0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : do_cvc5 %s %d
0.15/0.35	% Computer   : n006.cluster.edu
0.15/0.35	% Model      : x86_64 x86_64
0.15/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.15/0.35	% Memory     : 8042.1875MB
0.15/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.15/0.35	% CPULimit   : 1200
0.15/0.35	% WCLimit    : 120
0.15/0.35	% DateTime   : Tue Jul 13 15:04:10 EDT 2021
0.15/0.35	% CPUTime    : 
0.22/0.49	%----THF division
0.22/0.49	------- cvc5-thf casc 28 : /export/starexec/sandbox/benchmark/theBenchmark.p at 120...
0.22/0.49	--- Run --ho-elim --full-saturate-quant at 10...
10.42/10.58	--- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
10.44/10.77	% SZS status Theorem for theBenchmark
10.61/10.78	% SZS output start Proof for theBenchmark
10.61/10.78	(proof
10.61/10.78	(let ((_let_1 (not (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (((mimplies (god X)) ((essence god) X)) __flatten_var_0))))))) (let ((_let_2 (mvalid (mforall_indset (lambda ((Phi (-> mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (positive Phi))) (((mimplies _let_1) (mbox _let_1)) __flatten_var_0))))))) (let ((_let_3 (mvalid (mforall_indset (lambda ((Phi (-> mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mequiv (positive (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mnot (Phi X)) __flatten_var_0)))) (mnot (positive Phi))) __flatten_var_0)))))) (let ((_let_4 (= necessary_existence (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mforall_indset (lambda ((Phi (-> mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mimplies ((essence Phi) X)) (mbox (mexists_ind (lambda ((Y mu) (__flatten_var_0 $$unsorted)) ((Phi Y) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0))))) (let ((_let_5 (= essence (lambda ((Phi (-> mu $$unsorted Bool)) (X mu) (__flatten_var_0 $$unsorted)) (((mand (Phi X)) (mforall_indset (lambda ((Psi (-> mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mimplies (Psi X)) (mbox (mforall_ind (lambda ((Y mu) (__flatten_var_0 $$unsorted)) (((mimplies (Phi Y)) (Psi Y)) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_6 (= god (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mforall_indset (lambda ((Phi (-> mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mimplies (positive Phi)) (Phi X)) __flatten_var_0))) __flatten_var_0))))) (let ((_let_7 (= minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (Phi W))))))) (let ((_let_8 (= mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (Phi W)))))) (let ((_let_9 (= mdia (mdia_generic rel)))) (let ((_let_10 (= mbox (mbox_generic rel)))) (let ((_let_11 (= mdia_generic (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (exists ((V $$unsorted)) (and ((R W) V) (Phi V))))))) (let ((_let_12 (= mbox_generic (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not ((R W) V)) (Phi V))))))) (let ((_let_13 (= mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (exists ((P (-> $$unsorted Bool))) ((Phi P) W)))))) (let ((_let_14 (= mexists_indset (lambda ((Phi (-> (-> mu $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (exists ((X (-> mu $$unsorted Bool))) ((Phi X) W)))))) (let ((_let_15 (= mexists_ind (lambda ((Phi (-> mu $$unsorted Bool)) (W $$unsorted)) (exists ((X mu)) ((Phi X) W)))))) (let ((_let_16 (= mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) ((Phi P) W)))))) (let ((_let_17 (= mforall_indset (lambda ((Phi (-> (-> mu $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((X (-> mu $$unsorted Bool))) ((Phi X) W)))))) (let ((_let_18 (= mforall_ind (lambda ((Phi (-> mu $$unsorted Bool)) (W $$unsorted)) (forall ((X mu)) ((Phi X) W)))))) (let ((_let_19 (= mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (let ((_let_1 (Psi W))) (let ((_let_2 (Phi W))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))) (let ((_let_20 (= mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (= (Phi W) (Psi W)))))) (let ((_let_21 (= mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (=> (Psi W) (Phi W)))))) (let ((_let_22 (= mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (=> (Phi W) (Psi W)))))) (let ((_let_23 (= mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (and (Phi W) (Psi W)))))) (let ((_let_24 (= mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (Phi W) (Psi W)))))) (let ((_let_25 (= mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (Phi W)))))) (let ((_let_26 (= mfalse (lambda ((W $$unsorted)) false)))) (let ((_let_27 (= mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_28 (= meq_ind (lambda ((X mu) (Y mu) (W $$unsorted)) (= X Y))))) (let ((_let_29 (forall ((BOUND_VARIABLE_2168 $$unsorted) (BOUND_VARIABLE_2893 |u_(-> mu $$unsorted Bool)|) (BOUND_VARIABLE_2173 $$unsorted)) (let ((_let_1 (ho_7 k_6 BOUND_VARIABLE_2893))) (or (not (ho_5 _let_1 BOUND_VARIABLE_2168)) (not (ho_5 (ho_10 k_9 BOUND_VARIABLE_2168) BOUND_VARIABLE_2173)) (ho_5 _let_1 BOUND_VARIABLE_2173)))))) (let ((_let_30 (ho_7 k_6 skv_18))) (let ((_let_31 (ho_5 _let_30 skv_16))) (let ((_let_32 (ho_5 (ho_10 k_9 skv_14) skv_16))) (let ((_let_33 (not _let_32))) (let ((_let_34 (ho_5 _let_30 skv_14))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_31))) (let ((_let_37 (ASSUME |:args| (_let_28)))) (let ((_let_38 (EQ_RESOLVE (ASSUME |:args| (_let_27)) (MACRO_SR_EQ_INTRO |:args| (_let_27 7 12))))) (let ((_let_39 (EQ_RESOLVE (ASSUME |:args| (_let_26)) (MACRO_SR_EQ_INTRO |:args| (_let_26 7 12))))) (let ((_let_40 (ASSUME |:args| (_let_25)))) (let ((_let_41 (ASSUME |:args| (_let_24)))) (let ((_let_42 (ASSUME |:args| (_let_23)))) (let ((_let_43 (ASSUME |:args| (_let_22)))) (let ((_let_44 (ASSUME |:args| (_let_21)))) (let ((_let_45 (ASSUME |:args| (_let_20)))) (let ((_let_46 (ASSUME |:args| (_let_19)))) (let ((_let_47 (ASSUME |:args| (_let_18)))) (let ((_let_48 (ASSUME |:args| (_let_17)))) (let ((_let_49 (ASSUME |:args| (_let_16)))) (let ((_let_50 (EQ_RESOLVE (ASSUME |:args| (_let_15)) (MACRO_SR_EQ_INTRO |:args| (_let_15 7 12))))) (let ((_let_51 (EQ_RESOLVE (ASSUME |:args| (_let_14)) (MACRO_SR_EQ_INTRO |:args| (_let_14 7 12))))) (let ((_let_52 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (MACRO_SR_EQ_INTRO |:args| (_let_13 7 12))))) (let ((_let_53 (ASSUME |:args| (_let_12)))) (let ((_let_54 (EQ_RESOLVE (ASSUME |:args| (_let_11)) (MACRO_SR_EQ_INTRO |:args| (_let_11 7 12))))) (let ((_let_55 (EQ_RESOLVE (ASSUME |:args| (_let_10)) (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 |:args| (_let_10 7 12))))) (let ((_let_56 (EQ_RESOLVE (ASSUME |:args| (_let_9)) (MACRO_SR_EQ_INTRO _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 |:args| (_let_9 7 12))))) (let ((_let_57 (ASSUME |:args| (_let_8)))) (let ((_let_58 (ASSUME |:args| (_let_7)))) (let ((_let_59 (EQ_RESOLVE (ASSUME |:args| (_let_6)) (MACRO_SR_EQ_INTRO _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 |:args| (_let_6 7 12))))) (let ((_let_60 (EQ_RESOLVE (ASSUME |:args| (_let_5)) (MACRO_SR_EQ_INTRO _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 |:args| (_let_5 7 12))))) (let ((_let_61 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (MACRO_SR_EQ_INTRO _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 |:args| (_let_4 7 12))))) (let ((_let_62 (EQ_RESOLVE (ASSUME |:args| (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 |:args| (_let_2 7 12)) (PREPROCESS |:args| ((= (forall ((BOUND_VARIABLE_2168 $$unsorted) (BOUND_VARIABLE_2172 (-> mu $$unsorted Bool)) (BOUND_VARIABLE_2173 $$unsorted)) (let ((_let_1 (positive BOUND_VARIABLE_2172))) (or (not (_let_1 BOUND_VARIABLE_2168)) (not ((rel BOUND_VARIABLE_2168) BOUND_VARIABLE_2173)) (_let_1 BOUND_VARIABLE_2173)))) _let_29))))))) (let ((_let_63 (not _let_36))) (let ((_let_64 (ho_13 k_12 skv_18))) (let ((_let_65 (ho_5 (ho_7 k_6 _let_64) skv_14))) (let ((_let_66 (= _let_65 _let_35))) (let ((_let_67 (forall ((BOUND_VARIABLE_1625 $$unsorted) (BOUND_VARIABLE_2852 |u_(-> mu $$unsorted Bool)|)) (= (ho_5 (ho_7 k_6 (ho_13 k_12 BOUND_VARIABLE_2852)) BOUND_VARIABLE_1625) (not (ho_5 (ho_7 k_6 BOUND_VARIABLE_2852) BOUND_VARIABLE_1625)))))) (let ((_let_68 (forall ((BOUND_VARIABLE_1625 $$unsorted) (BOUND_VARIABLE_1629 (-> mu $$unsorted Bool))) (= ((positive (ll_1 BOUND_VARIABLE_1629)) BOUND_VARIABLE_1625) (not ((positive BOUND_VARIABLE_1629) BOUND_VARIABLE_1625)))))) (let ((_let_69 (EQ_RESOLVE (ASSUME |:args| (_let_3)) (TRANS (MACRO_SR_EQ_INTRO _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 |:args| (_let_3 7 12)) (PREPROCESS |:args| ((= (forall ((BOUND_VARIABLE_1625 $$unsorted) (BOUND_VARIABLE_1629 (-> mu $$unsorted Bool))) (= ((positive (lambda ((BOUND_VARIABLE_1633 mu) (BOUND_VARIABLE_1634 $$unsorted)) (not ((BOUND_VARIABLE_1629 BOUND_VARIABLE_1633) BOUND_VARIABLE_1634)))) BOUND_VARIABLE_1625) (not ((positive BOUND_VARIABLE_1629) BOUND_VARIABLE_1625)))) _let_68))) (PREPROCESS |:args| ((= _let_68 _let_67))))))) (let ((_let_70 (ho_5 (ho_4 _let_64 skv_15) skv_14))) (let ((_let_71 (not _let_65))) (let ((_let_72 (or _let_71 _let_70))) (let ((_let_73 (forall ((BOUND_VARIABLE_2933 |u_(-> mu $$unsorted Bool)|)) (or (not (ho_5 (ho_7 k_6 BOUND_VARIABLE_2933) skv_14)) (ho_5 (ho_4 BOUND_VARIABLE_2933 skv_15) skv_14))))) (let ((_let_74 (ho_5 (ho_4 skv_18 skv_17) skv_16))) (let ((_let_75 (forall ((BOUND_VARIABLE_2908 |u_(-> mu $$unsorted Bool)|)) (or (not (ho_5 (ho_7 k_6 BOUND_VARIABLE_2908) skv_16)) (ho_5 (ho_4 BOUND_VARIABLE_2908 skv_17) skv_16))))) (let ((_let_76 (not _let_75))) (let ((_let_77 (ho_5 (ho_4 skv_18 skv_15) skv_14))) (let ((_let_78 (not _let_77))) (let ((_let_79 (or _let_78 _let_33 _let_76 _let_74))) (let ((_let_80 (or (not (ho_5 (ho_7 k_6 skv_19) skv_14)) (ho_5 (ho_4 skv_19 skv_15) skv_14)))) (let ((_let_81 (and _let_80 _let_79))) (let ((_let_82 (not _let_73))) (let ((_let_83 (or _let_82 _let_81))) (let ((_let_84 (forall ((BOUND_VARIABLE_2582 $$unsorted) (BOUND_VARIABLE_2586 mu) (BOUND_VARIABLE_2587 $$unsorted) (BOUND_VARIABLE_2588 mu) (BOUND_VARIABLE_2905 |u_(-> mu $$unsorted Bool)|) (BOUND_VARIABLE_2925 |u_(-> mu $$unsorted Bool)|)) (or (not (forall ((BOUND_VARIABLE_2933 |u_(-> mu $$unsorted Bool)|)) (or (not (ho_5 (ho_7 k_6 BOUND_VARIABLE_2933) BOUND_VARIABLE_2582)) (ho_5 (ho_4 BOUND_VARIABLE_2933 BOUND_VARIABLE_2586) BOUND_VARIABLE_2582)))) (and (or (not (ho_5 (ho_7 k_6 BOUND_VARIABLE_2925) BOUND_VARIABLE_2582)) (ho_5 (ho_4 BOUND_VARIABLE_2925 BOUND_VARIABLE_2586) BOUND_VARIABLE_2582)) (or (not (ho_5 (ho_4 BOUND_VARIABLE_2905 BOUND_VARIABLE_2586) BOUND_VARIABLE_2582)) (not (ho_5 (ho_10 k_9 BOUND_VARIABLE_2582) BOUND_VARIABLE_2587)) (not (forall ((BOUND_VARIABLE_2908 |u_(-> mu $$unsorted Bool)|)) (or (not (ho_5 (ho_7 k_6 BOUND_VARIABLE_2908) BOUND_VARIABLE_2587)) (ho_5 (ho_4 BOUND_VARIABLE_2908 BOUND_VARIABLE_2588) BOUND_VARIABLE_2587)))) (ho_5 (ho_4 BOUND_VARIABLE_2905 BOUND_VARIABLE_2588) BOUND_VARIABLE_2587))))))) (let ((_let_85 (not _let_83))) (let ((_let_86 (not _let_84))) (let ((_let_87 (EQ_RESOLVE (ASSUME |:args| (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 |:args| (_let_1 7 12)) (PREPROCESS |:args| ((= (not (forall ((BOUND_VARIABLE_2582 $$unsorted) (BOUND_VARIABLE_2586 mu) (BOUND_VARIABLE_2587 $$unsorted) (BOUND_VARIABLE_2588 mu) (BOUND_VARIABLE_2589 (-> mu $$unsorted Bool)) (BOUND_VARIABLE_2590 (-> mu $$unsorted Bool))) (or (not (forall ((BOUND_VARIABLE_2617 (-> mu $$unsorted Bool))) (or (not ((positive BOUND_VARIABLE_2617) BOUND_VARIABLE_2582)) ((BOUND_VARIABLE_2617 BOUND_VARIABLE_2586) BOUND_VARIABLE_2582)))) (and (or (not ((positive BOUND_VARIABLE_2590) BOUND_VARIABLE_2582)) ((BOUND_VARIABLE_2590 BOUND_VARIABLE_2586) BOUND_VARIABLE_2582)) (or (not ((BOUND_VARIABLE_2589 BOUND_VARIABLE_2586) BOUND_VARIABLE_2582)) (not ((rel BOUND_VARIABLE_2582) BOUND_VARIABLE_2587)) (not (forall ((BOUND_VARIABLE_2593 (-> mu $$unsorted Bool))) (or (not ((positive BOUND_VARIABLE_2593) BOUND_VARIABLE_2587)) ((BOUND_VARIABLE_2593 BOUND_VARIABLE_2588) BOUND_VARIABLE_2587)))) ((BOUND_VARIABLE_2589 BOUND_VARIABLE_2588) BOUND_VARIABLE_2587)))))) _let_86))))))) (let ((_let_88 (20))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_87) |:args| (_let_86))) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_86) _let_84))) (REFL |:args| (_let_85)) |:args| _let_88)) _let_87 |:args| (_let_85 true _let_84)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_83 0)) (CONG (REFL |:args| (_let_83)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_82) _let_73))) |:args| _let_88)) |:args| ((or _let_73 _let_83))) _let_89 |:args| (_let_73 true _let_83)))) (let ((_let_91 (_let_73))) (let ((_let_92 (ASSUME |:args| _let_91))) (let ((_let_93 (= _let_70 _let_78))) (let ((_let_94 (not _let_70))) (let ((_let_95 (forall ((BOUND_VARIABLE_2831 |u_(-> mu $$unsorted Bool)|) (BOUND_VARIABLE_2714 mu) (BOUND_VARIABLE_2715 $$unsorted)) (= (ho_5 (ho_4 (ho_13 k_12 BOUND_VARIABLE_2831) BOUND_VARIABLE_2714) BOUND_VARIABLE_2715) (not (ho_5 (ho_4 BOUND_VARIABLE_2831 BOUND_VARIABLE_2714) BOUND_VARIABLE_2715)))))) (let ((_let_96 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> mu $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i mu)) (not (forall ((v |u_(-> mu $$unsorted Bool)|)) (not (forall ((ii mu)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> mu $$unsorted Bool)|) (y |u_(-> mu $$unsorted Bool)|)) (or (not (forall ((z mu)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> _u_(-> mu $$unsorted Bool)_ mu $$unsorted Bool)|) (e |u_(-> mu $$unsorted Bool)|) (i |u_(-> mu $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> mu $$unsorted Bool)_ mu $$unsorted Bool)|)) (not (forall ((ii |u_(-> mu $$unsorted Bool)|)) (= (ho_13 v ii) (ite (= i ii) e (ho_13 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> _u_(-> mu $$unsorted Bool)_ mu $$unsorted Bool)|) (y |u_(-> _u_(-> mu $$unsorted Bool)_ mu $$unsorted Bool)|)) (or (not (forall ((z |u_(-> mu $$unsorted Bool)|)) (= (ho_13 x z) (ho_13 y z)))) (= x y))))) (let ((_let_102 (forall ((u |u_(-> _u_(-> mu $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i |u_(-> mu $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> mu $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> mu $$unsorted Bool)|)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> _u_(-> mu $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> mu $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> mu $$unsorted Bool)|)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_10 v ii) (ite (= i ii) e (ho_10 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_10 x z) (ho_10 y z)))) (= x y))))) (let ((_let_106 (forall ((BOUND_VARIABLE_2745 mu) (BOUND_VARIABLE_2746 $$unsorted)) (= (ho_5 (ho_4 k_8 BOUND_VARIABLE_2745) BOUND_VARIABLE_2746) (forall ((BOUND_VARIABLE_2761 |u_(-> mu $$unsorted Bool)|)) (or (not (ho_5 (ho_7 k_6 BOUND_VARIABLE_2761) BOUND_VARIABLE_2746)) (ho_5 (ho_4 BOUND_VARIABLE_2761 BOUND_VARIABLE_2745) BOUND_VARIABLE_2746))))))) (let ((_let_107 (forall ((BOUND_VARIABLE_2723 mu) (BOUND_VARIABLE_2724 $$unsorted)) (= (ho_5 (ho_4 k_11 BOUND_VARIABLE_2723) BOUND_VARIABLE_2724) (forall ((BOUND_VARIABLE_2789 |u_(-> mu $$unsorted Bool)|) (BOUND_VARIABLE_1470 $$unsorted)) (or (not (ho_5 (ho_4 BOUND_VARIABLE_2789 BOUND_VARIABLE_2723) BOUND_VARIABLE_2724)) (not (forall ((BOUND_VARIABLE_2803 |u_(-> mu $$unsorted Bool)|) (BOUND_VARIABLE_1482 mu) (BOUND_VARIABLE_1483 $$unsorted)) (or (not (ho_5 (ho_4 BOUND_VARIABLE_2803 BOUND_VARIABLE_2723) BOUND_VARIABLE_2724)) (not (ho_5 (ho_10 k_9 BOUND_VARIABLE_2724) BOUND_VARIABLE_1483)) (not (ho_5 (ho_4 BOUND_VARIABLE_2789 BOUND_VARIABLE_1482) BOUND_VARIABLE_1483)) (ho_5 (ho_4 BOUND_VARIABLE_2803 BOUND_VARIABLE_1482) BOUND_VARIABLE_1483)))) (not (ho_5 (ho_10 k_9 BOUND_VARIABLE_2724) BOUND_VARIABLE_1470)) (not (forall ((BOUND_VARIABLE_1471 mu)) (not (ho_5 (ho_4 BOUND_VARIABLE_2789 BOUND_VARIABLE_1471) BOUND_VARIABLE_1470)))))))))) (let ((_let_108 (and (forall ((BOUND_VARIABLE_2713 (-> mu $$unsorted Bool)) (BOUND_VARIABLE_2714 mu) (BOUND_VARIABLE_2715 $$unsorted)) (= (ll_1 BOUND_VARIABLE_2713 BOUND_VARIABLE_2714 BOUND_VARIABLE_2715) (not ((BOUND_VARIABLE_2713 BOUND_VARIABLE_2714) BOUND_VARIABLE_2715)))) (forall ((BOUND_VARIABLE_2723 mu) (BOUND_VARIABLE_2724 $$unsorted)) (= (ll_2 BOUND_VARIABLE_2723 BOUND_VARIABLE_2724) (forall ((BOUND_VARIABLE_1469 (-> mu $$unsorted Bool)) (BOUND_VARIABLE_1470 $$unsorted)) (or (not ((BOUND_VARIABLE_1469 BOUND_VARIABLE_2723) BOUND_VARIABLE_2724)) (not (forall ((BOUND_VARIABLE_1481 (-> mu $$unsorted Bool)) (BOUND_VARIABLE_1482 mu) (BOUND_VARIABLE_1483 $$unsorted)) (or (not ((BOUND_VARIABLE_1481 BOUND_VARIABLE_2723) BOUND_VARIABLE_2724)) (not ((rel BOUND_VARIABLE_2724) BOUND_VARIABLE_1483)) (not ((BOUND_VARIABLE_1469 BOUND_VARIABLE_1482) BOUND_VARIABLE_1483)) ((BOUND_VARIABLE_1481 BOUND_VARIABLE_1482) BOUND_VARIABLE_1483)))) (not ((rel BOUND_VARIABLE_2724) BOUND_VARIABLE_1470)) (not (forall ((BOUND_VARIABLE_1471 mu)) (not ((BOUND_VARIABLE_1469 BOUND_VARIABLE_1471) BOUND_VARIABLE_1470)))))))) (forall ((BOUND_VARIABLE_2745 mu) (BOUND_VARIABLE_2746 $$unsorted)) (= (ll_3 BOUND_VARIABLE_2745 BOUND_VARIABLE_2746) (forall ((BOUND_VARIABLE_864 (-> mu $$unsorted Bool))) (or (not ((positive BOUND_VARIABLE_864) BOUND_VARIABLE_2746)) ((BOUND_VARIABLE_864 BOUND_VARIABLE_2745) BOUND_VARIABLE_2746)))))))) (let ((_let_109 (_let_95))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG |:args| (_let_81)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_83 1)) _let_89 |:args| ((not _let_81) true _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 |:args| (skv_19)) |:args| _let_91)) _let_90 |:args| (_let_80 false _let_73)) |:args| ((not _let_79) true _let_81 false _let_80)))) (let ((_let_111 (REFL |:args| (_let_79)))) (let ((_let_112 (not _let_66))) (let ((_let_113 (not _let_31))) (let ((_let_114 (or _let_113 _let_74))) (let ((_let_115 (_let_75))) (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 |:args| (skv_14 skv_18 skv_16)) |:args| (_let_29))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_36)) |:args| ((or _let_33 _let_31 _let_35 _let_63))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_79 1)) (CONG _let_111 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_33) _let_32))) |:args| _let_88)) |:args| ((or _let_32 _let_79))) _let_110 |:args| (_let_32 true _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_114)) |:args| ((or _let_74 _let_113 (not _let_114)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_79 3)) _let_110 |:args| ((not _let_74) true _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_115) |:args| (skv_18)) |:args| _let_115)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_79 2)) (CONG _let_111 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_76) _let_75))) |:args| _let_88)) |:args| ((or _let_75 _let_79))) _let_110 |:args| (_let_75 true _let_79)) |:args| (_let_114 false _let_75)) |:args| (_let_113 true _let_74 false _let_114)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 |:args| (_let_66)) (CONG (REFL |:args| (_let_112)) (REFL |:args| (_let_65)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_35) _let_34))) |:args| _let_88)) |:args| ((or _let_34 _let_65 _let_112))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_72)) |:args| ((or _let_70 _let_71 (not _let_72)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 |:args| (_let_93)) |:args| ((or _let_78 _let_94 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_79 0)) (CONG _let_111 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_78) _let_77))) |:args| _let_88)) |:args| ((or _let_77 _let_79))) _let_110 |:args| (_let_77 true _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_109) |:args| (skv_18 skv_15 skv_14)) |:args| _let_109)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (PREPROCESS_LEMMA |:args| (_let_108)) (PREPROCESS |:args| ((= _let_108 (and _let_95 _let_107 _let_106))))) (PREPROCESS |:args| ((and _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96)))) |:args| ((and _let_95 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96))) |:args| (0)) |:args| (_let_93 false _let_95)) |:args| (_let_94 false _let_77 false _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 |:args| (_let_64)) |:args| _let_91)) _let_90 |:args| (_let_72 false _let_73)) |:args| (_let_71 true _let_70 false _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 |:args| (skv_14 skv_18)) |:args| (_let_67))) _let_69 |:args| (_let_66 false _let_67)) |:args| (_let_34 true _let_65 false _let_66)) |:args| (_let_63 false _let_32 true _let_31 false _let_34)) _let_62 |:args| (false true _let_36 false _let_29)) |:args| (_let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 (mvalid (positive necessary_existence)) (mvalid (positive god)) (mvalid (mforall_indset (lambda ((Phi (-> mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mforall_indset (lambda ((Psi (-> mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mimplies ((mand (positive Phi)) (mbox (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (((mimplies (Phi X)) (Psi X)) __flatten_var_0)))))) (positive Psi)) __flatten_var_0))) __flatten_var_0)))) _let_2 _let_1 (not false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
10.61/10.78	)
10.61/10.78	% SZS output end Proof for theBenchmark
10.61/10.78	EOF