0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : do_cvc5 %s %d 0.13/0.34 % Computer : n005.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 02:20:49 EDT 2022 0.13/0.34 % CPUTime : 0.19/0.48 %----Proving TH0 0.95/1.13 ------- cvc5-thf casc j11 : /export/starexec/sandbox/benchmark/theBenchmark.p at /export/starexec/sandbox/benchmark/theBenchmark.p... 0.95/1.13 --- Run --ho-elim --full-saturate-quant at 10... 0.95/1.13 % SZS status Theorem for theBenchmark 0.95/1.13 % SZS output start Proof for theBenchmark 0.95/1.13 (let ((_let_1 (forall ((W mworld)) (@ (@ mrel W) W)))) (let ((_let_2 (not (@ mlocal (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ qmltpeq (@ (@ union B) B)) B)) __flatten_var_0)))))))) (let ((_let_3 (@ mlocal (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ subset B) C))) (@ mbox (@ (@ qmltpeq (@ (@ union B) C)) C)))) __flatten_var_0)))) __flatten_var_0))))))) (let ((_let_4 (@ mlocal (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ subset B) B)) __flatten_var_0))))))) (let ((_let_5 (= mexists_di (lambda ((A (-> $$unsorted mworld Bool)) (W mworld)) (exists ((X $$unsorted)) (and (@ (@ eiw_di X) W) (@ (@ A X) W))))))) (let ((_let_6 (= mforall_di (lambda ((A (-> $$unsorted mworld Bool)) (W mworld)) (forall ((X $$unsorted)) (=> (@ (@ eiw_di X) W) (@ (@ A X) W))))))) (let ((_let_7 (= mdia (lambda ((Phi (-> mworld Bool)) (W mworld)) (exists ((V mworld)) (and (@ (@ mrel W) V) (@ Phi V))))))) (let ((_let_8 (= mbox (lambda ((Phi (-> mworld Bool)) (W mworld)) (forall ((V mworld)) (=> (@ (@ mrel W) V) (@ Phi V))))))) (let ((_let_9 (= mequiv (lambda ((A (-> mworld Bool)) (B (-> mworld Bool)) (W mworld)) (= (@ A W) (@ B W)))))) (let ((_let_10 (= mimplies (lambda ((A (-> mworld Bool)) (B (-> mworld Bool)) (W mworld)) (=> (@ A W) (@ B W)))))) (let ((_let_11 (= mor (lambda ((A (-> mworld Bool)) (B (-> mworld Bool)) (W mworld)) (or (@ A W) (@ B W)))))) (let ((_let_12 (= mand (lambda ((A (-> mworld Bool)) (B (-> mworld Bool)) (W mworld)) (and (@ A W) (@ B W)))))) (let ((_let_13 (= mnot (lambda ((A (-> mworld Bool)) (W mworld)) (not (@ A W)))))) (let ((_let_14 (= mlocal (lambda ((Phi (-> mworld Bool))) (@ Phi mactual))))) (let ((_let_15 (forall ((BOUND_VARIABLE_3882 mworld) (BOUND_VARIABLE_3883 mworld) (BOUND_VARIABLE_3884 $$unsorted)) (or (not (ho_4 (ho_6 k_5 mactual) BOUND_VARIABLE_3882)) (not (ho_4 (ho_3 k_7 BOUND_VARIABLE_3884) BOUND_VARIABLE_3882)) (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_3882) BOUND_VARIABLE_3883)) (ho_4 (ho_3 (ho_2 k_11 BOUND_VARIABLE_3884) BOUND_VARIABLE_3884) BOUND_VARIABLE_3883))))) (let ((_let_16 (ho_4 (ho_3 (ho_2 k_11 skv_15) skv_15) skv_16))) (let ((_let_17 (ho_6 k_5 skv_13))) (let ((_let_18 (ho_4 _let_17 skv_16))) (let ((_let_19 (not _let_18))) (let ((_let_20 (ho_4 (ho_3 k_7 skv_15) skv_13))) (let ((_let_21 (not _let_20))) (let ((_let_22 (ho_4 (ho_6 k_5 mactual) skv_13))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_19 _let_16))) (let ((_let_25 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_9)) (ASSUME :args (_let_10)) (ASSUME :args (_let_11)) (ASSUME :args (_let_12)) (ASSUME :args (_let_13)) (ASSUME :args (_let_14))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_25 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((BOUND_VARIABLE_3882 mworld) (BOUND_VARIABLE_3883 mworld) (BOUND_VARIABLE_3884 $$unsorted)) (or (not (@ (@ mrel mactual) BOUND_VARIABLE_3882)) (not (@ (@ eiw_di BOUND_VARIABLE_3884) BOUND_VARIABLE_3882)) (not (@ (@ mrel BOUND_VARIABLE_3882) BOUND_VARIABLE_3883)) (@ (@ (@ subset BOUND_VARIABLE_3884) BOUND_VARIABLE_3884) BOUND_VARIABLE_3883))) _let_15))))))) (let ((_let_27 (not _let_24))) (let ((_let_28 (or _let_19 _let_16))) (let ((_let_29 (forall ((BOUND_VARIABLE_3712 mworld)) (or (not (ho_4 (ho_6 k_5 skv_13) BOUND_VARIABLE_3712)) (ho_4 (ho_3 (ho_2 k_11 skv_15) skv_15) BOUND_VARIABLE_3712))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (forall ((BOUND_VARIABLE_4620 mworld)) (or (not (ho_4 (ho_6 k_5 skv_13) BOUND_VARIABLE_4620)) (ho_4 (ho_3 (ho_2 k_11 skv_15) skv_15) BOUND_VARIABLE_4620))))) (let ((_let_32 (not _let_29))) (let ((_let_33 (ho_4 (ho_3 (ho_2 k_1 (ho_10 (ho_9 k_8 skv_15) skv_15)) skv_15) skv_14))) (let ((_let_34 (ho_4 _let_17 skv_14))) (let ((_let_35 (not _let_34))) (let ((_let_36 (not _let_31))) (let ((_let_37 (ho_4 _let_17 skv_13))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_23 _let_21 _let_38 _let_21 _let_38 _let_36 _let_35 _let_33))) (let ((_let_40 (forall ((BOUND_VARIABLE_4606 mworld) (BOUND_VARIABLE_4607 mworld) (BOUND_VARIABLE_4608 mworld) (BOUND_VARIABLE_4609 mworld) (BOUND_VARIABLE_4610 $$unsorted) (BOUND_VARIABLE_4611 $$unsorted)) (or (not (ho_4 (ho_6 k_5 mactual) BOUND_VARIABLE_4606)) (not (ho_4 (ho_3 k_7 BOUND_VARIABLE_4611) BOUND_VARIABLE_4606)) (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_4606) BOUND_VARIABLE_4607)) (not (ho_4 (ho_3 k_7 BOUND_VARIABLE_4610) BOUND_VARIABLE_4607)) (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_4607) BOUND_VARIABLE_4608)) (not (forall ((BOUND_VARIABLE_4620 mworld)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_4608) BOUND_VARIABLE_4620)) (ho_4 (ho_3 (ho_2 k_11 BOUND_VARIABLE_4611) BOUND_VARIABLE_4610) BOUND_VARIABLE_4620)))) (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_4608) BOUND_VARIABLE_4609)) (ho_4 (ho_3 (ho_2 k_1 (ho_10 (ho_9 k_8 BOUND_VARIABLE_4611) BOUND_VARIABLE_4610)) BOUND_VARIABLE_4610) BOUND_VARIABLE_4609))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO _let_25 :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((BOUND_VARIABLE_4606 mworld) (BOUND_VARIABLE_4607 mworld) (BOUND_VARIABLE_4608 mworld) (BOUND_VARIABLE_4609 mworld) (BOUND_VARIABLE_4610 $$unsorted) (BOUND_VARIABLE_4611 $$unsorted)) (or (not (@ (@ mrel mactual) BOUND_VARIABLE_4606)) (not (@ (@ eiw_di BOUND_VARIABLE_4611) BOUND_VARIABLE_4606)) (not (@ (@ mrel BOUND_VARIABLE_4606) BOUND_VARIABLE_4607)) (not (@ (@ eiw_di BOUND_VARIABLE_4610) BOUND_VARIABLE_4607)) (not (@ (@ mrel BOUND_VARIABLE_4607) BOUND_VARIABLE_4608)) (not (forall ((BOUND_VARIABLE_4620 mworld)) (or (not (@ (@ mrel BOUND_VARIABLE_4608) BOUND_VARIABLE_4620)) (@ (@ (@ subset BOUND_VARIABLE_4611) BOUND_VARIABLE_4610) BOUND_VARIABLE_4620)))) (not (@ (@ mrel BOUND_VARIABLE_4608) BOUND_VARIABLE_4609)) (@ (@ (@ qmltpeq (@ (@ union BOUND_VARIABLE_4611) BOUND_VARIABLE_4610)) BOUND_VARIABLE_4610) BOUND_VARIABLE_4609))) _let_40))))))) (let ((_let_42 (forall ((W mworld)) (ho_4 (ho_6 k_5 W) W)))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 _let_42)))))) (let ((_let_44 (or _let_23 _let_21 _let_35 _let_33))) (let ((_let_45 (forall ((BOUND_VARIABLE_19558 mworld) (BOUND_VARIABLE_19559 mworld) (BOUND_VARIABLE_19560 $$unsorted)) (or (not (ho_4 (ho_6 k_5 mactual) BOUND_VARIABLE_19558)) (not (ho_4 (ho_3 k_7 BOUND_VARIABLE_19560) BOUND_VARIABLE_19558)) (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_19558) BOUND_VARIABLE_19559)) (ho_4 (ho_3 (ho_2 k_1 (ho_10 (ho_9 k_8 BOUND_VARIABLE_19560) BOUND_VARIABLE_19560)) BOUND_VARIABLE_19560) BOUND_VARIABLE_19559))))) (let ((_let_46 (not _let_44))) (let ((_let_47 (not _let_45))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_25 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((BOUND_VARIABLE_19558 mworld) (BOUND_VARIABLE_19559 mworld) (BOUND_VARIABLE_19560 $$unsorted)) (or (not (@ (@ mrel mactual) BOUND_VARIABLE_19558)) (not (@ (@ eiw_di BOUND_VARIABLE_19560) BOUND_VARIABLE_19558)) (not (@ (@ mrel BOUND_VARIABLE_19558) BOUND_VARIABLE_19559)) (@ (@ (@ qmltpeq (@ (@ union BOUND_VARIABLE_19560) BOUND_VARIABLE_19560)) BOUND_VARIABLE_19560) BOUND_VARIABLE_19559)))) _let_47))))))) (let ((_let_49 (OR))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_48) :args (_let_47))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_45))) (REFL :args (_let_46)) :args _let_49)) _let_48 :args (_let_46 true _let_45)))) (let ((_let_51 (REFL :args (_let_44)))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_44 1)) (CONG _let_51 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_49)) :args ((or _let_20 _let_44))) _let_50 :args (_let_20 true _let_44)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_44 0)) (CONG _let_51 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_49)) :args ((or _let_22 _let_44))) _let_50 :args (_let_22 true _let_44)))) (let ((_let_54 (_let_32))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_54)) :args _let_54)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_29))) (REFL :args (_let_30)) :args _let_49)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_29 (= BOUND_VARIABLE_3712 BOUND_VARIABLE_4620)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_39))) :args ((or _let_23 _let_35 _let_21 _let_33 _let_38 _let_36 (not _let_39)))) _let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_44 2)) (CONG _let_51 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_49)) :args ((or _let_34 _let_44))) _let_50 :args (_let_34 true _let_44)) _let_52 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_44 3)) _let_50 :args ((not _let_33) true _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (skv_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_5 W)))) :args (_let_42))) _let_43 :args (_let_37 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (skv_13 skv_13 skv_13 skv_14 skv_15 skv_15 QUANTIFIERS_INST_E_MATCHING ((ho_3 k_7 BOUND_VARIABLE_4611) (not (= (ho_4 (ho_6 k_5 BOUND_VARIABLE_4606) BOUND_VARIABLE_4607) false)) (ho_3 k_7 BOUND_VARIABLE_4610) (not (= (ho_4 (ho_6 k_5 BOUND_VARIABLE_4608) BOUND_VARIABLE_4609) false))))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_36 false _let_22 false _let_34 false _let_20 true _let_33 false _let_37 false _let_39)) :args (_let_32 true _let_31)) :args (_let_30 true _let_29)))) (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (skv_13 skv_16 skv_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_15))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_21 _let_19 _let_16 _let_27))) _let_53 _let_52 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_49)) :args ((or _let_18 _let_28))) _let_55 :args (_let_18 true _let_28)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 1)) _let_55 :args ((not _let_16) true _let_28)) :args (_let_27 false _let_22 false _let_20 false _let_18 true _let_16)) _let_26 :args (false true _let_24 false _let_15)) :args (_let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 (@ mlocal (@ mbox (@ mforall_di (lambda ((X $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((Z $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ qmltpeq X))) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ _let_1 Y))) (@ mbox (@ (@ qmltpeq Y) Z)))) (@ mbox (@ _let_1 Z)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))) (forall ((W mworld)) (exists ((X $$unsorted)) (@ (@ eiw_di X) W))) (@ mlocal (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ qmltpeq (@ (@ union B) C)) (@ (@ union C) B))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ (@ qmltpeq A) B))) (@ mbox (@ (@ subset A) C)))) (@ mbox (@ (@ subset B) C)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) _let_4 (@ mlocal (@ mbox (@ mforall_di (lambda ((X $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ qmltpeq X) X)) __flatten_var_0))))) _let_3 (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ qmltpeq A) B))) (@ mbox (@ (@ qmltpeq (@ (@ union A) C)) (@ (@ union B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ mbox (@ (@ qmltpeq B) C)))) (@ (@ (@ mand (@ mbox (@ (@ mimplies _let_1) (@ mbox (@ mforall_di (lambda ((D $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ member D))) (let ((_let_2 (@ mbox (@ _let_1 B)))) (let ((_let_3 (@ mbox (@ _let_1 C)))) (@ (@ (@ mand (@ mbox (@ (@ mimplies _let_2) _let_3))) (@ mbox (@ (@ mimplies _let_3) _let_2))) __flatten_var_0)))))))))) (@ mbox (@ (@ mimplies (@ mbox (@ mforall_di (lambda ((D $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ member D))) (let ((_let_2 (@ mbox (@ _let_1 B)))) (let ((_let_3 (@ mbox (@ _let_1 C)))) (@ (@ (@ mand (@ mbox (@ (@ mimplies _let_2) _let_3))) (@ mbox (@ (@ mimplies _let_3) _let_2))) __flatten_var_0)))))))) _let_1))) __flatten_var_0))))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ subset C))) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ (@ qmltpeq A) B))) (@ mbox (@ _let_1 A)))) (@ mbox (@ _let_1 B)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ mbox (@ (@ subset B) C)))) (@ (@ (@ mand (@ mbox (@ (@ mimplies _let_1) (@ mbox (@ mforall_di (lambda ((D $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ member D))) (@ (@ mbox (@ (@ mimplies (@ mbox (@ _let_1 B))) (@ mbox (@ _let_1 C)))) __flatten_var_0)))))))) (@ mbox (@ (@ mimplies (@ mbox (@ mforall_di (lambda ((D $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ member D))) (@ (@ mbox (@ (@ mimplies (@ mbox (@ _let_1 B))) (@ mbox (@ _let_1 C)))) __flatten_var_0)))))) _let_1))) __flatten_var_0))))) __flatten_var_0))))) (forall ((W mworld) (V mworld) (U mworld)) (let ((_let_1 (@ mrel W))) (=> (and (@ _let_1 V) (@ (@ mrel V) U)) (@ _let_1 U)))) (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ (@ qmltpeq A) B))) (@ mbox (@ (@ member A) C)))) (@ mbox (@ (@ member B) C)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) _let_2 (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ union C))) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ qmltpeq A) B))) (@ mbox (@ (@ qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((X $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ qmltpeq X) Y))) (@ mbox (@ (@ qmltpeq Y) X)))) __flatten_var_0)))) __flatten_var_0))))) _let_1 (@ mlocal (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((D $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ member D))) (let ((_let_2 (@ mbox (@ _let_1 (@ (@ union B) C))))) (let ((_let_3 (@ (@ mor (@ mbox (@ _let_1 B))) (@ mbox (@ _let_1 C))))) (@ (@ (@ mand (@ mbox (@ (@ mimplies _let_2) _let_3))) (@ mbox (@ (@ mimplies _let_3) _let_2))) __flatten_var_0))))))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ member C))) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ (@ qmltpeq A) B))) (@ mbox (@ _let_1 A)))) (@ mbox (@ _let_1 B)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ mbox (@ (@ qmltpeq B) C)))) (let ((_let_2 (@ (@ mand (@ mbox (@ (@ subset B) C))) (@ mbox (@ (@ subset C) B))))) (@ (@ (@ mand (@ mbox (@ (@ mimplies _let_1) _let_2))) (@ mbox (@ (@ mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.95/1.14 % SZS output end Proof for theBenchmark 0.95/1.14 EOF