0.08/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.11	% Command    : do_cvc5 %s %d
0.10/0.31	% Computer   : n021.cluster.edu
0.10/0.31	% Model      : x86_64 x86_64
0.10/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory     : 8042.1875MB
0.10/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 1200
0.10/0.31	% WCLimit    : 120
0.10/0.31	% DateTime   : Tue Jul 13 15:52:25 EDT 2021
0.10/0.32	% CPUTime    : 
0.16/0.45	%----THF division
0.16/0.46	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.16/0.46	--- Run --ho-elim --full-saturate-quant at 10...
0.90/1.08	% SZS status Theorem for theBenchmark
0.90/1.10	% SZS output start Proof for theBenchmark
0.90/1.10	(proof
0.90/1.10	(let ((_let_1 (= bNF_Gr756940202on_fml (lambda ((A2 set_char) (F2 (-> char option_game)) (G (-> char option_fml))) (collec749447393on_fml (lambda ((Uu produc1739631244on_fml)) (exists ((A4 char)) (and ((member_char A4) A2) (= Uu ((produc2124676926on_fml (F2 A4)) (G A4))))))))))) (let ((_let_2 (= bNF_Gr1866170027on_fml (lambda ((A2 set_char) (F2 (-> char option_fml)) (G (-> char option_fml))) (collec670974098on_fml (lambda ((Uu produc46605351on_fml)) (exists ((A4 char)) (and ((member_char A4) A2) (= Uu ((produc909629463on_fml (F2 A4)) (G A4))))))))))) (let ((_let_3 (= bNF_Gr1666135339on_trm (lambda ((A2 set_char) (F2 (-> char option_trm)) (G (-> char option_trm))) (collec1697116690on_trm (lambda ((Uu produc1072747943on_trm)) (exists ((A4 char)) (and (= Uu ((produc709594775on_trm (F2 A4)) (G A4))) ((member_char A4) A2))))))))) (let ((_let_4 (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (=> (not (= (((uSubst516392804stappf Sigma) U) ((geq Theta) Eta)) none_fml)) (and (not (= (_let_1 Eta) none_trm)) (not (= (_let_1 Theta) none_trm)))))))) (let ((_let_5 (= bNF_Gr951178926on_trm (lambda ((A2 set_char) (F2 (-> char char)) (G (-> char option_trm))) (collec1756633317on_trm (lambda ((Uu produc464795408on_trm)) (exists ((A4 char)) (and ((member_char A4) A2) (= Uu ((produc1500300866on_trm (F2 A4)) (G A4))))))))))) (let ((_let_6 (= bNF_Gr2142503190on_fml (lambda ((A2 set_variable) (F2 (-> variable option_game)) (G (-> variable option_fml))) (collec749447393on_fml (lambda ((Uu produc1739631244on_fml)) (exists ((A4 variable)) (and ((member_variable A4) A2) (= Uu ((produc2124676926on_fml (F2 A4)) (G A4))))))))))) (let ((_let_7 (= bNF_Gr852774302le_trm (lambda ((A2 set_char) (F2 (-> char set_variable)) (G (-> char trm))) (collec575343829le_trm (lambda ((Uu produc1367888000le_trm)) (exists ((A4 char)) (and (= Uu ((produc1482344242le_trm (F2 A4)) (G A4))) ((member_char A4) A2))))))))) (let ((_let_8 (= ord_less_eq_set_char (lambda ((A2 set_char) (B2 set_char)) ((ord_less_eq_char_o (lambda ((X3 char)) ((member_char X3) A2))) (lambda ((X3 char)) ((member_char X3) B2))))))) (let ((_let_9 (= (uSubst1367128042_Testo none_fml) none_game))) (let ((_let_10 (= bNF_Gr1933470746on_trm (lambda ((A2 set_variable) (F2 (-> variable char)) (G (-> variable option_trm))) (collec1756633317on_trm (lambda ((Uu produc464795408on_trm)) (exists ((A4 variable)) (and ((member_variable A4) A2) (= Uu ((produc1500300866on_trm (F2 A4)) (G A4))))))))))) (let ((_let_11 (= bNF_Gr806120164on_fml (lambda ((R6 set_Pr927595527on_fml) (F2 (-> option_fml option_fml))) (collec670974098on_fml (lambda ((Uu produc46605351on_fml)) (exists ((A12 option_fml) (A22 option_fml)) (and ((member1287158352on_fml ((produc909629463on_fml A12) A22)) R6) (= Uu ((produc909629463on_fml (F2 A12)) (F2 A22))))))))))) (let ((_let_12 (((uSubst516392804stappf sigma) ua) ((geq theta) eta)))) (let ((_let_13 (not (= _let_12 none_fml)))) (let ((_let_14 (= bNF_Gr400922303on_trm (lambda ((A2 set_variable) (F2 (-> variable option_trm)) (G (-> variable option_trm))) (collec1697116690on_trm (lambda ((Uu produc1072747943on_trm)) (exists ((A4 variable)) (and (= Uu ((produc709594775on_trm (F2 A4)) (G A4))) ((member_variable A4) A2))))))))) (let ((_let_15 (= ord_le282106107riable (lambda ((A2 set_variable) (B2 set_variable)) (forall ((T variable)) (let ((_let_1 (member_variable T))) (=> (_let_1 A2) (_let_1 B2)))))))) (let ((_let_16 (= bNF_Gr1330108682le_trm (lambda ((A2 set_variable) (F2 (-> variable set_variable)) (G (-> variable trm))) (collec575343829le_trm (lambda ((Uu produc1367888000le_trm)) (exists ((A4 variable)) (and (= Uu ((produc1482344242le_trm (F2 A4)) (G A4))) ((member_variable A4) A2))))))))) (let ((_let_17 (not (not (= (((uSubst516392818stappt sigma) ua) theta) none_trm))))) (let ((_let_18 (= bNF_Gr600956991on_fml (lambda ((A2 set_variable) (F2 (-> variable option_fml)) (G (-> variable option_fml))) (collec670974098on_fml (lambda ((Uu produc46605351on_fml)) (exists ((A4 variable)) (and (= Uu ((produc909629463on_fml (F2 A4)) (G A4))) ((member_variable A4) A2))))))))) (let ((_let_19 (= denota1419872369iation (lambda ((Nu3 (-> variable real)) (Nu4 (-> variable real)) (U2 set_variable)) (forall ((I variable)) (=> (not ((member_variable I) U2)) (= (Nu3 I) (Nu4 I)))))))) (let ((_let_20 (= none_fml (ho_246 (ho_458 (ho_457 k_456 sigma) ua) (ho_414 (ho_413 k_412 theta) eta))))) (let ((_let_21 (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 (ho_187 (ho_186 k_185 Sigma) U))) (let ((_let_2 (ho_188 (ho_187 (ho_186 k_185 sigma) ua) theta))) (or (= none_fml (ho_246 (ho_458 (ho_457 k_456 Sigma) U) (ho_414 (ho_413 k_412 Theta) Eta))) (and (not (= _let_2 (ho_188 _let_1 Eta))) (not (= _let_2 (ho_188 _let_1 Theta)))))))))) (let ((_let_22 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_4 7 12)) (MACRO_SR_EQ_INTRO (EQ_RESOLVE (ASSUME |:args| (_let_1)) (MACRO_SR_EQ_INTRO |:args| (_let_1 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_2)) (MACRO_SR_EQ_INTRO |:args| (_let_2 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_3)) (MACRO_SR_EQ_INTRO |:args| (_let_3 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_5)) (MACRO_SR_EQ_INTRO |:args| (_let_5 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_6)) (MACRO_SR_EQ_INTRO |:args| (_let_6 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_7)) (MACRO_SR_EQ_INTRO |:args| (_let_7 7 12))) (ASSUME |:args| (_let_8)) (SYMM (ASSUME |:args| (_let_9))) (EQ_RESOLVE (ASSUME |:args| (_let_10)) (MACRO_SR_EQ_INTRO |:args| (_let_10 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_11)) (MACRO_SR_EQ_INTRO |:args| (_let_11 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_14)) (MACRO_SR_EQ_INTRO |:args| (_let_14 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_15)) (MACRO_SR_EQ_INTRO |:args| (_let_15 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_16)) (MACRO_SR_EQ_INTRO |:args| (_let_16 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_17)) (MACRO_SR_EQ_INTRO |:args| (_let_17 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_18)) (MACRO_SR_EQ_INTRO |:args| (_let_18 7 12))) (EQ_RESOLVE (ASSUME |:args| (_let_19)) (MACRO_SR_EQ_INTRO |:args| (_let_19 7 12))) |:args| ((forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (or (= none_fml (((uSubst516392804stappf Sigma) U) ((geq Theta) Eta))) (and (not (= none_trm (_let_1 Eta))) (not (= none_trm (_let_1 Theta))))))) 7 12)) (PREPROCESS |:args| ((= (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (let ((_let_2 (((uSubst516392818stappt sigma) ua) theta))) (or (= none_fml (((uSubst516392804stappf Sigma) U) ((geq Theta) Eta))) (and (not (= _let_2 (_let_1 Eta))) (not (= _let_2 (_let_1 Theta)))))))) _let_21))))))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_22 |:args| (sigma ua theta eta)) |:args| (_let_21)))) |:args| ((or _let_20 (not _let_21)))) _let_22 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_13 7 12)) (PREPROCESS |:args| ((= (not (= none_fml _let_12)) (not _let_20)))))) |:args| (false false _let_21 true _let_20)) |:args| ((forall ((Option option_trm)) (=> (not (= Option none_trm)) (= Option (some_trm (the_trm Option))))) (= (lambda ((Y set_variable) (Z set_variable)) (= Y Z)) (lambda ((X3 set_variable) (Y3 set_variable)) (and ((ord_le282106107riable X3) Y3) ((ord_le282106107riable Y3) X3)))) (forall ((D (-> produc464795408on_trm Bool)) (R (-> produc464795408on_trm produc464795408on_trm Bool)) (X2 produc464795408on_trm) (P (-> produc464795408on_trm Bool))) (=> ((ord_le1222882015_trm_o D) (accp_P419951815on_trm R)) (=> (forall ((X produc464795408on_trm) (Z4 produc464795408on_trm)) (=> (D X) (=> ((R Z4) X) (D Z4)))) (=> (D X2) (=> (forall ((X produc464795408on_trm)) (=> (D X) (=> (forall ((Z5 produc464795408on_trm)) (=> ((R Z5) X) (P Z5))) (P X)))) (P X2)))))) (forall ((Theta trm) (Eta trm)) (= ((uSubst152838031e_Geqo (some_trm Theta)) (some_trm Eta)) (some_fml ((geq Theta) Eta)))) (forall ((X2 option_trm) (Xa option_trm) (Y2 option_trm)) (let ((_let_1 (not (= Y2 none_trm)))) (=> (= ((uSubst918876924Timeso X2) Xa) Y2) (=> (forall ((Theta2 trm)) (=> (= X2 (some_trm Theta2)) (forall ((Eta2 trm)) (=> (= Xa (some_trm Eta2)) (not (= Y2 (some_trm ((times Theta2) Eta2)))))))) (=> (=> (= X2 none_trm) _let_1) (not (=> (exists ((V2 trm)) (= X2 (some_trm V2))) (=> (= Xa none_trm) _let_1)))))))) (forall ((X2 variable) (Z3 set_variable) (X4 set_variable) (P (-> variable Bool))) (=> ((member_variable X2) Z3) (=> ((ord_le282106107riable Z3) (collect_variable (lambda ((X3 variable)) (and (P X3) ((member_variable X3) X4))))) (P X2)))) (forall ((R3 set_Pr943832262on_trm) (S2 set_Pr943832262on_trm)) (=> (forall ((X char) (Y4 option_trm)) (let ((_let_1 (member694524327on_trm ((produc1500300866on_trm X) Y4)))) (=> (_let_1 R3) (_let_1 S2)))) ((ord_le541293862on_trm R3) S2))) (forall ((X23 game) (Y23 game)) (= (= (some_game X23) (some_game Y23)) (= X23 Y23))) (forall ((B3 option_game) (F (-> variable option_game)) (X2 variable) (C option_fml) (G2 (-> variable option_fml)) (A set_variable)) (=> (= B3 (F X2)) (=> (= C (G2 X2)) (=> ((member_variable X2) A) ((member1883102883on_fml ((produc2124676926on_fml B3) C)) (((bNF_Gr2142503190on_fml A) F) G2)))))) (forall ((R (-> produc464795408on_trm produc464795408on_trm Bool)) (X2 produc464795408on_trm)) (=> (not ((accp_P419951815on_trm R) X2)) (not (forall ((Z4 produc464795408on_trm)) (=> ((R Z4) X2) ((accp_P419951815on_trm R) Z4)))))) (forall ((Theta option_trm)) (= (= (uSubst716837505ntialo Theta) none_trm) (= Theta none_trm))) (forall ((B set_char) (A set_char) (P (-> char Bool))) (let ((_let_1 (ord_less_eq_set_char B))) (=> (_let_1 A) (= (_let_1 (collect_char (lambda ((X3 char)) (and ((member_char X3) A) (P X3))))) (forall ((X3 char)) (=> ((member_char X3) B) (P X3))))))) (forall ((X2 option_trm) (P (-> option_trm option_trm Bool)) (Y2 option_trm)) (let ((_let_1 ((P X2) Y2))) (=> (=> (= X2 none_trm) _let_1) (=> (=> (= Y2 none_trm) _let_1) (=> (forall ((A5 trm) (B5 trm)) (=> (= X2 (some_trm A5)) (=> (= Y2 (some_trm B5)) ((P X2) Y2)))) _let_1))))) (forall ((X23 game)) (not (= none_game (some_game X23)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (F char)) (= (((uSubst516392818stappt Sigma) U) (const F)) (((uSubst1559070963pconst Sigma) U) F))) (forall ((Omega (-> variable real)) (Nu (-> variable real)) (U set_variable)) (=> (((denota1419872369iation Omega) Nu) U) (((denota1419872369iation Nu) Omega) U))) (forall ((Option option_game)) (= (not (= Option none_game)) (((case_option_o_game false) (lambda ((Uu game)) true)) Option))) (forall ((A set_variable)) ((ord_le282106107riable A) A)) (forall ((X2 option_game) (P (-> option_game option_game Bool)) (Y2 option_game)) (let ((_let_1 ((P X2) Y2))) (=> (=> (= X2 none_game) _let_1) (=> (=> (= Y2 none_game) _let_1) (=> (forall ((A5 game) (B5 game)) (=> (= X2 (some_game A5)) (=> (= Y2 (some_game B5)) ((P X2) Y2)))) _let_1))))) (forall ((R set_Pr927595527on_fml) (S set_Pr927595527on_fml)) (= (= (lambda ((X3 option_fml) (Y3 option_fml)) ((member1287158352on_fml ((produc909629463on_fml X3) Y3)) R)) (lambda ((X3 option_fml) (Y3 option_fml)) ((member1287158352on_fml ((produc909629463on_fml X3) Y3)) S))) (= R S))) (forall ((B3 char) (F (-> variable char)) (X2 variable) (C option_trm) (G2 (-> variable option_trm)) (A set_variable)) (=> (= B3 (F X2)) (=> (= C (G2 X2)) (=> ((member_variable X2) A) ((member694524327on_trm ((produc1500300866on_trm B3) C)) (((bNF_Gr1933470746on_trm A) F) G2)))))) (forall ((B3 set_variable) (F (-> char set_variable)) (X2 char) (C trm) (G2 (-> char trm)) (A set_char)) (=> (= B3 (F X2)) (=> (= C (G2 X2)) (=> ((member_char X2) A) ((member2122665623le_trm ((produc1482344242le_trm B3) C)) (((bNF_Gr852774302le_trm A) F) G2)))))) (forall ((A3 char) (P (-> char Bool))) (= ((member_char A3) (collect_char P)) (P A3))) (forall ((R3 (-> produc1072747943on_trm produc1072747943on_trm Bool)) (B3 produc1072747943on_trm) (A3 produc1072747943on_trm)) (let ((_let_1 (accp_P758790320on_trm R3))) (=> (_let_1 B3) (=> ((R3 A3) B3) (_let_1 A3))))) (forall ((X23 real) (X7 trm)) (not (= (number X23) (differential X7)))) (forall ((P (-> option_game option_fml Bool)) (A0 option_game) (A1 option_fml)) (=> (forall ((Alpha game) (Phi2 fml)) ((P (some_game Alpha)) (some_fml Phi2))) (=> (forall ((X_1 option_fml)) ((P none_game) X_1)) (=> (forall ((V2 game)) ((P (some_game V2)) none_fml)) ((P A0) A1))))) (forall ((X2 option_trm) (Y2 option_trm)) (let ((_let_1 (accp_option_trm uSubst2051024824lo_rel))) (=> (= (uSubst716837505ntialo X2) Y2) (=> (_let_1 X2) (=> (forall ((Theta2 trm)) (let ((_let_1 (some_trm Theta2))) (=> (= X2 _let_1) (=> (= Y2 (some_trm (differential Theta2))) (not ((accp_option_trm uSubst2051024824lo_rel) _let_1)))))) (not (=> (= X2 none_trm) (=> (= Y2 none_trm) (not (_let_1 none_trm)))))))))) _let_19 (forall ((Option option_trm) (Option2 option_trm)) (let ((_let_1 (= Option2 none_trm))) (let ((_let_2 (= Option none_trm))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (the_trm Option) (the_trm Option2)))) (= Option Option2)))))) (forall ((R3 (-> produc464795408on_trm produc464795408on_trm Bool)) (A3 produc464795408on_trm)) (=> ((accp_P419951815on_trm R3) A3) (forall ((Y5 produc464795408on_trm)) (=> ((R3 Y5) A3) ((accp_P419951815on_trm R3) Y5))))) (forall ((X23 trm)) (= (the_trm (some_trm X23)) X23)) (forall ((R3 (-> option_fml option_fml Bool)) (A3 option_fml)) (=> ((accp_option_fml R3) A3) (forall ((Y5 option_fml)) (=> ((R3 Y5) A3) ((accp_option_fml R3) Y5))))) (forall ((Option option_trm)) (= (= Option none_trm) (((case_option_o_trm true) (lambda ((Uu trm)) false)) Option))) (= (uSubst716837505ntialo none_trm) none_trm) _let_18 _let_17 (forall ((X2 option_fml)) (= (forall ((Y3 fml)) (not (= X2 (some_fml Y3)))) (= X2 none_fml))) (forall ((B3 char) (F (-> char char)) (X2 char) (C option_trm) (G2 (-> char option_trm)) (A set_char)) (=> (= B3 (F X2)) (=> (= C (G2 X2)) (=> ((member_char X2) A) ((member694524327on_trm ((produc1500300866on_trm B3) C)) (((bNF_Gr951178926on_trm A) F) G2)))))) (forall ((R3 (-> produc464795408on_trm produc464795408on_trm Bool)) (A3 produc464795408on_trm) (P (-> produc464795408on_trm Bool))) (=> ((accp_P419951815on_trm R3) A3) (=> (forall ((X produc464795408on_trm)) (=> ((accp_P419951815on_trm R3) X) (=> (forall ((Y5 produc464795408on_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P A3)))) (forall ((B3 option_trm) (F (-> char option_trm)) (X2 char) (C option_trm) (G2 (-> char option_trm)) (A set_char)) (=> (= B3 (F X2)) (=> (= C (G2 X2)) (=> ((member_char X2) A) ((member165817296on_trm ((produc709594775on_trm B3) C)) (((bNF_Gr1666135339on_trm A) F) G2)))))) (forall ((Option option_fml) (X23 fml)) (=> (= Option (some_fml X23)) (not (= Option none_fml)))) (forall ((P (-> trm Bool)) (Trm trm)) (=> (forall ((X variable)) (P (var X))) (=> (forall ((X real)) (P (number X))) (=> (forall ((X char)) (P (const X))) (=> (forall ((X1a char) (X2a trm)) (=> (P X2a) (P ((func X1a) X2a)))) (=> (forall ((X1a trm) (X2a trm)) (=> (P X1a) (=> (P X2a) (P ((plus X1a) X2a))))) (=> (forall ((X1a trm) (X2a trm)) (=> (P X1a) (=> (P X2a) (P ((times X1a) X2a))))) (=> (forall ((X trm)) (=> (P X) (P (differential X)))) (P Trm))))))))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Phi fml) (V set_variable)) (let ((_let_1 (uSubst516392804stappf Sigma))) (let ((_let_2 ((_let_1 V) Phi))) (let ((_let_3 ((_let_1 U) Phi))) (=> (not (= _let_3 none_fml)) (=> (not (= _let_2 none_fml)) (= _let_3 _let_2))))))) (forall ((X32 char) (X51 trm) (X52 trm)) (not (= (const X32) ((plus X51) X52)))) (forall ((Option option_fml)) (=> (not (= Option none_fml)) (= Option (some_fml (the_fml Option))))) _let_16 (forall ((X41 char) (X42 trm) (X61 trm) (X62 trm)) (not (= ((func X41) X42) ((times X61) X62)))) (forall ((R3 (-> produc1072747943on_trm produc1072747943on_trm Bool)) (X2 produc1072747943on_trm)) (=> (forall ((Y4 produc1072747943on_trm)) (=> ((R3 Y4) X2) ((accp_P758790320on_trm R3) Y4))) ((accp_P758790320on_trm R3) X2))) (forall ((X4 set_variable) (P (-> variable Bool))) ((ord_le282106107riable (collect_variable (lambda ((X3 variable)) (and (P X3) ((member_variable X3) X4))))) X4)) (forall ((R3 (-> option_trm option_trm Bool)) (X2 option_trm) (P (-> option_trm Bool))) (=> ((accp_option_trm R3) X2) (=> (forall ((X option_trm)) (=> (forall ((Y5 option_trm)) (=> ((R3 Y5) X) ((accp_option_trm R3) Y5))) (=> (forall ((Y5 option_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P X2)))) (forall ((X32 char) (Y32 char)) (= (= (const X32) (const Y32)) (= X32 Y32))) (forall ((X21 variable) (X22 trm) (Y21 variable) (Y22 trm)) (= (= ((assign X21) X22) ((assign Y21) Y22)) (and (= X22 Y22) (= X21 Y21)))) (forall ((B3 set_variable) (F (-> variable set_variable)) (X2 variable) (C trm) (G2 (-> variable trm)) (A set_variable)) (=> (= B3 (F X2)) (=> (= C (G2 X2)) (=> ((member_variable X2) A) ((member2122665623le_trm ((produc1482344242le_trm B3) C)) (((bNF_Gr1330108682le_trm A) F) G2)))))) (forall ((P (-> variable Bool)) (Q (-> variable Bool))) (= ((ord_le282106107riable (collect_variable P)) (collect_variable Q)) (forall ((X3 variable)) (=> (P X3) (Q X3))))) (forall ((X1 variable) (X41 char) (X42 trm)) (not (= (var X1) ((func X41) X42)))) (= accp_option_trm (lambda ((R4 (-> option_trm option_trm Bool)) (A4 option_trm)) (exists ((X3 option_trm)) (and (= A4 X3) (forall ((Y3 option_trm)) (=> ((R4 Y3) X3) ((accp_option_trm R4) Y3))))))) (forall ((P (-> char option_trm Bool)) (A0 char) (A1 option_trm)) (=> (forall ((X char) (Theta2 trm)) ((P X) (some_trm Theta2))) (=> (forall ((X char)) ((P X) none_trm)) ((P A0) A1)))) (forall ((X61 trm) (X62 trm) (X7 trm)) (not (= ((times X61) X62) (differential X7)))) (forall ((A3 set_variable) (B3 set_variable) (C set_variable)) (let ((_let_1 (ord_le282106107riable A3))) (=> (_let_1 B3) (=> (= B3 C) (_let_1 C))))) (forall ((Nu (-> variable real)) (V set_variable)) (((denota1419872369iation Nu) Nu) V)) (forall ((X1 variable) (Y1 variable)) (= (= (var X1) (var Y1)) (= X1 Y1))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (let ((_let_2 (((uSubst516392804stappf Sigma) U) ((geq Theta) Eta)))) (=> (not (= _let_2 none_fml)) (= _let_2 (some_fml ((geq (the_trm (_let_1 Theta))) (the_trm (_let_1 Eta))))))))) (forall ((X4 set_char) (P (-> char Bool))) ((ord_less_eq_set_char (collect_char (lambda ((X3 char)) (and ((member_char X3) X4) (P X3))))) X4)) (forall ((R set_variable) (S set_variable)) (= ((ord_le1407353162able_o (lambda ((X3 variable)) ((member_variable X3) R))) (lambda ((X3 variable)) ((member_variable X3) S))) ((ord_le282106107riable R) S))) (forall ((Sigma produc1418842292n_game) (U set_variable) (X2 variable)) (let ((_let_1 (var X2))) (=> ((accp_P1877119646le_trm uSubst1917534215pt_rel) ((produc2015636557le_trm Sigma) ((produc1482344242le_trm U) _let_1))) (= (((uSubst516392818stappt Sigma) U) _let_1) (some_trm _let_1))))) (forall ((X81 char) (X82 trm) (Y81 char) (Y82 trm)) (= (= ((ode X81) X82) ((ode Y81) Y82)) (and (= X81 Y81) (= X82 Y82)))) (forall ((X2 option_game) (P (-> option_game option_fml Bool)) (Y2 option_fml)) (let ((_let_1 ((P X2) Y2))) (=> (=> (= X2 none_game) _let_1) (=> (=> (= Y2 none_fml) _let_1) (=> (forall ((A5 game) (B5 fml)) (=> (= X2 (some_game A5)) (=> (= Y2 (some_fml B5)) ((P X2) Y2)))) _let_1))))) (forall ((D (-> option_trm Bool)) (R (-> option_trm option_trm Bool)) (X2 option_trm) (P (-> option_trm Bool))) (=> ((ord_le1957133745_trm_o D) (accp_option_trm R)) (=> (forall ((X option_trm) (Z4 option_trm)) (=> (D X) (=> ((R Z4) X) (D Z4)))) (=> (D X2) (=> (forall ((X option_trm)) (=> (D X) (=> (forall ((Z5 option_trm)) (=> ((R Z5) X) (P Z5))) (P X)))) (P X2)))))) (forall ((Sigma produc1418842292n_game) (U set_variable) (R3 real)) (let ((_let_1 (number R3))) (= (((uSubst516392818stappt Sigma) U) _let_1) (some_trm _let_1)))) (forall ((X32 fml) (X81 char) (X82 trm)) (not (= (test X32) ((ode X81) X82)))) (forall ((V3 trm)) (= ((uSubst152838031e_Geqo (some_trm V3)) none_trm) none_fml)) (forall ((X2 option_trm) (Xa option_trm) (Y2 option_trm)) (let ((_let_1 (not (= Y2 none_trm)))) (=> (= ((uSubst141955042_Pluso X2) Xa) Y2) (=> (forall ((Theta2 trm)) (=> (= X2 (some_trm Theta2)) (forall ((Eta2 trm)) (=> (= Xa (some_trm Eta2)) (not (= Y2 (some_trm ((plus Theta2) Eta2)))))))) (=> (=> (= X2 none_trm) _let_1) (not (=> (exists ((V2 trm)) (= X2 (some_trm V2))) (=> (= Xa none_trm) _let_1)))))))) (forall ((R3 option_trm) (S2 option_trm) (R set_Pr1471344007on_trm) (S3 option_trm)) (let ((_let_1 (produc709594775on_trm R3))) (=> ((member165817296on_trm (_let_1 S2)) R) (=> (= S3 S2) ((member165817296on_trm (_let_1 S3)) R))))) (forall ((X2 produc1072747943on_trm)) (=> (forall ((Theta2 trm) (Eta2 trm)) (not (= X2 ((produc709594775on_trm (some_trm Theta2)) (some_trm Eta2))))) (=> (forall ((Eta2 option_trm)) (not (= X2 ((produc709594775on_trm none_trm) Eta2)))) (not (forall ((V2 trm)) (not (= X2 ((produc709594775on_trm (some_trm V2)) none_trm)))))))) (= (lambda ((Y set_variable) (Z set_variable)) (= Y Z)) (lambda ((A4 set_variable) (B4 set_variable)) (and ((ord_le282106107riable A4) B4) ((ord_le282106107riable B4) A4)))) (forall ((R3 (-> produc1024976764on_trm produc1024976764on_trm Bool)) (B3 produc1024976764on_trm) (A3 produc1024976764on_trm)) (let ((_let_1 (accp_P394694195on_trm R3))) (=> (_let_1 B3) (=> ((R3 A3) B3) (_let_1 A3))))) (forall ((R3 (-> option_fml option_fml Bool)) (A3 option_fml) (P (-> option_fml Bool))) (=> ((accp_option_fml R3) A3) (=> (forall ((X option_fml)) (=> ((accp_option_fml R3) X) (=> (forall ((Y5 option_fml)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P A3)))) (forall ((R3 (-> produc1024976764on_trm produc1024976764on_trm Bool)) (X2 produc1024976764on_trm) (P (-> produc1024976764on_trm Bool))) (=> ((accp_P394694195on_trm R3) X2) (=> (forall ((X produc1024976764on_trm)) (=> (forall ((Y5 produc1024976764on_trm)) (=> ((R3 Y5) X) ((accp_P394694195on_trm R3) Y5))) (=> (forall ((Y5 produc1024976764on_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P X2)))) (forall ((D (-> option_fml Bool)) (R (-> option_fml option_fml Bool)) (X2 option_fml) (P (-> option_fml Bool))) (=> ((ord_le181580155_fml_o D) (accp_option_fml R)) (=> (forall ((X option_fml) (Z4 option_fml)) (=> (D X) (=> ((R Z4) X) (D Z4)))) (=> (D X2) (=> (forall ((X option_fml)) (=> (D X) (=> (forall ((Z5 option_fml)) (=> ((R Z5) X) (P Z5))) (P X)))) (P X2)))))) (forall ((P (-> option_fml Bool)) (Option option_fml)) (=> (P none_fml) (=> (forall ((X fml)) (P (some_fml X))) (P Option)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (X2 variable)) (let ((_let_1 (var X2))) (= (((uSubst516392818stappt Sigma) U) _let_1) (some_trm _let_1)))) (forall ((Theta trm)) (= (uSubst716837505ntialo (some_trm Theta)) (some_trm (differential Theta)))) (forall ((X2 variable) (Xa option_trm) (Y2 option_game)) (=> (= ((uSubst834381837ssigno X2) Xa) Y2) (=> (forall ((Theta2 trm)) (=> (= Xa (some_trm Theta2)) (not (= Y2 (some_game ((assign X2) Theta2)))))) (not (=> (= Xa none_trm) (not (= Y2 none_game))))))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (let ((_let_2 (_let_1 Eta))) (let ((_let_3 (_let_1 Theta))) (=> (not (= _let_3 none_trm)) (=> (not (= _let_2 none_trm)) (= (((uSubst516392804stappf Sigma) U) ((geq Theta) Eta)) (some_fml ((geq (the_trm _let_3)) (the_trm _let_2)))))))))) (forall ((B3 set_variable) (A3 set_variable) (C set_variable)) (let ((_let_1 (ord_le282106107riable C))) (=> ((ord_le282106107riable B3) A3) (=> (_let_1 B3) (_let_1 A3))))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (let ((_let_2 ((plus Theta) Eta))) (=> ((accp_P1877119646le_trm uSubst1917534215pt_rel) ((produc2015636557le_trm Sigma) ((produc1482344242le_trm U) _let_2))) (= (_let_1 _let_2) ((uSubst141955042_Pluso (_let_1 Theta)) (_let_1 Eta))))))) (forall ((X7 trm) (Y7 trm)) (= (= (differential X7) (differential Y7)) (= X7 Y7))) (forall ((Eta option_trm)) (= ((uSubst918876924Timeso none_trm) Eta) none_trm)) (forall ((P (-> option_game option_game Bool)) (A0 option_game) (A1 option_game)) (=> (forall ((Alpha game) (Beta game)) ((P (some_game Alpha)) (some_game Beta))) (=> (forall ((Alpha option_game)) ((P Alpha) none_game)) (=> (forall ((V2 game)) ((P none_game) (some_game V2))) ((P A0) A1))))) (forall ((X2 char) (Theta option_trm)) (= (= ((uSubst1827052306e_ODEo X2) Theta) none_game) (= Theta none_trm))) (forall ((R3 (-> produc464795408on_trm produc464795408on_trm Bool)) (A3 produc464795408on_trm) (P (-> produc464795408on_trm Bool))) (=> ((accp_P419951815on_trm R3) A3) (=> (forall ((X produc464795408on_trm)) (=> ((accp_P419951815on_trm R3) X) (=> (forall ((Y5 produc464795408on_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P A3)))) (forall ((R3 (-> produc464795408on_trm produc464795408on_trm Bool)) (B3 produc464795408on_trm) (A3 produc464795408on_trm)) (let ((_let_1 (accp_P419951815on_trm R3))) (=> (_let_1 B3) (=> ((R3 A3) B3) (_let_1 A3))))) (forall ((A3 set_variable)) ((ord_le282106107riable A3) A3)) (forall ((R set_Pr622314946on_fml) (S set_Pr622314946on_fml)) (= (= (lambda ((X3 option_game) (Y3 option_fml)) ((member1883102883on_fml ((produc2124676926on_fml X3) Y3)) R)) (lambda ((X3 option_game) (Y3 option_fml)) ((member1883102883on_fml ((produc2124676926on_fml X3) Y3)) S))) (= R S))) (forall ((X2 option_fml) (Y2 option_game)) (let ((_let_1 (accp_option_fml uSubst954181007to_rel))) (=> (= (uSubst1367128042_Testo X2) Y2) (=> (_let_1 X2) (=> (forall ((Phi2 fml)) (let ((_let_1 (some_fml Phi2))) (=> (= X2 _let_1) (=> (= Y2 (some_game (test Phi2))) (not ((accp_option_fml uSubst954181007to_rel) _let_1)))))) (not (=> (= X2 none_fml) (=> (= Y2 none_game) (not (_let_1 none_fml)))))))))) (((denota1419872369iation nu2) omega2) ua) (forall ((X2 produc1739631244on_fml)) (=> (forall ((Alpha game) (Phi2 fml)) (not (= X2 ((produc2124676926on_fml (some_game Alpha)) (some_fml Phi2))))) (=> (forall ((Phi2 option_fml)) (not (= X2 ((produc2124676926on_fml none_game) Phi2)))) (not (forall ((V2 game)) (not (= X2 ((produc2124676926on_fml (some_game V2)) none_fml)))))))) (forall ((A3 set_variable) (B3 set_variable) (C set_variable)) (let ((_let_1 (ord_le282106107riable A3))) (=> (_let_1 B3) (=> ((ord_le282106107riable B3) C) (_let_1 C))))) (forall ((X23 real) (X41 char) (X42 trm)) (not (= (number X23) ((func X41) X42)))) (forall ((Y2 option_trm)) (=> (not (= Y2 none_trm)) (not (forall ((X24 trm)) (not (= Y2 (some_trm X24))))))) (forall ((X2 set_variable) (Y2 set_variable) (Z2 set_variable)) (let ((_let_1 (ord_le282106107riable X2))) (=> (_let_1 Y2) (=> ((ord_le282106107riable Y2) Z2) (_let_1 Z2))))) (forall ((R3 (-> produc464795408on_trm produc464795408on_trm Bool)) (X2 produc464795408on_trm) (P (-> produc464795408on_trm Bool))) (=> ((accp_P419951815on_trm R3) X2) (=> (forall ((X produc464795408on_trm)) (=> (forall ((Y5 produc464795408on_trm)) (=> ((R3 Y5) X) ((accp_P419951815on_trm R3) Y5))) (=> (forall ((Y5 produc464795408on_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P X2)))) (forall ((X1 variable) (X7 trm)) (not (= (var X1) (differential X7)))) (forall ((P (-> option_game Bool)) (A0 option_game)) (=> (forall ((Alpha game)) (P (some_game Alpha))) (=> (P none_game) (P A0)))) (forall ((P (-> char Bool)) (Q (-> char Bool))) (= ((ord_less_eq_set_char (collect_char P)) (collect_char Q)) (forall ((X3 char)) (=> (P X3) (Q X3))))) _let_15 (forall ((R (-> option_fml option_fml Bool)) (X2 option_fml)) (=> (not ((accp_option_fml R) X2)) (not (forall ((Z4 option_fml)) (=> ((R Z4) X2) ((accp_option_fml R) Z4)))))) (= (lambda ((P2 (-> option_trm Bool))) (exists ((X5 option_trm)) (P2 X5))) (lambda ((P3 (-> option_trm Bool))) (or (P3 none_trm) (exists ((X3 trm)) (P3 (some_trm X3)))))) (forall ((X21 variable) (X22 trm) (X32 fml)) (not (= ((assign X21) X22) (test X32)))) (forall ((A3 variable) (P (-> variable Bool))) (= ((member_variable A3) (collect_variable P)) (P A3))) _let_14 (forall ((V3 trm)) (= ((uSubst141955042_Pluso (some_trm V3)) none_trm) none_trm)) (forall ((A3 set_variable) (F (-> set_variable set_variable)) (B3 set_variable) (C set_variable)) (=> (= A3 (F B3)) (=> ((ord_le282106107riable B3) C) (=> (forall ((X set_variable) (Y4 set_variable)) (=> ((ord_le282106107riable X) Y4) ((ord_le282106107riable (F X)) (F Y4)))) ((ord_le282106107riable A3) (F C)))))) (= denota1419872369iation (lambda ((Omega2 (-> variable real)) (Nu3 (-> variable real)) (__flatten_var_0 set_variable)) (((denota1419872369iation Nu3) Omega2) __flatten_var_0))) (forall ((R3 (-> option_fml option_fml Bool)) (A3 option_fml) (P (-> option_fml Bool))) (=> ((accp_option_fml R3) A3) (=> (forall ((X option_fml)) (=> ((accp_option_fml R3) X) (=> (forall ((Y5 option_fml)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P A3)))) (forall ((X2 char) (Xa option_trm) (Y2 option_game)) (let ((_let_1 (produc1500300866on_trm X2))) (let ((_let_2 (accp_P419951815on_trm uSubst299938919Eo_rel))) (=> (= ((uSubst1827052306e_ODEo X2) Xa) Y2) (=> (_let_2 (_let_1 Xa)) (=> (forall ((Theta2 trm)) (let ((_let_1 (some_trm Theta2))) (=> (= Xa _let_1) (=> (= Y2 (some_game ((ode X2) Theta2))) (not ((accp_P419951815on_trm uSubst299938919Eo_rel) ((produc1500300866on_trm X2) _let_1))))))) (not (=> (= Xa none_trm) (=> (= Y2 none_game) (not (_let_2 (_let_1 none_trm)))))))))))) (forall ((X2 option_trm) (Xa option_trm) (Y2 option_fml)) (let ((_let_1 (accp_P758790320on_trm uSubst1304144938qo_rel))) (=> (= ((uSubst152838031e_Geqo X2) Xa) Y2) (=> (_let_1 ((produc709594775on_trm X2) Xa)) (=> (forall ((Theta2 trm)) (=> (= X2 (some_trm Theta2)) (forall ((Eta2 trm)) (let ((_let_1 (some_trm Eta2))) (=> (= Xa _let_1) (=> (= Y2 (some_fml ((geq Theta2) Eta2))) (not ((accp_P758790320on_trm uSubst1304144938qo_rel) ((produc709594775on_trm (some_trm Theta2)) _let_1))))))))) (=> (=> (= X2 none_trm) (=> (= Y2 none_fml) (not (_let_1 ((produc709594775on_trm none_trm) Xa))))) (not (forall ((V2 trm)) (let ((_let_1 (some_trm V2))) (=> (= X2 _let_1) (=> (= Xa none_trm) (=> (= Y2 none_fml) (not ((accp_P758790320on_trm uSubst1304144938qo_rel) ((produc709594775on_trm _let_1) none_trm))))))))))))))) (forall ((X41 char) (X42 trm) (X51 trm) (X52 trm)) (not (= ((func X41) X42) ((plus X51) X52)))) (forall ((R3 (-> produc1072747943on_trm produc1072747943on_trm Bool)) (A3 produc1072747943on_trm) (P (-> produc1072747943on_trm Bool))) (=> ((accp_P758790320on_trm R3) A3) (=> (forall ((X produc1072747943on_trm)) (=> ((accp_P758790320on_trm R3) X) (=> (forall ((Y5 produc1072747943on_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P A3)))) (forall ((R set_char) (S set_char)) (= ((ord_less_eq_char_o (lambda ((X3 char)) ((member_char X3) R))) (lambda ((X3 char)) ((member_char X3) S))) ((ord_less_eq_set_char R) S))) (forall ((X32 char) (X7 trm)) (not (= (const X32) (differential X7)))) (forall ((X2 char) (Z3 set_char) (X4 set_char) (P (-> char Bool))) (=> ((member_char X2) Z3) (=> ((ord_less_eq_set_char Z3) (collect_char (lambda ((X3 char)) (and ((member_char X3) X4) (P X3))))) (P X2)))) (= accp_P419951815on_trm (lambda ((R4 (-> produc464795408on_trm produc464795408on_trm Bool)) (A4 produc464795408on_trm)) (exists ((X3 produc464795408on_trm)) (and (= A4 X3) (forall ((Y3 produc464795408on_trm)) (=> ((R4 Y3) X3) ((accp_P419951815on_trm R4) Y3))))))) (forall ((Sigma produc1418842292n_game) (U set_variable) (R3 real)) (let ((_let_1 (number R3))) (=> ((accp_P1877119646le_trm uSubst1917534215pt_rel) ((produc2015636557le_trm Sigma) ((produc1482344242le_trm U) _let_1))) (= (((uSubst516392818stappt Sigma) U) _let_1) (some_trm _let_1))))) (= (lambda ((Y set_variable) (Z set_variable)) (= Y Z)) (lambda ((A2 set_variable) (B2 set_variable)) (and ((ord_le282106107riable B2) A2) ((ord_le282106107riable A2) B2)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm)) (let ((_let_1 (uSubst516392818stappt Sigma))) (= ((_let_1 U) (differential Theta)) (uSubst716837505ntialo ((_let_1 (collect_variable (lambda ((X3 variable)) true))) Theta))))) (forall ((R set_Pr1235432374le_trm) (S set_Pr1235432374le_trm)) (= (= (lambda ((X3 set_variable) (Y3 trm)) ((member2122665623le_trm ((produc1482344242le_trm X3) Y3)) R)) (lambda ((X3 set_variable) (Y3 trm)) ((member2122665623le_trm ((produc1482344242le_trm X3) Y3)) S))) (= R S))) (forall ((Eta option_trm)) (= ((uSubst152838031e_Geqo none_trm) Eta) none_fml)) (= ord_le282106107riable (lambda ((A2 set_variable) (B2 set_variable)) (forall ((X3 variable)) (let ((_let_1 (member_variable X3))) (=> (_let_1 A2) (_let_1 B2)))))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm)) (let ((_let_1 (uSubst516392818stappt Sigma))) (let ((_let_2 (differential Theta))) (=> ((accp_P1877119646le_trm uSubst1917534215pt_rel) ((produc2015636557le_trm Sigma) ((produc1482344242le_trm U) _let_2))) (= ((_let_1 U) _let_2) (uSubst716837505ntialo ((_let_1 (collect_variable (lambda ((X3 variable)) true))) Theta))))))) (forall ((P (-> option_trm Bool)) (Option option_trm)) (=> (P none_trm) (=> (forall ((X trm)) (P (some_trm X))) (P Option)))) (forall ((X2 produc1024976764on_trm)) (=> (forall ((X variable) (Theta2 trm)) (not (= X2 ((produc1743721902on_trm X) (some_trm Theta2))))) (not (forall ((X variable)) (not (= X2 ((produc1743721902on_trm X) none_trm))))))) _let_13 (forall ((X21 trm) (X22 trm) (Y21 trm) (Y22 trm)) (= (= ((geq X21) X22) ((geq Y21) Y22)) (and (= X22 Y22) (= X21 Y21)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm)) (let ((_let_1 (uSubst516392818stappt Sigma))) (=> (not (= ((_let_1 U) (differential Theta)) none_trm)) (not (= ((_let_1 (collect_variable (lambda ((X3 variable)) true))) Theta) none_trm))))) (forall ((X2 variable)) (= ((uSubst834381837ssigno X2) none_trm) none_game)) (forall ((R3 option_game) (S2 option_fml) (R set_Pr622314946on_fml) (S3 option_fml)) (let ((_let_1 (produc2124676926on_fml R3))) (=> ((member1883102883on_fml (_let_1 S2)) R) (=> (= S3 S2) ((member1883102883on_fml (_let_1 S3)) R))))) (((denota1419872369iation nu) omega) u) (forall ((X23 real) (X51 trm) (X52 trm)) (not (= (number X23) ((plus X51) X52)))) (forall ((R (-> produc1024976764on_trm produc1024976764on_trm Bool)) (X2 produc1024976764on_trm)) (=> (not ((accp_P394694195on_trm R) X2)) (not (forall ((Z4 produc1024976764on_trm)) (=> ((R Z4) X2) ((accp_P394694195on_trm R) Z4)))))) (forall ((D (-> produc1024976764on_trm Bool)) (R (-> produc1024976764on_trm produc1024976764on_trm Bool)) (X2 produc1024976764on_trm) (P (-> produc1024976764on_trm Bool))) (=> ((ord_le373274227_trm_o D) (accp_P394694195on_trm R)) (=> (forall ((X produc1024976764on_trm) (Z4 produc1024976764on_trm)) (=> (D X) (=> ((R Z4) X) (D Z4)))) (=> (D X2) (=> (forall ((X produc1024976764on_trm)) (=> (D X) (=> (forall ((Z5 produc1024976764on_trm)) (=> ((R Z5) X) (P Z5))) (P X)))) (P X2)))))) (forall ((P (-> variable Bool)) (Q (-> variable Bool))) (=> (forall ((X variable)) (= (P X) (Q X))) (= (collect_variable P) (collect_variable Q)))) (forall ((X1 variable) (X23 real)) (not (= (var X1) (number X23)))) (forall ((R3 (-> option_fml option_fml Bool)) (X2 option_fml) (P (-> option_fml Bool))) (=> ((accp_option_fml R3) X2) (=> (forall ((X option_fml)) (=> (forall ((Y5 option_fml)) (=> ((R3 Y5) X) ((accp_option_fml R3) Y5))) (=> (forall ((Y5 option_fml)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P X2)))) (forall ((Option option_game)) (=> (not (= Option none_game)) (= Option (some_game (the_game Option))))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (=> (not (= (_let_1 ((plus Theta) Eta)) none_trm)) (and (not (= (_let_1 Eta) none_trm)) (not (= (_let_1 Theta) none_trm)))))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (= (_let_1 ((plus Theta) Eta)) ((uSubst141955042_Pluso (_let_1 Theta)) (_let_1 Eta))))) (forall ((X2 variable) (Theta option_trm)) (= (= ((uSubst834381837ssigno X2) Theta) none_game) (= Theta none_trm))) (forall ((R3 set_Pr1471344007on_trm) (S2 set_Pr1471344007on_trm)) (=> (forall ((X option_trm) (Y4 option_trm)) (let ((_let_1 (member165817296on_trm ((produc709594775on_trm X) Y4)))) (=> (_let_1 R3) (_let_1 S2)))) ((ord_le1322722599on_trm R3) S2))) (forall ((B set_char) (A set_char) (Q (-> char Bool)) (P (-> char Bool))) (=> ((ord_less_eq_set_char B) A) (=> (forall ((X char)) (=> ((member_char X) B) (=> (Q X) (P X)))) ((ord_less_eq_set_char (collect_char (lambda ((X3 char)) (and (Q X3) ((member_char X3) B))))) (collect_char (lambda ((X3 char)) (and (P X3) ((member_char X3) A)))))))) (forall ((P (-> char Bool)) (Q (-> char Bool))) (=> (forall ((X char)) (=> (P X) (Q X))) ((ord_less_eq_set_char (collect_char P)) (collect_char Q)))) (forall ((R3 (-> produc1024976764on_trm produc1024976764on_trm Bool)) (X2 produc1024976764on_trm)) (=> (forall ((Y4 produc1024976764on_trm)) (=> ((R3 Y4) X2) ((accp_P394694195on_trm R3) Y4))) ((accp_P394694195on_trm R3) X2))) (forall ((P (-> variable Bool)) (Q (-> variable Bool))) (=> (forall ((X variable)) (=> (P X) (Q X))) ((ord_le282106107riable (collect_variable P)) (collect_variable Q)))) (forall ((B3 option_fml) (F (-> char option_fml)) (X2 char) (C option_fml) (G2 (-> char option_fml)) (A set_char)) (=> (= B3 (F X2)) (=> (= C (G2 X2)) (=> ((member_char X2) A) ((member1287158352on_fml ((produc909629463on_fml B3) C)) (((bNF_Gr1866170027on_fml A) F) G2)))))) (forall ((Y2 trm)) (=> (forall ((X12 variable)) (not (= Y2 (var X12)))) (=> (forall ((X24 real)) (not (= Y2 (number X24)))) (=> (forall ((X33 char)) (not (= Y2 (const X33)))) (=> (forall ((X412 char) (X422 trm)) (not (= Y2 ((func X412) X422)))) (=> (forall ((X512 trm) (X522 trm)) (not (= Y2 ((plus X512) X522)))) (=> (forall ((X612 trm) (X622 trm)) (not (= Y2 ((times X612) X622)))) (not (forall ((X72 trm)) (not (= Y2 (differential X72)))))))))))) _let_11 (= (lambda ((P2 (-> option_game Bool))) (exists ((X5 option_game)) (P2 X5))) (lambda ((P3 (-> option_game Bool))) (or (P3 none_game) (exists ((X3 game)) (P3 (some_game X3)))))) (forall ((A set_char) (B set_char) (C char)) (let ((_let_1 (member_char C))) (=> ((ord_less_eq_set_char A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((P (-> option_trm option_trm Bool)) (A0 option_trm) (A1 option_trm)) (=> (forall ((Theta2 trm) (Eta2 trm)) ((P (some_trm Theta2)) (some_trm Eta2))) (=> (forall ((X_1 option_trm)) ((P none_trm) X_1)) (=> (forall ((V2 trm)) ((P (some_trm V2)) none_trm)) ((P A0) A1))))) (forall ((A3 option_trm) (B3 option_fml) (A6 option_trm) (B6 option_fml) (R3 set_Pr1471344007on_trm) (S2 set_Pr927595527on_fml)) (= ((member1316917136on_fml ((produc1235825367on_fml ((produc171850061on_fml A3) B3)) ((produc171850061on_fml A6) B6))) ((lex_pr1724583269on_fml R3) S2)) (or (and (= A3 A6) ((member1287158352on_fml ((produc909629463on_fml B3) B6)) S2)) ((member165817296on_trm ((produc709594775on_trm A3) A6)) R3)))) (forall ((A set_variable)) (= (collect_variable (lambda ((X3 variable)) ((member_variable X3) A))) A)) (forall ((R set_Pr1235432374le_trm) (S set_Pr1235432374le_trm)) (= ((ord_le691957041_trm_o (lambda ((X3 set_variable) (Y3 trm)) ((member2122665623le_trm ((produc1482344242le_trm X3) Y3)) R))) (lambda ((X3 set_variable) (Y3 trm)) ((member2122665623le_trm ((produc1482344242le_trm X3) Y3)) S))) ((ord_le2102862870le_trm R) S))) (forall ((X2 option_fml)) (=> (forall ((Phi2 fml)) (not (= X2 (some_fml Phi2)))) (= X2 none_fml))) (= (lambda ((P2 (-> option_fml Bool))) (forall ((X5 option_fml)) (P2 X5))) (lambda ((P3 (-> option_fml Bool))) (and (P3 none_fml) (forall ((X3 fml)) (P3 (some_fml X3)))))) (forall ((Eta option_trm)) (= ((uSubst141955042_Pluso none_trm) Eta) none_trm)) (forall ((X2 option_trm) (Xa option_trm) (Y2 option_fml)) (let ((_let_1 (not (= Y2 none_fml)))) (=> (= ((uSubst152838031e_Geqo X2) Xa) Y2) (=> (forall ((Theta2 trm)) (=> (= X2 (some_trm Theta2)) (forall ((Eta2 trm)) (=> (= Xa (some_trm Eta2)) (not (= Y2 (some_fml ((geq Theta2) Eta2)))))))) (=> (=> (= X2 none_trm) _let_1) (not (=> (exists ((V2 trm)) (= X2 (some_trm V2))) (=> (= Xa none_trm) _let_1)))))))) (forall ((B3 set_variable) (A3 set_variable)) (=> ((ord_le282106107riable B3) A3) (=> ((ord_le282106107riable A3) B3) (= A3 B3)))) (forall ((Option option_game) (X23 game)) (=> (= Option (some_game X23)) (not (= Option none_game)))) (forall ((X2 option_trm) (P (-> option_trm option_fml Bool)) (Y2 option_fml)) (let ((_let_1 ((P X2) Y2))) (=> (=> (= X2 none_trm) _let_1) (=> (=> (= Y2 none_fml) _let_1) (=> (forall ((A5 trm) (B5 fml)) (=> (= X2 (some_trm A5)) (=> (= Y2 (some_fml B5)) ((P X2) Y2)))) _let_1))))) (= some_trm some_trm) (forall ((R3 (-> option_fml option_fml Bool)) (X2 option_fml)) (=> (forall ((Y4 option_fml)) (=> ((R3 Y4) X2) ((accp_option_fml R3) Y4))) ((accp_option_fml R3) X2))) (forall ((R set_Pr622314946on_fml) (S set_Pr622314946on_fml)) (= ((ord_le1588489637_fml_o (lambda ((X3 option_game) (Y3 option_fml)) ((member1883102883on_fml ((produc2124676926on_fml X3) Y3)) R))) (lambda ((X3 option_game) (Y3 option_fml)) ((member1883102883on_fml ((produc2124676926on_fml X3) Y3)) S))) ((ord_le782333474on_fml R) S))) (forall ((Option option_fml)) (= (= Option none_fml) (((case_option_o_fml true) (lambda ((Uu fml)) false)) Option))) (forall ((X2 produc1016592119n_game)) (=> (forall ((Alpha game) (Beta game)) (not (= X2 ((produc1111617711n_game (some_game Alpha)) (some_game Beta))))) (=> (forall ((Alpha option_game)) (not (= X2 ((produc1111617711n_game Alpha) none_game)))) (not (forall ((V2 game)) (not (= X2 ((produc1111617711n_game none_game) (some_game V2))))))))) (= accp_option_fml (lambda ((R4 (-> option_fml option_fml Bool)) (A4 option_fml)) (exists ((X3 option_fml)) (and (= A4 X3) (forall ((Y3 option_fml)) (=> ((R4 Y3) X3) ((accp_option_fml R4) Y3))))))) (forall ((X2 option_fml) (Y2 option_game)) (=> (= (uSubst1367128042_Testo X2) Y2) (=> (forall ((Phi2 fml)) (=> (= X2 (some_fml Phi2)) (not (= Y2 (some_game (test Phi2)))))) (not (=> (= X2 none_fml) (not (= Y2 none_game))))))) (forall ((R3 set_variable) (S2 trm) (R set_Pr1235432374le_trm) (S3 trm)) (let ((_let_1 (produc1482344242le_trm R3))) (=> ((member2122665623le_trm (_let_1 S2)) R) (=> (= S3 S2) ((member2122665623le_trm (_let_1 S3)) R))))) (forall ((X2 option_fml) (P (-> option_fml option_fml Bool)) (Y2 option_fml)) (let ((_let_1 ((P X2) Y2))) (=> (=> (= X2 none_fml) _let_1) (=> (=> (= Y2 none_fml) _let_1) (=> (forall ((A5 fml) (B5 fml)) (=> (= X2 (some_fml A5)) (=> (= Y2 (some_fml B5)) ((P X2) Y2)))) _let_1))))) _let_10 _let_9 (forall ((P (-> option_game Bool)) (Option option_game)) (=> (P none_game) (=> (forall ((X game)) (P (some_game X))) (P Option)))) (forall ((A set_char) (P (-> char Bool)) (Q (-> char Bool))) (let ((_let_1 (ord_less_eq_set_char A))) (= (_let_1 (collect_char (lambda ((X3 char)) (and (Q X3) (P X3))))) (and (_let_1 (collect_char P)) (_let_1 (collect_char Q)))))) (= (lambda ((Y set_variable) (Z set_variable)) (= Y Z)) (lambda ((A4 set_variable) (B4 set_variable)) (and ((ord_le282106107riable A4) B4) ((ord_le282106107riable B4) A4)))) (forall ((A set_variable) (B set_variable)) (=> (= A B) (not (=> ((ord_le282106107riable A) B) (not ((ord_le282106107riable B) A)))))) (forall ((R3 (-> produc1072747943on_trm produc1072747943on_trm Bool)) (X2 produc1072747943on_trm) (P (-> produc1072747943on_trm Bool))) (=> ((accp_P758790320on_trm R3) X2) (=> (forall ((X produc1072747943on_trm)) (=> (forall ((Y5 produc1072747943on_trm)) (=> ((R3 Y5) X) ((accp_P758790320on_trm R3) Y5))) (=> (forall ((Y5 produc1072747943on_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P X2)))) (forall ((Theta option_trm) (Eta option_trm)) (= (= ((uSubst918876924Timeso Theta) Eta) none_trm) (or (= Eta none_trm) (= Theta none_trm)))) (forall ((X2 option_fml)) (= (not (= X2 none_fml)) (exists ((Y3 fml)) (= X2 (some_fml Y3))))) (forall ((B3 option_trm) (F (-> variable option_trm)) (X2 variable) (C option_trm) (G2 (-> variable option_trm)) (A set_variable)) (=> (= B3 (F X2)) (=> (= C (G2 X2)) (=> ((member_variable X2) A) ((member165817296on_trm ((produc709594775on_trm B3) C)) (((bNF_Gr400922303on_trm A) F) G2)))))) (forall ((R1 (-> option_trm option_trm Bool)) (R2 (-> option_trm option_trm Bool))) (=> ((ord_le847028878_trm_o R1) R2) ((ord_le1957133745_trm_o (accp_option_trm R2)) (accp_option_trm R1)))) (forall ((A set_variable) (B set_variable)) (=> (= A B) ((ord_le282106107riable B) A))) (forall ((X2 produc833882726rp_trm)) (=> (forall ((I2 denotational_interp) (X variable)) (not (= X2 ((produc1132922070rp_trm I2) (var X))))) (=> (forall ((I2 denotational_interp) (R5 real)) (not (= X2 ((produc1132922070rp_trm I2) (number R5))))) (=> (forall ((I2 denotational_interp) (F3 char)) (not (= X2 ((produc1132922070rp_trm I2) (const F3))))) (=> (forall ((I2 denotational_interp) (F3 char) (Theta2 trm)) (not (= X2 ((produc1132922070rp_trm I2) ((func F3) Theta2))))) (=> (forall ((I2 denotational_interp) (Theta2 trm) (Eta2 trm)) (not (= X2 ((produc1132922070rp_trm I2) ((plus Theta2) Eta2))))) (=> (forall ((I2 denotational_interp) (Theta2 trm) (Eta2 trm)) (not (= X2 ((produc1132922070rp_trm I2) ((times Theta2) Eta2))))) (not (forall ((I2 denotational_interp) (Theta2 trm)) (not (= X2 ((produc1132922070rp_trm I2) (differential Theta2))))))))))))) (forall ((B3 option_game) (F (-> char option_game)) (X2 char) (C option_fml) (G2 (-> char option_fml)) (A set_char)) (=> (= B3 (F X2)) (=> (= C (G2 X2)) (=> ((member_char X2) A) ((member1883102883on_fml ((produc2124676926on_fml B3) C)) (((bNF_Gr756940202on_fml A) F) G2)))))) (forall ((R3 (-> option_trm option_trm Bool)) (A3 option_trm) (P (-> option_trm Bool))) (=> ((accp_option_trm R3) A3) (=> (forall ((X option_trm)) (=> ((accp_option_trm R3) X) (=> (forall ((Y5 option_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P A3)))) (forall ((Option option_fml)) (=> (not (= Option none_fml)) (= (some_fml (the_fml Option)) Option))) (forall ((R3 (-> produc1024976764on_trm produc1024976764on_trm Bool)) (A3 produc1024976764on_trm) (P (-> produc1024976764on_trm Bool))) (=> ((accp_P394694195on_trm R3) A3) (=> (forall ((X produc1024976764on_trm)) (=> ((accp_P394694195on_trm R3) X) (=> (forall ((Y5 produc1024976764on_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P A3)))) (forall ((P (-> variable option_trm Bool)) (A0 variable) (A1 option_trm)) (=> (forall ((X variable) (Theta2 trm)) ((P X) (some_trm Theta2))) (=> (forall ((X variable)) ((P X) none_trm)) ((P A0) A1)))) (forall ((A set_variable) (B set_variable)) (=> (forall ((X variable)) (let ((_let_1 (member_variable X))) (=> (_let_1 A) (_let_1 B)))) ((ord_le282106107riable A) B))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (=> (not (= (_let_1 ((times Theta) Eta)) none_trm)) (and (not (= (_let_1 Theta) none_trm)) (not (= (_let_1 Eta) none_trm)))))) (forall ((A3 set_variable) (F (-> set_variable set_variable)) (B3 set_variable) (C set_variable)) (let ((_let_1 (ord_le282106107riable A3))) (=> (_let_1 (F B3)) (=> ((ord_le282106107riable B3) C) (=> (forall ((X set_variable) (Y4 set_variable)) (=> ((ord_le282106107riable X) Y4) ((ord_le282106107riable (F X)) (F Y4)))) (_let_1 (F C))))))) (forall ((A set_char) (B set_char)) (=> (forall ((X char)) (let ((_let_1 (member_char X))) (=> (_let_1 A) (_let_1 B)))) ((ord_less_eq_set_char A) B))) (forall ((X41 char) (X42 trm) (X7 trm)) (not (= ((func X41) X42) (differential X7)))) (forall ((A set_variable) (P (-> variable Bool)) (Q (-> variable Bool))) (let ((_let_1 (ord_le282106107riable A))) (= (_let_1 (collect_variable (lambda ((X3 variable)) (and (P X3) (Q X3))))) (and (_let_1 (collect_variable Q)) (_let_1 (collect_variable P)))))) (forall ((X2 char) (Xa option_trm) (Y2 option_game)) (=> (= ((uSubst1827052306e_ODEo X2) Xa) Y2) (=> (forall ((Theta2 trm)) (=> (= Xa (some_trm Theta2)) (not (= Y2 (some_game ((ode X2) Theta2)))))) (not (=> (= Xa none_trm) (not (= Y2 none_game))))))) (forall ((X23 trm)) (not (= none_trm (some_trm X23)))) (forall ((A3 set_variable) (B3 set_variable) (F (-> set_variable set_variable)) (C set_variable)) (=> ((ord_le282106107riable A3) B3) (=> (= (F B3) C) (=> (forall ((X set_variable) (Y4 set_variable)) (=> ((ord_le282106107riable X) Y4) ((ord_le282106107riable (F X)) (F Y4)))) ((ord_le282106107riable (F A3)) C))))) (forall ((P (-> set_variable Bool)) (X2 set_variable)) (=> (P X2) (=> (forall ((Y4 set_variable)) (=> (P Y4) ((ord_le282106107riable Y4) X2))) (= (order_272405634riable P) X2)))) (forall ((X32 char) (X41 char) (X42 trm)) (not (= (const X32) ((func X41) X42)))) (forall ((Option option_fml) (Option2 option_fml)) (let ((_let_1 (= Option2 none_fml))) (let ((_let_2 (= Option none_fml))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (the_fml Option) (the_fml Option2)))) (= Option Option2)))))) (forall ((R1 (-> produc1024976764on_trm produc1024976764on_trm Bool)) (R2 (-> produc1024976764on_trm produc1024976764on_trm Bool))) (=> ((ord_le370603054_trm_o R1) R2) ((ord_le373274227_trm_o (accp_P394694195on_trm R2)) (accp_P394694195on_trm R1)))) (forall ((Alpha2 option_game)) (= (not (= Alpha2 none_game)) (exists ((G game)) (= Alpha2 (some_game G))))) (forall ((V3 trm)) (= ((uSubst918876924Timeso (some_trm V3)) none_trm) none_trm)) (forall ((X1 variable) (X51 trm) (X52 trm)) (not (= (var X1) ((plus X51) X52)))) (forall ((P (-> denotational_interp trm Bool)) (A0 denotational_interp) (A1 trm)) (=> (forall ((I2 denotational_interp) (X variable)) ((P I2) (var X))) (=> (forall ((I2 denotational_interp) (R5 real)) ((P I2) (number R5))) (=> (forall ((I2 denotational_interp) (F3 char)) ((P I2) (const F3))) (=> (forall ((I2 denotational_interp) (F3 char) (Theta2 trm)) (let ((_let_1 (P I2))) (=> (_let_1 Theta2) (_let_1 ((func F3) Theta2))))) (=> (forall ((I2 denotational_interp) (Theta2 trm)) (=> ((P I2) Theta2) (forall ((Eta2 trm)) (let ((_let_1 (P I2))) (=> (_let_1 Eta2) (_let_1 ((plus Theta2) Eta2))))))) (=> (forall ((I2 denotational_interp) (Theta2 trm)) (=> ((P I2) Theta2) (forall ((Eta2 trm)) (let ((_let_1 (P I2))) (=> (_let_1 Eta2) (_let_1 ((times Theta2) Eta2))))))) (=> (forall ((I2 denotational_interp) (Theta2 trm)) (let ((_let_1 (P I2))) (=> (=> (exists ((Xa2 char)) ((member_char Xa2) (collect_char (lambda ((Uu char)) true)))) (_let_1 Theta2)) (_let_1 (differential Theta2))))) ((P A0) A1))))))))) (forall ((X2 variable) (Xa option_trm) (Y2 option_game)) (let ((_let_1 (produc1743721902on_trm X2))) (let ((_let_2 (accp_P394694195on_trm uSubst157155628no_rel))) (=> (= ((uSubst834381837ssigno X2) Xa) Y2) (=> (_let_2 (_let_1 Xa)) (=> (forall ((Theta2 trm)) (let ((_let_1 (some_trm Theta2))) (=> (= Xa _let_1) (=> (= Y2 (some_game ((assign X2) Theta2))) (not ((accp_P394694195on_trm uSubst157155628no_rel) ((produc1743721902on_trm X2) _let_1))))))) (not (=> (= Xa none_trm) (=> (= Y2 none_game) (not (_let_2 (_let_1 none_trm)))))))))))) (forall ((Theta option_trm) (Eta option_trm)) (= (= ((uSubst152838031e_Geqo Theta) Eta) none_fml) (or (= Theta none_trm) (= Eta none_trm)))) (= ord_le282106107riable (lambda ((A2 set_variable) (B2 set_variable)) ((ord_le1407353162able_o (lambda ((X3 variable)) ((member_variable X3) A2))) (lambda ((X3 variable)) ((member_variable X3) B2))))) (forall ((X2 option_trm) (Xa option_trm) (Y2 option_trm)) (let ((_let_1 (accp_P758790320on_trm uSubst691094423so_rel))) (=> (= ((uSubst141955042_Pluso X2) Xa) Y2) (=> (_let_1 ((produc709594775on_trm X2) Xa)) (=> (forall ((Theta2 trm)) (=> (= X2 (some_trm Theta2)) (forall ((Eta2 trm)) (let ((_let_1 (some_trm Eta2))) (=> (= Xa _let_1) (=> (= Y2 (some_trm ((plus Theta2) Eta2))) (not ((accp_P758790320on_trm uSubst691094423so_rel) ((produc709594775on_trm (some_trm Theta2)) _let_1))))))))) (=> (=> (= X2 none_trm) (=> (= Y2 none_trm) (not (_let_1 ((produc709594775on_trm none_trm) Xa))))) (not (forall ((V2 trm)) (let ((_let_1 (some_trm V2))) (=> (= X2 _let_1) (=> (= Xa none_trm) (=> (= Y2 none_trm) (not ((accp_P758790320on_trm uSubst691094423so_rel) ((produc709594775on_trm _let_1) none_trm))))))))))))))) (forall ((X2 option_trm) (P (-> option_trm option_game Bool)) (Y2 option_game)) (let ((_let_1 ((P X2) Y2))) (=> (=> (= X2 none_trm) _let_1) (=> (=> (= Y2 none_game) _let_1) (=> (forall ((A5 trm) (B5 game)) (=> (= X2 (some_trm A5)) (=> (= Y2 (some_game B5)) ((P X2) Y2)))) _let_1))))) (forall ((A set_variable) (B set_variable) (X2 variable)) (let ((_let_1 (member_variable X2))) (=> ((ord_le282106107riable A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((Y2 option_game)) (=> (not (= Y2 none_game)) (not (forall ((X24 game)) (not (= Y2 (some_game X24))))))) (forall ((Phi option_fml)) (= (= (uSubst1367128042_Testo Phi) none_game) (= Phi none_fml))) (forall ((V set_variable) (U set_variable) (Sigma produc1418842292n_game) (Theta trm)) (let ((_let_1 (uSubst516392818stappt Sigma))) (let ((_let_2 ((_let_1 U) Theta))) (=> ((ord_le282106107riable V) U) (=> (not (= _let_2 none_trm)) (= _let_2 ((_let_1 V) Theta))))))) (forall ((A3 set_variable) (B3 trm) (A6 set_variable) (B6 trm) (R3 set_Pr181266295riable) (S2 set_Pr491793543rm_trm)) (= ((member1150310282le_trm ((produc1056455193le_trm ((produc1482344242le_trm A3) B3)) ((produc1482344242le_trm A6) B6))) ((lex_pr1522821402le_trm R3) S2)) (or (and (= A3 A6) ((member1735386832rm_trm ((product_Pair_trm_trm B3) B6)) S2)) ((member1978718144riable ((produc1766592463riable A3) A6)) R3)))) _let_8 (forall ((A set_variable) (P (-> variable Bool))) ((ord_le282106107riable (collect_variable (lambda ((X3 variable)) (and ((member_variable X3) A) (P X3))))) A)) (forall ((X23 fml) (Y23 fml)) (= (= (some_fml X23) (some_fml Y23)) (= X23 Y23))) (forall ((A set_variable) (B set_variable)) (=> (= A B) ((ord_le282106107riable A) B))) (forall ((Option option_trm)) (= (not (= Option none_trm)) (((case_option_o_trm false) (lambda ((Uu trm)) true)) Option))) (forall ((P (-> char Bool)) (Q (-> char Bool))) (=> (forall ((X char)) (= (P X) (Q X))) (= (collect_char P) (collect_char Q)))) (forall ((R3 (-> produc1024976764on_trm produc1024976764on_trm Bool)) (A3 produc1024976764on_trm)) (=> ((accp_P394694195on_trm R3) A3) (forall ((Y5 produc1024976764on_trm)) (=> ((R3 Y5) A3) ((accp_P394694195on_trm R3) Y5))))) (forall ((Option option_game)) (= (= Option none_game) (((case_option_o_game true) (lambda ((Uu game)) false)) Option))) (forall ((R1 (-> option_fml option_fml Bool)) (R2 (-> option_fml option_fml Bool))) (=> ((ord_le802833166_fml_o R1) R2) ((ord_le181580155_fml_o (accp_option_fml R2)) (accp_option_fml R1)))) (forall ((R3 (-> produc1072747943on_trm produc1072747943on_trm Bool)) (A3 produc1072747943on_trm) (P (-> produc1072747943on_trm Bool))) (=> ((accp_P758790320on_trm R3) A3) (=> (forall ((X produc1072747943on_trm)) (=> ((accp_P758790320on_trm R3) X) (=> (forall ((Y5 produc1072747943on_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P A3)))) (forall ((P (-> set_variable Bool)) (X2 set_variable) (Q (-> set_variable Bool))) (=> (P X2) (=> (forall ((Y4 set_variable)) (=> (P Y4) ((ord_le282106107riable Y4) X2))) (=> (forall ((X set_variable)) (=> (P X) (=> (forall ((Y5 set_variable)) (=> (P Y5) ((ord_le282106107riable Y5) X))) (Q X)))) (Q (order_272405634riable P)))))) (forall ((R3 (-> option_trm option_trm Bool)) (A3 option_trm) (P (-> option_trm Bool))) (=> ((accp_option_trm R3) A3) (=> (forall ((X option_trm)) (=> ((accp_option_trm R3) X) (=> (forall ((Y5 option_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P A3)))) _let_7 (= (lambda ((P2 (-> option_fml Bool))) (exists ((X5 option_fml)) (P2 X5))) (lambda ((P3 (-> option_fml Bool))) (or (exists ((X3 fml)) (P3 (some_fml X3))) (P3 none_fml)))) (forall ((R3 (-> produc464795408on_trm produc464795408on_trm Bool)) (X2 produc464795408on_trm)) (=> (forall ((Y4 produc464795408on_trm)) (=> ((R3 Y4) X2) ((accp_P419951815on_trm R3) Y4))) ((accp_P419951815on_trm R3) X2))) (forall ((P Bool) (Q (-> fml Bool)) (X2 option_fml)) (=> (((case_option_o_fml P) Q) X2) (=> (=> (= X2 none_fml) (not P)) (not (forall ((Y4 fml)) (=> (= X2 (some_fml Y4)) (not (Q Y4)))))))) (forall ((Option option_trm) (X23 trm)) (=> (= Option (some_trm X23)) (not (= Option none_trm)))) (forall ((X61 trm) (X62 trm) (Y61 trm) (Y62 trm)) (= (= ((times X61) X62) ((times Y61) Y62)) (and (= X61 Y61) (= X62 Y62)))) _let_6 (forall ((Sigma produc1418842292n_game) (U set_variable) (F char)) (let ((_let_1 (const F))) (=> ((accp_P1877119646le_trm uSubst1917534215pt_rel) ((produc2015636557le_trm Sigma) ((produc1482344242le_trm U) _let_1))) (= (((uSubst516392818stappt Sigma) U) _let_1) (((uSubst1559070963pconst Sigma) U) F))))) (forall ((R3 (-> produc1024976764on_trm produc1024976764on_trm Bool)) (A3 produc1024976764on_trm) (P (-> produc1024976764on_trm Bool))) (=> ((accp_P394694195on_trm R3) A3) (=> (forall ((X produc1024976764on_trm)) (=> ((accp_P394694195on_trm R3) X) (=> (forall ((Y5 produc1024976764on_trm)) (=> ((R3 Y5) X) (P Y5))) (P X)))) (P A3)))) (forall ((X23 real) (X61 trm) (X62 trm)) (not (= (number X23) ((times X61) X62)))) (forall ((Theta trm) (Eta trm)) (= ((uSubst918876924Timeso (some_trm Theta)) (some_trm Eta)) (some_trm ((times Theta) Eta)))) (forall ((Nu (-> variable real)) (Nu2 (-> variable real))) (((denota1419872369iation Nu) Nu2) (collect_variable (lambda ((X3 variable)) true)))) _let_5 (forall ((X2 option_fml) (P (-> option_fml option_trm Bool)) (Y2 option_trm)) (let ((_let_1 ((P X2) Y2))) (=> (=> (= X2 none_fml) _let_1) (=> (=> (= Y2 none_trm) _let_1) (=> (forall ((A5 fml) (B5 trm)) (=> (= X2 (some_fml A5)) (=> (= Y2 (some_trm B5)) ((P X2) Y2)))) _let_1))))) (forall ((X2 produc1699626005le_trm)) (=> (forall ((Sigma2 produc1418842292n_game) (U3 set_variable) (X variable)) (not (= X2 ((produc2015636557le_trm Sigma2) ((produc1482344242le_trm U3) (var X)))))) (=> (forall ((Sigma2 produc1418842292n_game) (U3 set_variable) (R5 real)) (not (= X2 ((produc2015636557le_trm Sigma2) ((produc1482344242le_trm U3) (number R5)))))) (=> (forall ((Sigma2 produc1418842292n_game) (U3 set_variable) (F3 char)) (not (= X2 ((produc2015636557le_trm Sigma2) ((produc1482344242le_trm U3) (const F3)))))) (=> (forall ((Sigma2 produc1418842292n_game) (U3 set_variable) (F3 char) (Theta2 trm)) (not (= X2 ((produc2015636557le_trm Sigma2) ((produc1482344242le_trm U3) ((func F3) Theta2)))))) (=> (forall ((Sigma2 produc1418842292n_game) (U3 set_variable) (Theta2 trm) (Eta2 trm)) (not (= X2 ((produc2015636557le_trm Sigma2) ((produc1482344242le_trm U3) ((plus Theta2) Eta2)))))) (=> (forall ((Sigma2 produc1418842292n_game) (U3 set_variable) (Theta2 trm) (Eta2 trm)) (not (= X2 ((produc2015636557le_trm Sigma2) ((produc1482344242le_trm U3) ((times Theta2) Eta2)))))) (not (forall ((Sigma2 produc1418842292n_game) (U3 set_variable) (Theta2 trm)) (not (= X2 ((produc2015636557le_trm Sigma2) ((produc1482344242le_trm U3) (differential Theta2)))))))))))))) (forall ((X2 option_trm)) (= (forall ((Y3 trm)) (not (= X2 (some_trm Y3)))) (= X2 none_trm))) (forall ((X2 produc1408538418on_fml)) (=> (forall ((X variable) (Phi2 fml)) (not (= X2 ((produc1205977188on_fml X) (some_fml Phi2))))) (not (forall ((X variable)) (not (= X2 ((produc1205977188on_fml X) none_fml))))))) _let_4 (forall ((Y2 set_variable) (X2 set_variable)) (=> ((ord_le282106107riable Y2) X2) (= ((ord_le282106107riable X2) Y2) (= X2 Y2)))) (forall ((A3 set_variable) (B3 set_variable)) (=> ((ord_le282106107riable A3) B3) (=> ((ord_le282106107riable B3) A3) (= A3 B3)))) (forall ((A set_variable) (B set_variable) (C2 set_variable)) (let ((_let_1 (ord_le282106107riable A))) (=> (_let_1 B) (=> ((ord_le282106107riable B) C2) (_let_1 C2))))) (forall ((R3 (-> option_trm option_trm Bool)) (B3 option_trm) (A3 option_trm)) (let ((_let_1 (accp_option_trm R3))) (=> (_let_1 B3) (=> ((R3 A3) B3) (_let_1 A3))))) (forall ((X32 char) (X61 trm) (X62 trm)) (not (= (const X32) ((times X61) X62)))) (forall ((X2 set_variable)) ((ord_le282106107riable X2) X2)) (= none_trm none_trm) (forall ((R3 set_Pr1235432374le_trm) (S2 set_Pr1235432374le_trm)) (=> (forall ((X set_variable) (Y4 trm)) (let ((_let_1 (member2122665623le_trm ((produc1482344242le_trm X) Y4)))) (=> (_let_1 R3) (_let_1 S2)))) ((ord_le2102862870le_trm R3) S2))) (forall ((X41 char) (X42 trm) (Y41 char) (Y42 trm)) (= (= ((func X41) X42) ((func Y41) Y42)) (and (= X42 Y42) (= X41 Y41)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (= (((uSubst516392804stappf Sigma) U) ((geq Theta) Eta)) ((uSubst152838031e_Geqo (_let_1 Theta)) (_let_1 Eta))))) (= accp_P394694195on_trm (lambda ((R4 (-> produc1024976764on_trm produc1024976764on_trm Bool)) (A4 produc1024976764on_trm)) (exists ((X3 produc1024976764on_trm)) (and (forall ((Y3 produc1024976764on_trm)) (=> ((R4 Y3) X3) ((accp_P394694195on_trm R4) Y3))) (= A4 X3))))) (forall ((A3 option_trm) (B3 option_trm) (A6 option_trm) (B6 option_trm) (R3 set_Pr1471344007on_trm) (S2 set_Pr1471344007on_trm)) (let ((_let_1 (produc709594775on_trm A3))) (= ((member602811152on_trm ((produc2001752919on_trm (_let_1 B3)) ((produc709594775on_trm A6) B6))) ((lex_pr114844335on_trm R3) S2)) (or (and ((member165817296on_trm ((produc709594775on_trm B3) B6)) S2) (= A3 A6)) ((member165817296on_trm (_let_1 A6)) R3))))) (forall ((X2 set_variable) (Y2 set_variable)) (=> ((ord_le282106107riable X2) Y2) (=> ((ord_le282106107riable Y2) X2) (= X2 Y2)))) (= accp_P758790320on_trm (lambda ((R4 (-> produc1072747943on_trm produc1072747943on_trm Bool)) (A4 produc1072747943on_trm)) (exists ((X3 produc1072747943on_trm)) (and (forall ((Y3 produc1072747943on_trm)) (=> ((R4 Y3) X3) ((accp_P758790320on_trm R4) Y3))) (= A4 X3))))) (forall ((B set_variable) (A set_variable) (Q (-> variable Bool)) (P (-> variable Bool))) (=> ((ord_le282106107riable B) A) (=> (forall ((X variable)) (=> ((member_variable X) B) (=> (Q X) (P X)))) ((ord_le282106107riable (collect_variable (lambda ((X3 variable)) (and ((member_variable X3) B) (Q X3))))) (collect_variable (lambda ((X3 variable)) (and (P X3) ((member_variable X3) A)))))))) (forall ((X23 fml)) (= (the_fml (some_fml X23)) X23)) (forall ((X23 trm) (Y23 trm)) (= (= (some_trm X23) (some_trm Y23)) (= X23 Y23))) (forall ((R3 option_fml) (S2 option_fml) (R set_Pr927595527on_fml) (S3 option_fml)) (let ((_let_1 (produc909629463on_fml R3))) (=> ((member1287158352on_fml (_let_1 S2)) R) (=> (= S3 S2) ((member1287158352on_fml (_let_1 S3)) R))))) (forall ((X1 variable) (X61 trm) (X62 trm)) (not (= (var X1) ((times X61) X62)))) (forall ((A set_variable) (B set_variable)) (=> ((ord_le282106107riable A) B) (=> ((ord_le282106107riable B) A) (= A B)))) (forall ((A set_char) (B set_char) (X2 char)) (let ((_let_1 (member_char X2))) (=> ((ord_less_eq_set_char A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((X51 trm) (X52 trm) (X7 trm)) (not (= ((plus X51) X52) (differential X7)))) (forall ((Option option_fml)) (= (not (= Option none_fml)) (((case_option_o_fml false) (lambda ((Uu fml)) true)) Option))) (forall ((Phi option_fml)) (= (not (= Phi none_fml)) (exists ((F2 fml)) (= Phi (some_fml F2))))) (forall ((R set_Pr1471344007on_trm) (S set_Pr1471344007on_trm)) (= ((ord_le847028878_trm_o (lambda ((X3 option_trm) (Y3 option_trm)) ((member165817296on_trm ((produc709594775on_trm X3) Y3)) R))) (lambda ((X3 option_trm) (Y3 option_trm)) ((member165817296on_trm ((produc709594775on_trm X3) Y3)) S))) ((ord_le1322722599on_trm R) S))) (forall ((P Bool) (Q (-> game Bool)) (X2 option_game)) (=> (((case_option_o_game P) Q) X2) (=> (=> (= X2 none_game) (not P)) (not (forall ((Y4 game)) (=> (= X2 (some_game Y4)) (not (Q Y4)))))))) (forall ((X2 option_fml) (P (-> option_fml option_game Bool)) (Y2 option_game)) (let ((_let_1 ((P X2) Y2))) (=> (=> (= X2 none_fml) _let_1) (=> (=> (= Y2 none_game) _let_1) (=> (forall ((A5 fml) (B5 game)) (=> (= X2 (some_fml A5)) (=> (= Y2 (some_game B5)) ((P X2) Y2)))) _let_1))))) (forall ((Theta option_trm)) (= (not (= Theta none_trm)) (exists ((T trm)) (= Theta (some_trm T))))) (forall ((P (-> option_fml Bool)) (A0 option_fml)) (=> (forall ((Phi2 fml)) (P (some_fml Phi2))) (=> (P none_fml) (P A0)))) (forall ((R set_Pr1471344007on_trm) (S set_Pr1471344007on_trm)) (= (= (lambda ((X3 option_trm) (Y3 option_trm)) ((member165817296on_trm ((produc709594775on_trm X3) Y3)) R)) (lambda ((X3 option_trm) (Y3 option_trm)) ((member165817296on_trm ((produc709594775on_trm X3) Y3)) S))) (= R S))) (forall ((R set_Pr943832262on_trm) (S set_Pr943832262on_trm)) (= ((ord_le1890124833_trm_o (lambda ((X3 char) (Y3 option_trm)) ((member694524327on_trm ((produc1500300866on_trm X3) Y3)) R))) (lambda ((X3 char) (Y3 option_trm)) ((member694524327on_trm ((produc1500300866on_trm X3) Y3)) S))) ((ord_le541293862on_trm R) S))) (forall ((A3 set_variable) (B3 set_variable) (F (-> set_variable set_variable)) (C set_variable)) (=> ((ord_le282106107riable A3) B3) (=> ((ord_le282106107riable (F B3)) C) (=> (forall ((X set_variable) (Y4 set_variable)) (=> ((ord_le282106107riable X) Y4) ((ord_le282106107riable (F X)) (F Y4)))) ((ord_le282106107riable (F A3)) C))))) (forall ((Option option_game)) (=> (not (= Option none_game)) (= (some_game (the_game Option)) Option))) (forall ((A set_variable) (B set_variable) (C variable)) (let ((_let_1 (member_variable C))) (=> ((ord_le282106107riable A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((Option option_game) (Option2 option_game)) (let ((_let_1 (= Option2 none_game))) (let ((_let_2 (= Option none_game))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (the_game Option) (the_game Option2)))) (= Option Option2)))))) (forall ((D (-> produc1072747943on_trm Bool)) (R (-> produc1072747943on_trm produc1072747943on_trm Bool)) (X2 produc1072747943on_trm) (P (-> produc1072747943on_trm Bool))) (=> ((ord_le1721128566_trm_o D) (accp_P758790320on_trm R)) (=> (forall ((X produc1072747943on_trm) (Z4 produc1072747943on_trm)) (=> (D X) (=> ((R Z4) X) (D Z4)))) (=> (D X2) (=> (forall ((X produc1072747943on_trm)) (=> (D X) (=> (forall ((Z5 produc1072747943on_trm)) (=> ((R Z5) X) (P Z5))) (P X)))) (P X2)))))) (forall ((A3 set_variable) (B3 set_variable) (C set_variable)) (=> (= A3 B3) (=> ((ord_le282106107riable B3) C) ((ord_le282106107riable A3) C)))) (forall ((X2 option_trm) (Y2 option_trm)) (=> (= (uSubst716837505ntialo X2) Y2) (=> (forall ((Theta2 trm)) (=> (= X2 (some_trm Theta2)) (not (= Y2 (some_trm (differential Theta2)))))) (not (=> (= X2 none_trm) (not (= Y2 none_trm))))))) (forall ((B set_variable) (A set_variable) (P (-> variable Bool))) (let ((_let_1 (ord_le282106107riable B))) (=> (_let_1 A) (= (_let_1 (collect_variable (lambda ((X3 variable)) (and ((member_variable X3) A) (P X3))))) (forall ((X3 variable)) (=> ((member_variable X3) B) (P X3))))))) (forall ((B3 option_fml) (F (-> variable option_fml)) (X2 variable) (C option_fml) (G2 (-> variable option_fml)) (A set_variable)) (=> (= B3 (F X2)) (=> (= C (G2 X2)) (=> ((member_variable X2) A) ((member1287158352on_fml ((produc909629463on_fml B3) C)) (((bNF_Gr600956991on_fml A) F) G2)))))) (forall ((V set_variable) (U set_variable) (Sigma produc1418842292n_game) (Phi fml)) (let ((_let_1 (uSubst516392804stappf Sigma))) (let ((_let_2 ((_let_1 U) Phi))) (=> ((ord_le282106107riable V) U) (=> (not (= _let_2 none_fml)) (= _let_2 ((_let_1 V) Phi))))))) (forall ((X51 trm) (X52 trm) (X61 trm) (X62 trm)) (not (= ((plus X51) X52) ((times X61) X62)))) (forall ((X23 fml)) (not (= none_fml (some_fml X23)))) (forall ((R (-> produc1072747943on_trm produc1072747943on_trm Bool)) (X2 produc1072747943on_trm)) (=> (not ((accp_P758790320on_trm R) X2)) (not (forall ((Z4 produc1072747943on_trm)) (=> ((R Z4) X2) ((accp_P758790320on_trm R) Z4)))))) (forall ((A3 option_fml) (B3 option_fml) (A6 option_fml) (B6 option_fml) (R3 set_Pr927595527on_fml) (S2 set_Pr927595527on_fml)) (let ((_let_1 (produc909629463on_fml A3))) (= ((member450497296on_fml ((produc1367044951on_fml (_let_1 B3)) ((produc909629463on_fml A6) B6))) ((lex_pr314879023on_fml R3) S2)) (or (and ((member1287158352on_fml ((produc909629463on_fml B3) B6)) S2) (= A3 A6)) ((member1287158352on_fml (_let_1 A6)) R3))))) (forall ((R3 (-> option_fml option_fml Bool)) (B3 option_fml) (A3 option_fml)) (let ((_let_1 (accp_option_fml R3))) (=> (_let_1 B3) (=> ((R3 A3) B3) (_let_1 A3))))) (forall ((A3 option_game) (B3 option_fml) (A6 option_game) (B6 option_fml) (R3 set_Pr1625152599n_game) (S2 set_Pr927595527on_fml)) (= ((member113767842on_fml ((produc556056113on_fml ((produc2124676926on_fml A3) B3)) ((produc2124676926on_fml A6) B6))) ((lex_pr425996582on_fml R3) S2)) (or (and (= A3 A6) ((member1287158352on_fml ((produc909629463on_fml B3) B6)) S2)) ((member191809696n_game ((produc1111617711n_game A3) A6)) R3)))) (forall ((X23 game)) (= (the_game (some_game X23)) X23)) (forall ((X2 variable) (Theta trm)) (= ((uSubst834381837ssigno X2) (some_trm Theta)) (some_game ((assign X2) Theta)))) _let_3 (forall ((A3 char) (B3 option_trm) (A6 char) (B6 option_trm) (R3 set_Pr604539619r_char) (S2 set_Pr1471344007on_trm)) (= ((member1950256170on_trm ((produc444919481on_trm ((produc1500300866on_trm A3) B3)) ((produc1500300866on_trm A6) B6))) ((lex_pr1901327402on_trm R3) S2)) (or (and ((member165817296on_trm ((produc709594775on_trm B3) B6)) S2) (= A3 A6)) ((member1866856748r_char ((produc19545147r_char A3) A6)) R3)))) (forall ((A set_char)) (= (collect_char (lambda ((X3 char)) ((member_char X3) A))) A)) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (V set_variable)) (let ((_let_1 (uSubst516392818stappt Sigma))) (let ((_let_2 ((_let_1 V) Theta))) (let ((_let_3 ((_let_1 U) Theta))) (=> (not (= _let_3 none_trm)) (=> (not (= _let_2 none_trm)) (= _let_3 _let_2))))))) (forall ((P (-> variable option_fml Bool)) (A0 variable) (A1 option_fml)) (=> (forall ((X variable) (Phi2 fml)) ((P X) (some_fml Phi2))) (=> (forall ((X variable)) ((P X) none_fml)) ((P A0) A1)))) _let_2 (forall ((X2 option_game)) (= (forall ((Y3 game)) (not (= X2 (some_game Y3)))) (= X2 none_game))) (forall ((X2 char)) (= ((uSubst1827052306e_ODEo X2) none_trm) none_game)) (forall ((X1 variable) (X32 char)) (not (= (var X1) (const X32)))) (forall ((R1 (-> produc464795408on_trm produc464795408on_trm Bool)) (R2 (-> produc464795408on_trm produc464795408on_trm Bool))) (=> ((ord_le157637894_trm_o R1) R2) ((ord_le1222882015_trm_o (accp_P419951815on_trm R2)) (accp_P419951815on_trm R1)))) (forall ((X2 set_variable) (Y2 set_variable)) (=> (= X2 Y2) ((ord_le282106107riable X2) Y2))) (forall ((Theta trm) (Eta trm)) (= ((uSubst141955042_Pluso (some_trm Theta)) (some_trm Eta)) (some_trm ((plus Theta) Eta)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (let ((_let_2 ((times Theta) Eta))) (=> ((accp_P1877119646le_trm uSubst1917534215pt_rel) ((produc2015636557le_trm Sigma) ((produc1482344242le_trm U) _let_2))) (= (_let_1 _let_2) ((uSubst918876924Timeso (_let_1 Theta)) (_let_1 Eta))))))) (forall ((X51 trm) (X52 trm) (Y51 trm) (Y52 trm)) (= (= ((plus X51) X52) ((plus Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))) (forall ((P (-> option_fml option_fml Bool)) (A0 option_fml) (A1 option_fml)) (=> (forall ((Phi2 fml) (Psi fml)) ((P (some_fml Phi2)) (some_fml Psi))) (=> (forall ((X_1 option_fml)) ((P none_fml) X_1)) (=> (forall ((V2 fml)) ((P (some_fml V2)) none_fml)) ((P A0) A1))))) (forall ((R set_Pr927595527on_fml) (S set_Pr927595527on_fml)) (= ((ord_le802833166_fml_o (lambda ((X3 option_fml) (Y3 option_fml)) ((member1287158352on_fml ((produc909629463on_fml X3) Y3)) R))) (lambda ((X3 option_fml) (Y3 option_fml)) ((member1287158352on_fml ((produc909629463on_fml X3) Y3)) S))) ((ord_le778974119on_fml R) S))) (= (lambda ((P2 (-> option_trm Bool))) (forall ((X5 option_trm)) (P2 X5))) (lambda ((P3 (-> option_trm Bool))) (and (forall ((X3 trm)) (P3 (some_trm X3))) (P3 none_trm)))) (forall ((A set_char) (P (-> char Bool))) ((ord_less_eq_set_char (collect_char (lambda ((X3 char)) (and ((member_char X3) A) (P X3))))) A)) (forall ((X23 real) (Y23 real)) (= (= (number X23) (number Y23)) (= X23 Y23))) (forall ((U set_variable) (V set_variable) (Omega (-> variable real)) (Nu (-> variable real))) (let ((_let_1 ((denota1419872369iation Omega) Nu))) (=> ((ord_le282106107riable U) V) (=> (_let_1 U) (_let_1 V))))) (forall ((X2 option_game) (P (-> option_game option_trm Bool)) (Y2 option_trm)) (let ((_let_1 ((P X2) Y2))) (=> (=> (= X2 none_game) _let_1) (=> (=> (= Y2 none_trm) _let_1) (=> (forall ((A5 game) (B5 trm)) (=> (= X2 (some_game A5)) (=> (= Y2 (some_trm B5)) ((P X2) Y2)))) _let_1))))) (forall ((Theta option_trm) (Eta option_trm)) (= (= ((uSubst141955042_Pluso Theta) Eta) none_trm) (or (= Eta none_trm) (= Theta none_trm)))) (forall ((P (-> option_trm Bool)) (A0 option_trm)) (=> (forall ((Theta2 trm)) (P (some_trm Theta2))) (=> (P none_trm) (P A0)))) (forall ((R3 set_Pr927595527on_fml) (S2 set_Pr927595527on_fml)) (=> (forall ((X option_fml) (Y4 option_fml)) (let ((_let_1 (member1287158352on_fml ((produc909629463on_fml X) Y4)))) (=> (_let_1 R3) (_let_1 S2)))) ((ord_le778974119on_fml R3) S2))) (forall ((R3 set_Pr622314946on_fml) (S2 set_Pr622314946on_fml)) (=> (forall ((X option_game) (Y4 option_fml)) (let ((_let_1 (member1883102883on_fml ((produc2124676926on_fml X) Y4)))) (=> (_let_1 R3) (_let_1 S2)))) ((ord_le782333474on_fml R3) S2))) (forall ((X2 option_game)) (=> (forall ((Alpha game)) (not (= X2 (some_game Alpha)))) (= X2 none_game))) (forall ((R set_Pr943832262on_trm) (S set_Pr943832262on_trm)) (= (= (lambda ((X3 char) (Y3 option_trm)) ((member694524327on_trm ((produc1500300866on_trm X3) Y3)) R)) (lambda ((X3 char) (Y3 option_trm)) ((member694524327on_trm ((produc1500300866on_trm X3) Y3)) S))) (= R S))) (forall ((P Bool) (Q (-> trm Bool)) (X2 option_trm)) (=> (((case_option_o_trm P) Q) X2) (=> (=> (= X2 none_trm) (not P)) (not (forall ((Y4 trm)) (=> (= X2 (some_trm Y4)) (not (Q Y4)))))))) (forall ((X23 real) (X32 char)) (not (= (number X23) (const X32)))) _let_1 (forall ((R1 (-> produc1072747943on_trm produc1072747943on_trm Bool)) (R2 (-> produc1072747943on_trm produc1072747943on_trm Bool))) (=> ((ord_le90123726_trm_o R1) R2) ((ord_le1721128566_trm_o (accp_P758790320on_trm R2)) (accp_P758790320on_trm R1)))) (forall ((Y2 option_fml)) (=> (not (= Y2 none_fml)) (not (forall ((X24 fml)) (not (= Y2 (some_fml X24))))))) (= ord_less_eq_set_char (lambda ((A2 set_char) (B2 set_char)) (forall ((X3 char)) (let ((_let_1 (member_char X3))) (=> (_let_1 A2) (_let_1 B2)))))) (= ord_less_eq_set_char (lambda ((A2 set_char) (B2 set_char)) (forall ((T char)) (let ((_let_1 (member_char T))) (=> (_let_1 A2) (_let_1 B2)))))) (forall ((Phi fml)) (= (uSubst1367128042_Testo (some_fml Phi)) (some_game (test Phi)))) (forall ((X2 produc464795408on_trm)) (=> (forall ((X char) (Theta2 trm)) (not (= X2 ((produc1500300866on_trm X) (some_trm Theta2))))) (not (forall ((X char)) (not (= X2 ((produc1500300866on_trm X) none_trm))))))) (forall ((R3 char) (S2 option_trm) (R set_Pr943832262on_trm) (S3 option_trm)) (let ((_let_1 (produc1500300866on_trm R3))) (=> ((member694524327on_trm (_let_1 S2)) R) (=> (= S3 S2) ((member694524327on_trm (_let_1 S3)) R))))) (forall ((R (-> option_trm option_trm Bool)) (X2 option_trm)) (=> (not ((accp_option_trm R) X2)) (not (forall ((Z4 option_trm)) (=> ((R Z4) X2) ((accp_option_trm R) Z4)))))) (forall ((R3 (-> option_trm option_trm Bool)) (A3 option_trm)) (=> ((accp_option_trm R3) A3) (forall ((Y5 option_trm)) (=> ((R3 Y5) A3) ((accp_option_trm R3) Y5))))) (forall ((R3 (-> produc1072747943on_trm produc1072747943on_trm Bool)) (A3 produc1072747943on_trm)) (=> ((accp_P758790320on_trm R3) A3) (forall ((Y5 produc1072747943on_trm)) (=> ((R3 Y5) A3) ((accp_P758790320on_trm R3) Y5))))) (forall ((Option option_trm)) (=> (not (= Option none_trm)) (= (some_trm (the_trm Option)) Option))) (forall ((X2 option_trm)) (=> (forall ((Theta2 trm)) (not (= X2 (some_trm Theta2)))) (= X2 none_trm))) (forall ((X32 fml) (Y32 fml)) (= (= (test X32) (test Y32)) (= X32 Y32))) (forall ((X2 option_game)) (= (not (= X2 none_game)) (exists ((Y3 game)) (= X2 (some_game Y3))))) (forall ((X2 option_trm)) (= (not (= X2 none_trm)) (exists ((Y3 trm)) (= X2 (some_trm Y3))))) (forall ((X2 produc46605351on_fml)) (=> (forall ((Phi2 fml) (Psi fml)) (not (= X2 ((produc909629463on_fml (some_fml Phi2)) (some_fml Psi))))) (=> (forall ((Psi option_fml)) (not (= X2 ((produc909629463on_fml none_fml) Psi)))) (not (forall ((V2 fml)) (not (= X2 ((produc909629463on_fml (some_fml V2)) none_fml)))))))) (forall ((A3 option_fml) (B3 option_trm) (A6 option_fml) (B6 option_trm) (R3 set_Pr927595527on_fml) (S2 set_Pr1471344007on_trm)) (= ((member1883874960on_trm ((produc2132972503on_trm ((produc1447374177on_trm A3) B3)) ((produc1447374177on_trm A6) B6))) ((lex_pr852623737on_trm R3) S2)) (or (and (= A3 A6) ((member165817296on_trm ((produc709594775on_trm B3) B6)) S2)) ((member1287158352on_fml ((produc909629463on_fml A3) A6)) R3)))) (forall ((X2 option_trm) (Xa option_trm) (Y2 option_trm)) (let ((_let_1 (accp_P758790320on_trm uSubst924844285so_rel))) (=> (= ((uSubst918876924Timeso X2) Xa) Y2) (=> (_let_1 ((produc709594775on_trm X2) Xa)) (=> (forall ((Theta2 trm)) (=> (= X2 (some_trm Theta2)) (forall ((Eta2 trm)) (let ((_let_1 (some_trm Eta2))) (=> (= Xa _let_1) (=> (= Y2 (some_trm ((times Theta2) Eta2))) (not ((accp_P758790320on_trm uSubst924844285so_rel) ((produc709594775on_trm (some_trm Theta2)) _let_1))))))))) (=> (=> (= X2 none_trm) (=> (= Y2 none_trm) (not (_let_1 ((produc709594775on_trm none_trm) Xa))))) (not (forall ((V2 trm)) (let ((_let_1 (some_trm V2))) (=> (= X2 _let_1) (=> (= Xa none_trm) (=> (= Y2 none_trm) (not ((accp_P758790320on_trm uSubst924844285so_rel) ((produc709594775on_trm _let_1) none_trm))))))))))))))) (= (lambda ((P2 (-> option_game Bool))) (forall ((X5 option_game)) (P2 X5))) (lambda ((P3 (-> option_game Bool))) (and (P3 none_game) (forall ((X3 game)) (P3 (some_game X3)))))) (forall ((R3 (-> option_trm option_trm Bool)) (X2 option_trm)) (=> (forall ((Y4 option_trm)) (=> ((R3 Y4) X2) ((accp_option_trm R3) Y4))) ((accp_option_trm R3) X2))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta trm)) (let ((_let_1 ((uSubst516392818stappt Sigma) U))) (= (_let_1 ((times Theta) Eta)) ((uSubst918876924Timeso (_let_1 Theta)) (_let_1 Eta))))) (not false)))))))))))))))))))))))))
0.90/1.11	)
0.90/1.11	% SZS output end Proof for theBenchmark
0.90/1.11	EOF