0.02/0.09 % Problem : Vampire---4.8_4145 : TPTP v0.0.0. Released v0.0.0. 0.02/0.10 % Command : do_cvc5 %s %d 0.09/0.30 % Computer : n022.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 : 1440 0.09/0.30 % WCLimit : 180 0.09/0.30 % DateTime : Mon Jul 3 13:06:29 EDT 2023 0.09/0.30 % CPUTime : 0.15/0.40 %----Proving TH0 46.88/47.42 thf(a_type,type, 46.88/47.42 a: $tType ). 46.88/47.42 46.88/47.42 thf(cC,type, 46.88/47.42 cC: a > $o ). 46.88/47.42 46.88/47.42 thf(cTHM551_pme,conjecture, 46.88/47.42 ( ! [P: ( a > $o ) > $o] : 46.88/47.42 ( ( P @ cC ) 46.88/47.42 <= ( ! [E: a > $o] : 46.88/47.42 ( ~ ? [Xt: a] : ( E @ Xt ) 46.88/47.42 => ( P @ E ) ) 46.88/47.42 & ! [Y: a > $o,Xx: a,Z: a > $o] : 46.88/47.42 ( ( P @ Z ) 46.88/47.42 <= ( ( P @ Y ) 46.88/47.42 & ! [Xx_16: a] : 46.88/47.42 ( ( ( Xx_16 = Xx ) 46.88/47.42 | ( Y @ Xx_16 ) ) 46.88/47.42 <=> ( Z @ Xx_16 ) ) ) ) ) ) 46.88/47.42 <= ! [Xw: ( a > $o ) > $o] : 46.88/47.42 ( ( Xw @ cC ) 46.88/47.42 <= ( ! [Xr: a > $o,Xx: a] : 46.88/47.42 ( ( Xw @ Xr ) 46.88/47.42 => ( Xw 46.88/47.42 @ ^ [Xt: a] : 46.88/47.42 ( ( Xt = Xx ) 46.88/47.42 | ( Xr @ Xt ) ) ) ) 46.88/47.42 & ( Xw 46.88/47.42 @ ^ [Xx: a] : $false ) ) ) ) ). 46.88/47.42 46.88/47.42 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.PrUlXqfmj9/cvc5---1.0.5_4246.p... 46.88/47.42 (declare-sort $$unsorted 0) 46.88/47.42 (declare-sort tptp.a 0) 46.88/47.42 (declare-fun tptp.cC (tptp.a) Bool) 46.88/47.42 (assert (not (=> (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (= Xt Xx) (@ Xr Xt)))))) (@ Xw (lambda ((Xx tptp.a)) false))) (@ Xw tptp.cC))) (forall ((P (-> (-> tptp.a Bool) Bool))) (=> (and (forall ((E (-> tptp.a Bool))) (=> (not (exists ((Xt tptp.a)) (@ E Xt))) (@ P E))) (forall ((Y (-> tptp.a Bool)) (Xx tptp.a) (Z (-> tptp.a Bool))) (=> (and (@ P Y) (forall ((Xx_16 tptp.a)) (= (or (= Xx_16 Xx) (@ Y Xx_16)) (@ Z Xx_16)))) (@ P Z)))) (@ P tptp.cC)))))) 46.88/47.42 (set-info :filename cvc5---1.0.5_4246) 46.88/47.42 (check-sat-assuming ( true )) 46.88/47.42 ------- get file name : TPTP file name is 46.88/47.42 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4246.smt2... 46.88/47.42 --- Run --ho-elim --full-saturate-quant at 10... 46.88/47.42 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 46.88/47.42 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10... 46.88/47.42 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 46.88/47.42 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 46.88/47.42 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10... 46.88/47.42 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10... 46.88/47.42 % SZS status Theorem for 46.88/47.42 % SZS output start Proof for 46.88/47.42 ( 46.88/47.42 (let ((_let_1 (not (=> (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (= Xt Xx) (@ Xr Xt)))))) (@ Xw (lambda ((Xx tptp.a)) false))) (@ Xw tptp.cC))) (forall ((P (-> (-> tptp.a Bool) Bool))) (=> (and (forall ((E (-> tptp.a Bool))) (=> (not (exists ((Xt tptp.a)) (@ E Xt))) (@ P E))) (forall ((Y (-> tptp.a Bool)) (Xx tptp.a) (Z (-> tptp.a Bool))) (=> (and (@ P Y) (forall ((Xx_16 tptp.a)) (= (or (= Xx_16 Xx) (@ Y Xx_16)) (@ Z Xx_16)))) (@ P Z)))) (@ P tptp.cC))))))) (let ((_let_2 (forall ((Xt tptp.a)) (= (or (= Xt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xt)) (lambdaF_10 Xt))))) (let ((_let_3 (lambdaF_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_745))) (let ((_let_4 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_745))) (let ((_let_5 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_745))) (let ((_let_6 (or _let_5 _let_4))) (let ((_let_7 (= _let_6 _let_3))) (let ((_let_8 ((forall ((Xt tptp.a)) (= (lambdaF_10 Xt) (@ (lambda ((Xt tptp.a)) (or (= Xt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xt))) Xt)))))) (let ((_let_9 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_8) (REWRITE :args _let_8)))) (let ((_let_10 (forall ((Xx_16 tptp.a)) (= (@ lambdaF_10 Xx_16) (or (= Xx_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx_16)))))) (let ((_let_11 (not _let_7))) (let ((_let_12 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_10))) (let ((_let_13 (not _let_10))) (let ((_let_14 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13 _let_12))) (let ((_let_17 (forall ((Y (-> tptp.a Bool)) (Xx tptp.a) (Z (-> tptp.a Bool))) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y)) (not (forall ((Xx_16 tptp.a)) (= (@ Z Xx_16) (or (= Xx Xx_16) (@ Y Xx_16))))) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Z))))) (let ((_let_18 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.cC))) (let ((_let_19 (not _let_17))) (let ((_let_20 (forall ((E (-> tptp.a Bool))) (or (not (forall ((Xt tptp.a)) (not (@ E Xt)))) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E))))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_18))) (let ((_let_23 (forall ((P (-> (-> tptp.a Bool) Bool))) (or (not (forall ((E (-> tptp.a Bool))) (or (not (forall ((Xt tptp.a)) (not (@ E Xt)))) (@ P E)))) (not (forall ((Y (-> tptp.a Bool)) (Xx tptp.a) (Z (-> tptp.a Bool))) (or (not (@ P Y)) (not (forall ((Xx_16 tptp.a)) (= (@ Z Xx_16) (or (= Xx Xx_16) (@ Y Xx_16))))) (@ P Z)))) (@ P tptp.cC))))) (let ((_let_24 (not _let_22))) (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 (=>))) (let ((_let_29 (not))) (let ((_let_30 (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.cC) _let_18))))) (let ((_let_31 (_let_27))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_31)) :args _let_31) (CONG (REFL :args _let_31) (CONG (CONG (REFL :args (_let_21)) (REFL :args (_let_19)) _let_30 :args _let_26) :args _let_29) :args _let_28))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_23))) (REFL :args (_let_24)) :args _let_26)) (NOT_IMPLIES_ELIM2 _let_25) :args (_let_24 true _let_23)))) (let ((_let_33 (REFL :args (_let_22)))) (let ((_let_34 (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_10) _let_12))))) (let ((_let_35 (_let_13))) (let ((_let_36 (REFL :args _let_35))) (let ((_let_37 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_38 (CONG (THEORY_PREPROCESS :args ((= _let_37 _let_14))) :args _let_29))) (let ((_let_39 (_let_17))) (let ((_let_40 (or _let_15 _let_12))) (let ((_let_41 (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xr)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xt tptp.a)) (or (= Xx Xt) (@ Xr Xt)))))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_6))) (let ((_let_44 (not _let_43))) (let ((_let_45 (not _let_41))) (let ((_let_46 (or _let_45 _let_44 _let_18))) (let ((_let_47 (forall ((Xw (-> (-> tptp.a Bool) Bool))) (or (not (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ Xw Xr)) (@ Xw (lambda ((Xt tptp.a)) (or (= Xx Xt) (@ Xr Xt))))))) (not (@ Xw (lambda ((BOUND_VARIABLE_889 tptp.a)) false))) (@ Xw tptp.cC))))) (let ((_let_48 (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_6) _let_43))))) (let ((_let_49 (@))) (let ((_let_50 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_51 (_let_45))) (let ((_let_52 (REFL :args _let_51))) (let ((_let_53 (_let_47))) (let ((_let_54 (forall ((Xt tptp.a)) (not (@ lambdaF_6 Xt))))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_43))) (let ((_let_57 (_let_55))) (let ((_let_58 (REFL :args _let_57))) (let ((_let_59 (_let_20))) (let ((_let_60 (lambdaF_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_61 (forall ((BOUND_VARIABLE_889 tptp.a)) (not (lambdaF_6 BOUND_VARIABLE_889))))) (let ((_let_62 ((forall ((BOUND_VARIABLE_889 tptp.a)) (= (lambdaF_6 BOUND_VARIABLE_889) (@ (lambda ((BOUND_VARIABLE_889 tptp.a)) false) BOUND_VARIABLE_889)))))) (let ((_let_63 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_62) (REWRITE :args _let_62)))) (let ((_let_64 (@ lambdaF_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_51)) :args _let_51) (TRANS (REWRITE :args ((=> _let_45 (not (or (not _let_37) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xt tptp.a)) (or (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Xt) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xt))))))))) (CONG _let_52 (CONG (CONG _let_38 (TRANS (CONG _let_50 (MACRO_SR_PRED_INTRO :args ((= (lambda ((Xt tptp.a)) (or (= Xt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xt))) lambdaF_10))) :args _let_49) _let_34) :args _let_26) :args _let_29) :args _let_28)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) (REFL :args (_let_42)) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_18 _let_45 _let_44 (not _let_46)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 2)) _let_32 :args ((not _let_18) true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_43 _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_57)) :args _let_57) (TRANS (REWRITE :args ((=> _let_55 (not (not _let_64))))) (CONG _let_58 (THEORY_PREPROCESS :args ((= _let_64 _let_60))) :args _let_28)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) (REFL :args (_let_60)) :args _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_61))) _let_63 :args ((not _let_60) false _let_61)) :args (_let_54 true _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (lambdaF_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E) true))))) :args _let_59) (CONG (REFL :args _let_59) (CONG _let_58 _let_48 :args _let_26) :args _let_28))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_26)) :args ((or _let_20 _let_22))) _let_32 :args (_let_20 true _let_22)) :args (_let_56 false _let_20)) :args (_let_43 false _let_54 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_53) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING)) :args _let_53) (CONG (REFL :args _let_53) (CONG _let_52 (CONG (TRANS (CONG _let_50 (MACRO_SR_PRED_INTRO :args ((= (lambda ((BOUND_VARIABLE_889 tptp.a)) false) lambdaF_6))) :args _let_49) _let_48) :args _let_29) _let_30 :args _let_26) :args _let_28))) (NOT_IMPLIES_ELIM1 _let_25) :args (_let_46 false _let_47)) :args (_let_45 true _let_18 false _let_43 false _let_46)) :args (_let_42 true _let_41)))) (let ((_let_66 (=))) (let ((_let_67 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_745))) (let ((_let_68 (CONG (REFL :args (_let_5)) (THEORY_PREPROCESS :args ((= _let_67 _let_4))) :args _let_26))) (let ((_let_69 (@ lambdaF_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_745))) (let ((_let_70 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_9 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_745 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_70)) (CONG (REFL :args _let_70) (CONG _let_68 (REFL :args (_let_3)) :args _let_66) :args _let_28))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_35)) :args _let_35) (TRANS (REWRITE :args ((=> _let_13 (not (= _let_69 (or (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_745 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) _let_67)))))) (CONG _let_36 (CONG (TRANS (CONG (THEORY_PREPROCESS :args ((= _let_69 _let_3))) _let_68 :args _let_66) (REWRITE :args ((= _let_3 _let_6)))) :args _let_29) :args _let_28)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_10))) (REFL :args (_let_11)) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_12 _let_15 _let_13 (not _let_16)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 1)) _let_65 :args ((not _let_12) true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_26)) :args ((or _let_14 _let_40))) _let_65 :args (_let_14 true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_39) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 lambdaF_10 QUANTIFIERS_INST_ENUM)) :args _let_39)) (CONG (REFL :args _let_39) (CONG _let_38 _let_36 _let_34 :args _let_26) :args _let_28))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 1)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_17))) :args _let_26)) :args ((or _let_17 _let_22))) _let_32 :args (_let_17 true _let_22)) :args (_let_16 false _let_17)) :args (_let_13 true _let_12 false _let_14 false _let_16)) :args (_let_11 true _let_10)) _let_9 :args (false true _let_7 false _let_2)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 46.88/47.42 ) 46.88/47.42 % SZS output end Proof for 46.88/47.42 % cvc5---1.0.5 exiting 46.88/47.42 % cvc5---1.0.5 exiting 46.88/47.42 EOF