TSTP Solution File: ITP305_1 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP305_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n024.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 03:33:22 EDT 2023

% Result   : Theorem 0.56s 1.17s
% Output   : Proof 0.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.26  % Problem    : ITP305_1 : TPTP v8.1.2. Released v8.0.0.
% 0.12/0.27  % Command    : do_cvc5 %s %d
% 0.27/0.47  % Computer : n024.cluster.edu
% 0.27/0.47  % Model    : x86_64 x86_64
% 0.27/0.47  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.47  % Memory   : 8042.1875MB
% 0.27/0.47  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.27/0.47  % CPULimit   : 300
% 0.27/0.47  % WCLimit    : 300
% 0.27/0.47  % DateTime   : Sun Aug 27 12:53:23 EDT 2023
% 0.27/0.47  % CPUTime    : 
% 0.32/0.73  %----Proving TF0_NAR, FOF, or CNF
% 0.56/1.17  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8R4bfa9fS7/cvc5---1.0.5_11388.p...
% 0.56/1.17  ------- get file name : TPTP file name is ITP305_1
% 0.56/1.17  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11388.smt2...
% 0.56/1.17  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.56/1.17  % SZS status Theorem for ITP305_1
% 0.56/1.17  % SZS output start Proof for ITP305_1
% 0.56/1.17  (
% 0.56/1.17  (let ((_let_1 (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'zF2mor$'| A__questionmark_v0 A__questionmark_v3))) (let ((_let_2 (|tptp.'obj$b'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 _let_2) (|tptp.'member$i'| A__questionmark_v2 _let_2) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2))) (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 _let_1 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) _let_1) A__questionmark_v3)))))))) (let ((_let_2 (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (= (|tptp.'mapO$'| (|tptp.'yFtor$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'homFtorContra$'| A__questionmark_v0 A__questionmark_v1)))))) (let ((_let_3 (|tptp.'yFtor$'| |tptp.'c$'|))) (let ((_let_4 (|tptp.'mapO$'| _let_3 |tptp.'y$'|))) (let ((_let_5 (|tptp.'yMap$'| |tptp.'c$'| |tptp.'x$'| |tptp.'eta$'|))) (let ((_let_6 (|tptp.'elem$'| _let_5))) (let ((_let_7 (|tptp.'zF2mor$'| |tptp.'c$'| _let_5))) (let ((_let_8 (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| |tptp.'c$'| _let_7 |tptp.'x$'|) |tptp.'y$'|))) (let ((_let_9 (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| |tptp.'c$'|) _let_7))) (let ((_let_10 (|tptp.'yMapInv$'| |tptp.'c$'| |tptp.'x$'| _let_4 _let_9))) (let ((_let_11 (|tptp.'fun_app$b'| _let_6 (|tptp.'homSet$'| |tptp.'c$'| |tptp.'x$'| |tptp.'y$'|)))) (let ((_let_12 (|tptp.'obj$b'| |tptp.'c$'|))) (let ((_let_13 (|tptp.'member$i'| |tptp.'y$'| _let_12))) (let ((_let_14 (|tptp.'member$i'| |tptp.'x$'| _let_12))) (let ((_let_15 (|tptp.'lSCategory$'| |tptp.'c$'|))) (let ((_let_16 (= _let_10 (|tptp.'yMapInv$'| |tptp.'c$'| |tptp.'x$'| _let_4 _let_5)))) (let ((_let_17 (not _let_16))) (let ((_let_18 (= _let_4 (|tptp.'homFtorContra$'| |tptp.'c$'| |tptp.'y$'|)))) (let ((_let_19 (= _let_5 _let_9))) (let ((_let_20 (not _let_13))) (let ((_let_21 (not _let_15))) (let ((_let_22 (or _let_21 _let_20 _let_18))) (let ((_let_23 (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (or (not (|tptp.'lSCategory$'| A__questionmark_v0)) (not (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (= (|tptp.'mapO$'| (|tptp.'yFtor$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'homFtorContra$'| A__questionmark_v0 A__questionmark_v1)))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (ASSUME :args (_let_13)))) (let ((_let_26 (ASSUME :args (_let_15)))) (let ((_let_27 (and _let_8 _let_19))) (let ((_let_28 (not _let_11))) (let ((_let_29 (not _let_14))) (let ((_let_30 (or _let_21 _let_29 _let_20 _let_28 _let_27))) (let ((_let_31 (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'zF2mor$'| A__questionmark_v0 A__questionmark_v3))) (let ((_let_2 (|tptp.'obj$b'| A__questionmark_v0))) (or (not (|tptp.'lSCategory$'| A__questionmark_v0)) (not (|tptp.'member$i'| A__questionmark_v1 _let_2)) (not (|tptp.'member$i'| A__questionmark_v2 _let_2)) (not (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2))) (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 _let_1 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) _let_1))))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (and _let_18 _let_19))) (let ((_let_34 (_let_18 _let_19))) (let ((_let_35 (APPLY_UF |tptp.'yMapInv$'|))) (let ((_let_36 (ASSUME :args (_let_19)))) (let ((_let_37 (ASSUME :args (_let_18)))) (let ((_let_38 (REFL :args (|tptp.'x$'|)))) (let ((_let_39 (REFL :args (|tptp.'c$'|)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_33)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_37 _let_36) (SCOPE (TRANS (CONG _let_39 _let_38 _let_37 (REFL :args (_let_9)) :args _let_35) (CONG _let_39 _let_38 (SYMM _let_37) (SYMM _let_36) :args _let_35)) :args _let_34)) :args _let_34)) :args (true _let_33)) :args ((or _let_16 (not _let_18) (not _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_27 1)) :args ((or _let_19 (not _let_27)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_21 _let_29 _let_20 _let_28 _let_27 (not _let_30)))) _let_26 (ASSUME :args (_let_14)) _let_25 (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (|tptp.'c$'| |tptp.'x$'| |tptp.'y$'| _let_5 QUANTIFIERS_INST_E_MATCHING ((not (= (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)) false))))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)) :args (_let_27 false _let_15 false _let_14 false _let_13 false _let_11 false _let_30)) :args (_let_19 false _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_21 _let_20 _let_18 (not _let_22)))) _let_26 _let_25 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (|tptp.'c$'| |tptp.'y$'| QUANTIFIERS_INST_E_MATCHING ((not (= (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) false))))) :args (_let_23))) _let_24 :args (_let_22 false _let_23)) :args (_let_18 false _let_15 false _let_13 false _let_22)) (ASSUME :args (_let_17)) :args (false false _let_19 false _let_18 true _let_16)) :args ((forall ((A__questionmark_v0 |tptp.'ZF$'|)) (= (|tptp.'fun_app$'| |tptp.'uuz$'| A__questionmark_v0) (|tptp.'zFfun$'| A__questionmark_v0 A__questionmark_v0 |tptp.'uux$'|))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_prod$'|)) (= (|tptp.'fun_app$a'| |tptp.'uvg$'| A__questionmark_v0) (exists ((A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (and (= A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v1) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'fun_app$c'| (|tptp.'uus$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'id$'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'fun_app$d'| (|tptp.'uut$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'id$a'| (|tptp.'catCod$a'| A__questionmark_v0)) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (= (|tptp.'fun_app$e'| (|tptp.'uui$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'fun_app$f'| (|tptp.'uuh$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$a'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_prod_set$'|) (A__questionmark_v1 |tptp.'ZF_ZF_prod$'|)) (= (|tptp.'fun_app$a'| (|tptp.'uub$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$b'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_b_prod_set$'|) (A__questionmark_v1 |tptp.'B_b_prod$'|)) (= (|tptp.'fun_app$g'| (|tptp.'uug$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$c'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_set$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (= (|tptp.'fun_app$b'| (|tptp.'uua$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$d'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_ZF_fun_set$'|) (A__questionmark_v1 |tptp.'B_ZF_fun$'|)) (= (|tptp.'fun_app$h'| (|tptp.'uud$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$e'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_a_fun_set$'|) (A__questionmark_v1 |tptp.'B_a_fun$'|)) (= (|tptp.'fun_app$i'| (|tptp.'uue$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$f'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_fun_set$'|) (A__questionmark_v1 |tptp.'A_b_fun$'|)) (= (|tptp.'fun_app$j'| (|tptp.'uuf$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$g'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_set$'|) (A__questionmark_v1 |tptp.'B$'|)) (= (|tptp.'fun_app$k'| (|tptp.'uuc$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$h'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_set$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'fun_app$l'| (|tptp.'uu$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$i'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_prod$'|)) (= (|tptp.'fun_app$a'| (|tptp.'uvd$'| A__questionmark_v0) A__questionmark_v1) (exists ((A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (and (= A__questionmark_v1 (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B_b_prod$'|)) (= (|tptp.'fun_app$g'| (|tptp.'uvb$'| A__questionmark_v0) A__questionmark_v1) (exists ((A__questionmark_v2 |tptp.'B$'|) (A__questionmark_v3 |tptp.'B$'|)) (and (= A__questionmark_v1 (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'uve$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'restrict$'| (|tptp.'case_prod$'| (|tptp.'comp$'| A__questionmark_v0)) (|tptp.'collect$'| (|tptp.'uvd$'| A__questionmark_v0)) (|tptp.'pair$'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'uvc$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'restrict$a'| (|tptp.'case_prod$a'| (|tptp.'comp$a'| A__questionmark_v0)) (|tptp.'collect$a'| (|tptp.'uvb$'| A__questionmark_v0)) (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (= (|tptp.'fun_app$p'| (|tptp.'uup$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'homFtorMapContra$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'fun_app$f'| (|tptp.'uum$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'functor_abbrev$'| A__questionmark_v2 A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'uuk$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'uuj$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catCod$'| A__questionmark_v0))) (= (|tptp.'fun_app$f'| (|tptp.'uuv$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (and (|tptp.'member$a'| A__questionmark_v2 (|tptp.'obj$'| _let_1)) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| (|tptp.'catDom$'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'id$'| _let_1 A__questionmark_v2)))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'catCod$a'| A__questionmark_v0))) (= (|tptp.'fun_app$b'| (|tptp.'uuu$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (and (|tptp.'member$d'| A__questionmark_v2 (|tptp.'obj$a'| _let_1)) (= (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| (|tptp.'catDom$a'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'id$a'| _let_1) A__questionmark_v2)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'B$'|)) (= (|tptp.'fun_app$k'| (|tptp.'uva$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (and (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0)) (= (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (= (|tptp.'fun_app$e'| (|tptp.'uun$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (and (|tptp.'fun_app$e'| |tptp.'natTrans$'| A__questionmark_v2) (= (|tptp.'nTCatDom$'| A__questionmark_v2) A__questionmark_v0) (= (|tptp.'nTCatCod$'| A__questionmark_v2) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (= (|tptp.'fun_app$'| (|tptp.'uuq$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) (|tptp.'zF2mor$'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (= (|tptp.'fun_app$'| (|tptp.'uuo$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'zF2mor$'| A__questionmark_v0 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'uuw$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| A__questionmark_v0) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'uul$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v1) (|tptp.'zF2mor$'| A__questionmark_v0 A__questionmark_v3))) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (= (|tptp.'fun_app$b'| (|tptp.'uvf$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (exists ((A__questionmark_v4 |tptp.'B$'|)) (and (= A__questionmark_v3 (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) A__questionmark_v4)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v4 A__questionmark_v1) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'ZF$'|) (A__questionmark_v4 |tptp.'A$'|)) (= (|tptp.'fun_app$d'| (|tptp.'uur$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3) A__questionmark_v4) (|tptp.'zFfun$'| (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v4 A__questionmark_v1) (|tptp.'mapO$a'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$m'| (|tptp.'uul$'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|)) (= (|tptp.'fun_app$'| |tptp.'uux$'| A__questionmark_v0) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'ZF$'|)) (= (|tptp.'fun_app$b'| |tptp.'uuy$'| A__questionmark_v0) true)) _let_17 _let_15 _let_14 _let_13 (|tptp.'fun_app$f'| (|tptp.'nt_abbrev$'| |tptp.'eta$'| (|tptp.'mapO$'| _let_3 |tptp.'x$'|)) _let_4) _let_11 (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| _let_3) _let_7) _let_10) _let_8 (|tptp.'fun_app$b'| _let_6 (|tptp.'mapO$a'| _let_4 |tptp.'x$'|)) (|tptp.'functor_abbrev$'| _let_4 (|tptp.'oppositeCategory$'| |tptp.'c$'|) |tptp.'set$'|) _let_2 (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (let ((_let_1 (|tptp.'yFtor$'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| _let_1) A__questionmark_v1) (|tptp.'yMapInv$'| A__questionmark_v0 A__questionmark_v2 (|tptp.'mapO$'| _let_1 A__questionmark_v3) (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'functor_abbrev$'| A__questionmark_v1 (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|) (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$f'| (|tptp.'nt_abbrev$'| A__questionmark_v3 (|tptp.'mapO$'| (|tptp.'yFtor$'| A__questionmark_v0) A__questionmark_v2)) A__questionmark_v1)) (= (|tptp.'yMapInv$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1 (|tptp.'yMap$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v3)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (= (|tptp.'yMapInv$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3) (|tptp.'makeNT$'| (|tptp.'yMapInv$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (let ((_let_1 (|tptp.'obj$b'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1)) (= (|tptp.'mapO$a'| (|tptp.'mapO$'| (|tptp.'yFtor$'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'B_ZF_fun$'|) (A__questionmark_v3 |tptp.'B_ZF_fun_b_ZF_fun_fun$'|) (A__questionmark_v4 |tptp.'B_ZF_fun_b_ZF_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'mor2ZF$'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'B_ZF_fun$'|)) (=> (= A__questionmark_v2 A__questionmark_v5) (= (|tptp.'fun_app$s'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$s'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'mor2ZF_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'mor2ZF_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'B_ZF_fun$'|) (A__questionmark_v3 |tptp.'B_ZF_fun_b_ZF_fun_fun$'|) (A__questionmark_v4 |tptp.'B_ZF_fun_b_ZF_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'mor2ZF$'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'B_ZF_fun$'|)) (=> (= A__questionmark_v5 A__questionmark_v2) (= (|tptp.'fun_app$s'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$s'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'mor2ZF_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'mor2ZF_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0))) (= (|tptp.'zF2mor$'| A__questionmark_v0 (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'homSet$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (= (|tptp.'mor$a'| (|tptp.'oppositeCategory$a'| A__questionmark_v0)) (|tptp.'mor$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= (|tptp.'mor$b'| (|tptp.'oppositeCategory$b'| A__questionmark_v0)) (|tptp.'mor$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'mor$'| (|tptp.'oppositeCategory$'| A__questionmark_v0)) (|tptp.'mor$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (= (|tptp.'obj$'| (|tptp.'oppositeCategory$a'| A__questionmark_v0)) (|tptp.'obj$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= (|tptp.'obj$a'| (|tptp.'oppositeCategory$b'| A__questionmark_v0)) (|tptp.'obj$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'obj$b'| (|tptp.'oppositeCategory$'| A__questionmark_v0)) (|tptp.'obj$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'oppositeCategory$a'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (= (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'oppositeCategory$b'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (= (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (let ((_let_1 (|tptp.'obj$b'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1)) (= (|tptp.'mapO$a'| (|tptp.'homFtorContra$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'lSCategory$'| (|tptp.'oppositeCategory$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (|tptp.'functor_abbrev$'| (|tptp.'homFtorContra$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'elem$'| (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mor2ZF$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'mor$'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 _let_2) (|tptp.'member$h'| A__questionmark_v2 _let_2) (= (|tptp.'fun_app$p'| _let_1 A__questionmark_v1) (|tptp.'fun_app$p'| _let_1 A__questionmark_v2))) (= A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'functor_abbrev$'| A__questionmark_v1 (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|) (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) (|tptp.'mapO$a'| A__questionmark_v1 A__questionmark_v2))) (= (|tptp.'yMap$'| A__questionmark_v0 A__questionmark_v2 (|tptp.'yMapInv$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1 A__questionmark_v3)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'functor_abbrev$'| A__questionmark_v1 (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|) (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) (|tptp.'mapO$a'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$f'| (|tptp.'nt_abbrev$'| (|tptp.'yMapInv$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1 A__questionmark_v3) (|tptp.'mapO$'| (|tptp.'yFtor$'| A__questionmark_v0) A__questionmark_v2)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'functor_abbrev$'| A__questionmark_v1 (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|) (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$f'| (|tptp.'nt_abbrev$'| A__questionmark_v3 (|tptp.'mapO$'| (|tptp.'yFtor$'| A__questionmark_v0) A__questionmark_v2)) A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'elem$'| (|tptp.'yMap$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v3)) (|tptp.'mapO$a'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'mor2ZF$'| (|tptp.'oppositeCategory$'| A__questionmark_v0)) (|tptp.'mor2ZF$'| A__questionmark_v0))) _let_1 (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (= (|tptp.'zF2mor$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'zF2mor$'| A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'ZF$'|) (A__questionmark_v4 |tptp.'ZF$'|) (A__questionmark_v5 |tptp.'ZF$'|)) (=> (and (|tptp.'functor_abbrev$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v1 A__questionmark_v3 A__questionmark_v4) A__questionmark_v5)) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| A__questionmark_v2 (|tptp.'mapM$b'| A__questionmark_v0 A__questionmark_v3) (|tptp.'mapO$b'| A__questionmark_v0 A__questionmark_v4)) (|tptp.'mapO$b'| A__questionmark_v0 A__questionmark_v5)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v4 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v5 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (|tptp.'functor_abbrev$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| A__questionmark_v1 A__questionmark_v3 A__questionmark_v4) A__questionmark_v5)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v2 (|tptp.'mapM$c'| A__questionmark_v0 A__questionmark_v3) (|tptp.'mapO$c'| A__questionmark_v0 A__questionmark_v4)) (|tptp.'mapO$c'| A__questionmark_v0 A__questionmark_v5)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'ZF$'|) (A__questionmark_v4 |tptp.'ZF$'|) (A__questionmark_v5 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'mapO$d'| A__questionmark_v0))) (=> (and (|tptp.'functor_abbrev$c'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v1 A__questionmark_v3 A__questionmark_v4) A__questionmark_v5)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v2 (|tptp.'fun_app$'| (|tptp.'mapM$d'| A__questionmark_v0) A__questionmark_v3) (|tptp.'fun_app$'| _let_1 A__questionmark_v4)) (|tptp.'fun_app$'| _let_1 A__questionmark_v5))))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v3 |tptp.'ZF$'|) (A__questionmark_v4 |tptp.'ZF$'|) (A__questionmark_v5 |tptp.'ZF$'|)) (=> (and (|tptp.'functor_abbrev$d'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v1 A__questionmark_v3 A__questionmark_v4) A__questionmark_v5)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v2 (|tptp.'mapM$e'| A__questionmark_v0 A__questionmark_v3) (|tptp.'mapO$e'| A__questionmark_v0 A__questionmark_v4)) (|tptp.'mapO$e'| A__questionmark_v0 A__questionmark_v5)))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v3 |tptp.'B$'|) (A__questionmark_v4 |tptp.'A$'|) (A__questionmark_v5 |tptp.'A$'|)) (=> (and (|tptp.'functor_abbrev$e'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v1 A__questionmark_v3 A__questionmark_v4) A__questionmark_v5)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v2 (|tptp.'mapM$f'| A__questionmark_v0 A__questionmark_v3) (|tptp.'mapO$f'| A__questionmark_v0 A__questionmark_v4)) (|tptp.'mapO$f'| A__questionmark_v0 A__questionmark_v5)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'B$'|) (A__questionmark_v4 |tptp.'A$'|) (A__questionmark_v5 |tptp.'A$'|)) (=> (and (|tptp.'functor_abbrev$f'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v1 A__questionmark_v3 A__questionmark_v4) A__questionmark_v5)) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| A__questionmark_v2 (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v3) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v4)) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v5)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'B$'|) (A__questionmark_v4 |tptp.'A$'|) (A__questionmark_v5 |tptp.'A$'|)) (=> (and (|tptp.'functor_abbrev$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v1 A__questionmark_v3 A__questionmark_v4) A__questionmark_v5)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v2 (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) A__questionmark_v3) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v4)) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v5)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'functor_abbrev$'| A__questionmark_v1 (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|) (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) (|tptp.'mapO$a'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$e'| |tptp.'natTransP$'| (|tptp.'yMapInv$a'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (let ((_let_1 (|tptp.'obj$b'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1)) (= (|tptp.'mapO$a'| (|tptp.'homFtor$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'functor_abbrev$'| A__questionmark_v1 (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|) (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) (|tptp.'mapO$a'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$e'| |tptp.'natTrans$'| (|tptp.'yMapInv$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$q'| (|tptp.'yFtorNT$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'yMapInv$'| A__questionmark_v0 A__questionmark_v2 (|tptp.'homFtorContra$'| A__questionmark_v0 A__questionmark_v3) (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0))) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| (|tptp.'yFtor$'| A__questionmark_v0)) A__questionmark_v1) (|tptp.'fun_app$q'| (|tptp.'yFtorNT$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'oppositeCategory$a'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'oppositeCategory$b'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'oppositeCategory$a'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'oppositeCategory$b'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v3) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'homFtorContra$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'homFtor$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (let ((_let_1 (|tptp.'homFtor$a'| A__questionmark_v0 A__questionmark_v1))) (let ((_let_2 (|tptp.'obj$b'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'fun_app$f'| |tptp.'preFunctor$'| _let_1) (|tptp.'member$i'| A__questionmark_v1 _let_2) (|tptp.'member$i'| A__questionmark_v2 _let_2)) (= (|tptp.'mapO$a'| _let_1 A__questionmark_v2) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= (|tptp.'oppositeCategory$b'| (|tptp.'oppositeCategory$b'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'oppositeCategory$'| (|tptp.'oppositeCategory$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'ZF$'|)) (|tptp.'member$d'| A__questionmark_v0 (|tptp.'obj$a'| |tptp.'set$'|))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'fun_app$e'| |tptp.'natTrans$'| (|tptp.'fun_app$q'| (|tptp.'yFtorNT$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_bool_fun$'|)) (= (|tptp.'member$i'| A__questionmark_v0 (|tptp.'collect$b'| A__questionmark_v1)) (|tptp.'fun_app$l'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_bool_fun$'|)) (= (|tptp.'member$d'| A__questionmark_v0 (|tptp.'collect$c'| A__questionmark_v1)) (|tptp.'fun_app$b'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_prod$'|) (A__questionmark_v1 |tptp.'ZF_ZF_prod_bool_fun$'|)) (= (|tptp.'member$b'| A__questionmark_v0 (|tptp.'collect$'| A__questionmark_v1)) (|tptp.'fun_app$a'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B$'|) (A__questionmark_v1 |tptp.'B_bool_fun$'|)) (= (|tptp.'member$h'| A__questionmark_v0 (|tptp.'collect$d'| A__questionmark_v1)) (|tptp.'fun_app$k'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_ZF_fun$'|) (A__questionmark_v1 |tptp.'B_ZF_fun_bool_fun$'|)) (= (|tptp.'member$e'| A__questionmark_v0 (|tptp.'collect$e'| A__questionmark_v1)) (|tptp.'fun_app$h'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_a_fun$'|) (A__questionmark_v1 |tptp.'B_a_fun_bool_fun$'|)) (= (|tptp.'member$f'| A__questionmark_v0 (|tptp.'collect$f'| A__questionmark_v1)) (|tptp.'fun_app$i'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_fun$'|) (A__questionmark_v1 |tptp.'A_b_fun_bool_fun$'|)) (= (|tptp.'member$g'| A__questionmark_v0 (|tptp.'collect$g'| A__questionmark_v1)) (|tptp.'fun_app$j'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'B_b_prod$'|) (A__questionmark_v1 |tptp.'B_b_prod_bool_fun$'|)) (= (|tptp.'member$c'| A__questionmark_v0 (|tptp.'collect$a'| A__questionmark_v1)) (|tptp.'fun_app$g'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'|)) (= (|tptp.'member$a'| A__questionmark_v0 (|tptp.'collect$h'| A__questionmark_v1)) (|tptp.'fun_app$f'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'|)) (= (|tptp.'member$'| A__questionmark_v0 (|tptp.'collect$i'| A__questionmark_v1)) (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_set$'|)) (= (|tptp.'collect$b'| (|tptp.'uu$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'ZF_set$'|)) (= (|tptp.'collect$c'| (|tptp.'uua$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_prod_set$'|)) (= (|tptp.'collect$'| (|tptp.'uub$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'B_set$'|)) (= (|tptp.'collect$d'| (|tptp.'uuc$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'B_ZF_fun_set$'|)) (= (|tptp.'collect$e'| (|tptp.'uud$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'B_a_fun_set$'|)) (= (|tptp.'collect$f'| (|tptp.'uue$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'A_b_fun_set$'|)) (= (|tptp.'collect$g'| (|tptp.'uuf$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'B_b_prod_set$'|)) (= (|tptp.'collect$a'| (|tptp.'uug$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$'|)) (= (|tptp.'collect$h'| (|tptp.'uuh$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$'|)) (= (|tptp.'collect$i'| (|tptp.'uui$'| A__questionmark_v0)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'A_bool_fun$'|) (A__questionmark_v1 |tptp.'A_bool_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$l'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$l'| A__questionmark_v1 A__questionmark_v2))) (= (|tptp.'collect$b'| A__questionmark_v0) (|tptp.'collect$b'| A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'fun_app$f'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$f'| A__questionmark_v1 A__questionmark_v2))) (= (|tptp.'collect$h'| A__questionmark_v0) (|tptp.'collect$h'| A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (= (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$e'| A__questionmark_v1 A__questionmark_v2))) (= (|tptp.'collect$i'| A__questionmark_v0) (|tptp.'collect$i'| A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'B_b_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'B_b_prod_bool_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'B_b_prod$'|)) (= (|tptp.'fun_app$g'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$g'| A__questionmark_v1 A__questionmark_v2))) (= (|tptp.'collect$a'| A__questionmark_v0) (|tptp.'collect$a'| A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_bool_fun$'|) (A__questionmark_v1 |tptp.'ZF_bool_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'ZF$'|)) (= (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$b'| A__questionmark_v1 A__questionmark_v2))) (= (|tptp.'collect$c'| A__questionmark_v0) (|tptp.'collect$c'| A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'ZF_ZF_prod_bool_fun$'|)) (=> (forall ((A__questionmark_v2 |tptp.'ZF_ZF_prod$'|)) (= (|tptp.'fun_app$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$a'| A__questionmark_v1 A__questionmark_v2))) (= (|tptp.'collect$'| A__questionmark_v0) (|tptp.'collect$'| A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'fun_app$e'| |tptp.'natTransP$'| (|tptp.'fun_app$q'| (|tptp.'yFtorNT$a'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (|tptp.'fun_app$e'| |tptp.'natTransP$'| A__questionmark_v0) (|tptp.'fun_app$e'| |tptp.'natTrans$'| (|tptp.'makeNT$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|)) (=> (|tptp.'natTransP$a'| A__questionmark_v0) (|tptp.'natTrans$a'| (|tptp.'makeNT$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (|tptp.'natTransP$b'| A__questionmark_v0) (|tptp.'natTrans$b'| (|tptp.'makeNT$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (=> (|tptp.'natTransP$c'| A__questionmark_v0) (|tptp.'natTrans$c'| (|tptp.'makeNT$c'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (=> (|tptp.'natTransP$d'| A__questionmark_v0) (|tptp.'natTrans$d'| (|tptp.'makeNT$d'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (= (|tptp.'fun_app$q'| (|tptp.'yFtorNT$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'makeNT$'| (|tptp.'fun_app$q'| (|tptp.'yFtorNT$a'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'homFtorContra$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'homFtor$a'| (|tptp.'oppositeCategory$'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'member$'| (|tptp.'fun_app$q'| (|tptp.'yFtorNT$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mor$a'| (|tptp.'catExp$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (|tptp.'fun_app$e'| |tptp.'natTrans$'| A__questionmark_v0) (|tptp.'fun_app$e'| |tptp.'natTransP$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|)) (=> (|tptp.'natTrans$a'| A__questionmark_v0) (|tptp.'natTransP$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (|tptp.'natTrans$b'| A__questionmark_v0) (|tptp.'natTransP$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (=> (|tptp.'natTrans$c'| A__questionmark_v0) (|tptp.'natTransP$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (=> (|tptp.'natTrans$d'| A__questionmark_v0) (|tptp.'natTransP$d'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'member$d'| (|tptp.'homFtorMapContra$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1) (|tptp.'mor$b'| |tptp.'set$'|)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'functor_abbrev$f'| (|tptp.'yFtor$'| A__questionmark_v0) A__questionmark_v0 (|tptp.'catExp$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0))) (= (|tptp.'fun_app$p'| (|tptp.'mapM$a'| (|tptp.'homFtorContra$'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1) (|tptp.'homFtorMapContra$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (|tptp.'fun_app$f'| |tptp.'functorM$'| (|tptp.'homFtor$a'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (=> (|tptp.'member$j'| A__questionmark_v0 (|tptp.'mor$c'| (|tptp.'catExp$a'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'natTrans$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'member$k'| A__questionmark_v0 (|tptp.'mor$d'| (|tptp.'catExp$b'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'natTrans$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'member$'| A__questionmark_v0 (|tptp.'mor$a'| (|tptp.'catExp$'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$e'| |tptp.'natTrans$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'fun_app$f'| |tptp.'functorM$'| A__questionmark_v0) (|tptp.'fun_app$f'| |tptp.'preFunctor$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|)) (=> (|tptp.'functorM$a'| A__questionmark_v0) (|tptp.'preFunctor$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|)) (=> (|tptp.'functorM$b'| A__questionmark_v0) (|tptp.'preFunctor$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'functorM$c'| A__questionmark_v0) (|tptp.'preFunctor$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'|)) (=> (|tptp.'functorM$d'| A__questionmark_v0) (|tptp.'preFunctor$d'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'member$d'| (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'mor$b'| |tptp.'set$'|)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|)) (=> (and (|tptp.'preFunctor$a'| A__questionmark_v0) (|tptp.'functorM_axioms$'| A__questionmark_v0)) (|tptp.'functorM$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|)) (=> (and (|tptp.'preFunctor$b'| A__questionmark_v0) (|tptp.'functorM_axioms$a'| A__questionmark_v0)) (|tptp.'functorM$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'|)) (=> (and (|tptp.'preFunctor$d'| A__questionmark_v0) (|tptp.'functorM_axioms$b'| A__questionmark_v0)) (|tptp.'functorM$d'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (|tptp.'preFunctor$c'| A__questionmark_v0) (|tptp.'functorM_axioms$c'| A__questionmark_v0)) (|tptp.'functorM$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (|tptp.'fun_app$f'| |tptp.'preFunctor$'| A__questionmark_v0) (|tptp.'fun_app$f'| |tptp.'functorM_axioms$d'| A__questionmark_v0)) (|tptp.'fun_app$f'| |tptp.'functorM$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|)) (= (|tptp.'functorM$a'| A__questionmark_v0) (and (|tptp.'preFunctor$a'| A__questionmark_v0) (|tptp.'functorM_axioms$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|)) (= (|tptp.'functorM$b'| A__questionmark_v0) (and (|tptp.'preFunctor$b'| A__questionmark_v0) (|tptp.'functorM_axioms$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'|)) (= (|tptp.'functorM$d'| A__questionmark_v0) (and (|tptp.'preFunctor$d'| A__questionmark_v0) (|tptp.'functorM_axioms$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'functorM$c'| A__questionmark_v0) (and (|tptp.'preFunctor$c'| A__questionmark_v0) (|tptp.'functorM_axioms$c'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'fun_app$f'| |tptp.'functorM$'| A__questionmark_v0) (and (|tptp.'fun_app$f'| |tptp.'preFunctor$'| A__questionmark_v0) (|tptp.'fun_app$f'| |tptp.'functorM_axioms$d'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'homFtor$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'makeFtor$'| (|tptp.'homFtor$a'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (and (|tptp.'fun_app$e'| |tptp.'natTransP$'| A__questionmark_v0) (|tptp.'fun_app$e'| |tptp.'natTransExt$'| A__questionmark_v0)) (|tptp.'fun_app$e'| |tptp.'natTrans$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|)) (=> (and (|tptp.'natTransP$a'| A__questionmark_v0) (|tptp.'natTransExt$a'| A__questionmark_v0)) (|tptp.'natTrans$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (and (|tptp.'natTransP$b'| A__questionmark_v0) (|tptp.'natTransExt$b'| A__questionmark_v0)) (|tptp.'natTrans$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (=> (and (|tptp.'natTransP$c'| A__questionmark_v0) (|tptp.'natTransExt$c'| A__questionmark_v0)) (|tptp.'natTrans$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (=> (and (|tptp.'natTransP$d'| A__questionmark_v0) (|tptp.'natTransExt$d'| A__questionmark_v0)) (|tptp.'natTrans$d'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (= (|tptp.'fun_app$e'| |tptp.'natTrans$'| A__questionmark_v0) (and (|tptp.'fun_app$e'| |tptp.'natTransP$'| A__questionmark_v0) (|tptp.'fun_app$e'| |tptp.'natTransExt$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|)) (= (|tptp.'natTrans$a'| A__questionmark_v0) (and (|tptp.'natTransP$a'| A__questionmark_v0) (|tptp.'natTransExt$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (= (|tptp.'natTrans$b'| A__questionmark_v0) (and (|tptp.'natTransP$b'| A__questionmark_v0) (|tptp.'natTransExt$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (= (|tptp.'natTrans$c'| A__questionmark_v0) (and (|tptp.'natTransP$c'| A__questionmark_v0) (|tptp.'natTransExt$c'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (= (|tptp.'natTrans$d'| A__questionmark_v0) (and (|tptp.'natTransP$d'| A__questionmark_v0) (|tptp.'natTransExt$d'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'homFtorContra$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'makeFtor$'| (|tptp.'homFtorContra$a'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'category$'| (|tptp.'catExp$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (|tptp.'fun_app$f'| |tptp.'functor$'| (|tptp.'homFtor$'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'category$a'| A__questionmark_v1)) (|tptp.'category$b'| (|tptp.'catExp$b'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'category$c'| A__questionmark_v1)) (|tptp.'category$d'| (|tptp.'catExp$c'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'category$a'| A__questionmark_v1)) (|tptp.'category$'| (|tptp.'catExp$'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'category$c'| A__questionmark_v1)) (|tptp.'category$e'| (|tptp.'catExp$d'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'category$b'| A__questionmark_v1)) (|tptp.'category$f'| (|tptp.'catExp$e'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (and (|tptp.'category$b'| A__questionmark_v0) (|tptp.'category$a'| A__questionmark_v1)) (|tptp.'category$g'| (|tptp.'catExp$f'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (and (|tptp.'category$b'| A__questionmark_v0) (|tptp.'category$c'| A__questionmark_v1)) (|tptp.'category$h'| (|tptp.'catExp$g'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'category$b'| A__questionmark_v1)) (|tptp.'category$i'| (|tptp.'catExp$h'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'category$'| A__questionmark_v1)) (|tptp.'category$j'| (|tptp.'catExp$i'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (and (|tptp.'category$'| A__questionmark_v0) (|tptp.'category$a'| A__questionmark_v1)) (|tptp.'category$k'| (|tptp.'catExp$j'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'|)) (=> (|tptp.'functorM$e'| A__questionmark_v0) (|tptp.'functor$a'| (|tptp.'makeFtor$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|)) (=> (|tptp.'functorM$a'| A__questionmark_v0) (|tptp.'functor$b'| (|tptp.'makeFtor$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|)) (=> (|tptp.'functorM$b'| A__questionmark_v0) (|tptp.'functor$c'| (|tptp.'makeFtor$c'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'fun_app$f'| |tptp.'functorM$'| A__questionmark_v0) (|tptp.'fun_app$f'| |tptp.'functor$'| (|tptp.'makeFtor$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'functorM$c'| A__questionmark_v0) (|tptp.'functor$d'| (|tptp.'makeFtor$d'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (=> (|tptp.'category$'| A__questionmark_v0) (|tptp.'category$'| (|tptp.'oppositeCategory$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (=> (|tptp.'category$b'| A__questionmark_v0) (|tptp.'category$b'| (|tptp.'oppositeCategory$c'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'category$a'| 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|tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'member$i'| A__questionmark_v3 (|tptp.'obj$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'member$d'| A__questionmark_v3 (|tptp.'obj$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (|tptp.'fun_app$e'| |tptp.'natTrans$'| A__questionmark_v0) (|tptp.'fun_app$e'| |tptp.'natTransExt$'| 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(|tptp.'natTransP$c'| (|tptp.'idNatTrans$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'|)) (=> (|tptp.'functor$a'| A__questionmark_v0) (|tptp.'natTransP$d'| (|tptp.'idNatTrans$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'fun_app$f'| |tptp.'functor$'| A__questionmark_v0) (|tptp.'fun_app$e'| |tptp.'natTransP$'| (|tptp.'idNatTrans$c'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'functor$d'| A__questionmark_v0) (|tptp.'natTransP$b'| (|tptp.'idNatTrans$d'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (=> (|tptp.'category$'| A__questionmark_v0) (|tptp.'functorM$k'| (|tptp.'identityFunctor$d'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (=> (|tptp.'category$b'| A__questionmark_v0) (|tptp.'functorM$l'| (|tptp.'identityFunctor$e'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'category$c'| A__questionmark_v0) (|tptp.'functorM$e'| (|tptp.'identityFunctor$f'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'category$a'| A__questionmark_v0) (|tptp.'functorM$a'| (|tptp.'identityFunctor$g'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (=> (|tptp.'category$'| A__questionmark_v0) (|tptp.'preFunctor$k'| (|tptp.'identityFunctor$d'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$'|)) (=> (|tptp.'category$b'| A__questionmark_v0) (|tptp.'preFunctor$l'| (|tptp.'identityFunctor$e'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'category$c'| A__questionmark_v0) (|tptp.'preFunctor$e'| (|tptp.'identityFunctor$f'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'category$a'| A__questionmark_v0) (|tptp.'preFunctor$a'| (|tptp.'identityFunctor$g'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'|)) (=> (and (|tptp.'functorM$e'| A__questionmark_v0) (|tptp.'functorExt$'| A__questionmark_v0)) (|tptp.'functor$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (|tptp.'fun_app$f'| |tptp.'functorM$'| A__questionmark_v0) (|tptp.'fun_app$f'| |tptp.'functorExt$a'| A__questionmark_v0)) (|tptp.'fun_app$f'| |tptp.'functor$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|)) (=> (and (|tptp.'functorM$a'| A__questionmark_v0) (|tptp.'functorExt$b'| A__questionmark_v0)) (|tptp.'functor$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|)) (=> (and (|tptp.'functorM$b'| A__questionmark_v0) (|tptp.'functorExt$c'| A__questionmark_v0)) (|tptp.'functor$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (|tptp.'functorM$c'| A__questionmark_v0) (|tptp.'functorExt$d'| A__questionmark_v0)) (|tptp.'functor$d'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'category$c'| A__questionmark_v0))) (|tptp.'category$a'| |tptp.'set$'|) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'identityFunctor$b'| A__questionmark_v0) (|tptp.'makeFtor$a'| (|tptp.'identityFunctor$f'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'category$a'| A__questionmark_v0) (|tptp.'functor$m'| (|tptp.'unitFunctor$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'preFunctor$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v0)))) (= (|tptp.'mapO$'| (|tptp.'makeFtor$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$f'| |tptp.'preFunctor$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v0)))) (= (|tptp.'mapO$a'| (|tptp.'makeFtor$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'functor_abbrev$f'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'member$i'| A__questionmark_v3 (|tptp.'obj$b'| A__questionmark_v1))) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v1) A__questionmark_v3)) (|tptp.'id$'| A__questionmark_v2 (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'functor_abbrev$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'member$i'| A__questionmark_v3 (|tptp.'obj$b'| A__questionmark_v1))) (= (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v1) A__questionmark_v3)) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v2) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (let ((_let_1 (|tptp.'identityFunctor$f'| A__questionmark_v0))) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'catDom$b'| _let_1)))) (= (|tptp.'mapO$f'| _let_1 A__questionmark_v1) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'identityFunctor$g'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| (|tptp.'catDom$c'| _let_1)))) (= (|tptp.'fun_app$'| (|tptp.'mapO$d'| _let_1) A__questionmark_v1) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'catExp$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|) (|tptp.'fun_app$q'| (|tptp.'yFtorNT$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'homFtorContra$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v1))) (|tptp.'homFtorContra$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v1))))) (= |tptp.'set$'| (|tptp.'makeCat$'| |tptp.'set$a'|)) (forall ((A__questionmark_v0 |tptp.'B$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'member$h'| A__questionmark_v0 (|tptp.'mor$'| A__questionmark_v1)) (= (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v1) A__questionmark_v0) A__questionmark_v2) (= (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v1) A__questionmark_v0) A__questionmark_v3)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v1 A__questionmark_v0 A__questionmark_v2) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'member$d'| A__questionmark_v0 (|tptp.'mor$b'| A__questionmark_v1)) (= (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v1) A__questionmark_v0) A__questionmark_v2) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v1) A__questionmark_v0) A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v1 A__questionmark_v0 A__questionmark_v2) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| A__questionmark_v1)) (= (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| (|tptp.'makeCat$a'| A__questionmark_v1)) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'member$d'| A__questionmark_v0 (|tptp.'obj$a'| A__questionmark_v1)) (= (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'id$a'| (|tptp.'makeCat$'| A__questionmark_v1)) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'member$d'| A__questionmark_v0 (|tptp.'mor$b'| A__questionmark_v1)) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'cod$a'| (|tptp.'makeCat$'| A__questionmark_v1)) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'member$d'| A__questionmark_v0 (|tptp.'mor$b'| A__questionmark_v1)) (= (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'dom$a'| (|tptp.'makeCat$'| A__questionmark_v1)) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (= (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (= (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (= (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (and (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0)) (= (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (= (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (and (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)) (= (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (=> (and (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0)) (= (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v3)) false)) false)) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (=> (and (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)) (= (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v3)) false)) false)) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'obj$b'| (|tptp.'makeCat$a'| A__questionmark_v0)) (|tptp.'obj$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= (|tptp.'obj$a'| (|tptp.'makeCat$'| A__questionmark_v0)) (|tptp.'obj$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= (|tptp.'mor$b'| (|tptp.'makeCat$'| A__questionmark_v0)) (|tptp.'mor$b'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'makeCat$a'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'makeCat$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (let ((_let_1 (|tptp.'id$b'| A__questionmark_v0))) (let ((_let_2 (|tptp.'obj$b'| A__questionmark_v0))) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 _let_2) (|tptp.'member$i'| A__questionmark_v2 _let_2) (= (|tptp.'fun_app$r'| _let_1 A__questionmark_v1) (|tptp.'fun_app$r'| _let_1 A__questionmark_v2))) (= A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'id$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'obj$a'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 _let_2) (|tptp.'member$d'| A__questionmark_v2 _let_2) (= (|tptp.'fun_app$'| _let_1 A__questionmark_v1) (|tptp.'fun_app$'| _let_1 A__questionmark_v2))) (= A__questionmark_v1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'catDom$a'| (|tptp.'homFtorContra$'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'oppositeCategory$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (let ((_let_1 (|tptp.'obj$b'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1)) (= (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$'| (|tptp.'id$a'| |tptp.'set$'|) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (let ((_let_1 (|tptp.'obj$b'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1)) (= (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$'| (|tptp.'id$a'| |tptp.'set$a'|) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (|tptp.'member$h'| (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mor$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| A__questionmark_v0))) (|tptp.'member$d'| (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mor$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'B$'|) (A__questionmark_v1 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'member$h'| A__questionmark_v0 (|tptp.'mor$'| (|tptp.'catDom$'| A__questionmark_v1))) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| (|tptp.'makeFtor$d'| A__questionmark_v1)) A__questionmark_v0) (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v1) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| |tptp.'set$'| (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v2))) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| |tptp.'set$'| (|tptp.'homFtorMapContra$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1) (|tptp.'homSet$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1)) (|tptp.'homSet$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| |tptp.'set$a'| (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v2))) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'member$i'| (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0))) (|tptp.'member$d'| (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0))) (|tptp.'member$i'| (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0))) (|tptp.'member$d'| (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0)) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v2)))) (|tptp.'fun_app$b'| (|tptp.'elem$'| (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) (|tptp.'zF2mor$'| A__questionmark_v0 A__questionmark_v3)) A__questionmark_v2))) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (let ((_let_1 (|tptp.'catDom$a'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$f'| |tptp.'functor$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| _let_1))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$a'| A__questionmark_v0) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$a'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'dom$'| _let_1) A__questionmark_v1))) (|tptp.'mapO$a'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'cod$'| _let_1) A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (let ((_let_1 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'functor$d'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| _let_1))) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'dom$'| _let_1) A__questionmark_v1))) (|tptp.'mapO$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'cod$'| _let_1) A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| |tptp.'set$'|) (|tptp.'homFtorMapContra$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1)) (|tptp.'homSet$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'dom$a'| |tptp.'set$'|) (|tptp.'homFtorMapContra$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1)) (|tptp.'homSet$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'dom$a'| |tptp.'set$'|) (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'member$h'| A__questionmark_v2 (|tptp.'mor$'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| |tptp.'set$'|) (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (let ((_let_1 (|tptp.'yFtor$a'| A__questionmark_v1))) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'catDom$'| _let_1))) (|tptp.'lSCategory$'| A__questionmark_v1)) (= (|tptp.'mapO$'| _let_1 A__questionmark_v0) (|tptp.'homFtorContra$'| A__questionmark_v1 A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (let ((_let_1 (|tptp.'cod$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$'| |tptp.'set$'|))) (let ((_let_3 (|tptp.'dom$'| A__questionmark_v0))) (let ((_let_4 (|tptp.'mor$'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 _let_4) (|tptp.'member$h'| A__questionmark_v2 _let_4)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 (|tptp.'homFtorMapContra$'| A__questionmark_v0 A__questionmark_v2 (|tptp.'fun_app$t'| _let_3 A__questionmark_v1))) (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v0 (|tptp.'fun_app$t'| _let_3 A__questionmark_v2)) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v0 (|tptp.'fun_app$t'| _let_1 A__questionmark_v2)) A__questionmark_v1)) (|tptp.'homFtorMapContra$'| A__questionmark_v0 A__questionmark_v2 (|tptp.'fun_app$t'| _let_1 A__questionmark_v1)))))))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|) (A__questionmark_v4 |tptp.'B$'|) (A__questionmark_v5 |tptp.'A$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v4 A__questionmark_v3) A__questionmark_v5)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v4) A__questionmark_v2) A__questionmark_v5))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|) (A__questionmark_v4 |tptp.'ZF$'|) (A__questionmark_v5 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v4 A__questionmark_v3) A__questionmark_v5)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v4) A__questionmark_v2) A__questionmark_v5))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'functorM$c'| (|tptp.'yFtor$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'preFunctor$c'| (|tptp.'yFtor$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'yFtor$'| A__questionmark_v0) (|tptp.'makeFtor$d'| (|tptp.'yFtor$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (let ((_let_1 (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v1))) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) _let_1) _let_1) _let_1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) A__questionmark_v1))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) _let_1) _let_1) _let_1)))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (let ((_let_1 (|tptp.'yFtor$a'| A__questionmark_v1))) (let ((_let_2 (|tptp.'catDom$'| _let_1))) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| _let_2)) (|tptp.'lSCategory$'| A__questionmark_v1)) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| _let_1) (|tptp.'fun_app$r'| (|tptp.'id$b'| _let_2) A__questionmark_v0)) (|tptp.'id$'| (|tptp.'catCod$'| _let_1) (|tptp.'homFtorContra$'| A__questionmark_v1 A__questionmark_v0))))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= (|tptp.'functor_abbrev$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (and (|tptp.'fun_app$f'| |tptp.'functor$'| A__questionmark_v0) (= (|tptp.'catDom$a'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'catCod$a'| A__questionmark_v0) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (and (|tptp.'functor_abbrev$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (=> (and (|tptp.'fun_app$f'| |tptp.'functor$'| A__questionmark_v0) (= (|tptp.'catDom$a'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'catCod$a'| A__questionmark_v0) A__questionmark_v2)) false)) false)) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1))) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1))) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (=> (and (|tptp.'functor$d'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| (|tptp.'catDom$'| A__questionmark_v0)))) (|tptp.'member$'| (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mor$a'| (|tptp.'catCod$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'preFunctor$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v0)))) (exists ((A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catCod$'| A__questionmark_v0))) (and (|tptp.'member$a'| A__questionmark_v2 (|tptp.'obj$'| _let_1)) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| (|tptp.'catDom$'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'id$'| _let_1 A__questionmark_v2))))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$f'| |tptp.'functorM$'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$a'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$a'| A__questionmark_v0) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'functorM$c'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$a'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$a'| A__questionmark_v0) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v3)))) (|tptp.'fun_app$f'| |tptp.'functorM_axioms$d'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v3)))) (|tptp.'functorM_axioms$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'fun_app$f'| |tptp.'functorM_axioms$d'| A__questionmark_v0) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$a'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$a'| A__questionmark_v0) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'functorM_axioms$c'| A__questionmark_v0) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catCod$'| A__questionmark_v0))) (let ((_let_3 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'functor$d'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| _let_3))) (= (|tptp.'fun_app$q'| _let_1 (|tptp.'fun_app$r'| (|tptp.'id$b'| _let_3) (|tptp.'fun_app$t'| (|tptp.'cod$'| _let_3) A__questionmark_v1))) (|tptp.'id$'| _let_2 (|tptp.'cod$b'| _let_2 (|tptp.'fun_app$q'| _let_1 A__questionmark_v1))))))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (let ((_let_1 (|tptp.'catDom$a'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$f'| |tptp.'functor$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| _let_1))) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| (|tptp.'catCod$a'| A__questionmark_v0)) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$a'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'cod$'| _let_1) A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (let ((_let_1 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'functor$d'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| _let_1))) (= (|tptp.'cod$b'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'cod$'| _let_1) A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catCod$'| A__questionmark_v0))) (let ((_let_3 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'functor$d'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| _let_3))) (= (|tptp.'fun_app$q'| _let_1 (|tptp.'fun_app$r'| (|tptp.'id$b'| _let_3) (|tptp.'fun_app$t'| (|tptp.'dom$'| _let_3) A__questionmark_v1))) (|tptp.'id$'| _let_2 (|tptp.'dom$b'| _let_2 (|tptp.'fun_app$q'| _let_1 A__questionmark_v1))))))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (let ((_let_1 (|tptp.'catDom$a'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$f'| |tptp.'functor$'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| _let_1))) (= (|tptp.'fun_app$'| (|tptp.'dom$a'| (|tptp.'catCod$a'| A__questionmark_v0)) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$a'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'dom$'| _let_1) A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (let ((_let_1 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'functor$d'| A__questionmark_v0) (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| _let_1))) (= (|tptp.'dom$b'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'dom$'| _let_1) A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'catCod$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catDom$a'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$f'| |tptp.'preFunctor$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| _let_2)) (|tptp.'member$d'| A__questionmark_v2 (|tptp.'obj$a'| _let_1)) (= (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| _let_2) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'id$a'| _let_1) A__questionmark_v2))) (= (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catCod$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'preFunctor$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| _let_2)) (|tptp.'member$a'| A__questionmark_v2 (|tptp.'obj$'| _let_1)) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| _let_2) A__questionmark_v1)) (|tptp.'id$'| _let_1 A__questionmark_v2))) (= (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (let ((_let_1 (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v1))) (let ((_let_2 (|tptp.'catCod$a'| A__questionmark_v0))) (let ((_let_3 (|tptp.'catDom$a'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$f'| |tptp.'preFunctor$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| _let_3))) (and (|tptp.'member$d'| _let_1 (|tptp.'obj$a'| _let_2)) (= (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| _let_3) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'id$a'| _let_2) _let_1)))))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (let ((_let_1 (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v1))) (let ((_let_2 (|tptp.'catCod$'| A__questionmark_v0))) (let ((_let_3 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'preFunctor$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| _let_3))) (and (|tptp.'member$a'| _let_1 (|tptp.'obj$'| _let_2)) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| _let_3) A__questionmark_v1)) (|tptp.'id$'| _let_2 _let_1)))))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (and (= (|tptp.'obj$b'| A__questionmark_v0) (|tptp.'obj$b'| A__questionmark_v1)) (= (|tptp.'mor$'| A__questionmark_v0) (|tptp.'mor$'| A__questionmark_v1)) (= (|tptp.'dom$'| A__questionmark_v0) (|tptp.'dom$'| A__questionmark_v1)) (= (|tptp.'cod$'| A__questionmark_v0) (|tptp.'cod$'| A__questionmark_v1)) (= (|tptp.'id$b'| A__questionmark_v0) (|tptp.'id$b'| A__questionmark_v1)) (= (|tptp.'comp$a'| A__questionmark_v0) (|tptp.'comp$a'| A__questionmark_v1)) (= (|tptp.'mor2ZF$'| A__questionmark_v0) (|tptp.'mor2ZF$'| A__questionmark_v1)) (= (|tptp.'more$'| A__questionmark_v0) (|tptp.'more$'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v0)))) (=> (and (|tptp.'fun_app$f'| |tptp.'equivalence$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$a'| A__questionmark_v0) A__questionmark_v3 (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v2))) (exists ((A__questionmark_v4 |tptp.'B$'|)) (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$a'| A__questionmark_v0) A__questionmark_v4 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) A__questionmark_v4) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v0)))) (=> (and (|tptp.'equivalence$a'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'catCod$'| A__questionmark_v0) A__questionmark_v3 (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v2))) (exists ((A__questionmark_v4 |tptp.'B$'|)) (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$'| A__questionmark_v0) A__questionmark_v4 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v4) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (and (= (|tptp.'obj$b'| A__questionmark_v0) (|tptp.'obj$b'| A__questionmark_v1)) (= (|tptp.'mor$'| A__questionmark_v0) (|tptp.'mor$'| A__questionmark_v1)) (= (|tptp.'dom$'| A__questionmark_v0) (|tptp.'dom$'| A__questionmark_v1)) (= (|tptp.'cod$'| A__questionmark_v0) (|tptp.'cod$'| A__questionmark_v1)) (= (|tptp.'id$b'| A__questionmark_v0) (|tptp.'id$b'| A__questionmark_v1)) (= (|tptp.'comp$a'| A__questionmark_v0) (|tptp.'comp$a'| A__questionmark_v1)) (= (|tptp.'more$a'| A__questionmark_v0) (|tptp.'more$a'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (and (= (|tptp.'obj$a'| A__questionmark_v0) (|tptp.'obj$a'| A__questionmark_v1)) (= (|tptp.'mor$b'| A__questionmark_v0) (|tptp.'mor$b'| A__questionmark_v1)) (= (|tptp.'dom$a'| A__questionmark_v0) (|tptp.'dom$a'| A__questionmark_v1)) (= (|tptp.'cod$a'| A__questionmark_v0) (|tptp.'cod$a'| A__questionmark_v1)) (= (|tptp.'id$a'| A__questionmark_v0) (|tptp.'id$a'| A__questionmark_v1)) (= (|tptp.'comp$'| A__questionmark_v0) (|tptp.'comp$'| A__questionmark_v1)) (= (|tptp.'more$b'| A__questionmark_v0) (|tptp.'more$b'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'B$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v0) (|tptp.'homSet$'| A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v1) A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| (|tptp.'homFtorMapContra$'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3)) A__questionmark_v0) (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v1) (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v1) A__questionmark_v2) (|tptp.'zF2mor$'| A__questionmark_v1 A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| |tptp.'set$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'elem$'| (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| A__questionmark_v0) A__questionmark_v3)) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| (|tptp.'fun_app$'| (|tptp.'id$a'| |tptp.'set$'|) A__questionmark_v1)) A__questionmark_v0) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|) (A__questionmark_v4 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'equivalence$a'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| _let_2 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| _let_2 A__questionmark_v4 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$q'| _let_1 A__questionmark_v1) (|tptp.'fun_app$q'| _let_1 A__questionmark_v4))) (= A__questionmark_v1 A__questionmark_v4))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (|tptp.'equivalence$a'| A__questionmark_v0) (|tptp.'member$a'| A__questionmark_v1 (|tptp.'obj$'| (|tptp.'catCod$'| A__questionmark_v0)))) (exists ((A__questionmark_v2 |tptp.'A$'|)) (and (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v0))) (|tptp.'fun_app$f'| (|tptp.'objIso$'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$f'| |tptp.'equivalence$'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| (|tptp.'catCod$a'| A__questionmark_v0)))) (exists ((A__questionmark_v2 |tptp.'A$'|)) (and (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'objIso$a'| (|tptp.'catCod$a'| A__questionmark_v0) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'B$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catDom$a'| A__questionmark_v1))) (=> (and (|tptp.'member$h'| A__questionmark_v0 (|tptp.'mor$'| (|tptp.'catDom$b'| (|tptp.'functorComp$'| A__questionmark_v1 A__questionmark_v2)))) (|tptp.'functor_comp_def$'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catCod$b'| A__questionmark_v2) (|tptp.'mapM$e'| A__questionmark_v2 (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v1) A__questionmark_v0)) (|tptp.'mapO$e'| A__questionmark_v2 (|tptp.'mapO$a'| A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'dom$'| _let_1) A__questionmark_v0)))) (|tptp.'mapO$e'| A__questionmark_v2 (|tptp.'mapO$a'| A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'cod$'| _let_1) A__questionmark_v0))))))) (forall ((A__questionmark_v0 |tptp.'B$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catDom$a'| A__questionmark_v1))) (let ((_let_2 (|tptp.'mapO$d'| A__questionmark_v2))) (=> (and (|tptp.'member$h'| A__questionmark_v0 (|tptp.'mor$'| (|tptp.'catDom$a'| (|tptp.'functorComp$a'| A__questionmark_v1 A__questionmark_v2)))) (|tptp.'functor_comp_def$a'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$c'| A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'mapM$d'| A__questionmark_v2) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v1) A__questionmark_v0)) (|tptp.'fun_app$'| _let_2 (|tptp.'mapO$a'| A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'dom$'| _let_1) A__questionmark_v0)))) (|tptp.'fun_app$'| _let_2 (|tptp.'mapO$a'| A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'cod$'| _let_1) A__questionmark_v0)))))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catDom$d'| A__questionmark_v1))) (=> (and (|tptp.'member$d'| A__questionmark_v0 (|tptp.'mor$b'| (|tptp.'catDom$c'| (|tptp.'functorComp$b'| A__questionmark_v1 A__questionmark_v2)))) (|tptp.'fun_app$f'| (|tptp.'functor_comp_def$b'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$a'| A__questionmark_v2) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v2) (|tptp.'mapM$e'| A__questionmark_v1 A__questionmark_v0)) (|tptp.'mapO$a'| A__questionmark_v2 (|tptp.'mapO$e'| A__questionmark_v1 (|tptp.'fun_app$'| (|tptp.'dom$a'| _let_1) A__questionmark_v0)))) (|tptp.'mapO$a'| A__questionmark_v2 (|tptp.'mapO$e'| A__questionmark_v1 (|tptp.'fun_app$'| (|tptp.'cod$a'| _let_1) A__questionmark_v0))))))) (forall ((A__questionmark_v0 |tptp.'B$'|) (A__questionmark_v1 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catDom$'| A__questionmark_v1))) (=> (and (|tptp.'member$h'| A__questionmark_v0 (|tptp.'mor$'| (|tptp.'catDom$b'| (|tptp.'functorComp$c'| A__questionmark_v1 A__questionmark_v2)))) (|tptp.'functor_comp_def$c'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catCod$d'| A__questionmark_v2) (|tptp.'mapM$c'| A__questionmark_v2 (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v1) A__questionmark_v0)) (|tptp.'mapO$c'| A__questionmark_v2 (|tptp.'mapO$'| A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'dom$'| _let_1) A__questionmark_v0)))) (|tptp.'mapO$c'| A__questionmark_v2 (|tptp.'mapO$'| A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'cod$'| _let_1) A__questionmark_v0))))))) (forall ((A__questionmark_v0 |tptp.'B$'|) (A__questionmark_v1 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catDom$'| A__questionmark_v1))) (=> (and (|tptp.'member$h'| A__questionmark_v0 (|tptp.'mor$'| (|tptp.'catDom$a'| (|tptp.'functorComp$d'| A__questionmark_v1 A__questionmark_v2)))) (|tptp.'functor_comp_def$d'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$e'| A__questionmark_v2) (|tptp.'mapM$g'| A__questionmark_v2 (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v1) A__questionmark_v0)) (|tptp.'mapO$g'| A__questionmark_v2 (|tptp.'mapO$'| A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'dom$'| _let_1) A__questionmark_v0)))) (|tptp.'mapO$g'| A__questionmark_v2 (|tptp.'mapO$'| A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'cod$'| _let_1) A__questionmark_v0))))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catDom$d'| A__questionmark_v1))) (=> (and (|tptp.'member$d'| A__questionmark_v0 (|tptp.'mor$b'| (|tptp.'catDom$e'| (|tptp.'functorComp$e'| A__questionmark_v1 A__questionmark_v2)))) (|tptp.'functor_comp_def$e'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'catCod$'| A__questionmark_v2) (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v2) (|tptp.'mapM$e'| A__questionmark_v1 A__questionmark_v0)) (|tptp.'mapO$'| A__questionmark_v2 (|tptp.'mapO$e'| A__questionmark_v1 (|tptp.'fun_app$'| (|tptp.'dom$a'| _let_1) A__questionmark_v0)))) (|tptp.'mapO$'| A__questionmark_v2 (|tptp.'mapO$e'| A__questionmark_v1 (|tptp.'fun_app$'| (|tptp.'cod$a'| _let_1) A__questionmark_v0))))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= A__questionmark_v0 (|tptp.'category_ext$'| (|tptp.'obj$b'| A__questionmark_v0) (|tptp.'mor$'| A__questionmark_v0) (|tptp.'dom$'| A__questionmark_v0) (|tptp.'cod$'| A__questionmark_v0) (|tptp.'id$b'| A__questionmark_v0) (|tptp.'comp$a'| A__questionmark_v0) (|tptp.'more$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= A__questionmark_v0 (|tptp.'category_ext$a'| (|tptp.'obj$a'| A__questionmark_v0) (|tptp.'mor$b'| A__questionmark_v0) (|tptp.'dom$a'| A__questionmark_v0) (|tptp.'cod$a'| A__questionmark_v0) (|tptp.'id$a'| A__questionmark_v0) (|tptp.'comp$'| A__questionmark_v0) (|tptp.'more$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catDom$'| A__questionmark_v0))) (=> (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| _let_2 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$q'| _let_1 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| _let_2) A__questionmark_v1) A__questionmark_v2)) (|tptp.'comp$b'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'fun_app$q'| _let_1 A__questionmark_v1) (|tptp.'fun_app$q'| _let_1 A__questionmark_v2))))))) (forall ((A__questionmark_v1 |tptp.'A$'|)) (=> (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v0))) (exists ((A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catCod$'| A__questionmark_v0))) (and (|tptp.'member$a'| A__questionmark_v2 (|tptp.'obj$'| _let_1)) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| (|tptp.'catDom$'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'id$'| _let_1 A__questionmark_v2))))))) (|tptp.'category$c'| (|tptp.'catDom$'| A__questionmark_v0)) (|tptp.'category$'| (|tptp.'catCod$'| A__questionmark_v0))) (|tptp.'preFunctor$c'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_set$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v6 |tptp.'Unit$'|) (A__questionmark_v7 |tptp.'ZF_set$'|) (A__questionmark_v8 |tptp.'ZF_set$'|) (A__questionmark_v9 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v10 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v11 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v12 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v13 |tptp.'Unit$'|)) (= (= (|tptp.'category_ext$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6) (|tptp.'category_ext$a'| A__questionmark_v7 A__questionmark_v8 A__questionmark_v9 A__questionmark_v10 A__questionmark_v11 A__questionmark_v12 A__questionmark_v13)) (and (= A__questionmark_v0 A__questionmark_v7) (= A__questionmark_v1 A__questionmark_v8) (= A__questionmark_v2 A__questionmark_v9) (= A__questionmark_v3 A__questionmark_v10) (= A__questionmark_v4 A__questionmark_v11) (= A__questionmark_v5 A__questionmark_v12) (= A__questionmark_v6 A__questionmark_v13)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'mor$b'| A__questionmark_v1))) (=> (and (|tptp.'member$d'| A__questionmark_v0 _let_1) (|tptp.'member$d'| A__questionmark_v2 _let_1) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v1) A__questionmark_v2))) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v1 A__questionmark_v0) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (forall ((A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v6 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v7 |tptp.'Unit$'|)) (=> (= A__questionmark_v0 (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7)) false)) false)) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|) (A__questionmark_v4 |tptp.'B$'|) (A__questionmark_v5 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v4 A__questionmark_v3) A__questionmark_v5)) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v4))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|) (A__questionmark_v4 |tptp.'ZF$'|) (A__questionmark_v5 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v4 A__questionmark_v3) A__questionmark_v5)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v4))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| (|tptp.'oppositeCategory$b'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| (|tptp.'oppositeCategory$'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_set$'|) (A__questionmark_v1 |tptp.'B_set$'|) (A__questionmark_v2 |tptp.'B_a_fun$'|) (A__questionmark_v3 |tptp.'B_a_fun$'|) (A__questionmark_v4 |tptp.'A_b_fun$'|) (A__questionmark_v5 |tptp.'B_b_b_fun_fun$'|) (A__questionmark_v6 |tptp.'B_c_LSCategory_ext$'|)) (= (|tptp.'obj$b'| (|tptp.'category_ext$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'ZF_set$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v6 |tptp.'Unit$'|)) (= (|tptp.'obj$a'| (|tptp.'category_ext$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'ZF_set$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v6 |tptp.'Unit$'|)) (= (|tptp.'mor$b'| (|tptp.'category_ext$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6)) A__questionmark_v1)) (forall ((A__questionmark_v0 |tptp.'ZF_set$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v6 |tptp.'Unit$'|)) (= (|tptp.'comp$'| (|tptp.'category_ext$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6)) A__questionmark_v5)) (forall ((A__questionmark_v0 |tptp.'ZF_set$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v6 |tptp.'Unit$'|)) (= (|tptp.'id$a'| (|tptp.'category_ext$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6)) A__questionmark_v4)) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (= (|tptp.'fun_app$b'| (|tptp.'compDefined$'| (|tptp.'makeCat$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'ZF_set$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v6 |tptp.'Unit$'|)) (= (|tptp.'cod$a'| (|tptp.'category_ext$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6)) A__questionmark_v3)) (forall ((A__questionmark_v0 |tptp.'ZF_set$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v6 |tptp.'Unit$'|)) (= (|tptp.'dom$a'| (|tptp.'category_ext$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6)) A__questionmark_v2)) (forall ((A__questionmark_v0 |tptp.'ZF_set$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v6 |tptp.'Unit$'|)) (= (|tptp.'more$b'| (|tptp.'category_ext$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6)) A__questionmark_v6)) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2)) A__questionmark_v3))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| _let_1 A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$b'| _let_1 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'comp$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'fun_app$m'| _let_1 A__questionmark_v1))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 (|tptp.'fun_app$'| _let_2 A__questionmark_v2)) A__questionmark_v3) (|tptp.'fun_app$'| _let_2 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 A__questionmark_v2) A__questionmark_v3))))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|) (A__questionmark_v3 |tptp.'B$'|)) (let ((_let_1 (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| |tptp.'set$a'| (|tptp.'fun_app$p'| _let_1 A__questionmark_v2)) (|tptp.'fun_app$p'| _let_1 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| (|tptp.'makeCat$'| A__questionmark_v0)) A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'makeCat$'| A__questionmark_v0))) (=> (|tptp.'fun_app$b'| (|tptp.'compDefined$'| _let_1 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| _let_1) A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'B$'|) (A__questionmark_v4 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (=> (and (|tptp.'functor_abbrev$f'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v1 A__questionmark_v3) A__questionmark_v4)) (|tptp.'fun_app$e'| (|tptp.'compDefined$b'| A__questionmark_v2 (|tptp.'fun_app$q'| _let_1 A__questionmark_v3)) (|tptp.'fun_app$q'| _let_1 A__questionmark_v4))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'B$'|) (A__questionmark_v4 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$a'| A__questionmark_v0))) (=> (and (|tptp.'functor_abbrev$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v1 A__questionmark_v3) A__questionmark_v4)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v2 (|tptp.'fun_app$p'| _let_1 A__questionmark_v3)) (|tptp.'fun_app$p'| _let_1 A__questionmark_v4))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (let ((_let_1 (|tptp.'yFtorNT$'| A__questionmark_v0))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$e'| (|tptp.'compDefined$b'| (|tptp.'catExp$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|) (|tptp.'fun_app$q'| _let_1 A__questionmark_v1)) (|tptp.'fun_app$q'| _let_1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (let ((_let_1 (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v1))) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 _let_1) _let_1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) A__questionmark_v1))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 _let_1) _let_1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (|tptp.'member$d'| (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'mor$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'cod$a'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (= (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$'| _let_1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'dom$a'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (= (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$'| _let_1 A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'mor$b'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (=> (and (|tptp.'member$d'| A__questionmark_v1 _let_1) (|tptp.'member$d'| A__questionmark_v2 _let_1) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v2))) false)) false))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'mor$b'| A__questionmark_v0))) (= (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (and (|tptp.'member$d'| A__questionmark_v1 _let_1) (|tptp.'member$d'| A__questionmark_v2 _let_1) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v2)))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'B$'|) (A__questionmark_v4 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (=> (and (|tptp.'functor_abbrev$f'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v1 A__questionmark_v3) A__questionmark_v4)) (= (|tptp.'fun_app$q'| _let_1 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v1) A__questionmark_v3) A__questionmark_v4)) (|tptp.'comp$b'| A__questionmark_v2 (|tptp.'fun_app$q'| _let_1 A__questionmark_v3) (|tptp.'fun_app$q'| _let_1 A__questionmark_v4)))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'B$'|) (A__questionmark_v4 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$a'| A__questionmark_v0))) (=> (and (|tptp.'functor_abbrev$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v1 A__questionmark_v3) A__questionmark_v4)) (= (|tptp.'fun_app$p'| _let_1 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v1) A__questionmark_v3) A__questionmark_v4)) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v2) (|tptp.'fun_app$p'| _let_1 A__questionmark_v3)) (|tptp.'fun_app$p'| _let_1 A__questionmark_v4)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v2) (forall ((A__questionmark_v3 |tptp.'B$'|)) (=> (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v1) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v3) A__questionmark_v1) A__questionmark_v3)))) (= (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v2) (forall ((A__questionmark_v3 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v1) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v3) A__questionmark_v1) A__questionmark_v3)))) (= (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (=> (and (|tptp.'functor$d'| A__questionmark_v0) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| (|tptp.'catDom$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$e'| (|tptp.'compDefined$b'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'fun_app$q'| _let_1 A__questionmark_v1)) (|tptp.'fun_app$q'| _let_1 A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'id$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v2))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v2)))) (= A__questionmark_v1 A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'preFunctor$c'| A__questionmark_v0) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| _let_2 A__questionmark_v1) A__questionmark_v2)) (= (|tptp.'fun_app$q'| _let_1 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| _let_2) A__questionmark_v1) A__questionmark_v2)) (|tptp.'comp$b'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'fun_app$q'| _let_1 A__questionmark_v1) (|tptp.'fun_app$q'| _let_1 A__questionmark_v2))))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'functorComp$f'| A__questionmark_v1 A__questionmark_v2))) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v1))) (|tptp.'preFunctor$c'| _let_1) (|tptp.'functor_comp_def$f'| A__questionmark_v1 A__questionmark_v2)) (= (|tptp.'mapO$'| _let_1 A__questionmark_v0) (|tptp.'mapO$h'| A__questionmark_v2 (|tptp.'mapO$'| A__questionmark_v1 A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'functorComp$g'| A__questionmark_v1 A__questionmark_v2))) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v1))) (|tptp.'preFunctor$c'| _let_1) (|tptp.'functor_comp_def$g'| A__questionmark_v1 A__questionmark_v2)) (= (|tptp.'mapO$'| _let_1 A__questionmark_v0) (|tptp.'mapO$b'| A__questionmark_v2 (|tptp.'mapO$a'| A__questionmark_v1 A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'functorComp$h'| A__questionmark_v1 A__questionmark_v2))) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'catDom$b'| A__questionmark_v1))) (|tptp.'preFunctor$c'| _let_1) (|tptp.'functor_comp_def$h'| A__questionmark_v1 A__questionmark_v2)) (= (|tptp.'mapO$'| _let_1 A__questionmark_v0) (|tptp.'mapO$'| A__questionmark_v2 (|tptp.'mapO$f'| A__questionmark_v1 A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'functorComp$d'| A__questionmark_v1 A__questionmark_v2))) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v1))) (|tptp.'fun_app$f'| |tptp.'preFunctor$'| _let_1) (|tptp.'functor_comp_def$d'| A__questionmark_v1 A__questionmark_v2)) (= (|tptp.'mapO$a'| _let_1 A__questionmark_v0) (|tptp.'mapO$g'| A__questionmark_v2 (|tptp.'mapO$'| A__questionmark_v1 A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'functorComp$a'| A__questionmark_v1 A__questionmark_v2))) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v1))) (|tptp.'fun_app$f'| |tptp.'preFunctor$'| _let_1) (|tptp.'functor_comp_def$a'| A__questionmark_v1 A__questionmark_v2)) (= (|tptp.'mapO$a'| _let_1 A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'mapO$d'| A__questionmark_v2) (|tptp.'mapO$a'| A__questionmark_v1 A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'functorComp$i'| A__questionmark_v1 A__questionmark_v2))) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'catDom$b'| A__questionmark_v1))) (|tptp.'fun_app$f'| |tptp.'preFunctor$'| _let_1) (|tptp.'fun_app$f'| (|tptp.'functor_comp_def$i'| A__questionmark_v1) A__questionmark_v2)) (= (|tptp.'mapO$a'| _let_1 A__questionmark_v0) (|tptp.'mapO$a'| A__questionmark_v2 (|tptp.'mapO$f'| A__questionmark_v1 A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'functorComp$e'| A__questionmark_v1 A__questionmark_v2))) (=> (and (|tptp.'member$d'| A__questionmark_v0 (|tptp.'obj$a'| (|tptp.'catDom$d'| A__questionmark_v1))) (|tptp.'preFunctor$d'| _let_1) (|tptp.'functor_comp_def$e'| A__questionmark_v1 A__questionmark_v2)) (= (|tptp.'mapO$b'| _let_1 A__questionmark_v0) (|tptp.'mapO$'| A__questionmark_v2 (|tptp.'mapO$e'| A__questionmark_v1 A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'functorComp$b'| A__questionmark_v1 A__questionmark_v2))) (=> (and (|tptp.'member$d'| A__questionmark_v0 (|tptp.'obj$a'| (|tptp.'catDom$d'| A__questionmark_v1))) (|tptp.'preFunctor$a'| _let_1) (|tptp.'fun_app$f'| (|tptp.'functor_comp_def$b'| A__questionmark_v1) A__questionmark_v2)) (= (|tptp.'fun_app$'| (|tptp.'mapO$d'| _let_1) A__questionmark_v0) (|tptp.'mapO$a'| A__questionmark_v2 (|tptp.'mapO$e'| A__questionmark_v1 A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|) (A__questionmark_v3 |tptp.'B$'|)) (let ((_let_1 (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| |tptp.'set$'|) (|tptp.'fun_app$p'| _let_1 A__questionmark_v2)) (|tptp.'fun_app$p'| _let_1 A__questionmark_v3)) (|tptp.'fun_app$p'| _let_1 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|) (A__questionmark_v3 |tptp.'B$'|)) (let ((_let_1 (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1))) (=> (and (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| |tptp.'set$a'|) (|tptp.'fun_app$p'| _let_1 A__questionmark_v2)) (|tptp.'fun_app$p'| _let_1 A__questionmark_v3)) (|tptp.'fun_app$p'| _let_1 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v2) A__questionmark_v3)))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'preFunctor$c'| A__questionmark_v0) (and (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catDom$'| A__questionmark_v0))) (=> (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| _let_2 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$q'| _let_1 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| _let_2) A__questionmark_v1) A__questionmark_v2)) (|tptp.'comp$b'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'fun_app$q'| _let_1 A__questionmark_v1) (|tptp.'fun_app$q'| _let_1 A__questionmark_v2))))))) (forall ((A__questionmark_v1 |tptp.'A$'|)) (=> (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v0))) (exists ((A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catCod$'| A__questionmark_v0))) (and (|tptp.'member$a'| A__questionmark_v2 (|tptp.'obj$'| _let_1)) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| (|tptp.'catDom$'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'id$'| _let_1 A__questionmark_v2))))))) (|tptp.'category$c'| (|tptp.'catDom$'| A__questionmark_v0)) (|tptp.'category$'| (|tptp.'catCod$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (forall ((A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v0)))) (=> (and (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$a'| A__questionmark_v0) A__questionmark_v3 (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v2))) (exists ((A__questionmark_v4 |tptp.'B$'|)) (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$a'| A__questionmark_v0) A__questionmark_v4 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) A__questionmark_v4) A__questionmark_v3)))))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|) (A__questionmark_v4 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catDom$a'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| _let_2 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| _let_2 A__questionmark_v4 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$p'| _let_1 A__questionmark_v1) (|tptp.'fun_app$p'| _let_1 A__questionmark_v4))) (= A__questionmark_v1 A__questionmark_v4))))) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| (|tptp.'catCod$a'| A__questionmark_v0))) (exists ((A__questionmark_v2 |tptp.'A$'|)) (and (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'objIso$a'| (|tptp.'catCod$a'| A__questionmark_v0) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1)))))) (|tptp.'fun_app$f'| |tptp.'equivalence_axioms$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (forall ((A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v0)))) (=> (and (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'catCod$'| A__questionmark_v0) A__questionmark_v3 (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v2))) (exists ((A__questionmark_v4 |tptp.'B$'|)) (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$'| A__questionmark_v0) A__questionmark_v4 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v4) A__questionmark_v3)))))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|) (A__questionmark_v4 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| _let_2 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| _let_2 A__questionmark_v4 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$q'| _let_1 A__questionmark_v1) (|tptp.'fun_app$q'| _let_1 A__questionmark_v4))) (= A__questionmark_v1 A__questionmark_v4))))) (forall ((A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'member$a'| A__questionmark_v1 (|tptp.'obj$'| (|tptp.'catCod$'| A__questionmark_v0))) (exists ((A__questionmark_v2 |tptp.'A$'|)) (and (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v0))) (|tptp.'fun_app$f'| (|tptp.'objIso$'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1)))))) (|tptp.'equivalence_axioms$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'fun_app$f'| |tptp.'equivalence_axioms$'| A__questionmark_v0) (and (forall ((A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v0)))) (=> (and (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$a'| A__questionmark_v0) A__questionmark_v3 (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v2))) (exists ((A__questionmark_v4 |tptp.'B$'|)) (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$a'| A__questionmark_v0) A__questionmark_v4 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$p'| (|tptp.'mapM$a'| A__questionmark_v0) A__questionmark_v4) A__questionmark_v3)))))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|) (A__questionmark_v4 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catDom$a'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| _let_2 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| _let_2 A__questionmark_v4 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$p'| _let_1 A__questionmark_v1) (|tptp.'fun_app$p'| _let_1 A__questionmark_v4))) (= A__questionmark_v1 A__questionmark_v4))))) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| (|tptp.'catCod$a'| A__questionmark_v0))) (exists ((A__questionmark_v2 |tptp.'A$'|)) (and (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'objIso$a'| (|tptp.'catCod$a'| A__questionmark_v0) (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1)))))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'equivalence_axioms$a'| A__questionmark_v0) (and (forall ((A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v0)))) (=> (and (|tptp.'member$i'| A__questionmark_v1 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'catCod$'| A__questionmark_v0) A__questionmark_v3 (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v2))) (exists ((A__questionmark_v4 |tptp.'B$'|)) (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catDom$'| A__questionmark_v0) A__questionmark_v4 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v4) A__questionmark_v3)))))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|) (A__questionmark_v4 |tptp.'B$'|)) (let ((_let_1 (|tptp.'mapM$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'catDom$'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| _let_2 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| _let_2 A__questionmark_v4 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$q'| _let_1 A__questionmark_v1) (|tptp.'fun_app$q'| _let_1 A__questionmark_v4))) (= A__questionmark_v1 A__questionmark_v4))))) (forall ((A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'member$a'| A__questionmark_v1 (|tptp.'obj$'| (|tptp.'catCod$'| A__questionmark_v0))) (exists ((A__questionmark_v2 |tptp.'A$'|)) (and (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v0))) (|tptp.'fun_app$f'| (|tptp.'objIso$'| (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v1)))))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (and (forall ((A__questionmark_v1 |tptp.'B$'|)) (=> (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0)) (|tptp.'member$i'| (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$b'| A__questionmark_v0)))) (forall ((A__questionmark_v1 |tptp.'B$'|)) (=> (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0)) (|tptp.'member$i'| (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$b'| A__questionmark_v0)))) (forall ((A__questionmark_v1 |tptp.'A$'|)) (=> (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'B$'|)) (=> (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0)) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v1))) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'B$'|)) (=> (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0)) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v1))) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|) (A__questionmark_v3 |tptp.'B$'|)) (let ((_let_1 (|tptp.'comp$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'fun_app$o'| _let_1 A__questionmark_v1))) (=> (and (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_1 (|tptp.'fun_app$n'| _let_2 A__questionmark_v2)) A__questionmark_v3) (|tptp.'fun_app$n'| _let_2 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_1 A__questionmark_v2) A__questionmark_v3))))))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|) (A__questionmark_v4 |tptp.'B$'|) (A__questionmark_v5 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v4 A__questionmark_v3) A__questionmark_v5)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v4) A__questionmark_v2) A__questionmark_v5)))) (|tptp.'category_axioms$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (and (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)) (|tptp.'member$d'| (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$a'| A__questionmark_v0)))) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)) (|tptp.'member$d'| (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$a'| A__questionmark_v0)))) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| A__questionmark_v0)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1))) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1))) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'comp$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'fun_app$m'| _let_1 A__questionmark_v1))) (=> (and (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 (|tptp.'fun_app$'| _let_2 A__questionmark_v2)) A__questionmark_v3) (|tptp.'fun_app$'| _let_2 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 A__questionmark_v2) A__questionmark_v3))))))) (forall ((A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|) (A__questionmark_v4 |tptp.'ZF$'|) (A__questionmark_v5 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v4 A__questionmark_v3) A__questionmark_v5)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v4) A__questionmark_v2) A__questionmark_v5)))) (|tptp.'category_axioms$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'category_axioms$'| A__questionmark_v0) (and (forall ((A__questionmark_v1 |tptp.'B$'|)) (=> (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0)) (|tptp.'member$i'| (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$b'| A__questionmark_v0)))) (forall ((A__questionmark_v1 |tptp.'B$'|)) (=> (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0)) (|tptp.'member$i'| (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$b'| A__questionmark_v0)))) (forall ((A__questionmark_v1 |tptp.'A$'|)) (=> (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'B$'|)) (=> (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0)) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v1))) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'B$'|)) (=> (|tptp.'member$h'| A__questionmark_v1 (|tptp.'mor$'| A__questionmark_v0)) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v1))) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|) (A__questionmark_v3 |tptp.'B$'|)) (let ((_let_1 (|tptp.'comp$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'fun_app$o'| _let_1 A__questionmark_v1))) (=> (and (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$k'| (|tptp.'compDefined$a'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_1 (|tptp.'fun_app$n'| _let_2 A__questionmark_v2)) A__questionmark_v3) (|tptp.'fun_app$n'| _let_2 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_1 A__questionmark_v2) A__questionmark_v3))))))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|) (A__questionmark_v4 |tptp.'B$'|) (A__questionmark_v5 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v4 A__questionmark_v3) A__questionmark_v5)) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| (|tptp.'comp$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v4) A__questionmark_v2) A__questionmark_v5)))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= (|tptp.'category_axioms$a'| A__questionmark_v0) (and (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)) (|tptp.'member$d'| (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$a'| A__questionmark_v0)))) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)) (|tptp.'member$d'| (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'obj$a'| A__questionmark_v0)))) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| A__questionmark_v0)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1))) A__questionmark_v1) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1))) A__questionmark_v1))) (forall ((A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'comp$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'fun_app$m'| _let_1 A__questionmark_v1))) (=> (and (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 (|tptp.'fun_app$'| _let_2 A__questionmark_v2)) A__questionmark_v3) (|tptp.'fun_app$'| _let_2 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 A__questionmark_v2) A__questionmark_v3))))))) (forall ((A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|) (A__questionmark_v4 |tptp.'ZF$'|) (A__questionmark_v5 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v4 A__questionmark_v3) A__questionmark_v5)) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v4) A__questionmark_v2) A__questionmark_v5)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= A__questionmark_v0 (|tptp.'category_ext$'| (|tptp.'obj$b'| A__questionmark_v0) (|tptp.'mor$'| A__questionmark_v0) (|tptp.'dom$'| A__questionmark_v0) (|tptp.'cod$'| A__questionmark_v0) (|tptp.'id$b'| A__questionmark_v0) (|tptp.'comp$a'| A__questionmark_v0) (|tptp.'lSCategory_ext$'| (|tptp.'mor2ZF$'| A__questionmark_v0) (|tptp.'more$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_set$'|) (A__questionmark_v1 |tptp.'B_set$'|) (A__questionmark_v2 |tptp.'B_a_fun$'|) (A__questionmark_v3 |tptp.'B_a_fun$'|) (A__questionmark_v4 |tptp.'A_b_fun$'|) (A__questionmark_v5 |tptp.'B_b_b_fun_fun$'|) (A__questionmark_v6 |tptp.'B_ZF_fun$'|) (A__questionmark_v7 |tptp.'C$'|)) (= (|tptp.'mor2ZF$'| (|tptp.'category_ext$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 (|tptp.'lSCategory_ext$'| A__questionmark_v6 A__questionmark_v7))) A__questionmark_v6)) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'category$a'| A__questionmark_v0) (|tptp.'category_axioms$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'category_axioms$'| A__questionmark_v0) (|tptp.'category_axioms$'| (|tptp.'oppositeCategory$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'category_axioms$a'| A__questionmark_v0) (|tptp.'category$a'| (|tptp.'makeCat$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'id$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'inverse_rel$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (=> (and (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 A__questionmark_v2) A__questionmark_v1) (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1)))) false)) false)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'id$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 A__questionmark_v2) A__questionmark_v1) (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1)))) (|tptp.'fun_app$b'| (|tptp.'inverse_rel$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$b'| (|tptp.'compDefined$'| |tptp.'set$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v2) (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| |tptp.'set$'|) A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| A__questionmark_v0) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'id$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$'| A__questionmark_v0))) (= (|tptp.'fun_app$b'| (|tptp.'inverse_rel$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (and (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 A__questionmark_v2) A__questionmark_v1) (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1)))))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'nt_abbrev$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'member$i'| A__questionmark_v3 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v1)))) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'catCod$'| A__questionmark_v2) (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v3) (|tptp.'mapO$'| A__questionmark_v1 A__questionmark_v3)) (|tptp.'mapO$'| A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'nt_abbrev$b'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'member$i'| A__questionmark_v3 (|tptp.'obj$b'| (|tptp.'catDom$b'| A__questionmark_v1)))) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catCod$f'| A__questionmark_v2) (|tptp.'fun_app$r'| (|tptp.'natTransMap$a'| A__questionmark_v0) A__questionmark_v3) (|tptp.'mapO$f'| A__questionmark_v1 A__questionmark_v3)) (|tptp.'mapO$f'| A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$f'| (|tptp.'nt_abbrev$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'member$i'| A__questionmark_v3 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v1)))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$a'| A__questionmark_v2) (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v3) (|tptp.'mapO$a'| A__questionmark_v1 A__questionmark_v3)) (|tptp.'mapO$a'| A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'nt_abbrev$c'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'member$d'| A__questionmark_v3 (|tptp.'obj$a'| (|tptp.'catDom$d'| A__questionmark_v1)))) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'catCod$b'| A__questionmark_v2) (|tptp.'natTransMap$c'| A__questionmark_v0 A__questionmark_v3) (|tptp.'mapO$e'| A__questionmark_v1 A__questionmark_v3)) (|tptp.'mapO$e'| A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'nt_abbrev$d'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'member$d'| A__questionmark_v3 (|tptp.'obj$a'| (|tptp.'catDom$c'| A__questionmark_v1)))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'catCod$c'| A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v0) A__questionmark_v3) (|tptp.'fun_app$'| (|tptp.'mapO$d'| A__questionmark_v1) A__questionmark_v3)) (|tptp.'fun_app$'| (|tptp.'mapO$d'| A__questionmark_v2) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'inverse_rel$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'inverse_rel$'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'inverse_rel$'| A__questionmark_v0 A__questionmark_v1))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| _let_1 A__questionmark_v2) (|tptp.'fun_app$b'| _let_1 A__questionmark_v3)) (= A__questionmark_v2 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'mor$b'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'inverse_rel$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (and (|tptp.'member$d'| A__questionmark_v1 _let_1) (|tptp.'member$d'| A__questionmark_v2 _let_1))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (let ((_let_1 (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v1))) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| A__questionmark_v0))) (|tptp.'fun_app$k'| (|tptp.'inverse_rel$a'| A__questionmark_v0 _let_1) _let_1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) A__questionmark_v1))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'inverse_rel$'| A__questionmark_v0 _let_1) _let_1)))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v4 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'catExp$'| A__questionmark_v1 A__questionmark_v2))) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| A__questionmark_v1)) (|tptp.'fun_app$e'| (|tptp.'compDefined$b'| _let_1 A__questionmark_v3) A__questionmark_v4)) (= (|tptp.'natTransMap$b'| (|tptp.'comp$b'| _let_1 A__questionmark_v3 A__questionmark_v4) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v2) (|tptp.'natTransMap$b'| A__questionmark_v3 A__questionmark_v0)) (|tptp.'natTransMap$b'| A__questionmark_v4 A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v3 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v4 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'catExp$b'| A__questionmark_v1 A__questionmark_v2))) (=> (and (|tptp.'member$d'| A__questionmark_v0 (|tptp.'obj$a'| A__questionmark_v1)) (|tptp.'compDefined$c'| _let_1 A__questionmark_v3 A__questionmark_v4)) (= (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| (|tptp.'comp$c'| _let_1 A__questionmark_v3 A__questionmark_v4)) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v3) A__questionmark_v0)) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v4) A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (= (|tptp.'yMap$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| (|tptp.'natTransMap$b'| A__questionmark_v2 A__questionmark_v1)) (|tptp.'fun_app$p'| (|tptp.'mor2ZF$'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'id$b'| A__questionmark_v0) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'catDom$'| A__questionmark_v1))) (= (|tptp.'natTransMap$'| (|tptp.'idNatTrans$e'| A__questionmark_v1) A__questionmark_v0) (|tptp.'id$'| (|tptp.'catCod$'| A__questionmark_v1) (|tptp.'mapO$'| A__questionmark_v1 A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'catDom$a'| A__questionmark_v1))) (= (|tptp.'natTransMap$b'| (|tptp.'fun_app$u'| |tptp.'idNatTrans$f'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'id$a'| (|tptp.'catCod$a'| A__questionmark_v1)) (|tptp.'mapO$a'| A__questionmark_v1 A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'|)) (=> (|tptp.'member$d'| A__questionmark_v0 (|tptp.'obj$a'| (|tptp.'catDom$c'| A__questionmark_v1))) (= (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| (|tptp.'idNatTrans$g'| A__questionmark_v1)) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'id$a'| (|tptp.'catCod$c'| A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'mapO$d'| A__questionmark_v1) A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'lSCategory_axioms$'| A__questionmark_v0)) (|tptp.'lSCategory$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'lSCategory$'| A__questionmark_v0) (and (|tptp.'category$c'| A__questionmark_v0) (|tptp.'lSCategory_axioms$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (= (|tptp.'catDom$'| A__questionmark_v0) (|tptp.'catDom$'| A__questionmark_v1)) (= (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'catCod$'| A__questionmark_v1)) (= (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'mapM$'| A__questionmark_v1)) (= (|tptp.'more$c'| A__questionmark_v0) (|tptp.'more$c'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'compDefined$'| |tptp.'set$'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| |tptp.'set$'|) A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'lSCategory_axioms$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= A__questionmark_v0 (|tptp.'functor_ext$'| (|tptp.'catDom$'| A__questionmark_v0) (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'more$c'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (=> (and (|tptp.'functor$d'| A__questionmark_v0) (|tptp.'fun_app$k'| (|tptp.'isomorphism$'| (|tptp.'catDom$'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'fun_app$e'| (|tptp.'isomorphism$a'| (|tptp.'catCod$'| A__questionmark_v0)) (|tptp.'fun_app$q'| (|tptp.'mapM$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'functorExt$d'| A__questionmark_v0) (|tptp.'member$m'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'extensional$'| (|tptp.'mor$'| (|tptp.'catDom$'| A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$'|) (A__questionmark_v3 |tptp.'Unit$'|)) (= (|tptp.'mapM$'| (|tptp.'functor_ext$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3)) A__questionmark_v2)) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'mor$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'inverse_rel$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$l'| (|tptp.'objIso$b'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (exists ((A__questionmark_v3 |tptp.'B$'|)) (and (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| A__questionmark_v0 A__questionmark_v3 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$k'| (|tptp.'isomorphism$'| A__questionmark_v0) A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (= (|tptp.'fun_app$b'| (|tptp.'objIso$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (exists ((A__questionmark_v3 |tptp.'ZF$'|)) (and (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| A__questionmark_v0 A__questionmark_v3 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v3))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'lSCategory$'| A__questionmark_v0) (|tptp.'member$e'| (|tptp.'mor2ZF$'| A__questionmark_v0) (|tptp.'extensional$a'| (|tptp.'mor$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'isomorphism$b'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| _let_1 A__questionmark_v1) (|tptp.'fun_app$b'| _let_1 A__questionmark_v2)) (|tptp.'fun_app$b'| _let_1 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'member$m'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'extensional$'| (|tptp.'mor$'| (|tptp.'catDom$'| A__questionmark_v0)))) (|tptp.'functorExt$d'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (|tptp.'functorExt$d'| A__questionmark_v0) (|tptp.'member$m'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'extensional$'| (|tptp.'mor$'| (|tptp.'catDom$'| A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (let ((_let_1 (|tptp.'catDom$'| A__questionmark_v0))) (= (|tptp.'makeFtor$d'| A__questionmark_v0) (|tptp.'functor_ext$'| _let_1 (|tptp.'catCod$'| A__questionmark_v0) (|tptp.'restrict$b'| (|tptp.'mapM$'| A__questionmark_v0) (|tptp.'mor$'| _let_1)) (|tptp.'more$c'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'inverse$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'inverse$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1)) (= (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'inverse$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'isomorphism$b'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| _let_1 A__questionmark_v1)) (|tptp.'fun_app$b'| _let_1 (|tptp.'fun_app$'| (|tptp.'inverse$'| A__questionmark_v0) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'inverse$'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1)) (= (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| _let_1 A__questionmark_v1)) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'inverse_rel$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2)) (= (|tptp.'fun_app$'| (|tptp.'inverse$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'member$d'| (|tptp.'fun_app$'| (|tptp.'inverse$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mor$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'inverse$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'inverse$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'isomorphism$b'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| _let_2 A__questionmark_v1) (|tptp.'fun_app$b'| _let_2 A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 (|tptp.'fun_app$'| _let_1 A__questionmark_v2)) (|tptp.'fun_app$'| _let_1 A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 (|tptp.'fun_app$'| (|tptp.'inverse$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'inverse_rel$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'inverse$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'inverse$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$'| A__questionmark_v0))) (let ((_let_3 (|tptp.'isomorphism$b'| A__questionmark_v0))) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'fun_app$b'| _let_3 A__questionmark_v1) (|tptp.'fun_app$b'| _let_3 A__questionmark_v2)) (= (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 (|tptp.'fun_app$'| _let_1 A__questionmark_v2)) (|tptp.'fun_app$'| _let_1 A__questionmark_v1)))))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'isomorphism$b'| A__questionmark_v0) A__questionmark_v1)) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'inverse$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'dom$a'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'extCategory$'| A__questionmark_v0) (|tptp.'member$n'| (|tptp.'dom$a'| A__questionmark_v0) (|tptp.'extensional$b'| (|tptp.'mor$b'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'extCategory$'| A__questionmark_v0) (|tptp.'member$n'| (|tptp.'cod$a'| A__questionmark_v0) (|tptp.'extensional$b'| (|tptp.'mor$b'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'category$a'| A__questionmark_v0) (|tptp.'extCategory$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'extCategory$a'| A__questionmark_v0) (|tptp.'extCategory$a'| (|tptp.'oppositeCategory$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (|tptp.'extCategory$'| (|tptp.'makeCat$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|)) (= (|tptp.'nTCatDom$'| (|tptp.'fun_app$q'| (|tptp.'yFtorNT$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'oppositeCategory$'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'B$'|)) (let ((_let_1 (|tptp.'fun_app$q'| (|tptp.'yFtorNT$'| A__questionmark_v1) A__questionmark_v2))) (=> (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'nTCatDom$'| _let_1))) (= (|tptp.'natTransMap$b'| _let_1 A__questionmark_v0) (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v1 A__questionmark_v0) A__questionmark_v2))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= (|tptp.'category$a'| A__questionmark_v0) (and (|tptp.'extCategory$'| A__questionmark_v0) (|tptp.'category_axioms$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (and (|tptp.'extCategory$'| A__questionmark_v0) (|tptp.'category_axioms$a'| A__questionmark_v0)) (|tptp.'category$a'| A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (=> (|tptp.'extCategory$a'| A__questionmark_v0) (|tptp.'member$g'| (|tptp.'id$b'| A__questionmark_v0) (|tptp.'extensional$c'| (|tptp.'obj$b'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'extCategory$'| A__questionmark_v0) (|tptp.'member$n'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'extensional$b'| (|tptp.'obj$a'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'nTDom$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'nTCod$'| A__questionmark_v0))) (= (|tptp.'natTransP$d'| A__questionmark_v0) (and (|tptp.'functor$a'| _let_1) (|tptp.'functor$a'| _let_2) (= (|tptp.'nTCatDom$a'| A__questionmark_v0) (|tptp.'catDom$b'| _let_2)) (= (|tptp.'nTCatCod$a'| A__questionmark_v0) (|tptp.'catCod$f'| _let_1)) (forall ((A__questionmark_v1 |tptp.'A$'|)) (=> (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'nTCatDom$a'| A__questionmark_v0))) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatCod$a'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'natTransMap$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$f'| (|tptp.'nTDom$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$f'| (|tptp.'nTCod$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (let ((_let_1 (|tptp.'natTransMap$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$a'| (|tptp.'nTCatCod$a'| A__questionmark_v0)))) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$a'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_2 (|tptp.'mapM$f'| (|tptp.'nTDom$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$r'| _let_1 A__questionmark_v3)) (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_2 (|tptp.'fun_app$r'| _let_1 A__questionmark_v2)) (|tptp.'mapM$f'| (|tptp.'nTCod$'| A__questionmark_v0) A__questionmark_v1)))))))))))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'nTDom$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'nTCod$a'| A__questionmark_v0))) (= (|tptp.'natTransP$c'| A__questionmark_v0) (and (|tptp.'functor$c'| _let_1) (|tptp.'functor$c'| _let_2) (= (|tptp.'nTCatDom$b'| A__questionmark_v0) (|tptp.'catDom$d'| _let_2)) (= (|tptp.'nTCatCod$b'| A__questionmark_v0) (|tptp.'catCod$b'| _let_1)) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| (|tptp.'nTCatDom$b'| A__questionmark_v0))) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatCod$b'| A__questionmark_v0) (|tptp.'natTransMap$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'mapO$e'| (|tptp.'nTDom$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$e'| (|tptp.'nTCod$a'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'comp$a'| (|tptp.'nTCatCod$b'| A__questionmark_v0)))) (=> (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatDom$b'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_1 (|tptp.'mapM$e'| (|tptp.'nTDom$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'natTransMap$c'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_1 (|tptp.'natTransMap$c'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'mapM$e'| (|tptp.'nTCod$a'| A__questionmark_v0) A__questionmark_v1))))))))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'nTDom$b'| A__questionmark_v0))) (let ((_let_2 (|tptp.'nTCod$b'| A__questionmark_v0))) (= (|tptp.'natTransP$b'| A__questionmark_v0) (and (|tptp.'functor$d'| _let_1) (|tptp.'functor$d'| _let_2) (= (|tptp.'nTCatDom$c'| A__questionmark_v0) (|tptp.'catDom$'| _let_2)) (= (|tptp.'nTCatCod$c'| A__questionmark_v0) (|tptp.'catCod$'| _let_1)) (forall ((A__questionmark_v1 |tptp.'A$'|)) (=> (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'nTCatDom$c'| A__questionmark_v0))) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'nTCatCod$c'| A__questionmark_v0) (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'mapO$'| (|tptp.'nTDom$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$'| (|tptp.'nTCod$b'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (let ((_let_1 (|tptp.'nTCatCod$c'| A__questionmark_v0))) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$c'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'comp$b'| _let_1 (|tptp.'fun_app$q'| (|tptp.'mapM$'| (|tptp.'nTDom$b'| A__questionmark_v0)) A__questionmark_v1) (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'comp$b'| _let_1 (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$q'| (|tptp.'mapM$'| (|tptp.'nTCod$b'| A__questionmark_v0)) A__questionmark_v1))))))))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0))) (let ((_let_2 (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0))) (= (|tptp.'fun_app$e'| |tptp.'natTransP$'| A__questionmark_v0) (and (|tptp.'fun_app$f'| |tptp.'functor$'| _let_1) (|tptp.'fun_app$f'| |tptp.'functor$'| _let_2) (= (|tptp.'nTCatDom$'| A__questionmark_v0) (|tptp.'catDom$a'| _let_2)) (= (|tptp.'nTCatCod$'| A__questionmark_v0) (|tptp.'catCod$a'| _let_1)) (forall ((A__questionmark_v1 |tptp.'A$'|)) (=> (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'nTCatDom$'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatCod$'| A__questionmark_v0) (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'mapO$a'| (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$a'| (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (let ((_let_1 (|tptp.'comp$'| (|tptp.'nTCatCod$'| A__questionmark_v0)))) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 (|tptp.'fun_app$p'| (|tptp.'mapM$a'| (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0)) A__questionmark_v1))))))))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'nTDom$d'| A__questionmark_v0))) (let ((_let_2 (|tptp.'nTCod$d'| A__questionmark_v0))) (= (|tptp.'natTransP$a'| A__questionmark_v0) (and (|tptp.'functor$b'| _let_1) (|tptp.'functor$b'| _let_2) (= (|tptp.'nTCatDom$d'| A__questionmark_v0) (|tptp.'catDom$c'| _let_2)) (= (|tptp.'nTCatCod$d'| A__questionmark_v0) (|tptp.'catCod$c'| _let_1)) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| (|tptp.'nTCatDom$d'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatCod$d'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'mapO$d'| (|tptp.'nTDom$d'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'mapO$d'| (|tptp.'nTCod$d'| A__questionmark_v0)) A__questionmark_v1)))) (forall ((A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'natTransMap$d'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$'| (|tptp.'nTCatCod$d'| A__questionmark_v0)))) (=> (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatDom$d'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 (|tptp.'fun_app$'| (|tptp.'mapM$d'| (|tptp.'nTDom$d'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'fun_app$'| _let_1 A__questionmark_v3)) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 (|tptp.'fun_app$'| _let_1 A__questionmark_v2)) (|tptp.'fun_app$'| (|tptp.'mapM$d'| (|tptp.'nTCod$d'| A__questionmark_v0)) A__questionmark_v1)))))))))))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'nTDom$'| A__questionmark_v0))) (let ((_let_2 (|tptp.'nTCod$'| A__questionmark_v0))) (=> (and (|tptp.'functor$a'| _let_1) (|tptp.'functor$a'| _let_2) (= (|tptp.'nTCatDom$a'| A__questionmark_v0) (|tptp.'catDom$b'| _let_2)) (= (|tptp.'nTCatCod$a'| A__questionmark_v0) (|tptp.'catCod$f'| _let_1)) (forall ((A__questionmark_v1 |tptp.'A$'|)) (=> (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'nTCatDom$a'| A__questionmark_v0))) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatCod$a'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'natTransMap$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$f'| (|tptp.'nTDom$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$f'| (|tptp.'nTCod$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (let ((_let_1 (|tptp.'natTransMap$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$a'| (|tptp.'nTCatCod$a'| A__questionmark_v0)))) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$a'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_2 (|tptp.'mapM$f'| (|tptp.'nTDom$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$r'| _let_1 A__questionmark_v3)) (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_2 (|tptp.'fun_app$r'| _let_1 A__questionmark_v2)) (|tptp.'mapM$f'| (|tptp.'nTCod$'| A__questionmark_v0) A__questionmark_v1)))))))) (|tptp.'natTransP$d'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'nTDom$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'nTCod$a'| A__questionmark_v0))) (=> (and (|tptp.'functor$c'| _let_1) (|tptp.'functor$c'| _let_2) (= (|tptp.'nTCatDom$b'| A__questionmark_v0) (|tptp.'catDom$d'| _let_2)) (= (|tptp.'nTCatCod$b'| A__questionmark_v0) (|tptp.'catCod$b'| _let_1)) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| (|tptp.'nTCatDom$b'| A__questionmark_v0))) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatCod$b'| A__questionmark_v0) (|tptp.'natTransMap$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'mapO$e'| (|tptp.'nTDom$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$e'| (|tptp.'nTCod$a'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'comp$a'| (|tptp.'nTCatCod$b'| A__questionmark_v0)))) (=> (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatDom$b'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_1 (|tptp.'mapM$e'| (|tptp.'nTDom$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'natTransMap$c'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| _let_1 (|tptp.'natTransMap$c'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'mapM$e'| (|tptp.'nTCod$a'| A__questionmark_v0) A__questionmark_v1))))))) (|tptp.'natTransP$c'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'nTDom$b'| A__questionmark_v0))) (let ((_let_2 (|tptp.'nTCod$b'| A__questionmark_v0))) (=> (and (|tptp.'functor$d'| _let_1) (|tptp.'functor$d'| _let_2) (= (|tptp.'nTCatDom$c'| A__questionmark_v0) (|tptp.'catDom$'| _let_2)) (= (|tptp.'nTCatCod$c'| A__questionmark_v0) (|tptp.'catCod$'| _let_1)) (forall ((A__questionmark_v1 |tptp.'A$'|)) (=> (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'nTCatDom$c'| A__questionmark_v0))) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'nTCatCod$c'| A__questionmark_v0) (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'mapO$'| (|tptp.'nTDom$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$'| (|tptp.'nTCod$b'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (let ((_let_1 (|tptp.'nTCatCod$c'| A__questionmark_v0))) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$c'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'comp$b'| _let_1 (|tptp.'fun_app$q'| (|tptp.'mapM$'| (|tptp.'nTDom$b'| A__questionmark_v0)) A__questionmark_v1) (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'comp$b'| _let_1 (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$q'| (|tptp.'mapM$'| (|tptp.'nTCod$b'| A__questionmark_v0)) A__questionmark_v1))))))) (|tptp.'natTransP$b'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0))) (let ((_let_2 (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$f'| |tptp.'functor$'| _let_1) (|tptp.'fun_app$f'| |tptp.'functor$'| _let_2) (= (|tptp.'nTCatDom$'| A__questionmark_v0) (|tptp.'catDom$a'| _let_2)) (= (|tptp.'nTCatCod$'| A__questionmark_v0) (|tptp.'catCod$a'| _let_1)) (forall ((A__questionmark_v1 |tptp.'A$'|)) (=> (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'nTCatDom$'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatCod$'| A__questionmark_v0) (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'mapO$a'| (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$a'| (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (let ((_let_1 (|tptp.'comp$'| (|tptp.'nTCatCod$'| A__questionmark_v0)))) (=> (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 (|tptp.'fun_app$p'| (|tptp.'mapM$a'| (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0)) A__questionmark_v1))))))) (|tptp.'fun_app$e'| |tptp.'natTransP$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|)) (let ((_let_1 (|tptp.'nTDom$d'| A__questionmark_v0))) (let ((_let_2 (|tptp.'nTCod$d'| A__questionmark_v0))) (=> (and (|tptp.'functor$b'| _let_1) (|tptp.'functor$b'| _let_2) (= (|tptp.'nTCatDom$d'| A__questionmark_v0) (|tptp.'catDom$c'| _let_2)) (= (|tptp.'nTCatCod$d'| A__questionmark_v0) (|tptp.'catCod$c'| _let_1)) (forall ((A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| (|tptp.'nTCatDom$d'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatCod$d'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'mapO$d'| (|tptp.'nTDom$d'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'mapO$d'| (|tptp.'nTCod$d'| A__questionmark_v0)) A__questionmark_v1)))) (forall ((A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'natTransMap$d'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$'| (|tptp.'nTCatCod$d'| A__questionmark_v0)))) (=> (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatDom$d'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 (|tptp.'fun_app$'| (|tptp.'mapM$d'| (|tptp.'nTDom$d'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'fun_app$'| _let_1 A__questionmark_v3)) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 (|tptp.'fun_app$'| _let_1 A__questionmark_v2)) (|tptp.'fun_app$'| (|tptp.'mapM$d'| (|tptp.'nTCod$d'| A__questionmark_v0)) A__questionmark_v1)))))))) (|tptp.'natTransP$a'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'fun_app$f'| (|tptp.'nt_abbrev$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (and (|tptp.'fun_app$e'| |tptp.'natTrans$'| A__questionmark_v0) (= (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (=> (and (|tptp.'fun_app$f'| (|tptp.'nt_abbrev$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (=> (and (|tptp.'fun_app$e'| |tptp.'natTrans$'| A__questionmark_v0) (= (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0) A__questionmark_v2)) false)) false)) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'natTransP$b'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'nTCatDom$c'| A__questionmark_v0)))) (|tptp.'fun_app$f'| (|tptp.'mapsTo$a'| (|tptp.'nTCatCod$c'| A__questionmark_v0) (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'mapO$'| (|tptp.'nTDom$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$'| (|tptp.'nTCod$b'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'natTransP$d'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'nTCatDom$a'| A__questionmark_v0)))) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatCod$a'| A__questionmark_v0) (|tptp.'fun_app$r'| (|tptp.'natTransMap$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'mapO$f'| (|tptp.'nTDom$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$f'| (|tptp.'nTCod$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$e'| |tptp.'natTransP$'| A__questionmark_v0) (|tptp.'member$i'| A__questionmark_v1 (|tptp.'obj$b'| (|tptp.'nTCatDom$'| A__questionmark_v0)))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatCod$'| A__questionmark_v0) (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'mapO$a'| (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$a'| (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'natTransP$c'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| (|tptp.'nTCatDom$b'| A__questionmark_v0)))) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatCod$b'| A__questionmark_v0) (|tptp.'natTransMap$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'mapO$e'| (|tptp.'nTDom$a'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'mapO$e'| (|tptp.'nTCod$a'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'natTransP$a'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v1 (|tptp.'obj$a'| (|tptp.'nTCatDom$d'| A__questionmark_v0)))) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatCod$d'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$'| (|tptp.'mapO$d'| (|tptp.'nTDom$d'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'mapO$d'| (|tptp.'nTCod$d'| A__questionmark_v0)) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (let ((_let_1 (|tptp.'nTCatCod$c'| A__questionmark_v0))) (=> (and (|tptp.'natTransP$b'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$c'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'comp$b'| _let_1 (|tptp.'fun_app$q'| (|tptp.'mapM$'| (|tptp.'nTDom$b'| A__questionmark_v0)) A__questionmark_v1) (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'comp$b'| _let_1 (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$q'| (|tptp.'mapM$'| (|tptp.'nTCod$b'| A__questionmark_v0)) A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (let ((_let_1 (|tptp.'comp$'| (|tptp.'nTCatCod$'| A__questionmark_v0)))) (=> (and (|tptp.'fun_app$e'| |tptp.'natTransP$'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 (|tptp.'fun_app$p'| (|tptp.'mapM$a'| (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_1 (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0)) A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'natTransMap$d'| A__questionmark_v0))) (let ((_let_2 (|tptp.'comp$'| (|tptp.'nTCatCod$d'| A__questionmark_v0)))) (=> (and (|tptp.'natTransP$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatDom$d'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 (|tptp.'fun_app$'| (|tptp.'mapM$d'| (|tptp.'nTDom$d'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'fun_app$'| _let_1 A__questionmark_v3)) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| _let_2 (|tptp.'fun_app$'| _let_1 A__questionmark_v2)) (|tptp.'fun_app$'| (|tptp.'mapM$d'| (|tptp.'nTCod$d'| A__questionmark_v0)) A__questionmark_v1))))))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$e'| |tptp.'natTrans$'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| (|tptp.'nTCatCod$'| A__questionmark_v0) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| (|tptp.'fun_app$v'| |tptp.'nTDom$c'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'natTrans$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatDom$d'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| (|tptp.'nTCatCod$d'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'mapM$d'| (|tptp.'nTDom$d'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v0) A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'natTrans$b'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$c'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$e'| (|tptp.'compDefined$b'| (|tptp.'nTCatCod$c'| A__questionmark_v0) (|tptp.'fun_app$q'| (|tptp.'mapM$'| (|tptp.'nTDom$b'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v3)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$e'| |tptp.'natTrans$'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| (|tptp.'nTCatCod$'| A__questionmark_v0) (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'fun_app$p'| (|tptp.'mapM$a'| (|tptp.'fun_app$v'| |tptp.'nTCod$c'| A__questionmark_v0)) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (|tptp.'natTrans$a'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| (|tptp.'nTCatDom$d'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| (|tptp.'nTCatCod$d'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$'| (|tptp.'mapM$d'| (|tptp.'nTCod$d'| A__questionmark_v0)) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (|tptp.'natTrans$b'| A__questionmark_v0) (|tptp.'fun_app$l'| (|tptp.'mapsTo$'| (|tptp.'nTCatDom$c'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$e'| (|tptp.'compDefined$b'| (|tptp.'nTCatCod$c'| A__questionmark_v0) (|tptp.'natTransMap$'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'fun_app$q'| (|tptp.'mapM$'| (|tptp.'nTCod$b'| A__questionmark_v0)) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (and (|tptp.'fun_app$e'| (|tptp.'nTCompDefined$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'member$i'| A__questionmark_v2 (|tptp.'obj$b'| (|tptp.'nTCatDom$'| A__questionmark_v0)))) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| (|tptp.'nTCatCod$'| A__questionmark_v0) (|tptp.'natTransMap$b'| A__questionmark_v0 A__questionmark_v2)) (|tptp.'natTransMap$b'| A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (and (|tptp.'nTCompDefined$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'member$d'| A__questionmark_v2 (|tptp.'obj$a'| (|tptp.'nTCatDom$d'| A__questionmark_v0)))) (|tptp.'fun_app$b'| (|tptp.'compDefined$'| (|tptp.'nTCatCod$d'| A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v1) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'nTCatDom$'| A__questionmark_v1))) (|tptp.'fun_app$e'| (|tptp.'nTCompDefined$'| A__questionmark_v1) A__questionmark_v2)) (= (|tptp.'natTransMap$b'| (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'natTransComp$'| A__questionmark_v1) A__questionmark_v2) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| (|tptp.'nTCatCod$'| A__questionmark_v1)) (|tptp.'natTransMap$b'| A__questionmark_v1 A__questionmark_v0)) (|tptp.'natTransMap$b'| A__questionmark_v2 A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|)) (=> (and (|tptp.'member$d'| A__questionmark_v0 (|tptp.'obj$a'| (|tptp.'nTCatDom$d'| A__questionmark_v1))) (|tptp.'nTCompDefined$a'| A__questionmark_v1 A__questionmark_v2)) (= (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| (|tptp.'natTransComp$a'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| (|tptp.'nTCatCod$d'| A__questionmark_v1)) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v1) A__questionmark_v0)) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v2) A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)) (=> (and (|tptp.'member$i'| A__questionmark_v0 (|tptp.'obj$b'| (|tptp.'nTCatDom$'| A__questionmark_v1))) (|tptp.'fun_app$e'| (|tptp.'nTCompDefined$'| A__questionmark_v1) A__questionmark_v2)) (= (|tptp.'natTransMap$b'| (|tptp.'fun_app$w'| (|tptp.'fun_app$x'| |tptp.'natTransComp$'| A__questionmark_v1) A__questionmark_v2) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| (|tptp.'nTCatCod$'| A__questionmark_v2)) (|tptp.'natTransMap$b'| A__questionmark_v1 A__questionmark_v0)) (|tptp.'natTransMap$b'| A__questionmark_v2 A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'|)) (=> (and (|tptp.'member$d'| A__questionmark_v0 (|tptp.'obj$a'| (|tptp.'nTCatDom$d'| A__questionmark_v1))) (|tptp.'nTCompDefined$a'| A__questionmark_v1 A__questionmark_v2)) (= (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| (|tptp.'natTransComp$a'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v0) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| (|tptp.'comp$'| (|tptp.'nTCatCod$d'| A__questionmark_v2)) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v1) A__questionmark_v0)) (|tptp.'fun_app$'| (|tptp.'natTransMap$d'| A__questionmark_v2) A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'oppositeCategory$'| A__questionmark_v0) (|tptp.'category_ext$'| (|tptp.'obj$b'| A__questionmark_v0) (|tptp.'mor$'| A__questionmark_v0) (|tptp.'cod$'| A__questionmark_v0) (|tptp.'dom$'| A__questionmark_v0) (|tptp.'id$b'| A__questionmark_v0) (|tptp.'uuj$'| A__questionmark_v0) (|tptp.'more$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= (|tptp.'oppositeCategory$b'| A__questionmark_v0) (|tptp.'category_ext$a'| (|tptp.'obj$a'| A__questionmark_v0) (|tptp.'mor$b'| A__questionmark_v0) (|tptp.'cod$a'| A__questionmark_v0) (|tptp.'dom$a'| A__questionmark_v0) (|tptp.'id$a'| A__questionmark_v0) (|tptp.'uuk$'| A__questionmark_v0) (|tptp.'more$b'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (and (|tptp.'category$a'| A__questionmark_v0) (|tptp.'category$a'| A__questionmark_v1)) (|tptp.'category_axioms$b'| (|tptp.'catExp$k'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v4 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'obj$b'| A__questionmark_v1))) (=> (and (|tptp.'member$i'| A__questionmark_v0 _let_1) (|tptp.'member$i'| A__questionmark_v2 _let_1) (|tptp.'lSCategory$'| A__questionmark_v1)) (= (|tptp.'natTransMap$b'| (|tptp.'yMapInv$'| A__questionmark_v1 A__questionmark_v0 A__questionmark_v3 A__questionmark_v4) A__questionmark_v2) (|tptp.'zFfun$'| (|tptp.'homSet$'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v0) (|tptp.'mapO$a'| A__questionmark_v3 A__questionmark_v2) (|tptp.'fun_app$m'| (|tptp.'uul$'| A__questionmark_v1 A__questionmark_v3) A__questionmark_v4)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|)) (= (|tptp.'catExp$l'| A__questionmark_v0 A__questionmark_v1) (|tptp.'category_ext$b'| (|tptp.'collect$h'| (|tptp.'uum$'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'collect$i'| (|tptp.'uun$'| A__questionmark_v0 A__questionmark_v1)) |tptp.'nTDom$c'| |tptp.'nTCod$c'| |tptp.'idNatTrans$f'| |tptp.'natTransComp$'| |tptp.'unity$'|))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'homFtorMapContra$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'zFfun$'| (|tptp.'homSet$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'homSet$'| A__questionmark_v0 (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2) (|tptp.'uuo$'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (forall ((A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v6 |tptp.'ZF_ZF_ZF_fun_fun$'|)) (=> (= A__questionmark_v0 (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 |tptp.'unity$'|)) false)) false)) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (=> (forall ((A__questionmark_v4 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v4) A__questionmark_v0) (= (|tptp.'fun_app$'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$'| A__questionmark_v2 A__questionmark_v4)))) (= (|tptp.'zFfun$'| A__questionmark_v0 A__questionmark_v3 A__questionmark_v1) (|tptp.'zFfun$'| A__questionmark_v0 A__questionmark_v3 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|)) (= (|tptp.'fun_app$'| |tptp.'zFfunDom$'| (|tptp.'zFfun$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)) A__questionmark_v0)) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| (|tptp.'zFfun$'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3)) A__questionmark_v0) (|tptp.'fun_app$'| A__questionmark_v3 A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| |tptp.'set$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v0 (|tptp.'zFfun$'| A__questionmark_v1 A__questionmark_v2 (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'homFtorContra$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'functor_ext$a'| (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'| (|tptp.'uup$'| A__questionmark_v0 A__questionmark_v1) |tptp.'unity$'|))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (= (|tptp.'yFtor$a'| A__questionmark_v0) (|tptp.'functor_ext$'| A__questionmark_v0 (|tptp.'catExp$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) |tptp.'set$'|) (|tptp.'yFtorNT$'| A__questionmark_v0) |tptp.'unity$'|))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'B$'|)) (= (|tptp.'fun_app$p'| (|tptp.'homFtorMap$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'zFfun$'| (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'dom$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 (|tptp.'fun_app$t'| (|tptp.'cod$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'uuq$'| A__questionmark_v0 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v3 |tptp.'ZF$'|)) (= (|tptp.'yMapInv$a'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3) (|tptp.'natTrans_ext$'| (|tptp.'mapO$'| (|tptp.'yFtor$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v2 (|tptp.'uur$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2 A__questionmark_v3) |tptp.'unity$'|))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'idNatTrans$d'| A__questionmark_v0) (|tptp.'natTrans_ext$a'| A__questionmark_v0 A__questionmark_v0 (|tptp.'uus$'| A__questionmark_v0) |tptp.'unity$'|))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)) (= (|tptp.'idNatTrans$c'| A__questionmark_v0) (|tptp.'natTrans_ext$'| A__questionmark_v0 A__questionmark_v0 (|tptp.'uut$'| A__questionmark_v0) |tptp.'unity$'|))) (forall ((A__questionmark_v0 |tptp.'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'mapO$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'the$'| (|tptp.'uuu$'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'mapO$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'the$a'| (|tptp.'uuv$'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'zFfun$'| (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v0) (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v1) (|tptp.'fun_app$m'| (|tptp.'uuw$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|)) (let ((_let_1 (|tptp.'zFfun$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2))) (=> (|tptp.'fun_app$b'| |tptp.'isZFfun$'| _let_1) (= (|tptp.'fun_app$'| (|tptp.'dom$a'| |tptp.'set$'|) _let_1) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| A__questionmark_v0))) (=> (and (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v1) (= (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v2) (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v2) (= (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v0) (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v2))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| (|tptp.'fun_app$'| _let_1 A__questionmark_v2)) A__questionmark_v1) (|tptp.'fun_app$'| _let_1 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| A__questionmark_v2) A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v1) (= (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v1) (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v0))) (|tptp.'fun_app$b'| |tptp.'isZFfun$'| (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| A__questionmark_v0) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| A__questionmark_v0) A__questionmark_v1))) (=> (and (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v1) (= (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v1) (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v0))) (and (= (|tptp.'fun_app$'| |tptp.'zFfunDom$'| _let_1) (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v0)) (= (|tptp.'fun_app$'| |tptp.'zFfunCod$'| _let_1) (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|)) (= (|tptp.'fun_app$'| |tptp.'zFfunCod$'| (|tptp.'zFfun$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)) A__questionmark_v1)) (forall ((A__questionmark_v0 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v0))) (=> (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| A__questionmark_v0) (|tptp.'zFfun$'| _let_1 _let_1 |tptp.'uux$'|)) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v1) (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v0))) (|tptp.'fun_app$b'| (|tptp.'elem$'| (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (= (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v0) (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v1)) (= (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v0) (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v2) (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v0)) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| A__questionmark_v0) A__questionmark_v2) (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| A__questionmark_v1) A__questionmark_v2))))) (= A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'mapsTo$b'| |tptp.'set$'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (and (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (= (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v0) A__questionmark_v1) (= (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v0) A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$b'| (|tptp.'compDefined$'| |tptp.'set$'| A__questionmark_v0) A__questionmark_v1) (=> (and (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v1) (= (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v0) (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v1))) false)) false)) (forall ((A__questionmark_v0 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (= A__questionmark_v0 (|tptp.'zFfun$'| (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v0) (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v0) (|tptp.'fun_app$m'| |tptp.'zFfunApp$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (forall ((A__questionmark_v3 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'elem$'| (|tptp.'fun_app$'| A__questionmark_v1 A__questionmark_v3)) A__questionmark_v2))) (|tptp.'fun_app$b'| |tptp.'isZFfun$'| (|tptp.'zFfun$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v1) (= (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v1) (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v0))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'zFfun$'| (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v0) (|tptp.'fun_app$'| |tptp.'zFfunCod$'| A__questionmark_v1) (|tptp.'fun_app$m'| (|tptp.'uuw$'| A__questionmark_v0) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|)) (= (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (|tptp.'member$d'| A__questionmark_v0 (|tptp.'mor$b'| |tptp.'set$'|)))) (= |tptp.'set$a'| (|tptp.'category_ext$a'| (|tptp.'collect$c'| |tptp.'uuy$'|) (|tptp.'collect$c'| |tptp.'isZFfun$'|) |tptp.'zFfunDom$'| |tptp.'zFfunCod$'| |tptp.'uuz$'| |tptp.'zFfunComp$'| |tptp.'unity$'|)) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (= (|tptp.'zF2mor$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'the$b'| (|tptp.'uva$'| A__questionmark_v0 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'fun_app$'| |tptp.'zFfunDom$'| A__questionmark_v0))) (=> (|tptp.'fun_app$b'| |tptp.'isZFfun$'| A__questionmark_v0) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| (|tptp.'zFfun$'| _let_1 _let_1 |tptp.'uux$'|)) A__questionmark_v0) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|)) (let ((_let_1 (|tptp.'zFfun$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2))) (=> (|tptp.'fun_app$b'| |tptp.'isZFfun$'| _let_1) (= (|tptp.'fun_app$'| (|tptp.'cod$a'| |tptp.'set$'|) _let_1) A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (let ((_let_1 (|tptp.'obj$b'| A__questionmark_v0))) (let ((_let_2 (|tptp.'mor$'| A__questionmark_v0))) (= (|tptp.'makeCat$a'| A__questionmark_v0) (|tptp.'category_ext$'| _let_1 _let_2 (|tptp.'restrict$c'| (|tptp.'dom$'| A__questionmark_v0) _let_2) (|tptp.'restrict$c'| (|tptp.'cod$'| A__questionmark_v0) _let_2) (|tptp.'restrict$d'| (|tptp.'id$b'| A__questionmark_v0) _let_1) (|tptp.'uvc$'| A__questionmark_v0) (|tptp.'more$a'| A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (let ((_let_1 (|tptp.'obj$a'| A__questionmark_v0))) (let ((_let_2 (|tptp.'mor$b'| A__questionmark_v0))) (= (|tptp.'makeCat$'| A__questionmark_v0) (|tptp.'category_ext$a'| _let_1 _let_2 (|tptp.'restrict$e'| (|tptp.'dom$a'| A__questionmark_v0) _let_2) (|tptp.'restrict$e'| (|tptp.'cod$a'| A__questionmark_v0) _let_2) (|tptp.'restrict$e'| (|tptp.'id$a'| A__questionmark_v0) _let_1) (|tptp.'uve$'| A__questionmark_v0) (|tptp.'more$b'| A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (=> (|tptp.'extCategory$'| A__questionmark_v0) (|tptp.'member$o'| (|tptp.'case_prod$'| (|tptp.'comp$'| A__questionmark_v0)) (|tptp.'extensional$d'| (|tptp.'collect$'| (|tptp.'uvd$'| A__questionmark_v0)))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (let ((_let_1 (|tptp.'extensional$e'| (|tptp.'mor$'| A__questionmark_v0)))) (= (|tptp.'extCategory$a'| A__questionmark_v0) (and (|tptp.'member$f'| (|tptp.'dom$'| A__questionmark_v0) _let_1) (|tptp.'member$f'| (|tptp.'cod$'| A__questionmark_v0) _let_1) (|tptp.'member$g'| (|tptp.'id$b'| A__questionmark_v0) (|tptp.'extensional$c'| (|tptp.'obj$b'| A__questionmark_v0))) (|tptp.'member$p'| (|tptp.'case_prod$a'| (|tptp.'comp$a'| A__questionmark_v0)) (|tptp.'extensional$f'| (|tptp.'collect$a'| (|tptp.'uvb$'| A__questionmark_v0)))))))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (let ((_let_1 (|tptp.'extensional$b'| (|tptp.'mor$b'| A__questionmark_v0)))) (= (|tptp.'extCategory$'| A__questionmark_v0) (and (|tptp.'member$n'| (|tptp.'dom$a'| A__questionmark_v0) _let_1) (|tptp.'member$n'| (|tptp.'cod$a'| A__questionmark_v0) _let_1) (|tptp.'member$n'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'extensional$b'| (|tptp.'obj$a'| A__questionmark_v0))) (|tptp.'member$o'| (|tptp.'case_prod$'| (|tptp.'comp$'| A__questionmark_v0)) (|tptp.'extensional$d'| (|tptp.'collect$'| (|tptp.'uvd$'| A__questionmark_v0)))))))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|)) (let ((_let_1 (|tptp.'extensional$e'| (|tptp.'mor$'| A__questionmark_v0)))) (=> (and (|tptp.'member$f'| (|tptp.'dom$'| A__questionmark_v0) _let_1) (|tptp.'member$f'| (|tptp.'cod$'| A__questionmark_v0) _let_1) (|tptp.'member$g'| (|tptp.'id$b'| A__questionmark_v0) (|tptp.'extensional$c'| (|tptp.'obj$b'| A__questionmark_v0))) (|tptp.'member$p'| (|tptp.'case_prod$a'| (|tptp.'comp$a'| A__questionmark_v0)) (|tptp.'extensional$f'| (|tptp.'collect$a'| (|tptp.'uvb$'| A__questionmark_v0))))) (|tptp.'extCategory$a'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|)) (let ((_let_1 (|tptp.'extensional$b'| (|tptp.'mor$b'| A__questionmark_v0)))) (=> (and (|tptp.'member$n'| (|tptp.'dom$a'| A__questionmark_v0) _let_1) (|tptp.'member$n'| (|tptp.'cod$a'| A__questionmark_v0) _let_1) (|tptp.'member$n'| (|tptp.'id$a'| A__questionmark_v0) (|tptp.'extensional$b'| (|tptp.'obj$a'| A__questionmark_v0))) (|tptp.'member$o'| (|tptp.'case_prod$'| (|tptp.'comp$'| A__questionmark_v0)) (|tptp.'extensional$d'| (|tptp.'collect$'| (|tptp.'uvd$'| A__questionmark_v0))))) (|tptp.'extCategory$'| A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'hOMCollection$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'collect$c'| (|tptp.'uvf$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'hOMCollection$'| (|tptp.'oppositeCategory$'| A__questionmark_v0) A__questionmark_v1 A__questionmark_v2) (|tptp.'hOMCollection$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'homSet$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2) (|tptp.'implode$'| (|tptp.'hOMCollection$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)))) (forall ((A__questionmark_v0 |tptp.'Unit_unit_fun$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v6 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v7 |tptp.'Unit$'|)) (= (|tptp.'more_update$'| A__questionmark_v0 (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7)) (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 (|tptp.'fun_app$y'| A__questionmark_v0 A__questionmark_v7)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'elem$'| A__questionmark_v2))) (= (|tptp.'fun_app$b'| _let_1 A__questionmark_v0) (|tptp.'fun_app$b'| _let_1 A__questionmark_v1)))))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (not (and (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v1) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|)) (not (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v0) A__questionmark_v0))) (forall ((A__questionmark_v0 |tptp.'ZF_bool_fun$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (and (exists ((A__questionmark_v2 |tptp.'ZF$'|)) (forall ((A__questionmark_v3 |tptp.'ZF$'|)) (=> (not (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) A__questionmark_v2)) (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v3)))) (forall ((A__questionmark_v2 |tptp.'ZF$'|)) (=> (forall ((A__questionmark_v3 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) A__questionmark_v2) (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v3))) (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v2)))) (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_bool_fun$'|) (A__questionmark_v2 |tptp.'ZF$'|)) (=> (and (forall ((A__questionmark_v3 |tptp.'ZF$'|)) (=> (and (forall ((A__questionmark_v4 |tptp.'ZF$'|)) (let ((_let_1 (|tptp.'elem$'| A__questionmark_v4))) (=> (and (|tptp.'fun_app$b'| _let_1 A__questionmark_v3) (|tptp.'fun_app$b'| _let_1 A__questionmark_v0)) (|tptp.'fun_app$b'| A__questionmark_v1 A__questionmark_v4)))) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v3) A__questionmark_v0)) (|tptp.'fun_app$b'| A__questionmark_v1 A__questionmark_v3))) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v2) A__questionmark_v0)) (|tptp.'fun_app$b'| A__questionmark_v1 A__questionmark_v2))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v0) A__questionmark_v1) (not (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v1) A__questionmark_v0)))) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'Nat_ZF_fun$'|)) (= (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v0) (|tptp.'seqSum$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v0) (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v2))))) (= |tptp.'is_Elem_of$'| (|tptp.'collect$'| |tptp.'uvg$'|)) (forall ((A__questionmark_v0 |tptp.'ZF$'|) (A__questionmark_v1 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v2 |tptp.'ZF$'|) (A__questionmark_v3 |tptp.'ZF$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|)) (=> (forall ((A__questionmark_v5 |tptp.'ZF$'|)) (=> (|tptp.'fun_app$b'| (|tptp.'elem$'| A__questionmark_v5) A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'elem$'| (|tptp.'fun_app$'| A__questionmark_v1 A__questionmark_v5)) A__questionmark_v2))) (= (|tptp.'fun_app$'| (|tptp.'fun_app$m'| |tptp.'zFfunComp$'| (|tptp.'zFfun$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1)) (|tptp.'zFfun$'| A__questionmark_v2 A__questionmark_v3 A__questionmark_v4)) (|tptp.'zFfun$'| A__questionmark_v0 A__questionmark_v3 (|tptp.'fun_app$aa'| (|tptp.'comp$d'| A__questionmark_v4) A__questionmark_v1))))) (forall ((A__questionmark_v0 |tptp.'ZF_set_ZF_set_fun$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v6 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v7 |tptp.'Unit$'|)) (= (|tptp.'obj_update$'| A__questionmark_v0 (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7)) (|tptp.'category_ext$a'| (|tptp.'fun_app$ab'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'A_set$'|) (A__questionmark_v3 |tptp.'A_set_a_set_fun$'|) (A__questionmark_v4 |tptp.'A_set_a_set_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'obj$b'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'A_set$'|)) (=> (= A__questionmark_v5 A__questionmark_v2) (= (|tptp.'fun_app$ac'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$ac'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'obj_update$a'| A__questionmark_v3 A__questionmark_v0) (|tptp.'obj_update$a'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_set_ZF_set_fun$'|) (A__questionmark_v4 |tptp.'ZF_set_ZF_set_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'obj$a'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_set$'|)) (=> (= A__questionmark_v5 A__questionmark_v2) (= (|tptp.'fun_app$ab'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$ab'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'obj_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'obj_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v1 |tptp.'A_b_b_c_LSCategory_ext_Category_ext$'|) (A__questionmark_v2 |tptp.'A_set$'|) (A__questionmark_v3 |tptp.'A_set_a_set_fun$'|) (A__questionmark_v4 |tptp.'A_set_a_set_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'obj$b'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'A_set$'|)) (=> (= A__questionmark_v2 A__questionmark_v5) (= (|tptp.'fun_app$ac'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$ac'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'obj_update$a'| A__questionmark_v3 A__questionmark_v0) (|tptp.'obj_update$a'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_set_ZF_set_fun$'|) (A__questionmark_v4 |tptp.'ZF_set_ZF_set_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'obj$a'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_set$'|)) (=> (= A__questionmark_v2 A__questionmark_v5) (= (|tptp.'fun_app$ab'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$ab'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'obj_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'obj_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_set_ZF_set_fun$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v6 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v7 |tptp.'Unit$'|)) (= (|tptp.'mor_update$'| A__questionmark_v0 (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7)) (|tptp.'category_ext$a'| A__questionmark_v1 (|tptp.'fun_app$ab'| A__questionmark_v0 A__questionmark_v2) A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_set_ZF_set_fun$'|) (A__questionmark_v4 |tptp.'ZF_set_ZF_set_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'mor$b'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_set$'|)) (=> (= A__questionmark_v2 A__questionmark_v5) (= (|tptp.'fun_app$ab'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$ab'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'mor_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'mor_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_set_ZF_set_fun$'|) (A__questionmark_v4 |tptp.'ZF_set_ZF_set_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'mor$b'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_set$'|)) (=> (= A__questionmark_v5 A__questionmark_v2) (= (|tptp.'fun_app$ab'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$ab'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'mor_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'mor_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v6 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v7 |tptp.'Unit$'|)) (= (|tptp.'dom_update$'| A__questionmark_v0 (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7)) (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 (|tptp.'fun_app$aa'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$'|) (A__questionmark_v3 |tptp.'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$'|) (A__questionmark_v4 |tptp.'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'mapM$'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$'|)) (=> (= A__questionmark_v5 A__questionmark_v2) (= (|tptp.'fun_app$ad'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$ad'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'mapM_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'mapM_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v1 |tptp.'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|) (A__questionmark_v2 |tptp.'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$'|) (A__questionmark_v3 |tptp.'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$'|) (A__questionmark_v4 |tptp.'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'mapM$'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$'|)) (=> (= A__questionmark_v2 A__questionmark_v5) (= (|tptp.'fun_app$ad'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$ad'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'mapM_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'mapM_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'dom$a'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_ZF_fun$'|)) (=> (= A__questionmark_v2 A__questionmark_v5) (= (|tptp.'fun_app$aa'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$aa'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'dom_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'dom_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'dom$a'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_ZF_fun$'|)) (=> (= A__questionmark_v5 A__questionmark_v2) (= (|tptp.'fun_app$aa'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$aa'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'dom_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'dom_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v6 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v7 |tptp.'Unit$'|)) (= (|tptp.'comp_update$'| A__questionmark_v0 (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7)) (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 (|tptp.'fun_app$ae'| A__questionmark_v0 A__questionmark_v6) A__questionmark_v7))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v6 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v7 |tptp.'Unit$'|)) (= (|tptp.'id_update$'| A__questionmark_v0 (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7)) (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 (|tptp.'fun_app$aa'| A__questionmark_v0 A__questionmark_v5) A__questionmark_v6 A__questionmark_v7))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'comp$'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_ZF_ZF_fun_fun$'|)) (=> (= A__questionmark_v2 A__questionmark_v5) (= (|tptp.'fun_app$ae'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$ae'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'comp_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'comp_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'comp$'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_ZF_ZF_fun_fun$'|)) (=> (= A__questionmark_v5 A__questionmark_v2) (= (|tptp.'fun_app$ae'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$ae'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'comp_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'comp_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'id$a'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_ZF_fun$'|)) (=> (= A__questionmark_v2 A__questionmark_v5) (= (|tptp.'fun_app$aa'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$aa'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'id_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'id_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'id$a'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_ZF_fun$'|)) (=> (= A__questionmark_v5 A__questionmark_v2) (= (|tptp.'fun_app$aa'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$aa'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'id_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'id_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|) (A__questionmark_v1 |tptp.'ZF_set$'|) (A__questionmark_v2 |tptp.'ZF_set$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v5 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v6 |tptp.'ZF_ZF_ZF_fun_fun$'|) (A__questionmark_v7 |tptp.'Unit$'|)) (= (|tptp.'cod_update$'| A__questionmark_v0 (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 A__questionmark_v4 A__questionmark_v5 A__questionmark_v6 A__questionmark_v7)) (|tptp.'category_ext$a'| A__questionmark_v1 A__questionmark_v2 A__questionmark_v3 (|tptp.'fun_app$aa'| A__questionmark_v0 A__questionmark_v4) A__questionmark_v5 A__questionmark_v6 A__questionmark_v7))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'cod$a'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_ZF_fun$'|)) (=> (= A__questionmark_v5 A__questionmark_v2) (= (|tptp.'fun_app$aa'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$aa'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'cod_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'cod_update$'| A__questionmark_v4 A__questionmark_v1)))) (forall ((A__questionmark_v0 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v1 |tptp.'ZF_ZF_unit_Category_ext$'|) (A__questionmark_v2 |tptp.'ZF_ZF_fun$'|) (A__questionmark_v3 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|) (A__questionmark_v4 |tptp.'ZF_ZF_fun_ZF_ZF_fun_fun$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'cod$a'| A__questionmark_v1) A__questionmark_v2) (forall ((A__questionmark_v5 |tptp.'ZF_ZF_fun$'|)) (=> (= A__questionmark_v2 A__questionmark_v5) (= (|tptp.'fun_app$aa'| A__questionmark_v3 A__questionmark_v5) (|tptp.'fun_app$aa'| A__questionmark_v4 A__questionmark_v5))))) (= (|tptp.'cod_update$'| A__questionmark_v3 A__questionmark_v0) (|tptp.'cod_update$'| A__questionmark_v4 A__questionmark_v1)))) true))))))))))))))))))))))))))))))))))))))))))
% 0.56/1.17  )
% 0.56/1.17  % SZS output end Proof for ITP305_1
% 0.56/1.17  % cvc5---1.0.5 exiting
% 0.56/1.17  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------