0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : do_cvc5 %s %d 0.12/0.34 % Computer : n022.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 02:14:16 EDT 2022 0.12/0.34 % CPUTime : 0.19/0.47 %----Proving TF0_NAR, FOF, or CNF 0.38/0.61 ------- cvc5-fof casc J11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 0.38/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 0.38/0.61 % SZS status Theorem for theBenchmark 0.38/0.61 % SZS output start Proof for theBenchmark 0.38/0.61 (let ((_let_1 (forall ((P $$unsorted) (Q $$unsorted)) (is_a_theorem (implies (or P Q) (or Q P)))))) (let ((_let_2 (= r3 _let_1))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies Y (or X Y)))))) (let ((_let_4 (= or_2 _let_3))) (let ((_let_5 (forall ((P $$unsorted) (Q $$unsorted)) (is_a_theorem (implies Q (or P Q)))))) (let ((_let_6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (is_a_theorem (implies (implies X Z) (implies (implies Y Z) (implies (or X Y) Z))))))) (let ((_let_7 (= _let_6 or_3))) (let ((_let_8 (= modus_ponens (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (is_a_theorem X) (is_a_theorem (implies X Y))) (is_a_theorem Y)))))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies X (or X Y)))))) (let ((_let_10 (= or_1 _let_9))) (let ((_let_11 (not r3))) (let ((_let_12 (or skv_3 skv_2))) (let ((_let_13 (implies (or skv_2 skv_3) _let_12))) (let ((_let_14 (is_a_theorem _let_13))) (let ((_let_15 (implies skv_3 _let_12))) (let ((_let_16 (is_a_theorem _let_15))) (let ((_let_17 (implies _let_15 _let_13))) (let ((_let_18 (is_a_theorem _let_17))) (let ((_let_19 (not _let_18))) (let ((_let_20 (not _let_16))) (let ((_let_21 (or _let_20 _let_19 _let_14))) (let ((_let_22 (not _let_14))) (let ((_let_23 (not _let_1))) (let ((_let_24 (_let_23))) (let ((_let_25 (_let_9))) (let ((_let_26 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (is_a_theorem X)) (not (is_a_theorem (implies X Y))) (is_a_theorem Y))))) (let ((_let_27 (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_26 (not modus_ponens)))) (ASSUME :args (modus_ponens)) :args (_let_26 false modus_ponens)))) (let ((_let_28 (_let_26))) (let ((_let_29 ((implies X Y)))) (let ((_let_30 (ASSUME :args _let_28))) (let ((_let_31 (implies skv_2 _let_12))) (let ((_let_32 (is_a_theorem (implies _let_31 _let_17)))) (let ((_let_33 (not _let_32))) (let ((_let_34 (is_a_theorem _let_31))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_18))) (let ((_let_37 (_let_5))) (let ((_let_38 (_let_6))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_14 _let_20 _let_19 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_33 _let_35 _let_18 (not _let_36)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_38) :args (skv_2 skv_3 _let_12 QUANTIFIERS_INST_E_MATCHING ((implies (or X Y) Z)))) :args _let_38)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ASSUME :args (_let_7))) (ASSUME :args (or_3)) :args (_let_6 false or_3)) :args (_let_32 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_37) :args (skv_3 skv_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((or P Q)))) :args _let_37)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_5 (= Q Y) (= P X)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ASSUME :args (_let_4))) :args ((or _let_3 (not or_2)))) (ASSUME :args (or_2)) :args (_let_3 false or_2)) :args (_let_5 false _let_3)) :args (_let_34 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_31 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_36 false _let_26)) :args (_let_18 false _let_32 false _let_34 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_15 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_21 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_25) :args (skv_3 skv_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((or X Y)))) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ASSUME :args (_let_10))) :args ((or _let_9 (not or_1)))) (ASSUME :args (or_1)) :args (_let_9 false or_1)) :args (_let_16 false _let_9)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_24)) :args _let_24)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_1))) (REFL :args (_let_22)) :args (OR))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ASSUME :args (_let_2))) (ASSUME :args (_let_11)) :args (_let_23 true r3)) :args (_let_22 true _let_1)) :args (false false _let_18 false _let_21 false _let_16 true _let_14)) :args (_let_11 op_implies_or op_and implies_1 op_equiv and_1 equivalence_1 equivalence_2 modus_tollens modus_ponens and_3 or_3 implies_3 true substitution_of_equivalents implies_2 and_2 (=> op_or (forall ((X $$unsorted) (Y $$unsorted)) (= (not (and (not X) (not Y))) (or X Y)))) (=> op_implies_and (forall ((X $$unsorted) (Y $$unsorted)) (= (implies X Y) (not (and X (not Y)))))) _let_10 (= kn2 (forall ((P $$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 $$unsorted)) (is_a_theorem (implies X (implies Y (and X Y)))))) (= (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (is_a_theorem (implies (implies P Q) (implies (implies Q R) (implies P R))))) cn1) op_implies_and (= cn3 (forall ((P $$unsorted)) (is_a_theorem (implies (implies (not P) P) P)))) _let_8 _let_7 (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (is_a_theorem (implies (implies X Y) (implies (implies Y Z) (implies X Z))))) implies_3) (= (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 $$unsorted)) (is_a_theorem (implies (implies P Q) (implies (not (and Q R)) (not (and R P))))))) or_1 (= and_1 (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies (and X Y) X)))) (=> op_and (forall ((X $$unsorted) (Y $$unsorted)) (= (and X Y) (not (or (not X) (not Y)))))) (= (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (is_a_theorem (implies (implies Q R) (implies (or P Q) (or P R))))) r5) (= (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) (= _let_5 r2) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (implies X Y))) (is_a_theorem (implies (implies X _let_1) _let_1)))) implies_2) equivalence_3 (= (forall ((P $$unsorted)) (is_a_theorem (implies P (and P P)))) kn1) _let_4 op_or (= substitution_of_equivalents (forall ((X $$unsorted) (Y $$unsorted)) (=> (is_a_theorem (equiv X Y)) (= Y X)))) (= r1 (forall ((P $$unsorted)) (is_a_theorem (implies (or P P) P)))) _let_2 or_2 (= r4 (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (is_a_theorem (implies (or P (or Q R)) (or Q (or P R)))))) (= (forall ((X $$unsorted) (Y $$unsorted)) (is_a_theorem (implies X (implies Y X)))) implies_1) (=> op_implies_or (forall ((X $$unsorted) (Y $$unsorted)) (= (or (not X) Y) (implies X Y)))))))))))))))))))))))))))))))))))))))))))) 0.38/0.61 % SZS output end Proof for theBenchmark 0.38/0.61 EOF