TSTP Solution File: SCT171_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT171_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:12:22 EDT 2023
% Result : Theorem 0.25s 0.76s
% Output : Proof 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18 % Problem : SCT171_1 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.19 % Command : do_cvc5 %s %d
% 0.18/0.40 % Computer : n003.cluster.edu
% 0.18/0.40 % Model : x86_64 x86_64
% 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40 % Memory : 8042.1875MB
% 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Thu Aug 24 16:50:37 EDT 2023
% 0.18/0.40 % CPUTime :
% 0.25/0.59 %----Proving TF0_NAR, FOF, or CNF
% 0.25/0.76 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.wD3VWSO5XO/cvc5---1.0.5_19010.p...
% 0.25/0.76 ------- get file name : TPTP file name is SCT171_1
% 0.25/0.76 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19010.smt2...
% 0.25/0.76 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.25/0.76 % SZS status Theorem for SCT171_1
% 0.25/0.76 % SZS output start Proof for SCT171_1
% 0.25/0.76 (
% 0.25/0.76 (let ((_let_1 (tptp.member1484933012le_alt (tptp.produc170576535le_alt tptp.c tptp.d)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_f718157575t_bool tptp.f tptp.p))))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.member1484933012le_alt (tptp.produc170576535le_alt tptp.b tptp.a)))) (let ((_let_5 (tptp.member1484933012le_alt (tptp.produc170576535le_alt tptp.a tptp.b)))) (let ((_let_6 (tptp.cOMBB_124649523e_indi tptp.if_fun95824985t_bool (tptp.cOMBC_998415407t_bool (tptp.cOMBB_1514803447e_indi tptp.ord_less_nat tptp.h) tptp.n)))) (let ((_let_7 (tptp.cOMBS_1688227464t_bool (tptp.cOMBS_1833320732t_bool _let_6 (tptp.cOMBC_377836265t_bool (tptp.cOMBB_1932856316e_indi tptp.arrow_1275257820_mktop tptp.p) tptp.e)) (tptp.cOMBS_1688227464t_bool (tptp.cOMBS_1833320732t_bool (tptp.cOMBB_124649523e_indi tptp.if_fun95824985t_bool (tptp.cOMBC_998415407t_bool (tptp.cOMBB_1514803447e_indi tptp.fequal_nat tptp.h) tptp.n)) (tptp.cOMBC_377836265t_bool (tptp.cOMBC_1994570734t_bool (tptp.cOMBB_715840641e_indi tptp.arrow_2009189698_above tptp.p) tptp.c) tptp.e)) (tptp.cOMBC_377836265t_bool (tptp.cOMBB_1932856316e_indi tptp.arrow_1126550734_mkbot tptp.p) tptp.e))))) (let ((_let_8 (tptp.hAPP_f718157575t_bool tptp.f _let_7))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt tptp.e tptp.d)) _let_8)))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 _let_8)))) (let ((_let_11 (= _let_2 _let_10))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (SYMM (ASSUME :args (_let_11)))) :args ((or _let_2 (not _let_10)))) (ASSUME :args (_let_10)) :args (_let_2 false _let_10)) :args (false false _let_2)) :args ((tptp.hBOOL (tptp.hAPP_f725100827l_bool tptp.arrow_981905126le_IIA tptp.f)) (tptp.hBOOL (tptp.hAPP_f725100827l_bool tptp.arrow_807483785nimity tptp.f)) (not (= tptp.c tptp.d)) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool tptp.p) tptp.arrow_1880704820e_Prof)) (forall ((X_2 tptp.arrow_1621810872le_alt) (Y_1 tptp.arrow_1621810872le_alt) (L tptp.fun_Pr1639951081t_bool) (Z_1 tptp.arrow_1621810872le_alt)) (let ((_let_1 (tptp.member1484933012le_alt (tptp.produc170576535le_alt X_2 Y_1)))) (let ((_let_2 (= X_2 Z_1))) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_A476679046t_bool (tptp.hAPP_f1699392794t_bool tptp.arrow_1126550734_mkbot L) Z_1))) (and (not (= Y_1 Z_1)) (=> _let_2 (not (= X_2 Y_1))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 L)))))))) (forall ((X_2 tptp.arrow_1621810872le_alt) (Y_1 tptp.arrow_1621810872le_alt) (L tptp.fun_Pr1639951081t_bool) (Z_1 tptp.arrow_1621810872le_alt)) (let ((_let_1 (tptp.member1484933012le_alt (tptp.produc170576535le_alt X_2 Y_1)))) (let ((_let_2 (= Y_1 Z_1))) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_A476679046t_bool (tptp.hAPP_f1699392794t_bool tptp.arrow_1275257820_mktop L) Z_1))) (and (not (= X_2 Z_1)) (=> _let_2 (not (= X_2 Y_1))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 L)))))))) (forall ((P_1 tptp.fun_Ar2047178847t_bool) (Pa tptp.fun_Ar2047178847t_bool) (A_8 tptp.arrow_1621810872le_alt) (B_8 tptp.arrow_1621810872le_alt) (Aa tptp.arrow_1621810872le_alt) (Ba tptp.arrow_1621810872le_alt)) (=> (not (= Aa Ba)) (=> (not (= A_8 B_8)) (=> (not (= Aa B_8)) (=> (not (= Ba A_8)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool Pa) tptp.arrow_1880704820e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool P_1) tptp.arrow_1880704820e_Prof)) (=> (forall ((I tptp.arrow_501706939e_indi)) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) (tptp.hAPP_A2044747691t_bool Pa I))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_8 B_8)) (tptp.hAPP_A2044747691t_bool P_1 I))))) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) (tptp.hAPP_f718157575t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_8 B_8)) (tptp.hAPP_f718157575t_bool tptp.f P_1)))))))))))) (forall ((P_1 tptp.fun_Ar2047178847t_bool) (Pa tptp.fun_Ar2047178847t_bool) (A_8 tptp.arrow_1621810872le_alt) (B_8 tptp.arrow_1621810872le_alt) (Aa tptp.arrow_1621810872le_alt) (Ba tptp.arrow_1621810872le_alt)) (=> (not (= Aa Ba)) (=> (not (= A_8 B_8)) (=> (not (= Aa B_8)) (=> (not (= Ba A_8)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool Pa) tptp.arrow_1880704820e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool P_1) tptp.arrow_1880704820e_Prof)) (=> (forall ((I tptp.arrow_501706939e_indi)) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) (tptp.hAPP_A2044747691t_bool Pa I))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_8 B_8)) (tptp.hAPP_A2044747691t_bool P_1 I))))) (=> (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) (tptp.hAPP_f718157575t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_8 B_8)) (tptp.hAPP_f718157575t_bool tptp.f P_1)))))))))))) (forall ((P_1 tptp.fun_Ar2047178847t_bool) (Pa tptp.fun_Ar2047178847t_bool) (Ca tptp.arrow_1621810872le_alt) (Aa tptp.arrow_1621810872le_alt) (Ba tptp.arrow_1621810872le_alt)) (=> (not (= Aa Ba)) (=> (not (= Ba Ca)) (=> (not (= Aa Ca)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool Pa) tptp.arrow_1880704820e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool P_1) tptp.arrow_1880704820e_Prof)) (=> (forall ((I tptp.arrow_501706939e_indi)) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) (tptp.hAPP_A2044747691t_bool Pa I))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Ba Ca)) (tptp.hAPP_A2044747691t_bool P_1 I))))) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) (tptp.hAPP_f718157575t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Ba Ca)) (tptp.hAPP_f718157575t_bool tptp.f P_1))))))))))) (forall ((P_1 tptp.fun_Ar2047178847t_bool) (Pa tptp.fun_Ar2047178847t_bool) (A_8 tptp.arrow_1621810872le_alt) (B_8 tptp.arrow_1621810872le_alt) (Aa tptp.arrow_1621810872le_alt) (Ba tptp.arrow_1621810872le_alt)) (=> (not (= Aa Ba)) (=> (not (= A_8 B_8)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool Pa) tptp.arrow_1880704820e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool P_1) tptp.arrow_1880704820e_Prof)) (=> (forall ((I tptp.arrow_501706939e_indi)) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) (tptp.hAPP_A2044747691t_bool Pa I))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_8 B_8)) (tptp.hAPP_A2044747691t_bool P_1 I))))) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) (tptp.hAPP_f718157575t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_8 B_8)) (tptp.hAPP_f718157575t_bool tptp.f P_1)))))))))) (forall ((P_1 tptp.fun_Ar2047178847t_bool) (Pa tptp.fun_Ar2047178847t_bool) (Aa tptp.arrow_1621810872le_alt) (Ba tptp.arrow_1621810872le_alt)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool Pa) tptp.arrow_1880704820e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool P_1) tptp.arrow_1880704820e_Prof)) (=> (forall ((I tptp.arrow_501706939e_indi)) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) (tptp.hAPP_A2044747691t_bool Pa I))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Ba Aa)) (tptp.hAPP_A2044747691t_bool P_1 I))))) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) (tptp.hAPP_f718157575t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Ba Aa)) (tptp.hAPP_f718157575t_bool tptp.f P_1))))))))) (forall ((I tptp.arrow_501706939e_indi)) (let ((_let_1 (tptp.hAPP_A2044747691t_bool tptp.p I))) (let ((_let_2 (tptp.member1484933012le_alt (tptp.produc170576535le_alt tptp.c tptp.d)))) (let ((_let_3 (tptp.hAPP_A1741215436di_nat tptp.h I))) (let ((_let_4 (= _let_3 tptp.n))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_3) tptp.n)))) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_2 _let_1)) (and (=> _let_5 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_2 (tptp.hAPP_A476679046t_bool (tptp.hAPP_f1699392794t_bool tptp.arrow_1275257820_mktop _let_1) tptp.e)))) (=> (not _let_5) (and (=> _let_4 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_2 (tptp.hAPP_A476679046t_bool (tptp.hAPP_A272835723t_bool (tptp.hAPP_f1560118175t_bool tptp.arrow_2009189698_above _let_1) tptp.c) tptp.e)))) (=> (not _let_4) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_2 (tptp.hAPP_A476679046t_bool (tptp.hAPP_f1699392794t_bool tptp.arrow_1126550734_mkbot _let_1) tptp.e)))))))))))))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_A2044747691t_bool tptp.p (tptp.hAPP_n1582158000e_indi (tptp.hilber797233813di_nat tptp.top_to850136695i_bool tptp.h) tptp.n)))) _let_10 _let_11 (forall ((Pa tptp.fun_Pr1639951081t_bool)) (= (forall ((X1 tptp.produc624534567le_alt)) (tptp.hBOOL (tptp.hAPP_P751176071t_bool Pa X1))) (forall ((A_1 tptp.arrow_1621810872le_alt) (B_1 tptp.arrow_1621810872le_alt)) (tptp.hBOOL (tptp.hAPP_P751176071t_bool Pa (tptp.produc170576535le_alt A_1 B_1)))))) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool _let_7) tptp.arrow_1880704820e_Prof)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt tptp.c tptp.e)) _let_8)) _let_9 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.n) (tptp.finite1317065577e_indi tptp.top_to850136695i_bool))) (tptp.hBOOL (tptp.inj_on1177549232di_nat tptp.h tptp.top_to850136695i_bool)) (forall ((A_10 tptp.arrow_1621810872le_alt) (B_10 tptp.arrow_1621810872le_alt) (A_9 tptp.arrow_1621810872le_alt) (B_9 tptp.arrow_1621810872le_alt)) (=> (= (tptp.produc170576535le_alt A_10 B_10) (tptp.produc170576535le_alt A_9 B_9)) (not (=> (= A_10 A_9) (not (= B_10 B_9)))))) (forall ((Aa tptp.arrow_1621810872le_alt) (Ba tptp.arrow_1621810872le_alt) (A_8 tptp.arrow_1621810872le_alt) (B_8 tptp.arrow_1621810872le_alt)) (= (= (tptp.produc170576535le_alt Aa Ba) (tptp.produc170576535le_alt A_8 B_8)) (and (= Aa A_8) (= Ba B_8)))) (forall ((Fa tptp.fun_fu50365883t_bool)) (= (tptp.hBOOL (tptp.hAPP_f725100827l_bool tptp.arrow_981905126le_IIA Fa)) (forall ((X_1 tptp.fun_Ar2047178847t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_1) tptp.arrow_1880704820e_Prof)) (forall ((Xa tptp.fun_Ar2047178847t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool Xa) tptp.arrow_1880704820e_Prof)) (forall ((A_1 tptp.arrow_1621810872le_alt) (B_1 tptp.arrow_1621810872le_alt)) (let ((_let_1 (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_1 B_1)))) (=> (forall ((I tptp.arrow_501706939e_indi)) (let ((_let_1 (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_1 B_1)))) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_A2044747691t_bool X_1 I))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_A2044747691t_bool Xa I)))))) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_f718157575t_bool Fa X_1))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_f718157575t_bool Fa Xa))))))))))))) (forall ((Fa tptp.fun_fu50365883t_bool)) (= (tptp.hBOOL (tptp.hAPP_f725100827l_bool tptp.arrow_807483785nimity Fa)) (forall ((X_1 tptp.fun_Ar2047178847t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_1) tptp.arrow_1880704820e_Prof)) (forall ((A_1 tptp.arrow_1621810872le_alt) (B_1 tptp.arrow_1621810872le_alt)) (=> (forall ((I tptp.arrow_501706939e_indi)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_1 B_1)) (tptp.hAPP_A2044747691t_bool X_1 I)))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_1 B_1)) (tptp.hAPP_f718157575t_bool Fa X_1))))))))) (forall ((X_2 tptp.fun_Pr1639951081t_bool)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool tptp.top_to1057791589l_bool X_2))) (forall ((X_2 tptp.fun_Ar2047178847t_bool)) (tptp.hBOOL (tptp.hAPP_f1095388607l_bool tptp.top_to653038619l_bool X_2))) (forall ((X_2 tptp.fun_fu50365883t_bool)) (tptp.hBOOL (tptp.hAPP_f725100827l_bool tptp.top_to2127553399l_bool X_2))) (forall ((X_2 tptp.produc624534567le_alt)) (tptp.hBOOL (tptp.hAPP_P751176071t_bool tptp.top_to710777827t_bool X_2))) (forall ((X_2 tptp.arrow_501706939e_indi)) (tptp.hBOOL (tptp.hAPP_A1059798043i_bool tptp.top_to850136695i_bool X_2))) (forall ((X_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) tptp.top_to1647826457l_bool))) (forall ((X_2 tptp.arrow_501706939e_indi)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) tptp.top_to850136695i_bool))) (forall ((X_2 tptp.produc624534567le_alt)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt X_2) tptp.top_to710777827t_bool))) (forall ((X_2 tptp.fun_Ar2047178847t_bool)) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) tptp.top_to653038619l_bool))) (forall ((X_2 tptp.fun_fu50365883t_bool)) (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool X_2) tptp.top_to2127553399l_bool))) (forall ((X_2 tptp.fun_Pr1639951081t_bool)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool X_2) tptp.top_to1057791589l_bool))) (forall ((X_2 tptp.bool)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) tptp.top_to1647826457l_bool))) (forall ((X_2 tptp.arrow_501706939e_indi)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) tptp.top_to850136695i_bool))) (forall ((X_2 tptp.produc624534567le_alt)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt X_2) tptp.top_to710777827t_bool))) (forall ((X_2 tptp.fun_Ar2047178847t_bool)) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) tptp.top_to653038619l_bool))) (forall ((X_2 tptp.fun_fu50365883t_bool)) (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool X_2) tptp.top_to2127553399l_bool))) (forall ((X_2 tptp.fun_Pr1639951081t_bool)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool X_2) tptp.top_to1057791589l_bool))) (forall ((X_2 tptp.fun_Pr1639951081t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool tptp.top_to1057791589l_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 tptp.fun_Ar2047178847t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1095388607l_bool tptp.top_to653038619l_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 tptp.fun_fu50365883t_bool)) (= (tptp.hBOOL (tptp.hAPP_f725100827l_bool tptp.top_to2127553399l_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 tptp.produc624534567le_alt)) (= (tptp.hBOOL (tptp.hAPP_P751176071t_bool tptp.top_to710777827t_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 tptp.arrow_501706939e_indi)) (= (tptp.hBOOL (tptp.hAPP_A1059798043i_bool tptp.top_to850136695i_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((Aa tptp.fun_fu383145951l_bool)) (not (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.hAPP_f279586623l_bool tptp.ord_le1472193545l_bool tptp.top_to1057791589l_bool) Aa)))) (forall ((Aa tptp.fun_fu103733537l_bool)) (not (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.hAPP_f786935331l_bool tptp.ord_le2059466615l_bool tptp.top_to653038619l_bool) Aa)))) (forall ((Aa tptp.fun_fu1251737213l_bool)) (not (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.hAPP_f1303771867l_bool tptp.ord_le1419690707l_bool tptp.top_to2127553399l_bool) Aa)))) (forall ((Aa tptp.bool)) (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool tptp.top_top_bool) Aa)))) (forall ((Aa tptp.fun_Pr1639951081t_bool)) (not (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.hAPP_f1911990195l_bool tptp.ord_le1051050815t_bool tptp.top_to710777827t_bool) Aa)))) (forall ((Aa tptp.fun_Ar1871347069i_bool)) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool tptp.top_to850136695i_bool) Aa)))) (forall ((X_14 tptp.nat) (Y_13 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_14) Y_13))) (=> (not (= X_14 Y_13)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_13) X_14))))) (forall ((X_2 tptp.fun_Ar1871347069i_bool) (Y_1 tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool X_2) Y_1)) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Y_1) X_2))))) (forall ((X_13 tptp.nat) (Y_12 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_13) Y_12)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_12) X_13))))) (forall ((Z_1 tptp.fun_Ar1871347069i_bool) (Y_1 tptp.fun_Ar1871347069i_bool) (X_2 tptp.fun_Ar1871347069i_bool)) (let ((_let_1 (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Z_1))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Y_1) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool _let_1 X_2)))))) (forall ((Z_2 tptp.nat) (Y_11 tptp.nat) (X_12 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Z_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_11) X_12)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_11)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_12)))))) (forall ((Z_1 tptp.fun_Ar1871347069i_bool) (X_2 tptp.fun_Ar1871347069i_bool) (Y_1 tptp.fun_Ar1871347069i_bool)) (let ((_let_1 (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Y_1) Z_1)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool _let_1 Z_1)))))) (forall ((Z tptp.nat) (X_11 tptp.nat) (Y_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_11))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_10)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_10) Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)))))) (forall ((Ca tptp.fun_Ar1871347069i_bool) (Ba tptp.fun_Ar1871347069i_bool) (Aa tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Ca) Aa))))) (forall ((C_3 tptp.nat) (B_7 tptp.nat) (A_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_7) A_7)) (=> (= B_7 C_3) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_3) A_7))))) (forall ((Ca tptp.fun_Ar1871347069i_bool) (Aa tptp.fun_Ar1871347069i_bool) (Ba tptp.fun_Ar1871347069i_bool)) (let ((_let_1 (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f90330565l_bool _let_1 Ca)))))) (forall ((C_2 tptp.nat) (A_6 tptp.nat) (B_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_6)) (=> (= B_6 C_2) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_2)))))) (forall ((Ca tptp.fun_Ar1871347069i_bool) (Aa tptp.fun_Ar1871347069i_bool) (Ba tptp.fun_Ar1871347069i_bool)) (let ((_let_1 (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool _let_1 Aa)))))) (forall ((C_1 tptp.nat) (A_5 tptp.nat) (B_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_1))) (=> (= A_5 B_5) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_5)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_5)))))) (forall ((Ca tptp.fun_Ar1871347069i_bool) (Aa tptp.fun_Ar1871347069i_bool) (Ba tptp.fun_Ar1871347069i_bool)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Aa) Ca))))) (forall ((C tptp.nat) (A_4 tptp.nat) (B_4 tptp.nat)) (=> (= A_4 B_4) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_4) C)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_4) C))))) (forall ((Ba tptp.fun_Ar1871347069i_bool) (Aa tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Ba) Aa)) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Aa) Ba))))) (forall ((B_3 tptp.nat) (A_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_3) A_3)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_3) B_3))))) (forall ((Aa tptp.fun_Ar1871347069i_bool) (Ba tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Aa) Ba)) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Ba) Aa))))) (forall ((A_2 tptp.nat) (B_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_2) B_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_2) A_2))))) (forall ((Pa tptp.bool) (X_2 tptp.fun_Ar1871347069i_bool) (Y_1 tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool X_2) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Y_1) X_2)) (tptp.hBOOL Pa)))) (forall ((Pa tptp.bool) (X_2 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_2)) (tptp.hBOOL Pa)))) (forall ((X_2 tptp.fun_Ar1871347069i_bool) (Y_1 tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool X_2) Y_1)) (not (= Y_1 X_2)))) (forall ((X_10 tptp.nat) (Y_9 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_10) Y_9)) (not (= Y_9 X_10)))) (forall ((X_2 tptp.fun_Ar1871347069i_bool) (Y_1 tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool X_2) Y_1)) (not (= X_2 Y_1)))) (forall ((X_9 tptp.nat) (Y_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_9) Y_8)) (not (= X_9 Y_8)))) (forall ((X_2 tptp.fun_Ar1871347069i_bool) (Y_1 tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool X_2) Y_1)) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Y_1) X_2))))) (forall ((X_8 tptp.nat) (Y_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_8) Y_7)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_7) X_8))))) (forall ((X_2 tptp.fun_Ar1871347069i_bool) (Y_1 tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool X_2) Y_1)) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Y_1) X_2))))) (forall ((X_7 tptp.nat) (Y_6 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_7) Y_6)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_6) X_7))))) (forall ((X_2 tptp.fun_Ar1871347069i_bool) (Y_1 tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool X_2) Y_1)) (not (= X_2 Y_1)))) (forall ((X_6 tptp.nat) (Y_5 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_6) Y_5)) (not (= X_6 Y_5)))) (forall ((X_5 tptp.nat) (Y_4 tptp.nat)) (=> (not (= X_5 Y_4)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_5) Y_4))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_4) X_5))))) (forall ((Y_1 tptp.nat) (X_2 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_2))) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_1))) (= X_2 Y_1)))) (forall ((X_4 tptp.nat) (Y_3 tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_4) Y_3)) (= X_4 Y_3) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_3) X_4)))) (forall ((X_2 tptp.nat) (Y_1 tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_1))) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_2)) (= X_2 Y_1)))) (forall ((X_2 tptp.nat) (Y_1 tptp.nat)) (= (not (= X_2 Y_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y_1) X_2))))) (forall ((X_2 tptp.fun_Ar1871347069i_bool)) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool X_2) X_2)))) (forall ((X_3 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_3) X_3)))) (= tptp.top_to1057791589l_bool (tptp.collec1697917566t_bool (tptp.hAPP_b1017527359l_bool tptp.cOMBK_1801013008t_bool tptp.fTrue))) (= tptp.top_to653038619l_bool (tptp.collec861220362t_bool (tptp.hAPP_b1178471617l_bool tptp.cOMBK_70145528t_bool tptp.fTrue))) (= tptp.top_to2127553399l_bool (tptp.collec154865254t_bool (tptp.hAPP_b930206237l_bool tptp.cOMBK_1362474068t_bool tptp.fTrue))) (= tptp.top_to710777827t_bool (tptp.collec2140722898le_alt (tptp.hAPP_b1848524425t_bool tptp.cOMBK_350462144le_alt tptp.fTrue))) (= tptp.top_to850136695i_bool (tptp.collec1241994086e_indi (tptp.hAPP_b611520797i_bool tptp.cOMBK_206372180e_indi tptp.fTrue))) (forall ((S tptp.fun_Pr1639951081t_bool) (R_1 tptp.fun_Pr1639951081t_bool)) (= (forall ((X_1 tptp.arrow_1621810872le_alt) (Xa tptp.arrow_1621810872le_alt)) (let ((_let_1 (tptp.member1484933012le_alt (tptp.produc170576535le_alt X_1 Xa)))) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 R_1)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 S))))) (= R_1 S))) (forall ((Aa tptp.fun_fu383145951l_bool)) (= (not (= Aa tptp.top_to1057791589l_bool)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.hAPP_f279586623l_bool tptp.ord_le1472193545l_bool Aa) tptp.top_to1057791589l_bool)))) (forall ((Aa tptp.fun_fu103733537l_bool)) (= (not (= Aa tptp.top_to653038619l_bool)) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.hAPP_f786935331l_bool tptp.ord_le2059466615l_bool Aa) tptp.top_to653038619l_bool)))) (forall ((Aa tptp.fun_fu1251737213l_bool)) (= (not (= Aa tptp.top_to2127553399l_bool)) (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.hAPP_f1303771867l_bool tptp.ord_le1419690707l_bool Aa) tptp.top_to2127553399l_bool)))) (forall ((Aa tptp.bool)) (= (not (= (tptp.hBOOL Aa) (tptp.hBOOL tptp.top_top_bool))) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool Aa) tptp.top_top_bool)))) (forall ((Aa tptp.fun_Pr1639951081t_bool)) (= (not (= Aa tptp.top_to710777827t_bool)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.hAPP_f1911990195l_bool tptp.ord_le1051050815t_bool Aa) tptp.top_to710777827t_bool)))) (forall ((Aa tptp.fun_Ar1871347069i_bool)) (= (not (= Aa tptp.top_to850136695i_bool)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.hAPP_f1993665755l_bool tptp.ord_le287438291i_bool Aa) tptp.top_to850136695i_bool)))) (forall ((X_2 tptp.arrow_501706939e_indi) (Y_1 tptp.nat) (F tptp.fun_Ar2035712896di_nat)) (=> (tptp.hBOOL (tptp.inj_on1177549232di_nat F tptp.top_to850136695i_bool)) (=> (= (tptp.hAPP_A1741215436di_nat F X_2) Y_1) (= (tptp.hAPP_n1582158000e_indi (tptp.hilber797233813di_nat tptp.top_to850136695i_bool F) Y_1) X_2)))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2035712896di_nat)) (=> (tptp.hBOOL (tptp.inj_on1177549232di_nat F tptp.top_to850136695i_bool)) (= (tptp.hAPP_n1582158000e_indi (tptp.hilber797233813di_nat tptp.top_to850136695i_bool F) (tptp.hAPP_A1741215436di_nat F X_2)) X_2))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2035712896di_nat) (A tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.inj_on1177549232di_nat F A)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (= (tptp.hAPP_n1582158000e_indi (tptp.hilber797233813di_nat A F) (tptp.hAPP_A1741215436di_nat F X_2)) X_2)))) (forall ((Y_1 tptp.nat) (X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2035712896di_nat) (A tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.inj_on1177549232di_nat F A)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (=> (= (tptp.hAPP_A1741215436di_nat F X_2) Y_1) (= (tptp.hAPP_n1582158000e_indi (tptp.hilber797233813di_nat A F) Y_1) X_2))))) (forall ((X_2 tptp.arrow_501706939e_indi) (Y_1 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2035712896di_nat)) (=> (tptp.hBOOL (tptp.inj_on1177549232di_nat F tptp.top_to850136695i_bool)) (= (= (tptp.hAPP_A1741215436di_nat F X_2) (tptp.hAPP_A1741215436di_nat F Y_1)) (= X_2 Y_1)))) (forall ((F tptp.fun_Ar2035712896di_nat) (A tptp.fun_Ar1871347069i_bool)) (= (tptp.hBOOL (tptp.inj_on1177549232di_nat F A)) (forall ((X_1 tptp.arrow_501706939e_indi)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_1) A)) (forall ((Xa tptp.arrow_501706939e_indi)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi Xa) A)) (=> (= (tptp.hAPP_A1741215436di_nat F X_1) (tptp.hAPP_A1741215436di_nat F Xa)) (= X_1 Xa)))))))) (forall ((X_2 tptp.arrow_501706939e_indi) (Y_1 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2035712896di_nat) (A tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.inj_on1177549232di_nat F A)) (=> (not (= X_2 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi Y_1) A)) (not (= (tptp.hAPP_A1741215436di_nat F X_2) (tptp.hAPP_A1741215436di_nat F Y_1)))))))) (forall ((Y_1 tptp.arrow_501706939e_indi) (X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2035712896di_nat) (A tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.inj_on1177549232di_nat F A)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi Y_1) A)) (= (= (tptp.hAPP_A1741215436di_nat F X_2) (tptp.hAPP_A1741215436di_nat F Y_1)) (= X_2 Y_1)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (Y_1 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2035712896di_nat) (A tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.inj_on1177549232di_nat F A)) (=> (= (tptp.hAPP_A1741215436di_nat F X_2) (tptp.hAPP_A1741215436di_nat F Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi Y_1) A)) (= X_2 Y_1)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (Y_1 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2035712896di_nat)) (=> (tptp.hBOOL (tptp.inj_on1177549232di_nat F tptp.top_to850136695i_bool)) (=> (= (tptp.hAPP_A1741215436di_nat F X_2) (tptp.hAPP_A1741215436di_nat F Y_1)) (= X_2 Y_1)))) (forall ((G tptp.fun_na1602142942e_indi) (F tptp.fun_Ar2035712896di_nat)) (=> (tptp.hBOOL (tptp.inj_on1177549232di_nat F tptp.top_to850136695i_bool)) (=> (forall ((X_1 tptp.nat)) (= (tptp.hAPP_A1741215436di_nat F (tptp.hAPP_n1582158000e_indi G X_1)) X_1)) (= (tptp.hilber797233813di_nat tptp.top_to850136695i_bool F) G)))) (forall ((F tptp.fun_Ar2035712896di_nat)) (=> (forall ((X_1 tptp.arrow_501706939e_indi) (Y_2 tptp.arrow_501706939e_indi)) (=> (= (tptp.hAPP_A1741215436di_nat F X_1) (tptp.hAPP_A1741215436di_nat F Y_2)) (= X_1 Y_2))) (tptp.hBOOL (tptp.inj_on1177549232di_nat F tptp.top_to850136695i_bool)))) (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool tptp.f) (tptp.pi_fun456133649t_bool tptp.arrow_1880704820e_Prof (tptp.hAPP_f459175489l_bool tptp.cOMBK_639770490t_bool tptp.arrow_1008788854le_Lin)))) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool tptp.lba) tptp.arrow_1008788854le_Lin)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool tptp.lab) tptp.arrow_1008788854le_Lin)) (forall ((Aa tptp.arrow_1621810872le_alt) (Ba tptp.arrow_1621810872le_alt) (L tptp.fun_Pr1639951081t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool L) tptp.arrow_1008788854le_Lin)) (=> (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) L)) (not (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Ba Aa)) L)))))) (forall ((X_2 tptp.arrow_1621810872le_alt) (Y_1 tptp.arrow_1621810872le_alt) (L tptp.fun_Pr1639951081t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool L) tptp.arrow_1008788854le_Lin)) (=> (not (= X_2 Y_1)) (= (not (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt X_2 Y_1)) L))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Y_1 X_2)) L)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (A tptp.fun_Ar1871347069i_bool)) (= (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_A1059798043i_bool A X_2)))) (forall ((X_2 tptp.bool) (A tptp.fun_bool_bool)) (= (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_bool_bool A X_2)))) (forall ((X_2 tptp.produc624534567le_alt) (A tptp.fun_Pr1639951081t_bool)) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_P751176071t_bool A X_2)))) (forall ((X_2 tptp.fun_Ar2047178847t_bool) (A tptp.fun_fu103733537l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1095388607l_bool A X_2)))) (forall ((X_2 tptp.fun_fu50365883t_bool) (A tptp.fun_fu1251737213l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f725100827l_bool A X_2)))) (forall ((X_2 tptp.fun_Pr1639951081t_bool) (A tptp.fun_fu383145951l_bool)) (= (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool A X_2)))) (forall ((Pa tptp.fun_Ar1871347069i_bool)) (= (tptp.collec1241994086e_indi Pa) Pa)) (forall ((X_2 tptp.arrow_1621810872le_alt) (L tptp.fun_Pr1639951081t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool L) tptp.arrow_1008788854le_Lin)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_A476679046t_bool (tptp.hAPP_f1699392794t_bool tptp.arrow_1275257820_mktop L) X_2)) tptp.arrow_1008788854le_Lin)))) (forall ((X_2 tptp.arrow_1621810872le_alt) (L tptp.fun_Pr1639951081t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool L) tptp.arrow_1008788854le_Lin)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_A476679046t_bool (tptp.hAPP_f1699392794t_bool tptp.arrow_1126550734_mkbot L) X_2)) tptp.arrow_1008788854le_Lin)))) (forall ((L tptp.fun_Pr1639951081t_bool) (X_2 tptp.arrow_1621810872le_alt) (Y_1 tptp.arrow_1621810872le_alt)) (=> (not (= X_2 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool L) tptp.arrow_1008788854le_Lin)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_A476679046t_bool (tptp.hAPP_A272835723t_bool (tptp.hAPP_f1560118175t_bool tptp.arrow_2009189698_above L) X_2) Y_1)) tptp.arrow_1008788854le_Lin))))) (forall ((L tptp.fun_Pr1639951081t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool L) tptp.arrow_1008788854le_Lin)) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool (tptp.hAPP_f1172974131t_bool tptp.cOMBK_164791446e_indi L)) tptp.arrow_1880704820e_Prof)))) (forall ((X_2 tptp.arrow_1621810872le_alt) (Y_1 tptp.arrow_1621810872le_alt) (L tptp.fun_Pr1639951081t_bool) (Aa tptp.arrow_1621810872le_alt) (Ba tptp.arrow_1621810872le_alt)) (let ((_let_1 (tptp.member1484933012le_alt (tptp.produc170576535le_alt X_2 Y_1)))) (let ((_let_2 (= Y_1 Ba))) (let ((_let_3 (= X_2 Ba))) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool L) tptp.arrow_1008788854le_Lin)) (= (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_A476679046t_bool (tptp.hAPP_A272835723t_bool (tptp.hAPP_f1560118175t_bool tptp.arrow_2009189698_above L) Aa) Ba))) (and (not (= X_2 Y_1)) (=> _let_3 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Y_1)) L))) (=> (not _let_3) (and (=> _let_2 (or (= X_2 Aa) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt X_2 Aa)) L)))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 L))))))))))))) (forall ((I_1 tptp.arrow_501706939e_indi) (Fa tptp.fun_fu50365883t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool Fa) (tptp.pi_fun456133649t_bool tptp.arrow_1880704820e_Prof (tptp.hAPP_f459175489l_bool tptp.cOMBK_639770490t_bool tptp.arrow_1008788854le_Lin)))) (=> (forall ((X_1 tptp.fun_Ar2047178847t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_1) tptp.arrow_1880704820e_Prof)) (forall ((A_1 tptp.arrow_1621810872le_alt) (B_1 tptp.arrow_1621810872le_alt)) (let ((_let_1 (tptp.member1484933012le_alt (tptp.produc170576535le_alt A_1 B_1)))) (=> (not (= A_1 B_1)) (=> (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_A2044747691t_bool X_1 I_1))) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 (tptp.hAPP_f718157575t_bool Fa X_1))))))))) (tptp.hBOOL (tptp.hAPP_A1059798043i_bool (tptp.hAPP_f1559864639i_bool tptp.arrow_1322316103ctator Fa) I_1))))) (forall ((X_2 tptp.produc624534567le_alt) (F tptp.fun_Pr1639951081t_bool) (A tptp.fun_Pr1639951081t_bool) (B tptp.fun_Pr534938793l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool F) (tptp.pi_Pro811330557t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_P751176071t_bool F X_2)) (tptp.hAPP_P2005668213l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt X_2) A)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar795681735le_alt) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_Ar2047178847t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f748921117l_bool (tptp.member844573594le_alt F) (tptp.pi_Arr447918939le_alt A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.hAPP_A2034733541le_alt F X_2)) (tptp.hAPP_A2044747691t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1156530537le_alt) (A tptp.fun_bool_bool) (B tptp.fun_bo230129725t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f899216831l_bool (tptp.member158436796le_alt F) (tptp.pi_boo158890749le_alt A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.hAPP_b98736263le_alt F X_2)) (tptp.hAPP_b1848524425t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar1200683263t_bool) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_Ar1784032663l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1753158741l_bool (tptp.member1701178322t_bool F) (tptp.pi_Arr1077238675t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool (tptp.hAPP_A1159468061t_bool F X_2)) (tptp.hAPP_A1790795747l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo478202017t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo1613497205l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1481710327l_bool (tptp.member1494646772t_bool F) (tptp.pi_boo2120406325t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool (tptp.hAPP_b114674879t_bool F X_2)) (tptp.hAPP_b1178471617l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar1570071899t_bool) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_Ar884201459l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f598211249l_bool (tptp.member2069173038t_bool F) (tptp.pi_Arr478149871t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool (tptp.hAPP_A1168502649t_bool F X_2)) (tptp.hAPP_A107624255l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo2136393469t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo2138151889l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f759862099l_bool (tptp.member1211611472t_bool F) (tptp.pi_boo853084305t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool (tptp.hAPP_b1112685083t_bool F X_2)) (tptp.hAPP_b930206237l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo230129725t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo1803678369l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f639792199l_bool (tptp.member2079888426t_bool F) (tptp.pi_boo683563155t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_b1848524425t_bool F X_2)) (tptp.hAPP_b1017527359l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)))))) (forall ((X_2 tptp.produc624534567le_alt) (F tptp.fun_Pr506339783e_indi) (A tptp.fun_Pr1639951081t_bool) (B tptp.fun_Pr123985543i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1270259485l_bool (tptp.member555231642e_indi F) (tptp.pi_Pro723839835e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_P163170789e_indi F X_2)) (tptp.hAPP_P259956691i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt X_2) A)))))) (forall ((X_2 tptp.fun_Ar2047178847t_bool) (F tptp.fun_fu2069019647e_indi) (A tptp.fun_fu103733537l_bool) (B tptp.fun_fu23838287i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f243652437l_bool (tptp.member422031058e_indi F) (tptp.pi_fun1549517203e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_f1631746589e_indi F X_2)) (tptp.hAPP_f1511451035i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) A)))))) (forall ((X_2 tptp.fun_Ar2047178847t_bool) (F tptp.fun_fu103733537l_bool) (A tptp.fun_fu103733537l_bool) (B tptp.fun_fu658952305l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1394256759l_bool (tptp.member1120178292l_bool F) (tptp.pi_fun953636405l_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f1095388607l_bool F X_2)) (tptp.hAPP_f1418708797l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) A)))))) (forall ((X_2 tptp.fun_fu50365883t_bool) (F tptp.fun_fu1743730523e_indi) (A tptp.fun_fu1251737213l_bool) (B tptp.fun_fu1950461939i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f174050481l_bool (tptp.member95348014e_indi F) (tptp.pi_fun1545124079e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_f87993209e_indi F X_2)) (tptp.hAPP_f1559864639i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool X_2) A)))))) (forall ((X_2 tptp.fun_fu50365883t_bool) (F tptp.fun_fu1251737213l_bool) (A tptp.fun_fu1251737213l_bool) (B tptp.fun_fu1734842389l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1827424979l_bool (tptp.member326955216l_bool F) (tptp.pi_fun465500049l_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f725100827l_bool F X_2)) (tptp.hAPP_f626809057l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool X_2) A)))))) (forall ((X_2 tptp.fun_Pr1639951081t_bool) (F tptp.fun_fu334384573e_indi) (A tptp.fun_fu383145951l_bool) (B tptp.fun_fu1867632401i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f359017159l_bool (tptp.member993084970e_indi F) (tptp.pi_fun2132478361e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_f671542927e_indi F X_2)) (tptp.hAPP_f906860201i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool X_2) A)))))) (forall ((X_2 tptp.fun_Pr1639951081t_bool) (F tptp.fun_fu383145951l_bool) (A tptp.fun_fu383145951l_bool) (B tptp.fun_fu1903211571l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1347377641l_bool (tptp.member85421004l_bool F) (tptp.pi_fun779925307l_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f1944886577l_bool F X_2)) (tptp.hAPP_f2128533835l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool X_2) A)))))) (forall ((X_2 tptp.fun_Ar2047178847t_bool) (F tptp.fun_fu50365883t_bool) (A tptp.fun_fu103733537l_bool) (B tptp.fun_fu746839971l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool F) (tptp.pi_fun456133649t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_f718157575t_bool F X_2)) (tptp.hAPP_f1265202753l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) A)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2047178847t_bool) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_Ar1821573119l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool F) (tptp.pi_Arr1358199477t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_A2044747691t_bool F X_2)) (tptp.hAPP_A1710743709l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)))))) (forall ((Aa tptp.arrow_1621810872le_alt) (Ba tptp.arrow_1621810872le_alt)) (=> (not (= Aa Ba)) (exists ((X_1 tptp.fun_Pr1639951081t_bool)) (and (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool X_1) tptp.arrow_1008788854le_Lin)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.produc170576535le_alt Aa Ba)) X_1)))))) (forall ((Na tptp.nat)) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool (tptp.cOMBC_1257424504t_bool (tptp.cOMBC_64563468t_bool (tptp.cOMBB_124649523e_indi tptp.if_fun95824985t_bool (tptp.cOMBC_998415407t_bool (tptp.cOMBB_1514803447e_indi tptp.ord_less_nat tptp.h) Na)) tptp.lab) tptp.lba)) tptp.arrow_1880704820e_Prof))) (forall ((X_2 tptp.produc624534567le_alt) (F tptp.fun_Pr1639951081t_bool) (A tptp.fun_Pr1639951081t_bool) (B tptp.fun_Pr534938793l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool F) (tptp.pi_Pro811330557t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_P751176071t_bool F X_2)) (tptp.hAPP_P2005668213l_bool B X_2)))))) (forall ((X_2 tptp.produc624534567le_alt) (F tptp.fun_Pr506339783e_indi) (A tptp.fun_Pr1639951081t_bool) (B tptp.fun_Pr123985543i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1270259485l_bool (tptp.member555231642e_indi F) (tptp.pi_Pro723839835e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_P163170789e_indi F X_2)) (tptp.hAPP_P259956691i_bool B X_2)))))) (forall ((X_2 tptp.fun_Ar2047178847t_bool) (F tptp.fun_fu2069019647e_indi) (A tptp.fun_fu103733537l_bool) (B tptp.fun_fu23838287i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f243652437l_bool (tptp.member422031058e_indi F) (tptp.pi_fun1549517203e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_f1631746589e_indi F X_2)) (tptp.hAPP_f1511451035i_bool B X_2)))))) (forall ((X_2 tptp.fun_Ar2047178847t_bool) (F tptp.fun_fu103733537l_bool) (A tptp.fun_fu103733537l_bool) (B tptp.fun_fu658952305l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1394256759l_bool (tptp.member1120178292l_bool F) (tptp.pi_fun953636405l_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f1095388607l_bool F X_2)) (tptp.hAPP_f1418708797l_bool B X_2)))))) (forall ((X_2 tptp.fun_fu50365883t_bool) (F tptp.fun_fu1743730523e_indi) (A tptp.fun_fu1251737213l_bool) (B tptp.fun_fu1950461939i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f174050481l_bool (tptp.member95348014e_indi F) (tptp.pi_fun1545124079e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_f87993209e_indi F X_2)) (tptp.hAPP_f1559864639i_bool B X_2)))))) (forall ((X_2 tptp.fun_fu50365883t_bool) (F tptp.fun_fu1251737213l_bool) (A tptp.fun_fu1251737213l_bool) (B tptp.fun_fu1734842389l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1827424979l_bool (tptp.member326955216l_bool F) (tptp.pi_fun465500049l_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f725100827l_bool F X_2)) (tptp.hAPP_f626809057l_bool B X_2)))))) (forall ((X_2 tptp.fun_Pr1639951081t_bool) (F tptp.fun_fu334384573e_indi) (A tptp.fun_fu383145951l_bool) (B tptp.fun_fu1867632401i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f359017159l_bool (tptp.member993084970e_indi F) (tptp.pi_fun2132478361e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_f671542927e_indi F X_2)) (tptp.hAPP_f906860201i_bool B X_2)))))) (forall ((X_2 tptp.fun_Pr1639951081t_bool) (F tptp.fun_fu383145951l_bool) (A tptp.fun_fu383145951l_bool) (B tptp.fun_fu1903211571l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1347377641l_bool (tptp.member85421004l_bool F) (tptp.pi_fun779925307l_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f1944886577l_bool F X_2)) (tptp.hAPP_f2128533835l_bool B X_2)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar795681735le_alt) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_Ar2047178847t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f748921117l_bool (tptp.member844573594le_alt F) (tptp.pi_Arr447918939le_alt A B))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.hAPP_A2034733541le_alt F X_2)) (tptp.hAPP_A2044747691t_bool B X_2)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1156530537le_alt) (A tptp.fun_bool_bool) (B tptp.fun_bo230129725t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f899216831l_bool (tptp.member158436796le_alt F) (tptp.pi_boo158890749le_alt A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.hAPP_b98736263le_alt F X_2)) (tptp.hAPP_b1848524425t_bool B X_2)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar1200683263t_bool) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_Ar1784032663l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1753158741l_bool (tptp.member1701178322t_bool F) (tptp.pi_Arr1077238675t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool (tptp.hAPP_A1159468061t_bool F X_2)) (tptp.hAPP_A1790795747l_bool B X_2)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo478202017t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo1613497205l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1481710327l_bool (tptp.member1494646772t_bool F) (tptp.pi_boo2120406325t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool (tptp.hAPP_b114674879t_bool F X_2)) (tptp.hAPP_b1178471617l_bool B X_2)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar1570071899t_bool) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_Ar884201459l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f598211249l_bool (tptp.member2069173038t_bool F) (tptp.pi_Arr478149871t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool (tptp.hAPP_A1168502649t_bool F X_2)) (tptp.hAPP_A107624255l_bool B X_2)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo2136393469t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo2138151889l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f759862099l_bool (tptp.member1211611472t_bool F) (tptp.pi_boo853084305t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool (tptp.hAPP_b1112685083t_bool F X_2)) (tptp.hAPP_b930206237l_bool B X_2)))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo230129725t_bool) (A tptp.fun_bool_bool) (B tptp.fun_bo1803678369l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f639792199l_bool (tptp.member2079888426t_bool F) (tptp.pi_boo683563155t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_b1848524425t_bool F X_2)) (tptp.hAPP_b1017527359l_bool B X_2)))))) (forall ((X_2 tptp.fun_Ar2047178847t_bool) (F tptp.fun_fu50365883t_bool) (A tptp.fun_fu103733537l_bool) (B tptp.fun_fu746839971l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool F) (tptp.pi_fun456133649t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_f718157575t_bool F X_2)) (tptp.hAPP_f1265202753l_bool B X_2)))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2047178847t_bool) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_Ar1821573119l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool F) (tptp.pi_Arr1358199477t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_A2044747691t_bool F X_2)) (tptp.hAPP_A1710743709l_bool B X_2)))))) (= tptp.arrow_1880704820e_Prof (tptp.pi_Arr1358199477t_bool tptp.top_to850136695i_bool (tptp.hAPP_f1651042461l_bool tptp.cOMBK_2098615510e_indi tptp.arrow_1008788854le_Lin))) (forall ((X_2 tptp.produc624534567le_alt) (F tptp.fun_Pr1639951081t_bool) (A tptp.fun_Pr1639951081t_bool) (B tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool F) (tptp.pi_Pro811330557t_bool A (tptp.hAPP_f1601816755l_bool tptp.cOMBK_290363320le_alt B)))) (=> (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_P751176071t_bool F X_2)) B))))) (forall ((X_2 tptp.produc624534567le_alt) (F tptp.fun_Pr506339783e_indi) (A tptp.fun_Pr1639951081t_bool) (B tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1270259485l_bool (tptp.member555231642e_indi F) (tptp.pi_Pro723839835e_indi A (tptp.hAPP_f1561296623i_bool tptp.cOMBK_328807062le_alt B)))) (=> (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_P163170789e_indi F X_2)) B))))) (forall ((X_2 tptp.fun_Ar2047178847t_bool) (F tptp.fun_fu2069019647e_indi) (A tptp.fun_fu103733537l_bool) (B tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f243652437l_bool (tptp.member422031058e_indi F) (tptp.pi_fun1549517203e_indi A (tptp.hAPP_f823592631i_bool tptp.cOMBK_269839822t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_f1631746589e_indi F X_2)) B))))) (forall ((X_2 tptp.fun_Ar2047178847t_bool) (F tptp.fun_fu103733537l_bool) (A tptp.fun_fu103733537l_bool) (B tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1394256759l_bool (tptp.member1120178292l_bool F) (tptp.pi_fun953636405l_bool A (tptp.hAPP_f1325493883l_bool tptp.cOMBK_167511280t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f1095388607l_bool F X_2)) B))))) (forall ((X_2 tptp.fun_fu50365883t_bool) (F tptp.fun_fu1743730523e_indi) (A tptp.fun_fu1251737213l_bool) (B tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f174050481l_bool (tptp.member95348014e_indi F) (tptp.pi_fun1545124079e_indi A (tptp.hAPP_f1224613979i_bool tptp.cOMBK_519762474t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_f87993209e_indi F X_2)) B))))) (forall ((X_2 tptp.fun_fu50365883t_bool) (F tptp.fun_fu1251737213l_bool) (A tptp.fun_fu1251737213l_bool) (B tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1827424979l_bool (tptp.member326955216l_bool F) (tptp.pi_fun465500049l_bool A (tptp.hAPP_f1364914207l_bool tptp.cOMBK_1853791052t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f725100827l_bool F X_2)) B))))) (forall ((X_2 tptp.fun_Pr1639951081t_bool) (F tptp.fun_fu334384573e_indi) (A tptp.fun_fu383145951l_bool) (B tptp.fun_Ar1871347069i_bool)) (=> (tptp.hBOOL (tptp.hAPP_f359017159l_bool (tptp.member993084970e_indi F) (tptp.pi_fun2132478361e_indi A (tptp.hAPP_f1364159657i_bool tptp.cOMBK_1207925178t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi (tptp.hAPP_f671542927e_indi F X_2)) B))))) (forall ((X_2 tptp.fun_Pr1639951081t_bool) (F tptp.fun_fu383145951l_bool) (A tptp.fun_fu383145951l_bool) (B tptp.fun_bool_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1347377641l_bool (tptp.member85421004l_bool F) (tptp.pi_fun779925307l_bool A (tptp.hAPP_f1230984105l_bool tptp.cOMBK_1838733848t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f1944886577l_bool F X_2)) B))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar795681735le_alt) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_Pr1639951081t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f748921117l_bool (tptp.member844573594le_alt F) (tptp.pi_Arr447918939le_alt A (tptp.hAPP_f1172974131t_bool tptp.cOMBK_164791446e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.hAPP_A2034733541le_alt F X_2)) B))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo1156530537le_alt) (A tptp.fun_bool_bool) (B tptp.fun_Pr1639951081t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f899216831l_bool (tptp.member158436796le_alt F) (tptp.pi_boo158890749le_alt A (tptp.hAPP_f1758973969t_bool tptp.cOMBK_1897375160l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool (tptp.member1484933012le_alt (tptp.hAPP_b98736263le_alt F X_2)) B))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar1200683263t_bool) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_fu103733537l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1753158741l_bool (tptp.member1701178322t_bool F) (tptp.pi_Arr1077238675t_bool A (tptp.hAPP_f466810275l_bool tptp.cOMBK_30438862e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool (tptp.hAPP_A1159468061t_bool F X_2)) B))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo478202017t_bool) (A tptp.fun_bool_bool) (B tptp.fun_fu103733537l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1481710327l_bool (tptp.member1494646772t_bool F) (tptp.pi_boo2120406325t_bool A (tptp.hAPP_f2013855105l_bool tptp.cOMBK_1481288432l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool (tptp.hAPP_b114674879t_bool F X_2)) B))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar1570071899t_bool) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_fu1251737213l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f598211249l_bool (tptp.member2069173038t_bool F) (tptp.pi_Arr478149871t_bool A (tptp.hAPP_f544895323l_bool tptp.cOMBK_869185066e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool (tptp.hAPP_A1168502649t_bool F X_2)) B))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo2136393469t_bool) (A tptp.fun_bool_bool) (B tptp.fun_fu1251737213l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f759862099l_bool (tptp.member1211611472t_bool F) (tptp.pi_boo853084305t_bool A (tptp.hAPP_f989466937l_bool tptp.cOMBK_343479628l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool (tptp.hAPP_b1112685083t_bool F X_2)) B))))) (forall ((X_2 tptp.bool) (F tptp.fun_bo230129725t_bool) (A tptp.fun_bool_bool) (B tptp.fun_fu383145951l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f639792199l_bool (tptp.member2079888426t_bool F) (tptp.pi_boo683563155t_bool A (tptp.hAPP_f71505983l_bool tptp.cOMBK_648664568l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_b1848524425t_bool F X_2)) B))))) (forall ((X_2 tptp.fun_Ar2047178847t_bool) (F tptp.fun_fu50365883t_bool) (A tptp.fun_fu103733537l_bool) (B tptp.fun_fu383145951l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1435434693l_bool (tptp.member256508712t_bool F) (tptp.pi_fun456133649t_bool A (tptp.hAPP_f459175489l_bool tptp.cOMBK_639770490t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_f718157575t_bool F X_2)) B))))) (forall ((X_2 tptp.arrow_501706939e_indi) (F tptp.fun_Ar2047178847t_bool) (A tptp.fun_Ar1871347069i_bool) (B tptp.fun_fu383145951l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool F) (tptp.pi_Arr1358199477t_bool A (tptp.hAPP_f1651042461l_bool tptp.cOMBK_2098615510e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f90330565l_bool (tptp.member1124131880e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f180608831l_bool (tptp.member641857340t_bool (tptp.hAPP_A2044747691t_bool F X_2)) B))))) (forall ((Fa tptp.fun_fu50365883t_bool) (I_1 tptp.arrow_501706939e_indi)) (= (tptp.hBOOL (tptp.hAPP_A1059798043i_bool (tptp.hAPP_f1559864639i_bool tptp.arrow_1322316103ctator Fa) I_1)) (forall ((X_1 tptp.fun_Ar2047178847t_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1237345129l_bool (tptp.member558395596t_bool X_1) tptp.arrow_1880704820e_Prof)) (= (tptp.hAPP_f718157575t_bool Fa X_1) (tptp.hAPP_A2044747691t_bool X_1 I_1)))))) (forall ((A tptp.fun_Pr1639951081t_bool)) (= (tptp.pi_Pro811330557t_bool A (tptp.hAPP_f1601816755l_bool tptp.cOMBK_290363320le_alt tptp.top_to1647826457l_bool)) tptp.top_to1057791589l_bool)) (forall ((A tptp.fun_fu103733537l_bool)) (= (tptp.pi_fun456133649t_bool A (tptp.hAPP_f459175489l_bool tptp.cOMBK_639770490t_bool tptp.top_to1057791589l_bool)) tptp.top_to2127553399l_bool)) (forall ((A tptp.fun_Ar1871347069i_bool)) (= (tptp.pi_Arr1358199477t_bool A (tptp.hAPP_f1651042461l_bool tptp.cOMBK_2098615510e_indi tptp.top_to1057791589l_bool)) tptp.top_to653038619l_bool)) (= _let_9 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_4 (tptp.hAPP_f718157575t_bool tptp.f (tptp.cOMBC_1257424504t_bool (tptp.cOMBC_64563468t_bool _let_6 tptp.lab) tptp.lba))))) (forall ((I tptp.arrow_501706939e_indi)) (let ((_let_1 (tptp.member1484933012le_alt (tptp.produc170576535le_alt tptp.b tptp.a)))) (let ((_let_2 (tptp.hAPP_A1741215436di_nat tptp.h I))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_2) tptp.n)))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.hAPP_A2044747691t_bool tptp.p I))) (let ((_let_6 (tptp.member1484933012le_alt (tptp.produc170576535le_alt tptp.e tptp.d)))) (let ((_let_7 (= _let_2 tptp.n))) (= (and (=> _let_3 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_6 (tptp.hAPP_A476679046t_bool (tptp.hAPP_f1699392794t_bool tptp.arrow_1275257820_mktop _let_5) tptp.e)))) (=> _let_4 (and (=> _let_7 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_6 (tptp.hAPP_A476679046t_bool (tptp.hAPP_A272835723t_bool (tptp.hAPP_f1560118175t_bool tptp.arrow_2009189698_above _let_5) tptp.c) tptp.e)))) (=> (not _let_7) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_6 (tptp.hAPP_A476679046t_bool (tptp.hAPP_f1699392794t_bool tptp.arrow_1126550734_mkbot _let_5) tptp.e))))))) (and (=> _let_3 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 tptp.lab))) (=> _let_4 (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_1 tptp.lba))))))))))))) (not (= tptp.a tptp.b)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_4 tptp.lba)) (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_5 tptp.lab)) (not (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_5 tptp.lba))) (not (tptp.hBOOL (tptp.hAPP_f1944886577l_bool _let_4 tptp.lab))) (tptp.hBOOL tptp.fTrue) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y))) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y)))) (forall ((P tptp.bool) (Q tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A1059798043i_bool (tptp.hAPP_b611520797i_bool tptp.cOMBK_206372180e_indi P) Q) P)) (forall ((P tptp.fun_Ar156616864t_bool) (Q tptp.nat) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A1059798043i_bool (tptp.cOMBC_998415407t_bool P Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_A1239621182t_bool P R) Q))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.fun_Ar2035712896di_nat) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A1239621182t_bool (tptp.cOMBB_1514803447e_indi P Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_A1741215436di_nat Q R)))) (forall ((P tptp.bool) (Q tptp.produc624534567le_alt)) (= (tptp.hAPP_P751176071t_bool (tptp.hAPP_b1848524425t_bool tptp.cOMBK_350462144le_alt P) Q) P)) (forall ((X tptp.fun_Pr1639951081t_bool) (Y tptp.fun_Pr1639951081t_bool)) (= (tptp.hAPP_f727188501t_bool (tptp.hAPP_f910728105t_bool (tptp.hAPP_b1702702257t_bool tptp.if_fun95824985t_bool tptp.fTrue) X) Y) X)) (forall ((X tptp.fun_Pr1639951081t_bool) (Y tptp.fun_Pr1639951081t_bool)) (= (tptp.hAPP_f727188501t_bool (tptp.hAPP_f910728105t_bool (tptp.hAPP_b1702702257t_bool tptp.if_fun95824985t_bool tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((P tptp.bool) (Q tptp.fun_Pr1639951081t_bool)) (= (tptp.hAPP_f1944886577l_bool (tptp.hAPP_b1017527359l_bool tptp.cOMBK_1801013008t_bool P) Q) P)) (forall ((P tptp.fun_bool_bool) (Q tptp.produc624534567le_alt)) (= (tptp.hAPP_P2005668213l_bool (tptp.hAPP_f1601816755l_bool tptp.cOMBK_290363320le_alt P) Q) P)) (forall ((P tptp.fun_Pr1639951081t_bool) (Q tptp.bool)) (= (tptp.hAPP_b1848524425t_bool (tptp.hAPP_f1758973969t_bool tptp.cOMBK_1897375160l_bool P) Q) P)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_Pr1639951081t_bool)) (= (tptp.hAPP_f2128533835l_bool (tptp.hAPP_f1230984105l_bool tptp.cOMBK_1838733848t_bool P) Q) P)) (forall ((P tptp.fun_fu383145951l_bool) (Q tptp.bool)) (= (tptp.hAPP_b1017527359l_bool (tptp.hAPP_f71505983l_bool tptp.cOMBK_648664568l_bool P) Q) P)) (forall ((P tptp.fun_Ar1871347069i_bool) (Q tptp.produc624534567le_alt)) (= (tptp.hAPP_P259956691i_bool (tptp.hAPP_f1561296623i_bool tptp.cOMBK_328807062le_alt P) Q) P)) (forall ((P tptp.fun_Pr1639951081t_bool) (Q tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A2044747691t_bool (tptp.hAPP_f1172974131t_bool tptp.cOMBK_164791446e_indi P) Q) P)) (forall ((P tptp.bool) (Q tptp.fun_Ar2047178847t_bool)) (= (tptp.hAPP_f1095388607l_bool (tptp.hAPP_b1178471617l_bool tptp.cOMBK_70145528t_bool P) Q) P)) (forall ((P tptp.fun_Ar1871347069i_bool) (Q tptp.fun_Pr1639951081t_bool)) (= (tptp.hAPP_f906860201i_bool (tptp.hAPP_f1364159657i_bool tptp.cOMBK_1207925178t_bool P) Q) P)) (forall ((P tptp.fun_fu383145951l_bool) (Q tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A1710743709l_bool (tptp.hAPP_f1651042461l_bool tptp.cOMBK_2098615510e_indi P) Q) P)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_Ar2047178847t_bool)) (= (tptp.hAPP_f1418708797l_bool (tptp.hAPP_f1325493883l_bool tptp.cOMBK_167511280t_bool P) Q) P)) (forall ((P tptp.fun_fu103733537l_bool) (Q tptp.bool)) (= (tptp.hAPP_b1178471617l_bool (tptp.hAPP_f2013855105l_bool tptp.cOMBK_1481288432l_bool P) Q) P)) (forall ((P tptp.fun_Ar1757019876t_bool) (Q tptp.arrow_1621810872le_alt) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A2044747691t_bool (tptp.cOMBC_377836265t_bool P Q) R) (tptp.hAPP_A476679046t_bool (tptp.hAPP_A711829680t_bool P R) Q))) (forall ((P tptp.fun_Ar1871347069i_bool) (Q tptp.fun_Ar2047178847t_bool)) (= (tptp.hAPP_f1511451035i_bool (tptp.hAPP_f823592631i_bool tptp.cOMBK_269839822t_bool P) Q) P)) (forall ((P tptp.fun_fu103733537l_bool) (Q tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A1790795747l_bool (tptp.hAPP_f466810275l_bool tptp.cOMBK_30438862e_indi P) Q) P)) (forall ((P tptp.fun_Ar2079322857t_bool) (Q tptp.arrow_1621810872le_alt) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A711829680t_bool (tptp.cOMBC_1994570734t_bool P Q) R) (tptp.hAPP_A272835723t_bool (tptp.hAPP_A784015157t_bool P R) Q))) (forall ((P tptp.fun_Ar2040671475t_bool) (Q tptp.fun_Pr1639951081t_bool) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A2044747691t_bool (tptp.cOMBC_1257424504t_bool P Q) R) (tptp.hAPP_f727188501t_bool (tptp.hAPP_A301260095t_bool P R) Q))) (forall ((P tptp.fun_Ar2040671475t_bool) (Q tptp.fun_Ar2047178847t_bool) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A2044747691t_bool (tptp.cOMBS_1688227464t_bool P Q) R) (tptp.hAPP_f727188501t_bool (tptp.hAPP_A301260095t_bool P R) (tptp.hAPP_A2044747691t_bool Q R)))) (forall ((P tptp.bool) (Q tptp.fun_fu50365883t_bool)) (= (tptp.hAPP_f725100827l_bool (tptp.hAPP_b930206237l_bool tptp.cOMBK_1362474068t_bool P) Q) P)) (forall ((P tptp.fun_fu383145951l_bool) (Q tptp.fun_Ar2047178847t_bool)) (= (tptp.hAPP_f1265202753l_bool (tptp.hAPP_f459175489l_bool tptp.cOMBK_639770490t_bool P) Q) P)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_fu50365883t_bool)) (= (tptp.hAPP_f626809057l_bool (tptp.hAPP_f1364914207l_bool tptp.cOMBK_1853791052t_bool P) Q) P)) (forall ((P tptp.fun_fu1251737213l_bool) (Q tptp.bool)) (= (tptp.hAPP_b930206237l_bool (tptp.hAPP_f989466937l_bool tptp.cOMBK_343479628l_bool P) Q) P)) (forall ((P tptp.fun_fu1760369922t_bool) (Q tptp.fun_Ar2047178847t_bool) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A711829680t_bool (tptp.cOMBB_1932856316e_indi P Q) R) (tptp.hAPP_f1699392794t_bool P (tptp.hAPP_A2044747691t_bool Q R)))) (forall ((P tptp.fun_Ar1871347069i_bool) (Q tptp.fun_fu50365883t_bool)) (= (tptp.hAPP_f1559864639i_bool (tptp.hAPP_f1224613979i_bool tptp.cOMBK_519762474t_bool P) Q) P)) (forall ((P tptp.fun_fu1251737213l_bool) (Q tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A107624255l_bool (tptp.hAPP_f544895323l_bool tptp.cOMBK_869185066e_indi P) Q) P)) (forall ((P tptp.fun_fu193278215t_bool) (Q tptp.fun_Ar2047178847t_bool) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A784015157t_bool (tptp.cOMBB_715840641e_indi P Q) R) (tptp.hAPP_f1560118175t_bool P (tptp.hAPP_A2044747691t_bool Q R)))) (forall ((P tptp.fun_Ar2100459655t_bool) (Q tptp.fun_Pr1639951081t_bool) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A301260095t_bool (tptp.cOMBC_64563468t_bool P Q) R) (tptp.hAPP_f910728105t_bool (tptp.hAPP_A1985966547t_bool P R) Q))) (forall ((P tptp.fun_Ar2100459655t_bool) (Q tptp.fun_Ar2047178847t_bool) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A301260095t_bool (tptp.cOMBS_1833320732t_bool P Q) R) (tptp.hAPP_f910728105t_bool (tptp.hAPP_A1985966547t_bool P R) (tptp.hAPP_A2044747691t_bool Q R)))) (forall ((P tptp.fun_bo292969573t_bool) (Q tptp.fun_Ar1871347069i_bool) (R tptp.arrow_501706939e_indi)) (= (tptp.hAPP_A1985966547t_bool (tptp.cOMBB_124649523e_indi P Q) R) (tptp.hAPP_b1702702257t_bool P (tptp.hAPP_A1059798043i_bool Q R)))) _let_3 true))))))))))))))
% 0.25/0.76 )
% 0.25/0.76 % SZS output end Proof for SCT171_1
% 0.25/0.76 % cvc5---1.0.5 exiting
% 0.25/0.76 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------