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 : n022.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 0.23s 0.73s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : SCT171+1 : TPTP v8.1.2. Released v5.3.0.
% 0.16/0.16 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n022.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 24 14:57:10 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.53 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.73 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.WHJ1qySVWn/cvc5---1.0.5_28666.p...
% 0.23/0.73 ------- get file name : TPTP file name is SCT171+1
% 0.23/0.73 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_28666.smt2...
% 0.23/0.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.23/0.73 % SZS status Theorem for SCT171+1
% 0.23/0.73 % SZS output start Proof for SCT171+1
% 0.23/0.73 (
% 0.23/0.73 (let ((_let_1 (tptp.member1056080916le_alt (tptp.produc171383831le_alt tptp.c tptp.d)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_f695124765t_bool tptp.f tptp.p))))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.member1056080916le_alt (tptp.produc171383831le_alt tptp.b tptp.a)))) (let ((_let_5 (tptp.member1056080916le_alt (tptp.produc171383831le_alt tptp.a tptp.b)))) (let ((_let_6 (tptp.cOMBB_963584201e_indi tptp.if_fun1419651289t_bool (tptp.cOMBC_277798809t_bool (tptp.cOMBB_317992461e_indi tptp.ord_less_nat tptp.h) tptp.n)))) (let ((_let_7 (tptp.cOMBS_867867294t_bool (tptp.cOMBS_102864562t_bool _let_6 (tptp.cOMBC_1778077589t_bool (tptp.cOMBB_1292070696e_indi tptp.arrow_78446834_mktop tptp.p) tptp.e)) (tptp.cOMBS_867867294t_bool (tptp.cOMBS_102864562t_bool (tptp.cOMBB_963584201e_indi tptp.if_fun1419651289t_bool (tptp.cOMBC_277798809t_bool (tptp.cOMBB_317992461e_indi tptp.fequal_nat tptp.h) tptp.n)) (tptp.cOMBC_1778077589t_bool (tptp.cOMBC_493523632t_bool (tptp.cOMBB_69933763e_indi tptp.arrow_812378712_above tptp.p) tptp.c) tptp.e)) (tptp.cOMBC_1778077589t_bool (tptp.cOMBB_1292070696e_indi tptp.arrow_2077223396_mkbot tptp.p) tptp.e))))) (let ((_let_8 (tptp.hAPP_f695124765t_bool tptp.f _let_7))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt tptp.e tptp.d)) _let_8)))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP_f745298353l_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.is_fun631676118l_bool tptp.arrow_1212118780le_IIA) (tptp.is_fun432044380l_bool tptp.arrow_1239002508le_Lin) (tptp.is_fun959573582l_bool tptp.arrow_413697182e_Prof) (tptp.is_fun631676118l_bool tptp.arrow_467566751nimity) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun917378774i_bool (tptp.cOMBC_277798809t_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun917378774i_bool B_2_1) (tptp.is_bool (tptp.inj_on24934938di_nat B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun917378774i_bool B_1_1) (tptp.is_fun959573582l_bool (tptp.pi_Arr688267935t_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun959573582l_bool B_1_1) (tptp.is_fun631676118l_bool (tptp.pi_fun433100839t_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun282293932t_bool B_1_1) (tptp.is_fun432044380l_bool (tptp.pi_Pro2135156861t_bool B_1_1 B_2_1)))) (tptp.is_Arr553848933le_alt (tptp.undefi1301554228le_alt tptp.arrow_1812558424le_alt)) (tptp.is_Arr625519182e_indi (tptp.undefi818645567e_indi tptp.arrow_2110637339e_indi)) (tptp.is_fun282293932t_bool (tptp.undefi802509179t_bool (tptp.fun (tptp.product_prod tptp.arrow_1812558424le_alt tptp.arrow_1812558424le_alt) tptp.bool))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun917378774i_bool B_1_1) (tptp.is_fun1016509681e_indi (tptp.hilber1792103167di_nat B_1_1 B_2_1)))) (tptp.is_bool tptp.top_top_bool) (tptp.is_fun917378774i_bool tptp.top_to1256827021i_bool) (tptp.is_fun959573582l_bool tptp.top_to1194196741l_bool) (tptp.is_fun631676118l_bool tptp.top_to40512653l_bool) (tptp.is_fun432044380l_bool tptp.top_to2005687013l_bool) (tptp.is_fun282293932t_bool tptp.top_to2034604131t_bool) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun917378774i_bool B_1_1) (tptp.is_fun917378774i_bool (tptp.collec45183100e_indi B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun959573582l_bool B_1_1) (tptp.is_fun959573582l_bool (tptp.collec1580242420t_bool B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun631676118l_bool B_1_1) (tptp.is_fun631676118l_bool (tptp.collec1520786044t_bool B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun432044380l_bool B_1_1) (tptp.is_fun432044380l_bool (tptp.collec874260222t_bool B_1_1)))) (forall ((B_1_1 $$unsorted)) (=> (tptp.is_fun282293932t_bool B_1_1) (tptp.is_fun282293932t_bool (tptp.collec1711870802le_alt B_1_1)))) (tptp.is_bool tptp.fFalse) (tptp.is_bool tptp.fTrue) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_Arr553848933le_alt B_2_1) (tptp.is_fun282293932t_bool (tptp.hAPP_A619995676t_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun917378774i_bool B_1_1) (tptp.is_Arr625519182e_indi B_2_1)) (tptp.is_bool (tptp.hAPP_A1466488369i_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_Arr625519182e_indi B_2_1) (tptp.is_fun959573582l_bool (tptp.hAPP_A1912483895l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_Arr625519182e_indi B_2_1) (tptp.is_fun631676118l_bool (tptp.hAPP_A1964572607l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_Arr625519182e_indi B_2_1) (tptp.is_fun432044380l_bool (tptp.hAPP_A1944296755l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_Arr625519182e_indi B_2_1) (tptp.is_fun282293932t_bool (tptp.hAPP_A1374816149t_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$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 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_fun917378774i_bool (tptp.hAPP_b1018211123i_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_fun959573582l_bool (tptp.hAPP_b1719629739l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_fun631676118l_bool (tptp.hAPP_b990649139l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_fun432044380l_bool (tptp.hAPP_b1965422783l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_bool B_2_1) (tptp.is_fun282293932t_bool (tptp.hAPP_b1024867081t_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun1016509681e_indi B_1_1) (tptp.is_Arr625519182e_indi (tptp.hAPP_n385347014e_indi B_1_1 B_2_1)))) (forall ((B_1_1 $$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 $$unsorted)) (=> (tptp.is_fun917378774i_bool B_2_1) (tptp.is_bool (tptp.hAPP_f919661787l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_Arr625519182e_indi (tptp.hAPP_f1818473245e_indi B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun959573582l_bool B_1_1) (tptp.is_bool (tptp.hAPP_f1636546729l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun917378774i_bool (tptp.hAPP_f749892423i_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun432044380l_bool (tptp.hAPP_f861484971l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun282293932t_bool (tptp.hAPP_f695124765t_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f387058535l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f204273237l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1012384989l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun959573582l_bool B_2_1) (tptp.is_bool (tptp.hAPP_f453661011l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_Arr625519182e_indi (tptp.hAPP_f618619045e_indi B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun631676118l_bool B_1_1) (tptp.is_bool (tptp.hAPP_f785543729l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun917378774i_bool (tptp.hAPP_f355113919i_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f483434675l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1018082273l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1271180905l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1550037191l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1895985727l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f234874197l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f500145249l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun631676118l_bool B_2_1) (tptp.is_bool (tptp.hAPP_f213304539l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1766869725l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f1279200745l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f592909149l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f526292585l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_bool (tptp.hAPP_f460310451l_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun432044380l_bool B_2_1) (tptp.is_bool (tptp.hAPP_f503012287l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun282293932t_bool B_2_1) (tptp.is_Arr625519182e_indi (tptp.hAPP_f1659504677e_indi B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (and (tptp.is_fun432044380l_bool B_1_1) (tptp.is_fun282293932t_bool B_2_1)) (tptp.is_bool (tptp.hAPP_f745298353l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun282293932t_bool B_2_1) (tptp.is_fun917378774i_bool (tptp.hAPP_f352490559i_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun282293932t_bool B_2_1) (tptp.is_fun432044380l_bool (tptp.hAPP_f2056167603l_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun282293932t_bool B_2_1) (tptp.is_fun282293932t_bool (tptp.hAPP_f1673487381t_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_Arr625519182e_indi (tptp.hAPP_P2024088443e_indi B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (=> (tptp.is_fun282293932t_bool B_1_1) (tptp.is_bool (tptp.hAPP_P2075002375t_bool B_1_1 B_2_1)))) (forall ((B_1_1 $$unsorted) (B_2_1 $$unsorted)) (tptp.is_fun917378774i_bool (tptp.hAPP_P907763049i_bool B_1_1 B_2_1))) (forall ((B_1_1 $$unsorted)) (tptp.is_fun432044380l_bool (tptp.member1056080916le_alt B_1_1))) (tptp.is_fun282293932t_bool tptp.lab) (tptp.is_fun282293932t_bool tptp.lba) (tptp.is_Arr553848933le_alt tptp.a) (tptp.is_Arr553848933le_alt tptp.b) (tptp.is_Arr553848933le_alt tptp.c) (tptp.is_Arr553848933le_alt tptp.d) (tptp.is_Arr553848933le_alt tptp.e) (tptp.hBOOL (tptp.hAPP_f785543729l_bool tptp.arrow_1212118780le_IIA tptp.f)) (tptp.hBOOL (tptp.hAPP_f785543729l_bool tptp.arrow_467566751nimity tptp.f)) (not (= tptp.c tptp.d)) (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool tptp.p) tptp.arrow_413697182e_Prof)) (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (L $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.member1056080916le_alt (tptp.produc171383831le_alt X_2 Y_1)))) (let ((_let_2 (= X_2 Z_1))) (=> (and (tptp.is_Arr553848933le_alt X_2) (tptp.is_Arr553848933le_alt Y_1) (tptp.is_Arr553848933le_alt Z_1)) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_A619995676t_bool (tptp.hAPP_f1290184496t_bool tptp.arrow_2077223396_mkbot L) Z_1))) (and (not (= Y_1 Z_1)) (=> _let_2 (not (= X_2 Y_1))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 L))))))))) (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (L $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.member1056080916le_alt (tptp.produc171383831le_alt X_2 Y_1)))) (let ((_let_2 (= Y_1 Z_1))) (=> (and (tptp.is_Arr553848933le_alt X_2) (tptp.is_Arr553848933le_alt Y_1) (tptp.is_Arr553848933le_alt Z_1)) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_A619995676t_bool (tptp.hAPP_f1290184496t_bool tptp.arrow_78446834_mktop L) Z_1))) (and (not (= X_2 Z_1)) (=> _let_2 (not (= X_2 Y_1))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 L))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (A_8 $$unsorted) (B_8 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt A_8) (tptp.is_Arr553848933le_alt B_8) (tptp.is_Arr553848933le_alt Aa) (tptp.is_Arr553848933le_alt Ba)) (=> (not (= Aa Ba)) (=> (not (= A_8 B_8)) (=> (not (= Aa B_8)) (=> (not (= Ba A_8)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool Pa) tptp.arrow_413697182e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool P_1) tptp.arrow_413697182e_Prof)) (=> (forall ((I $$unsorted)) (=> (tptp.is_Arr625519182e_indi I) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) (tptp.hAPP_A1374816149t_bool Pa I))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_8 B_8)) (tptp.hAPP_A1374816149t_bool P_1 I)))))) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) (tptp.hAPP_f695124765t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_8 B_8)) (tptp.hAPP_f695124765t_bool tptp.f P_1))))))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (A_8 $$unsorted) (B_8 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt A_8) (tptp.is_Arr553848933le_alt B_8) (tptp.is_Arr553848933le_alt Aa) (tptp.is_Arr553848933le_alt Ba)) (=> (not (= Aa Ba)) (=> (not (= A_8 B_8)) (=> (not (= Aa B_8)) (=> (not (= Ba A_8)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool Pa) tptp.arrow_413697182e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool P_1) tptp.arrow_413697182e_Prof)) (=> (forall ((I $$unsorted)) (=> (tptp.is_Arr625519182e_indi I) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) (tptp.hAPP_A1374816149t_bool Pa I))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_8 B_8)) (tptp.hAPP_A1374816149t_bool P_1 I)))))) (=> (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) (tptp.hAPP_f695124765t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_8 B_8)) (tptp.hAPP_f695124765t_bool tptp.f P_1))))))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (Ca $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt Ca) (tptp.is_Arr553848933le_alt Aa) (tptp.is_Arr553848933le_alt Ba)) (=> (not (= Aa Ba)) (=> (not (= Ba Ca)) (=> (not (= Aa Ca)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool Pa) tptp.arrow_413697182e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool P_1) tptp.arrow_413697182e_Prof)) (=> (forall ((I $$unsorted)) (=> (tptp.is_Arr625519182e_indi I) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) (tptp.hAPP_A1374816149t_bool Pa I))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Ba Ca)) (tptp.hAPP_A1374816149t_bool P_1 I)))))) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) (tptp.hAPP_f695124765t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Ba Ca)) (tptp.hAPP_f695124765t_bool tptp.f P_1)))))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (A_8 $$unsorted) (B_8 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt A_8) (tptp.is_Arr553848933le_alt B_8) (tptp.is_Arr553848933le_alt Aa) (tptp.is_Arr553848933le_alt Ba)) (=> (not (= Aa Ba)) (=> (not (= A_8 B_8)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool Pa) tptp.arrow_413697182e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool P_1) tptp.arrow_413697182e_Prof)) (=> (forall ((I $$unsorted)) (=> (tptp.is_Arr625519182e_indi I) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) (tptp.hAPP_A1374816149t_bool Pa I))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_8 B_8)) (tptp.hAPP_A1374816149t_bool P_1 I)))))) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) (tptp.hAPP_f695124765t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_8 B_8)) (tptp.hAPP_f695124765t_bool tptp.f P_1))))))))))) (forall ((P_1 $$unsorted) (Pa $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt Aa) (tptp.is_Arr553848933le_alt Ba)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool Pa) tptp.arrow_413697182e_Prof)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool P_1) tptp.arrow_413697182e_Prof)) (=> (forall ((I $$unsorted)) (=> (tptp.is_Arr625519182e_indi I) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) (tptp.hAPP_A1374816149t_bool Pa I))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Ba Aa)) (tptp.hAPP_A1374816149t_bool P_1 I)))))) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) (tptp.hAPP_f695124765t_bool tptp.f Pa))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Ba Aa)) (tptp.hAPP_f695124765t_bool tptp.f P_1)))))))))) (forall ((I $$unsorted)) (let ((_let_1 (tptp.hAPP_A1374816149t_bool tptp.p I))) (let ((_let_2 (tptp.member1056080916le_alt (tptp.produc171383831le_alt tptp.c tptp.d)))) (let ((_let_3 (tptp.hAPP_A588601142di_nat tptp.h I))) (let ((_let_4 (= _let_3 tptp.n))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_3) tptp.n)))) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_2 _let_1)) (and (=> _let_5 (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_2 (tptp.hAPP_A619995676t_bool (tptp.hAPP_f1290184496t_bool tptp.arrow_78446834_mktop _let_1) tptp.e)))) (=> (not _let_5) (and (=> _let_4 (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_2 (tptp.hAPP_A619995676t_bool (tptp.hAPP_A384644407t_bool (tptp.hAPP_f1336478923t_bool tptp.arrow_812378712_above _let_1) tptp.c) tptp.e)))) (=> (not _let_4) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_2 (tptp.hAPP_A619995676t_bool (tptp.hAPP_f1290184496t_bool tptp.arrow_2077223396_mkbot _let_1) tptp.e)))))))))))))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_A1374816149t_bool tptp.p (tptp.hAPP_n385347014e_indi (tptp.hilber1792103167di_nat tptp.top_to1256827021i_bool tptp.h) tptp.n)))) _let_10 _let_11 (forall ((Pa $$unsorted)) (= (forall ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP_P2075002375t_bool Pa X1))) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt A_1) (tptp.is_Arr553848933le_alt B_1)) (tptp.hBOOL (tptp.hAPP_P2075002375t_bool Pa (tptp.produc171383831le_alt A_1 B_1))))))) (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool _let_7) tptp.arrow_413697182e_Prof)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt tptp.c tptp.e)) _let_8)) _let_9 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.n) (tptp.finite120254591e_indi tptp.top_to1256827021i_bool))) (tptp.hBOOL (tptp.inj_on24934938di_nat tptp.h tptp.top_to1256827021i_bool)) (forall ((A_10 $$unsorted) (B_10 $$unsorted) (A_9 $$unsorted) (B_9 $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt A_10) (tptp.is_Arr553848933le_alt B_10) (tptp.is_Arr553848933le_alt A_9) (tptp.is_Arr553848933le_alt B_9)) (=> (= (tptp.produc171383831le_alt A_10 B_10) (tptp.produc171383831le_alt A_9 B_9)) (not (=> (= A_10 A_9) (not (= B_10 B_9))))))) (forall ((Aa $$unsorted) (Ba $$unsorted) (A_8 $$unsorted) (B_8 $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt Aa) (tptp.is_Arr553848933le_alt Ba) (tptp.is_Arr553848933le_alt A_8) (tptp.is_Arr553848933le_alt B_8)) (= (= (tptp.produc171383831le_alt Aa Ba) (tptp.produc171383831le_alt A_8 B_8)) (and (= Aa A_8) (= Ba B_8))))) (forall ((Fa $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f785543729l_bool tptp.arrow_1212118780le_IIA Fa)) (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_1) tptp.arrow_413697182e_Prof)) (forall ((Xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool Xa) tptp.arrow_413697182e_Prof)) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_1 B_1)))) (=> (and (tptp.is_Arr553848933le_alt A_1) (tptp.is_Arr553848933le_alt B_1)) (=> (forall ((I $$unsorted)) (let ((_let_1 (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_1 B_1)))) (=> (tptp.is_Arr625519182e_indi I) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_A1374816149t_bool X_1 I))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_A1374816149t_bool Xa I))))))) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_f695124765t_bool Fa X_1))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_f695124765t_bool Fa Xa)))))))))))))) (forall ((Fa $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f785543729l_bool tptp.arrow_467566751nimity Fa)) (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_1) tptp.arrow_413697182e_Prof)) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt A_1) (tptp.is_Arr553848933le_alt B_1)) (=> (forall ((I $$unsorted)) (=> (tptp.is_Arr625519182e_indi I) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_1 B_1)) (tptp.hAPP_A1374816149t_bool X_1 I))))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_1 B_1)) (tptp.hAPP_f695124765t_bool Fa X_1)))))))))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool tptp.top_to2005687013l_bool X_2))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f1636546729l_bool tptp.top_to1194196741l_bool X_2))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f785543729l_bool tptp.top_to40512653l_bool X_2))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_P2075002375t_bool tptp.top_to2034604131t_bool X_2))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_A1466488369i_bool tptp.top_to1256827021i_bool X_2))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) tptp.top_to1647826457l_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) tptp.top_to1256827021i_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt X_2) tptp.top_to2034604131t_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_2) tptp.top_to1194196741l_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool X_2) tptp.top_to40512653l_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool X_2) tptp.top_to2005687013l_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) tptp.top_to1647826457l_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) tptp.top_to1256827021i_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt X_2) tptp.top_to2034604131t_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_2) tptp.top_to1194196741l_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool X_2) tptp.top_to40512653l_bool))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool X_2) tptp.top_to2005687013l_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool tptp.top_to2005687013l_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f1636546729l_bool tptp.top_to1194196741l_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f785543729l_bool tptp.top_to40512653l_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_P2075002375t_bool tptp.top_to2034604131t_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((X_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_A1466488369i_bool tptp.top_to1256827021i_bool X_2)) (tptp.hBOOL tptp.top_top_bool))) (forall ((Aa $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.hAPP_f1669465919l_bool tptp.ord_le272605321l_bool tptp.top_to2005687013l_bool) Aa)))) (forall ((Aa $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.hAPP_f1760255479l_bool tptp.ord_le453141089l_bool tptp.top_to1194196741l_bool) Aa)))) (forall ((Aa $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.hAPP_f281286919l_bool tptp.ord_le1480133609l_bool tptp.top_to40512653l_bool) Aa)))) (forall ((Aa $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_bool tptp.top_top_bool) Aa)))) (forall ((Aa $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.hAPP_f2056167603l_bool tptp.ord_le227393471t_bool tptp.top_to2034604131t_bool) Aa)))) (forall ((Aa $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool tptp.top_to1256827021i_bool) Aa)))) (forall ((X_14 $$unsorted) (Y_13 $$unsorted)) (=> (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 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool X_2) Y_1)) (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Y_1) X_2))))) (forall ((X_13 $$unsorted) (Y_12 $$unsorted)) (=> (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 $$unsorted) (Y_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Z_1))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Y_1) X_2)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool _let_1 X_2)))))) (forall ((Z_2 $$unsorted) (Y_11 $$unsorted) (X_12 $$unsorted)) (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 $$unsorted) (X_2 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool X_2))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Y_1) Z_1)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool _let_1 Z_1)))))) (forall ((Z $$unsorted) (X_11 $$unsorted) (Y_10 $$unsorted)) (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 $$unsorted) (Ba $$unsorted) (Aa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Ba) Aa)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Ca) Aa))))) (forall ((C_3 $$unsorted) (B_7 $$unsorted) (A_7 $$unsorted)) (=> (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 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Aa))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f919661787l_bool _let_1 Ca)))))) (forall ((C_2 $$unsorted) (A_6 $$unsorted) (B_6 $$unsorted)) (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 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Ca))) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool _let_1 Aa)))))) (forall ((C_1 $$unsorted) (A_5 $$unsorted) (B_5 $$unsorted)) (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 $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (=> (= Aa Ba) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Aa) Ca))))) (forall ((C $$unsorted) (A_4 $$unsorted) (B_4 $$unsorted)) (=> (= 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 $$unsorted) (Aa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Ba) Aa)) (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Aa) Ba))))) (forall ((B_3 $$unsorted) (A_3 $$unsorted)) (=> (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 $$unsorted) (Ba $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Aa) Ba)) (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Ba) Aa))))) (forall ((A_2 $$unsorted) (B_2 $$unsorted)) (=> (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 $$unsorted) (X_2 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool X_2) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Y_1) X_2)) (tptp.hBOOL Pa)))) (forall ((Pa $$unsorted) (X_2 $$unsorted) (Y_1 $$unsorted)) (=> (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 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool X_2) Y_1)) (not (= Y_1 X_2)))) (forall ((X_10 $$unsorted) (Y_9 $$unsorted)) (=> (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 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool X_2) Y_1)) (not (= X_2 Y_1)))) (forall ((X_9 $$unsorted) (Y_8 $$unsorted)) (=> (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 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool X_2) Y_1)) (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Y_1) X_2))))) (forall ((X_8 $$unsorted) (Y_7 $$unsorted)) (=> (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 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool X_2) Y_1)) (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Y_1) X_2))))) (forall ((X_7 $$unsorted) (Y_6 $$unsorted)) (=> (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 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool X_2) Y_1)) (not (= X_2 Y_1)))) (forall ((X_6 $$unsorted) (Y_5 $$unsorted)) (=> (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 $$unsorted) (Y_4 $$unsorted)) (=> (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 $$unsorted) (X_2 $$unsorted)) (=> (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 $$unsorted) (Y_3 $$unsorted)) (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 $$unsorted) (Y_1 $$unsorted)) (= (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 $$unsorted) (Y_1 $$unsorted)) (= (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 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool X_2) X_2)))) (forall ((X_3 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_3) X_3)))) (= tptp.top_to2005687013l_bool (tptp.collec874260222t_bool (tptp.hAPP_b1965422783l_bool tptp.cOMBK_977355664t_bool tptp.fTrue))) (= tptp.top_to1194196741l_bool (tptp.collec1580242420t_bool (tptp.hAPP_b1719629739l_bool tptp.cOMBK_789167586t_bool tptp.fTrue))) (= tptp.top_to40512653l_bool (tptp.collec1520786044t_bool (tptp.hAPP_b990649139l_bool tptp.cOMBK_580911210t_bool tptp.fTrue))) (= tptp.top_to2034604131t_bool (tptp.collec1711870802le_alt (tptp.hAPP_b1024867081t_bool tptp.cOMBK_2069093696le_alt tptp.fTrue))) (= tptp.top_to1256827021i_bool (tptp.collec45183100e_indi (tptp.hAPP_b1018211123i_bool tptp.cOMBK_1157044842e_indi tptp.fTrue))) (forall ((S $$unsorted) (R_1 $$unsorted)) (=> (and (tptp.is_fun282293932t_bool S) (tptp.is_fun282293932t_bool R_1)) (= (forall ((X_1 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.member1056080916le_alt (tptp.produc171383831le_alt X_1 Xa)))) (=> (and (tptp.is_Arr553848933le_alt X_1) (tptp.is_Arr553848933le_alt Xa)) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 R_1)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 S)))))) (= R_1 S)))) (forall ((Aa $$unsorted)) (=> (tptp.is_fun432044380l_bool Aa) (= (not (= Aa tptp.top_to2005687013l_bool)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.hAPP_f1669465919l_bool tptp.ord_le272605321l_bool Aa) tptp.top_to2005687013l_bool))))) (forall ((Aa $$unsorted)) (=> (tptp.is_fun959573582l_bool Aa) (= (not (= Aa tptp.top_to1194196741l_bool)) (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.hAPP_f1760255479l_bool tptp.ord_le453141089l_bool Aa) tptp.top_to1194196741l_bool))))) (forall ((Aa $$unsorted)) (=> (tptp.is_fun631676118l_bool Aa) (= (not (= Aa tptp.top_to40512653l_bool)) (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.hAPP_f281286919l_bool tptp.ord_le1480133609l_bool Aa) tptp.top_to40512653l_bool))))) (forall ((Aa $$unsorted)) (= (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 $$unsorted)) (=> (tptp.is_fun282293932t_bool Aa) (= (not (= Aa tptp.top_to2034604131t_bool)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.hAPP_f2056167603l_bool tptp.ord_le227393471t_bool Aa) tptp.top_to2034604131t_bool))))) (forall ((Aa $$unsorted)) (=> (tptp.is_fun917378774i_bool Aa) (= (not (= Aa tptp.top_to1256827021i_bool)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.hAPP_f1710416135l_bool tptp.ord_le694128617i_bool Aa) tptp.top_to1256827021i_bool))))) (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (tptp.is_Arr625519182e_indi X_2) (=> (tptp.hBOOL (tptp.inj_on24934938di_nat F tptp.top_to1256827021i_bool)) (=> (= (tptp.hAPP_A588601142di_nat F X_2) Y_1) (= (tptp.hAPP_n385347014e_indi (tptp.hilber1792103167di_nat tptp.top_to1256827021i_bool F) Y_1) X_2))))) (forall ((X_2 $$unsorted) (F $$unsorted)) (=> (tptp.is_Arr625519182e_indi X_2) (=> (tptp.hBOOL (tptp.inj_on24934938di_nat F tptp.top_to1256827021i_bool)) (= (tptp.hAPP_n385347014e_indi (tptp.hilber1792103167di_nat tptp.top_to1256827021i_bool F) (tptp.hAPP_A588601142di_nat F X_2)) X_2)))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.is_Arr625519182e_indi X_2) (=> (tptp.hBOOL (tptp.inj_on24934938di_nat F A)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (= (tptp.hAPP_n385347014e_indi (tptp.hilber1792103167di_nat A F) (tptp.hAPP_A588601142di_nat F X_2)) X_2))))) (forall ((Y_1 $$unsorted) (X_2 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (tptp.is_Arr625519182e_indi X_2) (=> (tptp.hBOOL (tptp.inj_on24934938di_nat F A)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (=> (= (tptp.hAPP_A588601142di_nat F X_2) Y_1) (= (tptp.hAPP_n385347014e_indi (tptp.hilber1792103167di_nat A F) Y_1) X_2)))))) (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (and (tptp.is_Arr625519182e_indi X_2) (tptp.is_Arr625519182e_indi Y_1)) (=> (tptp.hBOOL (tptp.inj_on24934938di_nat F tptp.top_to1256827021i_bool)) (= (= (tptp.hAPP_A588601142di_nat F X_2) (tptp.hAPP_A588601142di_nat F Y_1)) (= X_2 Y_1))))) (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.inj_on24934938di_nat F A)) (forall ((X_1 $$unsorted)) (=> (tptp.is_Arr625519182e_indi X_1) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_1) A)) (forall ((Xa $$unsorted)) (=> (tptp.is_Arr625519182e_indi Xa) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi Xa) A)) (=> (= (tptp.hAPP_A588601142di_nat F X_1) (tptp.hAPP_A588601142di_nat F Xa)) (= X_1 Xa)))))))))) (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (and (tptp.is_Arr625519182e_indi X_2) (tptp.is_Arr625519182e_indi Y_1)) (=> (tptp.hBOOL (tptp.inj_on24934938di_nat F A)) (=> (not (= X_2 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi Y_1) A)) (not (= (tptp.hAPP_A588601142di_nat F X_2) (tptp.hAPP_A588601142di_nat F Y_1))))))))) (forall ((Y_1 $$unsorted) (X_2 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (and (tptp.is_Arr625519182e_indi Y_1) (tptp.is_Arr625519182e_indi X_2)) (=> (tptp.hBOOL (tptp.inj_on24934938di_nat F A)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi Y_1) A)) (= (= (tptp.hAPP_A588601142di_nat F X_2) (tptp.hAPP_A588601142di_nat F Y_1)) (= X_2 Y_1))))))) (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (F $$unsorted) (A $$unsorted)) (=> (and (tptp.is_Arr625519182e_indi X_2) (tptp.is_Arr625519182e_indi Y_1)) (=> (tptp.hBOOL (tptp.inj_on24934938di_nat F A)) (=> (= (tptp.hAPP_A588601142di_nat F X_2) (tptp.hAPP_A588601142di_nat F Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi Y_1) A)) (= X_2 Y_1))))))) (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (and (tptp.is_Arr625519182e_indi X_2) (tptp.is_Arr625519182e_indi Y_1)) (=> (tptp.hBOOL (tptp.inj_on24934938di_nat F tptp.top_to1256827021i_bool)) (=> (= (tptp.hAPP_A588601142di_nat F X_2) (tptp.hAPP_A588601142di_nat F Y_1)) (= X_2 Y_1))))) (forall ((G $$unsorted) (F $$unsorted)) (=> (tptp.is_fun1016509681e_indi G) (=> (tptp.hBOOL (tptp.inj_on24934938di_nat F tptp.top_to1256827021i_bool)) (=> (forall ((X_1 $$unsorted)) (= (tptp.hAPP_A588601142di_nat F (tptp.hAPP_n385347014e_indi G X_1)) X_1)) (= (tptp.hilber1792103167di_nat tptp.top_to1256827021i_bool F) G))))) (forall ((F $$unsorted)) (=> (forall ((X_1 $$unsorted) (Y_2 $$unsorted)) (=> (and (tptp.is_Arr625519182e_indi X_1) (tptp.is_Arr625519182e_indi Y_2)) (=> (= (tptp.hAPP_A588601142di_nat F X_1) (tptp.hAPP_A588601142di_nat F Y_2)) (= X_1 Y_2)))) (tptp.hBOOL (tptp.inj_on24934938di_nat F tptp.top_to1256827021i_bool)))) (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool tptp.f) (tptp.pi_fun433100839t_bool tptp.arrow_413697182e_Prof (tptp.hAPP_f20355883l_bool tptp.cOMBK_1088865252t_bool tptp.arrow_1239002508le_Lin)))) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool tptp.lba) tptp.arrow_1239002508le_Lin)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool tptp.lab) tptp.arrow_1239002508le_Lin)) (forall ((Aa $$unsorted) (Ba $$unsorted) (L $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool L) tptp.arrow_1239002508le_Lin)) (=> (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Ba)) L)) (not (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Ba Aa)) L)))))) (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (L $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt X_2) (tptp.is_Arr553848933le_alt Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool L) tptp.arrow_1239002508le_Lin)) (=> (not (= X_2 Y_1)) (= (not (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt X_2 Y_1)) L))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Y_1 X_2)) L))))))) (forall ((X_2 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_A1466488369i_bool A X_2)))) (forall ((X_2 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_bool_bool A X_2)))) (forall ((X_2 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_P2075002375t_bool A X_2)))) (forall ((X_2 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f1636546729l_bool A X_2)))) (forall ((X_2 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f785543729l_bool A X_2)))) (forall ((X_2 $$unsorted) (A $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool A X_2)))) (forall ((Pa $$unsorted)) (=> (tptp.is_fun917378774i_bool Pa) (= (tptp.collec45183100e_indi Pa) Pa))) (forall ((X_2 $$unsorted) (L $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool L) tptp.arrow_1239002508le_Lin)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool (tptp.hAPP_A619995676t_bool (tptp.hAPP_f1290184496t_bool tptp.arrow_78446834_mktop L) X_2)) tptp.arrow_1239002508le_Lin)))) (forall ((X_2 $$unsorted) (L $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool L) tptp.arrow_1239002508le_Lin)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool (tptp.hAPP_A619995676t_bool (tptp.hAPP_f1290184496t_bool tptp.arrow_2077223396_mkbot L) X_2)) tptp.arrow_1239002508le_Lin)))) (forall ((L $$unsorted) (X_2 $$unsorted) (Y_1 $$unsorted)) (=> (and (tptp.is_Arr553848933le_alt X_2) (tptp.is_Arr553848933le_alt Y_1)) (=> (not (= X_2 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool L) tptp.arrow_1239002508le_Lin)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool (tptp.hAPP_A619995676t_bool (tptp.hAPP_A384644407t_bool (tptp.hAPP_f1336478923t_bool tptp.arrow_812378712_above L) X_2) Y_1)) tptp.arrow_1239002508le_Lin)))))) (forall ((L $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool L) tptp.arrow_1239002508le_Lin)) (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool (tptp.hAPP_f1507266205t_bool tptp.cOMBK_1152753196e_indi L)) tptp.arrow_413697182e_Prof)))) (forall ((X_2 $$unsorted) (Y_1 $$unsorted) (L $$unsorted) (Aa $$unsorted) (Ba $$unsorted)) (let ((_let_1 (tptp.member1056080916le_alt (tptp.produc171383831le_alt X_2 Y_1)))) (let ((_let_2 (= Y_1 Ba))) (let ((_let_3 (= X_2 Ba))) (=> (and (tptp.is_Arr553848933le_alt X_2) (tptp.is_Arr553848933le_alt Y_1) (tptp.is_Arr553848933le_alt Aa) (tptp.is_Arr553848933le_alt Ba)) (=> (not (= Aa Ba)) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool L) tptp.arrow_1239002508le_Lin)) (= (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_A619995676t_bool (tptp.hAPP_A384644407t_bool (tptp.hAPP_f1336478923t_bool tptp.arrow_812378712_above L) Aa) Ba))) (and (not (= X_2 Y_1)) (=> _let_3 (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt Aa Y_1)) L))) (=> (not _let_3) (and (=> _let_2 (or (= X_2 Aa) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.produc171383831le_alt X_2 Aa)) L)))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 L)))))))))))))) (forall ((I_1 $$unsorted) (Fa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool Fa) (tptp.pi_fun433100839t_bool tptp.arrow_413697182e_Prof (tptp.hAPP_f20355883l_bool tptp.cOMBK_1088865252t_bool tptp.arrow_1239002508le_Lin)))) (=> (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_1) tptp.arrow_413697182e_Prof)) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.member1056080916le_alt (tptp.produc171383831le_alt A_1 B_1)))) (=> (and (tptp.is_Arr553848933le_alt A_1) (tptp.is_Arr553848933le_alt B_1)) (=> (not (= A_1 B_1)) (=> (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_A1374816149t_bool X_1 I_1))) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 (tptp.hAPP_f695124765t_bool Fa X_1)))))))))) (tptp.hBOOL (tptp.hAPP_A1466488369i_bool (tptp.hAPP_f355113919i_bool tptp.arrow_2061665457ctator Fa) I_1))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool F) (tptp.pi_Pro2135156861t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_P2075002375t_bool F X_2)) (tptp.hAPP_P2127852789l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f483434675l_bool (tptp.member859582768le_alt F) (tptp.pi_Arr149813489le_alt A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.hAPP_A1736628091le_alt F X_2)) (tptp.hAPP_A1374816149t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1895985727l_bool (tptp.member42699324le_alt F) (tptp.pi_boo1877522301le_alt A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.hAPP_b1817367815le_alt F X_2)) (tptp.hAPP_b1024867081t_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f204273237l_bool (tptp.member1833291218t_bool F) (tptp.pi_Arr1511953043t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool (tptp.hAPP_A1594182429t_bool F X_2)) (tptp.hAPP_A1912483895l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1018082273l_bool (tptp.member1911067358t_bool F) (tptp.pi_boo691944735t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool (tptp.hAPP_b833696937t_bool F X_2)) (tptp.hAPP_b1719629739l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1012384989l_bool (tptp.member1467476314t_bool F) (tptp.pi_Arr372473371t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool (tptp.hAPP_A1062826149t_bool F X_2)) (tptp.hAPP_A1964572607l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1271180905l_bool (tptp.member2081512038t_bool F) (tptp.pi_boo71521447t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool (tptp.hAPP_b331122225t_bool F X_2)) (tptp.hAPP_b990649139l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1550037191l_bool (tptp.member497701034t_bool F) (tptp.pi_boo2007389459t_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool (tptp.hAPP_b1024867081t_bool F X_2)) (tptp.hAPP_b1965422783l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f460310451l_bool (tptp.member765089840e_indi F) (tptp.pi_Pro437273841e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi (tptp.hAPP_P2024088443e_indi F X_2)) (tptp.hAPP_P907763049i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f234874197l_bool (tptp.member1105181906e_indi F) (tptp.pi_fun1736243859e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi (tptp.hAPP_f1818473245e_indi F X_2)) (tptp.hAPP_f749892423i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f500145249l_bool (tptp.member1661336414l_bool F) (tptp.pi_fun1494794527l_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f1636546729l_bool F X_2)) (tptp.hAPP_f313042899l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1766869725l_bool (tptp.member1122398042e_indi F) (tptp.pi_fun2075749915e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi (tptp.hAPP_f618619045e_indi F X_2)) (tptp.hAPP_f355113919i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1279200745l_bool (tptp.member387398118l_bool F) (tptp.pi_fun525942951l_bool A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f785543729l_bool F X_2)) (tptp.hAPP_f497468491l_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f592909149l_bool (tptp.member329987264e_indi F) (tptp.pi_fun972956463e_indi A B))) (=> (not (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi (tptp.hAPP_f1659504677e_indi F X_2)) (tptp.hAPP_f352490559i_bool B X_2)))) (not (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool X_2) A)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f526292585l_bool 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(=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool F) (tptp.pi_Pro2135156861t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_P2075002375t_bool F X_2)) (tptp.hAPP_P2127852789l_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f460310451l_bool (tptp.member765089840e_indi F) (tptp.pi_Pro437273841e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi (tptp.hAPP_P2024088443e_indi F X_2)) (tptp.hAPP_P907763049i_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f234874197l_bool (tptp.member1105181906e_indi F) (tptp.pi_fun1736243859e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool 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$$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1279200745l_bool (tptp.member387398118l_bool F) (tptp.pi_fun525942951l_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f785543729l_bool F X_2)) (tptp.hAPP_f497468491l_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f592909149l_bool (tptp.member329987264e_indi F) (tptp.pi_fun972956463e_indi A B))) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi (tptp.hAPP_f1659504677e_indi F X_2)) (tptp.hAPP_f352490559i_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f526292585l_bool (tptp.member1033316428l_bool F) (tptp.pi_fun1727820731l_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f745298353l_bool F X_2)) (tptp.hAPP_f417299659l_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f483434675l_bool (tptp.member859582768le_alt F) (tptp.pi_Arr149813489le_alt A B))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.hAPP_A1736628091le_alt F X_2)) (tptp.hAPP_A1374816149t_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1895985727l_bool (tptp.member42699324le_alt F) (tptp.pi_boo1877522301le_alt A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.hAPP_b1817367815le_alt F X_2)) (tptp.hAPP_b1024867081t_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f204273237l_bool (tptp.member1833291218t_bool F) (tptp.pi_Arr1511953043t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool (tptp.hAPP_A1594182429t_bool F X_2)) (tptp.hAPP_A1912483895l_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1018082273l_bool (tptp.member1911067358t_bool F) (tptp.pi_boo691944735t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool (tptp.hAPP_b833696937t_bool F X_2)) (tptp.hAPP_b1719629739l_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1012384989l_bool (tptp.member1467476314t_bool F) (tptp.pi_Arr372473371t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool (tptp.hAPP_A1062826149t_bool F X_2)) (tptp.hAPP_A1964572607l_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1271180905l_bool (tptp.member2081512038t_bool F) (tptp.pi_boo71521447t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool (tptp.hAPP_b331122225t_bool F X_2)) (tptp.hAPP_b990649139l_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1550037191l_bool (tptp.member497701034t_bool F) (tptp.pi_boo2007389459t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool (tptp.hAPP_b1024867081t_bool F X_2)) (tptp.hAPP_b1965422783l_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool F) (tptp.pi_fun433100839t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool (tptp.hAPP_f695124765t_bool F X_2)) (tptp.hAPP_f861484971l_bool B X_2)))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool F) (tptp.pi_Arr688267935t_bool A B))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool (tptp.hAPP_A1374816149t_bool F X_2)) (tptp.hAPP_A1944296755l_bool B X_2)))))) (= tptp.arrow_413697182e_Prof (tptp.pi_Arr688267935t_bool tptp.top_to1256827021i_bool (tptp.hAPP_f1979025587l_bool tptp.cOMBK_1158753900e_indi tptp.arrow_1239002508le_Lin))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool F) (tptp.pi_Pro2135156861t_bool A (tptp.hAPP_f1724001331l_bool tptp.cOMBK_2008994872le_alt B)))) (=> (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_P2075002375t_bool F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f460310451l_bool (tptp.member765089840e_indi F) (tptp.pi_Pro437273841e_indi A (tptp.hAPP_f1970593179i_bool tptp.cOMBK_100791596le_alt B)))) (=> (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt X_2) A)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi (tptp.hAPP_P2024088443e_indi F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f234874197l_bool (tptp.member1105181906e_indi F) (tptp.pi_fun1736243859e_indi A (tptp.hAPP_f681113465i_bool tptp.cOMBK_454107598t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi (tptp.hAPP_f1818473245e_indi F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f500145249l_bool (tptp.member1661336414l_bool F) (tptp.pi_fun1494794527l_bool A (tptp.hAPP_f219827985l_bool tptp.cOMBK_886533338t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f1636546729l_bool F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1766869725l_bool (tptp.member1122398042e_indi F) (tptp.pi_fun2075749915e_indi A (tptp.hAPP_f1677452273i_bool tptp.cOMBK_1372975190t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi (tptp.hAPP_f618619045e_indi F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1279200745l_bool (tptp.member387398118l_bool F) (tptp.pi_fun525942951l_bool A (tptp.hAPP_f1235573641l_bool tptp.cOMBK_1072228194t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f785543729l_bool F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f592909149l_bool (tptp.member329987264e_indi F) (tptp.pi_fun972956463e_indi A (tptp.hAPP_f1903519657i_bool tptp.cOMBK_2076140708t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi (tptp.hAPP_f1659504677e_indi F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f526292585l_bool (tptp.member1033316428l_bool F) (tptp.pi_fun1727820731l_bool A (tptp.hAPP_f1667233577l_bool tptp.cOMBK_1015076504t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool (tptp.hAPP_f745298353l_bool F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f483434675l_bool (tptp.member859582768le_alt F) (tptp.pi_Arr149813489le_alt A (tptp.hAPP_f1507266205t_bool tptp.cOMBK_1152753196e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.hAPP_A1736628091le_alt F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1895985727l_bool (tptp.member42699324le_alt F) (tptp.pi_boo1877522301le_alt A (tptp.hAPP_f1520552209t_bool tptp.cOMBK_697786936l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool (tptp.member1056080916le_alt (tptp.hAPP_b1817367815le_alt F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f204273237l_bool (tptp.member1833291218t_bool F) (tptp.pi_Arr1511953043t_bool A (tptp.hAPP_f813556705l_bool tptp.cOMBK_116240846e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool (tptp.hAPP_A1594182429t_bool F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1018082273l_bool (tptp.member1911067358t_bool F) (tptp.pi_boo691944735t_bool A (tptp.hAPP_f371807573l_bool tptp.cOMBK_697604314l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool (tptp.hAPP_b833696937t_bool F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1012384989l_bool (tptp.member1467476314t_bool F) (tptp.pi_Arr372473371t_bool A (tptp.hAPP_f1697527281l_bool tptp.cOMBK_1292462166e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool (tptp.hAPP_A1062826149t_bool F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1271180905l_bool (tptp.member2081512038t_bool F) (tptp.pi_boo71521447t_bool A (tptp.hAPP_f448497509l_bool tptp.cOMBK_1268833122l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool (tptp.hAPP_b331122225t_bool F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f1550037191l_bool (tptp.member497701034t_bool F) (tptp.pi_boo2007389459t_bool A (tptp.hAPP_f2135750719l_bool tptp.cOMBK_971068024l_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f387058535l_bool (tptp.member_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool (tptp.hAPP_b1024867081t_bool F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f213304539l_bool (tptp.member1622429502t_bool F) (tptp.pi_fun433100839t_bool A (tptp.hAPP_f20355883l_bool tptp.cOMBK_1088865252t_bool B)))) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_2) A)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool (tptp.hAPP_f695124765t_bool F X_2)) B))))) (forall ((X_2 $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool F) (tptp.pi_Arr688267935t_bool A (tptp.hAPP_f1979025587l_bool tptp.cOMBK_1158753900e_indi B)))) (=> (tptp.hBOOL (tptp.hAPP_f919661787l_bool (tptp.member2074804542e_indi X_2) A)) (tptp.hBOOL (tptp.hAPP_f503012287l_bool (tptp.member1965683644t_bool (tptp.hAPP_A1374816149t_bool F X_2)) B))))) (forall ((Fa $$unsorted) (I_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP_A1466488369i_bool (tptp.hAPP_f355113919i_bool tptp.arrow_2061665457ctator Fa) I_1)) (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP_f453661011l_bool (tptp.member1277417654t_bool X_1) tptp.arrow_413697182e_Prof)) (= (tptp.hAPP_f695124765t_bool Fa X_1) (tptp.hAPP_A1374816149t_bool X_1 I_1)))))) (forall ((A $$unsorted)) (= (tptp.pi_Pro2135156861t_bool A (tptp.hAPP_f1724001331l_bool tptp.cOMBK_2008994872le_alt tptp.top_to1647826457l_bool)) tptp.top_to2005687013l_bool)) (forall ((A $$unsorted)) (= (tptp.pi_fun433100839t_bool A (tptp.hAPP_f20355883l_bool tptp.cOMBK_1088865252t_bool tptp.top_to2005687013l_bool)) tptp.top_to40512653l_bool)) (forall ((A $$unsorted)) (= (tptp.pi_Arr688267935t_bool A (tptp.hAPP_f1979025587l_bool tptp.cOMBK_1158753900e_indi tptp.top_to2005687013l_bool)) tptp.top_to1194196741l_bool)) (= _let_9 (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_4 (tptp.hAPP_f695124765t_bool tptp.f (tptp.cOMBC_437064334t_bool (tptp.cOMBC_481590946t_bool _let_6 tptp.lab) tptp.lba))))) (forall ((I $$unsorted)) (let ((_let_1 (tptp.member1056080916le_alt (tptp.produc171383831le_alt tptp.b tptp.a)))) (let ((_let_2 (tptp.hAPP_A588601142di_nat tptp.h I))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_2) tptp.n)))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.hAPP_A1374816149t_bool tptp.p I))) (let ((_let_6 (tptp.member1056080916le_alt (tptp.produc171383831le_alt tptp.e tptp.d)))) (let ((_let_7 (= _let_2 tptp.n))) (= (and (=> _let_3 (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_6 (tptp.hAPP_A619995676t_bool (tptp.hAPP_f1290184496t_bool tptp.arrow_78446834_mktop _let_5) tptp.e)))) (=> _let_4 (and (=> _let_7 (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_6 (tptp.hAPP_A619995676t_bool (tptp.hAPP_A384644407t_bool (tptp.hAPP_f1336478923t_bool tptp.arrow_812378712_above _let_5) tptp.c) tptp.e)))) (=> (not _let_7) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_6 (tptp.hAPP_A619995676t_bool (tptp.hAPP_f1290184496t_bool tptp.arrow_2077223396_mkbot _let_5) tptp.e))))))) (and (=> _let_3 (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 tptp.lab))) (=> _let_4 (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_1 tptp.lba))))))))))))) (not (= tptp.a tptp.b)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_4 tptp.lba)) (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_5 tptp.lab)) (not (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_5 tptp.lba))) (not (tptp.hBOOL (tptp.hAPP_f745298353l_bool _let_4 tptp.lab))) (tptp.hBOOL tptp.fTrue) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (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 ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_A1466488369i_bool (tptp.hAPP_b1018211123i_bool tptp.cOMBK_1157044842e_indi P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A1466488369i_bool (tptp.cOMBC_277798809t_bool P Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_A1922697556t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A1922697556t_bool (tptp.cOMBB_317992461e_indi P Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_A588601142di_nat Q R)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_P2075002375t_bool (tptp.hAPP_b1024867081t_bool tptp.cOMBK_2069093696le_alt P) Q) P))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.is_fun282293932t_bool X) (= (tptp.hAPP_f1673487381t_bool (tptp.hAPP_f159424297t_bool (tptp.hAPP_b1915039793t_bool tptp.if_fun1419651289t_bool tptp.fTrue) X) Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.is_fun282293932t_bool Y) (= (tptp.hAPP_f1673487381t_bool (tptp.hAPP_f159424297t_bool (tptp.hAPP_b1915039793t_bool tptp.if_fun1419651289t_bool tptp.fFalse) X) Y) Y))) (forall ((P $$unsorted)) (=> (tptp.is_bool P) (or (= P tptp.fTrue) (= P tptp.fFalse)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f745298353l_bool (tptp.hAPP_b1965422783l_bool tptp.cOMBK_977355664t_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_P2127852789l_bool (tptp.hAPP_f1724001331l_bool tptp.cOMBK_2008994872le_alt P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun282293932t_bool P) (= (tptp.hAPP_b1024867081t_bool (tptp.hAPP_f1520552209t_bool tptp.cOMBK_697786936l_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_f417299659l_bool (tptp.hAPP_f1667233577l_bool tptp.cOMBK_1015076504t_bool P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun432044380l_bool P) (= (tptp.hAPP_b1965422783l_bool (tptp.hAPP_f2135750719l_bool tptp.cOMBK_971068024l_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun917378774i_bool P) (= (tptp.hAPP_P907763049i_bool (tptp.hAPP_f1970593179i_bool tptp.cOMBK_100791596le_alt P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun282293932t_bool P) (= (tptp.hAPP_A1374816149t_bool (tptp.hAPP_f1507266205t_bool tptp.cOMBK_1152753196e_indi P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f1636546729l_bool (tptp.hAPP_b1719629739l_bool tptp.cOMBK_789167586t_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun917378774i_bool P) (= (tptp.hAPP_f352490559i_bool (tptp.hAPP_f1903519657i_bool tptp.cOMBK_2076140708t_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun432044380l_bool P) (= (tptp.hAPP_A1944296755l_bool (tptp.hAPP_f1979025587l_bool tptp.cOMBK_1158753900e_indi P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_f313042899l_bool (tptp.hAPP_f219827985l_bool tptp.cOMBK_886533338t_bool P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun959573582l_bool P) (= (tptp.hAPP_b1719629739l_bool (tptp.hAPP_f371807573l_bool tptp.cOMBK_697604314l_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A1374816149t_bool (tptp.cOMBC_1778077589t_bool P Q) R) (tptp.hAPP_A619995676t_bool (tptp.hAPP_A702630576t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun917378774i_bool P) (= (tptp.hAPP_f749892423i_bool (tptp.hAPP_f681113465i_bool tptp.cOMBK_454107598t_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun959573582l_bool P) (= (tptp.hAPP_A1912483895l_bool (tptp.hAPP_f813556705l_bool tptp.cOMBK_116240846e_indi P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A702630576t_bool (tptp.cOMBC_493523632t_bool P Q) R) (tptp.hAPP_A384644407t_bool (tptp.hAPP_A460042315t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A1374816149t_bool (tptp.cOMBC_437064334t_bool P Q) R) (tptp.hAPP_f1673487381t_bool (tptp.hAPP_A1333445289t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A1374816149t_bool (tptp.cOMBS_867867294t_bool P Q) R) (tptp.hAPP_f1673487381t_bool (tptp.hAPP_A1333445289t_bool P R) (tptp.hAPP_A1374816149t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_bool P) (= (tptp.hAPP_f785543729l_bool (tptp.hAPP_b990649139l_bool tptp.cOMBK_580911210t_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun432044380l_bool P) (= (tptp.hAPP_f861484971l_bool (tptp.hAPP_f20355883l_bool tptp.cOMBK_1088865252t_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP_f497468491l_bool (tptp.hAPP_f1235573641l_bool tptp.cOMBK_1072228194t_bool P) Q) P)) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun631676118l_bool P) (= (tptp.hAPP_b990649139l_bool (tptp.hAPP_f448497509l_bool tptp.cOMBK_1268833122l_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A702630576t_bool (tptp.cOMBB_1292070696e_indi P Q) R) (tptp.hAPP_f1290184496t_bool P (tptp.hAPP_A1374816149t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun917378774i_bool P) (= (tptp.hAPP_f355113919i_bool (tptp.hAPP_f1677452273i_bool tptp.cOMBK_1372975190t_bool P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted)) (=> (tptp.is_fun631676118l_bool P) (= (tptp.hAPP_A1964572607l_bool (tptp.hAPP_f1697527281l_bool tptp.cOMBK_1292462166e_indi P) Q) P))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A460042315t_bool (tptp.cOMBB_69933763e_indi P Q) R) (tptp.hAPP_f1336478923t_bool P (tptp.hAPP_A1374816149t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A1333445289t_bool (tptp.cOMBC_481590946t_bool P Q) R) (tptp.hAPP_f159424297t_bool (tptp.hAPP_A869356733t_bool P R) Q))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A1333445289t_bool (tptp.cOMBS_102864562t_bool P Q) R) (tptp.hAPP_f159424297t_bool (tptp.hAPP_A869356733t_bool P R) (tptp.hAPP_A1374816149t_bool Q R)))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP_A869356733t_bool (tptp.cOMBB_963584201e_indi P Q) R) (tptp.hAPP_b1915039793t_bool P (tptp.hAPP_A1466488369i_bool Q R)))) _let_3 true))))))))))))))
% 0.23/0.73 )
% 0.23/0.73 % SZS output end Proof for SCT171+1
% 0.23/0.73 % cvc5---1.0.5 exiting
% 0.23/0.73 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------