0.03/0.12	% Problem    : SLH010^1 : TPTP v7.5.0. Released v7.5.0.
0.03/0.13	% Command    : do_cvc5 %s %d
0.13/0.34	% Computer : n005.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 30
0.13/0.34	% WCLimit    : 30
0.13/0.34	% DateTime   : Tue Aug  9 02:17:19 EDT 2022
0.13/0.35	% CPUTime    : 
0.20/0.50	%----Proving TH0 SLH
0.89/1.11	------- cvc5-slh casc 28 : /export/starexec/sandbox/benchmark/theBenchmark.p at 30...
0.89/1.11	--- Run --ho-elim --full-saturate-quant at 5...
0.89/1.11	% SZS status Theorem for theBenchmark
0.89/1.11	% SZS output start Proof for theBenchmark
0.89/1.11	(let ((_let_1 (= produc1420172399on_fml (lambda ((F (-> (-> char option_fml) (-> char option_game) char option_fml)) (X4 produc799602994n_game) (Y char)) (@ (@ produc347802313on_fml (lambda ((L (-> char option_fml)) (R3 (-> char option_game))) (@ (@ (@ F L) R3) Y))) X4))))) (let ((_let_2 (= produc1250175341on_fml (lambda ((F (-> (-> char option_trm) produc62062515n_game char option_fml)) (X4 produc1418842292n_game) (Y char)) (@ (@ produc1499310791on_fml (lambda ((L (-> char option_trm)) (R3 produc62062515n_game)) (@ (@ (@ F L) R3) Y))) X4))))) (let ((_let_3 (= 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_4 (= produc1615133358on_fml (lambda ((F (-> (-> char option_trm) produc799602994n_game char option_fml)) (X4 produc62062515n_game) (Y char)) (@ (@ produc154833544on_fml (lambda ((L (-> char option_trm)) (R3 produc799602994n_game)) (@ (@ (@ F L) R3) Y))) X4))))) (let ((_let_5 (= ord_le282106107riable (lambda ((A4 set_variable) (B4 set_variable)) (@ (@ ord_le1407353162able_o (lambda ((X4 variable)) (@ (@ member_variable X4) A4))) (lambda ((X4 variable)) (@ (@ member_variable X4) B4))))))) (let ((_let_6 (= (@ (@ inf_inf_set_variable (@ static_FVF r)) ua) bot_bot_set_variable))) (let ((_let_7 (= inf_in1556002680e_real (lambda ((A4 set_variable_real) (B4 set_variable_real)) (@ collec633296133e_real (@ (@ inf_in450528013real_o (lambda ((X4 (-> variable real))) (@ (@ member_variable_real X4) A4))) (lambda ((X4 (-> variable real))) (@ (@ member_variable_real X4) B4)))))))) (let ((_let_8 (= ord_le1113654598e_real (lambda ((A4 set_variable_real) (B4 set_variable_real)) (@ (@ ord_le1354144447real_o (lambda ((X4 (-> variable real))) (@ (@ member_variable_real X4) A4))) (lambda ((X4 (-> variable real))) (@ (@ member_variable_real X4) B4))))))) (let ((_let_9 (@ (@ (@ uSubst516392804stappf sigma) ua) (@ (@ pred p) theta)))) (let ((_let_10 (not (= _let_9 none_fml)))) (let ((_let_11 (= case_o325794063ml_trm (lambda ((F12 option_fml) (F23 (-> trm option_fml)) (Option3 option_trm)) (@ (@ (@ if_option_fml (= Option3 none_trm)) F12) (@ F23 (@ the_trm Option3))))))) (let ((_let_12 (forall ((Sigma produc1418842292n_game) (U set_variable) (P2 char) (Theta trm)) (=> (not (= (@ (@ (@ uSubst516392804stappf Sigma) U) (@ (@ pred P2) Theta)) none_fml)) (and (not (= (@ (@ (@ uSubst516392818stappt Sigma) U) Theta) none_trm)) (or (= (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) Sigma) P2) none_fml) (exists ((R fml)) (and (= (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) Sigma) P2) (@ some_fml R)) (= (@ (@ inf_inf_set_variable (@ static_FVF R)) U) bot_bot_set_variable))))))))) (let ((_let_13 (= inf_inf_set_variable (lambda ((A4 set_variable) (B4 set_variable)) (@ collect_variable (@ (@ inf_inf_variable_o (lambda ((X4 variable)) (@ (@ member_variable X4) A4))) (lambda ((X4 variable)) (@ (@ member_variable X4) B4)))))))) (let ((_let_14 (= case_o209804997ml_fml (lambda ((F12 option_fml) (F23 (-> fml option_fml)) (Option3 option_fml)) (@ (@ (@ if_option_fml (= Option3 none_fml)) F12) (@ F23 (@ the_fml Option3))))))) (let ((_let_15 (= case_o1836798020_o_fml (lambda ((F12 (-> real Bool)) (F23 (-> fml real Bool)) (Option3 option_fml) (__flatten_var_0 real)) (@ (@ (@ (@ if_real_o (= Option3 none_fml)) F12) (@ F23 (@ the_fml Option3))) __flatten_var_0))))) (let ((_let_16 (= bot_bo1661475211real_o (lambda ((X4 (-> variable real))) (@ (@ member_variable_real X4) bot_bo721182586e_real))))) (let ((_let_17 (= bot_bot_variable_o (lambda ((X4 variable)) (@ (@ member_variable X4) bot_bot_set_variable))))) (let ((_let_18 (not (not (= (@ (@ (@ uSubst516392818stappt sigma) ua) theta) none_trm))))) (let ((_let_19 (= none_fml (ho_864 (ho_1650 (ho_1649 k_1648 sigma) ua) (ho_1647 (ho_1646 k_1645 p) theta))))) (let ((_let_20 (forall ((Sigma produc1418842292n_game) (U set_variable) (P2 char) (Theta trm)) (or (= none_fml (ho_864 (ho_1650 (ho_1649 k_1648 Sigma) U) (ho_1647 (ho_1646 k_1645 P2) Theta))) (and (not (= (ho_1624 (ho_1627 (ho_1626 k_1625 sigma) ua) theta) (ho_1624 (ho_1627 (ho_1626 k_1625 Sigma) U) Theta))) (or (= none_fml (ho_793 (ho_792 k_791 (ho_778 k_1637 P2)) Sigma)) (not (forall ((R fml)) (or (not (= (ho_793 (ho_792 k_791 (ho_778 k_1638 P2)) Sigma) (ho_864 k_1192 R))) (not (= (ho_884 k_883 (ho_826 (ho_1066 k_1065 k_1064) k_1063)) (ho_884 k_883 (ho_826 (ho_1066 k_1065 (ho_1213 k_1639 R)) (ho_837 k_1640 U)))))))))))))) (let ((_let_21 (forall ((Sigma produc1418842292n_game) (U set_variable) (P2 char) (Theta trm)) (or (= none_fml (@ (@ (@ uSubst516392804stappf Sigma) U) (@ (@ pred P2) Theta))) (and (not (= (@ (@ (@ uSubst516392818stappt Sigma) U) Theta) (@ (@ (@ uSubst516392818stappt sigma) ua) theta))) (or (= none_fml (@ (@ produc1499310791on_fml (@ ll_8 P2)) Sigma)) (not (forall ((R fml)) (or (not (= (@ some_fml R) (@ (@ produc1499310791on_fml (@ ll_7 P2)) Sigma))) (not (= (@ collect_variable (@ (@ inf_inf_variable_o (@ ll_4 R)) (@ ll_3 U))) (@ collect_variable (@ (@ inf_inf_variable_o ll_6) ll_5))))))))))))) (let ((_let_22 (SYMM (ASSUME :args (_let_6))))) (let ((_let_23 (ASSUME :args (_let_7)))) (let ((_let_24 (ASSUME :args (_let_13)))) (let ((_let_25 (ASSUME :args (_let_8)))) (let ((_let_26 (ASSUME :args (_let_5)))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (ASSUME :args (_let_2)))) (let ((_let_29 (ASSUME :args (_let_4)))) (let ((_let_30 (ASSUME :args (_let_1)))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (ASSUME :args (_let_16)))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22) :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22) :args ((forall ((Sigma produc1418842292n_game) (U set_variable) (P2 char) (Theta trm)) (or (= none_fml (@ (@ (@ uSubst516392804stappf Sigma) U) (@ (@ pred P2) Theta))) (and (not (= none_trm (@ (@ (@ uSubst516392818stappt Sigma) U) Theta))) (or (= none_fml (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) Sigma) P2)) (not (forall ((R fml)) (or (not (= (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) Sigma) P2) (@ some_fml R))) (not (= bot_bot_set_variable (@ (@ inf_inf_set_variable (@ static_FVF R)) U)))))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Sigma produc1418842292n_game) (U set_variable) (P2 char) (Theta trm)) (or (= none_fml (@ (@ (@ uSubst516392804stappf Sigma) U) (@ (@ pred P2) Theta))) (and (not (= (@ (@ (@ uSubst516392818stappt Sigma) U) Theta) (@ (@ (@ uSubst516392818stappt sigma) ua) theta))) (or (= none_fml (@ (@ produc1499310791on_fml (lambda ((BOUND_VARIABLE_18001 (-> char option_trm)) (BOUND_VARIABLE_18002 produc62062515n_game)) (@ (@ produc154833544on_fml (lambda ((BOUND_VARIABLE_18003 (-> char option_trm)) (BOUND_VARIABLE_18004 produc799602994n_game)) (@ (@ produc347802313on_fml (lambda ((BOUND_VARIABLE_18005 (-> char option_fml)) (BOUND_VARIABLE_18006 (-> char option_game))) (@ BOUND_VARIABLE_18005 P2))) BOUND_VARIABLE_18004))) BOUND_VARIABLE_18002))) Sigma)) (not (forall ((R fml)) (or (not (= (@ some_fml R) (@ (@ produc1499310791on_fml (lambda ((BOUND_VARIABLE_18304 (-> char option_trm)) (BOUND_VARIABLE_18305 produc62062515n_game)) (@ (@ produc154833544on_fml (lambda ((BOUND_VARIABLE_18306 (-> char option_trm)) (BOUND_VARIABLE_18307 produc799602994n_game)) (@ (@ produc347802313on_fml (lambda ((BOUND_VARIABLE_18308 (-> char option_fml)) (BOUND_VARIABLE_18309 (-> char option_game))) (@ BOUND_VARIABLE_18308 P2))) BOUND_VARIABLE_18307))) BOUND_VARIABLE_18305))) Sigma))) (not (= (@ collect_variable (@ (@ inf_inf_variable_o (lambda ((BOUND_VARIABLE_8146 variable)) (@ (@ member_variable BOUND_VARIABLE_8146) (@ static_FVF r)))) (lambda ((BOUND_VARIABLE_8141 variable)) (@ (@ member_variable BOUND_VARIABLE_8141) ua)))) (@ collect_variable (@ (@ inf_inf_variable_o (lambda ((BOUND_VARIABLE_18354 variable)) (@ (@ member_variable BOUND_VARIABLE_18354) (@ static_FVF R)))) (lambda ((BOUND_VARIABLE_18349 variable)) (@ (@ member_variable BOUND_VARIABLE_18349) U))))))))))))) _let_21))) (PREPROCESS :args ((= _let_21 _let_20))))))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (sigma ua p theta QUANTIFIERS_INST_E_MATCHING ((not (= (ho_864 (ho_1650 (ho_1649 k_1648 Sigma) U) (ho_1647 (ho_1646 k_1645 P2) Theta)) none_fml))))) :args (_let_20)))) :args ((or _let_19 (not _let_20)))) _let_35 (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (= none_fml _let_9)) (not _let_19)))))) :args (false false _let_20 true _let_19)) :args (true _let_18 (forall ((X2 option_fml) (Y3 option_fml)) (= (@ (@ (@ if_option_fml false) X2) Y3) Y3)) (forall ((X2 (-> real Bool)) (Y3 (-> real Bool))) (= (@ (@ (@ if_real_o true) X2) Y3) X2)) (forall ((Sigma produc1418842292n_game) (I2 denotational_interp) (Omega (-> variable real)) (P2 char)) (= (@ (@ denotational_Preds (@ (@ (@ uSubst1599435252djoint Sigma) I2) Omega)) P2) (@ (@ (@ case_o1836798020_o_fml (@ (@ denotational_Preds I2) P2)) (lambda ((R3 fml) (D3 real)) (@ (@ member_variable_real Omega) (@ (@ denotational_fml_sem (@ (@ (@ uSubst1505767257e_repc I2) (@ (@ (@ (@ (@ (@ (@ (@ char2 false) true) true) true) false) true) false) false)) D3)) R3)))) (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) Sigma) P2)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta2 trm)) (let ((_let_1 (@ (@ uSubst516392818stappt Sigma) U))) (let ((_let_2 (@ (@ (@ uSubst516392804stappf Sigma) U) (@ (@ geq Theta) Eta2)))) (=> (not (= _let_2 none_fml)) (= _let_2 (@ some_fml (@ (@ geq (@ the_trm (@ _let_1 Theta))) (@ the_trm (@ _let_1 Eta2))))))))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta2 trm)) (let ((_let_1 (@ (@ uSubst516392818stappt Sigma) U))) (let ((_let_2 (@ _let_1 Eta2))) (let ((_let_3 (@ _let_1 Theta))) (=> (not (= _let_3 none_trm)) (=> (not (= _let_2 none_trm)) (= (@ (@ (@ uSubst516392804stappf Sigma) U) (@ (@ geq Theta) Eta2)) (@ some_fml (@ (@ geq (@ the_trm _let_3)) (@ the_trm _let_2)))))))))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta2 trm)) (let ((_let_1 (@ (@ uSubst516392818stappt Sigma) U))) (= (@ (@ (@ uSubst516392804stappf Sigma) U) (@ (@ geq Theta) Eta2)) (@ (@ uSubst152838031e_Geqo (@ _let_1 Theta)) (@ _let_1 Eta2))))) (forall ((X11 char) (X12 trm) (X21 trm) (X222 trm)) (not (= (@ (@ pred X11) X12) (@ (@ geq X21) X222)))) (forall ((I2 denotational_interp) (F2 char) (D real)) (= (@ denotational_Preds (@ (@ (@ uSubst1505767257e_repc I2) F2) D)) (@ denotational_Preds I2))) (forall ((Theta trm) (Eta2 trm)) (= (@ (@ uSubst141955042_Pluso (@ some_trm Theta)) (@ some_trm Eta2)) (@ some_trm (@ (@ plus Theta) Eta2)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta2 trm)) (let ((_let_1 (@ (@ uSubst516392818stappt Sigma) U))) (= (@ _let_1 (@ (@ plus Theta) Eta2)) (@ (@ uSubst141955042_Pluso (@ _let_1 Theta)) (@ _let_1 Eta2))))) (forall ((Eta2 option_trm)) (= (@ (@ uSubst152838031e_Geqo none_trm) Eta2) none_fml)) (forall ((Theta option_trm) (Eta2 option_trm)) (= (= (@ (@ uSubst152838031e_Geqo Theta) Eta2) none_fml) (or (= Theta none_trm) (= Eta2 none_trm)))) (forall ((V3 trm)) (= (@ (@ uSubst152838031e_Geqo (@ some_trm V3)) none_trm) none_fml)) (forall ((X2 option_trm) (Xa option_trm) (Y3 option_trm)) (let ((_let_1 (not (= Y3 none_trm)))) (=> (= (@ (@ uSubst141955042_Pluso X2) Xa) Y3) (=> (forall ((Theta2 trm)) (=> (= X2 (@ some_trm Theta2)) (forall ((Eta trm)) (=> (= Xa (@ some_trm Eta)) (not (= Y3 (@ some_trm (@ (@ plus Theta2) Eta)))))))) (=> (=> (= X2 none_trm) _let_1) (not (=> (exists ((V2 trm)) (= X2 (@ some_trm V2))) (=> (= Xa none_trm) _let_1)))))))) (forall ((Theta trm) (Eta2 trm)) (= (@ (@ uSubst918876924Timeso (@ some_trm Theta)) (@ some_trm Eta2)) (@ some_trm (@ (@ times Theta) Eta2)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta2 trm)) (let ((_let_1 (@ (@ uSubst516392818stappt Sigma) U))) (= (@ _let_1 (@ (@ times Theta) Eta2)) (@ (@ uSubst918876924Timeso (@ _let_1 Theta)) (@ _let_1 Eta2))))) (forall ((Eta2 option_trm)) (= (@ (@ uSubst918876924Timeso none_trm) Eta2) none_trm)) (forall ((X2 option_trm) (Xa option_trm) (Y3 option_trm)) (let ((_let_1 (not (= Y3 none_trm)))) (=> (= (@ (@ uSubst918876924Timeso X2) Xa) Y3) (=> (forall ((Theta2 trm)) (=> (= X2 (@ some_trm Theta2)) (forall ((Eta trm)) (=> (= Xa (@ some_trm Eta)) (not (= Y3 (@ some_trm (@ (@ times Theta2) Eta)))))))) (=> (=> (= X2 none_trm) _let_1) (not (=> (exists ((V2 trm)) (= X2 (@ some_trm V2))) (=> (= Xa none_trm) _let_1)))))))) (forall ((P Bool) (Q (-> trm Bool)) (X2 option_trm) (R4 (-> option_fml Bool)) (F2 option_fml) (G2 (-> trm option_fml))) (=> (@ (@ (@ case_option_o_trm P) Q) X2) (=> (=> P (@ R4 F2)) (=> (forall ((Q2 trm)) (=> (@ Q Q2) (@ R4 (@ G2 Q2)))) (@ R4 (@ (@ (@ case_o325794063ml_trm F2) G2) X2)))))) (forall ((X2 variable) (Z4 set_variable) (X5 set_variable) (P (-> variable Bool))) (=> (@ (@ member_variable X2) Z4) (=> (@ (@ ord_le282106107riable Z4) (@ collect_variable (lambda ((X4 variable)) (and (@ (@ member_variable X4) X5) (@ P X4))))) (@ P X2)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta2 trm)) (let ((_let_1 (@ (@ uSubst516392818stappt Sigma) U))) (=> (not (= (@ (@ (@ uSubst516392804stappf Sigma) U) (@ (@ geq Theta) Eta2)) none_fml)) (and (not (= (@ _let_1 Theta) none_trm)) (not (= (@ _let_1 Eta2) none_trm)))))) (forall ((X2 (-> variable real)) (Z4 set_variable_real) (X5 set_variable_real) (P (-> (-> variable real) Bool))) (=> (@ (@ member_variable_real X2) Z4) (=> (@ (@ ord_le1113654598e_real Z4) (@ collec633296133e_real (lambda ((X4 (-> variable real))) (and (@ (@ member_variable_real X4) X5) (@ P X4))))) (@ P X2)))) (forall ((A2 set_variable)) (=> (forall ((X variable)) (not (@ (@ member_variable X) A2))) (@ (@ ord_le282106107riable A2) bot_bot_set_variable))) (forall ((A2 set_variable_real)) (=> (forall ((X (-> variable real))) (not (@ (@ member_variable_real X) A2))) (@ (@ ord_le1113654598e_real A2) bot_bo721182586e_real))) (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 ((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 ((Option option_game)) (= (= Option none_game) (@ (@ (@ case_option_o_game true) (lambda ((Uu game)) false)) Option))) (forall ((Option option_fml)) (= (= Option none_fml) (@ (@ (@ case_option_o_fml true) (lambda ((Uu fml)) false)) Option))) (forall ((Option option_game)) (= (not (= Option none_game)) (@ (@ (@ case_option_o_game false) (lambda ((Uu game)) true)) Option))) (forall ((Option option_fml)) (= (not (= Option none_fml)) (@ (@ (@ case_option_o_fml false) (lambda ((Uu fml)) true)) Option))) _let_17 _let_16 (forall ((R4 set_variable) (S set_variable)) (= (@ (@ ord_le1407353162able_o (lambda ((X4 variable)) (@ (@ member_variable X4) R4))) (lambda ((X4 variable)) (@ (@ member_variable X4) S))) (@ (@ ord_le282106107riable R4) S))) (forall ((R4 set_variable_real) (S set_variable_real)) (= (@ (@ ord_le1354144447real_o (lambda ((X4 (-> variable real))) (@ (@ member_variable_real X4) R4))) (lambda ((X4 (-> variable real))) (@ (@ member_variable_real X4) S))) (@ (@ ord_le1113654598e_real R4) S))) (forall ((R4 set_variable) (S set_variable)) (= (@ (@ inf_inf_variable_o (lambda ((X4 variable)) (@ (@ member_variable X4) R4))) (lambda ((X4 variable)) (@ (@ member_variable X4) S))) (lambda ((X4 variable)) (@ (@ member_variable X4) (@ (@ inf_inf_set_variable R4) S))))) (forall ((R4 set_variable_real) (S set_variable_real)) (= (@ (@ inf_in450528013real_o (lambda ((X4 (-> variable real))) (@ (@ member_variable_real X4) R4))) 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none_trm) (or (= Theta none_trm) (= Eta2 none_trm)))) (= inf_in1556002680e_real (lambda ((A4 set_variable_real) (B4 set_variable_real)) (@ collec633296133e_real (lambda ((X4 (-> variable real))) (let ((_let_1 (@ member_variable_real X4))) (and (@ _let_1 A4) (@ _let_1 B4))))))) (forall ((A3 set_variable)) (= (@ (@ inf_inf_set_variable A3) A3) A3)) (forall ((X2 option_game)) (= (forall ((Y game)) (not (= X2 (@ some_game Y)))) (= X2 none_game))) (forall ((Sigma produc1418842292n_game) (P2 char) (R2 fml) (U set_variable) (Theta trm)) (=> (= (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) Sigma) P2) (@ some_fml R2)) (=> (not (= (@ (@ inf_inf_set_variable (@ static_FVF R2)) U) bot_bot_set_variable)) (= (@ (@ (@ uSubst516392804stappf Sigma) U) (@ (@ pred P2) Theta)) none_fml)))) (@ (@ (@ denota1419872369iation nu2) omega2) ua) (forall ((X2 option_fml)) (= (not (= X2 none_fml)) (exists ((Y fml)) (= X2 (@ some_fml Y))))) (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)))))) _let_11 (forall ((A3 set_variable) (X2 set_variable) (B3 set_variable)) (=> (@ (@ ord_le282106107riable A3) X2) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A3) B3)) X2))) (= none_trm none_trm) (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 ((C2 variable)) (not (@ (@ member_variable C2) bot_bot_set_variable))) (forall ((X22 fml) (Y2 fml)) (= (= (@ some_fml X22) (@ some_fml Y2)) (= X22 Y2))) (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 ((A2 set_variable) (B2 set_variable)) (=> (forall ((X variable)) (let ((_let_1 (@ member_variable X))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ inf_inf_set_variable A2) B2) bot_bot_set_variable))) (forall ((A2 set_variable) (C set_variable) (B2 set_variable) (D2 set_variable)) (=> (@ (@ ord_le282106107riable A2) C) (=> (@ (@ ord_le282106107riable B2) D2) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A2) B2)) (@ (@ inf_inf_set_variable C) D2))))) (forall ((X22 fml)) (= (@ the_fml (@ some_fml X22)) X22)) (forall ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta2 trm)) (let ((_let_1 (@ (@ uSubst516392818stappt Sigma) U))) (=> (not (= (@ _let_1 (@ (@ times Theta) Eta2)) none_trm)) (and (not (= (@ _let_1 Theta) none_trm)) (not (= (@ _let_1 Eta2) none_trm)))))) (forall ((X2 set_variable)) (= (@ (@ inf_inf_set_variable X2) bot_bot_set_variable) bot_bot_set_variable)) (forall ((A3 variable)) (not (@ (@ member_variable A3) bot_bot_set_variable))) (forall ((C2 variable) (A2 set_variable) (B2 set_variable)) (let ((_let_1 (@ member_variable C2))) (=> (@ _let_1 (@ (@ inf_inf_set_variable A2) B2)) (@ _let_1 B2)))) (forall ((A2 set_variable_real) (B2 set_variable_real)) (=> (forall ((X (-> variable real))) (let ((_let_1 (@ member_variable_real X))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ ord_le1113654598e_real A2) B2))) (forall ((X2 set_variable) (Y3 set_variable)) (=> (@ (@ ord_le282106107riable X2) Y3) (=> (@ (@ ord_le282106107riable Y3) X2) (= X2 Y3)))) _let_10 (forall ((Theta option_trm)) (= (not (= Theta none_trm)) (exists ((T trm)) (= Theta (@ some_trm T))))) (forall ((X22 game) (Y2 game)) (= (= (@ some_game X22) (@ some_game Y2)) (= X22 Y2))) (= (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) sigma) p) (@ some_fml r)) (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 ((A3 set_variable) (B3 set_variable) (C2 set_variable)) (let ((_let_1 (@ ord_le282106107riable A3))) (=> (@ _let_1 (@ (@ inf_inf_set_variable B3) C2)) (not (=> (@ _let_1 B3) (not (@ _let_1 C2))))))) _let_8 (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 ((X2 option_game) (P (-> option_game option_trm Bool)) (Y3 option_trm)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 none_game) _let_1) (=> (=> (= Y3 none_trm) _let_1) (=> (forall ((A game) (B trm)) (=> (= X2 (@ some_game A)) (=> (= Y3 (@ some_trm B)) (@ (@ P X2) Y3)))) _let_1))))) (forall ((Option option_fml) (X22 fml)) (=> (= Option (@ some_fml X22)) (not (= Option none_fml)))) (forall ((P (-> option_trm option_trm Bool)) (A0 option_trm) (A1 option_trm)) (=> (forall ((Theta2 trm) (Eta trm)) (@ (@ P (@ some_trm Theta2)) (@ some_trm Eta))) (=> (forall ((X_1 option_trm)) (@ (@ P none_trm) X_1)) (=> (forall ((V2 trm)) (@ (@ P (@ some_trm V2)) none_trm)) (@ (@ P A0) A1))))) (forall ((X2 option_game)) (=> (forall ((Alpha game)) (not (= X2 (@ some_game Alpha)))) (= X2 none_game))) (forall ((P (-> variable Bool))) (= (= (@ collect_variable P) bot_bot_set_variable) (= P bot_bot_variable_o))) (forall ((X2 set_variable_real) (Y3 set_variable_real) (Z set_variable_real)) (let ((_let_1 (@ ord_le1113654598e_real X2))) (= (@ _let_1 (@ (@ inf_in1556002680e_real Y3) Z)) (and (@ _let_1 Y3) (@ _let_1 Z))))) (forall ((Option option_fml)) (=> (not (= Option none_fml)) (= Option (@ some_fml (@ the_fml Option))))) (= (lambda ((P4 (-> option_trm Bool))) (exists ((X3 option_trm)) (@ P4 X3))) (lambda ((P3 (-> option_trm Bool))) (or (@ P3 none_trm) (exists ((X4 trm)) (@ P3 (@ some_trm X4)))))) (forall ((C2 (-> variable real)) (A2 set_variable_real) (B2 set_variable_real)) (let ((_let_1 (@ member_variable_real C2))) (=> (@ _let_1 (@ (@ inf_in1556002680e_real A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((X2 set_variable)) (= (@ (@ inf_inf_set_variable bot_bot_set_variable) X2) bot_bot_set_variable)) (forall ((X51 trm) (X52 trm) (Y51 trm) (Y52 trm)) (= (= (@ (@ plus X51) X52) (@ (@ plus Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))) (forall ((X2 (-> variable Bool))) (= (@ (@ inf_inf_variable_o bot_bot_variable_o) X2) bot_bot_variable_o)) (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 ((Sigma produc1418842292n_game) (U set_variable) (Theta trm) (Eta2 trm)) (let ((_let_1 (@ (@ uSubst516392818stappt Sigma) U))) (=> (not (= (@ _let_1 (@ (@ plus Theta) Eta2)) none_trm)) (and (not (= (@ _let_1 Theta) none_trm)) (not (= (@ _let_1 Eta2) none_trm)))))) (forall ((A3 set_variable) (B3 set_variable)) (=> (@ (@ ord_le282106107riable A3) B3) (=> (@ (@ ord_le282106107riable B3) A3) (= A3 B3)))) _let_7 (forall ((A2 set_variable) (B2 set_variable)) (=> (= A2 B2) (@ (@ ord_le282106107riable A2) B2))) (forall ((C set_variable_real) (A2 set_variable_real) (B2 set_variable_real)) (let ((_let_1 (@ ord_le1113654598e_real C))) (= (@ _let_1 (@ (@ inf_in1556002680e_real A2) B2)) (and (@ _let_1 A2) (@ _let_1 B2))))) (forall ((X2 option_game) (P (-> option_game option_fml Bool)) (Y3 option_fml)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 none_game) _let_1) (=> (=> (= Y3 none_fml) _let_1) (=> (forall ((A game) (B fml)) (=> (= X2 (@ some_game A)) (=> (= Y3 (@ some_fml B)) (@ (@ P X2) Y3)))) _let_1))))) (= (lambda ((P4 (-> option_fml Bool))) (exists ((X3 option_fml)) (@ P4 X3))) (lambda ((P3 (-> option_fml Bool))) (or (@ P3 none_fml) (exists ((X4 fml)) (@ P3 (@ some_fml X4)))))) (forall ((F2 (-> set_variable set_variable set_variable)) (X2 set_variable) (Y3 set_variable)) (=> (forall ((X set_variable) (Y4 set_variable)) (@ (@ ord_le282106107riable (@ (@ F2 X) Y4)) X)) (=> (forall ((X set_variable) (Y4 set_variable)) (@ (@ ord_le282106107riable (@ (@ F2 X) Y4)) Y4)) (=> (forall ((X set_variable) (Y4 set_variable) (Z3 set_variable)) (let ((_let_1 (@ ord_le282106107riable X))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ F2 Y4) Z3)))))) (= (@ (@ inf_inf_set_variable X2) Y3) (@ (@ F2 X2) Y3)))))) (forall ((X2 option_trm) (P (-> option_trm option_fml Bool)) (Y3 option_fml)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 none_trm) _let_1) (=> (=> (= Y3 none_fml) _let_1) (=> (forall ((A trm) (B fml)) (=> (= X2 (@ some_trm A)) (=> (= Y3 (@ some_fml B)) (@ (@ P X2) Y3)))) _let_1))))) (forall ((A3 set_variable_real) (B3 set_variable_real) (C2 set_variable_real)) (let ((_let_1 (@ ord_le1113654598e_real A3))) (= (@ _let_1 (@ (@ inf_in1556002680e_real B3) C2)) (and (@ _let_1 B3) (@ _let_1 C2))))) (forall ((X2 option_trm)) (= (not (= X2 none_trm)) (exists ((Y trm)) (= X2 (@ some_trm Y))))) (forall ((X2 option_trm)) (= (forall ((Y trm)) (not (= X2 (@ some_trm Y)))) (= X2 none_trm))) (= (lambda ((P4 (-> option_game Bool))) (exists ((X3 option_game)) (@ P4 X3))) (lambda ((P3 (-> option_game Bool))) (or (@ P3 none_game) (exists ((X4 game)) (@ P3 (@ some_game X4)))))) (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 ((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 ((A2 set_variable_real) (B2 set_variable_real)) (=> (forall ((X (-> variable real))) (let ((_let_1 (@ member_variable_real X))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ inf_in1556002680e_real A2) B2) bot_bo721182586e_real))) (forall ((X2 option_fml) (P (-> option_fml option_fml Bool)) (Y3 option_fml)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 none_fml) _let_1) (=> (=> (= Y3 none_fml) _let_1) (=> (forall ((A fml) (B fml)) (=> (= X2 (@ some_fml A)) (=> (= Y3 (@ some_fml B)) (@ (@ P X2) Y3)))) _let_1))))) (forall ((X2 option_game) (P (-> option_game option_game Bool)) (Y3 option_game)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 none_game) _let_1) (=> (=> (= Y3 none_game) _let_1) (=> (forall ((A game) (B game)) (=> (= X2 (@ some_game A)) (=> (= Y3 (@ some_game B)) (@ (@ P X2) Y3)))) _let_1))))) (forall ((P (-> (-> variable real) Bool))) (= (= bot_bo721182586e_real (@ collec633296133e_real P)) (forall ((X4 (-> variable real))) (not (@ P X4))))) (= (lambda ((P4 (-> option_trm Bool))) (forall ((X3 option_trm)) (@ P4 X3))) (lambda ((P3 (-> option_trm Bool))) (and (@ P3 none_trm) (forall ((X4 trm)) (@ P3 (@ some_trm X4)))))) (forall ((H (-> (-> real Bool) real Bool)) (F1 (-> real Bool)) (F22 (-> fml real Bool)) (Option option_fml)) (= (@ H (@ (@ (@ case_o1836798020_o_fml F1) F22) Option)) (@ (@ (@ case_o1836798020_o_fml (@ H F1)) (lambda ((X4 fml) (__flatten_var_0 real)) (@ (@ H (@ F22 X4)) __flatten_var_0))) Option))) (forall ((X22 trm)) (not (= none_trm (@ some_trm X22)))) (forall ((A2 set_variable_real) (B2 set_variable_real) (P (-> (-> variable real) Bool)) (Q (-> (-> variable real) Bool))) (=> (@ (@ ord_le1113654598e_real A2) B2) (=> (forall ((X (-> variable real))) (=> (@ (@ member_variable_real X) A2) (=> (@ P X) (@ Q X)))) (@ (@ ord_le1113654598e_real (@ (@ inf_in1556002680e_real A2) (@ collec633296133e_real P))) (@ (@ inf_in1556002680e_real B2) (@ collec633296133e_real Q)))))) (= ord_le1113654598e_real (lambda ((A4 set_variable_real) (B4 set_variable_real)) (forall ((X4 (-> variable real))) (let ((_let_1 (@ member_variable_real X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))))) (forall ((X21 trm) (X222 trm) (Y21 trm) (Y22 trm)) (= (= (@ (@ geq X21) X222) (@ (@ geq Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))) (forall ((X11 char) (X12 trm) (Y11 char) (Y12 trm)) (= (= (@ (@ pred X11) X12) (@ (@ pred Y11) Y12)) (and (= X11 Y11) (= X12 Y12)))) (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) (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 ((A2 set_variable_real)) (@ (@ ord_le1113654598e_real bot_bo721182586e_real) A2)) (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))))) (= ord_le282106107riable (lambda ((A4 set_variable) (B4 set_variable)) (forall ((X4 variable)) (let ((_let_1 (@ member_variable X4))) (=> (@ _let_1 A4) (@ _let_1 B4)))))) (forall ((X22 game)) (not (= none_game (@ some_game X22)))) (forall ((P (-> (-> variable real) Bool)) (Q (-> (-> variable real) Bool))) (=> (forall ((X (-> variable real))) (= (@ P X) (@ Q X))) (= (@ collec633296133e_real P) (@ collec633296133e_real Q)))) (forall ((A2 set_variable)) (= (@ (@ inf_inf_set_variable A2) bot_bot_set_variable) bot_bot_set_variable)) (forall ((P (-> option_trm Bool)) (Option option_trm)) (=> (@ P none_trm) (=> (forall ((X trm)) (@ P (@ some_trm X))) (@ P Option)))) (forall ((X2 set_variable) (Y3 set_variable)) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable X2) Y3)) X2)) (forall ((X22 trm) (Y2 trm)) (= (= (@ some_trm X22) (@ some_trm Y2)) (= X22 Y2))) (forall ((Option option_trm)) (=> (not (= Option none_trm)) (= Option (@ some_trm (@ the_trm Option))))) (forall ((X2 option_trm) (P (-> option_trm option_trm Bool)) (Y3 option_trm)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 none_trm) _let_1) (=> (=> (= Y3 none_trm) _let_1) (=> (forall ((A trm) (B trm)) (=> (= X2 (@ some_trm A)) (=> (= Y3 (@ some_trm B)) (@ (@ P X2) Y3)))) _let_1))))) (forall ((Y3 option_fml)) (=> (not (= Y3 none_fml)) (not (forall ((X23 fml)) (not (= Y3 (@ some_fml X23))))))) (forall ((A2 set_variable)) (= (@ (@ ord_le282106107riable A2) bot_bot_set_variable) (= A2 bot_bot_set_variable))) _let_6 (forall ((A2 set_variable)) (@ (@ ord_le282106107riable bot_bot_set_variable) A2)) (= ord_le282106107riable (lambda ((A5 set_variable) (B5 set_variable)) (= (@ (@ inf_inf_set_variable A5) B5) A5))) (forall ((Y3 option_game)) (=> (not (= Y3 none_game)) (not (forall ((X23 game)) (not (= Y3 (@ some_game X23))))))) _let_5 (forall ((X2 option_trm) (P (-> option_trm option_game Bool)) (Y3 option_game)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 none_trm) _let_1) (=> (=> (= Y3 none_game) _let_1) (=> (forall ((A trm) (B game)) (=> (= X2 (@ some_trm A)) (=> (= Y3 (@ some_game B)) (@ (@ P X2) Y3)))) _let_1))))) (@ (@ (@ denota1419872369iation nu) omega) u) (forall ((A2 set_variable_real) (B2 set_variable_real) (X2 (-> variable real))) (let ((_let_1 (@ member_variable_real X2))) (=> (@ (@ ord_le1113654598e_real A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((Option option_trm) (X22 trm)) (=> (= Option (@ some_trm X22)) (not (= Option none_trm)))) (forall ((P Bool) (Q (-> fml Bool)) (X2 option_fml) (R4 (-> (-> real Bool) Bool)) (F2 (-> real Bool)) (G2 (-> fml real Bool))) (=> (@ (@ (@ case_option_o_fml P) Q) X2) (=> (=> P (@ R4 F2)) (=> (forall ((Q2 fml)) (=> (@ Q Q2) (@ R4 (@ G2 Q2)))) (@ R4 (@ (@ (@ case_o1836798020_o_fml F2) G2) X2)))))) (forall ((X2 set_variable) (Y3 set_variable)) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable X2) Y3)) X2)) (forall ((A2 set_variable) (B2 set_variable)) (=> (@ (@ ord_le282106107riable A2) B2) (=> (@ (@ ord_le282106107riable B2) A2) (= A2 B2)))) (forall ((X2 (-> variable Bool)) (Y3 (-> variable Bool)) (Z (-> variable Bool))) (let ((_let_1 (@ ord_le1407353162able_o X2))) (= (@ _let_1 (@ (@ inf_inf_variable_o Y3) Z)) (and (@ _let_1 Y3) (@ _let_1 Z))))) (forall ((X2 option_fml)) (= (forall ((Y fml)) (not (= X2 (@ some_fml Y)))) (= X2 none_fml))) (forall ((Option option_game) (X22 game)) (=> (= Option (@ some_game X22)) (not (= Option none_game)))) (forall ((X22 fml)) (not (= none_fml (@ some_fml X22)))) (forall ((P (-> (-> real Bool) Bool)) (F1 (-> real Bool)) (F22 (-> fml real Bool)) (Option option_fml)) (let ((_let_1 (@ the_fml Option))) (= (@ P (@ (@ (@ case_o1836798020_o_fml F1) F22) Option)) (not (or (and (= Option none_fml) (not (@ P F1))) (and (= Option (@ some_fml _let_1)) (not (@ P (@ F22 _let_1))))))))) (forall ((A2 set_variable) (B2 set_variable)) (= (= (@ (@ inf_inf_set_variable A2) B2) bot_bot_set_variable) (forall ((X4 variable)) (=> (@ (@ member_variable X4) A2) (forall ((Y variable)) (=> (@ (@ member_variable Y) B2) (not (= X4 Y)))))))) (forall ((C2 (-> variable real))) (not (@ (@ member_variable_real C2) bot_bo721182586e_real))) (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 ((X2 option_fml) (P (-> option_fml option_game Bool)) (Y3 option_game)) (let ((_let_1 (@ (@ P X2) Y3))) (=> (=> (= X2 none_fml) _let_1) (=> (=> (= Y3 none_game) _let_1) (=> (forall ((A fml) (B game)) (=> (= X2 (@ some_fml A)) (=> (= Y3 (@ some_game B)) (@ (@ P X2) Y3)))) _let_1))))) (forall ((A3 set_variable) (F2 (-> set_variable set_variable)) (B3 set_variable) (C2 set_variable)) (let ((_let_1 (@ ord_le282106107riable A3))) (=> (@ _let_1 (@ F2 B3)) (=> (@ (@ ord_le282106107riable B3) C2) (=> (forall ((X set_variable) (Y4 set_variable)) (=> (@ (@ ord_le282106107riable X) Y4) (@ (@ ord_le282106107riable (@ F2 X)) (@ F2 Y4)))) (@ _let_1 (@ F2 C2))))))) (forall ((A3 set_variable) (B3 set_variable)) (let ((_let_1 (@ inf_inf_set_variable A3))) (let ((_let_2 (@ _let_1 B3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X22 trm) (X2a fml) (Nu (-> variable real)) (Omega (-> variable real))) (let ((_let_1 (@ uSubst1408967625substt X22))) (let ((_let_2 (@ member_variable_real Nu))) (let ((_let_3 (@ (@ (@ uSubst516392804stappf _let_1) bot_bot_set_variable) X2a))) (=> (= (@ (@ (@ uSubst516392818stappt sigma) ua) theta) (@ some_trm X22)) (=> (= (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) sigma) p) (@ some_fml X2a)) (=> (= (@ (@ inf_inf_set_variable (@ static_FVF X2a)) ua) bot_bot_set_variable) (=> (not (= _let_3 none_fml)) (=> (@ (@ (@ denota1419872369iation Nu) Omega) bot_bot_set_variable) (= (@ _let_2 (@ (@ denotational_fml_sem i) (@ the_fml _let_3))) (@ _let_2 (@ (@ denotational_fml_sem (@ (@ (@ uSubst1599435252djoint _let_1) i) Omega)) X2a)))))))))))) (forall ((C2 (-> variable real)) (A2 set_variable_real) (B2 set_variable_real)) (let ((_let_1 (@ member_variable_real C2))) (=> (@ _let_1 (@ (@ inf_in1556002680e_real A2) B2)) (@ _let_1 A2)))) (= some_trm some_trm) (forall ((Option option_trm)) (=> (not (= Option none_trm)) (= (@ some_trm (@ the_trm Option)) Option))) (forall ((Option option_trm)) (= (not (= Option none_trm)) (@ (@ (@ case_option_o_trm false) (lambda ((Uu trm)) true)) Option))) (forall ((Option option_fml)) (=> (not (= Option none_fml)) (= (@ some_fml (@ the_fml Option)) Option))) (forall ((A2 set_variable_real)) (=> (forall ((Y4 (-> variable real))) (not (@ (@ member_variable_real Y4) A2))) (= A2 bot_bo721182586e_real))) (forall ((A2 set_variable_real) (A3 (-> variable real))) (=> (= A2 bot_bo721182586e_real) (not (@ (@ member_variable_real A3) A2)))) (forall ((X2 (-> (-> variable real) Bool)) (Y3 (-> (-> variable real) Bool))) (let ((_let_1 (@ inf_in450528013real_o X2))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 set_variable) (B2 set_variable)) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A2) B2)) B2)) (forall ((P (-> variable Bool)) (Q (-> variable Bool))) (= (@ (@ ord_le282106107riable (@ collect_variable P)) (@ collect_variable Q)) (forall ((X4 variable)) (=> (@ P X4) (@ Q X4))))) (= (lambda ((Y5 set_variable) (Z2 set_variable)) (= Y5 Z2)) (lambda ((A4 set_variable) (B4 set_variable)) (and (@ (@ ord_le282106107riable A4) B4) (@ (@ ord_le282106107riable B4) A4)))) (forall ((P (-> option_game Bool)) (Option option_game)) (=> (@ P none_game) (=> (forall ((X game)) (@ P (@ some_game X))) (@ P Option)))) (forall ((A2 set_variable) (B2 set_variable) (C set_variable)) (let ((_let_1 (@ ord_le282106107riable A2))) (=> (@ _let_1 B2) (=> (@ (@ ord_le282106107riable B2) C) (@ _let_1 C))))) (forall ((P (-> variable Bool)) (Q (-> variable Bool))) (=> (forall ((X variable)) (=> (@ P X) (@ Q X))) (@ (@ ord_le282106107riable (@ collect_variable P)) (@ collect_variable Q)))) (forall ((X2 set_variable) (Y3 set_variable)) (=> (= X2 Y3) (@ (@ ord_le282106107riable X2) Y3))) (forall ((X2 set_variable) (Y3 set_variable) (Z set_variable)) (let ((_let_1 (@ inf_inf_set_variable X2))) (let ((_let_2 (@ inf_inf_set_variable Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (= ord_le1113654598e_real (lambda ((A4 set_variable_real) (B4 set_variable_real)) (forall ((T (-> variable real))) (let ((_let_1 (@ member_variable_real T))) (=> (@ _let_1 A4) (@ _let_1 B4)))))) (forall ((A3 set_variable) (B3 set_variable) (C2 set_variable)) (let ((_let_1 (@ ord_le282106107riable A3))) (=> (@ _let_1 B3) (=> (@ _let_1 C2) (@ _let_1 (@ (@ inf_inf_set_variable B3) C2)))))) (forall ((A3 set_variable)) (= (@ (@ ord_le282106107riable A3) bot_bot_set_variable) (= A3 bot_bot_set_variable))) (= ord_le282106107riable (lambda ((A4 set_variable) (B4 set_variable)) (forall ((T variable)) (let ((_let_1 (@ member_variable T))) (=> (@ _let_1 A4) (@ _let_1 B4)))))) (forall ((A2 set_variable_real) (B2 set_variable_real) (C2 (-> variable real))) (let ((_let_1 (@ member_variable_real C2))) (=> (@ (@ ord_le1113654598e_real A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 set_variable) (B2 set_variable) (X2 variable)) (let ((_let_1 (@ member_variable X2))) (=> (@ (@ ord_le282106107riable A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((X2 set_variable) (Y3 set_variable) (Z set_variable)) (let ((_let_1 (@ inf_inf_set_variable X2))) (let ((_let_2 (@ inf_inf_set_variable Y3))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((B3 set_variable) (A3 set_variable) (C2 set_variable)) (let ((_let_1 (@ inf_inf_set_variable B3))) (let ((_let_2 (@ inf_inf_set_variable A3))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((B3 set_variable) (A3 set_variable)) (=> (@ (@ ord_le282106107riable B3) A3) (=> (@ (@ ord_le282106107riable A3) B3) (= A3 B3)))) (forall ((A3 set_variable) (B3 set_variable) (C2 set_variable)) (let ((_let_1 (@ ord_le282106107riable A3))) (= (@ _let_1 (@ (@ inf_inf_set_variable B3) C2)) (and (@ _let_1 B3) (@ _let_1 C2))))) (forall ((B3 set_variable) (X2 set_variable) (A3 set_variable)) (=> (@ (@ ord_le282106107riable B3) X2) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A3) B3)) X2))) (= inf_inf_set_variable (lambda ((X4 set_variable) (Y set_variable)) (@ (@ inf_inf_set_variable Y) X4))) (forall ((A2 set_variable) (B2 set_variable)) (=> (@ (@ ord_le282106107riable A2) B2) (= (@ (@ inf_inf_set_variable A2) B2) A2))) (forall ((Option option_game)) (=> (not (= Option none_game)) (= (@ some_game (@ the_game Option)) Option))) (= inf_inf_set_variable (lambda ((A5 set_variable) (B5 set_variable)) (@ (@ inf_inf_set_variable B5) A5))) (forall ((B2 set_variable) (K set_variable) (B3 set_variable) (A3 set_variable)) (let ((_let_1 (@ inf_inf_set_variable A3))) (let ((_let_2 (@ inf_inf_set_variable K))) (=> (= B2 (@ _let_2 B3)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B3))))))) (= inf_inf_set_variable (lambda ((X4 set_variable) (Y set_variable)) (@ (@ inf_inf_set_variable Y) X4))) (forall ((C2 variable) (A2 set_variable) (B2 set_variable)) (let ((_let_1 (@ member_variable C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ inf_inf_set_variable A2) B2)))))) (forall ((A3 set_variable) (B3 set_variable)) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A3) B3)) B3)) (forall ((A2 set_variable) (B2 set_variable) (C set_variable)) (let ((_let_1 (@ inf_inf_set_variable A2))) (let ((_let_2 (@ inf_inf_set_variable B2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 set_variable)) (= (@ (@ inf_inf_set_variable bot_bot_set_variable) B2) bot_bot_set_variable)) (forall ((A2 set_variable)) (= (@ (@ inf_inf_set_variable A2) A2) A2)) (= bot_bot_set_variable (@ collect_variable bot_bot_variable_o)) (forall ((A2 set_variable) (B2 set_variable) (C set_variable)) (let ((_let_1 (@ inf_inf_set_variable A2))) (= (@ (@ inf_inf_set_variable (@ _let_1 B2)) C) (@ _let_1 (@ (@ inf_inf_set_variable B2) C))))) (forall ((C2 (-> variable real)) (A2 set_variable_real) (B2 set_variable_real)) (let ((_let_1 (@ member_variable_real C2))) (=> (@ _let_1 (@ (@ inf_in1556002680e_real A2) B2)) (@ _let_1 B2)))) (forall ((Omega (-> variable real)) (Nu (-> variable real)) (U set_variable)) (=> (@ (@ (@ denota1419872369iation Omega) Nu) U) (@ (@ (@ denota1419872369iation Nu) Omega) U))) _let_4 (forall ((Nu (-> variable real)) (V set_variable)) (@ (@ (@ denota1419872369iation Nu) Nu) V)) _let_3 (forall ((X22 trm)) (= (@ the_trm (@ some_trm X22)) X22)) (forall ((X2 option_fml) (Y3 option_fml)) (= (@ (@ (@ if_option_fml true) X2) Y3) X2)) (forall ((A3 (-> variable real))) (not (@ (@ member_variable_real A3) bot_bo721182586e_real))) (forall ((A2 set_variable_real)) (= (@ collec633296133e_real (lambda ((X4 (-> variable real))) (@ (@ member_variable_real X4) A2))) A2)) (forall ((P (-> variable Bool)) (Q (-> variable Bool))) (= (@ collect_variable (lambda ((X4 variable)) (and (@ P X4) (@ Q X4)))) (@ (@ inf_inf_set_variable (@ collect_variable P)) (@ collect_variable Q)))) (forall ((X2 (-> variable real)) (A2 set_variable_real) (P (-> (-> variable real) Bool))) (let ((_let_1 (@ member_variable_real X2))) (= (@ _let_1 (@ (@ inf_in1556002680e_real A2) (@ collec633296133e_real P))) (and (@ _let_1 A2) (@ P X2))))) (forall ((X2 variable) (A2 set_variable) (P (-> variable Bool))) (let ((_let_1 (@ member_variable X2))) (= (@ _let_1 (@ (@ inf_inf_set_variable A2) (@ collect_variable P))) (and (@ _let_1 A2) (@ P X2))))) (forall ((V3 trm)) (= (@ (@ uSubst918876924Timeso (@ some_trm V3)) none_trm) none_trm)) (= inf_inf_set_variable (lambda ((A4 set_variable) (B4 set_variable)) (@ collect_variable (lambda ((X4 variable)) (let ((_let_1 (@ member_variable X4))) (and (@ _let_1 A4) (@ _let_1 B4))))))) (forall ((X2 option_fml)) (=> (forall ((Phi2 fml)) (not (= X2 (@ some_fml Phi2)))) (= X2 none_fml))) (forall ((P (-> option_fml Bool)) (A0 option_fml)) (=> (forall ((Phi2 fml)) (@ P (@ some_fml Phi2))) (=> (@ P none_fml) (@ P A0)))) (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)))) (forall ((Nu (-> variable real)) (Nu2 (-> variable real))) (@ (@ (@ denota1419872369iation Nu) Nu2) (@ collect_variable (lambda ((X4 variable)) true)))) (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 ((A3 set_variable) (B3 set_variable)) (=> (= A3 (@ (@ inf_inf_set_variable A3) B3)) (@ (@ ord_le282106107riable A3) B3))) (forall ((X22 game)) (= (@ the_game (@ some_game X22)) X22)) (= (lambda ((P4 (-> option_fml Bool))) (forall ((X3 option_fml)) (@ P4 X3))) (lambda ((P3 (-> option_fml Bool))) (and (@ P3 none_fml) (forall ((X4 fml)) (@ P3 (@ some_fml X4)))))) (forall ((A3 set_variable) (C2 set_variable) (B3 set_variable) (D set_variable)) (=> (@ (@ ord_le282106107riable A3) C2) (=> (@ (@ ord_le282106107riable B3) D) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A3) B3)) (@ (@ inf_inf_set_variable C2) D))))) (forall ((A3 set_variable) (B3 set_variable) (F2 (-> set_variable set_variable)) (C2 set_variable)) (=> (@ (@ ord_le282106107riable A3) B3) (=> (@ (@ ord_le282106107riable (@ F2 B3)) C2) (=> (forall ((X set_variable) (Y4 set_variable)) (=> (@ (@ ord_le282106107riable X) Y4) (@ (@ ord_le282106107riable (@ F2 X)) (@ F2 Y4)))) (@ (@ ord_le282106107riable (@ F2 A3)) C2))))) (forall ((B3 set_variable) (C2 set_variable) (A3 set_variable)) (=> (@ (@ ord_le282106107riable B3) C2) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A3) B3)) C2))) (forall ((X2 set_variable) (Y3 set_variable) (Z set_variable)) (let ((_let_1 (@ inf_inf_set_variable X2))) (= (@ (@ inf_inf_set_variable (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ inf_inf_set_variable Y3) Z))))) (forall ((A3 set_variable) (C2 set_variable) (B3 set_variable)) (=> (@ (@ ord_le282106107riable A3) C2) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A3) B3)) C2))) (= ord_le282106107riable (lambda ((B5 set_variable) (A5 set_variable)) (= (@ (@ inf_inf_set_variable A5) B5) B5))) (forall ((A3 set_variable) (B3 set_variable)) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A3) B3)) A3)) (= ord_le282106107riable (lambda ((A5 set_variable) (B5 set_variable)) (= A5 (@ (@ inf_inf_set_variable A5) B5)))) (forall ((X2 set_variable) (Y3 set_variable) (Z set_variable)) (let ((_let_1 (@ ord_le282106107riable X2))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ inf_inf_set_variable Y3) Z)))))) (forall ((Y3 set_variable) (X2 set_variable)) (=> (@ (@ ord_le282106107riable Y3) X2) (= (@ (@ inf_inf_set_variable X2) Y3) Y3))) (forall ((Sigma produc1418842292n_game) (P2 char) (R2 fml) (I2 denotational_interp) (Omega (-> variable real))) (=> (= (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) Sigma) P2) (@ some_fml R2)) (= (@ (@ denotational_Preds (@ (@ (@ uSubst1599435252djoint Sigma) I2) Omega)) P2) (lambda ((D3 real)) (@ (@ member_variable_real Omega) (@ (@ denotational_fml_sem (@ (@ (@ uSubst1505767257e_repc I2) (@ (@ (@ (@ (@ (@ (@ (@ char2 false) true) true) true) false) true) false) false)) D3)) R2)))))) (forall ((X2 set_variable) (Y3 set_variable) (Z set_variable)) (let ((_let_1 (@ inf_inf_set_variable X2))) (= (@ (@ inf_inf_set_variable (@ _let_1 Y3)) Z) (@ _let_1 (@ (@ inf_inf_set_variable Y3) Z))))) (forall ((X61 trm) (X62 trm) (Y61 trm) (Y62 trm)) (= (= (@ (@ times X61) X62) (@ (@ times Y61) Y62)) (and (= X61 Y61) (= X62 Y62)))) (forall ((X2 set_variable) (Y3 set_variable)) (=> (@ (@ ord_le282106107riable X2) Y3) (= (@ (@ inf_inf_set_variable X2) Y3) X2))) (forall ((A2 set_variable_real) (B2 set_variable_real)) (=> (@ (@ ord_le1113654598e_real A2) B2) (=> (@ (@ ord_le1113654598e_real B2) A2) (= A2 B2)))) (forall ((Y3 option_trm)) (=> (not (= Y3 none_trm)) (not (forall ((X23 trm)) (not (= Y3 (@ some_trm X23))))))) (forall ((A2 set_variable) (B2 set_variable)) (= (= (@ (@ inf_inf_set_variable A2) B2) bot_bot_set_variable) (forall ((X4 variable)) (let ((_let_1 (@ member_variable X4))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (= inf_inf_set_variable (lambda ((A4 set_variable) (B4 set_variable)) (@ (@ inf_inf_set_variable B4) A4))) (forall ((B3 set_variable) (A3 set_variable)) (=> (@ (@ ord_le282106107riable B3) A3) (= (@ (@ inf_inf_set_variable A3) B3) B3))) (forall ((X2 set_variable) (A3 set_variable) (B3 set_variable)) (let ((_let_1 (@ ord_le282106107riable X2))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ inf_inf_set_variable A3) B3)))))) (forall ((X2 set_variable) (A3 set_variable) (B3 set_variable)) (let ((_let_1 (@ ord_le282106107riable X2))) (=> (@ _let_1 (@ (@ inf_inf_set_variable A3) B3)) (not (=> (@ _let_1 A3) (not (@ _let_1 B3))))))) (forall ((X2 set_variable) (Y3 set_variable)) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable X2) Y3)) Y3)) (forall ((A2 set_variable_real) (B2 set_variable_real)) (= (= (@ (@ inf_in1556002680e_real A2) B2) bot_bo721182586e_real) (forall ((X4 (-> variable real))) (let ((_let_1 (@ member_variable_real X4))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((Theta option_trm) (Eta2 option_trm)) (= (= (@ (@ uSubst141955042_Pluso Theta) Eta2) none_trm) (or (= Theta none_trm) (= Eta2 none_trm)))) (forall ((A2 set_variable) (B2 set_variable) (P (-> variable Bool)) (Q (-> variable Bool))) (=> (@ (@ ord_le282106107riable A2) B2) (=> (forall ((X variable)) (=> (@ (@ member_variable X) A2) (=> (@ P X) (@ Q X)))) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A2) (@ collect_variable P))) (@ (@ inf_inf_set_variable B2) (@ collect_variable Q)))))) (forall ((C set_variable) (A2 set_variable) (B2 set_variable)) (let ((_let_1 (@ ord_le282106107riable C))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ inf_inf_set_variable A2) B2)))))) (forall ((X2 (-> variable Bool)) (Y3 (-> variable Bool))) (let ((_let_1 (@ inf_inf_variable_o X2))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((B2 set_variable) (A2 set_variable)) (=> (@ (@ ord_le282106107riable B2) A2) (= (@ (@ inf_inf_set_variable A2) B2) B2))) (forall ((X2 set_variable) (Y3 set_variable)) (let ((_let_1 (@ inf_inf_set_variable X2))) (let ((_let_2 (@ _let_1 Y3))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 set_variable) (B2 set_variable)) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable A2) B2)) A2)) (forall ((C2 (-> variable real)) (A2 set_variable_real) (B2 set_variable_real)) (let ((_let_1 (@ member_variable_real C2))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ inf_in1556002680e_real A2) B2)))))) (forall ((Option option_game)) (=> (not (= Option none_game)) (= Option (@ some_game (@ the_game Option))))) (forall ((Omega (-> variable real)) (Omega3 (-> variable real)) (U set_variable) (Phi fml) (I2 denotational_interp)) (let ((_let_1 (@ (@ denotational_fml_sem I2) Phi))) (=> (@ (@ (@ denota1419872369iation Omega) Omega3) U) (=> (= (@ (@ inf_inf_set_variable (@ static_FVF Phi)) U) bot_bot_set_variable) (= (@ (@ member_variable_real Omega) _let_1) (@ (@ member_variable_real Omega3) _let_1)))))) (forall ((A3 set_variable) (B3 set_variable)) (=> (@ (@ ord_le282106107riable A3) B3) (= (@ (@ inf_inf_set_variable A3) B3) A3))) (forall ((Sigma produc1418842292n_game) (P2 char) (I2 denotational_interp) (Omega (-> variable real))) (=> (= (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) Sigma) P2) none_fml) (= (@ (@ denotational_Preds (@ (@ (@ uSubst1599435252djoint Sigma) I2) Omega)) P2) (@ (@ denotational_Preds I2) P2)))) (forall ((A3 set_variable) (B3 set_variable)) (=> (@ (@ ord_le282106107riable A3) B3) (= A3 (@ (@ inf_inf_set_variable A3) B3)))) (forall ((Sigma produc1418842292n_game) (U set_variable) (P2 char) (Theta trm)) (= (@ (@ (@ uSubst516392804stappf Sigma) U) (@ (@ pred P2) Theta)) (@ (@ (@ case_o325794063ml_trm none_fml) (lambda ((Sigma_theta2 trm)) (@ (@ (@ case_o209804997ml_fml (@ some_fml (@ (@ pred P2) Sigma_theta2))) (lambda ((R3 fml)) (@ (@ (@ if_option_fml (= (@ (@ inf_inf_set_variable (@ static_FVF R3)) U) bot_bot_set_variable)) (@ (@ (@ uSubst516392804stappf (@ uSubst1408967625substt Sigma_theta2)) bot_bot_set_variable) R3)) none_fml))) (@ (@ (@ produc1250175341on_fml (lambda ((Uu (-> char option_trm)) (__flatten_var_0 produc62062515n_game) (__flatten_var_1 char)) (@ (@ (@ produc1615133358on_fml (lambda ((Uv (-> char option_trm)) (__flatten_var_0 produc799602994n_game) (__flatten_var_1 char)) (@ (@ (@ produc1420172399on_fml (lambda ((P3 (-> char option_fml)) (Uw (-> char option_game)) (__flatten_var_0 char)) (@ P3 __flatten_var_0))) __flatten_var_0) __flatten_var_1))) __flatten_var_0) __flatten_var_1))) Sigma) P2)))) (@ (@ (@ uSubst516392818stappt Sigma) U) Theta)))) (forall ((P (-> option_trm Bool)) (A0 option_trm)) (=> (forall ((Theta2 trm)) (@ P (@ some_trm Theta2))) (=> (@ P none_trm) (@ P A0)))) _let_2 (forall ((A2 set_variable_real)) (= (exists ((X4 (-> variable real))) (@ (@ member_variable_real X4) A2)) (not (= A2 bot_bo721182586e_real)))) _let_1 (forall ((X2 set_variable)) (@ (@ ord_le282106107riable X2) X2)) (forall ((A2 set_variable)) (= (forall ((X4 variable)) (not (@ (@ member_variable X4) A2))) (= A2 bot_bot_set_variable))) (forall ((X2 set_variable) (Y3 set_variable)) (@ (@ ord_le282106107riable (@ (@ inf_inf_set_variable X2) Y3)) Y3)) (forall ((P (-> option_game Bool)) (A0 option_game)) (=> (forall ((Alpha game)) (@ P (@ some_game Alpha))) (=> (@ P none_game) (@ P A0)))) (forall ((Alpha2 option_game)) (= (not (= Alpha2 none_game)) (exists ((G game)) (= Alpha2 (@ some_game G))))))))))))))))))))))))))))))))))))))))))
0.89/1.12	% SZS output end Proof for theBenchmark
0.89/1.12	EOF