0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : do_cvc5 %s %d 0.14/0.34 % Computer : n028.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 1200 0.14/0.34 % WCLimit : 120 0.14/0.34 % DateTime : Tue Jul 13 16:01:47 EDT 2021 0.14/0.34 % CPUTime : 0.20/0.49 %----THF division 0.20/0.50 ------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120... 0.20/0.50 --- Run --ho-elim --full-saturate-quant at 10... 0.87/1.05 % SZS status Theorem for theBenchmark 0.87/1.06 % SZS output start Proof for theBenchmark 0.87/1.06 (proof 0.87/1.06 (let ((_let_1 (= bot_bo513358416_nat_o (lambda ((X product_prod_nat_nat)) ((member701585322at_nat X) bot_bo2130386637at_nat))))) (let ((_let_2 (= bot_bo935656620te_o_o (lambda ((X com) (Y5 (-> a state Bool))) ((member221067728tate_o ((produc1948644831tate_o X) Y5)) bot_bo1692783091tate_o))))) (let ((_let_3 (= order_aboveS_state (lambda ((R3 set_Pr795498619_state) (A3 state)) (collect_state (lambda ((B7 state)) (and ((member1389040324_state ((produc64584659_state A3) B7)) R3) (not (= B7 A3))))))))) (let ((_let_4 (= wf_Pro309705690tate_o (lambda ((R3 set_Pr1702239303tate_o)) (forall ((Q4 set_Pr1590995257tate_o)) (=> (exists ((X produc696469763tate_o)) ((member1838112666tate_o X) Q4)) (exists ((X produc696469763tate_o)) (and (forall ((Y5 produc696469763tate_o)) (=> ((member1629320336tate_o ((produc1684562079tate_o Y5) X)) R3) (not ((member1838112666tate_o Y5) Q4)))) ((member1838112666tate_o X) Q4))))))))) (let ((_let_5 (= insert2053719859tate_o (lambda ((A3 produc696469763tate_o) (B4 set_Pr1590995257tate_o)) (collec1499596504tate_o (lambda ((X produc696469763tate_o)) (or ((member1838112666tate_o X) B4) (= X A3)))))))) (let ((_let_6 (forall ((Y4 state)) (=> ((member1389040324_state ((produc64584659_state Y4) x)) r) (and (forall ((S7 state) (T4 state)) (=> (((exec S7) body) T4) (forall ((Z2 a)) (=> (and ((pa Z2) S7) (= S7 Y4)) ((qa Z2) T4))))) (forall ((Z2 a) (S7 state)) (=> (and (= S7 Y4) ((pa Z2) S7)) ((termi body) S7)))))))) (let ((_let_7 (= is_emp807847857tate_o (lambda ((A5 set_Pr1590995257tate_o)) (= A5 bot_bo170732493tate_o))))) (let ((_let_8 (not (and (forall ((S state) (T state)) (or (forall ((Z a)) (or (not ((pa Z) S)) (not (= S x)) ((qa Z) T))) (not (((exec S) body) T)))) (forall ((Z a) (S state)) (or (not ((pa Z) S)) ((termi body) S) (not (= S x)))))))) (let ((_let_9 (= produc385877620_nat_o produc949581770_nat_o))) (let ((_let_10 (= is_sin1547905295tate_o (lambda ((A5 set_Pr1590995257tate_o)) (exists ((X produc696469763tate_o)) (= A5 ((insert2053719859tate_o X) bot_bo170732493tate_o))))))) (let ((_let_11 (= insert271595217at_nat (lambda ((A3 product_prod_nat_nat) (B4 set_Pr1986765409at_nat)) (collec7649004at_nat (lambda ((X product_prod_nat_nat)) (or (= X A3) ((member701585322at_nat X) B4)))))))) (let ((_let_12 (= bot_bo446391478tate_o (lambda ((X produc1115495963_state)) ((member1389040324_state X) bot_bo1625160935_state))))) (let ((_let_13 (= order_665764460at_nat (lambda ((R3 set_Pr1490359111at_nat) (A3 product_prod_nat_nat)) (collec7649004at_nat (lambda ((B7 product_prod_nat_nat)) (and (not (= B7 A3)) ((member2027625872at_nat ((produc1168807639at_nat A3) B7)) R3)))))))) (let ((_let_14 (= produc938968666tate_o produc789892016tate_o))) (let ((_let_15 (= bot_bo2130564770te_o_o (lambda ((X (-> a state Bool)) (Y5 produc204914599tate_o)) ((member1838112666tate_o ((produc33908149tate_o X) Y5)) bot_bo170732493tate_o))))) (let ((_let_16 (= bot_bo1625160935_state (collec496201222_state (lambda ((X produc1115495963_state)) false))))) (let ((_let_17 (= bot_bot_nat_nat_o (lambda ((X nat) (Y5 nat)) ((member701585322at_nat ((product_Pair_nat_nat X) Y5)) bot_bo2130386637at_nat))))) (let ((_let_18 (= total_on_nat (lambda ((A5 set_nat) (R3 set_Pr1986765409at_nat)) (forall ((X nat)) (=> ((member_nat X) A5) (forall ((Y5 nat)) (=> ((member_nat Y5) A5) (=> (not (= X Y5)) (or ((member701585322at_nat ((product_Pair_nat_nat Y5) X)) R3) ((member701585322at_nat ((product_Pair_nat_nat X) Y5)) R3))))))))))) (let ((_let_19 (= insert311944171_state (lambda ((A3 produc1115495963_state) (B4 set_Pr795498619_state)) (collec496201222_state (lambda ((X produc1115495963_state)) (or (= X A3) ((member1389040324_state X) B4)))))))) (let ((_let_20 (forall ((S6 state)) (and (=> (and (forall ((Z a) (S state)) (=> (and ((pa Z) S) ((member1389040324_state ((produc64584659_state S) S6)) r)) ((termi body) S))) (forall ((S state) (T state)) (=> (((exec S) body) T) (forall ((Z a)) (=> (and ((member1389040324_state ((produc64584659_state S) S6)) r) ((pa Z) S)) ((qa Z) T)))))) (and (forall ((Z2 a) (S7 state)) (=> (and ((pa Z2) S7) (= S7 S6)) ((termi body) S7))) (forall ((S7 state) (T4 state)) (=> (((exec S7) body) T4) (forall ((Z2 a)) (=> (and ((pa Z2) S7) (= S7 S6)) ((qa Z2) T4))))))) ((((pHoare382919414oare_a ((insert2053719859tate_o ((produc33908149tate_o (lambda ((Z4 a) (S4 state)) (and ((member1389040324_state ((produc64584659_state S4) S6)) r) ((pa Z4) S4)))) ((produc1948644831tate_o call) qa))) bot_bo170732493tate_o)) (lambda ((Z4 a) (S4 state)) (and ((pa Z4) S4) (= S4 S6)))) body) qa))))) (let ((_let_21 (= is_sin1132515087_state (lambda ((A5 set_Pr795498619_state)) (= A5 ((insert311944171_state (the_el1967402896_state A5)) bot_bo1625160935_state)))))) (let ((_let_22 (= wf_Pro745352042at_nat (lambda ((R3 set_Pr1490359111at_nat)) (forall ((Q4 set_Pr1986765409at_nat)) (=> (exists ((X product_prod_nat_nat)) ((member701585322at_nat X) Q4)) (exists ((X product_prod_nat_nat)) (and ((member701585322at_nat X) Q4) (forall ((Y5 product_prod_nat_nat)) (=> ((member2027625872at_nat ((produc1168807639at_nat Y5) X)) R3) (not ((member701585322at_nat Y5) Q4)))))))))))) (let ((_let_23 (= is_emp825011411at_nat (lambda ((A5 set_Pr1986765409at_nat)) (= A5 bot_bo2130386637at_nat))))) (let ((_let_24 (= wf_Pro1783588484_state (lambda ((R3 set_Pr778812871_state)) (forall ((Q4 set_Pr795498619_state)) (=> (exists ((X produc1115495963_state)) ((member1389040324_state X) Q4)) (exists ((X produc1115495963_state)) (and ((member1389040324_state X) Q4) (forall ((Y5 produc1115495963_state)) (=> ((member768948240_state ((produc1964772951_state Y5) X)) R3) (not ((member1389040324_state Y5) Q4)))))))))))) (let ((_let_25 (= bot_bo51534648tate_o (lambda ((X state) (Y5 state)) ((member1389040324_state ((produc64584659_state X) Y5)) bot_bo1625160935_state))))) (let ((_let_26 (= bot_bo2130386637at_nat (collec7649004at_nat (lambda ((X product_prod_nat_nat)) false))))) (let ((_let_27 (= order_1121016664tate_o (lambda ((R3 set_Pr1702239303tate_o) (A3 produc696469763tate_o)) (collec1499596504tate_o (lambda ((B7 produc696469763tate_o)) (and (not (= B7 A3)) ((member1629320336tate_o ((produc1684562079tate_o A3) B7)) R3)))))))) (let ((_let_28 (= wf_nat (lambda ((R3 set_Pr1986765409at_nat)) (forall ((Q4 set_nat)) (=> (exists ((X nat)) ((member_nat X) Q4)) (exists ((X nat)) (and ((member_nat X) Q4) (forall ((Y5 nat)) (=> ((member701585322at_nat ((product_Pair_nat_nat Y5) X)) R3) (not ((member_nat Y5) Q4)))))))))))) (let ((_let_29 (= order_aboveS_nat (lambda ((R3 set_Pr1986765409at_nat) (A3 nat)) (collect_nat (lambda ((B7 nat)) (and ((member701585322at_nat ((product_Pair_nat_nat A3) B7)) R3) (not (= B7 A3))))))))) (let ((_let_30 (= is_sin1352690165at_nat (lambda ((A5 set_Pr1986765409at_nat)) (= A5 ((insert271595217at_nat (the_el1949240438at_nat A5)) bot_bo2130386637at_nat)))))) (let ((_let_31 (= exec (lambda ((S4 state) (C5 com) (T3 state)) (exists ((N2 nat)) ((((execn S4) C5) N2) T3)))))) (let ((_let_32 (= bot_bo250281208te_o_o (lambda ((X produc696469763tate_o)) ((member1838112666tate_o X) bot_bo170732493tate_o))))) (let ((_let_33 (= wf_state (lambda ((R3 set_Pr795498619_state)) (forall ((Q4 set_state)) (=> (exists ((X state)) ((member_state X) Q4)) (exists ((X state)) (and ((member_state X) Q4) (forall ((Y5 state)) (=> ((member1389040324_state ((produc64584659_state Y5) X)) R3) (not ((member_state Y5) Q4)))))))))))) (let ((_let_34 (= is_emp1062983149_state (lambda ((A5 set_Pr795498619_state)) (= A5 bot_bo1625160935_state))))) (let ((_let_35 (= pred_nat (collec7649004at_nat (produc949581770_nat_o (lambda ((M nat) (N2 nat)) (= N2 (suc M)))))))) (let ((_let_36 (= total_on_state (lambda ((A5 set_state) (R3 set_Pr795498619_state)) (forall ((X state)) (=> ((member_state X) A5) (forall ((Y5 state)) (=> ((member_state Y5) A5) (=> (not (= X Y5)) (or ((member1389040324_state ((produc64584659_state Y5) X)) R3) ((member1389040324_state ((produc64584659_state X) Y5)) R3))))))))))) (let ((_let_37 (= bot_bo170732493tate_o (collec1499596504tate_o (lambda ((X produc696469763tate_o)) false))))) (let ((_let_38 (= order_2027321734_state (lambda ((R3 set_Pr778812871_state) (A3 produc1115495963_state)) (collec496201222_state (lambda ((B7 produc1115495963_state)) (and (not (= B7 A3)) ((member768948240_state ((produc1964772951_state A3) B7)) R3)))))))) (let ((_let_39 (forall ((Z a) (S state)) (or (not (ho_226 (ho_225 k_280 Z) S)) (not (ho_232 (ho_231 k_230 (ho_229 (ho_228 k_227 S) x)) r)) (ho_226 (ho_336 k_335 body) S))))) (let ((_let_40 (forall ((S state) (T state) (BOUND_VARIABLE_7358 a) (BOUND_VARIABLE_10051 nat)) (or (not (ho_226 (ho_340 (ho_339 (ho_338 k_337 S) body) BOUND_VARIABLE_10051) T)) (not (ho_232 (ho_231 k_230 (ho_229 (ho_228 k_227 S) x)) r)) (not (ho_226 (ho_225 k_280 BOUND_VARIABLE_7358) S)) (ho_226 (ho_225 k_447 BOUND_VARIABLE_7358) T))))) (let ((_let_41 (ho_226 (ho_225 k_280 skv_682) x))) (let ((_let_42 (not _let_41))) (let ((_let_43 (ho_340 (ho_339 (ho_338 k_337 x) body) skv_667))) (let ((_let_44 (ho_336 k_335 body))) (let ((_let_45 (ho_226 _let_44 x))) (let ((_let_46 (or _let_45 _let_42))) (let ((_let_47 (and _let_46 (or (not (ho_226 _let_43 x)) _let_42 (ho_226 (ho_225 k_447 skv_682) x))))) (let ((_let_48 (not _let_40))) (let ((_let_49 (not _let_39))) (let ((_let_50 (or _let_49 _let_48 _let_47))) (let ((_let_51 (ho_226 _let_44 skv_677))) (let ((_let_52 (ho_232 (ho_231 k_230 (ho_229 (ho_228 k_227 skv_677) x)) r))) (let ((_let_53 (not _let_52))) (let ((_let_54 (ho_226 (ho_225 k_280 skv_676) skv_677))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_53 _let_51))) (let ((_let_57 (or _let_51 _let_55))) (let ((_let_58 (ho_225 k_447 skv_666))) (let ((_let_59 (ho_225 k_280 skv_666))) (let ((_let_60 (and (or (not (ho_226 (ho_340 (ho_339 (ho_338 k_337 skv_677) body) skv_667) x)) (not (ho_226 _let_59 skv_677)) (ho_226 _let_58 x)) _let_57))) (let ((_let_61 (or _let_53 _let_60))) (let ((_let_62 (20))) (let ((_let_63 (REFL |:args| (_let_56)))) (let ((_let_64 (forall ((Y4 state) (BOUND_VARIABLE_8662 a) (BOUND_VARIABLE_8652 a) (BOUND_VARIABLE_8650 state) (BOUND_VARIABLE_11967 nat)) (or (not (ho_232 (ho_231 k_230 (ho_229 (ho_228 k_227 Y4) x)) r)) (and (or (not (ho_226 (ho_340 (ho_339 (ho_338 k_337 Y4) body) BOUND_VARIABLE_11967) BOUND_VARIABLE_8650)) (not (ho_226 (ho_225 k_280 BOUND_VARIABLE_8652) Y4)) (ho_226 (ho_225 k_447 BOUND_VARIABLE_8652) BOUND_VARIABLE_8650)) (or (ho_226 (ho_336 k_335 body) Y4) (not (ho_226 (ho_225 k_280 BOUND_VARIABLE_8662) Y4)))))))) (let ((_let_65 (EQ_RESOLVE (ASSUME |:args| (_let_38)) (MACRO_SR_EQ_INTRO |:args| (_let_38 7 12))))) (let ((_let_66 (EQ_RESOLVE (ASSUME |:args| (_let_37)) (MACRO_SR_EQ_INTRO |:args| (_let_37 7 12))))) (let ((_let_67 (EQ_RESOLVE (ASSUME |:args| (_let_36)) (MACRO_SR_EQ_INTRO |:args| (_let_36 7 12))))) (let ((_let_68 (ASSUME |:args| (_let_35)))) (let ((_let_69 (EQ_RESOLVE (ASSUME |:args| (_let_34)) (MACRO_SR_EQ_INTRO |:args| (_let_34 7 12))))) (let ((_let_70 (EQ_RESOLVE (ASSUME |:args| (_let_33)) (MACRO_SR_EQ_INTRO |:args| (_let_33 7 12))))) (let ((_let_71 (EQ_RESOLVE (ASSUME |:args| (_let_32)) (MACRO_SR_EQ_INTRO _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| (_let_32 7 12))))) (let ((_let_72 (EQ_RESOLVE (ASSUME |:args| (_let_31)) (MACRO_SR_EQ_INTRO |:args| (_let_31 7 12))))) (let ((_let_73 (ASSUME |:args| (_let_30)))) (let ((_let_74 (EQ_RESOLVE (ASSUME |:args| (_let_29)) (MACRO_SR_EQ_INTRO |:args| (_let_29 7 12))))) (let ((_let_75 (EQ_RESOLVE (ASSUME |:args| (_let_28)) (MACRO_SR_EQ_INTRO |:args| (_let_28 7 12))))) (let ((_let_76 (EQ_RESOLVE (ASSUME |:args| (_let_27)) (MACRO_SR_EQ_INTRO |:args| (_let_27 7 12))))) (let ((_let_77 (EQ_RESOLVE (ASSUME |:args| (_let_26)) (MACRO_SR_EQ_INTRO |:args| (_let_26 7 12))))) (let ((_let_78 (ASSUME |:args| (_let_25)))) (let ((_let_79 (EQ_RESOLVE (ASSUME |:args| (_let_24)) (MACRO_SR_EQ_INTRO |:args| (_let_24 7 12))))) (let ((_let_80 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_23)) (MACRO_SR_EQ_INTRO |:args| (_let_23 7 12))) (MACRO_SR_EQ_INTRO _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| ((= is_emp825011411at_nat (lambda ((A5 set_Pr1986765409at_nat)) (= bot_bo2130386637at_nat A5))) 7 12))))) (let ((_let_81 (EQ_RESOLVE (ASSUME |:args| (_let_22)) (MACRO_SR_EQ_INTRO |:args| (_let_22 7 12))))) (let ((_let_82 (ASSUME |:args| (_let_21)))) (let ((_let_83 (EQ_RESOLVE (ASSUME |:args| (_let_19)) (MACRO_SR_EQ_INTRO |:args| (_let_19 7 12))))) (let ((_let_84 (EQ_RESOLVE (ASSUME |:args| (_let_18)) (MACRO_SR_EQ_INTRO |:args| (_let_18 7 12))))) (let ((_let_85 (EQ_RESOLVE (ASSUME |:args| (_let_17)) (MACRO_SR_EQ_INTRO _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| (_let_17 7 12))))) (let ((_let_86 (EQ_RESOLVE (ASSUME |:args| (_let_16)) (MACRO_SR_EQ_INTRO |:args| (_let_16 7 12))))) (let ((_let_87 (EQ_RESOLVE (ASSUME |:args| (_let_15)) (MACRO_SR_EQ_INTRO _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| (_let_15 7 12))))) (let ((_let_88 (ASSUME |:args| (_let_14)))) (let ((_let_89 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (MACRO_SR_EQ_INTRO |:args| (_let_13 7 12))))) (let ((_let_90 (EQ_RESOLVE (ASSUME |:args| (_let_12)) (MACRO_SR_EQ_INTRO _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| (_let_12 7 12))))) (let ((_let_91 (EQ_RESOLVE (ASSUME |:args| (_let_11)) (MACRO_SR_EQ_INTRO |:args| (_let_11 7 12))))) (let ((_let_92 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_10)) (MACRO_SR_EQ_INTRO |:args| (_let_10 7 12))) (MACRO_SR_EQ_INTRO _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| ((= is_sin1547905295tate_o (lambda ((A5 set_Pr1590995257tate_o)) (not (forall ((X produc696469763tate_o)) (not (= A5 ((insert2053719859tate_o X) bot_bo170732493tate_o))))))) 7 12))))) (let ((_let_93 (ASSUME |:args| (_let_9)))) (let ((_let_94 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_7)) (MACRO_SR_EQ_INTRO |:args| (_let_7 7 12))) (MACRO_SR_EQ_INTRO _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| ((= is_emp807847857tate_o (lambda ((A5 set_Pr1590995257tate_o)) (= bot_bo170732493tate_o A5))) 7 12))))) (let ((_let_95 (EQ_RESOLVE (ASSUME |:args| (_let_5)) (MACRO_SR_EQ_INTRO |:args| (_let_5 7 12))))) (let ((_let_96 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (MACRO_SR_EQ_INTRO |:args| (_let_4 7 12))))) (let ((_let_97 (EQ_RESOLVE (ASSUME |:args| (_let_3)) (MACRO_SR_EQ_INTRO |:args| (_let_3 7 12))))) (let ((_let_98 (ASSUME |:args| (_let_2)))) (let ((_let_99 (EQ_RESOLVE (ASSUME |:args| (_let_1)) (MACRO_SR_EQ_INTRO _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| (_let_1 7 12))))) (let ((_let_100 (EQ_RESOLVE (ASSUME |:args| (_let_6)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_6 7 12)) (MACRO_SR_EQ_INTRO _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| ((forall ((Y4 state) (BOUND_VARIABLE_8662 a) (BOUND_VARIABLE_8652 a) (BOUND_VARIABLE_8650 state)) (or (not ((member1389040324_state ((produc64584659_state Y4) x)) r)) (and (or (not (((exec Y4) body) BOUND_VARIABLE_8650)) (not ((pa BOUND_VARIABLE_8652) Y4)) ((qa BOUND_VARIABLE_8652) BOUND_VARIABLE_8650)) (or ((termi body) Y4) (not ((pa BOUND_VARIABLE_8662) Y4)))))) 7 12)) (PREPROCESS |:args| ((= (forall ((Y4 state) (BOUND_VARIABLE_8662 a) (BOUND_VARIABLE_8652 a) (BOUND_VARIABLE_8650 state) (BOUND_VARIABLE_11967 nat)) (or (not ((member1389040324_state ((produc64584659_state Y4) x)) r)) (and (or (not ((((execn Y4) body) BOUND_VARIABLE_11967) BOUND_VARIABLE_8650)) (not ((pa BOUND_VARIABLE_8652) Y4)) ((qa BOUND_VARIABLE_8652) BOUND_VARIABLE_8650)) (or ((termi body) Y4) (not ((pa BOUND_VARIABLE_8662) Y4)))))) _let_64))))))) (let ((_let_101 (_let_64))) (let ((_let_102 (_let_49))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_102)) |:args| _let_102)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_49) _let_39))) (REFL |:args| ((not _let_56))) |:args| _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS |:args| (_let_60 1)) |:args| ((or _let_57 (not _let_60)))) (REORDERING (CNF_OR_POS |:args| (_let_57)) |:args| ((or _let_55 _let_51 (not _let_57)))) (REORDERING (CNF_OR_POS |:args| (_let_61)) |:args| ((or _let_53 _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 |:args| (skv_677 skv_676 skv_666 x skv_667)) |:args| _let_101)) _let_100 |:args| (_let_61 false _let_64)) (CNF_OR_NEG |:args| (_let_56 2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_56 1)) (CONG _let_63 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_53) _let_52))) |:args| _let_62)) |:args| ((or _let_52 _let_56))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_56 0)) (CONG _let_63 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_55) _let_54))) |:args| _let_62)) |:args| ((or _let_54 _let_56))) |:args| (_let_56 true _let_57 false _let_60 false _let_61 true _let_51 false _let_52 false _let_54)) |:args| (_let_39 false _let_56)))) (let ((_let_104 (ho_226 (ho_225 k_447 skv_680) skv_679))) (let ((_let_105 (ho_226 (ho_225 k_280 skv_680) skv_678))) (let ((_let_106 (not _let_105))) (let ((_let_107 (ho_232 (ho_231 k_230 (ho_229 (ho_228 k_227 skv_678) x)) r))) (let ((_let_108 (not _let_107))) (let ((_let_109 (ho_226 (ho_340 (ho_339 (ho_338 k_337 skv_678) body) skv_681) skv_679))) (let ((_let_110 (not _let_109))) (let ((_let_111 (or _let_110 _let_108 _let_106 _let_104))) (let ((_let_112 (or _let_110 _let_106 _let_104))) (let ((_let_113 (and _let_112 (or (ho_226 _let_44 skv_678) (not (ho_226 _let_59 skv_678)))))) (let ((_let_114 (or _let_108 _let_113))) (let ((_let_115 (REFL |:args| (_let_111)))) (let ((_let_116 (_let_48))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_116)) |:args| _let_116)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_48) _let_40))) (REFL |:args| ((not _let_111))) |:args| _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS |:args| (_let_113 0)) |:args| ((or _let_112 (not _let_113)))) (REORDERING (CNF_OR_POS |:args| (_let_112)) |:args| ((or _let_106 _let_104 _let_110 (not _let_112)))) (REORDERING (CNF_OR_POS |:args| (_let_114)) |:args| ((or _let_108 _let_113 (not _let_114)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 |:args| (skv_678 skv_666 skv_680 skv_679 skv_681)) |:args| _let_101)) _let_100 |:args| (_let_114 false _let_64)) (CNF_OR_NEG |:args| (_let_111 3)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_111 2)) (CONG _let_115 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_106) _let_105))) |:args| _let_62)) |:args| ((or _let_105 _let_111))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_111 1)) (CONG _let_115 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_108) _let_107))) |:args| _let_62)) |:args| ((or _let_107 _let_111))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_111 0)) (CONG _let_115 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_110) _let_109))) |:args| _let_62)) |:args| ((or _let_109 _let_111))) |:args| (_let_111 true _let_112 false _let_113 false _let_114 true _let_104 false _let_105 false _let_107 false _let_109)) |:args| (_let_40 false _let_111)))) (let ((_let_118 (forall ((BOUND_VARIABLE_7455 state) (BOUND_VARIABLE_7517 a) (BOUND_VARIABLE_7515 state) (BOUND_VARIABLE_7509 a) (BOUND_VARIABLE_10100 nat)) (or (not (forall ((Z a) (S state)) (or (not (ho_226 (ho_225 k_280 Z) S)) (not (ho_232 (ho_231 k_230 (ho_229 (ho_228 k_227 S) BOUND_VARIABLE_7455)) r)) (ho_226 (ho_336 k_335 body) S)))) (not (forall ((S state) (T state) (BOUND_VARIABLE_7358 a) (BOUND_VARIABLE_10051 nat)) (or (not (ho_226 (ho_340 (ho_339 (ho_338 k_337 S) body) BOUND_VARIABLE_10051) T)) (not (ho_232 (ho_231 k_230 (ho_229 (ho_228 k_227 S) BOUND_VARIABLE_7455)) r)) (not (ho_226 (ho_225 k_280 BOUND_VARIABLE_7358) S)) (ho_226 (ho_225 k_447 BOUND_VARIABLE_7358) T)))) (and (or (ho_226 (ho_336 k_335 body) BOUND_VARIABLE_7455) (not (ho_226 (ho_225 k_280 BOUND_VARIABLE_7509) BOUND_VARIABLE_7455))) (or (not (ho_226 (ho_340 (ho_339 (ho_338 k_337 BOUND_VARIABLE_7455) body) BOUND_VARIABLE_10100) BOUND_VARIABLE_7515)) (not (ho_226 (ho_225 k_280 BOUND_VARIABLE_7517) BOUND_VARIABLE_7455)) (ho_226 (ho_225 k_447 BOUND_VARIABLE_7517) BOUND_VARIABLE_7515))))))) (let ((_let_119 (forall ((BOUND_VARIABLE_7455 state) (BOUND_VARIABLE_7517 a) (BOUND_VARIABLE_7515 state) (BOUND_VARIABLE_7509 a) (BOUND_VARIABLE_10100 nat)) (or (not (forall ((Z a) (S state)) (or (not ((pa Z) S)) (not ((member1389040324_state ((produc64584659_state S) BOUND_VARIABLE_7455)) r)) ((termi body) S)))) (not (forall ((S state) (T state) (BOUND_VARIABLE_7358 a) (BOUND_VARIABLE_10051 nat)) (or (not ((((execn S) body) BOUND_VARIABLE_10051) T)) (not ((member1389040324_state ((produc64584659_state S) BOUND_VARIABLE_7455)) r)) (not ((pa BOUND_VARIABLE_7358) S)) ((qa BOUND_VARIABLE_7358) T)))) (and (or ((termi body) BOUND_VARIABLE_7455) (not ((pa BOUND_VARIABLE_7509) BOUND_VARIABLE_7455))) (or (not ((((execn BOUND_VARIABLE_7455) body) BOUND_VARIABLE_10100) BOUND_VARIABLE_7515)) (not ((pa BOUND_VARIABLE_7517) BOUND_VARIABLE_7455)) ((qa BOUND_VARIABLE_7517) BOUND_VARIABLE_7515))))))) (let ((_let_120 (and _let_119 (forall ((BOUND_VARIABLE_7488 state)) ((((pHoare382919414oare_a (collec1499596504tate_o (ll_97 BOUND_VARIABLE_7488))) (ll_96 BOUND_VARIABLE_7488)) body) qa))))) (let ((_let_121 (AND_ELIM (EQ_RESOLVE (ASSUME |:args| (_let_20)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_20 7 12)) (MACRO_SR_EQ_INTRO _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| ((and (forall ((BOUND_VARIABLE_7455 state) (BOUND_VARIABLE_7517 a) (BOUND_VARIABLE_7515 state) (BOUND_VARIABLE_7509 a)) (or (not (forall ((Z a) (S state)) (or (not ((pa Z) S)) (not ((member1389040324_state ((produc64584659_state S) BOUND_VARIABLE_7455)) r)) ((termi body) S)))) (not (forall ((S state) (T state) (BOUND_VARIABLE_7358 a)) (or (not (((exec S) body) T)) (not ((member1389040324_state ((produc64584659_state S) BOUND_VARIABLE_7455)) r)) (not ((pa BOUND_VARIABLE_7358) S)) ((qa BOUND_VARIABLE_7358) T)))) (and (or ((termi body) BOUND_VARIABLE_7455) (not ((pa BOUND_VARIABLE_7509) BOUND_VARIABLE_7455))) (or (not (((exec BOUND_VARIABLE_7455) body) BOUND_VARIABLE_7515)) (not ((pa BOUND_VARIABLE_7517) BOUND_VARIABLE_7455)) ((qa BOUND_VARIABLE_7517) BOUND_VARIABLE_7515))))) (forall ((BOUND_VARIABLE_7488 state)) ((((pHoare382919414oare_a ((insert2053719859tate_o ((produc33908149tate_o (lambda ((Z4 a) (S4 state)) (and ((member1389040324_state ((produc64584659_state S4) BOUND_VARIABLE_7488)) r) ((pa Z4) S4)))) ((produc1948644831tate_o call) qa))) bot_bo170732493tate_o)) (lambda ((Z4 a) (S4 state)) (and ((pa Z4) S4) (= S4 BOUND_VARIABLE_7488)))) body) qa))) 7 12)) (PREPROCESS |:args| ((= (and _let_119 (forall ((BOUND_VARIABLE_7488 state)) ((((pHoare382919414oare_a (collec1499596504tate_o (lambda ((BOUND_VARIABLE_15519 produc696469763tate_o)) (or ((member1838112666tate_o BOUND_VARIABLE_15519) (collec1499596504tate_o (lambda ((BOUND_VARIABLE_6002 produc696469763tate_o)) false))) (= BOUND_VARIABLE_15519 ((produc33908149tate_o (lambda ((BOUND_VARIABLE_15520 a) (BOUND_VARIABLE_15521 state)) (and ((member1389040324_state ((produc64584659_state BOUND_VARIABLE_15521) BOUND_VARIABLE_7488)) r) ((pa BOUND_VARIABLE_15520) BOUND_VARIABLE_15521)))) ((produc1948644831tate_o call) qa))))))) (lambda ((Z4 a) (S4 state)) (and ((pa Z4) S4) (= S4 BOUND_VARIABLE_7488)))) body) qa))) _let_120))) (PREPROCESS |:args| ((= _let_120 (and _let_118 (forall ((BOUND_VARIABLE_7488 state)) (ho_504 (ho_503 (ho_628 (ho_627 k_626 (ho_271 k_270 (ho_449 k_448 BOUND_VARIABLE_7488))) (ho_282 k_450 BOUND_VARIABLE_7488)) body) k_447)))))))) |:args| (0)))) (let ((_let_122 (_let_118))) (let ((_let_123 (ASSUME |:args| _let_122))) (let ((_let_124 (not _let_47))) (let ((_let_125 (not _let_46))) (let ((_let_126 (forall ((Z a)) (not (ho_226 (ho_225 k_280 Z) x))))) (let ((_let_127 (or _let_45 _let_126))) (let ((_let_128 (not _let_126))) (let ((_let_129 (forall ((T state) (BOUND_VARIABLE_8287 a) (BOUND_VARIABLE_16490 nat)) (or (not (ho_226 (ho_340 (ho_339 (ho_338 k_337 x) body) BOUND_VARIABLE_16490) T)) (not (ho_226 (ho_225 k_280 BOUND_VARIABLE_8287) x)) (ho_226 (ho_225 k_447 BOUND_VARIABLE_8287) T))))) (let ((_let_130 (not (ho_226 _let_59 x)))) (let ((_let_131 (or (not (ho_226 _let_43 skv_665)) _let_130 (ho_226 _let_58 skv_665)))) (let ((_let_132 (and (or _let_45 _let_130) _let_131))) (let ((_let_133 (or _let_49 _let_48 _let_132))) (let ((_let_134 (not _let_129))) (let ((_let_135 (_let_134))) (let ((_let_136 (or ((termi body) x) (forall ((Z a)) (not ((pa Z) x)))))) (let ((_let_137 (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME |:args| (_let_8)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_8 7 12)) (MACRO_SR_EQ_INTRO _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 |:args| ((not (and (forall ((T state) (BOUND_VARIABLE_8287 a)) (or (not (((exec x) body) T)) (not ((pa BOUND_VARIABLE_8287) x)) ((qa BOUND_VARIABLE_8287) T))) _let_136)) 7 12)) (PREPROCESS |:args| ((= (not (and (forall ((T state) (BOUND_VARIABLE_8287 a) (BOUND_VARIABLE_16490 nat)) (or (not ((((execn x) body) BOUND_VARIABLE_16490) T)) (not ((pa BOUND_VARIABLE_8287) x)) ((qa BOUND_VARIABLE_8287) T))) _let_136)) (not (and _let_129 _let_127)))))))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_135)) |:args| _let_135)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_134) _let_129))) (REFL |:args| ((not _let_131))) |:args| _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS |:args| (_let_132 1)) |:args| ((or _let_131 (not _let_132)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_133)) |:args| ((or _let_49 _let_48 _let_132 (not _let_133)))) _let_103 _let_117 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_123 |:args| (x skv_666 skv_665 skv_666 skv_667)) |:args| _let_122)) _let_121 |:args| (_let_133 false _let_118)) |:args| (_let_132 false _let_39 false _let_40 false _let_133)) |:args| (_let_131 false _let_132)) |:args| (_let_129 false _let_131)) |:args| ((not _let_127) false _let_129)))) (let ((_let_138 (_let_128))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_50)) |:args| ((or _let_49 _let_48 _let_47 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS |:args| (_let_47 0)) |:args| ((or _let_46 _let_124))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_46)) |:args| ((or _let_45 _let_42 _let_125))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_127 0)) _let_137 |:args| ((not _let_45) true _let_127)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME |:args| _let_138)) |:args| _let_138) (REWRITE |:args| ((=> _let_128 (not _let_42)))))) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_128) _let_126))) (REFL |:args| (_let_41)) |:args| _let_62)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_127 1)) _let_137 |:args| (_let_128 true _let_127)) |:args| (_let_41 true _let_126)) |:args| (_let_125 true _let_45 false _let_41)) |:args| (_let_124 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_123 |:args| (x skv_682 x skv_682 skv_667)) |:args| _let_122)) _let_121 |:args| (_let_50 false _let_118)) _let_117 _let_103 |:args| (false true _let_47 false _let_50 false _let_40 false _let_39)) |:args| ((forall ((A product_prod_nat_nat) (A2 set_Pr1986765409at_nat)) (not (= ((insert271595217at_nat A) A2) bot_bo2130386637at_nat))) (forall ((X1 state) (X22 state) (Y1 state) (Y22 state)) (= (= ((produc64584659_state X1) X22) ((produc64584659_state Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((F (-> state state Bool)) (A state) (B2 state)) (= ((produc789892016tate_o F) ((produc64584659_state A) B2)) ((F A) B2))) (forall ((B2 (-> state Bool)) (S2 state) (C2 com) (T2 state) (U2 state)) (let ((_let_1 ((while B2) C2))) (let ((_let_2 (exec S2))) (=> (B2 S2) (=> ((_let_2 C2) T2) (=> (((exec T2) _let_1) U2) ((_let_2 _let_1) U2))))))) (forall ((A2 set_nat) (R set_Pr1986765409at_nat)) (=> (forall ((X3 nat) (Y2 nat)) (=> ((member_nat X3) A2) (=> ((member_nat Y2) A2) (=> (not (= X3 Y2)) (or ((member701585322at_nat ((product_Pair_nat_nat X3) Y2)) R) ((member701585322at_nat ((product_Pair_nat_nat Y2) X3)) R)))))) ((total_on_nat A2) R))) (forall ((P3 produc696469763tate_o)) (exists ((X3 (-> a state Bool)) (Y2 produc204914599tate_o)) (= P3 ((produc33908149tate_o X3) Y2)))) _let_38 (forall ((A produc696469763tate_o)) (not ((member1838112666tate_o A) bot_bo170732493tate_o))) (forall ((X2 produc1115495963_state)) ((refl_o1438232218_state ((insert311944171_state X2) bot_bo1625160935_state)) ((insert1616594103_state ((produc1964772951_state X2) X2)) bot_bo1331673139_state))) (forall ((F (-> com (-> a state Bool) Bool)) (A com) (B2 (-> a state Bool))) (=> ((produc281270436te_o_o F) ((produc1948644831tate_o A) B2)) ((F A) B2))) (forall ((F (-> nat nat))) (wf_nat (measure_nat F))) (forall ((R2 set_Pr1986765409at_nat) (Q set_nat)) (=> (wf_nat R2) (=> (not (= Q bot_bot_set_nat)) (not (forall ((Z nat)) (=> ((member_nat Z) Q) (not (forall ((Y4 nat)) (=> ((member701585322at_nat ((product_Pair_nat_nat Y4) Z)) R2) (not ((member_nat Y4) Q))))))))))) (forall ((A produc696469763tate_o) (B2 produc696469763tate_o)) (=> (= ((insert2053719859tate_o A) bot_bo170732493tate_o) ((insert2053719859tate_o B2) bot_bo170732493tate_o)) (= A B2))) (forall ((P (-> produc1115495963_state Bool)) (P3 produc1115495963_state)) (=> (forall ((A6 state) (B6 state)) (P ((produc64584659_state A6) B6))) (P P3))) _let_37 _let_36 (forall ((Q5 product_prod_nat_nat) (F (-> nat nat Bool)) (G (-> nat nat Bool)) (P3 product_prod_nat_nat)) (=> (forall ((X3 nat) (Y2 nat)) (=> (= ((product_Pair_nat_nat X3) Y2) Q5) (= ((F X3) Y2) ((G X3) Y2)))) (=> (= P3 Q5) (= ((produc949581770_nat_o F) P3) ((produc949581770_nat_o G) Q5))))) (forall ((X2 product_prod_nat_nat) (A2 set_Pr1986765409at_nat)) (let ((_let_1 (insert271595217at_nat X2))) (let ((_let_2 (_let_1 A2))) (= (_let_1 _let_2) _let_2)))) (forall ((P (-> produc696469763tate_o Bool)) (A produc696469763tate_o)) (let ((_let_1 (P A))) (and (=> (not _let_1) (= (collec1499596504tate_o (lambda ((X produc696469763tate_o)) (and (= A X) (P X)))) bot_bo170732493tate_o)) (=> _let_1 (= (collec1499596504tate_o (lambda ((X produc696469763tate_o)) (and (= A X) (P X)))) ((insert2053719859tate_o A) bot_bo170732493tate_o)))))) (forall ((R2 set_Pr1986765409at_nat) (S5 set_Pr1986765409at_nat)) (= (= (lambda ((X nat) (Y5 nat)) ((member701585322at_nat ((product_Pair_nat_nat X) Y5)) R2)) (lambda ((X nat) (Y5 nat)) ((member701585322at_nat ((product_Pair_nat_nat X) Y5)) S5))) (= R2 S5))) ((order_286167592_state bot_bot_set_state) bot_bo1625160935_state) (forall ((X2 produc696469763tate_o) (Y3 produc696469763tate_o) (A2 set_Pr1590995257tate_o)) (let ((_let_1 (insert2053719859tate_o X2))) (let ((_let_2 (insert2053719859tate_o Y3))) (= (_let_1 (_let_2 A2)) (_let_2 (_let_1 A2)))))) (forall ((A2 set_Pr1986765409at_nat) (R set_Pr1490359111at_nat) (X2 product_prod_nat_nat) (Y3 product_prod_nat_nat)) (=> ((refl_o1619599232at_nat A2) R) (=> ((member2027625872at_nat ((produc1168807639at_nat X2) Y3)) R) ((member701585322at_nat X2) A2)))) (forall ((X41 (-> state Bool)) (X42 com)) (not (= ((while X41) X42) call))) (forall ((F (-> state nat))) (wf_state (measure_state F))) (forall ((A produc1115495963_state) (A2 set_Pr795498619_state)) (not (= ((insert311944171_state A) A2) bot_bo1625160935_state))) (forall ((P (-> produc696469763tate_o Bool)) (X2 produc696469763tate_o)) (=> (forall ((A6 (-> a state Bool)) (B6 com) (C4 (-> a state Bool))) (P ((produc33908149tate_o A6) ((produc1948644831tate_o B6) C4)))) (P X2))) (forall ((X2 nat)) ((refl_on_nat ((insert_nat X2) bot_bot_set_nat)) ((insert271595217at_nat ((product_Pair_nat_nat X2) X2)) bot_bo2130386637at_nat))) (forall ((X2 state)) ((total_on_state ((insert_state X2) bot_bot_set_state)) ((insert311944171_state ((produc64584659_state X2) X2)) bot_bo1625160935_state))) (forall ((P (-> produc696469763tate_o Bool)) (A produc696469763tate_o)) (let ((_let_1 (P A))) (and (=> (not _let_1) (= (collec1499596504tate_o (lambda ((X produc696469763tate_o)) (and (P X) (= X A)))) bot_bo170732493tate_o)) (=> _let_1 (= (collec1499596504tate_o (lambda ((X produc696469763tate_o)) (and (= X A) (P X)))) ((insert2053719859tate_o A) bot_bo170732493tate_o)))))) (forall ((A2 set_Pr795498619_state)) (= (exists ((X produc1115495963_state)) ((member1389040324_state X) A2)) (not (= A2 bot_bo1625160935_state)))) (forall ((A produc1115495963_state)) (not ((member1389040324_state A) bot_bo1625160935_state))) (forall ((A produc696469763tate_o)) (= (collec1499596504tate_o ((lambda ((Y produc696469763tate_o) (Z3 produc696469763tate_o)) (= Y Z3)) A)) ((insert2053719859tate_o A) bot_bo170732493tate_o))) _let_35 (forall ((Q (-> Bool Bool)) (P (-> state state Bool)) (Z5 produc1115495963_state)) (=> (Q ((produc789892016tate_o P) Z5)) (not (forall ((X3 state) (Y2 state)) (=> (= Z5 ((produc64584659_state X3) Y2)) (not (Q ((P X3) Y2)))))))) (forall ((P (-> product_prod_nat_nat Bool))) (= (= (collec7649004at_nat P) bot_bo2130386637at_nat) (forall ((X product_prod_nat_nat)) (not (P X))))) (forall ((A2 set_state) (R set_Pr795498619_state) (A state)) (=> ((refl_on_state A2) R) (=> ((member_state A) A2) ((member1389040324_state ((produc64584659_state A) A)) R)))) (forall ((R set_Pr1986765409at_nat)) (=> (forall ((P5 (-> nat Bool)) (X3 nat)) (=> (forall ((Xa nat)) (=> (forall ((Y2 nat)) (=> ((member701585322at_nat ((product_Pair_nat_nat Y2) Xa)) R) (P5 Y2))) (P5 Xa))) (P5 X3))) (wf_nat R))) ((refl_o1438232218_state bot_bo1625160935_state) bot_bo1331673139_state) _let_34 _let_33 (forall ((X1 nat) (X22 nat) (Y1 nat) (Y22 nat)) (= (= ((product_Pair_nat_nat X1) X22) ((product_Pair_nat_nat Y1) Y22)) (and (= X22 Y22) (= X1 Y1)))) (forall ((A produc696469763tate_o) (A2 set_Pr1590995257tate_o) (B2 produc696469763tate_o) (B set_Pr1590995257tate_o)) (let ((_let_1 (= A B2))) (=> (not ((member1838112666tate_o A) A2)) (=> (not ((member1838112666tate_o B2) B)) (= (= ((insert2053719859tate_o A) A2) ((insert2053719859tate_o B2) B)) (and (=> (not _let_1) (exists ((C3 set_Pr1590995257tate_o)) (and (= B ((insert2053719859tate_o A) C3)) (not ((member1838112666tate_o A) C3)) (not ((member1838112666tate_o B2) C3)) (= A2 ((insert2053719859tate_o B2) C3))))) (=> _let_1 (= A2 B)))))))) (forall ((R2 set_Pr1702239303tate_o)) (=> (forall ((X3 produc696469763tate_o) (Q3 set_Pr1590995257tate_o)) (=> ((member1838112666tate_o X3) Q3) (exists ((Xa produc696469763tate_o)) (and ((member1838112666tate_o Xa) Q3) (forall ((Y2 produc696469763tate_o)) (=> ((member1629320336tate_o ((produc1684562079tate_o Y2) Xa)) R2) (not ((member1838112666tate_o Y2) Q3)))))))) (wf_Pro309705690tate_o R2))) (forall ((F (-> (-> a state Bool) produc204914599tate_o Bool)) (A (-> a state Bool)) (B2 produc204914599tate_o)) (=> ((produc1271576886te_o_o F) ((produc33908149tate_o A) B2)) ((F A) B2))) _let_32 (forall ((A2 set_Pr795498619_state) (R set_Pr778812871_state)) (=> (forall ((X3 produc1115495963_state) (Y2 produc1115495963_state)) (=> ((member1389040324_state X3) A2) (=> ((member1389040324_state Y2) A2) (=> (not (= X3 Y2)) (or ((member768948240_state ((produc1964772951_state Y2) X3)) R) ((member768948240_state ((produc1964772951_state X3) Y2)) R)))))) ((total_1316653983_state A2) R))) (forall ((F (-> nat nat Bool)) (A nat) (B2 nat)) (=> ((F A) B2) ((produc949581770_nat_o F) ((product_Pair_nat_nat A) B2)))) _let_31 (forall ((X41 (-> state Bool)) (X42 com) (Y41 (-> state Bool)) (Y42 com)) (= (= ((while X41) X42) ((while Y41) Y42)) (and (= X42 Y42) (= X41 Y41)))) (forall ((A produc696469763tate_o) (B2 produc696469763tate_o) (C2 produc696469763tate_o) (D produc696469763tate_o)) (= (= ((insert2053719859tate_o A) ((insert2053719859tate_o B2) bot_bo170732493tate_o)) ((insert2053719859tate_o C2) ((insert2053719859tate_o D) bot_bo170732493tate_o))) (or (and (= B2 C2) (= A D)) (and (= B2 D) (= A C2))))) (forall ((A product_prod_nat_nat) (B2 product_prod_nat_nat) (A2 set_Pr1986765409at_nat)) (let ((_let_1 (member701585322at_nat A))) (= (_let_1 ((insert271595217at_nat B2) A2)) (or (= A B2) (_let_1 A2))))) (forall ((Y3 produc696469763tate_o)) (not (forall ((A6 (-> a state Bool)) (B6 com) (C4 (-> a state Bool))) (not (= Y3 ((produc33908149tate_o A6) ((produc1948644831tate_o B6) C4))))))) (forall ((C set_Pr1590995257tate_o) (P (-> a state Bool)) (C2 com) (Q (-> a state Bool)) (Q2 (-> a state Bool))) (let ((_let_1 (((pHoare382919414oare_a C) P) C2))) (=> (_let_1 Q) (=> (forall ((Z a) (S state)) (=> ((Q Z) S) ((Q2 Z) S))) (_let_1 Q2))))) (forall ((P (-> produc1115495963_state Bool)) (A produc1115495963_state)) (let ((_let_1 (P A))) (and (=> _let_1 (= (collec496201222_state (lambda ((X produc1115495963_state)) (and (P X) (= X A)))) ((insert311944171_state A) bot_bo1625160935_state))) (=> (not _let_1) (= (collec496201222_state (lambda ((X produc1115495963_state)) (and (P X) (= X A)))) bot_bo1625160935_state))))) (forall ((A2 set_Pr795498619_state) (R set_Pr778812871_state) (X2 produc1115495963_state) (Y3 produc1115495963_state)) (=> ((refl_o1438232218_state A2) R) (=> ((member768948240_state ((produc1964772951_state X2) Y3)) R) ((member1389040324_state X2) A2)))) (forall ((A product_prod_nat_nat) (B set_Pr1986765409at_nat)) ((member701585322at_nat A) ((insert271595217at_nat A) B))) (forall ((P (-> a state Bool)) (Q (-> a state Bool))) ((((pHoare382919414oare_a ((insert2053719859tate_o ((produc33908149tate_o P) ((produc1948644831tate_o call) Q))) bot_bo170732493tate_o)) P) call) Q)) (forall ((A2 set_Pr1590995257tate_o)) (=> (forall ((Y2 produc696469763tate_o)) (not ((member1838112666tate_o Y2) A2))) (= A2 bot_bo170732493tate_o))) (forall ((Y3 product_prod_nat_nat)) (not (forall ((A6 nat) (B6 nat)) (not (= Y3 ((product_Pair_nat_nat A6) B6)))))) (forall ((X1 com) (X22 (-> a state Bool)) (Y1 com) (Y22 (-> a state Bool))) (= (= ((produc1948644831tate_o X1) X22) ((produc1948644831tate_o Y1) Y22)) (and (= X22 Y22) (= X1 Y1)))) (forall ((A product_prod_nat_nat) (A2 set_Pr1986765409at_nat) (B2 product_prod_nat_nat) (B set_Pr1986765409at_nat)) (let ((_let_1 (= A B2))) (=> (not ((member701585322at_nat A) A2)) (=> (not ((member701585322at_nat B2) B)) (= (= ((insert271595217at_nat A) A2) ((insert271595217at_nat B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C3 set_Pr1986765409at_nat)) (and (not ((member701585322at_nat A) C3)) (= B ((insert271595217at_nat A) C3)) (not ((member701585322at_nat B2) C3)) (= A2 ((insert271595217at_nat B2) C3))))))))))) (forall ((C2 produc696469763tate_o)) (not ((member1838112666tate_o C2) bot_bo170732493tate_o))) (forall ((A2 set_Pr795498619_state) (A produc1115495963_state)) (=> (= A2 bot_bo1625160935_state) (not ((member1389040324_state A) A2)))) (= wf_state (lambda ((R3 set_Pr795498619_state)) (forall ((P4 (-> state Bool))) (=> (forall ((X state)) (=> (forall ((Y5 state)) (=> ((member1389040324_state ((produc64584659_state Y5) X)) R3) (P4 Y5))) (P4 X))) (forall ((X4 state)) (P4 X4)))))) (forall ((P (-> produc696469763tate_o Bool))) (= (= (collec1499596504tate_o P) bot_bo170732493tate_o) (forall ((X produc696469763tate_o)) (not (P X))))) (forall ((A2 set_nat) (R set_Pr1986765409at_nat) (A nat)) (=> ((refl_on_nat A2) R) (=> ((member_nat A) A2) ((member701585322at_nat ((product_Pair_nat_nat A) A)) R)))) (forall ((R set_Pr795498619_state) (P (-> state Bool)) (A state)) (=> (wf_state R) (=> (forall ((X3 state)) (=> (forall ((Y4 state)) (=> ((member1389040324_state ((produc64584659_state Y4) X3)) R) (P Y4))) (P X3))) (P A)))) _let_30 (forall ((P (-> produc696469763tate_o Bool))) (= (= (collec1499596504tate_o P) bot_bo170732493tate_o) (= P bot_bo250281208te_o_o))) (forall ((P (-> produc1115495963_state Bool)) (Prod produc1115495963_state)) (=> (forall ((A6 state) (B6 state)) (P ((produc64584659_state A6) B6))) (P Prod))) (forall ((A (-> a state Bool)) (B2 produc204914599tate_o) (A4 (-> a state Bool)) (B5 produc204914599tate_o)) (= (= ((produc33908149tate_o A) B2) ((produc33908149tate_o A4) B5)) (and (= B2 B5) (= A A4)))) _let_29 (forall ((A nat) (B2 nat) (A4 nat) (B5 nat)) (=> (= ((product_Pair_nat_nat A) B2) ((product_Pair_nat_nat A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))) ((refl_o1619599232at_nat bot_bo2130386637at_nat) bot_bo34127283at_nat) (forall ((X2 produc1115495963_state) (A2 set_Pr795498619_state)) (=> ((member1389040324_state X2) A2) (not (forall ((B3 set_Pr795498619_state)) (=> (= A2 ((insert311944171_state X2) B3)) ((member1389040324_state X2) B3)))))) (forall ((F (-> nat nat Bool)) (X1 nat) (X22 nat)) (= ((produc949581770_nat_o F) ((product_Pair_nat_nat X1) X22)) ((F X1) X22))) (forall ((R2 set_Pr795498619_state) (S5 set_Pr795498619_state)) (= (= (lambda ((X state) (Y5 state)) ((member1389040324_state ((produc64584659_state X) Y5)) R2)) (lambda ((X state) (Y5 state)) ((member1389040324_state ((produc64584659_state X) Y5)) S5))) (= R2 S5))) (forall ((F (-> state state Bool)) (A state) (B2 state)) (=> ((F A) B2) ((produc789892016tate_o F) ((produc64584659_state A) B2)))) (forall ((P (-> produc1115495963_state Bool))) (= (= bot_bo1625160935_state (collec496201222_state P)) (forall ((X produc1115495963_state)) (not (P X))))) (forall ((C1 com) (S0 state) (C22 com)) (=> ((termi C1) S0) (=> (forall ((S1 state)) (=> (((exec S0) C1) S1) ((termi C22) S1))) ((termi ((semi C1) C22)) S0)))) (forall ((A produc696469763tate_o) (B set_Pr1590995257tate_o)) ((member1838112666tate_o A) ((insert2053719859tate_o A) B))) (forall ((A2 set_Pr795498619_state)) (=> (forall ((Y2 produc1115495963_state)) (not ((member1389040324_state Y2) A2))) (= A2 bot_bo1625160935_state))) (forall ((X2 product_prod_nat_nat)) (is_sin1352690165at_nat ((insert271595217at_nat X2) bot_bo2130386637at_nat))) (forall ((R set_Pr1986765409at_nat)) ((total_on_nat bot_bot_set_nat) R)) (forall ((X1 (-> a state Bool)) (X22 produc204914599tate_o) (Y1 (-> a state Bool)) (Y22 produc204914599tate_o)) (= (= ((produc33908149tate_o X1) X22) ((produc33908149tate_o Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X2 produc696469763tate_o)) ((refl_o489021252tate_o ((insert2053719859tate_o X2) bot_bo170732493tate_o)) ((insert1597128631tate_o ((produc1684562079tate_o X2) X2)) bot_bo1714653363tate_o))) (forall ((W com) (Fk state) (F (-> nat state)) (K nat) (B2 (-> state Bool)) (C2 com)) (=> ((termi W) Fk) (=> (and (forall ((I nat)) (((exec (F I)) C2) (F (suc I)))) (= W ((while B2) C2)) (= Fk (F K))) (exists ((I nat)) (not (B2 (F I))))))) (= bot_bo170732493tate_o (collec1499596504tate_o bot_bo250281208te_o_o)) (forall ((A product_prod_nat_nat)) (not ((member701585322at_nat A) bot_bo2130386637at_nat))) (forall ((P (-> produc696469763tate_o Bool)) (Prod produc696469763tate_o)) (=> (forall ((A6 (-> a state Bool)) (B6 produc204914599tate_o)) (P ((produc33908149tate_o A6) B6))) (P Prod))) ((order_721919926at_nat bot_bo2130386637at_nat) bot_bo34127283at_nat) (forall ((X2 product_prod_nat_nat)) (= (the_el1949240438at_nat ((insert271595217at_nat X2) bot_bo2130386637at_nat)) X2)) (forall ((A produc696469763tate_o) (A2 set_Pr1590995257tate_o)) (=> ((member1838112666tate_o A) A2) (exists ((B3 set_Pr1590995257tate_o)) (and (not ((member1838112666tate_o A) B3)) (= A2 ((insert2053719859tate_o A) B3)))))) (forall ((A2 set_nat) (R set_Pr1986765409at_nat) (X2 nat) (Y3 nat)) (=> ((refl_on_nat A2) R) (=> ((member701585322at_nat ((product_Pair_nat_nat X2) Y3)) R) ((member_nat X2) A2)))) (forall ((P (-> product_prod_nat_nat Bool)) (P3 product_prod_nat_nat)) (=> (forall ((A6 nat) (B6 nat)) (P ((product_Pair_nat_nat A6) B6))) (P P3))) (forall ((B2 produc696469763tate_o) (A produc696469763tate_o)) (= ((member1838112666tate_o B2) ((insert2053719859tate_o A) bot_bo170732493tate_o)) (= B2 A))) (forall ((A2 set_Pr1590995257tate_o) (R set_Pr1702239303tate_o) (X2 produc696469763tate_o) (Y3 produc696469763tate_o)) (=> ((refl_o489021252tate_o A2) R) (=> ((member1629320336tate_o ((produc1684562079tate_o X2) Y3)) R) ((member1838112666tate_o X2) A2)))) (forall ((Q5 produc1115495963_state) (F (-> state state Bool)) (G (-> state state Bool)) (P3 produc1115495963_state)) (=> (forall ((X3 state) (Y2 state)) (=> (= ((produc64584659_state X3) Y2) Q5) (= ((F X3) Y2) ((G X3) Y2)))) (=> (= P3 Q5) (= ((produc789892016tate_o F) P3) ((produc789892016tate_o G) Q5))))) (forall ((A produc1115495963_state) (B2 produc1115495963_state)) (=> (= ((insert311944171_state A) bot_bo1625160935_state) ((insert311944171_state B2) bot_bo1625160935_state)) (= A B2))) (forall ((S2 state) (N nat) (T2 state)) (let ((_let_1 (execn S2))) (=> (((_let_1 body) N) T2) (((_let_1 call) (suc N)) T2)))) (forall ((P (-> produc204914599tate_o Bool)) (Prod produc204914599tate_o)) (=> (forall ((A6 com) (B6 (-> a state Bool))) (P ((produc1948644831tate_o A6) B6))) (P Prod))) (forall ((A2 set_Pr1986765409at_nat) (A product_prod_nat_nat)) (=> (= A2 bot_bo2130386637at_nat) (not ((member701585322at_nat A) A2)))) (forall ((H (-> Bool Bool)) (F (-> nat nat Bool)) (Prod product_prod_nat_nat)) (= (H ((produc949581770_nat_o F) Prod)) ((produc949581770_nat_o (lambda ((X12 nat) (X23 nat)) (H ((F X12) X23)))) Prod))) _let_28 (forall ((A product_prod_nat_nat) (B2 product_prod_nat_nat) (C2 product_prod_nat_nat) (D product_prod_nat_nat)) (= (= ((insert271595217at_nat A) ((insert271595217at_nat B2) bot_bo2130386637at_nat)) ((insert271595217at_nat C2) ((insert271595217at_nat D) bot_bo2130386637at_nat))) (or (and (= A C2) (= B2 D)) (and (= B2 C2) (= A D))))) (forall ((Prod produc1115495963_state)) ((produc789892016tate_o (lambda ((Uu state) (Uv state)) true)) Prod)) (wf_nat bot_bo2130386637at_nat) ((refl_on_state bot_bot_set_state) bot_bo1625160935_state) (forall ((R2 set_Pr778812871_state) (Q set_Pr795498619_state)) (=> (wf_Pro1783588484_state R2) (=> (not (= Q bot_bo1625160935_state)) (not (forall ((Z produc1115495963_state)) (=> ((member1389040324_state Z) Q) (not (forall ((Y4 produc1115495963_state)) (=> ((member768948240_state ((produc1964772951_state Y4) Z)) R2) (not ((member1389040324_state Y4) Q))))))))))) (forall ((A2 set_Pr795498619_state) (R set_Pr778812871_state) (A produc1115495963_state)) (=> ((refl_o1438232218_state A2) R) (=> ((member1389040324_state A) A2) ((member768948240_state ((produc1964772951_state A) A)) R)))) (forall ((S0 state) (C1 com) (S12 state) (C22 com) (S22 state)) (let ((_let_1 (exec S0))) (=> ((_let_1 C1) S12) (=> (((exec S12) C22) S22) ((_let_1 ((semi C1) C22)) S22))))) (forall ((A product_prod_nat_nat) (A2 set_Pr1986765409at_nat)) (=> ((member701585322at_nat A) A2) (exists ((B3 set_Pr1986765409at_nat)) (and (= A2 ((insert271595217at_nat A) B3)) (not ((member701585322at_nat A) B3)))))) (forall ((P (-> product_prod_nat_nat Bool))) (= (= bot_bo2130386637at_nat (collec7649004at_nat P)) (forall ((X product_prod_nat_nat)) (not (P X))))) (forall ((X2 product_prod_nat_nat) (Y3 product_prod_nat_nat) (A2 set_Pr1986765409at_nat)) (let ((_let_1 (insert271595217at_nat X2))) (let ((_let_2 (insert271595217at_nat Y3))) (= (_let_1 (_let_2 A2)) (_let_2 (_let_1 A2)))))) (forall ((A produc696469763tate_o) (A2 set_Pr1590995257tate_o)) (not (= ((insert2053719859tate_o A) A2) bot_bo170732493tate_o))) (forall ((A (-> a state Bool)) (B2 produc204914599tate_o) (A4 (-> a state Bool)) (B5 produc204914599tate_o)) (=> (= ((produc33908149tate_o A) B2) ((produc33908149tate_o A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))) (forall ((F (-> nat nat Bool)) (A nat) (B2 nat)) (= ((produc949581770_nat_o F) ((product_Pair_nat_nat A) B2)) ((F A) B2))) (forall ((A2 set_nat) (R set_Pr1986765409at_nat) (A nat) (B2 nat)) (=> ((refl_on_nat A2) R) (=> ((member701585322at_nat ((product_Pair_nat_nat A) B2)) R) (and ((member_nat B2) A2) ((member_nat A) A2))))) (forall ((R2 set_Pr1702239303tate_o) (X2 produc696469763tate_o) (Q set_Pr1590995257tate_o)) (=> (wf_Pro309705690tate_o R2) (=> ((member1838112666tate_o X2) Q) (not (forall ((Z produc696469763tate_o)) (=> ((member1838112666tate_o Z) Q) (not (forall ((Y4 produc696469763tate_o)) (=> ((member1629320336tate_o ((produc1684562079tate_o Y4) Z)) R2) (not ((member1838112666tate_o Y4) Q))))))))))) _let_27 (forall ((C2 (-> (-> a state Bool) produc204914599tate_o Bool)) (P3 produc696469763tate_o)) (=> ((produc1271576886te_o_o C2) P3) (not (forall ((X3 (-> a state Bool)) (Y2 produc204914599tate_o)) (=> (= P3 ((produc33908149tate_o X3) Y2)) (not ((C2 X3) Y2))))))) (forall ((P3 product_prod_nat_nat) (Z5 product_prod_nat_nat) (C2 (-> nat nat set_Pr1986765409at_nat))) (=> (forall ((A6 nat) (B6 nat)) (=> (= P3 ((product_Pair_nat_nat A6) B6)) ((member701585322at_nat Z5) ((C2 A6) B6)))) ((member701585322at_nat Z5) ((produc1915186323at_nat C2) P3)))) _let_26 (forall ((P (-> produc696469763tate_o Bool)) (Q (-> produc696469763tate_o Bool))) (=> (forall ((X3 produc696469763tate_o)) (= (P X3) (Q X3))) (= (collec1499596504tate_o P) (collec1499596504tate_o Q)))) (wf_nat pred_nat) (forall ((R2 set_Pr1740974983tate_o) (S5 set_Pr1740974983tate_o)) (= (= (lambda ((X com) (Y5 (-> a state Bool))) ((member221067728tate_o ((produc1948644831tate_o X) Y5)) R2)) (lambda ((X com) (Y5 (-> a state Bool))) ((member221067728tate_o ((produc1948644831tate_o X) Y5)) S5))) (= R2 S5))) (forall ((A produc1115495963_state) (B2 produc1115495963_state) (A2 set_Pr795498619_state)) (let ((_let_1 (member1389040324_state A))) (= (_let_1 ((insert311944171_state B2) A2)) (or (= A B2) (_let_1 A2))))) (forall ((R set_Pr795498619_state) (C set_Pr1590995257tate_o) (P (-> a state Bool)) (B2 (-> state Bool)) (C2 com)) (=> (wf_state R) (=> (forall ((S3 state)) ((((pHoare382919414oare_a C) (lambda ((Z4 a) (S4 state)) (and ((P Z4) S4) (B2 S4) (= S3 S4)))) C2) (lambda ((Z4 a) (S4 state)) (and ((P Z4) S4) ((member1389040324_state ((produc64584659_state S4) S3)) R))))) ((((pHoare382919414oare_a C) P) ((while B2) C2)) (lambda ((Z4 a) (S4 state)) (and (not (B2 S4)) ((P Z4) S4))))))) (forall ((A2 set_Pr1986765409at_nat) (R set_Pr1490359111at_nat)) (=> (forall ((X3 product_prod_nat_nat) (Y2 product_prod_nat_nat)) (=> ((member701585322at_nat X3) A2) (=> ((member701585322at_nat Y2) A2) (=> (not (= X3 Y2)) (or ((member2027625872at_nat ((produc1168807639at_nat Y2) X3)) R) ((member2027625872at_nat ((produc1168807639at_nat X3) Y2)) R)))))) ((total_1775715973at_nat A2) R))) _let_25 (forall ((A produc1115495963_state)) ((member1389040324_state A) ((insert311944171_state A) bot_bo1625160935_state))) (= wf_nat (lambda ((R3 set_Pr1986765409at_nat)) (forall ((P4 (-> nat Bool))) (=> (forall ((X nat)) (=> (forall ((Y5 nat)) (=> ((member701585322at_nat ((product_Pair_nat_nat Y5) X)) R3) (P4 Y5))) (P4 X))) (forall ((X4 nat)) (P4 X4)))))) (forall ((B2 (-> state Bool)) (C2 com) (F (-> nat state)) (K nat)) (=> ((termi ((while B2) C2)) (F K)) (=> (forall ((I nat)) (((exec (F I)) C2) (F (suc I)))) (exists ((I nat)) (not (B2 (F I))))))) (forall ((R2 set_Pr1490359111at_nat)) (=> (forall ((X3 product_prod_nat_nat) (Q3 set_Pr1986765409at_nat)) (=> ((member701585322at_nat X3) Q3) (exists ((Xa product_prod_nat_nat)) (and ((member701585322at_nat Xa) Q3) (forall ((Y2 product_prod_nat_nat)) (=> ((member2027625872at_nat ((produc1168807639at_nat Y2) Xa)) R2) (not ((member701585322at_nat Y2) Q3)))))))) (wf_Pro745352042at_nat R2))) (forall ((R set_Pr795498619_state) (A state)) (=> (wf_state R) (not ((member1389040324_state ((produc64584659_state A) A)) R)))) (forall ((A com) (B2 (-> a state Bool)) (A4 com) (B5 (-> a state Bool))) (=> (= ((produc1948644831tate_o A) B2) ((produc1948644831tate_o A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))) (forall ((S2 state) (T2 state)) (let ((_let_1 (exec S2))) (=> ((_let_1 body) T2) ((_let_1 call) T2)))) (forall ((A produc1115495963_state) (B set_Pr795498619_state) (B2 produc1115495963_state)) (let ((_let_1 (member1389040324_state A))) (=> (_let_1 B) (_let_1 ((insert311944171_state B2) B))))) (forall ((R set_Pr1702239303tate_o)) ((total_795385983tate_o bot_bo170732493tate_o) R)) (forall ((X2 produc696469763tate_o)) ((order_50454158tate_o ((insert2053719859tate_o X2) bot_bo170732493tate_o)) ((insert1597128631tate_o ((produc1684562079tate_o X2) X2)) bot_bo1714653363tate_o))) (forall ((P3 product_prod_nat_nat) (C2 (-> nat nat Bool))) (=> (forall ((A6 nat) (B6 nat)) (=> (= P3 ((product_Pair_nat_nat A6) B6)) ((C2 A6) B6))) ((produc949581770_nat_o C2) P3))) (forall ((Prod product_prod_nat_nat)) ((produc949581770_nat_o (lambda ((Uu nat) (Uv nat)) true)) Prod)) (forall ((A2 set_Pr1590995257tate_o) (R set_Pr1702239303tate_o) (X2 produc696469763tate_o) (Y3 produc696469763tate_o)) (=> ((refl_o489021252tate_o A2) R) (=> ((member1629320336tate_o ((produc1684562079tate_o X2) Y3)) R) ((member1838112666tate_o Y3) A2)))) (forall ((R set_Pr1986765409at_nat) (P (-> nat Bool)) (A nat)) (=> (wf_nat R) (=> (forall ((X3 nat)) (=> (forall ((Y4 nat)) (=> ((member701585322at_nat ((product_Pair_nat_nat Y4) X3)) R) (P Y4))) (P X3))) (P A)))) (forall ((A produc696469763tate_o) (B set_Pr1590995257tate_o) (B2 produc696469763tate_o)) (let ((_let_1 (member1838112666tate_o A))) (=> (=> (not (_let_1 B)) (= A B2)) (_let_1 ((insert2053719859tate_o B2) B))))) (forall ((X2 nat) (Y3 nat)) (= ((member701585322at_nat ((product_Pair_nat_nat X2) Y3)) less_than) ((ord_less_nat X2) Y3))) (forall ((P (-> produc1115495963_state Bool)) (Q (-> produc1115495963_state Bool))) (=> (forall ((X3 produc1115495963_state)) (= (P X3) (Q X3))) (= (collec496201222_state P) (collec496201222_state Q)))) (forall ((X2 produc1115495963_state)) ((order_178668240_state ((insert311944171_state X2) bot_bo1625160935_state)) ((insert1616594103_state ((produc1964772951_state X2) X2)) bot_bo1331673139_state))) (forall ((P3 product_prod_nat_nat)) (exists ((X3 nat) (Y2 nat)) (= P3 ((product_Pair_nat_nat X3) Y2)))) (forall ((P3 product_prod_nat_nat) (Z5 produc696469763tate_o) (C2 (-> nat nat set_Pr1590995257tate_o))) (=> (forall ((A6 nat) (B6 nat)) (=> (= P3 ((product_Pair_nat_nat A6) B6)) ((member1838112666tate_o Z5) ((C2 A6) B6)))) ((member1838112666tate_o Z5) ((produc1610543495tate_o C2) P3)))) (forall ((X2 produc696469763tate_o) (A2 set_Pr1590995257tate_o) (B set_Pr1590995257tate_o)) (let ((_let_1 (insert2053719859tate_o X2))) (let ((_let_2 (member1838112666tate_o X2))) (=> (not (_let_2 A2)) (=> (not (_let_2 B)) (= (= (_let_1 A2) (_let_1 B)) (= A2 B))))))) _let_24 (forall ((A2 set_Pr795498619_state)) (= (collec496201222_state (lambda ((X produc1115495963_state)) ((member1389040324_state X) A2))) A2)) (forall ((R2 set_Pr1590995257tate_o) (S5 set_Pr1590995257tate_o)) (= (= (lambda ((X (-> a state Bool)) (Y5 produc204914599tate_o)) ((member1838112666tate_o ((produc33908149tate_o X) Y5)) R2)) (lambda ((X (-> a state Bool)) (Y5 produc204914599tate_o)) ((member1838112666tate_o ((produc33908149tate_o X) Y5)) S5))) (= R2 S5))) (forall ((R set_Pr795498619_state) (A state)) (=> (wf_state R) (not ((member1389040324_state ((produc64584659_state A) A)) R)))) _let_23 (forall ((A produc696469763tate_o) (B set_Pr1590995257tate_o) (B2 produc696469763tate_o)) (let ((_let_1 (member1838112666tate_o A))) (=> (_let_1 B) (_let_1 ((insert2053719859tate_o B2) B))))) (forall ((A2 set_Pr795498619_state)) (=> (not (= A2 bot_bo1625160935_state)) (=> (forall ((X3 produc1115495963_state) (Y2 produc1115495963_state)) (=> ((member1389040324_state X3) A2) (=> ((member1389040324_state Y2) A2) (= X3 Y2)))) (is_sin1132515087_state A2)))) (forall ((B2 (-> state Bool)) (S2 state) (C2 com)) (=> (B2 S2) (=> ((termi C2) S2) (=> (forall ((T state)) (=> (((exec S2) C2) T) ((termi ((while B2) C2)) T))) ((termi ((while B2) C2)) S2))))) (forall ((A2 set_Pr795498619_state)) (= (forall ((X produc1115495963_state)) (not ((member1389040324_state X) A2))) (= A2 bot_bo1625160935_state))) (= bot_bo2130386637at_nat (collec7649004at_nat bot_bo513358416_nat_o)) (forall ((P (-> product_prod_nat_nat Bool))) (= (= (collec7649004at_nat P) bot_bo2130386637at_nat) (= P bot_bo513358416_nat_o))) (forall ((Y3 produc204914599tate_o)) (not (forall ((A6 com) (B6 (-> a state Bool))) (not (= Y3 ((produc1948644831tate_o A6) B6)))))) (forall ((R set_Pr1490359111at_nat)) ((total_1775715973at_nat bot_bo2130386637at_nat) R)) (forall ((P Bool) (Q (-> state state Bool))) (= (produc789892016tate_o (lambda ((A3 state) (B7 state)) (and ((Q A3) B7) P))) (lambda ((Ab produc1115495963_state)) (and P ((produc789892016tate_o Q) Ab))))) (forall ((R2 set_Pr795498619_state) (Q set_state)) (=> (wf_state R2) (=> (not (= Q bot_bot_set_state)) (not (forall ((Z state)) (=> ((member_state Z) Q) (not (forall ((Y4 state)) (=> ((member1389040324_state ((produc64584659_state Y4) Z)) R2) (not ((member_state Y4) Q))))))))))) (forall ((X2 produc1115495963_state) (Y3 produc1115495963_state) (A2 set_Pr795498619_state)) (let ((_let_1 (insert311944171_state X2))) (let ((_let_2 (insert311944171_state Y3))) (= (_let_1 (_let_2 A2)) (_let_2 (_let_1 A2)))))) (forall ((R2 set_Pr1490359111at_nat) (Q set_Pr1986765409at_nat)) (=> (wf_Pro745352042at_nat R2) (=> (not (= Q bot_bo2130386637at_nat)) (not (forall ((Z product_prod_nat_nat)) (=> ((member701585322at_nat Z) Q) (not (forall ((Y4 product_prod_nat_nat)) (=> ((member2027625872at_nat ((produc1168807639at_nat Y4) Z)) R2) (not ((member701585322at_nat Y4) Q))))))))))) (forall ((A2 set_nat)) ((total_on_nat A2) less_than)) (forall ((B2 product_prod_nat_nat) (A product_prod_nat_nat)) (= ((member701585322at_nat B2) ((insert271595217at_nat A) bot_bo2130386637at_nat)) (= B2 A))) _let_22 (forall ((A2 set_Pr1590995257tate_o) (R set_Pr1702239303tate_o) (A produc696469763tate_o) (B2 produc696469763tate_o)) (=> ((refl_o489021252tate_o A2) R) (=> ((member1629320336tate_o ((produc1684562079tate_o A) B2)) R) (and ((member1838112666tate_o A) A2) ((member1838112666tate_o B2) A2))))) _let_21 (forall ((P (-> a state Bool)) (Q (-> a state Bool))) ((((hoare_a ((insert2053719859tate_o ((produc33908149tate_o P) ((produc1948644831tate_o call) Q))) bot_bo170732493tate_o)) P) call) Q)) (forall ((A product_prod_nat_nat)) (= (collec7649004at_nat (lambda ((X product_prod_nat_nat)) (= X A))) ((insert271595217at_nat A) bot_bo2130386637at_nat))) (forall ((R2 set_Pr778812871_state) (X2 produc1115495963_state) (Q set_Pr795498619_state)) (=> (wf_Pro1783588484_state R2) (=> ((member1389040324_state X2) Q) (not (forall ((Z produc1115495963_state)) (=> ((member1389040324_state Z) Q) (not (forall ((Y4 produc1115495963_state)) (=> ((member768948240_state ((produc1964772951_state Y4) Z)) R2) (not ((member1389040324_state Y4) Q))))))))))) (forall ((A nat) (B2 nat) (A4 nat) (B5 nat)) (= (= ((product_Pair_nat_nat A) B2) ((product_Pair_nat_nat A4) B5)) (and (= A A4) (= B2 B5)))) _let_20 (forall ((X2 produc696469763tate_o) (A2 set_Pr1590995257tate_o)) (=> ((member1838112666tate_o X2) A2) (not (forall ((B3 set_Pr1590995257tate_o)) (=> (= A2 ((insert2053719859tate_o X2) B3)) ((member1838112666tate_o X2) B3)))))) (forall ((X2 produc1115495963_state)) ((total_1316653983_state ((insert311944171_state X2) bot_bo1625160935_state)) ((insert1616594103_state ((produc1964772951_state X2) X2)) bot_bo1331673139_state))) (forall ((A2 set_state) (R set_Pr795498619_state) (X2 state) (Y3 state)) (=> ((refl_on_state A2) R) (=> ((member1389040324_state ((produc64584659_state X2) Y3)) R) ((member_state Y3) A2)))) (forall ((B2 produc1115495963_state) (A produc1115495963_state)) (= ((member1389040324_state B2) ((insert311944171_state A) bot_bo1625160935_state)) (= B2 A))) (forall ((X2 product_prod_nat_nat)) ((refl_o1619599232at_nat ((insert271595217at_nat X2) bot_bo2130386637at_nat)) ((insert584009271at_nat ((produc1168807639at_nat X2) X2)) bot_bo34127283at_nat))) (forall ((Q (-> Bool Bool)) (P (-> nat nat Bool)) (Z5 product_prod_nat_nat)) (=> (Q ((produc949581770_nat_o P) Z5)) (not (forall ((X3 nat) (Y2 nat)) (=> (= Z5 ((product_Pair_nat_nat X3) Y2)) (not (Q ((P X3) Y2)))))))) (forall ((C2 product_prod_nat_nat)) (not ((member701585322at_nat C2) bot_bo2130386637at_nat))) (forall ((A state) (B2 state) (A4 state) (B5 state)) (= (= ((produc64584659_state A) B2) ((produc64584659_state A4) B5)) (and (= A A4) (= B2 B5)))) (forall ((A produc1115495963_state) (B2 produc1115495963_state) (C2 produc1115495963_state) (D produc1115495963_state)) (= (= ((insert311944171_state A) ((insert311944171_state B2) bot_bo1625160935_state)) ((insert311944171_state C2) ((insert311944171_state D) bot_bo1625160935_state))) (or (and (= A C2) (= B2 D)) (and (= B2 C2) (= A D))))) _let_19 (forall ((A produc696469763tate_o)) ((member1838112666tate_o A) ((insert2053719859tate_o A) bot_bo170732493tate_o))) (forall ((A produc1115495963_state) (P (-> produc1115495963_state Bool))) (= ((insert311944171_state A) (collec496201222_state P)) (collec496201222_state (lambda ((U produc1115495963_state)) (=> (not (= U A)) (P U)))))) (forall ((A product_prod_nat_nat) (B2 product_prod_nat_nat) (A2 set_Pr1986765409at_nat)) (let ((_let_1 (member701585322at_nat A))) (=> (_let_1 ((insert271595217at_nat B2) A2)) (=> (not (= A B2)) (_let_1 A2))))) (forall ((X2 product_prod_nat_nat)) ((order_721919926at_nat ((insert271595217at_nat X2) bot_bo2130386637at_nat)) ((insert584009271at_nat ((produc1168807639at_nat X2) X2)) bot_bo34127283at_nat))) (forall ((X2 produc696469763tate_o)) (= (the_el1569055182tate_o ((insert2053719859tate_o X2) bot_bo170732493tate_o)) X2)) (forall ((B2 produc696469763tate_o) (A produc696469763tate_o)) (=> ((member1838112666tate_o B2) ((insert2053719859tate_o A) bot_bo170732493tate_o)) (= B2 A))) (forall ((A produc696469763tate_o) (A2 set_Pr1590995257tate_o)) (=> ((member1838112666tate_o A) A2) (= ((insert2053719859tate_o A) A2) A2))) _let_18 (forall ((P3 produc696469763tate_o) (C2 (-> (-> a state Bool) produc204914599tate_o Bool))) (=> (forall ((A6 (-> a state Bool)) (B6 produc204914599tate_o)) (=> (= P3 ((produc33908149tate_o A6) B6)) ((C2 A6) B6))) ((produc1271576886te_o_o C2) P3))) (forall ((F (-> produc1115495963_state Bool))) (= (produc789892016tate_o (lambda ((X state) (Y5 state)) (F ((produc64584659_state X) Y5)))) F)) (forall ((C2 (-> state state Bool)) (P3 produc1115495963_state)) (=> ((produc789892016tate_o C2) P3) (not (forall ((X3 state) (Y2 state)) (=> (= P3 ((produc64584659_state X3) Y2)) (not ((C2 X3) Y2))))))) (forall ((A produc1115495963_state)) (= (collec496201222_state ((lambda ((Y produc1115495963_state) (Z3 produc1115495963_state)) (= Y Z3)) A)) ((insert311944171_state A) bot_bo1625160935_state))) (forall ((P3 produc204914599tate_o)) (exists ((X3 com) (Y2 (-> a state Bool))) (= P3 ((produc1948644831tate_o X3) Y2)))) (forall ((P Bool) (Q (-> nat nat Bool))) (= (produc949581770_nat_o (lambda ((A3 nat) (B7 nat)) (and P ((Q A3) B7)))) (lambda ((Ab product_prod_nat_nat)) (and P ((produc949581770_nat_o Q) Ab))))) (forall ((F (-> (-> a state Bool) produc204914599tate_o Bool)) (A (-> a state Bool)) (B2 produc204914599tate_o)) (=> ((F A) B2) ((produc1271576886te_o_o F) ((produc33908149tate_o A) B2)))) (forall ((A product_prod_nat_nat) (B set_Pr1986765409at_nat) (B2 product_prod_nat_nat)) (let ((_let_1 (member701585322at_nat A))) (=> (_let_1 B) (_let_1 ((insert271595217at_nat B2) B))))) (forall ((A2 set_Pr1590995257tate_o)) (=> (is_sin1547905295tate_o A2) (not (forall ((X3 produc696469763tate_o)) (not (= A2 ((insert2053719859tate_o X3) bot_bo170732493tate_o))))))) (forall ((X2 nat)) ((order_130026331on_nat ((insert_nat X2) bot_bot_set_nat)) ((insert271595217at_nat ((product_Pair_nat_nat X2) X2)) bot_bo2130386637at_nat))) _let_17 (forall ((A produc696469763tate_o)) (= (collec1499596504tate_o (lambda ((X produc696469763tate_o)) (= X A))) ((insert2053719859tate_o A) bot_bo170732493tate_o))) (forall ((P2 (-> a state Bool)) (P (-> a state Bool)) (C set_Pr1590995257tate_o) (C2 com) (Q (-> a state Bool))) (let ((_let_1 (pHoare382919414oare_a C))) (=> (forall ((Z a) (S state)) (=> ((P2 Z) S) ((P Z) S))) (=> (((_let_1 P) C2) Q) (((_let_1 P2) C2) Q))))) (forall ((R set_Pr1986765409at_nat) (A nat) (X2 nat)) (=> (wf_nat R) (=> ((member701585322at_nat ((product_Pair_nat_nat A) X2)) R) (not ((member701585322at_nat ((product_Pair_nat_nat X2) A)) R))))) _let_16 (forall ((A2 set_Pr1590995257tate_o) (A produc696469763tate_o)) (=> (= A2 bot_bo170732493tate_o) (not ((member1838112666tate_o A) A2)))) (forall ((R2 set_Pr1986765409at_nat)) (=> (forall ((X3 nat) (Q3 set_nat)) (=> ((member_nat X3) Q3) (exists ((Xa nat)) (and ((member_nat Xa) Q3) (forall ((Y2 nat)) (=> ((member701585322at_nat ((product_Pair_nat_nat Y2) Xa)) R2) (not ((member_nat Y2) Q3)))))))) (wf_nat R2))) (forall ((X2 product_prod_nat_nat)) ((total_1775715973at_nat ((insert271595217at_nat X2) bot_bo2130386637at_nat)) ((insert584009271at_nat ((produc1168807639at_nat X2) X2)) bot_bo34127283at_nat))) (forall ((P (-> produc1115495963_state Bool))) (= (= (collec496201222_state P) bot_bo1625160935_state) (forall ((X produc1115495963_state)) (not (P X))))) (forall ((Y3 produc696469763tate_o)) (not (forall ((A6 (-> a state Bool)) (B6 produc204914599tate_o)) (not (= Y3 ((produc33908149tate_o A6) B6)))))) (forall ((R set_Pr795498619_state)) (=> (forall ((P5 (-> state Bool)) (X3 state)) (=> (forall ((Xa state)) (=> (forall ((Y2 state)) (=> ((member1389040324_state ((produc64584659_state Y2) Xa)) R) (P5 Y2))) (P5 Xa))) (P5 X3))) (wf_state R))) (forall ((R2 set_Pr1986765409at_nat) (X2 nat) (Q set_nat)) (=> (wf_nat R2) (=> ((member_nat X2) Q) (not (forall ((Z nat)) (=> ((member_nat Z) Q) (not (forall ((Y4 nat)) (=> ((member701585322at_nat ((product_Pair_nat_nat Y4) Z)) R2) (not ((member_nat Y4) Q))))))))))) (forall ((A state) (B2 state) (A4 state) (B5 state)) (=> (= ((produc64584659_state A) B2) ((produc64584659_state A4) B5)) (not (=> (= A A4) (not (= B2 B5)))))) (forall ((X2 produc1115495963_state) (A2 set_Pr795498619_state) (B set_Pr795498619_state)) (let ((_let_1 (insert311944171_state X2))) (let ((_let_2 (member1389040324_state X2))) (=> (not (_let_2 A2)) (=> (not (_let_2 B)) (= (= (_let_1 A2) (_let_1 B)) (= A2 B))))))) (forall ((R set_Pr1986765409at_nat) (A nat)) (=> (wf_nat R) (not ((member701585322at_nat ((product_Pair_nat_nat A) A)) R)))) (forall ((A2 set_state) (R set_Pr795498619_state) (X2 state) (Y3 state)) (=> ((refl_on_state A2) R) (=> ((member1389040324_state ((produc64584659_state X2) Y3)) R) ((member_state X2) A2)))) (forall ((A produc1115495963_state) (A2 set_Pr795498619_state)) (=> ((member1389040324_state A) A2) (= ((insert311944171_state A) A2) A2))) (forall ((A2 set_Pr1986765409at_nat)) (=> (is_sin1352690165at_nat A2) (not (forall ((X3 product_prod_nat_nat)) (not (= A2 ((insert271595217at_nat X3) bot_bo2130386637at_nat))))))) (forall ((R set_Pr778812871_state)) ((total_1316653983_state bot_bo1625160935_state) R)) (forall ((R2 set_Pr1490359111at_nat) (X2 product_prod_nat_nat) (Q set_Pr1986765409at_nat)) (=> (wf_Pro745352042at_nat R2) (=> ((member701585322at_nat X2) Q) (not (forall ((Z product_prod_nat_nat)) (=> ((member701585322at_nat Z) Q) (not (forall ((Y4 product_prod_nat_nat)) (=> ((member2027625872at_nat ((produc1168807639at_nat Y4) Z)) R2) (not ((member701585322at_nat Y4) Q))))))))))) (forall ((X2 produc696469763tate_o)) ((total_795385983tate_o ((insert2053719859tate_o X2) bot_bo170732493tate_o)) ((insert1597128631tate_o ((produc1684562079tate_o X2) X2)) bot_bo1714653363tate_o))) (forall ((P (-> product_prod_nat_nat Bool)) (Prod product_prod_nat_nat)) (=> (forall ((A6 nat) (B6 nat)) (P ((product_Pair_nat_nat A6) B6))) (P Prod))) (forall ((A2 set_Pr1986765409at_nat)) (= (forall ((X product_prod_nat_nat)) (not ((member701585322at_nat X) A2))) (= A2 bot_bo2130386637at_nat))) (forall ((H (-> Bool Bool)) (F (-> state state Bool)) (Prod produc1115495963_state)) (= (H ((produc789892016tate_o F) Prod)) ((produc789892016tate_o (lambda ((X12 state) (X23 state)) (H ((F X12) X23)))) Prod))) ((order_50454158tate_o bot_bo170732493tate_o) bot_bo1714653363tate_o) _let_15 (forall ((B2 (-> state Bool)) (S2 state) (C2 com) (N nat)) (=> (not (B2 S2)) ((((execn S2) ((while B2) C2)) N) S2))) (forall ((A product_prod_nat_nat) (P (-> product_prod_nat_nat Bool))) (= ((member701585322at_nat A) (collec7649004at_nat P)) (P A))) (forall ((R set_Pr1986765409at_nat) (P (-> nat Bool)) (A nat)) (=> (wf_nat R) (=> (forall ((X3 nat)) (=> (forall ((Y4 nat)) (=> ((member701585322at_nat ((product_Pair_nat_nat Y4) X3)) R) (P Y4))) (P X3))) (P A)))) (forall ((F (-> state state Bool)) (A state) (B2 state)) (=> ((produc789892016tate_o F) ((produc64584659_state A) B2)) ((F A) B2))) _let_14 (forall ((A produc1115495963_state)) (= (collec496201222_state (lambda ((X produc1115495963_state)) (= X A))) ((insert311944171_state A) bot_bo1625160935_state))) (forall ((A2 set_Pr795498619_state)) (=> (is_sin1132515087_state A2) (not (forall ((X3 produc1115495963_state)) (not (= A2 ((insert311944171_state X3) bot_bo1625160935_state))))))) (forall ((B2 produc1115495963_state) (A produc1115495963_state)) (=> ((member1389040324_state B2) ((insert311944171_state A) bot_bo1625160935_state)) (= B2 A))) _let_13 (forall ((P (-> product_prod_nat_nat Bool)) (A product_prod_nat_nat)) (let ((_let_1 (P A))) (and (=> (not _let_1) (= (collec7649004at_nat (lambda ((X product_prod_nat_nat)) (and (= A X) (P X)))) bot_bo2130386637at_nat)) (=> _let_1 (= (collec7649004at_nat (lambda ((X product_prod_nat_nat)) (and (P X) (= A X)))) ((insert271595217at_nat A) bot_bo2130386637at_nat)))))) (forall ((P (-> produc1115495963_state Bool))) (= (= (collec496201222_state P) bot_bo1625160935_state) (= P bot_bo446391478tate_o))) _let_12 (forall ((A produc1115495963_state) (A2 set_Pr795498619_state)) (=> ((member1389040324_state A) A2) (exists ((B3 set_Pr795498619_state)) (and (= A2 ((insert311944171_state A) B3)) (not ((member1389040324_state A) B3)))))) (forall ((X2 state)) ((refl_on_state ((insert_state X2) bot_bot_set_state)) ((insert311944171_state ((produc64584659_state X2) X2)) bot_bo1625160935_state))) _let_11 (forall ((A2 set_Pr1590995257tate_o)) (= (exists ((X produc696469763tate_o)) ((member1838112666tate_o X) A2)) (not (= A2 bot_bo170732493tate_o)))) (forall ((A product_prod_nat_nat) (P (-> product_prod_nat_nat Bool))) (= ((insert271595217at_nat A) (collec7649004at_nat P)) (collec7649004at_nat (lambda ((U product_prod_nat_nat)) (=> (not (= U A)) (P U)))))) (forall ((C2 produc1115495963_state)) (not ((member1389040324_state C2) bot_bo1625160935_state))) (forall ((A2 set_Pr1986765409at_nat)) (=> (forall ((Y2 product_prod_nat_nat)) (not ((member701585322at_nat Y2) A2))) (= A2 bot_bo2130386637at_nat))) (forall ((X2 produc696469763tate_o)) (is_sin1547905295tate_o ((insert2053719859tate_o X2) bot_bo170732493tate_o))) (forall ((C2 (-> nat nat Bool)) (P3 product_prod_nat_nat)) (=> ((produc949581770_nat_o C2) P3) (not (forall ((X3 nat) (Y2 nat)) (=> (= P3 ((product_Pair_nat_nat X3) Y2)) (not ((C2 X3) Y2))))))) (forall ((R2 set_Pr795498619_state)) (=> (forall ((X3 state) (Q3 set_state)) (=> ((member_state X3) Q3) (exists ((Xa state)) (and ((member_state Xa) Q3) (forall ((Y2 state)) (=> ((member1389040324_state ((produc64584659_state Y2) Xa)) R2) (not ((member_state Y2) Q3)))))))) (wf_state R2))) (forall ((A2 set_Pr1590995257tate_o)) (= (collec1499596504tate_o (lambda ((X produc696469763tate_o)) ((member1838112666tate_o X) A2))) A2)) (forall ((A produc696469763tate_o) (P (-> produc696469763tate_o Bool))) (= ((member1838112666tate_o A) (collec1499596504tate_o P)) (P A))) _let_10 _let_9 (forall ((B2 product_prod_nat_nat) (A product_prod_nat_nat)) (=> ((member701585322at_nat B2) ((insert271595217at_nat A) bot_bo2130386637at_nat)) (= B2 A))) (forall ((A produc696469763tate_o) (B2 produc696469763tate_o) (A2 set_Pr1590995257tate_o)) (let ((_let_1 (member1838112666tate_o A))) (= (_let_1 ((insert2053719859tate_o B2) A2)) (or (_let_1 A2) (= A B2))))) (forall ((R2 set_Pr1702239303tate_o) (Q set_Pr1590995257tate_o)) (=> (wf_Pro309705690tate_o R2) (=> (not (= Q bot_bo170732493tate_o)) (not (forall ((Z produc696469763tate_o)) (=> ((member1838112666tate_o Z) Q) (not (forall ((Y4 produc696469763tate_o)) (=> ((member1629320336tate_o ((produc1684562079tate_o Y4) Z)) R2) (not ((member1838112666tate_o Y4) Q))))))))))) (forall ((A2 set_nat) (R set_Pr1986765409at_nat) (X2 nat) (Y3 nat)) (=> ((refl_on_nat A2) R) (=> ((member701585322at_nat ((product_Pair_nat_nat X2) Y3)) R) ((member_nat Y3) A2)))) (wf_state bot_bo1625160935_state) (forall ((P (-> produc1115495963_state Bool)) (A produc1115495963_state)) (let ((_let_1 (P A))) (and (=> (not _let_1) (= (collec496201222_state (lambda ((X produc1115495963_state)) (and (= A X) (P X)))) bot_bo1625160935_state)) (=> _let_1 (= (collec496201222_state (lambda ((X produc1115495963_state)) (and (= A X) (P X)))) ((insert311944171_state A) bot_bo1625160935_state)))))) (forall ((R2 set_Pr778812871_state)) (=> (forall ((X3 produc1115495963_state) (Q3 set_Pr795498619_state)) (=> ((member1389040324_state X3) Q3) (exists ((Xa produc1115495963_state)) (and (forall ((Y2 produc1115495963_state)) (=> ((member768948240_state ((produc1964772951_state Y2) Xa)) R2) (not ((member1389040324_state Y2) Q3)))) ((member1389040324_state Xa) Q3))))) (wf_Pro1783588484_state R2))) ((order_130026331on_nat bot_bot_set_nat) bot_bo2130386637at_nat) (forall ((A product_prod_nat_nat)) ((member701585322at_nat A) ((insert271595217at_nat A) bot_bo2130386637at_nat))) (forall ((A product_prod_nat_nat) (B2 product_prod_nat_nat)) (=> (= ((insert271595217at_nat A) bot_bo2130386637at_nat) ((insert271595217at_nat B2) bot_bo2130386637at_nat)) (= A B2))) (forall ((C2 (-> com (-> a state Bool) Bool)) (P3 produc204914599tate_o)) (=> ((produc281270436te_o_o C2) P3) (not (forall ((X3 com) (Y2 (-> a state Bool))) (=> (= P3 ((produc1948644831tate_o X3) Y2)) (not ((C2 X3) Y2))))))) (forall ((F (-> nat nat Bool)) (A nat) (B2 nat)) (=> ((produc949581770_nat_o F) ((product_Pair_nat_nat A) B2)) ((F A) B2))) (forall ((F (-> state state Bool)) (X1 state) (X22 state)) (= ((produc789892016tate_o F) ((produc64584659_state X1) X22)) ((F X1) X22))) (forall ((R set_Pr795498619_state) (A state) (X2 state)) (=> (wf_state R) (=> ((member1389040324_state ((produc64584659_state A) X2)) R) (not ((member1389040324_state ((produc64584659_state X2) A)) R))))) (forall ((A2 set_Pr795498619_state) (R set_Pr778812871_state) (X2 produc1115495963_state) (Y3 produc1115495963_state)) (=> ((refl_o1438232218_state A2) R) (=> ((member768948240_state ((produc1964772951_state X2) Y3)) R) ((member1389040324_state Y3) A2)))) (forall ((A2 set_Pr1986765409at_nat) (R set_Pr1490359111at_nat) (A product_prod_nat_nat) (B2 product_prod_nat_nat)) (=> ((refl_o1619599232at_nat A2) R) (=> ((member2027625872at_nat ((produc1168807639at_nat A) B2)) R) (and ((member701585322at_nat A) A2) ((member701585322at_nat B2) A2))))) (forall ((X2 product_prod_nat_nat) (A2 set_Pr1986765409at_nat)) (=> ((member701585322at_nat X2) A2) (not (forall ((B3 set_Pr1986765409at_nat)) (=> (= A2 ((insert271595217at_nat X2) B3)) ((member701585322at_nat X2) B3)))))) (= bot_bo1625160935_state (collec496201222_state bot_bo446391478tate_o)) (forall ((X2 state)) ((order_286167592_state ((insert_state X2) bot_bot_set_state)) ((insert311944171_state ((produc64584659_state X2) X2)) bot_bo1625160935_state))) (forall ((A2 set_Pr1590995257tate_o) (R set_Pr1702239303tate_o)) (=> (forall ((X3 produc696469763tate_o) (Y2 produc696469763tate_o)) (=> ((member1838112666tate_o X3) A2) (=> ((member1838112666tate_o Y2) A2) (=> (not (= X3 Y2)) (or ((member1629320336tate_o ((produc1684562079tate_o X3) Y2)) R) ((member1629320336tate_o ((produc1684562079tate_o Y2) X3)) R)))))) ((total_795385983tate_o A2) R))) (forall ((P3 produc1115495963_state)) (exists ((X3 state) (Y2 state)) (= P3 ((produc64584659_state X3) Y2)))) ((refl_o489021252tate_o bot_bo170732493tate_o) bot_bo1714653363tate_o) (forall ((A produc1115495963_state) (B2 produc1115495963_state) (A2 set_Pr795498619_state)) (let ((_let_1 (member1389040324_state A))) (=> (_let_1 ((insert311944171_state B2) A2)) (=> (not (= A B2)) (_let_1 A2))))) (forall ((X2 produc1115495963_state)) (is_sin1132515087_state ((insert311944171_state X2) bot_bo1625160935_state))) (forall ((P3 produc204914599tate_o) (C2 (-> com (-> a state Bool) Bool))) (=> (forall ((A6 com) (B6 (-> a state Bool))) (=> (= P3 ((produc1948644831tate_o A6) B6)) ((C2 A6) B6))) ((produc281270436te_o_o C2) P3))) (forall ((A com) (B2 (-> a state Bool)) (A4 com) (B5 (-> a state Bool))) (= (= ((produc1948644831tate_o A) B2) ((produc1948644831tate_o A4) B5)) (and (= B2 B5) (= A A4)))) (forall ((A product_prod_nat_nat)) (= (collec7649004at_nat ((lambda ((Y product_prod_nat_nat) (Z3 product_prod_nat_nat)) (= Y Z3)) A)) ((insert271595217at_nat A) bot_bo2130386637at_nat))) (forall ((A2 set_Pr1590995257tate_o) (R set_Pr1702239303tate_o) (A produc696469763tate_o)) (=> ((refl_o489021252tate_o A2) R) (=> ((member1838112666tate_o A) A2) ((member1629320336tate_o ((produc1684562079tate_o A) A)) R)))) (forall ((P (-> produc696469763tate_o Bool)) (P3 produc696469763tate_o)) (=> (forall ((A6 (-> a state Bool)) (B6 produc204914599tate_o)) (P ((produc33908149tate_o A6) B6))) (P P3))) (forall ((P (-> product_prod_nat_nat Bool)) (Q (-> product_prod_nat_nat Bool))) (=> (forall ((X3 product_prod_nat_nat)) (= (P X3) (Q X3))) (= (collec7649004at_nat P) (collec7649004at_nat Q)))) _let_8 _let_7 (forall ((A produc1115495963_state) (B set_Pr795498619_state) (B2 produc1115495963_state)) (let ((_let_1 (member1389040324_state A))) (=> (=> (not (_let_1 B)) (= A B2)) (_let_1 ((insert311944171_state B2) B))))) (forall ((A produc1115495963_state) (A2 set_Pr795498619_state) (B2 produc1115495963_state) (B set_Pr795498619_state)) (let ((_let_1 (= A B2))) (=> (not ((member1389040324_state A) A2)) (=> (not ((member1389040324_state B2) B)) (= (= ((insert311944171_state A) A2) ((insert311944171_state B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C3 set_Pr795498619_state)) (and (= A2 ((insert311944171_state B2) C3)) (= B ((insert311944171_state A) C3)) (not ((member1389040324_state A) C3)) (not ((member1389040324_state B2) C3))))))))))) (forall ((A2 set_Pr1590995257tate_o)) (= (forall ((X produc696469763tate_o)) (not ((member1838112666tate_o X) A2))) (= A2 bot_bo170732493tate_o))) (forall ((S2 state) (W com) (N nat) (T2 state) (B2 (-> state Bool)) (C2 com) (P (-> state Bool))) (=> ((((execn S2) W) N) T2) (=> (and (P S2) (forall ((S state) (S3 state)) (=> (and (P S) ((((execn S) C2) N) S3) (B2 S)) (P S3))) (= W ((while B2) C2))) (and (P T2) (not (B2 T2)))))) (forall ((A product_prod_nat_nat) (A2 set_Pr1986765409at_nat)) (=> ((member701585322at_nat A) A2) (= ((insert271595217at_nat A) A2) A2))) (forall ((X2 nat)) ((total_on_nat ((insert_nat X2) bot_bot_set_nat)) ((insert271595217at_nat ((product_Pair_nat_nat X2) X2)) bot_bo2130386637at_nat))) (forall ((A2 set_state) (R set_Pr795498619_state)) (=> (forall ((X3 state) (Y2 state)) (=> ((member_state X3) A2) (=> ((member_state Y2) A2) (=> (not (= X3 Y2)) (or ((member1389040324_state ((produc64584659_state X3) Y2)) R) ((member1389040324_state ((produc64584659_state Y2) X3)) R)))))) ((total_on_state A2) R))) (forall ((A2 set_Pr1986765409at_nat) (R set_Pr1490359111at_nat) (A product_prod_nat_nat)) (=> ((refl_o1619599232at_nat A2) R) (=> ((member701585322at_nat A) A2) ((member2027625872at_nat ((produc1168807639at_nat A) A)) R)))) (forall ((X2 product_prod_nat_nat) (A2 set_Pr1986765409at_nat) (B set_Pr1986765409at_nat)) (let ((_let_1 (insert271595217at_nat X2))) (let ((_let_2 (member701585322at_nat X2))) (=> (not (_let_2 A2)) (=> (not (_let_2 B)) (= (= (_let_1 A2) (_let_1 B)) (= A2 B))))))) (forall ((F (-> nat nat Bool)) (G (-> product_prod_nat_nat Bool))) (=> (forall ((X3 nat) (Y2 nat)) (= ((F X3) Y2) (G ((product_Pair_nat_nat X3) Y2)))) (= (produc949581770_nat_o F) G))) (forall ((R2 set_Pr795498619_state) (X2 state) (Q set_state)) (=> (wf_state R2) (=> ((member_state X2) Q) (not (forall ((Z state)) (=> ((member_state Z) Q) (not (forall ((Y4 state)) (=> ((member1389040324_state ((produc64584659_state Y4) Z)) R2) (not ((member_state Y4) Q))))))))))) (forall ((X21 com) (X222 com) (X41 (-> state Bool)) (X42 com)) (not (= ((semi X21) X222) ((while X41) X42)))) (forall ((S0 state) (C1 com) (N nat) (S12 state) (C22 com) (S22 state)) (let ((_let_1 (execn S0))) (=> (((_let_1 C1) N) S12) (=> ((((execn S12) C22) N) S22) (((_let_1 ((semi C1) C22)) N) S22))))) (forall ((P (-> product_prod_nat_nat Bool)) (A product_prod_nat_nat)) (let ((_let_1 (P A))) (and (=> _let_1 (= (collec7649004at_nat (lambda ((X product_prod_nat_nat)) (and (P X) (= X A)))) ((insert271595217at_nat A) bot_bo2130386637at_nat))) (=> (not _let_1) (= (collec7649004at_nat (lambda ((X product_prod_nat_nat)) (and (= X A) (P X)))) bot_bo2130386637at_nat))))) (forall ((P3 product_prod_nat_nat) (Z5 produc1115495963_state) (C2 (-> nat nat set_Pr795498619_state))) (=> (forall ((A6 nat) (B6 nat)) (=> (= P3 ((product_Pair_nat_nat A6) B6)) ((member1389040324_state Z5) ((C2 A6) B6)))) ((member1389040324_state Z5) ((produc1654445_state C2) P3)))) _let_6 (forall ((F (-> com (-> a state Bool) Bool)) (A com) (B2 (-> a state Bool))) (=> ((F A) B2) ((produc281270436te_o_o F) ((produc1948644831tate_o A) B2)))) (forall ((P3 produc1115495963_state) (C2 (-> state state Bool))) (=> (forall ((A6 state) (B6 state)) (=> (= P3 ((produc64584659_state A6) B6)) ((C2 A6) B6))) ((produc789892016tate_o C2) P3))) ((order_178668240_state bot_bo1625160935_state) bot_bo1331673139_state) (forall ((A2 set_Pr1986765409at_nat) (R set_Pr1490359111at_nat) (X2 product_prod_nat_nat) (Y3 product_prod_nat_nat)) (=> ((refl_o1619599232at_nat A2) R) (=> ((member2027625872at_nat ((produc1168807639at_nat X2) Y3)) R) ((member701585322at_nat Y3) A2)))) (forall ((R set_Pr795498619_state) (P (-> state Bool)) (A state)) (=> (wf_state R) (=> (forall ((X3 state)) (=> (forall ((Y4 state)) (=> ((member1389040324_state ((produc64584659_state Y4) X3)) R) (P Y4))) (P X3))) (P A)))) (irrefl_nat less_than) (= is_sin1547905295tate_o (lambda ((A5 set_Pr1590995257tate_o)) (= A5 ((insert2053719859tate_o (the_el1569055182tate_o A5)) bot_bo170732493tate_o)))) (forall ((X2 produc1115495963_state)) (= (the_el1967402896_state ((insert311944171_state X2) bot_bo1625160935_state)) X2)) (forall ((F (-> state state Bool)) (G (-> produc1115495963_state Bool))) (=> (forall ((X3 state) (Y2 state)) (= ((F X3) Y2) (G ((produc64584659_state X3) Y2)))) (= (produc789892016tate_o F) G))) (forall ((A produc696469763tate_o) (P (-> produc696469763tate_o Bool))) (= ((insert2053719859tate_o A) (collec1499596504tate_o P)) (collec1499596504tate_o (lambda ((U produc696469763tate_o)) (=> (not (= U A)) (P U)))))) _let_5 (forall ((A2 set_Pr1986765409at_nat)) (= (exists ((X product_prod_nat_nat)) ((member701585322at_nat X) A2)) (not (= A2 bot_bo2130386637at_nat)))) (forall ((B2 (-> state Bool)) (C2 com)) (wf_state (collec496201222_state (produc789892016tate_o (lambda ((T3 state) (S4 state)) (and (((exec S4) C2) T3) (B2 S4) ((termi ((while B2) C2)) S4))))))) (forall ((X2 produc696469763tate_o) (A2 set_Pr1590995257tate_o)) (let ((_let_1 (insert2053719859tate_o X2))) (let ((_let_2 (_let_1 A2))) (= (_let_1 _let_2) _let_2)))) (forall ((X2 produc1115495963_state) (A2 set_Pr795498619_state)) (let ((_let_1 (insert311944171_state X2))) (let ((_let_2 (_let_1 A2))) (= (_let_1 _let_2) _let_2)))) (forall ((A produc696469763tate_o) (B2 produc696469763tate_o) (A2 set_Pr1590995257tate_o)) (let ((_let_1 (member1838112666tate_o A))) (=> (_let_1 ((insert2053719859tate_o B2) A2)) (=> (not (= A B2)) (_let_1 A2))))) (forall ((B2 (-> state Bool)) (S2 state) (C2 com) (N nat) (T2 state) (U2 state)) (let ((_let_1 ((while B2) C2))) (let ((_let_2 (execn S2))) (=> (B2 S2) (=> (((_let_2 C2) N) T2) (=> ((((execn T2) _let_1) N) U2) (((_let_2 _let_1) N) U2))))))) (forall ((R set_Pr1986765409at_nat) (A nat)) (=> (wf_nat R) (not ((member701585322at_nat ((product_Pair_nat_nat A) A)) R)))) (forall ((A product_prod_nat_nat) (B set_Pr1986765409at_nat) (B2 product_prod_nat_nat)) (let ((_let_1 (member701585322at_nat A))) (=> (=> (not (_let_1 B)) (= A B2)) (_let_1 ((insert271595217at_nat B2) B))))) (forall ((R set_Pr1986765409at_nat) (A nat) (X2 nat)) (=> (wf_nat R) (=> ((member701585322at_nat ((product_Pair_nat_nat A) X2)) R) (not ((member701585322at_nat ((product_Pair_nat_nat X2) A)) R))))) (= is_sin1352690165at_nat (lambda ((A5 set_Pr1986765409at_nat)) (exists ((X product_prod_nat_nat)) (= A5 ((insert271595217at_nat X) bot_bo2130386637at_nat))))) _let_4 (forall ((S2 state)) (=> ((termi body) S2) ((termi call) S2))) (forall ((F (-> product_prod_nat_nat Bool))) (= (produc949581770_nat_o (lambda ((X nat) (Y5 nat)) (F ((product_Pair_nat_nat X) Y5)))) F)) (forall ((A produc1115495963_state) (B set_Pr795498619_state)) ((member1389040324_state A) ((insert311944171_state A) B))) (= is_sin1132515087_state (lambda ((A5 set_Pr795498619_state)) (exists ((X produc1115495963_state)) (= A5 ((insert311944171_state X) bot_bo1625160935_state))))) (forall ((A produc1115495963_state) (P (-> produc1115495963_state Bool))) (= ((member1389040324_state A) (collec496201222_state P)) (P A))) (wf_nat less_than) (forall ((A2 set_Pr1590995257tate_o)) (=> (not (= A2 bot_bo170732493tate_o)) (=> (forall ((X3 produc696469763tate_o) (Y2 produc696469763tate_o)) (=> ((member1838112666tate_o X3) A2) (=> ((member1838112666tate_o Y2) A2) (= X3 Y2)))) (is_sin1547905295tate_o A2)))) (forall ((P (-> produc204914599tate_o Bool)) (P3 produc204914599tate_o)) (=> (forall ((A6 com) (B6 (-> a state Bool))) (P ((produc1948644831tate_o A6) B6))) (P P3))) (forall ((A2 set_Pr795498619_state) (R set_Pr778812871_state) (A produc1115495963_state) (B2 produc1115495963_state)) (=> ((refl_o1438232218_state A2) R) (=> ((member768948240_state ((produc1964772951_state A) B2)) R) (and ((member1389040324_state B2) A2) ((member1389040324_state A) A2))))) (forall ((Y3 produc1115495963_state)) (not (forall ((A6 state) (B6 state)) (not (= Y3 ((produc64584659_state A6) B6)))))) (forall ((C set_Pr1590995257tate_o) (P2 (-> a state Bool)) (C2 com) (Q2 (-> a state Bool)) (P (-> a state Bool)) (Q (-> a state Bool))) (let ((_let_1 (pHoare382919414oare_a C))) (=> (((_let_1 P2) C2) Q2) (=> (and (forall ((S state) (T state)) (=> (forall ((Z2 a)) (=> ((P2 Z2) S) ((Q2 Z2) T))) (forall ((Z a)) (=> ((P Z) S) ((Q Z) T))))) (forall ((S state)) (=> (exists ((Z a)) ((P Z) S)) (exists ((Z2 a)) ((P2 Z2) S))))) (((_let_1 P) C2) Q))))) (forall ((X21 com) (X222 com)) (not (= ((semi X21) X222) call))) _let_3 (forall ((A2 set_Pr1986765409at_nat)) (= (collec7649004at_nat (lambda ((X product_prod_nat_nat)) ((member701585322at_nat X) A2))) A2)) (forall ((A2 set_state) (R set_Pr795498619_state) (A state) (B2 state)) (=> ((refl_on_state A2) R) (=> ((member1389040324_state ((produc64584659_state A) B2)) R) (and ((member_state B2) A2) ((member_state A) A2))))) _let_2 _let_1 ((refl_on_nat bot_bot_set_nat) bot_bo2130386637at_nat) (forall ((B2 (-> state Bool)) (S2 state) (C2 com)) (=> (not (B2 S2)) ((termi ((while B2) C2)) S2))) (forall ((R set_Pr795498619_state) (P (-> a state Bool)) (Q (-> a state Bool))) (=> (wf_state R) (=> (forall ((S3 state)) ((((pHoare382919414oare_a ((insert2053719859tate_o ((produc33908149tate_o (lambda ((Z4 a) (S4 state)) (and ((member1389040324_state ((produc64584659_state S4) S3)) R) ((P Z4) S4)))) ((produc1948644831tate_o call) Q))) bot_bo170732493tate_o)) (lambda ((Z4 a) (S4 state)) (and ((P Z4) S4) (= S4 S3)))) body) Q)) ((((pHoare382919414oare_a bot_bo170732493tate_o) P) call) Q)))) (forall ((R set_Pr795498619_state) (A state) (X2 state)) (=> (wf_state R) (=> ((member1389040324_state ((produc64584659_state A) X2)) R) (not ((member1389040324_state ((produc64584659_state X2) A)) R))))) (forall ((A2 set_Pr1986765409at_nat)) (=> (not (= A2 bot_bo2130386637at_nat)) (=> (forall ((X3 product_prod_nat_nat) (Y2 product_prod_nat_nat)) (=> ((member701585322at_nat X3) A2) (=> ((member701585322at_nat Y2) A2) (= X3 Y2)))) (is_sin1352690165at_nat A2)))) (forall ((B2 (-> state Bool)) (S2 state) (C2 com)) (=> (not (B2 S2)) (((exec S2) ((while B2) C2)) S2))) (trans_nat less_than) (forall ((P (-> produc696469763tate_o Bool))) (= (= bot_bo170732493tate_o (collec1499596504tate_o P)) (forall ((X produc696469763tate_o)) (not (P X))))) (forall ((X21 com) (X222 com) (Y21 com) (Y222 com)) (= (= ((semi X21) X222) ((semi Y21) Y222)) (and (= X222 Y222) (= X21 Y21)))) (forall ((S2 state) (B2 (-> state Bool)) (C2 com) (N nat) (T2 state) (P (-> state Bool))) (=> ((((execn S2) ((while B2) C2)) N) T2) (=> (P S2) (=> (forall ((S state) (S3 state)) (=> (P S) (=> (B2 S) (=> ((((execn S) C2) N) S3) (P S3))))) (and (not (B2 T2)) (P T2)))))) (forall ((P (-> a state Bool)) (Q (-> a state Bool))) (=> ((((hoare_a ((insert2053719859tate_o ((produc33908149tate_o P) ((produc1948644831tate_o call) Q))) bot_bo170732493tate_o)) P) body) Q) ((((hoare_a bot_bo170732493tate_o) P) call) Q))) (not false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.87/1.07 ) 0.87/1.07 % SZS output end Proof for theBenchmark 0.87/1.07 EOF