0.06/0.12 % Problem : Vampire---4.8_11632 : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : do_cvc5 %s %d 0.14/0.34 % Computer : n012.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 1440 0.14/0.34 % WCLimit : 180 0.14/0.34 % DateTime : Mon Jul 3 13:00:07 EDT 2023 0.14/0.34 % CPUTime : 0.20/0.48 %----Proving TH0 18.99/19.23 thf(in_type,type, 18.99/19.23 in: $i > $i > $o ). 18.99/19.23 18.99/19.23 thf(dsetconstr_type,type, 18.99/19.23 dsetconstr: $i > ( $i > $o ) > $i ). 18.99/19.23 18.99/19.23 thf(dsetconstrER_type,type, 18.99/19.23 dsetconstrER: $o ). 18.99/19.23 18.99/19.23 thf(dsetconstrER,definition, 18.99/19.23 ( dsetconstrER 18.99/19.23 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 18.99/19.23 ( ( in @ Xx 18.99/19.23 @ ( dsetconstr @ A 18.99/19.23 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 18.99/19.23 => ( Xphi @ Xx ) ) ) ) ). 18.99/19.23 18.99/19.23 thf(kpair_type,type, 18.99/19.23 kpair: $i > $i > $i ). 18.99/19.23 18.99/19.23 thf(cartprod_type,type, 18.99/19.23 cartprod: $i > $i > $i ). 18.99/19.23 18.99/19.23 thf(setukpairinjL_type,type, 18.99/19.23 setukpairinjL: $o ). 18.99/19.23 18.99/19.23 thf(setukpairinjL,definition, 18.99/19.23 ( setukpairinjL 18.99/19.23 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 18.99/19.23 ( ( ( kpair @ Xx @ Xy ) 18.99/19.23 = ( kpair @ Xz @ Xu ) ) 18.99/19.23 => ( Xx = Xz ) ) ) ) ). 18.99/19.23 18.99/19.23 thf(setukpairinjR_type,type, 18.99/19.23 setukpairinjR: $o ). 18.99/19.23 18.99/19.23 thf(setukpairinjR,definition, 18.99/19.23 ( setukpairinjR 18.99/19.23 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 18.99/19.23 ( ( ( kpair @ Xx @ Xy ) 18.99/19.23 = ( kpair @ Xz @ Xu ) ) 18.99/19.23 => ( Xy = Xu ) ) ) ) ). 18.99/19.23 18.99/19.23 thf(dpsetconstr_type,type, 18.99/19.23 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ). 18.99/19.23 18.99/19.23 thf(dpsetconstr,definition, 18.99/19.23 ( dpsetconstr 18.99/19.23 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] : 18.99/19.23 ( dsetconstr @ ( cartprod @ A @ B ) 18.99/19.23 @ ^ [Xu: $i] : 18.99/19.23 ? [Xx: $i] : 18.99/19.23 ( ( in @ Xx @ A ) 18.99/19.23 & ? [Xy: $i] : 18.99/19.23 ( ( in @ Xy @ B ) 18.99/19.23 & ( Xphi @ Xx @ Xy ) 18.99/19.23 & ( Xu 18.99/19.23 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ). 18.99/19.23 18.99/19.23 thf(dpsetconstrER,conjecture, 18.99/19.23 ( ( setukpairinjL 18.99/19.23 => ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] : 18.99/19.23 ( ( in @ ( kpair @ Xx @ Xy ) 18.99/19.23 @ ( dpsetconstr @ A @ B 18.99/19.23 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) 18.99/19.23 => ( Xphi @ Xx @ Xy ) ) 18.99/19.23 <= setukpairinjR ) ) 18.99/19.23 <= dsetconstrER ) ). 18.99/19.23 18.99/19.23 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.msjk3UugbU/cvc5---1.0.5_11794.p... 18.99/19.23 (declare-sort $$unsorted 0) 18.99/19.23 (declare-fun tptp.in ($$unsorted $$unsorted) Bool) 18.99/19.23 (declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted) 18.99/19.23 (declare-fun tptp.dsetconstrER () Bool) 18.99/19.23 (assert (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))) 18.99/19.23 (declare-fun tptp.kpair ($$unsorted $$unsorted) $$unsorted) 18.99/19.23 (declare-fun tptp.cartprod ($$unsorted $$unsorted) $$unsorted) 18.99/19.23 (declare-fun tptp.setukpairinjL () Bool) 18.99/19.23 (assert (= tptp.setukpairinjL (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xx Xz))))) 18.99/19.23 (declare-fun tptp.setukpairinjR () Bool) 18.99/19.23 (assert (= tptp.setukpairinjR (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xy Xu))))) 18.99/19.23 (declare-fun tptp.dpsetconstr ($$unsorted $$unsorted (-> $$unsorted $$unsorted Bool)) $$unsorted) 18.99/19.23 (assert (= tptp.dpsetconstr (lambda ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.dsetconstr (@ (@ tptp.cartprod A) B)) (lambda ((Xu $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) B) (@ (@ Xphi Xx) Xy) (= Xu (@ (@ tptp.kpair Xx) Xy))))))))))) 18.99/19.23 (assert (not (=> tptp.dsetconstrER (=> tptp.setukpairinjL (=> tptp.setukpairinjR (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy)))))))) 18.99/19.23 (set-info :filename cvc5---1.0.5_11794) 18.99/19.23 (check-sat-assuming ( true )) 18.99/19.23 ------- get file name : TPTP file name is 18.99/19.23 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11794.smt2... 18.99/19.23 --- Run --ho-elim --full-saturate-quant at 10... 18.99/19.23 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 18.99/19.23 % SZS status Theorem for 18.99/19.23 % SZS output start Proof for 18.99/19.23 ( 18.99/19.23 (let ((_let_1 (not (=> tptp.dsetconstrER (=> tptp.setukpairinjL (=> tptp.setukpairinjR (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy))))))))) (let ((_let_2 (= tptp.dpsetconstr (lambda ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.dsetconstr (@ (@ tptp.cartprod A) B)) (lambda ((Xu $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) B) (@ (@ Xphi Xx) Xy) (= Xu (@ (@ tptp.kpair Xx) Xy)))))))))))) (let ((_let_3 (= tptp.setukpairinjR (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xy Xu)))))) (let ((_let_4 (= tptp.setukpairinjL (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xx Xz)))))) (let ((_let_5 (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx)))))) (let ((_let_6 (ho_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_7 (ho_14 (ho_13 k_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_8 (ho_15 _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_9 (= _let_8 _let_6))) (let ((_let_10 (ho_6 k_5 _let_6))) (let ((_let_11 (ho_4 _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13290))) (let ((_let_12 (ho_6 k_5 _let_8))) (let ((_let_13 (ho_4 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13290))) (let ((_let_14 (= _let_12 termITE_352))) (let ((_let_15 (ho_4 termITE_352 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4801))) (let ((_let_16 (ho_4 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4801))) (let ((_let_17 (= _let_16 _let_15))) (let ((_let_18 (forall ((z $$unsorted)) (= (ho_4 (ho_15 (ho_14 (ho_13 k_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22) z) (ho_4 termITE_352 z))))) (let ((_let_19 (= _let_8 termITE_352))) (let ((_let_20 (not _let_18))) (let ((_let_21 (or _let_20 _let_19))) (let ((_let_22 (ho_9 (ho_8 k_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_23 (ho_18 k_17 _let_22))) (let ((_let_24 (ho_9 (ho_8 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_25 (ho_10 k_11 _let_24))) (let ((_let_26 (ho_4 _let_25 (ho_19 _let_23 _let_8)))) (let ((_let_27 (ho_4 _let_25 (ho_19 _let_23 _let_12)))) (let ((_let_28 (not _let_14))) (let ((_let_29 (ho_4 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4801))) (let ((_let_30 (= _let_16 _let_29))) (let ((_let_31 (not _let_16))) (let ((_let_32 (_let_17))) (let ((_let_33 (forall ((BOUND_VARIABLE_940 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_917 $$unsorted)) (= (ho_4 (ho_6 k_5 BOUND_VARIABLE_940) BOUND_VARIABLE_917) (ho_4 BOUND_VARIABLE_940 BOUND_VARIABLE_917))))) (let ((_let_34 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_35 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_36 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_37 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_38 (forall ((u |u_(-> $$unsorted $$unsorted $$unsorted)|) (e |u_(-> $$unsorted $$unsorted)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_39 (forall ((x |u_(-> $$unsorted $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_40 (forall ((u |u_(-> $$unsorted $$unsorted)|) (e $$unsorted) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_41 (forall ((x |u_(-> $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_42 (forall ((u |u_(-> $$unsorted _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_14 v ii) (ite (= i ii) e (ho_14 u ii)))))))))) (let ((_let_43 (forall ((x |u_(-> $$unsorted _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> $$unsorted _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_14 x z) (ho_14 y z)))) (= x y))))) (let ((_let_44 (forall ((u |u_(-> $$unsorted $$unsorted _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> $$unsorted _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_13 v ii) (ite (= i ii) e (ho_13 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> $$unsorted $$unsorted _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_13 x z) (ho_13 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_10 v ii) (ite (= i ii) e (ho_10 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_10 x z) (ho_10 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (e $$unsorted) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_19 v ii) (ite (= i ii) e (ho_19 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (y |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_19 x z) (ho_19 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> $$unsorted $$unsorted Bool)|)) (= (ho_15 v ii) (ite (= i ii) e (ho_15 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> $$unsorted $$unsorted Bool)|)) (= (ho_15 x z) (ho_15 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> $$unsorted _u_(-> $$unsorted Bool)_ $$unsorted)|) (e |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted _u_(-> $$unsorted Bool)_ $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_18 v ii) (ite (= i ii) e (ho_18 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> $$unsorted _u_(-> $$unsorted Bool)_ $$unsorted)|) (y |u_(-> $$unsorted _u_(-> $$unsorted Bool)_ $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_18 x z) (ho_18 y z)))) (= x y))))) (let ((_let_54 (forall ((BOUND_VARIABLE_896 $$unsorted) (BOUND_VARIABLE_897 $$unsorted) (BOUND_VARIABLE_965 |u_(-> $$unsorted $$unsorted Bool)|) (BOUND_VARIABLE_899 $$unsorted)) (= (ho_4 (ho_15 (ho_14 (ho_13 k_12 BOUND_VARIABLE_896) BOUND_VARIABLE_897) BOUND_VARIABLE_965) BOUND_VARIABLE_899) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_723 $$unsorted)) (or (not (ho_4 (ho_10 k_11 Xx) BOUND_VARIABLE_896)) (not (ho_4 (ho_10 k_11 BOUND_VARIABLE_723) BOUND_VARIABLE_897)) (not (ho_4 (ho_10 BOUND_VARIABLE_965 Xx) BOUND_VARIABLE_723)) (not (= BOUND_VARIABLE_899 (ho_9 (ho_8 k_7 Xx) BOUND_VARIABLE_723)))))))))) (let ((_let_55 (and (forall ((BOUND_VARIABLE_896 $$unsorted) (BOUND_VARIABLE_897 $$unsorted) (BOUND_VARIABLE_898 (-> $$unsorted $$unsorted Bool)) (BOUND_VARIABLE_899 $$unsorted)) (= (ll_2 BOUND_VARIABLE_896 BOUND_VARIABLE_897 BOUND_VARIABLE_898 BOUND_VARIABLE_899) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_723 $$unsorted)) (or (not (@ (@ tptp.in Xx) BOUND_VARIABLE_896)) (not (@ (@ tptp.in BOUND_VARIABLE_723) BOUND_VARIABLE_897)) (not (@ (@ BOUND_VARIABLE_898 Xx) BOUND_VARIABLE_723)) (not (= (@ (@ tptp.kpair Xx) BOUND_VARIABLE_723) BOUND_VARIABLE_899))))))) (forall ((BOUND_VARIABLE_916 (-> $$unsorted Bool)) (BOUND_VARIABLE_917 $$unsorted)) (= (@ BOUND_VARIABLE_916 BOUND_VARIABLE_917) (ll_3 BOUND_VARIABLE_916 BOUND_VARIABLE_917)))))) (let ((_let_56 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (PREPROCESS_LEMMA :args (_let_55)) (PREPROCESS :args ((= _let_55 (and _let_54 _let_33))))) (PREPROCESS :args ((and _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34)))) :args ((and _let_54 _let_33 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34))))) (let ((_let_57 (AND_ELIM _let_56 :args (1)))) (let ((_let_58 (_let_33))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_57 :args (_let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4801 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_58))) _let_57 :args (_let_30 false _let_33)))) (let ((_let_60 (not _let_30))) (let ((_let_61 (_let_30))) (let ((_let_62 (or))) (let ((_let_63 (not _let_29))) (let ((_let_64 (not _let_15))) (let ((_let_65 (_let_28))) (let ((_let_66 (REFL :args _let_65))) (let ((_let_67 (and _let_14 _let_64))) (let ((_let_68 (ASSUME :args (_let_64)))) (let ((_let_69 (APPLY_UF ho_4))) (let ((_let_70 (ASSUME :args (_let_14)))) (let ((_let_71 (SYMM (SYMM _let_70)))) (let ((_let_72 (CONG _let_71 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4801)) :args _let_69))) (let ((_let_73 (and _let_14 _let_15))) (let ((_let_74 (ASSUME :args (_let_15)))) (let ((_let_75 (_let_20))) (let ((_let_76 (AND_ELIM _let_56 :args (20)))) (let ((_let_77 (_let_35))) (let ((_let_78 (ho_4 _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_79 (not _let_26))) (let ((_let_80 (or _let_79 _let_78))) (let ((_let_81 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1019 |u_(-> $$unsorted $$unsorted Bool)|) (Xx $$unsorted) (Xy $$unsorted)) (or (not (ho_4 (ho_10 k_11 (ho_9 (ho_8 k_7 Xx) Xy)) (ho_19 (ho_18 k_17 (ho_9 (ho_8 k_16 A) B)) (ho_15 (ho_14 (ho_13 k_12 A) B) BOUND_VARIABLE_1019)))) (ho_4 (ho_10 BOUND_VARIABLE_1019 Xx) Xy))))) (let ((_let_82 (not _let_80))) (let ((_let_83 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (or (not (= (ho_9 (ho_8 k_7 Xz) Xu) (ho_9 (ho_8 k_7 Xx) Xy))) (= Xy Xu))))) (let ((_let_84 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (or (not (= (ho_9 (ho_8 k_7 Xz) Xu) (ho_9 (ho_8 k_7 Xx) Xy))) (= Xx Xz))))) (let ((_let_85 (forall ((A $$unsorted) (BOUND_VARIABLE_1065 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (or (not (ho_4 (ho_10 k_11 Xx) (ho_19 (ho_18 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((_let_152 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_151 :args (_let_7 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_ENUM)) :args (_let_50)))) _let_151 :args (_let_150 false _let_50)))) (let ((_let_153 (_let_148))) (let ((_let_154 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_152) :args (_let_150)) (REWRITE :args ((=> _let_150 (not (not (forall ((ii |u_(-> $$unsorted $$unsorted Bool)|)) (let ((_let_1 (ho_14 (ho_13 k_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (= (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74 ii) (ite (= ii SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22) (ho_15 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22) (ho_15 _let_1 ii)))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_150) _let_149))) (REFL :args _let_153) :args _let_62)) _let_152 :args (_let_148 true _let_149)))) (let ((_let_155 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_154 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_ENUM)) :args _let_153))) _let_154 :args (_let_142 false _let_148)))) (let ((_let_156 (forall ((ii |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_15 (ho_14 (ho_13 k_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (= (ite (= ii _let_1) _let_1 (ho_6 k_5 ii)) (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130 ii)))))) (let ((_let_157 (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_15 (ho_14 (ho_13 k_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (= (ho_6 v ii) (ite (= ii _let_1) _let_1 (ho_6 k_5 ii))))))))) (let ((_let_158 (not _let_157))) (let ((_let_159 (AND_ELIM _let_56 :args (19)))) (let ((_let_160 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_159 :args (k_5 _let_8 _let_8 QUANTIFIERS_INST_ENUM)) :args (_let_36)))) _let_159 :args (_let_158 false _let_36)))) (let ((_let_161 (_let_156))) (let ((_let_162 (REFL :args _let_161))) (let ((_let_163 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_160) :args (_let_158)) (REWRITE :args ((=> _let_158 (not (not (forall ((ii |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_15 (ho_14 (ho_13 k_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (= (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130 ii) (ite (= ii _let_1) _let_1 (ho_6 k_5 ii)))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_158) _let_157))) _let_162 :args _let_62)) _let_160 :args (_let_156 true _let_157)))) (let ((_let_164 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_163 :args (_let_8 QUANTIFIERS_INST_ENUM)) :args _let_161))) _let_163 :args (_let_143 false _let_156)))) (let ((_let_165 (=))) (let ((_let_166 (ite _let_9 _let_8 _let_10))) (let ((_let_167 (MACRO_SR_PRED_INTRO :args ((= _let_166 termITE_493))))) (let ((_let_168 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_163 :args (_let_6 QUANTIFIERS_INST_ENUM)) :args _let_161)) (CONG _let_162 (CONG (REFL :args (_let_144)) _let_167 :args _let_165) :args (=>)))) _let_163 :args (_let_145 false _let_156)))) (let ((_let_169 ((ite _let_9 (= termITE_493 _let_8) (= termITE_493 _let_10))))) (let ((_let_170 (not _let_146))) (let ((_let_171 (not _let_145))) (let ((_let_172 (not _let_143))) (let ((_let_173 (not _let_9))) (let ((_let_174 (not _let_142))) (let ((_let_175 (REFL :args (_let_173)))) (let ((_let_176 (not (= _let_10 termITE_493)))) (let ((_let_177 (ASSUME :args (_let_146)))) (let ((_let_178 (ASSUME :args (_let_139)))) (let ((_let_179 (ASSUME :args _let_65))) (let ((_let_180 (APPLY_UF ho_6))) (let ((_let_181 (ASSUME :args (_let_9)))) (let ((_let_182 (SYMM _let_181))) (let ((_let_183 (REFL :args (k_5)))) (let ((_let_184 (_let_140))) (let ((_let_185 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_184)) :args _let_184)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_140) _let_137))) (REFL :args (_let_138)) :args _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_141)) :args ((or _let_139 _let_140 (not _let_141)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_155 _let_178 _let_177 (MODUS_PONENS (AND_INTRO _let_179 _let_181 _let_128 _let_164 _let_168) (SCOPE (FALSE_ELIM (TRANS (CONG (CONG _let_183 _let_182 :args _let_180) (TRANS (SYMM _let_168) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130)) _let_182 :args _let_180) (SYMM _let_164) (SYMM _let_129)) :args _let_165) (FALSE_INTRO _let_179))) :args (_let_28 _let_9 _let_19 _let_143 _let_145)))) :args (_let_142 _let_9 _let_143 _let_19 _let_28 _let_139 _let_145 _let_146)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_176)))) (TRUE_INTRO (TRANS (SYMM _let_178) _let_155 (SYMM (TRANS (SYMM _let_177) _let_155)))))) :args (_let_142 _let_139 _let_146 _let_176)) :args ((not (and _let_142 _let_9 _let_143 _let_19 _let_28 _let_139 _let_145 _let_146)) SB_LITERAL))) (CONG (REFL :args (_let_174)) _let_175 (REFL :args (_let_172)) _let_127 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_14))) (REFL :args (_let_147)) (REFL :args (_let_171)) (REFL :args (_let_170)) :args _let_62)) :args ((or _let_174 _let_173 _let_172 _let_14 _let_126 _let_147 _let_171 _let_170))) (MACRO_RESOLUTION_TRUST (ITE_ELIM1 (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (REMOVE_TERM_FORMULA_AXIOM :args (_let_166)) _let_167 :args _let_169) (REWRITE :args _let_169))) _let_134 :args (_let_146 false _let_9)) (MACRO_RESOLUTION_TRUST (ITE_ELIM1 _let_133) _let_134 :args (_let_19 false _let_9)) _let_134 _let_130 _let_168 _let_164 _let_155 :args (_let_147 false _let_146 false _let_19 false _let_9 true _let_14 false _let_145 false _let_143 false _let_142)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (_let_8 _let_10 QUANTIFIERS_INST_ENUM)) :args _let_77)) _let_76 :args (_let_141 false _let_35)) :args (_let_140 true _let_139 false _let_141)) :args (_let_138 true _let_137)))) (let ((_let_186 (= _let_135 _let_13))) (let ((_let_187 (not _let_135))) (let ((_let_188 (_let_136))) (let ((_let_189 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_57 :args (_let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13290 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_58))) _let_57 :args (_let_186 false _let_33)))) (let ((_let_190 (not _let_186))) (let ((_let_191 (_let_186))) (let ((_let_192 (not _let_13))) (let ((_let_193 (not _let_11))) (let ((_let_194 (and _let_9 _let_193))) (let ((_let_195 (ASSUME :args (_let_193)))) (let ((_let_196 (CONG (CONG _let_183 (SYMM _let_182) :args _let_180) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13290)) :args _let_69))) (let ((_let_197 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_194)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_195 _let_181) (SCOPE (FALSE_ELIM (TRANS _let_196 (FALSE_INTRO _let_195))) :args (_let_193 _let_9))) :args (_let_9 _let_193))) :args (true _let_194)) (CONG _let_175 (MACRO_SR_PRED_INTRO :args ((= (not _let_193) _let_11))) (REFL :args (_let_192)) :args _let_62)) _let_134 (REORDERING (CNF_EQUIV_POS1 :args _let_191) :args ((or _let_187 _let_13 _let_190))) _let_189 (CNF_EQUIV_NEG2 :args _let_188) _let_185 :args (_let_187 false _let_9 false _let_13 false _let_186 true _let_11 true _let_136)))) (let ((_let_198 (and _let_9 _let_11))) (let ((_let_199 (ASSUME :args (_let_11)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_198)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_199 _let_181) (SCOPE (TRUE_ELIM (TRANS _let_196 (TRUE_INTRO _let_199))) :args (_let_11 _let_9))) :args (_let_9 _let_11))) :args (true _let_198)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_191) :args ((or _let_135 _let_192 _let_190))) _let_197 _let_189 :args (_let_192 true _let_135 false _let_186)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_188) :args ((or _let_135 _let_11 _let_136))) _let_197 _let_185 :args (_let_11 true _let_135 true _let_136)) _let_134 :args (false true _let_13 false _let_11 false _let_9)) :args (_let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 18.99/19.24 ) 18.99/19.24 % SZS output end Proof for 18.99/19.24 % cvc5---1.0.5 exiting 18.99/19.24 % cvc5---1.0.5 exiting 18.99/19.24 EOF