0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : do_cvc5 %s %d 0.12/0.33 % Computer : n010.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 960 0.12/0.33 % WCLimit : 120 0.12/0.33 % DateTime : Tue Aug 9 02:46:20 EDT 2022 0.12/0.33 % CPUTime : 0.18/0.45 %----Proving TF0_NAR, FOF, or CNF 0.18/0.50 ------- cvc5-fof casc J11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 0.18/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 0.18/0.50 % SZS status Theorem for theBenchmark 0.18/0.50 % SZS output start Proof for theBenchmark 0.18/0.50 (let ((_let_1 (not (forall ((U $$unsorted)) (=> (forall ((V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (less_than X W) (pair_in_list U V W)) (pair_in_list (update_slb U X) V W))) (forall ((Y $$unsorted) (Z $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (let ((_let_1 (insert_slb U (pair X2 X3)))) (=> (and (pair_in_list _let_1 Y Z) (less_than X1 Z)) (pair_in_list (update_slb _let_1 X1) Y Z))))))))) (let ((_let_2 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (pair V X))) (=> (less_than W X) (= (insert_slb (update_slb U W) _let_1) (update_slb (insert_slb U _let_1) W))))))) (let ((_let_3 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (or (and (= W V) (= Y X)) (pair_in_list U W Y)) (pair_in_list (insert_slb U (pair V X)) W Y))))) (let ((_let_4 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (strictly_less_than X W) (= (update_slb (insert_slb U (pair V X)) W) (insert_slb (update_slb U W) (pair V W))))))) (let ((_let_5 (forall ((U $$unsorted) (V $$unsorted)) (= (strictly_less_than U V) (and (less_than U V) (not (less_than V U))))))) (let ((_let_6 (forall ((U $$unsorted) (V $$unsorted)) (or (less_than V U) (less_than U V))))) (let ((_let_7 (pair skv_4 skv_3))) (let ((_let_8 (insert_slb skv_2 _let_7))) (let ((_let_9 (update_slb _let_8 skv_5))) (let ((_let_10 (pair_in_list _let_9 skv_7 skv_6))) (let ((_let_11 (update_slb skv_2 skv_5))) (let ((_let_12 (insert_slb _let_11 (pair skv_4 skv_5)))) (let ((_let_13 (= _let_9 _let_12))) (let ((_let_14 (pair_in_list _let_12 skv_7 skv_6))) (let ((_let_15 (less_than skv_5 skv_6))) (let ((_let_16 (not _let_15))) (let ((_let_17 (pair_in_list _let_8 skv_7 skv_6))) (let ((_let_18 (not _let_17))) (let ((_let_19 (forall ((V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (less_than X W)) (not (pair_in_list skv_2 V W)) (pair_in_list (update_slb skv_2 X) V W))))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18 _let_16 _let_10))) (let ((_let_22 (not _let_10))) (let ((_let_23 (forall ((U $$unsorted) (BOUND_VARIABLE_620 $$unsorted) (BOUND_VARIABLE_618 $$unsorted) (BOUND_VARIABLE_616 $$unsorted) (BOUND_VARIABLE_614 $$unsorted) (BOUND_VARIABLE_612 $$unsorted)) (let ((_let_1 (insert_slb U (pair BOUND_VARIABLE_618 BOUND_VARIABLE_620)))) (or (not (forall ((V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (less_than X W)) (not (pair_in_list U V W)) (pair_in_list (update_slb U X) V W)))) (not (pair_in_list _let_1 BOUND_VARIABLE_612 BOUND_VARIABLE_614)) (not (less_than BOUND_VARIABLE_616 BOUND_VARIABLE_614)) (pair_in_list (update_slb _let_1 BOUND_VARIABLE_616) BOUND_VARIABLE_612 BOUND_VARIABLE_614)))))) (let ((_let_24 (not _let_21))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (OR))) (let ((_let_27 (not _let_23))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_25) :args (_let_27))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_23))) (REFL :args (_let_24)) :args _let_26)) _let_25 :args (_let_24 true _let_23)))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_21 3)) _let_28 :args (_let_22 true _let_21)))) (let ((_let_30 (strictly_less_than skv_3 skv_5))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_13))) (let ((_let_33 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (strictly_less_than X W)) (= (insert_slb (update_slb U W) (pair V W)) (update_slb (insert_slb U (pair V X)) W)))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (less_than skv_5 skv_3))) (let ((_let_36 (not _let_35))) (let ((_let_37 (less_than skv_3 skv_5))) (let ((_let_38 (and _let_37 _let_36))) (let ((_let_39 (= _let_30 _let_38))) (let ((_let_40 (_let_5))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 (or _let_37 _let_35))) (let ((_let_43 (_let_6))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 (insert_slb _let_11 _let_7))) (let ((_let_46 (= _let_9 _let_45))) (let ((_let_47 (or _let_36 _let_46))) (let ((_let_48 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (pair V X))) (or (not (less_than W X)) (= (update_slb (insert_slb U _let_1) W) (insert_slb (update_slb U W) _let_1))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (pair_in_list _let_45 skv_7 skv_6))) (let ((_let_51 (not _let_46))) (let ((_let_52 (pair_in_list _let_11 skv_7 skv_6))) (let ((_let_53 (= skv_3 skv_6))) (let ((_let_54 (= skv_4 skv_7))) (let ((_let_55 (and _let_54 _let_53))) (let ((_let_56 (or _let_55 _let_52))) (let ((_let_57 (= _let_50 _let_56))) (let ((_let_58 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (pair_in_list (insert_slb U (pair V X)) W Y) (or (and (= V W) (= X Y)) (pair_in_list U W Y)))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (_let_58))) (let ((_let_61 ((pair_in_list (insert_slb U (pair V X)) W Y)))) (let ((_let_62 (pair_in_list skv_2 skv_7 skv_6))) (let ((_let_63 (or _let_55 _let_62))) (let ((_let_64 (not _let_62))) (let ((_let_65 (or _let_16 _let_64 _let_52))) (let ((_let_66 (not _let_55))) (let ((_let_67 (= _let_17 _let_63))) (let ((_let_68 (REFL :args (_let_21)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 2)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_26)) :args ((or _let_15 _let_21))) _let_28 :args (_let_15 true _let_21)))) (let ((_let_70 (_let_19))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_16 _let_64 _let_52 (not _let_65)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_70) :args (skv_7 skv_6 skv_5 QUANTIFIERS_INST_E_MATCHING ((not (= (pair_in_list (update_slb skv_2 X) V W) true))))) :args _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_26)) :args ((or _let_19 _let_21))) _let_28 :args (_let_19 true _let_21)) :args (_let_65 false _let_19)) _let_69 (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_55 _let_62 (not _let_63)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_67)) :args ((or _let_18 _let_63 (not _let_67)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 1)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_26)) :args ((or _let_17 _let_21))) _let_28 :args (_let_17 true _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (skv_2 skv_4 skv_7 skv_3 skv_6 QUANTIFIERS_INST_E_MATCHING _let_61)) :args _let_60)) _let_59 :args (_let_67 false _let_58)) :args (_let_63 false _let_17 false _let_67)) (CNF_OR_NEG :args (_let_56 1)) (REORDERING (CNF_OR_NEG :args (_let_56 0)) :args ((or _let_66 _let_56))) :args (_let_56 false _let_65 false _let_15 false _let_62 false _let_63 true _let_52 true _let_55)))) (let ((_let_72 (not _let_56))) (let ((_let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_10))))) (let ((_let_74 (ASSUME :args (_let_22)))) (let ((_let_75 (FALSE_INTRO _let_74))) (let ((_let_76 (APPLY_UF pair_in_list))) (let ((_let_77 (REFL :args (skv_6)))) (let ((_let_78 (REFL :args (skv_7)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_36 _let_46 (not _let_47)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (ASSUME :args (_let_50)))) (CONG (SYMM (ASSUME :args (_let_46))) _let_78 _let_77 :args _let_76) _let_75)) :args (_let_22 _let_46 _let_50))) (CONG _let_73 (REFL :args (_let_51)) (REFL :args ((not _let_50))) :args _let_26)) _let_29 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_57)) :args ((or _let_50 _let_72 (not _let_57)))) _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_11 skv_4 skv_7 skv_3 skv_6 QUANTIFIERS_INST_E_MATCHING _let_61)) :args _let_60)) _let_59 :args (_let_57 false _let_58)) :args (_let_50 false _let_56 false _let_57)) :args (_let_51 true _let_10 false _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (skv_2 skv_4 skv_5 skv_3 QUANTIFIERS_INST_E_MATCHING ((update_slb (insert_slb U (pair V X)) W)))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_36 true _let_46 false _let_47)))) (let ((_let_80 (not _let_37))) (let ((_let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))))) (let ((_let_82 (_let_38))) (let ((_let_83 (or (and _let_54 (= skv_5 skv_6)) _let_52))) (let ((_let_84 (= _let_14 _let_83))) (let ((_let_85 (not _let_53))) (let ((_let_86 (ASSUME :args (_let_36)))) (let ((_let_87 (ASSUME :args (_let_53)))) (let ((_let_88 (ASSUME :args (_let_15)))) (let ((_let_89 (ASSUME :args (_let_14)))) (let ((_let_90 (ASSUME :args (_let_13)))) (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_89 _let_90 _let_74) :args (_let_22 _let_13 _let_14)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_75) (CONG (SYMM (SYMM _let_90)) _let_78 _let_77 :args _let_76) (TRUE_INTRO _let_89))) :args (_let_14 _let_13 _let_22)) :args ((not (and _let_22 _let_13 _let_14)) SB_LITERAL))) (CONG _let_73 (REFL :args ((not _let_13))) (REFL :args ((not _let_14))) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_84)) :args ((or _let_14 (not _let_83) (not _let_84)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_83 1)) :args ((or (not _let_52) _let_83))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_55 _let_52 _let_72))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_55 1)) :args ((or _let_53 _let_66))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_86 _let_87 _let_88) :args (_let_15 _let_53 _let_36)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_88)) (CONG (REFL :args (skv_5)) (SYMM _let_87) :args (APPLY_UF less_than)) (FALSE_INTRO _let_86))) :args (_let_36 _let_53 _let_15)) :args ((not (and _let_15 _let_53 _let_36)) SB_LITERAL))) (CONG (REFL :args (_let_16)) (REFL :args (_let_85)) _let_81 :args _let_26)) :args ((or _let_16 _let_35 _let_85))) _let_69 _let_79 :args (_let_85 false _let_15 true _let_35)) :args (_let_66 true _let_53)) _let_71 :args (_let_52 true _let_55 false _let_56)) :args (_let_83 false _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_11 skv_4 skv_7 skv_5 skv_6 QUANTIFIERS_INST_E_MATCHING _let_61)) :args _let_60)) _let_59 :args (_let_84 false _let_58)) :args (_let_14 false _let_83 false _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_13 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_39)) :args ((or _let_30 (not _let_38) (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_82) (CONG (REFL :args _let_82) (REFL :args (_let_80)) _let_81 :args _let_26)) :args ((or _let_35 _let_38 _let_80))) _let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_35 _let_37 (not _let_42)))) _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (skv_5 skv_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (less_than U V) true))))) :args _let_43)) _let_44 :args (_let_42 false _let_6)) :args (_let_37 true _let_35 false _let_42)) :args (_let_38 true _let_35 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (skv_3 skv_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((strictly_less_than U V)))) :args _let_40)) _let_41 :args (_let_39 false _let_5)) :args (_let_30 false _let_38 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (skv_2 skv_4 skv_5 skv_3 QUANTIFIERS_INST_E_MATCHING ((update_slb (insert_slb U (pair V X)) W)))) :args (_let_33)))) _let_34 :args (_let_32 false _let_33)) :args (_let_13 false _let_30 false _let_32)) _let_29 :args (false false _let_14 false _let_13 true _let_10)) :args (_let_6 (forall ((U $$unsorted)) (less_than U U)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (and (less_than V W) (less_than U V)) (less_than U W))) (forall ((U $$unsorted)) (less_than bottom U)) _let_5 _let_4 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (pair V X))) (=> (and (contains_slb U W) (not (= V W))) (= (insert_slb (remove_slb U W) _let_1) (remove_slb (insert_slb U _let_1) W))))) (forall ((U $$unsorted)) (= create_slb (update_slb create_slb U))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (contains_slb (insert_slb U (pair V X)) W) (or (contains_slb U W) (= W V)))) (forall ((U $$unsorted) (V $$unsorted)) (not (pair_in_list create_slb U V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (not (= W V)) (contains_slb U W)) (= (lookup_slb U W) (lookup_slb (insert_slb U (pair V X)) W)))) (forall ((U $$unsorted)) (not (contains_slb create_slb U))) _let_3 (not (isnonempty_slb create_slb)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= U (remove_slb (insert_slb U (pair V W)) V))) _let_2 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (isnonempty_slb (insert_slb U (pair V W)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= W (lookup_slb (insert_slb U (pair V W)) V))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.18/0.51 % SZS output end Proof for theBenchmark 0.18/0.51 EOF