0.01/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.01/0.12 % Command : do_cvc5 %s %d 0.12/0.33 % Computer : n005.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 04:30:49 EDT 2022 0.12/0.33 % CPUTime : 0.18/0.46 %----Proving TF0_NAR, FOF, or CNF 2.89/3.07 ------- cvc5-fof casc J11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 2.89/3.07 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 2.89/3.07 % SZS status Theorem for theBenchmark 2.89/3.07 % SZS output start Proof for theBenchmark 2.89/3.07 (let ((_let_1 (=> op_implies_or (forall ((X $$unsorted) (Y $$unsorted)) (= (or (not X) Y) (implies X Y)))))) (let ((_let_2 (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (is_a_theorem (implies (or P (or Q R)) (or Q (or P R))))))) (let ((_let_3 (= r4 _let_2))) (let ((_let_4 (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (is_a_theorem (implies (implies Q R) (implies (or P Q) (or P R))))))) (let ((_let_5 (= _let_4 r5))) (let ((_let_6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (is_a_theorem (implies (implies X Y) (implies (implies Y Z) (implies X Z))))))) (let ((_let_7 (= _let_6 implies_3))) (let ((_let_8 (= modus_ponens (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (is_a_theorem X) (is_a_theorem (implies X Y))) (is_a_theorem Y)))))) (let ((_let_9 (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (is_a_theorem (implies (implies P Q) (implies (implies Q R) (implies P R))))))) (let ((_let_10 (not implies_3))) (let ((_let_11 (not skv_2))) (let ((_let_12 (or _let_11 skv_3))) (let ((_let_13 (implies skv_2 skv_3))) (let ((_let_14 (= _let_13 _let_12))) (let ((_let_15 (or _let_11 skv_4))) (let ((_let_16 (implies skv_2 skv_4))) (let ((_let_17 (= _let_16 _let_15))) (let ((_let_18 (not _let_13))) (let ((_let_19 (or _let_18 _let_16))) (let ((_let_20 (= _let_19 (implies _let_13 _let_16)))) (let ((_let_21 (implies skv_3 skv_4))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_19))) (let ((_let_24 (= _let_23 (implies _let_21 _let_19)))) (let ((_let_25 (is_a_theorem _let_23))) (let ((_let_26 (is_a_theorem (implies _let_21 (implies _let_12 _let_15))))) (let ((_let_27 (forall ((X $$unsorted) (Y $$unsorted)) (= (implies X Y) (or (not X) Y))))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_27 (not op_implies_or)))) (ASSUME :args (op_implies_or)) :args (_let_27 false op_implies_or)))) (let ((_let_29 (_let_27))) (let ((_let_30 ((implies X Y)))) (let ((_let_31 (ASSUME :args _let_29))) (let ((_let_32 ((or (not X) Y)))) (let ((_let_33 (or _let_22 _let_16))) (let ((_let_34 (or _let_18 _let_33))) (let ((_let_35 (is_a_theorem _let_34))) (let ((_let_36 (is_a_theorem (implies _let_23 _let_34)))) (let ((_let_37 (not _let_36))) (let ((_let_38 (not _let_25))) (let ((_let_39 (or _let_38 _let_37 _let_35))) (let ((_let_40 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (is_a_theorem X)) (not (is_a_theorem (implies X Y))) (is_a_theorem Y))))) (let ((_let_41 (_let_40))) (let ((_let_42 (implies _let_21 _let_16))) (let ((_let_43 (= _let_42 _let_33))) (let ((_let_44 (implies _let_13 _let_42))) (let ((_let_45 (= _let_44 (or _let_18 _let_42)))) (let ((_let_46 (is_a_theorem _let_44))) (let ((_let_47 (not _let_35))) (let ((_let_48 (not _let_46))) (let ((_let_49 (not _let_9))) (let ((_let_50 (not _let_6))) (let ((_let_51 (OR))) (let ((_let_52 (_let_48))) (let ((_let_53 (_let_49))) (let ((_let_54 (and _let_48 _let_45 _let_43))) (let ((_let_55 (_let_48 _let_45 _let_43))) (let ((_let_56 (ASSUME :args _let_52))) (let ((_let_57 (APPLY_UF is_a_theorem))) (let ((_let_58 (ASSUME :args (_let_45)))) (let ((_let_59 (ASSUME :args (_let_43)))) (let ((_let_60 (_let_2))) (let ((_let_61 (_let_4))) (let ((_let_62 (not _let_26))) (let ((_let_63 (not _let_24))) (let ((_let_64 (not _let_20))) (let ((_let_65 (not _let_17))) (let ((_let_66 (not _let_14))) (let ((_let_67 (ASSUME :args (_let_26)))) (let ((_let_68 (APPLY_UF implies))) (let ((_let_69 (ASSUME :args (_let_17)))) (let ((_let_70 (ASSUME :args (_let_14)))) (let ((_let_71 (ASSUME :args (_let_20)))) (let ((_let_72 (ASSUME :args (_let_24)))) (let ((_let_73 (ASSUME :args (_let_38)))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_67 _let_70 _let_69 _let_71 _let_72 _let_73) :args (_let_14 _let_17 _let_20 _let_24 _let_38 _let_26)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_73)) (CONG (TRANS (SYMM (SYMM _let_72)) (CONG (REFL :args (_let_21)) (TRANS (SYMM (SYMM _let_71)) (CONG (SYMM (SYMM _let_70)) (SYMM (SYMM _let_69)) :args _let_68)) :args _let_68)) :args _let_57) (TRUE_INTRO _let_67))) :args (_let_26 _let_14 _let_17 _let_20 _let_24 _let_38)) :args ((not (and _let_14 _let_17 _let_20 _let_24 _let_38 _let_26)) SB_LITERAL))) (CONG (REFL :args (_let_66)) (REFL :args (_let_65)) (REFL :args (_let_64)) (REFL :args (_let_63)) (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_25))) (REFL :args (_let_62)) :args _let_51)) :args ((or _let_66 _let_65 _let_25 _let_64 _let_63 _let_62))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_61) :args (_let_11 skv_3 skv_4 QUANTIFIERS_INST_E_MATCHING ((implies (or P Q) (or P R))))) :args _let_61)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ASSUME :args (_let_5))) (ASSUME :args (r5)) :args (_let_4 false r5)) :args (_let_26 false _let_4)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_37 _let_35 _let_38 (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_60) :args (_let_22 _let_18 _let_16 QUANTIFIERS_INST_E_MATCHING ((or Q (or P R))))) :args _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ASSUME :args (_let_3))) :args ((or _let_2 (not r4)))) (ASSUME :args (r4)) :args (_let_2 false r4)) :args (_let_36 false _let_2)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_54)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_56 _let_58 _let_59) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (CONG (REFL :args (_let_18)) (SYMM _let_59) :args (APPLY_UF or)) (SYMM _let_58)) :args _let_57) (FALSE_INTRO _let_56))) :args _let_55)) :args _let_55)) :args (true _let_54)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_46))) (REFL :args ((not _let_45))) (REFL :args ((not _let_43))) (REFL :args (_let_47)) :args _let_51)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_53)) :args _let_53)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_9))) (REFL :args _let_52) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_9 (= P X) (= Q Y) (= R Z)))) :args ((or _let_6 _let_49))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ASSUME :args (_let_7))) :args ((or implies_3 _let_50))) (ASSUME :args (_let_10)) :args (_let_50 true implies_3)) :args (_let_49 true _let_6)) :args (_let_48 true _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_13 _let_42 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_45 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_21 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_43 false _let_27)) :args (_let_47 true _let_46 false _let_45 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_41) :args (_let_23 _let_34 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((implies X Y)))) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_40 (not modus_ponens)))) (ASSUME :args (modus_ponens)) :args (_let_40 false modus_ponens)) :args (_let_39 false _let_40)) :args (_let_38 false _let_36 true _let_35 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_21 _let_19 QUANTIFIERS_INST_E_MATCHING _let_32)) :args _let_29))) _let_28 :args (_let_24 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_13 _let_16 QUANTIFIERS_INST_E_MATCHING _let_32)) :args _let_29))) _let_28 :args (_let_20 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (skv_2 skv_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_17 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (skv_2 skv_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_14 false _let_27)) :args (false false _let_26 true _let_25 false _let_24 false _let_20 false _let_17 false _let_14)) :args (_let_10 r2 op_equiv r5 true substitution_of_equivalents op_and modus_ponens op_implies_or r4 r3 (=> op_or (forall ((X $$unsorted) (Y $$unsorted)) (= (not (and (not X) (not Y))) (or X Y)))) (=> op_implies_and (forall ((X $$unsorted) (Y $$unsorted)) (= (implies X Y) (not (and X (not Y)))))) (= or_1 (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies X (or X Y))))) r1 (= kn2 (forall ((P $$unsorted) (Q $$unsorted)) (is_a_theorem (implies (and P Q) P)))) (=> op_equiv (forall ((X $$unsorted) (Y $$unsorted)) (= (equiv X Y) (and (implies X Y) (implies Y X))))) (= equivalence_1 (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies (equiv X Y) (implies X Y))))) (= equivalence_3 (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies (implies X Y) (implies (implies Y X) (equiv X Y)))))) (= and_3 (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies X (implies Y (and X Y)))))) (= _let_9 cn1) op_implies_and (= cn3 (forall ((P $$unsorted)) (is_a_theorem (implies (implies (not P) P) P)))) _let_8 (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (is_a_theorem (implies (implies X Z) (implies (implies Y Z) (implies (or X Y) Z))))) or_3) _let_7 (= (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies (and X Y) Y))) and_2) (= modus_tollens (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies (implies (not Y) (not X)) (implies X Y))))) (= kn3 (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (is_a_theorem (implies (implies P Q) (implies (not (and Q R)) (not (and R P))))))) (= and_1 (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies (and X Y) X)))) (=> op_and (forall ((X $$unsorted) (Y $$unsorted)) (= (and X Y) (not (or (not X) (not Y)))))) _let_5 (= (forall ((P $$unsorted) (Q $$unsorted)) (is_a_theorem (implies P (implies (not P) Q)))) cn2) (= (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies (equiv X Y) (implies Y X)))) equivalence_2) (= (forall ((P $$unsorted) (Q $$unsorted)) (is_a_theorem (implies Q (or P Q)))) r2) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (implies X Y))) (is_a_theorem (implies (implies X _let_1) _let_1)))) implies_2) (= (forall ((P $$unsorted)) (is_a_theorem (implies P (and P P)))) kn1) (= or_2 (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies Y (or X Y))))) op_or (= substitution_of_equivalents (forall ((X $$unsorted) (Y $$unsorted)) (=> (is_a_theorem (equiv X Y)) (= Y X)))) (= r1 (forall ((P $$unsorted)) (is_a_theorem (implies (or P P) P)))) (= r3 (forall ((P $$unsorted) (Q $$unsorted)) (is_a_theorem (implies (or P Q) (or Q P))))) _let_3 (= (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies X (implies Y X)))) implies_1) _let_1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2.89/3.09 % SZS output end Proof for theBenchmark 2.89/3.09 EOF