0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : do_cvc5 %s %d 0.09/0.30 % Computer : n008.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 960 0.09/0.30 % WCLimit : 120 0.09/0.30 % DateTime : Tue Aug 9 04:27:09 EDT 2022 0.09/0.30 % CPUTime : 0.15/0.41 %----Proving TH0 2.13/2.35 ------- cvc5-thf casc j11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 2.13/2.35 --- Run --ho-elim --full-saturate-quant at 10... 2.13/2.35 % SZS status Theorem for theBenchmark 2.13/2.35 % SZS output start Proof for theBenchmark 2.13/2.35 (let ((_let_1 (@ gt n5))) (let ((_let_2 (@ gt n3))) (let ((_let_3 (@ gt n4))) (let ((_let_4 (@ succ n0))) (let ((_let_5 (@ succ _let_4))) (let ((_let_6 (@ succ _let_5))) (let ((_let_7 (@ succ _let_6))) (let ((_let_8 (@ gt n2))) (let ((_let_9 (@ gt n1))) (let ((_let_10 (forall ((W mworld) (V mworld)) (@ (@ mrel W) V)))) (let ((_let_11 (@ mbox true))) (let ((_let_12 (@ mbox (@ (@ gt (@ (@ plus n1) loopcounter)) n1)))) (let ((_let_13 (not (@ mlocal (@ mbox (@ (@ mimplies (@ mbox (@ (@ geq pv65) tptp_float_0_001))) (@ (@ mand (@ mbox (@ (@ mimplies (@ mbox (@ mnot _let_12))) _let_11))) (@ mbox (@ (@ mimplies _let_12) _let_11))))))))) (let ((_let_14 (@ mlocal _let_11))) (let ((_let_15 (= mexists_di (lambda ((A (-> $$unsorted mworld Bool)) (W mworld)) (exists ((X $$unsorted)) (and (@ (@ eiw_di X) W) (@ (@ A X) W))))))) (let ((_let_16 (= mforall_di (lambda ((A (-> $$unsorted mworld Bool)) (W mworld)) (forall ((X $$unsorted)) (=> (@ (@ eiw_di X) W) (@ (@ A X) W))))))) (let ((_let_17 (= mdia (lambda ((Phi (-> mworld Bool)) (W mworld)) (exists ((V mworld)) (and (@ (@ mrel W) V) (@ Phi V))))))) (let ((_let_18 (= mbox (lambda ((Phi (-> mworld Bool)) (W mworld)) (forall ((V mworld)) (=> (@ (@ mrel W) V) (@ Phi V))))))) (let ((_let_19 (= mequiv (lambda ((A (-> mworld Bool)) (B (-> mworld Bool)) (W mworld)) (= (@ A W) (@ B W)))))) (let ((_let_20 (= mimplies (lambda ((A (-> mworld Bool)) (B (-> mworld Bool)) (W mworld)) (=> (@ A W) (@ B W)))))) (let ((_let_21 (= mor (lambda ((A (-> mworld Bool)) (B (-> mworld Bool)) (W mworld)) (or (@ A W) (@ B W)))))) (let ((_let_22 (= mand (lambda ((A (-> mworld Bool)) (B (-> mworld Bool)) (W mworld)) (and (@ A W) (@ B W)))))) (let ((_let_23 (= mnot (lambda ((A (-> mworld Bool)) (W mworld)) (not (@ A W)))))) (let ((_let_24 (= mlocal (lambda ((Phi (-> mworld Bool))) (@ Phi mactual))))) (let ((_let_25 (forall ((W mworld) (V mworld)) (ho_8 (ho_10 k_9 W) V)))) (let ((_let_26 (ho_10 k_9 mactual))) (let ((_let_27 (ho_8 _let_26 skv_38))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_10)) (PREPROCESS :args ((= _let_10 _let_25)))))) (let ((_let_29 (ho_8 k_22 skv_38))) (let ((_let_30 (not _let_27))) (let ((_let_31 (or _let_30 _let_29))) (let ((_let_32 (forall ((BOUND_VARIABLE_17409 mworld)) (or (not (ho_8 (ho_10 k_9 mactual) BOUND_VARIABLE_17409)) (ho_8 k_22 BOUND_VARIABLE_17409))))) (let ((_let_33 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_19)) (ASSUME :args (_let_20)) (ASSUME :args (_let_21)) (ASSUME :args (_let_22)) (ASSUME :args (_let_23)) (ASSUME :args (_let_24))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO _let_33 :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((BOUND_VARIABLE_17409 mworld)) (or (not (@ (@ mrel mactual) BOUND_VARIABLE_17409)) (@ true BOUND_VARIABLE_17409))) _let_32))))))) (let ((_let_35 (_let_32))) (let ((_let_36 ((not (= (ho_8 k_22 BOUND_VARIABLE_17409) true))))) (let ((_let_37 (ho_10 k_9 skv_35))) (let ((_let_38 (or (not (ho_8 _let_37 skv_39)) (not (forall ((BOUND_VARIABLE_168686 mworld)) (or (not (ho_8 (ho_10 k_9 skv_39) BOUND_VARIABLE_168686)) (not (forall ((BOUND_VARIABLE_168687 mworld)) (or (not (ho_8 (ho_10 k_9 BOUND_VARIABLE_168686) BOUND_VARIABLE_168687)) (ho_8 (ho_7 (ho_6 k_21 (ho_4 (ho_3 k_23 n1) loopcounter)) n1) BOUND_VARIABLE_168687))))))) (not (ho_8 (ho_10 k_9 skv_39) skv_38)) _let_29))) (let ((_let_39 (ho_8 k_22 skv_36))) (let ((_let_40 (or (not (ho_8 _let_37 skv_37)) (not (forall ((BOUND_VARIABLE_168670 mworld)) (or (not (ho_8 (ho_10 k_9 skv_37) BOUND_VARIABLE_168670)) (ho_8 (ho_7 (ho_6 k_21 (ho_4 (ho_3 k_23 n1) loopcounter)) n1) BOUND_VARIABLE_168670)))) (not (ho_8 (ho_10 k_9 skv_37) skv_36)) _let_39))) (let ((_let_41 (and _let_38 _let_40))) (let ((_let_42 (ho_8 _let_26 skv_36))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_39))) (let ((_let_45 (_let_25))) (let ((_let_46 (or (not (ho_8 _let_26 skv_35)) (not (forall ((BOUND_VARIABLE_168706 mworld)) (or (not (ho_8 (ho_10 k_9 skv_35) BOUND_VARIABLE_168706)) (ho_8 (ho_7 (ho_6 k_24 pv65) tptp_float_0_001) BOUND_VARIABLE_168706)))) _let_41))) (let ((_let_47 (forall ((BOUND_VARIABLE_168661 mworld) (BOUND_VARIABLE_168662 mworld) (BOUND_VARIABLE_168663 mworld) (BOUND_VARIABLE_168664 mworld) (BOUND_VARIABLE_168665 mworld)) (let ((_let_1 (ho_10 k_9 BOUND_VARIABLE_168661))) (or (not (ho_8 (ho_10 k_9 mactual) BOUND_VARIABLE_168661)) (not (forall ((BOUND_VARIABLE_168706 mworld)) (or (not (ho_8 (ho_10 k_9 BOUND_VARIABLE_168661) BOUND_VARIABLE_168706)) (ho_8 (ho_7 (ho_6 k_24 pv65) tptp_float_0_001) BOUND_VARIABLE_168706)))) (and (or (not (ho_8 _let_1 BOUND_VARIABLE_168665)) (not (forall ((BOUND_VARIABLE_168686 mworld)) (or (not (ho_8 (ho_10 k_9 BOUND_VARIABLE_168665) BOUND_VARIABLE_168686)) (not (forall ((BOUND_VARIABLE_168687 mworld)) (or (not (ho_8 (ho_10 k_9 BOUND_VARIABLE_168686) BOUND_VARIABLE_168687)) (ho_8 (ho_7 (ho_6 k_21 (ho_4 (ho_3 k_23 n1) loopcounter)) n1) BOUND_VARIABLE_168687))))))) (not (ho_8 (ho_10 k_9 BOUND_VARIABLE_168665) BOUND_VARIABLE_168664)) (ho_8 k_22 BOUND_VARIABLE_168664)) (or (not (ho_8 _let_1 BOUND_VARIABLE_168663)) (not (forall ((BOUND_VARIABLE_168670 mworld)) (or (not (ho_8 (ho_10 k_9 BOUND_VARIABLE_168663) BOUND_VARIABLE_168670)) (ho_8 (ho_7 (ho_6 k_21 (ho_4 (ho_3 k_23 n1) loopcounter)) n1) BOUND_VARIABLE_168670)))) (not (ho_8 (ho_10 k_9 BOUND_VARIABLE_168663) BOUND_VARIABLE_168662)) (ho_8 k_22 BOUND_VARIABLE_168662)))))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (not _let_47))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO _let_33 :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((BOUND_VARIABLE_168661 mworld) (BOUND_VARIABLE_168662 mworld) (BOUND_VARIABLE_168663 mworld) (BOUND_VARIABLE_168664 mworld) (BOUND_VARIABLE_168665 mworld)) (let ((_let_1 (@ mrel BOUND_VARIABLE_168661))) (or (not (@ (@ mrel mactual) BOUND_VARIABLE_168661)) (not (forall ((BOUND_VARIABLE_168706 mworld)) (or (not (@ (@ mrel BOUND_VARIABLE_168661) BOUND_VARIABLE_168706)) (@ (@ (@ geq pv65) tptp_float_0_001) BOUND_VARIABLE_168706)))) (and (or (not (@ _let_1 BOUND_VARIABLE_168665)) (not (forall ((BOUND_VARIABLE_168686 mworld)) (or (not (@ (@ mrel BOUND_VARIABLE_168665) BOUND_VARIABLE_168686)) (not (forall ((BOUND_VARIABLE_168687 mworld)) (or (not (@ (@ mrel BOUND_VARIABLE_168686) BOUND_VARIABLE_168687)) (@ (@ (@ gt (@ (@ plus n1) loopcounter)) n1) BOUND_VARIABLE_168687))))))) (not (@ (@ mrel BOUND_VARIABLE_168665) BOUND_VARIABLE_168664)) (@ true BOUND_VARIABLE_168664)) (or (not (@ _let_1 BOUND_VARIABLE_168663)) (not (forall ((BOUND_VARIABLE_168670 mworld)) (or (not (@ (@ mrel BOUND_VARIABLE_168663) BOUND_VARIABLE_168670)) (@ (@ (@ gt (@ (@ plus n1) loopcounter)) n1) BOUND_VARIABLE_168670)))) (not (@ (@ mrel BOUND_VARIABLE_168663) BOUND_VARIABLE_168662)) (@ true BOUND_VARIABLE_168662))))))) _let_49))))))) (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (mactual skv_38 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_29 _let_30 (not _let_31)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 3)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_41)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 2)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_50) :args (_let_49))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_47))) (REFL :args (_let_48)) :args (OR))) _let_50 :args (_let_48 true _let_47)) :args ((not _let_41) true _let_46)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_39 _let_43 (not _let_44)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (mactual skv_36 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_45)) _let_28 :args (_let_42 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (skv_36 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_44 false _let_32)) :args (_let_39 false _let_42 false _let_44)) :args (_let_40 false _let_39)) :args ((not _let_38) true _let_41 false _let_40)) :args ((not _let_29) true _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (skv_38 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_31 false _let_32)) :args (_let_30 true _let_29 false _let_31)) _let_28 :args (false true _let_27 false _let_25)) :args (_let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 (@ 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 $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((D $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ a_select3 C))) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ customqmltpeq A) B))) (@ mbox (@ (@ customqmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __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 $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ customqmltpeq A) B))) (@ mbox (@ (@ customqmltpeq (@ (@ minus A) C)) (@ (@ minus B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$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)) (@ (@ mbox (@ mforall_di (lambda ((D $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ (@ tptp_update2 C) D))) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ customqmltpeq A) B))) (@ mbox (@ (@ customqmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$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)) (@ (@ mbox (@ mforall_di (lambda ((D $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((E $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ tptp_update3 C))) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ customqmltpeq A) B))) (@ mbox (@ (@ customqmltpeq (@ (@ (@ _let_1 A) D) E)) (@ (@ (@ _let_1 B) D) E))))) __flatten_var_0))))) __flatten_var_0)))) __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)) (let ((_let_1 (@ mbox (@ (@ leq (@ succ X)) (@ succ Y))))) (let ((_let_2 (@ mbox (@ (@ leq X) Y)))) (@ (@ (@ mand (@ mbox (@ (@ mimplies _let_1) _let_2))) (@ mbox (@ (@ mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((X $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ customqmltpeq X))) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ (@ leq n0) X))) (@ mbox (@ (@ leq X) n1)))) (@ (@ mor (@ mbox (@ _let_1 n0))) (@ mbox (@ _let_1 n1))))) __flatten_var_0)))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((I $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((U $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((X $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((VAL $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ mforall_di (lambda ((I0 $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ (@ leq n0) I0))) (@ mbox (@ (@ leq I0) U)))) (@ mbox (@ (@ customqmltpeq (@ (@ a_select2 X) I0)) VAL)))) __flatten_var_0))))) (@ (@ mand (@ mbox (@ (@ leq n0) I))) (@ mbox (@ (@ leq I) U))))) (@ mbox (@ (@ customqmltpeq (@ (@ a_select2 (@ (@ (@ tptp_update2 X) U) VAL)) I)) VAL)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((I $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((L $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((U $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((Val $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ (@ leq L) I))) (@ mbox (@ (@ leq I) U)))) (@ mbox (@ (@ customqmltpeq (@ (@ a_select2 (@ (@ tptp_const_array1 (@ (@ dim L) U)) Val)) I)) Val)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ _let_2 n2))) (@ mlocal (@ mbox (@ _let_1 tptp_minus_1))) _let_14 (@ mlocal (@ mbox (@ mforall_di (lambda ((X $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ customqmltpeq (@ (@ plus X) n5)) (@ succ (@ succ (@ succ (@ succ (@ succ X))))))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((X $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ (@ leq X) Y))) (@ mbox (@ mnot (@ mbox (@ (@ customqmltpeq X) Y)))))) (@ mbox (@ (@ gt Y) X)))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((X $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ mbox (@ (@ geq X) Y)))) (let ((_let_2 (@ mbox (@ (@ leq Y) X)))) (@ (@ (@ mand (@ mbox (@ (@ mimplies _let_1) _let_2))) (@ mbox (@ (@ mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$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)) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ customqmltpeq A) B))) (@ mbox (@ (@ customqmltpeq (@ (@ tptp_madd A) C)) (@ (@ tptp_madd B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((X $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ gt (@ succ X)) X)) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$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 (@ a_select2 C))) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ customqmltpeq A) B))) (@ mbox (@ (@ customqmltpeq (@ _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 (@ (@ leq (@ succ X)) Y))) (@ mbox (@ (@ gt Y) X)))) __flatten_var_0)))) __flatten_var_0))))) _let_13 (@ 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 $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ gt X))) (@ (@ mbox (@ (@ mimplies (@ (@ mand (@ mbox (@ _let_1 Y))) (@ mbox (@ (@ gt Y) Z)))) (@ mbox (@ _let_1 Z)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((I $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((J $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((U $$unsorted) 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((A $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((B $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((C $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ mforall_di (lambda ((D $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ tptp_const_array2 C))) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ customqmltpeq A) B))) (@ mbox (@ (@ customqmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __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 $$unsorted) (__flatten_var_0 mworld)) (let ((_let_1 (@ plus C))) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ customqmltpeq A) B))) (@ mbox (@ (@ customqmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((Body $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ customqmltpeq (@ (@ (@ sum n0) tptp_minus_1) Body)) n0)) __flatten_var_0))))) (@ mlocal (@ mbox (@ _let_1 n1))) (@ mlocal (@ mbox (@ mforall_di (lambda ((X $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ customqmltpeq (@ (@ minus X) n1)) (@ pred X))) __flatten_var_0))))) (@ mlocal (@ mbox (@ mforall_di (lambda ((A $$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 (@ mforall_di (lambda ((D $$unsorted) (__flatten_var_0 mworld)) (@ (@ mbox (@ (@ mimplies (@ mbox (@ (@ customqmltpeq A) B))) (@ mbox (@ (@ customqmltpeq (@ (@ (@ tptp_update2 A) C) D)) (@ (@ (@ tptp_update2 B) C) D))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) true)))))))))))))))))))))))))))))))))))))))))))))))))))) 2.13/2.36 % SZS output end Proof for theBenchmark 2.13/2.36 EOF