249l_bool tptp.member_a _let_2))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname tptp.pn) tptp.u)))) (let ((_let_7 (tptp.hAPP_nat_nat tptp.suc tptp.na))) (let ((_let_8 (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a _let_1))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool tptp.g) _let_1)))) (let ((_let_10 (forall ((X_3 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.insert_a X_3 A_1)) B_6)) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_3) B_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6))))))) (let ((_let_11 (forall ((A_1 $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted)) (=> (= B_1 (tptp.hAPP_pname_a F X_3)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_1) (tptp.image_pname_a F A_1)))))))) (let ((_let_12 (tptp.fun tptp.pname tptp.bool))) (let ((_let_13 (tptp.fun tptp.x_a tptp.bool))) (let ((_let_14 (forall ((A_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_pname_a F X_3)) (tptp.image_pname_a F A_1))))))) (let ((_let_15 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_5 _let_1)))) (let ((_let_16 (not _let_6))) (let ((_let_17 (or _let_16 _let_15))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (not _let_17))) (let ((_let_20 (and _let_15 _let_9))) (let ((_let_21 (not _let_15))) (let ((_let_22 (= _let_3 _let_20))) (let ((_let_23 (not _let_20))) (let ((_let_24 (_let_10))) (let ((_let_25 (ASSUME :args _let_24))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (tptp.u tptp.mgt_call tptp.pn QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_pname_a F X_3)) (tptp.image_pname_a F A_1))))) :args (_let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_16 _let_15 _let_19))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_20)) :args ((or (not _let_9) _let_20 _let_21))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_22)) :args ((or _let_3 _let_23 (not _let_22)))) (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (_let_2 tptp.g _let_1 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.insert_a X_3 A_1)) B_6)))) :args _let_24)) _let_25 :args (_let_22 false _let_10)) :args (_let_23 true _let_3 false _let_22)) :args (_let_21 false _let_9 true _let_20)) :args (_let_19 false _let_6 true _let_15)) _let_18 :args (false true _let_17 false _let_14)) :args ((forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_2_1) (tptp.is_fun_a_bool (tptp.cOMBB_bool_bool_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun_pname_bool (tptp.cOMBB_647938656_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun949378684l_bool B_2_1) (tptp.is_fun949378684l_bool (tptp.cOMBB_2140588453a_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.cOMBB_307249310e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_bool B_1_1) (tptp.is_fun_a_bool (tptp.cOMBK_bool_a B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_bool B_1_1) (tptp.is_fun_pname_bool (tptp.cOMBK_bool_pname B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_bool B_1_1) (tptp.is_fun949378684l_bool (tptp.cOMBK_324466864a_bool B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_bool B_1_1) (tptp.is_fun1661590463l_bool (tptp.cOMBK_1857069011e_bool B_1_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_2_1) (tptp.is_fun_a_bool (tptp.cOMBS_a_bool_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun_pname_bool (tptp.cOMBS_568398431l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun949378684l_bool B_2_1) (tptp.is_fun949378684l_bool (tptp.cOMBS_1035972772l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.cOMBS_350070575l_bool B_1_1 B_2_1)))) (tptp.is_fun949378684l_bool tptp.finite_finite_a) (tptp.is_fun1661590463l_bool tptp.finite_finite_pname) (tptp.is_a (tptp.undefined_a tptp.x_a)) (tptp.is_pname (tptp.undefined_pname tptp.pname)) (tptp.is_fun_a_bool (tptp.undefined_fun_a_bool _let_13)) (tptp.is_fun_pname_bool (tptp.undefi17486888e_bool _let_12)) (tptp.is_fun949378684l_bool (tptp.undefi1699038445l_bool (tptp.fun _let_13 tptp.bool))) (tptp.is_fun1661590463l_bool (tptp.undefi64961550l_bool (tptp.fun _let_12 tptp.bool))) (tptp.is_bool tptp.bot_bot_bool) (tptp.is_fun_a_bool tptp.bot_bot_fun_a_bool) (tptp.is_fun_pname_bool tptp.bot_bo844097828e_bool) (tptp.is_fun949378684l_bool tptp.bot_bo1389914601l_bool) (tptp.is_fun1661590463l_bool tptp.bot_bo1649642514l_bool) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_1_1) (tptp.is_fun_a_bool (tptp.collect_a B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_1_1) (tptp.is_fun_pname_bool (tptp.collect_pname B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun949378684l_bool B_1_1) (tptp.is_fun949378684l_bool (tptp.collect_fun_a_bool B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_1_1) (tptp.is_fun1661590463l_bool (tptp.collec1974731493e_bool B_1_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_2_1) (tptp.is_fun_a_bool (tptp.image_a_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_2_1) (tptp.is_fun_pname_bool (tptp.image_a_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_2_1) (tptp.is_fun949378684l_bool (tptp.image_a_fun_a_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.image_819518260e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun_a_bool (tptp.image_pname_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun_pname_bool (tptp.image_pname_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun949378684l_bool (tptp.image_112932426a_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_2_1) (tptp.is_fun1661590463l_bool (tptp.image_47868345e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_a_bool (tptp.image_nat_a B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.image_nat_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun949378684l_bool (tptp.image_nat_fun_a_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.image_1655916159e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun949378684l_bool B_2_1) (tptp.is_fun_a_bool (tptp.image_fun_a_bool_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun949378684l_bool B_2_1) (tptp.is_fun_pname_bool (tptp.image_1854862208_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun_a_bool (tptp.image_876012084bool_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_2_1) (tptp.is_fun_pname_bool (tptp.image_1283814551_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_a_bool (tptp.image_fun_nat_bool_a B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.image_1921560913_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_a B_1_1) (tptp.is_fun_a_bool B_2_1)) (tptp.is_fun_a_bool (tptp.insert_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_pname B_1_1) (tptp.is_fun_pname_bool B_2_1)) (tptp.is_fun_pname_bool (tptp.insert_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun_a_bool B_1_1) (tptp.is_fun949378684l_bool B_2_1)) (tptp.is_fun949378684l_bool (tptp.insert_fun_a_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool B_1_1) (tptp.is_fun1661590463l_bool B_2_1)) (tptp.is_fun1661590463l_bool (tptp.insert1325755072e_bool B_1_1 B_2_1)))) (tptp.is_bool tptp.fFalse) (tptp.is_bool tptp.fTrue) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_a B_2_1) (tptp.is_a (tptp.hAPP_a_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_a B_2_1) (tptp.is_pname (tptp.hAPP_a_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun_a_bool B_1_1) (tptp.is_a B_2_1)) (tptp.is_bool (tptp.hAPP_a_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_a B_2_1) (tptp.is_fun_a_bool (tptp.hAPP_a_fun_a_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_a B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_a93125764e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_a B_2_1) (tptp.is_fun949378684l_bool (tptp.hAPP_a85458249l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_a B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_a217006258l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_a (tptp.hAPP_pname_a B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_pname (tptp.hAPP_pname_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun_pname_bool B_1_1) (tptp.is_pname B_2_1)) (tptp.is_bool (tptp.hAPP_pname_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_fun_a_bool (tptp.hAPP_p1534023578a_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_fun_pname_bool (tptp.hAPP_p61793385e_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_fun949378684l_bool (tptp.hAPP_p1824510254l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_pname B_2_1) (tptp.is_fun1661590463l_bool (tptp.hAPP_p338031245l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_bool (tptp.hAPP_bool_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_a (tptp.hAPP_nat_a B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_pname (tptp.hAPP_nat_pname B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_nat_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_a_bool (tptp.hAPP_nat_fun_a_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun_pname_bool (tptp.hAPP_n1025906991e_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun949378684l_bool (tptp.hAPP_n1414589940l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun1661590463l_bool (tptp.hAPP_n850744903l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_2_1) (tptp.is_pname (tptp.hAPP_f1128469712_pname B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun949378684l_bool B_1_1) (tptp.is_fun_a_bool B_2_1)) (tptp.is_bool (tptp.hAPP_fun_a_bool_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_2_1) (tptp.is_fun_a_bool 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(tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.image_876012084bool_a F A_1))) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A_1))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.image_fun_a_bool_a F A_1))) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A_1))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_pname_nat F A_1))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A_1))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_a_nat F A_1))) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A_1))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_496248727ol_nat F A_1))) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A_1))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_1551609309ol_nat F A_1))) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A_1))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_fun_a_bool_nat F A_1))) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A_1))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.image_a_pname F A_1))) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A_1))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.image_nat_pname F A_1))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A_1))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.image_pname_a F A_1))) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A_1)) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool B_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A_1)) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool B_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A_1)) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool B_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A_1)) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname B_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A_1)) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a B_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A_1)) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat B_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool B_6)) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A_1))) (= A_1 B_6))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (and (tptp.is_fun1661590463l_bool A_1) (tptp.is_fun1661590463l_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool B_6)) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A_1))) (= A_1 B_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (and (tptp.is_fun949378684l_bool A_1) (tptp.is_fun949378684l_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool B_6)) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A_1))) (= A_1 B_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (and (tptp.is_fun_pname_bool A_1) (tptp.is_fun_pname_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname B_6)) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A_1))) (= A_1 B_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (and (tptp.is_fun_a_bool A_1) (tptp.is_fun_a_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a B_6)) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A_1))) (= A_1 B_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat B_6)) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A_1))) (= A_1 B_6))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A_1)) (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool (tptp.insert_fun_nat_bool X_3 A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A_1)) (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool (tptp.insert1325755072e_bool X_3 A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A_1)) (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool (tptp.insert_fun_a_bool X_3 A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A_1)) (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.insert_pname X_3 A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A_1)) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.insert_nat X_3 A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A_1)) (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.insert_a X_3 A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A_1))) (let ((_let_2 (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool (tptp.insert_fun_nat_bool X_3 A_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool X_3) A_1)))) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A_1))) (let ((_let_2 (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool (tptp.insert1325755072e_bool X_3 A_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_3) A_1)))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A_1))) (let ((_let_2 (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool (tptp.insert_fun_a_bool X_3 A_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f285962445l_bool tptp.member_fun_a_bool X_3) A_1)))) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A_1))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.insert_nat X_3 A_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1)))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A_1))) (let ((_let_2 (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.insert_pname X_3 A_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A_1))) (let ((_let_2 (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.insert_a X_3 A_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_3) A_1)))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc _let_1))))))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool X_3) A_1))) (= (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool (tptp.insert_fun_nat_bool X_3 A_1)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f696928925ol_nat tptp.finite346522414t_bool A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_3) A_1))) (= (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool (tptp.insert1325755072e_bool X_3 A_1)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f55526627ol_nat tptp.finite1340463720e_bool A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f285962445l_bool tptp.member_fun_a_bool X_3) A_1))) (= (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool (tptp.insert_fun_a_bool X_3 A_1)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f2009550088ol_nat tptp.finite1306199131a_bool A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1))) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.insert_nat X_3 A_1)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1))) (= (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname (tptp.insert_pname X_3 A_1)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f921600141ol_nat tptp.finite_card_pname A_1)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_3) A_1))) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a (tptp.insert_a X_3 A_1)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a A_1)))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a Pa))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a Q_1)))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj Pa) Q_1)))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool Pa))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fconj Pa) Q_1)))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool Pa))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj Pa) Q_1)))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool Pa))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool Q_1)))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fconj Pa) Q_1)))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname Pa))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname Q_1)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj Pa) Q_1)))))) (forall ((Q_1 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Pa))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Q_1)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj Pa) Q_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M)) N) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N))))) (forall ((K_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) K_2))))) (forall ((Na $$unsorted)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) Na))) (tptp.hAPP_nat_nat tptp.suc Na))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (tptp.hAPP_nat_nat tptp.suc X) (tptp.hAPP_nat_nat tptp.suc Y)) (= X Y))) (forall ((Nat_3 $$unsorted) (Nat_2 $$unsorted)) (= (= (tptp.hAPP_nat_nat tptp.suc Nat_3) (tptp.hAPP_nat_nat tptp.suc Nat_2)) (= Nat_3 Nat_2))) (forall ((N $$unsorted)) (not (= (tptp.hAPP_nat_nat tptp.suc N) N))) (forall ((N $$unsorted)) (not (= N (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= M N)))) (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) K)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= M N) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) N))) (forall ((I $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.minus_minus_nat I))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_2)) K) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K)) J_2)))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fdisj Pa) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a Pa))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a Q_1)))))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fdisj Pa) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool Pa))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool Q_1)))))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj Pa) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool Pa))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool Q_1)))))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fdisj Pa) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool Pa))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool Q_1)))))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fdisj Pa) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname Pa))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname Q_1)))))) (forall ((Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fdisj Pa) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Pa))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat Q_1)))))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.insert_fun_nat_bool A_3 A_1))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1)))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.insert1325755072e_bool A_3 A_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.insert_fun_a_bool A_3 A_1))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1)))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.insert_pname A_3 A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.insert_nat A_3 A_1))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.insert_a A_3 A_1))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1)))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B_6)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B_6)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B_6)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N))) (= M _let_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N)))))) (forall ((Na $$unsorted) (M_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Na)) (tptp.hAPP_nat_nat tptp.suc M_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) M_1)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc Na))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Na)) (= M_1 _let_1)))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Na)) M_1)))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N)) N)))) (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M)) N)) (tptp.hAPP_nat_nat tptp.suc K)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N)) K))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N))) (forall ((Na $$unsorted) (K_2 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M_1) K_2)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat Na) K_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na))))))) (forall ((N $$unsorted) (K $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus_nat M))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) K)) (tptp.hAPP_nat_nat _let_1 N))))))) (forall ((Na $$unsorted) (K_2 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M_1) K_2) (tptp.hAPP_nat_nat (tptp.minus_minus_nat Na) K_2)) (= M_1 Na)))))) (forall ((I $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus_nat N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) N)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 I)) I)))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) L)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) L))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus_nat L))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N)) M))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_a_a F A_1))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_fun_nat_bool_a F A_1))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_876012084bool_a F A_1))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_fun_a_bool_a F A_1))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B_6) (tptp.image_2129980159t_bool F A_1))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B_6) (tptp.image_47868345e_bool F A_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B_6) (tptp.image_112932426a_bool F A_1))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_pname_pname F A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_pname_nat F A_1))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_nat_a F A_1))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B_6) (tptp.image_26036933t_bool F A_1))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B_6) (tptp.image_1655916159e_bool F A_1))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B_6) (tptp.image_nat_fun_a_bool F A_1))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_nat_pname F A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_nat_nat F A_1))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_a_pname F A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_1921560913_pname F A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_1283814551_pname F A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_1854862208_pname F A_1))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_a_nat F A_1))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_496248727ol_nat F A_1))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_1551609309ol_nat F A_1))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_fun_a_bool_nat F A_1))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_pname_a F A_1))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_a_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_fun_nat_bool_a F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool C_7)) (= B_6 (tptp.image_fun_nat_bool_a F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_a_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_876012084bool_a F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun1661590463l_bool C_7) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_7)) (= B_6 (tptp.image_876012084bool_a F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_a_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_fun_a_bool_a F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun949378684l_bool C_7) (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool C_7)) (= B_6 (tptp.image_fun_a_bool_a F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_a_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_a_a F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_a_bool C_7) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_7)) (= B_6 (tptp.image_a_a F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B_6) (tptp.image_a_fun_nat_bool F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_a_bool C_7) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_7)) (= B_6 (tptp.image_a_fun_nat_bool F C_7))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B_6) (tptp.image_819518260e_bool F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_a_bool C_7) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_7)) (= B_6 (tptp.image_819518260e_bool F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun949378684l_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B_6) (tptp.image_a_fun_a_bool F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_a_bool C_7) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_7)) (= B_6 (tptp.image_a_fun_a_bool F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_pname_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_a_pname F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_a_bool C_7) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_7)) (= B_6 (tptp.image_a_pname F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_pname_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_1921560913_pname F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool C_7)) (= B_6 (tptp.image_1921560913_pname F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_pname_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_1283814551_pname F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun1661590463l_bool C_7) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_7)) (= B_6 (tptp.image_1283814551_pname F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_pname_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_1854862208_pname F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun949378684l_bool C_7) (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool C_7)) (= B_6 (tptp.image_1854862208_pname F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_a_nat F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_a_bool C_7) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a C_7)) (= B_6 (tptp.image_a_nat F C_7))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_496248727ol_nat F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool C_7)) (= B_6 (tptp.image_496248727ol_nat F C_7))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_1551609309ol_nat F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun1661590463l_bool C_7) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool C_7)) (= B_6 (tptp.image_1551609309ol_nat F C_7))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_fun_a_bool_nat F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun949378684l_bool C_7) (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool C_7)) (= B_6 (tptp.image_fun_a_bool_nat F C_7))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B_6) (tptp.image_2129980159t_bool F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_pname_bool C_7) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_7)) (= B_6 (tptp.image_2129980159t_bool F C_7))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B_6) (tptp.image_47868345e_bool F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_pname_bool C_7) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_7)) (= B_6 (tptp.image_47868345e_bool F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun949378684l_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B_6) (tptp.image_112932426a_bool F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_pname_bool C_7) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_7)) (= B_6 (tptp.image_112932426a_bool F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_pname_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_pname_pname F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_pname_bool C_7) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_7)) (= B_6 (tptp.image_pname_pname F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_pname_nat F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_pname_bool C_7) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_7)) (= B_6 (tptp.image_pname_nat F C_7))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_a_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_nat_a F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_7)) (= B_6 (tptp.image_nat_a F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool B_6) (tptp.image_26036933t_bool F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_7)) (= B_6 (tptp.image_26036933t_bool F C_7))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun1661590463l_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool B_6) (tptp.image_1655916159e_bool F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_7)) (= B_6 (tptp.image_1655916159e_bool F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun949378684l_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool B_6) (tptp.image_nat_fun_a_bool F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_7)) (= B_6 (tptp.image_nat_fun_a_bool F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_pname_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_nat_pname F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_7)) (= B_6 (tptp.image_nat_pname F C_7)))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_nat_nat F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_7)) (= B_6 (tptp.image_nat_nat F C_7))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.is_fun_a_bool B_6) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_pname_a F A_1))) (exists ((C_7 $$unsorted)) (and (tptp.is_fun_pname_bool C_7) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_7) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname C_7)) (= B_6 (tptp.image_pname_a F C_7)))))))) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F N_2)) (tptp.hAPP_nat_bool F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F Na)) (tptp.hAPP_nat_bool F N_3)))))) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_n1025906991e_bool F N_2)) (tptp.hAPP_n1025906991e_bool F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.hAPP_n1025906991e_bool F Na)) (tptp.hAPP_n1025906991e_bool F N_3)))))) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F N_2)) (tptp.hAPP_n1699378549t_bool F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool F Na)) (tptp.hAPP_n1699378549t_bool F N_3)))))) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_nat_fun_a_bool F N_2)) (tptp.hAPP_nat_fun_a_bool F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.hAPP_nat_fun_a_bool F Na)) (tptp.hAPP_nat_fun_a_bool F N_3)))))) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F N_2)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) N_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F Na)) (tptp.hAPP_nat_nat F N_3)))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_nat_pname F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A_1)) (tptp.hAPP_p1499970991t_bool (tptp.cOMBC_nat_pname_bool (tptp.cOMBB_1212655066ol_nat tptp.fequal_pname F)) (tptp.hAPP_nat_pname F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_a_pname F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_a X_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) A_1)) (tptp.hAPP_p1534023578a_bool (tptp.cOMBC_a_pname_bool (tptp.cOMBB_610033911bool_a tptp.fequal_pname F)) (tptp.hAPP_a_pname F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_pname_pname F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) A_1)) (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool (tptp.cOMBB_542850580_pname tptp.fequal_pname F)) (tptp.hAPP_pname_pname F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1921560913_pname F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fconj (tptp.hAPP_f1246832597l_bool (tptp.cOMBC_1245412066l_bool tptp.member_fun_nat_bool) A_1)) (tptp.hAPP_p130839763l_bool (tptp.cOMBC_615407716e_bool (tptp.cOMBB_141086128t_bool tptp.fequal_pname F)) (tptp.hAPP_f1291551745_pname F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1283814551_pname F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_fun_pname_bool X_1) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) A_1)) (tptp.hAPP_p338031245l_bool (tptp.cOMBC_1004116266e_bool (tptp.cOMBB_598082538e_bool tptp.fequal_pname F)) (tptp.hAPP_f1297739591_pname F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.image_1854862208_pname F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_fun_a_bool X_1) (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f285962445l_bool tptp.member_fun_a_bool X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fconj (tptp.hAPP_f2117159681l_bool (tptp.cOMBC_1880041174l_bool tptp.member_fun_a_bool) A_1)) (tptp.hAPP_p1824510254l_bool (tptp.cOMBC_1738168533e_bool (tptp.cOMBB_1693087065a_bool tptp.fequal_pname F)) (tptp.hAPP_f1128469712_pname F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_nat_nat F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A_1)) (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool (tptp.cOMBB_800536526ol_nat tptp.fequal_nat F)) (tptp.hAPP_nat_nat F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_a_nat F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_a X_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) A_1)) (tptp.hAPP_nat_fun_a_bool (tptp.cOMBC_a_nat_bool (tptp.cOMBB_1321347587bool_a tptp.fequal_nat F)) (tptp.hAPP_a_nat F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_pname_nat F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) A_1)) (tptp.hAPP_n1025906991e_bool (tptp.cOMBC_pname_nat_bool (tptp.cOMBB_523834888_pname tptp.fequal_nat F)) (tptp.hAPP_pname_nat F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_496248727ol_nat F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fconj (tptp.hAPP_f1246832597l_bool (tptp.cOMBC_1245412066l_bool tptp.member_fun_nat_bool) A_1)) (tptp.hAPP_n215258509l_bool (tptp.cOMBC_385542954t_bool (tptp.cOMBB_1250273980t_bool tptp.fequal_nat F)) (tptp.hAPP_f22106695ol_nat F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_1551609309ol_nat F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_fun_pname_bool X_1) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) A_1)) (tptp.hAPP_n850744903l_bool (tptp.cOMBC_1666426608t_bool (tptp.cOMBB_1896684278e_bool tptp.fequal_nat F)) (tptp.hAPP_f921600141ol_nat F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_fun_a_bool_nat F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_fun_a_bool X_1) (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f285962445l_bool tptp.member_fun_a_bool X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fconj (tptp.hAPP_f2117159681l_bool (tptp.cOMBC_1880041174l_bool tptp.member_fun_a_bool) A_1)) (tptp.hAPP_n1414589940l_bool (tptp.cOMBC_619334683t_bool (tptp.cOMBB_164527437a_bool tptp.fequal_nat F)) (tptp.hAPP_fun_a_bool_nat F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_nat_a F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A_1)) (tptp.hAPP_a_fun_nat_bool (tptp.cOMBC_nat_a_bool (tptp.cOMBB_1885489796ol_nat tptp.fequal_a F)) (tptp.hAPP_nat_a F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.image_26036933t_bool F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A_1)) (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool (tptp.cOMBB_2026977092ol_nat tptp.fequal_fun_nat_bool F)) (tptp.hAPP_n1699378549t_bool F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_1655916159e_bool F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A_1)) (tptp.hAPP_f1066163005t_bool (tptp.cOMBC_386238098l_bool (tptp.cOMBB_2117322052ol_nat tptp.fequal533582459e_bool F)) (tptp.hAPP_n1025906991e_bool F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1))) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.image_nat_fun_a_bool F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) A_1)) (tptp.hAPP_f282463732t_bool (tptp.cOMBC_1928494297l_bool (tptp.cOMBB_1823939024ol_nat tptp.fequal_fun_a_bool F)) (tptp.hAPP_nat_fun_a_bool F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.image_2129980159t_bool F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) A_1)) (tptp.hAPP_f654413245e_bool (tptp.cOMBC_267053842l_bool (tptp.cOMBB_928955006_pname tptp.fequal_fun_nat_bool F)) (tptp.hAPP_p1499970991t_bool F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_47868345e_bool F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) A_1)) (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool (tptp.cOMBB_408569982_pname tptp.fequal533582459e_bool F)) (tptp.hAPP_p61793385e_bool F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.image_112932426a_bool F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) A_1)) (tptp.hAPP_f1794073134e_bool (tptp.cOMBC_445755039l_bool (tptp.cOMBB_392435466_pname tptp.fequal_fun_a_bool F)) (tptp.hAPP_p1534023578a_bool F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_a_a F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_a X_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) A_1)) (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool (tptp.cOMBB_a_fun_a_bool_a tptp.fequal_a F)) (tptp.hAPP_a_a F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.image_a_fun_nat_bool F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_a X_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) A_1)) (tptp.hAPP_f1549043526a_bool (tptp.cOMBC_777206479l_bool (tptp.cOMBB_743407885bool_a tptp.fequal_fun_nat_bool F)) (tptp.hAPP_a_fun_nat_bool F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool (tptp.image_819518260e_bool F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_a X_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) A_1)) (tptp.hAPP_f1051908748a_bool (tptp.cOMBC_1834145417l_bool (tptp.cOMBB_1137537805bool_a tptp.fequal533582459e_bool F)) (tptp.hAPP_a93125764e_bool F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a A_1))) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool (tptp.image_a_fun_a_bool F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_a X_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) A_1)) (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool (tptp.cOMBB_472261505bool_a tptp.fequal_fun_a_bool F)) (tptp.hAPP_a_fun_a_bool F X_1)))))))))))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname A_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a (tptp.image_pname_a F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) A_1)) (tptp.hAPP_a93125764e_bool (tptp.cOMBC_pname_a_bool (tptp.cOMBB_1897541054_pname tptp.fequal_a F)) (tptp.hAPP_pname_a F X_1)))))))))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted)) (=> (= B_1 (tptp.hAPP_pname_nat F X_3)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat B_1) (tptp.image_pname_nat F A_1)))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted)) (=> (= B_1 (tptp.hAPP_a_nat F X_3)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_3) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat B_1) (tptp.image_a_nat F A_1)))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted)) (=> (= B_1 (tptp.hAPP_nat_pname F X_3)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_nat_pname F A_1)))))) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted)) (=> (= B_1 (tptp.hAPP_nat_a F X_3)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_1) (tptp.image_nat_a F A_1)))))) _let_11 (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (and (tptp.is_fun_pname_bool A_1) (tptp.is_fun_pname_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) A_1)) (= A_1 B_6))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) A_1)) (= A_1 B_6)))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (and (tptp.is_fun_a_bool A_1) (tptp.is_fun_a_bool B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) A_1)) (= A_1 B_6))))) (forall ((C_1 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat C_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6)))))) (forall ((C_1 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname C_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6)))))) (forall ((C_1 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a C_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6)))))) (forall ((B_1 $$unsorted) (A_3 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_3))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6))) (= A_3 B_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat B_1 B_6)))))) (forall ((B_1 $$unsorted) (A_3 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_3))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6))) (= A_3 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 B_6)))))) (forall ((B_1 $$unsorted) (A_3 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_3))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6))) (= A_3 B_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a B_1 B_6)))))) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_3))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat B_1 A_1))) (=> (not (= A_3 B_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_1)))))) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_3))) (=> (and (tptp.is_pname A_3) (tptp.is_pname B_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 A_1))) (=> (not (= A_3 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1))))))) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_3))) (=> (and (tptp.is_a A_3) (tptp.is_a B_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a B_1 A_1))) (=> (not (= A_3 B_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_1))))))) (forall ((I_1 $$unsorted) (Pa $$unsorted) (K_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa K_2)) (=> (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa N_2)))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat (tptp.minus_minus_nat K_2) I_1)))))) (forall ((N $$unsorted) (M_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N)) M_3)) (exists ((M_2 $$unsorted)) (= M_3 (tptp.hAPP_nat_nat tptp.suc M_2))))) (forall ((A_3 $$unsorted) (B_6 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_3) (tptp.insert_nat A_3 B_6)))) (forall ((A_3 $$unsorted) (B_6 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_3) (tptp.insert_pname A_3 B_6)))) (forall ((A_3 $$unsorted) (B_6 $$unsorted)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_3) (tptp.insert_a A_3 B_6)))) (forall ((A_3 $$unsorted) (B_6 $$unsorted)) (= (tptp.insert_fun_nat_bool A_3 B_6) (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fdisj (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) A_3)) (tptp.hAPP_f1246832597l_bool (tptp.cOMBC_1245412066l_bool tptp.member_fun_nat_bool) B_6))))) (forall ((A_3 $$unsorted) (B_6 $$unsorted)) (= (tptp.insert1325755072e_bool A_3 B_6) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_3)) (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) B_6))))) (forall ((A_3 $$unsorted) (B_6 $$unsorted)) (= (tptp.insert_fun_a_bool A_3 B_6) (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fdisj (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool tptp.fequal_fun_a_bool) A_3)) (tptp.hAPP_f2117159681l_bool (tptp.cOMBC_1880041174l_bool tptp.member_fun_a_bool) B_6))))) (forall ((A_3 $$unsorted) (B_6 $$unsorted)) (= (tptp.insert_nat A_3 B_6) (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fdisj (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_3)) (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) B_6))))) (forall ((A_3 $$unsorted) (B_6 $$unsorted)) (= (tptp.insert_pname A_3 B_6) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fdisj (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_3)) (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) B_6))))) (forall ((A_3 $$unsorted) (B_6 $$unsorted)) (= (tptp.insert_a A_3 B_6) (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fdisj (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool tptp.fequal_a) A_3)) (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) B_6))))) (forall ((A_3 $$unsorted) (Pa $$unsorted)) (= (tptp.insert_pname A_3 (tptp.collect_pname Pa)) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fimplies (tptp.cOMBB_647938656_pname tptp.fNot (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_3))) Pa)))) (forall ((A_3 $$unsorted) (Pa $$unsorted)) (= (tptp.insert_fun_nat_bool A_3 (tptp.collect_fun_nat_bool Pa)) (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fimplies (tptp.cOMBB_238756964t_bool tptp.fNot (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) A_3))) Pa)))) (forall ((A_3 $$unsorted) (Pa $$unsorted)) (= (tptp.insert1325755072e_bool A_3 (tptp.collec1974731493e_bool Pa)) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fimplies (tptp.cOMBB_307249310e_bool tptp.fNot (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_3))) Pa)))) (forall ((A_3 $$unsorted) (Pa $$unsorted)) (= (tptp.insert_fun_a_bool A_3 (tptp.collect_fun_a_bool Pa)) (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fimplies (tptp.cOMBB_2140588453a_bool tptp.fNot (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool tptp.fequal_fun_a_bool) A_3))) Pa)))) (forall ((A_3 $$unsorted) (Pa $$unsorted)) (= (tptp.insert_nat A_3 (tptp.collect_nat Pa)) (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fimplies (tptp.cOMBB_bool_bool_nat tptp.fNot (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_3))) Pa)))) (forall ((A_3 $$unsorted) (Pa $$unsorted)) (= (tptp.insert_a A_3 (tptp.collect_a Pa)) (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fimplies (tptp.cOMBB_bool_bool_a tptp.fNot (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool tptp.fequal_a) A_3))) Pa)))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.insert_pname X_3 A_1))) (= (tptp.insert_pname X_3 _let_1) _let_1))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.insert_nat X_3 A_1))) (= (tptp.insert_nat X_3 _let_1) _let_1))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.insert_a X_3 A_1))) (= (tptp.insert_a X_3 _let_1) _let_1))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted) (A_1 $$unsorted)) (= (tptp.insert_pname X_3 (tptp.insert_pname Y_2 A_1)) (tptp.insert_pname Y_2 (tptp.insert_pname X_3 A_1)))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted) (A_1 $$unsorted)) (= (tptp.insert_nat X_3 (tptp.insert_nat Y_2 A_1)) (tptp.insert_nat Y_2 (tptp.insert_nat X_3 A_1)))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted) (A_1 $$unsorted)) (= (tptp.insert_a X_3 (tptp.insert_a Y_2 A_1)) (tptp.insert_a Y_2 (tptp.insert_a X_3 A_1)))) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_3))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat B_1 A_1))) (or (= A_3 B_1) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_1)))))) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_3))) (=> (and (tptp.is_pname A_3) (tptp.is_pname B_1)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 A_1))) (or (= A_3 B_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1))))))) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_3))) (=> (and (tptp.is_a A_3) (tptp.is_a B_1)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a B_1 A_1))) (or (= A_3 B_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_1))))))) (forall ((Y_2 $$unsorted) (A_1 $$unsorted) (X_3 $$unsorted)) (=> (and (tptp.is_pname Y_2) (tptp.is_pname X_3)) (= (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.insert_pname Y_2 A_1) X_3)) (or (= Y_2 X_3) (tptp.hBOOL (tptp.hAPP_pname_bool A_1 X_3)))))) (forall ((Y_2 $$unsorted) (A_1 $$unsorted) (X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.insert_nat Y_2 A_1) X_3)) (or (= Y_2 X_3) (tptp.hBOOL (tptp.hAPP_nat_bool A_1 X_3))))) (forall ((Y_2 $$unsorted) (A_1 $$unsorted) (X_3 $$unsorted)) (=> (and (tptp.is_a Y_2) (tptp.is_a X_3)) (= (tptp.hBOOL (tptp.hAPP_a_bool (tptp.insert_a Y_2 A_1) X_3)) (or (= Y_2 X_3) (tptp.hBOOL (tptp.hAPP_a_bool A_1 X_3)))))) (forall ((B_6 $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_3))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6))) (= (= (tptp.insert_nat X_3 A_1) (tptp.insert_nat X_3 B_6)) (= A_1 B_6)))))) (forall ((B_6 $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_3))) (=> (and (tptp.is_fun_pname_bool B_6) (tptp.is_fun_pname_bool A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6))) (= (= (tptp.insert_pname X_3 A_1) (tptp.insert_pname X_3 B_6)) (= A_1 B_6))))))) (forall ((B_6 $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_3))) (=> (and (tptp.is_fun_a_bool B_6) (tptp.is_fun_a_bool A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6))) (= (= (tptp.insert_a X_3 A_1) (tptp.insert_a X_3 B_6)) (= A_1 B_6))))))) (forall ((B_1 $$unsorted) (A_3 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_3))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat B_1 B_6)))))) (forall ((B_1 $$unsorted) (A_3 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_3))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 B_6)))))) (forall ((B_1 $$unsorted) (A_3 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_3))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a B_1 B_6)))))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_3) A_1)) (= (tptp.insert_nat A_3 A_1) A_1))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_3) A_1)) (= (tptp.insert_pname A_3 A_1) A_1)))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_a_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_3) A_1)) (= (tptp.insert_a A_3 A_1) A_1)))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) A_1))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) A_1))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) A_1))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (and (tptp.is_fun_pname_bool A_1) (tptp.is_fun_pname_bool B_6)) (= (= A_1 B_6) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) A_1)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (= (= A_1 B_6) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) A_1))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (and (tptp.is_fun_a_bool A_1) (tptp.is_fun_a_bool B_6)) (= (= A_1 B_6) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) A_1)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (= A_1 B_6) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (= A_1 B_6) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (= A_1 B_6) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (= A_1 B_6) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) A_1)))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (= A_1 B_6) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) A_1)))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (= A_1 B_6) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) A_1)))) (forall ((X_3 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_3))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_3))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_3))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6)))))) (forall ((B_6 $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_3))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6)))))) (forall ((B_6 $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_3))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6)))))) (forall ((B_6 $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_3))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_3))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_3))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_3))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6)))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool A_1 X_3)))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (tptp.hBOOL (tptp.hAPP_pname_bool A_1 X_3)))) (forall ((X_3 $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_3) A_1)) (tptp.hBOOL (tptp.hAPP_a_bool A_1 X_3)))) (forall ((Pa $$unsorted)) (=> (tptp.is_fun_a_bool Pa) (= (tptp.collect_a Pa) Pa))) (forall ((Pa $$unsorted)) (=> (tptp.is_fun_pname_bool Pa) (= (tptp.collect_pname Pa) Pa))) (forall ((Pa $$unsorted)) (= (tptp.collect_fun_nat_bool Pa) Pa)) (forall ((Pa $$unsorted)) (=> (tptp.is_fun1661590463l_bool Pa) (= (tptp.collec1974731493e_bool Pa) Pa))) (forall ((Pa $$unsorted)) (=> (tptp.is_fun949378684l_bool Pa) (= (tptp.collect_fun_a_bool Pa) Pa))) (forall ((Pa $$unsorted)) (= (tptp.collect_nat Pa) Pa)) (forall ((C_6 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) C_6)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 C_6)))))) (forall ((C_6 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) C_6)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 C_6)))))) (forall ((C_6 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) C_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 C_6)))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (= A_1 B_6) (not (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) A_1))))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (= A_1 B_6) (not (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) A_1))))))) (forall ((A_1 $$unsorted) (B_6 $$unsorted)) (=> (= A_1 B_6) (not (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) A_1))))))) (forall ((Z_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_a Z_1) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a Z_1) (tptp.image_pname_a F A_1))) (exists ((X_1 $$unsorted)) (and (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (= Z_1 (tptp.hAPP_pname_a F X_1))))))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_pname_nat F X_3)) (tptp.image_pname_nat F A_1))))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_3) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_a_nat F X_3)) (tptp.image_a_nat F A_1))))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_nat_pname F X_3)) (tptp.image_nat_pname F A_1))))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_nat_a F X_3)) (tptp.image_nat_a F A_1))))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_pname_a F X_3)) (tptp.image_pname_a F A_1))))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (=> (= B_1 (tptp.hAPP_pname_nat F X_3)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat B_1) (tptp.image_pname_nat F A_1)))))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_3) A_1)) (=> (= B_1 (tptp.hAPP_a_nat F X_3)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat B_1) (tptp.image_a_nat F A_1)))))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1)) (=> (= B_1 (tptp.hAPP_nat_pname F X_3)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_nat_pname F A_1)))))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1)) (=> (= B_1 (tptp.hAPP_nat_a F X_3)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_1) (tptp.image_nat_a F A_1)))))) (forall ((B_1 $$unsorted) (F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (=> (= B_1 (tptp.hAPP_pname_a F X_3)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_1) (tptp.image_pname_a F A_1)))))) (forall ((X_1 $$unsorted) (Xa $$unsorted)) (= (tptp.insert_fun_nat_bool X_1 Xa) (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fdisj (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) X_1)) (tptp.hAPP_f1246832597l_bool (tptp.cOMBC_1245412066l_bool tptp.member_fun_nat_bool) Xa))))) (forall ((X_1 $$unsorted) (Xa $$unsorted)) (= (tptp.insert1325755072e_bool X_1 Xa) (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fdisj (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) X_1)) (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool tptp.member799430823e_bool) Xa))))) (forall ((X_1 $$unsorted) (Xa $$unsorted)) (= (tptp.insert_fun_a_bool X_1 Xa) (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fdisj (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool tptp.fequal_fun_a_bool) X_1)) (tptp.hAPP_f2117159681l_bool (tptp.cOMBC_1880041174l_bool tptp.member_fun_a_bool) Xa))))) (forall ((X_1 $$unsorted) (Xa $$unsorted)) (= (tptp.insert_nat X_1 Xa) (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fdisj (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.fequal_nat) X_1)) (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool tptp.member_nat) Xa))))) (forall ((X_1 $$unsorted) (Xa $$unsorted)) (= (tptp.insert_pname X_1 Xa) (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fdisj (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) X_1)) (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool tptp.member_pname) Xa))))) (forall ((X_1 $$unsorted) (Xa $$unsorted)) (= (tptp.insert_a X_1 Xa) (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fdisj (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool tptp.fequal_a) X_1)) (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool tptp.member_a) Xa))))) (forall ((B_6 $$unsorted) (A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.insert_pname A_3 B_6)))) (forall ((B_6 $$unsorted) (A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.insert_nat A_3 B_6)))) (forall ((B_6 $$unsorted) (A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.insert_a A_3 B_6)))) (forall ((X_3 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.insert_nat X_3 A_1)) B_6)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) B_6)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6))))) (forall ((X_3 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.insert_pname X_3 A_1)) B_6)) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) B_6)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6))))) _let_10 (forall ((B_6 $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat X_3 B_6))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6)))))) (forall ((B_6 $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1))) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname X_3 B_6))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6)))))) (forall ((B_6 $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1))) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_3) A_1))) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a X_3 B_6))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6)))))) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 (tptp.insert_pname B_1 B_6)))))) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.insert_nat B_1 B_6)))))) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 (tptp.insert_a B_1 B_6)))))) (forall ((A_3 $$unsorted) (C_6 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_6) D_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.insert_pname A_3 C_6)) (tptp.insert_pname A_3 D_1))))) (forall ((A_3 $$unsorted) (C_6 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_6) D_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.insert_nat A_3 C_6)) (tptp.insert_nat A_3 D_1))))) (forall ((A_3 $$unsorted) (C_6 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_6) D_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.insert_a A_3 C_6)) (tptp.insert_a A_3 D_1))))) (forall ((F $$unsorted) (A_3 $$unsorted) (B_6 $$unsorted)) (= (tptp.image_a_pname F (tptp.insert_a A_3 B_6)) (tptp.insert_pname (tptp.hAPP_a_pname F A_3) (tptp.image_a_pname F B_6)))) (forall ((F $$unsorted) (A_3 $$unsorted) (B_6 $$unsorted)) (= (tptp.image_a_nat F (tptp.insert_a A_3 B_6)) (tptp.insert_nat (tptp.hAPP_a_nat F A_3) (tptp.image_a_nat F B_6)))) (forall ((F $$unsorted) (A_3 $$unsorted) (B_6 $$unsorted)) (= (tptp.image_nat_a F (tptp.insert_nat A_3 B_6)) (tptp.insert_a (tptp.hAPP_nat_a F A_3) (tptp.image_nat_a F B_6)))) (forall ((F $$unsorted) (A_3 $$unsorted) (B_6 $$unsorted)) (= (tptp.image_pname_a F (tptp.insert_pname A_3 B_6)) (tptp.insert_a (tptp.hAPP_pname_a F A_3) (tptp.image_pname_a F B_6)))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.image_pname_pname F A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (= (tptp.insert_pname (tptp.hAPP_pname_pname F X_3) _let_1) _let_1)))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.image_pname_nat F A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (= (tptp.insert_nat (tptp.hAPP_pname_nat F X_3) _let_1) _let_1)))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.image_a_pname F A_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_3) A_1)) (= (tptp.insert_pname (tptp.hAPP_a_pname F X_3) _let_1) _let_1)))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.image_a_nat F A_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_3) A_1)) (= (tptp.insert_nat (tptp.hAPP_a_nat F X_3) _let_1) _let_1)))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.image_nat_a F A_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_3) A_1)) (= (tptp.insert_a (tptp.hAPP_nat_a F X_3) _let_1) _let_1)))) (forall ((F $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.image_pname_a F A_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (= (tptp.insert_a (tptp.hAPP_pname_a F X_3) _let_1) _let_1)))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_6) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_nat_a F A_1))) (exists ((AA $$unsorted)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool AA) A_1)) (= B_6 (tptp.image_nat_a F AA))))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool B_6) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_6) (tptp.image_a_pname F A_1))) (exists ((AA $$unsorted)) (and (tptp.is_fun_a_bool AA) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool AA) A_1)) (= B_6 (tptp.image_a_pname F AA))))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_6) (tptp.image_a_nat F A_1))) (exists ((AA $$unsorted)) (and (tptp.is_fun_a_bool AA) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool AA) A_1)) (= B_6 (tptp.image_a_nat F AA)))))) (forall ((B_6 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_a_bool B_6) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_6) (tptp.image_pname_a F A_1))) (exists ((AA $$unsorted)) (and (tptp.is_fun_pname_bool AA) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool AA) A_1)) (= B_6 (tptp.image_pname_a F AA))))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.image_a_pname F A_1)) (tptp.image_a_pname F B_6))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.image_a_nat F A_1)) (tptp.image_a_nat F B_6))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.image_nat_a F A_1)) (tptp.image_nat_a F B_6))))) (forall ((F $$unsorted) (A_1 $$unsorted) (B_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.image_pname_a F A_1)) (tptp.image_pname_a F B_6))))) (forall ((B_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_pname B_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.image_nat_pname F A_1))) (not (forall ((X_1 $$unsorted)) (=> (= B_1 (tptp.hAPP_nat_pname F X_1)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1))))))))) (forall ((B_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_a B_1) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_1) (tptp.image_nat_a F A_1))) (not (forall ((X_1 $$unsorted)) (=> (= B_1 (tptp.hAPP_nat_a F X_1)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1))))))))) (forall ((B_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat B_1) (tptp.image_pname_nat F A_1))) (not (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (=> (= B_1 (tptp.hAPP_pname_nat F X_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1))))))))) (forall ((B_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat B_1) (tptp.image_a_nat F A_1))) (not (forall ((X_1 $$unsorted)) (=> (tptp.is_a X_1) (=> (= B_1 (tptp.hAPP_a_nat F X_1)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1))))))))) (forall ((B_1 $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_a B_1) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_1) (tptp.image_pname_a F A_1))) (not (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (=> (= B_1 (tptp.hAPP_pname_a F X_1)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)))))))))) (forall ((B_6 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_6))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_6)))) (forall ((B_6 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname X_1))) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_6)))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) B_6)))) (forall ((B_6 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a X_1))) (=> (tptp.is_a X_1) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_6)))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) B_6)))) (forall ((F $$unsorted) (B_6 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_pname_nat F X_1)) B_6))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.image_pname_nat F A_1)) B_6)))) (forall ((F $$unsorted) (B_6 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_pname_pname F X_1)) B_6))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.image_pname_pname F A_1)) B_6)))) (forall ((F $$unsorted) (B_6 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.is_a X_1) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_a_nat F X_1)) B_6))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.image_a_nat F A_1)) B_6)))) (forall ((F $$unsorted) (B_6 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.is_a X_1) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_a_pname F X_1)) B_6))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.image_a_pname F A_1)) B_6)))) (forall ((F $$unsorted) (B_6 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname (tptp.hAPP_nat_pname F X_1)) B_6)))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool (tptp.image_nat_pname F A_1)) B_6)))) (forall ((F $$unsorted) (B_6 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_nat_a F X_1)) B_6)))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.image_nat_a F A_1)) B_6)))) (forall ((F $$unsorted) (B_6 $$unsorted) (A_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a (tptp.hAPP_pname_a F X_1)) B_6))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool (tptp.image_pname_a F A_1)) B_6)))) (forall ((X_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_3) X_3))) (forall ((X_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_3) X_3))) (forall ((X_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_3) X_3))) (forall ((X_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_3) X_3))) (forall ((X_10 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_10) X_10))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_1)) (exists ((M_2 $$unsorted)) (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) M_2))))))) (forall ((G $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.wt C_1)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) tptp.u)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.p G) (tptp.insert_a (tptp.hAPP_pname_a tptp.mgt_call X_1) tptp.bot_bot_fun_a_bool)))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.p G) (tptp.insert_a (tptp.mgt C_1) tptp.bot_bot_fun_a_bool)))))) (forall ((F $$unsorted) (G_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G_1)) (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_1)) (tptp.hAPP_pname_bool G_1 X_1))))))) (forall ((F $$unsorted) (G_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G_1)) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool G_1 X_1)))))) (forall ((F $$unsorted) (G_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool F) G_1)) (forall ((X_1 $$unsorted)) (=> (tptp.is_a X_1) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_a_bool F X_1)) (tptp.hAPP_a_bool G_1 X_1))))))) (forall ((X_3 $$unsorted) (F $$unsorted) (G_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_3)) (tptp.hAPP_pname_bool G_1 X_3))))) (forall ((X_3 $$unsorted) (F $$unsorted) (G_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_3)) (tptp.hAPP_nat_bool G_1 X_3))))) (forall ((X_3 $$unsorted) (F $$unsorted) (G_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_a_bool F X_3)) (tptp.hAPP_a_bool G_1 X_3))))) (forall ((X_3 $$unsorted) (F $$unsorted) (G_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_pname_bool F X_3)) (tptp.hAPP_pname_bool G_1 X_3))))) (forall ((X_3 $$unsorted) (F $$unsorted) (G_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_3)) (tptp.hAPP_nat_bool G_1 X_3))))) (forall ((X_3 $$unsorted) (F $$unsorted) (G_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool F) G_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_a_bool F X_3)) (tptp.hAPP_a_bool G_1 X_3))))) (forall ((A_3 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_3) tptp.bot_bot_fun_nat_bool)))) (forall ((A_3 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_3) tptp.bot_bo844097828e_bool)))) (forall ((A_3 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_3) tptp.bot_bot_fun_a_bool)))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool tptp.bot_bo1701429464l_bool)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool tptp.bot_bo1649642514l_bool)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool tptp.bot_bo1389914601l_bool)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a tptp.bot_bot_fun_a_bool)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname tptp.bot_bo844097828e_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat tptp.bot_bot_fun_nat_bool)) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool tptp.bot_bo844097828e_bool) A_1))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.bot_bot_fun_nat_bool) A_1))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool tptp.bot_bot_fun_a_bool) A_1))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (=> (= A_1 tptp.bot_bot_fun_nat_bool) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_3) A_1))))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (=> (= A_1 tptp.bot_bo844097828e_bool) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname A_3) A_1))))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (=> (= A_1 tptp.bot_bot_fun_a_bool) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a A_3) A_1))))) (forall ((Pa $$unsorted)) (= (= (tptp.collect_pname Pa) tptp.bot_bo844097828e_bool) (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (not (tptp.hBOOL (tptp.hAPP_pname_bool Pa X_1))))))) (forall ((Pa $$unsorted)) (= (= (tptp.collect_fun_nat_bool Pa) tptp.bot_bo1701429464l_bool) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa X_1)))))) (forall ((Pa $$unsorted)) (= (= (tptp.collec1974731493e_bool Pa) tptp.bot_bo1649642514l_bool) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa X_1))))))) (forall ((Pa $$unsorted)) (= (= (tptp.collect_fun_a_bool Pa) tptp.bot_bo1389914601l_bool) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_a_bool X_1) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa X_1))))))) (forall ((Pa $$unsorted)) (= (= (tptp.collect_a Pa) tptp.bot_bot_fun_a_bool) (forall ((X_1 $$unsorted)) (=> (tptp.is_a X_1) (not (tptp.hBOOL (tptp.hAPP_a_bool Pa X_1))))))) (forall ((Pa $$unsorted)) (= (= (tptp.collect_nat Pa) tptp.bot_bot_fun_nat_bool) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)))))) (forall ((C_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat C_1) tptp.bot_bot_fun_nat_bool)))) (forall ((C_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname C_1) tptp.bot_bo844097828e_bool)))) (forall ((C_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a C_1) tptp.bot_bot_fun_a_bool)))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bo844097828e_bool (tptp.collect_pname Pa)) (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (not (tptp.hBOOL (tptp.hAPP_pname_bool Pa X_1))))))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bo1701429464l_bool (tptp.collect_fun_nat_bool Pa)) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa X_1)))))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bo1649642514l_bool (tptp.collec1974731493e_bool Pa)) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_pname_bool X_1) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa X_1))))))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bo1389914601l_bool (tptp.collect_fun_a_bool Pa)) (forall ((X_1 $$unsorted)) (=> (tptp.is_fun_a_bool X_1) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa X_1))))))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bot_fun_a_bool (tptp.collect_a Pa)) (forall ((X_1 $$unsorted)) (=> (tptp.is_a X_1) (not (tptp.hBOOL (tptp.hAPP_a_bool Pa X_1))))))) (forall ((Pa $$unsorted)) (= (= tptp.bot_bot_fun_nat_bool (tptp.collect_nat Pa)) (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)))))) (forall ((A_1 $$unsorted)) (= (exists ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1))) (not (= A_1 tptp.bot_bot_fun_nat_bool)))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (exists ((X_1 $$unsorted)) (and (tptp.is_pname X_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1)))) (not (= A_1 tptp.bot_bo844097828e_bool))))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_a_bool A_1) (= (exists ((X_1 $$unsorted)) (and (tptp.is_a X_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1)))) (not (= A_1 tptp.bot_bot_fun_a_bool))))) (forall ((A_1 $$unsorted)) (= (forall ((X_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)))) (= A_1 tptp.bot_bot_fun_nat_bool))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (forall ((X_1 $$unsorted)) (=> (tptp.is_pname X_1) (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_1) A_1))))) (= A_1 tptp.bot_bo844097828e_bool)))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_a_bool A_1) (= (forall ((X_1 $$unsorted)) (=> (tptp.is_a X_1) (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a X_1) A_1))))) (= A_1 tptp.bot_bot_fun_a_bool)))) (= tptp.bot_bo844097828e_bool (tptp.collect_pname (tptp.cOMBK_bool_pname tptp.fFalse))) (= tptp.bot_bo1701429464l_bool (tptp.collect_fun_nat_bool (tptp.cOMBK_1994329625t_bool tptp.fFalse))) (= tptp.bot_bo1649642514l_bool (tptp.collec1974731493e_bool (tptp.cOMBK_1857069011e_bool tptp.fFalse))) (= tptp.bot_bo1389914601l_bool (tptp.collect_fun_a_bool (tptp.cOMBK_324466864a_bool tptp.fFalse))) (= tptp.bot_bot_fun_a_bool (tptp.collect_a (tptp.cOMBK_bool_a tptp.fFalse))) (= tptp.bot_bot_fun_nat_bool (tptp.collect_nat (tptp.cOMBK_bool_nat tptp.fFalse))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_a_bool tptp.bot_bot_fun_a_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_pname_bool tptp.bot_bo844097828e_bool X_3)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_3)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_a_bool tptp.bot_bot_fun_a_bool X_3)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((A_3 $$unsorted)) (=> (tptp.is_fun_pname_bool A_3) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_3) tptp.bot_bo844097828e_bool)) (= A_3 tptp.bot_bo844097828e_bool)))) (forall ((A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_3) tptp.bot_bot_bool)) (= (tptp.hBOOL A_3) (tptp.hBOOL tptp.bot_bot_bool)))) (forall ((A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_3) tptp.bot_bot_fun_nat_bool)) (= A_3 tptp.bot_bot_fun_nat_bool))) (forall ((A_3 $$unsorted)) (=> (tptp.is_fun_a_bool A_3) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_3) tptp.bot_bot_fun_a_bool)) (= A_3 tptp.bot_bot_fun_a_bool)))) (forall ((A_9 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_9) tptp.bot_bot_nat)) (= A_9 tptp.bot_bot_nat))) (forall ((A_3 $$unsorted)) (=> (tptp.is_fun_pname_bool A_3) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_3) tptp.bot_bo844097828e_bool)) (= A_3 tptp.bot_bo844097828e_bool)))) (forall ((A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_3) tptp.bot_bot_bool)) (= (tptp.hBOOL A_3) (tptp.hBOOL tptp.bot_bot_bool)))) (forall ((A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_3) tptp.bot_bot_fun_nat_bool)) (= A_3 tptp.bot_bot_fun_nat_bool))) (forall ((A_3 $$unsorted)) (=> (tptp.is_fun_a_bool A_3) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_3) tptp.bot_bot_fun_a_bool)) (= A_3 tptp.bot_bot_fun_a_bool)))) (forall ((A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_3) tptp.bot_bot_nat)) (= A_3 tptp.bot_bot_nat))) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool tptp.bot_bo844097828e_bool) A_3))) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool tptp.bot_bot_bool) A_3))) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.bot_bot_fun_nat_bool) A_3))) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool tptp.bot_bot_fun_a_bool) A_3))) (forall ((A_8 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.bot_bot_nat) A_8))) (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (=> (and (tptp.is_pname A_3) (tptp.is_pname B_1)) (=> (= (tptp.insert_pname A_3 tptp.bot_bo844097828e_bool) (tptp.insert_pname B_1 tptp.bot_bo844097828e_bool)) (= A_3 B_1)))) (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.insert_nat A_3 tptp.bot_bot_fun_nat_bool) (tptp.insert_nat B_1 tptp.bot_bot_fun_nat_bool)) (= A_3 B_1))) (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (=> (and (tptp.is_a A_3) (tptp.is_a B_1)) (=> (= (tptp.insert_a A_3 tptp.bot_bot_fun_a_bool) (tptp.insert_a B_1 tptp.bot_bot_fun_a_bool)) (= A_3 B_1)))) (forall ((B_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat B_1) (tptp.insert_nat A_3 tptp.bot_bot_fun_nat_bool))) (= B_1 A_3))) (forall ((B_1 $$unsorted) (A_3 $$unsorted)) (=> (and (tptp.is_pname B_1) (tptp.is_pname A_3)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.insert_pname A_3 tptp.bot_bo844097828e_bool))) (= B_1 A_3)))) (forall ((B_1 $$unsorted) (A_3 $$unsorted)) (=> (and (tptp.is_a B_1) (tptp.is_a A_3)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_1) (tptp.insert_a A_3 tptp.bot_bot_fun_a_bool))) (= B_1 A_3)))) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (=> (and (tptp.is_pname A_3) (tptp.is_pname B_1) (tptp.is_pname C_1) (tptp.is_pname D)) (= (= (tptp.insert_pname A_3 (tptp.insert_pname B_1 tptp.bot_bo844097828e_bool)) (tptp.insert_pname C_1 (tptp.insert_pname D tptp.bot_bo844097828e_bool))) (or (and (= A_3 C_1) (= B_1 D)) (and (= A_3 D) (= B_1 C_1)))))) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (= (= (tptp.insert_nat A_3 (tptp.insert_nat B_1 tptp.bot_bot_fun_nat_bool)) (tptp.insert_nat C_1 (tptp.insert_nat D tptp.bot_bot_fun_nat_bool))) (or (and (= A_3 C_1) (= B_1 D)) (and (= A_3 D) (= B_1 C_1))))) (forall ((A_3 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D $$unsorted)) (=> (and (tptp.is_a A_3) (tptp.is_a B_1) (tptp.is_a C_1) (tptp.is_a D)) (= (= (tptp.insert_a A_3 (tptp.insert_a B_1 tptp.bot_bot_fun_a_bool)) (tptp.insert_a C_1 (tptp.insert_a D tptp.bot_bot_fun_a_bool))) (or (and (= A_3 C_1) (= B_1 D)) (and (= A_3 D) (= B_1 C_1)))))) (forall ((B_1 $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat B_1) (tptp.insert_nat A_3 tptp.bot_bot_fun_nat_bool))) (= B_1 A_3))) (forall ((B_1 $$unsorted) (A_3 $$unsorted)) (=> (and (tptp.is_pname B_1) (tptp.is_pname A_3)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname B_1) (tptp.insert_pname A_3 tptp.bot_bo844097828e_bool))) (= B_1 A_3)))) (forall ((B_1 $$unsorted) (A_3 $$unsorted)) (=> (and (tptp.is_a B_1) (tptp.is_a A_3)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool tptp.member_a B_1) (tptp.insert_a A_3 tptp.bot_bot_fun_a_bool))) (= B_1 A_3)))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (not (= (tptp.insert_pname A_3 A_1) tptp.bot_bo844097828e_bool))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (not (= (tptp.insert_nat A_3 A_1) tptp.bot_bot_fun_nat_bool))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (not (= (tptp.insert_a A_3 A_1) tptp.bot_bot_fun_a_bool))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (not (= tptp.bot_bo844097828e_bool (tptp.insert_pname A_3 A_1)))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (not (= tptp.bot_bot_fun_nat_bool (tptp.insert_nat A_3 A_1)))) (forall ((A_3 $$unsorted) (A_1 $$unsorted)) (not (= tptp.bot_bot_fun_a_bool (tptp.insert_a A_3 A_1)))) (forall ((A_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) tptp.bot_bot_fun_nat_bool)) (= A_1 tptp.bot_bot_fun_nat_bool))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) tptp.bot_bo844097828e_bool)) (= A_1 tptp.bot_bo844097828e_bool)))) (forall ((A_1 $$unsorted)) (=> (tptp.is_fun_a_bool A_1) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) tptp.bot_bot_fun_a_bool)) (= A_1 tptp.bot_bot_fun_a_bool)))) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (= (tptp.image_pname_a F A_1) tptp.bot_bot_fun_a_bool) (= A_1 tptp.bot_bo844097828e_bool)))) (forall ((F $$unsorted)) (= (tptp.image_pname_a F tptp.bot_bo844097828e_bool) tptp.bot_bot_fun_a_bool)) (forall ((F $$unsorted) (A_1 $$unsorted)) (=> (tptp.is_fun_pname_bool A_1) (= (= tptp.bot_bot_fun_a_bool (tptp.image_pname_a F A_1)) (= A_1 tptp.bot_bo844097828e_bool)))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert_nat A_3 tptp.bot_bot_fun_nat_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_nat_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_pname_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert_pname A_3 tptp.bot_bo844097828e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool tptp.fequal_a) A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_a_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert_a A_3 tptp.bot_bot_fun_a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_a_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fconj (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert_fun_nat_bool A_3 tptp.bot_bo1701429464l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1701429464l_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert1325755072e_bool A_3 tptp.bot_bo1649642514l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1649642514l_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fconj (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool tptp.fequal_fun_a_bool) A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert_fun_a_bool A_3 tptp.bot_bo1389914601l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1389914601l_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj (tptp.hAPP_n1699378549t_bool tptp.fequal_nat A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert_nat A_3 tptp.bot_bot_fun_nat_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_nat_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collect_pname (tptp.cOMBS_568398431l_bool (tptp.cOMBB_675860798_pname tptp.fconj (tptp.hAPP_p61793385e_bool tptp.fequal_pname A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_pname_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert_pname A_3 tptp.bot_bo844097828e_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo844097828e_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collect_a (tptp.cOMBS_a_bool_bool (tptp.cOMBB_1972296269bool_a tptp.fconj (tptp.hAPP_a_fun_a_bool tptp.fequal_a A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_a_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert_a A_3 tptp.bot_bot_fun_a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_a_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collect_fun_nat_bool (tptp.cOMBS_1187019125l_bool (tptp.cOMBB_444170502t_bool tptp.fconj (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert_fun_nat_bool A_3 tptp.bot_bo1701429464l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1701429464l_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collec1974731493e_bool (tptp.cOMBS_350070575l_bool (tptp.cOMBB_2095475776e_bool tptp.fconj (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert1325755072e_bool A_3 tptp.bot_bo1649642514l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1649642514l_bool)))))) (forall ((Pa $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.collect_fun_a_bool (tptp.cOMBS_1035972772l_bool (tptp.cOMBB_338059395a_bool tptp.fconj (tptp.hAPP_f1631501043l_bool tptp.fequal_fun_a_bool A_3)) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa A_3)))) (and (=> _let_2 (= _let_1 (tptp.insert_fun_a_bool A_3 tptp.bot_bo1389914601l_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo1389914601l_bool)))))) (forall ((A_3 $$unsorted)) (= (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_3)) (tptp.insert_nat A_3 tptp.bot_bot_fun_nat_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collect_pname (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool tptp.fequal_pname) A_3)) (tptp.insert_pname A_3 tptp.bot_bo844097828e_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collect_a (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool tptp.fequal_a) A_3)) (tptp.insert_a A_3 tptp.bot_bot_fun_a_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collect_fun_nat_bool (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool tptp.fequal_fun_nat_bool) A_3)) (tptp.insert_fun_nat_bool A_3 tptp.bot_bo1701429464l_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool tptp.fequal533582459e_bool) A_3)) (tptp.insert1325755072e_bool A_3 tptp.bot_bo1649642514l_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collect_fun_a_bool (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool tptp.fequal_fun_a_bool) A_3)) (tptp.insert_fun_a_bool A_3 tptp.bot_bo1389914601l_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collect_nat (tptp.hAPP_n1699378549t_bool tptp.fequal_nat A_3)) (tptp.insert_nat A_3 tptp.bot_bot_fun_nat_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collect_pname (tptp.hAPP_p61793385e_bool tptp.fequal_pname A_3)) (tptp.insert_pname A_3 tptp.bot_bo844097828e_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collect_a (tptp.hAPP_a_fun_a_bool tptp.fequal_a A_3)) (tptp.insert_a A_3 tptp.bot_bot_fun_a_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collect_fun_nat_bool (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool A_3)) (tptp.insert_fun_nat_bool A_3 tptp.bot_bo1701429464l_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collec1974731493e_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool A_3)) (tptp.insert1325755072e_bool A_3 tptp.bot_bo1649642514l_bool))) (forall ((A_3 $$unsorted)) (= (tptp.collect_fun_a_bool (tptp.hAPP_f1631501043l_bool tptp.fequal_fun_a_bool A_3)) (tptp.insert_fun_a_bool A_3 tptp.bot_bo1389914601l_bool))) (forall ((A_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.insert_nat X_3 tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) _let_1)) (or (= A_1 tptp.bot_bot_fun_nat_bool) (= A_1 _let_1))))) (forall ((A_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.insert_pname X_3 tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_1) _let_1)) (or (= A_1 tptp.bot_bo844097828e_bool) (= A_1 _let_1)))))) (forall ((A_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.insert_a X_3 tptp.bot_bot_fun_a_bool))) (=> (tptp.is_fun_a_bool A_1) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_1) _let_1)) (or (= A_1 tptp.bot_bot_fun_a_bool) (= A_1 _let_1)))))) (forall ((C_1 $$unsorted) (X_3 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname X_3) A_1)) (= (tptp.image_pname_a (tptp.cOMBK_a_pname C_1) A_1) (tptp.insert_a C_1 tptp.bot_bot_fun_a_bool)))) (forall ((C_1 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.image_pname_a (tptp.cOMBK_a_pname C_1) A_1))) (let ((_let_2 (= A_1 tptp.bot_bo844097828e_bool))) (=> (tptp.is_fun_pname_bool A_1) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_a_bool)) (=> (not _let_2) (= _let_1 (tptp.insert_a C_1 tptp.bot_bot_fun_a_bool)))))))) (forall ((X_9 $$unsorted) (Y_8 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_9) Y_8))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_8) X_9)))) (forall ((Z_1 $$unsorted) (Y_2 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Z_1))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_3)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 X_3)))))) (forall ((Z_1 $$unsorted) (Y_2 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Z_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_3)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 X_3)))))) (forall ((Z_1 $$unsorted) (Y_2 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Z_1))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_3)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 X_3)))))) (forall ((Z_3 $$unsorted) (Y_7 $$unsorted) (X_8 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Z_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_7) X_8)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_7)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_8)))))) (forall ((Z_1 $$unsorted) (Y_2 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Z_1))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_2) X_3)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 X_3)))))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_3)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_3) Y_2)) (= (tptp.hBOOL X_3) (tptp.hBOOL Y_2))))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_3)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_3) Y_2)) (= X_3 Y_2)))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (=> (and (tptp.is_fun_pname_bool Y_2) (tptp.is_fun_pname_bool X_3)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_3)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_3) Y_2)) (= X_3 Y_2))))) (forall ((Y_6 $$unsorted) (X_7 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_6) X_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_7) Y_6)) (= X_7 Y_6)))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (=> (and (tptp.is_fun_a_bool Y_2) (tptp.is_fun_a_bool X_3)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_2) X_3)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_3) Y_2)) (= X_3 Y_2))))) (forall ((Z_1 $$unsorted) (X_3 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_3))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) Z_1)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 Z_1)))))) (forall ((Z_1 $$unsorted) (X_3 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_3))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) Z_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Z_1)))))) (forall ((Z_1 $$unsorted) (X_3 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_3))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) Z_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 Z_1)))))) (forall ((Z_2 $$unsorted) (X_6 $$unsorted) (Y_5 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_5) Z_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_2)))))) (forall ((Z_1 $$unsorted) (X_3 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_3))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_2) Z_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 Z_1)))))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_3) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_3)) (= (tptp.hBOOL X_3) (tptp.hBOOL Y_2))))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_3) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_3)) (= X_3 Y_2)))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_3) (tptp.is_fun_pname_bool Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_3) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_3)) (= X_3 Y_2))))) (forall ((X_5 $$unsorted) (Y_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_5) Y_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_4) X_5)) (= X_5 Y_4)))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_a_bool X_3) (tptp.is_fun_a_bool Y_2)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_3) Y_2)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_2) X_3)) (= X_3 Y_2))))) (forall ((C_1 $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) A_3)) (=> (= (tptp.hBOOL B_1) (tptp.hBOOL C_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool C_1) A_3))))) (forall ((C_1 $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_1) A_3)) (=> (= B_1 C_1) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_1) A_3))))) (forall ((C_1 $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) A_3)) (=> (= B_1 C_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_1) A_3))))) (forall ((C_5 $$unsorted) (B_5 $$unsorted) (A_7 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_5) A_7)) (=> (= B_5 C_5) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_5) A_7))))) (forall ((C_1 $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_1) A_3)) (=> (= B_1 C_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_1) A_3))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_3))) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 B_1)) (=> (= (tptp.hBOOL B_1) (tptp.hBOOL C_1)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 C_1)))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_3))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_1)) (=> (= B_1 C_1) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 C_1)))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_3))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (=> (= B_1 C_1) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 C_1)))))) (forall ((C_4 $$unsorted) (A_6 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_4)) (=> (= B_4 C_4) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_4)))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_3))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_1)) (=> (= B_1 C_1) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 C_1)))))) (forall ((C_1 $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool C_1))) (=> (= (tptp.hBOOL A_3) (tptp.hBOOL B_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_bool_bool _let_1 A_3)))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_1))) (=> (= A_3 B_1) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_3)))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool C_1))) (=> (= A_3 B_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_3)))))) (forall ((C_3 $$unsorted) (A_5 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_3))) (=> (= A_5 B_3) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_3)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_5)))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool C_1))) (=> (= A_3 B_1) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 B_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_3)))))) (forall ((C_1 $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (=> (= (tptp.hBOOL A_3) (tptp.hBOOL B_1)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool B_1) C_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_3) C_1))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (=> (= A_3 B_1) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B_1) C_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_3) C_1))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (=> (= A_3 B_1) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool B_1) C_1)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool A_3) C_1))))) (forall ((C_2 $$unsorted) (A_4 $$unsorted) (B_2 $$unsorted)) (=> (= A_4 B_2) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_2) C_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_4) C_2))))) (forall ((C_1 $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (=> (= A_3 B_1) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool B_1) C_1)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool A_3) C_1))))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_3)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_3) Y_2)) (= (tptp.hBOOL X_3) (tptp.hBOOL Y_2))))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_3)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_3) Y_2)) (= X_3 Y_2)))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (=> (and (tptp.is_fun_pname_bool Y_2) (tptp.is_fun_pname_bool X_3)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_3)) (= (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_3) Y_2)) (= X_3 Y_2))))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_2) X_3)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_3) Y_2)) (= X_3 Y_2)))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (=> (and (tptp.is_fun_a_bool Y_2) (tptp.is_fun_a_bool X_3)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_2) X_3)) (= (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_3) Y_2)) (= X_3 Y_2))))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (=> (= (tptp.hBOOL X_3) (tptp.hBOOL Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_3) Y_2)))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (=> (= X_3 Y_2) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_3) Y_2)))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (=> (= X_3 Y_2) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_3) Y_2)))) (forall ((X_4 $$unsorted) (Y_3 $$unsorted)) (=> (= X_4 Y_3) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_4) Y_3)))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (=> (= X_3 Y_2) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_3) Y_2)))) (forall ((Y_2 $$unsorted) (X_3 $$unsorted)) (= (= (tptp.hBOOL X_3) (tptp.hBOOL Y_2)) (and (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool X_3) Y_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool Y_2) X_3))))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (= (= X_3 Y_2) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_3) Y_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_2) X_3))))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_3) (tptp.is_fun_pname_bool Y_2)) (= (= X_3 Y_2) (and (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool X_3) Y_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool Y_2) X_3)))))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (= (= X_3 Y_2) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_3) Y_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_2) X_3))))) (forall ((X_3 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_fun_a_bool X_3) (tptp.is_fun_a_bool Y_2)) (= (= X_3 Y_2) (and (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool X_3) Y_2)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool Y_2) X_3)))))) (forall ((X_2 $$unsorted) (Y_1 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_2)))) (forall ((Pa $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa tptp.bot_bot_fun_nat_bool)) (=> (forall ((A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.insert_nat A_2 F_2))))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_1))))))) (forall ((Pa $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.ord_le313189616e_bool F_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa tptp.bot_bo844097828e_bool)) (=> (forall ((A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_p338031245l_bool tptp.member_pname A_2))) (=> (and (tptp.is_pname A_2) (tptp.is_fun_pname_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa (tptp.insert_pname A_2 F_2)))))))))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool Pa F_1))))))) (forall ((Pa $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.ord_le1311769555a_bool F_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa tptp.bot_bot_fun_a_bool)) (=> (forall ((A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_a85458249l_bool tptp.member_a A_2))) (=> (and (tptp.is_a A_2) (tptp.is_fun_a_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool tptp.finite_finite_a F_2)) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa (tptp.insert_a A_2 F_2)))))))))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool Pa F_1))))))) (forall ((Pa $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool tptp.ord_le1454342156l_bool F_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool Pa tptp.bot_bo1701429464l_bool)) (=> (forall ((A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool A_2))) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1637334154l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool Pa (tptp.insert_fun_nat_bool A_2 F_2))))))))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool Pa F_1))))))) (forall ((Pa $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool tptp.ord_le675606854l_bool F_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool Pa tptp.bot_bo1649642514l_bool)) (=> (forall ((A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool A_2))) (=> (and (tptp.is_fun_pname_bool A_2) (tptp.is_fun1661590463l_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool Pa (tptp.insert1325755072e_bool A_2 F_2)))))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool Pa F_1))))))) (forall ((Pa $$unsorted) (A_1 $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool tptp.ord_le1375614389l_bool F_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool Pa tptp.bot_bo1389914601l_bool)) (=> (forall ((A_2 $$unsorted) (F_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f285962445l_bool tptp.member_fun_a_bool A_2))) (=> (and (tptp.is_fun_a_bool A_2) (tptp.is_fun949378684l_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool _let_1 A_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f621171935l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool Pa (tptp.insert_fun_a_bool A_2 F_2)))))))))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool Pa F_1))))))) (forall ((Pn $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.hAPP_pname_a tptp.mgt_call Pn))) (=> (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.p (tptp.insert_a _let_1 G)) (tptp.insert_a (tptp.mgt (tptp.the_com (tptp.body Pn))) tptp.bot_bot_fun_a_bool))) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.p G) (tptp.insert_a _let_1 tptp.bot_bot_fun_a_bool)))))) (forall ((Pa $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool Pa tptp.bot_bo1701429464l_bool)) (=> (forall ((X_1 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool tptp.member_fun_nat_bool X_1) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1637334154l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool Pa (tptp.insert_fun_nat_bool X_1 F_2))))))) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool Pa F_1)))))) (forall ((Pa $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool Pa tptp.bot_bo1649642514l_bool)) (=> (forall ((X_1 $$unsorted) (F_2 $$unsorted)) (=> (and (tptp.is_fun_pname_bool X_1) (tptp.is_fun1661590463l_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool tptp.finite595471783e_bool F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool tptp.member799430823e_bool X_1) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f1935102916l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool Pa (tptp.insert1325755072e_bool X_1 F_2)))))))) (tptp.hBOOL (tptp.hAPP_f1935102916l_bool Pa F_1)))))) (forall ((Pa $$unsorted) (F_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool F_1)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool Pa tptp.bot_bo1389914601l_bool)) (=> (forall ((X_1 $$unsorted) (F_2 $$unsorted)) (=> (and (tptp.is_fun_a_bool X_1) (tptp.is_fun949378684l_bool F_2)) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool tptp.finite347923420a_bool F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f621171935l_bool (tptp.hAPP_f285962445l_bool tptp.member_fun_a_bool X_1) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f621171935l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f621171935l_bool Pa (tptp.insert_fun_a_bool X_1 F_2)))))))) (tptp.hBOOL (tptp.hAPP_f621171935l_bool Pa F_1)))))) (forall ((U $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_2) (tptp.hAPP_nat_nat F N_2)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool (tptp.cOMBB_800536526ol_nat tptp.ord_less_eq_nat F)) U)))))) (forall ((Pn $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool tptp.member_pname Pn) tptp.u)) (tptp.hBOOL (tptp.wt (tptp.the_com (tptp.body Pn)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus_nat M))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 tptp.one_one_nat)) N)))) (forall ((N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc N)) tptp.one_one_nat) N)) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_1)) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.nat_case_bool tptp.fFalse (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1)) Na)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus_nat M))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.suc M)) N) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.suc M)) N) (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M_1 $$unsorted) (K_2 $$unsorted) (Na $$unsorted)) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) K_2) (tptp.hAPP_nat_nat (tptp.plus_plus_nat Na) K_2)) (= M_1 Na))) (forall ((K_2 $$unsorted) (M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.plus_plus_nat K_2))) (= (= (tptp.hAPP_nat_nat _let_1 M_1) (tptp.hAPP_nat_nat _let_1 Na)) (= M_1 Na)))) (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.plus_plus_nat M))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 N)) K) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) K))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.plus_plus_nat X))) (let ((_let_2 (tptp.plus_plus_nat Y))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z)))))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) M))) (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N)) N) M)) (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) M)) N) M)) (forall ((I $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.minus_minus_nat I))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_2)) K) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) K))))) (forall ((K $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus_nat K))) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N)))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) K)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) N)))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) M)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)) (exists ((K_1 $$unsorted)) (= Na (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) K_1))))) (forall ((K_2 $$unsorted) (M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.plus_plus_nat K_2))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na))))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) M)))))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) J_2)))))) (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) K))))) (forall ((K $$unsorted) (L $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) L)))))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N)))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K)) N)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N))))))) (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J_2)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) I)) K) (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K)) I)))) (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J_2)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K)) I) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) I)) K)))) (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J_2)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_2)) K) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K)))))) (forall ((K_2 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) I_1) K_2) (= J_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat K_2) I_1))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N)) N) M))) (forall ((I_1 $$unsorted) (K_2 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) J_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_2)) J_1))))) (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J_2)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_2)) K))))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N)) M))) (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) M)) K))))) (forall ((J_1 $$unsorted) (K_2 $$unsorted) (I_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_2)) I_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_2))))) (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J_2)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat I) (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I) K)) J_2)))) (forall ((N $$unsorted)) (= (tptp.hAPP_nat_nat tptp.suc N) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) tptp.one_one_nat))) (forall ((N $$unsorted)) (= (tptp.hAPP_nat_nat tptp.suc N) (tptp.hAPP_nat_nat (tptp.plus_plus_nat tptp.one_one_nat) N))) (forall ((M $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J_2)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K))) M) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc J_2)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat K) M))))) (forall ((M $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J_2)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) K))) (tptp.hAPP_nat_nat (tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K)) (tptp.hAPP_nat_nat tptp.suc J_2))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Y) Z)))))) (forall ((Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Y) Z)))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_nat_nat tptp.suc N))))) (forall ((K_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) K_2))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Y) Z)))))) (forall ((Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat Y) Z)))))) (forall ((I $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I) J_2)) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) K)))) (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted) (L $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K) L)) (=> (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) L) (tptp.hAPP_nat_nat (tptp.plus_plus_nat K) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))))) (forall ((K $$unsorted) (L $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K) L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) L)))))) (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) K))))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) J_2)))))) (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) M)))))) (forall ((K_2 $$unsorted) (M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.plus_plus_nat K_2))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_1)) (tptp.hAPP_nat_nat _let_1 Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na))))) (forall ((J_2 $$unsorted) (I $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat J_2) I)) I)))) (forall ((I $$unsorted) (J_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I) J_2)) I)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_nat_nat tptp.suc N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N))) (= M N))))) (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_2) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc I)) K))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (=> (not (= _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_1) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc M))) (= M N))))) (forall ((Na $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc M_1))) (= Na M_1))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M_1)) (tptp.hAPP_nat_nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc Na))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= M_1 Na))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) (tptp.hAPP_nat_nat tptp.suc M_1))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (= M N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (=> (not (= M N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)) (= M_1 Na)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)) (not (= M_1 Na))))) (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus_nat L))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 L)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat _let_1 M)))))))) (forall ((N $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_2) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_2) N)) K)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X) Y)))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (not (= M_1 Na)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) M_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y) X))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) M)) (not (= M N)))) (forall ((S $$unsorted) (T $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat S) T)) (not (= S T)))) (forall ((Pa $$unsorted) (M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool Pa Na) M_1)))) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)) _let_1) (=> (=> (= M_1 Na) _let_1) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) M_1)) _let_1) _let_1))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_1)) (exists ((M_2 $$unsorted)) (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) M_2))))))) (forall ((Na $$unsorted)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) Na))) Na)) (forall ((Pa $$unsorted) (I_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.cOMBS_nat_bool_bool (tptp.cOMBB_1015721476ol_nat tptp.fconj Pa) (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) I_1)))))) (forall ((I $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.plus_plus_nat I) M))))) (forall ((I $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) I))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)) (exists ((K_1 $$unsorted)) (= Na (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) K_1)))))) (forall ((Na $$unsorted) (M_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) M_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Na)) M_1)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) (tptp.hAPP_nat_nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M_1)) Na)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) (tptp.hAPP_nat_nat tptp.suc N))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M)) N)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Na) (tptp.hAPP_nat_nat tptp.suc M_1))) (= Na M_1)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N)) (tptp.hAPP_nat_nat tptp.suc M)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))) (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N)) M))) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (K_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) (tptp.hAPP_nat_nat (tptp.minus_minus_nat J_1) K_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat I_1) K_2)) J_1)))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C) A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat A) C)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat B) C)))))) (forall ((Na $$unsorted) (K_2 $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Na)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.minus_minus_nat M_1) K_2)) (tptp.hAPP_nat_nat (tptp.minus_minus_nat Na) K_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) Na))))))) (forall ((X_1 $$unsorted)) (= (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc X_1)))) (forall ((M_1 $$unsorted) (K_2 $$unsorted) (F $$unsorted)) (=> (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F M_2)) (tptp.hAPP_nat_nat F N_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.plus_plus_nat (tptp.hAPP_nat_nat F M_1)) K_2)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) K_2)))))) (forall ((Pa $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa J_1)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_nat_nat tptp.suc I_2))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa I_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa I_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (exists ((K_1 $$unsorted)) (= N (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.plus_plus_nat M) K_1)))))) (forall ((Na $$unsorted) (N_1 $$unsorted)) (=> (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Na)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_1)))) (forall ((I_1 $$unsorted) (J_1 $$unsorted) (F $$unsorted)) (=> (forall ((I_2 $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F I_2)) (tptp.hAPP_nat_nat F J))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F I_1)) (tptp.hAPP_nat_nat F J_1)))))) (forall ((I $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc I)) K)) (not (forall ((J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J)) (not (= K (tptp.hAPP_nat_nat tptp.suc J)))))))) (forall ((I $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) K)) (=> (not (= K (tptp.hAPP_nat_nat tptp.suc I))) (not (forall ((J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J)) (not (= K (tptp.hAPP_nat_nat tptp.suc J))))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) Na) _let_1) (or (and (= M_1 _let_1) (= Na tptp.zero_zero_nat)) (and (= M_1 tptp.zero_zero_nat) (= Na _let_1)))))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (tptp.hAPP_nat_nat (tptp.plus_plus_nat M_1) Na)) (or (and (= M_1 _let_1) (= Na tptp.zero_zero_nat)) (and (= M_1 tptp.zero_zero_nat) (= Na _let_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) (tptp.hAPP_nat_nat (tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N) tptp.zero_zero_nat))) (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M_1) Na) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) Na)))) (= tptp.one_one_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) (forall ((M $$unsorted) (N $$unsorted)) (=> (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))) (forall ((M $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((M $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((N $$unsorted)) (= (tptp.hAPP_nat_nat (tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M $$unsorted)) (not (= (tptp.hAPP_nat_nat tptp.suc M) tptp.zero_zero_nat))) (forall ((M $$unsorted)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc M)))) (forall ((Nat_1 $$unsorted)) (not (= (tptp.hAPP_nat_nat tptp.suc Nat_1) tptp.zero_zero_nat))) (forall ((M $$unsorted)) (not (= (tptp.hAPP_nat_nat tptp.suc M) tptp.zero_zero_nat))) (forall ((Nat $$unsorted)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc Nat)))) (forall ((M $$unsorted)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc M)))) (= tptp.bot_bot_nat tptp.zero_zero_nat) (forall ((Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Na) tptp.zero_zero_nat)) (= Na tptp.zero_zero_nat))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.is_a X) (tptp.is_a Y)) (or (not (tptp.hBOOL (tptp.hAPP_a_bool (tptp.hAPP_a_fun_a_bool tptp.fequal_a X) Y))) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_a_bool (tptp.hAPP_a_fun_a_bool tptp.fequal_a X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.is_pname X) (tptp.is_pname Y)) (or (not (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y))) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool tptp.fequal_pname X) Y)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_a_bool (tptp.cOMBK_bool_a P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_a P) (= (tptp.hAPP_pname_a (tptp.cOMBK_a_pname P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_bool (tptp.hAPP_a_fun_a_bool (tptp.cOMBC_a_a_bool P) Q) R) (tptp.hAPP_a_bool (tptp.hAPP_a_fun_a_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_nat_bool (tptp.cOMBK_bool_nat P) Q) P))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.is_fun_a_bool X) (tptp.is_fun_a_bool Y)) (or (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.fequal_fun_a_bool X) Y))) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool tptp.fequal_fun_a_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_pname_bool (tptp.cOMBK_bool_pname P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_bool (tptp.hAPP_nat_fun_a_bool (tptp.cOMBC_a_nat_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_a_fun_nat_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.hAPP_a_fun_nat_bool (tptp.cOMBC_nat_a_bool P) Q) R) (tptp.hAPP_a_bool (tptp.hAPP_nat_fun_a_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_bool (tptp.cOMBB_bool_bool_a P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_bool (tptp.cOMBS_a_bool_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_a_fun_bool_bool P R) (tptp.hAPP_a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_bool (tptp.hAPP_p1534023578a_bool (tptp.cOMBC_a_pname_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_a93125764e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_a93125764e_bool (tptp.cOMBC_pname_a_bool P) Q) R) (tptp.hAPP_a_bool (tptp.hAPP_p1534023578a_bool P R) Q))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X) Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.is_fun_pname_bool X) (tptp.is_fun_pname_bool Y)) (or (not (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y))) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool tptp.fequal533582459e_bool X) Y)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_fun_a_bool (tptp.cOMBB_a_fun_a_bool_a P Q) R) (tptp.hAPP_a_fun_a_bool P (tptp.hAPP_a_a Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool (tptp.cOMBC_nat_nat_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.cOMBB_bool_bool_nat P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_nat_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_fun_a_bool_bool (tptp.cOMBK_324466864a_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.cOMBS_nat_bool_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_n1006566506l_bool P R) (tptp.hAPP_nat_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_n1025906991e_bool (tptp.cOMBC_pname_nat_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_p1499970991t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.hAPP_p1499970991t_bool (tptp.cOMBC_nat_pname_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_n1025906991e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.cOMBB_647938656_pname P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.cOMBS_568398431l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_p393069232l_bool P R) (tptp.hAPP_pname_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool (tptp.cOMBC_1149511130e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_p61793385e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_fun_a_bool (tptp.cOMBB_1885489796ol_nat P Q) R) (tptp.hAPP_a_fun_a_bool P (tptp.hAPP_nat_a Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_bool (tptp.hAPP_f2050579477a_bool (tptp.cOMBC_1355376034l_bool P) Q) R) (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_a85458249l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1534023578a_bool (tptp.cOMBB_1897541054_pname P Q) R) (tptp.hAPP_a_fun_a_bool P (tptp.hAPP_pname_a Q R)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f54304608l_bool (tptp.cOMBK_1994329625t_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f1664156314l_bool (tptp.cOMBK_1857069011e_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_fun_nat_bool (tptp.cOMBB_1321347587bool_a P Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_a_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_bool (tptp.hAPP_f1549043526a_bool (tptp.cOMBC_777206479l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_a1392362872l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f282463732t_bool (tptp.cOMBC_1928494297l_bool P) Q) R) (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_n1414589940l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_n1414589940l_bool (tptp.cOMBC_619334683t_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_f282463732t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_fun_a_bool_bool (tptp.cOMBB_2140588453a_bool P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_fun_a_bool_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_fun_bool_bool (tptp.cOMBB_1972296269bool_a P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_fun_a_bool_bool (tptp.cOMBS_1035972772l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f198738859l_bool P R) (tptp.hAPP_fun_a_bool_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a_bool (tptp.hAPP_f1051908748a_bool (tptp.cOMBC_1834145417l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_a217006258l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f1794073134e_bool (tptp.cOMBC_445755039l_bool P) Q) R) (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_p1824510254l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_p1824510254l_bool (tptp.cOMBC_1738168533e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_f1794073134e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a93125764e_bool (tptp.cOMBB_610033911bool_a P Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_a_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n1699378549t_bool (tptp.cOMBB_800536526ol_nat P Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_nat_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.cOMBC_226598744l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool (tptp.cOMBC_385542954t_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f54304608l_bool (tptp.cOMBB_238756964t_bool P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f54304608l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n1006566506l_bool (tptp.cOMBB_1015721476ol_nat P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_nat_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1499970991t_bool (tptp.cOMBB_523834888_pname P Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_pname_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f54304608l_bool (tptp.cOMBS_1187019125l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f1748468828l_bool P R) (tptp.hAPP_f54304608l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f654413245e_bool (tptp.cOMBC_267053842l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_p130839763l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f1066163005t_bool (tptp.cOMBC_386238098l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_n850744903l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_n850744903l_bool (tptp.cOMBC_1666426608t_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_f1066163005t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f54304608l_bool (tptp.hAPP_p130839763l_bool (tptp.cOMBC_615407716e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_f654413245e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n1025906991e_bool (tptp.cOMBB_1212655066ol_nat P Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_nat_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.cOMBB_307249310e_bool P Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p393069232l_bool (tptp.cOMBB_675860798_pname P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_pname_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.cOMBS_350070575l_bool P Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_f1476298914l_bool P R) (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool (tptp.cOMBC_1058051404l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_p338031245l_bool (tptp.cOMBC_1004116266e_bool P) Q) R) (tptp.hAPP_pname_bool (tptp.hAPP_f759274231e_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p61793385e_bool (tptp.cOMBB_542850580_pname P Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_pname_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool (tptp.cOMBC_1732670874l_bool P) Q) R) (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f1631501043l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f282463732t_bool (tptp.cOMBB_164527437a_bool P Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_fun_a_bool_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f198738859l_bool (tptp.cOMBB_338059395a_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_fun_a_bool_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1794073134e_bool (tptp.cOMBB_1693087065a_bool P Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_f1128469712_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f800510211t_bool (tptp.cOMBB_1250273980t_bool P Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_f22106695ol_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a85458249l_bool (tptp.cOMBB_472261505bool_a P Q) R) (tptp.hAPP_f1631501043l_bool P (tptp.hAPP_a_fun_a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool (tptp.cOMBC_1693257480l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1748468828l_bool (tptp.cOMBB_444170502t_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f54304608l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1066163005t_bool (tptp.cOMBB_1896684278e_bool P Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_f921600141ol_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f654413245e_bool (tptp.cOMBB_141086128t_bool P Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_f1291551745_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1476298914l_bool (tptp.cOMBB_2095475776e_bool P Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_f1664156314l_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool (tptp.cOMBC_1284144636l_bool P) Q) R) (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f434788991l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f759274231e_bool (tptp.cOMBB_598082538e_bool P Q) R) (tptp.hAPP_p61793385e_bool P (tptp.hAPP_f1297739591_pname Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n1414589940l_bool (tptp.cOMBB_1823939024ol_nat P Q) R) (tptp.hAPP_f1631501043l_bool P (tptp.hAPP_nat_fun_a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_fun_a_bool_bool (tptp.hAPP_f2117159681l_bool (tptp.cOMBC_1880041174l_bool P) Q) R) (tptp.hAPP_f621171935l_bool (tptp.hAPP_f285962445l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p1824510254l_bool (tptp.cOMBB_392435466_pname P Q) R) (tptp.hAPP_f1631501043l_bool P (tptp.hAPP_p1534023578a_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a1392362872l_bool (tptp.cOMBB_743407885bool_a P Q) R) (tptp.hAPP_f103356543l_bool P (tptp.hAPP_a_fun_nat_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_a217006258l_bool (tptp.cOMBB_1137537805bool_a P Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_a93125764e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n215258509l_bool (tptp.cOMBB_2026977092ol_nat P Q) R) (tptp.hAPP_f103356543l_bool P (tptp.hAPP_n1699378549t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f54304608l_bool (tptp.hAPP_f1246832597l_bool (tptp.cOMBC_1245412066l_bool P) Q) R) (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1951378235l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p130839763l_bool (tptp.cOMBB_928955006_pname P Q) R) (tptp.hAPP_f103356543l_bool P (tptp.hAPP_p1499970991t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_n850744903l_bool (tptp.cOMBB_2117322052ol_nat P Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_n1025906991e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1664156314l_bool (tptp.hAPP_f559147733l_bool (tptp.cOMBC_1988546018l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f556039215l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_p338031245l_bool (tptp.cOMBB_408569982_pname P Q) R) (tptp.hAPP_f434788991l_bool P (tptp.hAPP_p61793385e_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool (tptp.cOMBC_331553030l_bool P) Q) R) (tptp.hAPP_f621171935l_bool (tptp.hAPP_f1434722111l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool (tptp.cOMBC_595898202l_bool P) Q) R) (tptp.hAPP_f1637334154l_bool (tptp.hAPP_f1772781669l_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool (tptp.cOMBC_7971162l_bool P) Q) R) (tptp.hAPP_f1935102916l_bool (tptp.hAPP_f510955609l_bool P R) Q))) (tptp.hBOOL (tptp.hAPP_f1664156314l_bool tptp.finite_finite_pname tptp.u)) _let_9 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat _let_7) _let_8)) (= (tptp.hAPP_fun_a_bool_nat tptp.finite_card_a tptp.g) (tptp.hAPP_nat_nat (tptp.minus_minus_nat _let_8) _let_7)) _let_6 (not (tptp.hBOOL (tptp.hAPP_fun_a_bool_bool _let_5 tptp.g))) _let_4 true))))))))))))))))))))))))))))
% 1.69/1.85 )
% 1.69/1.85 % SZS output end Proof for SWW473+2
% 1.69/1.85 % cvc5---1.0.5 exiting
% 1.69/1.85 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------