TSTP Solution File: NUM666^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:46:27 EDT 2023
% Result : Theorem 7.11s 7.30s
% Output : Proof 7.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% 0.08/0.15 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n009.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Aug 25 14:36:51 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.51 %----Proving TH0
% 7.11/7.30 %------------------------------------------------------------------------------
% 7.11/7.30 % File : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% 7.11/7.30 % Domain : Number Theory
% 7.11/7.30 % Problem : Landau theorem 16d
% 7.11/7.30 % Version : Especial.
% 7.11/7.30 % English : some (lambda u.diffprop x z u)
% 7.11/7.30
% 7.11/7.30 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 7.11/7.30 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 7.11/7.30 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 7.11/7.30 % Source : [Bro09]
% 7.11/7.30 % Names : satz16d [Lan30]
% 7.11/7.30
% 7.11/7.30 % Status : Theorem
% 7.11/7.30 % : Without extensionality : Theorem
% 7.11/7.30 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.00 v4.0.0, 0.33 v3.7.0
% 7.11/7.30 % Syntax : Number of formulae : 13 ( 1 unt; 8 typ; 0 def)
% 7.11/7.30 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 7.11/7.30 % Maximal formula atoms : 5 ( 2 avg)
% 7.11/7.30 % Number of connectives : 27 ( 0 ~; 0 |; 0 &; 24 @)
% 7.11/7.30 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 7.11/7.30 % Maximal formula depth : 11 ( 6 avg)
% 7.11/7.30 % Number of types : 2 ( 1 usr)
% 7.11/7.30 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 7.11/7.30 % Number of symbols : 7 ( 7 usr; 3 con; 0-3 aty)
% 7.11/7.30 % Number of variables : 9 ( 4 ^; 5 !; 0 ?; 9 :)
% 7.11/7.30 % SPC : TH0_THM_NEQ_NAR
% 7.11/7.30
% 7.11/7.30 % Comments :
% 7.11/7.30 %------------------------------------------------------------------------------
% 7.11/7.30 thf(nat_type,type,
% 7.11/7.30 nat: $tType ).
% 7.11/7.30
% 7.11/7.30 thf(x,type,
% 7.11/7.30 x: nat ).
% 7.11/7.30
% 7.11/7.30 thf(y,type,
% 7.11/7.30 y: nat ).
% 7.11/7.30
% 7.11/7.30 thf(z,type,
% 7.11/7.30 z: nat ).
% 7.11/7.30
% 7.11/7.30 thf(some,type,
% 7.11/7.30 some: ( nat > $o ) > $o ).
% 7.11/7.30
% 7.11/7.30 thf(diffprop,type,
% 7.11/7.30 diffprop: nat > nat > nat > $o ).
% 7.11/7.30
% 7.11/7.30 thf(m,axiom,
% 7.11/7.30 ( some
% 7.11/7.30 @ ^ [Xu: nat] : ( diffprop @ x @ y @ Xu ) ) ).
% 7.11/7.30
% 7.11/7.30 thf(moreis,type,
% 7.11/7.30 moreis: nat > nat > $o ).
% 7.11/7.30
% 7.11/7.30 thf(n,axiom,
% 7.11/7.30 moreis @ y @ z ).
% 7.11/7.30
% 7.11/7.30 thf(lessis,type,
% 7.11/7.30 lessis: nat > nat > $o ).
% 7.11/7.30
% 7.11/7.30 thf(satz16a,axiom,
% 7.11/7.30 ! [Xx: nat,Xy: nat,Xz: nat] :
% 7.11/7.30 ( ( lessis @ Xx @ Xy )
% 7.11/7.30 => ( ( some
% 7.11/7.30 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xy @ Xv ) )
% 7.11/7.30 => ( some
% 7.11/7.30 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) ).
% 7.11/7.30
% 7.11/7.30 thf(satz13,axiom,
% 7.11/7.30 ! [Xx: nat,Xy: nat] :
% 7.11/7.30 ( ( moreis @ Xx @ Xy )
% 7.11/7.30 => ( lessis @ Xy @ Xx ) ) ).
% 7.11/7.30
% 7.11/7.30 thf(satz16d,conjecture,
% 7.11/7.30 ( some
% 7.11/7.30 @ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) ) ).
% 7.11/7.30
% 7.11/7.30 %------------------------------------------------------------------------------
% 7.11/7.30 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ralJiKkfK7/cvc5---1.0.5_9933.p...
% 7.11/7.30 (declare-sort $$unsorted 0)
% 7.11/7.30 (declare-sort tptp.nat 0)
% 7.11/7.30 (declare-fun tptp.x () tptp.nat)
% 7.11/7.30 (declare-fun tptp.y () tptp.nat)
% 7.11/7.30 (declare-fun tptp.z () tptp.nat)
% 7.11/7.30 (declare-fun tptp.some ((-> tptp.nat Bool)) Bool)
% 7.11/7.30 (declare-fun tptp.diffprop (tptp.nat tptp.nat tptp.nat) Bool)
% 7.11/7.30 (assert (@ tptp.some (lambda ((Xu tptp.nat)) (@ (@ (@ tptp.diffprop tptp.x) tptp.y) Xu))))
% 7.11/7.30 (declare-fun tptp.moreis (tptp.nat tptp.nat) Bool)
% 7.11/7.30 (assert (@ (@ tptp.moreis tptp.y) tptp.z))
% 7.11/7.30 (declare-fun tptp.lessis (tptp.nat tptp.nat) Bool)
% 7.11/7.30 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (@ (@ tptp.lessis Xx) Xy) (=> (@ tptp.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xz) Xy) Xv))) (@ tptp.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xz) Xx) Xv)))))))
% 7.11/7.30 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.moreis Xx) Xy) (@ (@ tptp.lessis Xy) Xx))))
% 7.11/7.30 (assert (not (@ tptp.some (lambda ((Xu tptp.nat)) (@ (@ (@ tptp.diffprop tptp.x) tptp.z) Xu)))))
% 7.11/7.30 (set-info :filename cvc5---1.0.5_9933)
% 7.11/7.30 (check-sat-assuming ( true ))
% 7.11/7.30 ------- get file name : TPTP file name is NUM666^1
% 7.11/7.30 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9933.smt2...
% 7.11/7.30 --- Run --ho-elim --full-saturate-quant at 10...
% 7.11/7.30 % SZS status Theorem for NUM666^1
% 7.11/7.30 % SZS output start Proof for NUM666^1
% 7.11/7.30 (
% 7.11/7.30 (let ((_let_1 (not (@ tptp.some (lambda ((Xu tptp.nat)) (@ (@ (@ tptp.diffprop tptp.x) tptp.z) Xu)))))) (let ((_let_2 (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.moreis Xx) Xy) (@ (@ tptp.lessis Xy) Xx))))) (let ((_let_3 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (@ (@ tptp.lessis Xx) Xy) (=> (@ tptp.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xz) Xy) Xv))) (@ tptp.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xz) Xx) Xv)))))))) (let ((_let_4 (@ (@ tptp.moreis tptp.y) tptp.z))) (let ((_let_5 (@ tptp.some (lambda ((Xu tptp.nat)) (@ (@ (@ tptp.diffprop tptp.x) tptp.y) Xu))))) (let ((_let_6 (= k_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_110))) (let ((_let_7 (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1144 k_6))) (let ((_let_8 (ho_10 (ho_9 k_12 tptp.x) tptp.z))) (let ((_let_9 (ho_15 k_14 _let_8))) (let ((_let_10 (= k_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1144))) (let ((_let_11 (= k_6 gt_21))) (let ((_let_12 (= k_6 _let_8))) (let ((_let_13 (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_15 k_14 z) (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_110 z))))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_6))) (let ((_let_16 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_15 x z) (ho_15 y z)))) (= x y))))) (let ((_let_17 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_18 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_19 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_10 v ii) (ite (= i ii) e (ho_10 u ii)))))))))) (let ((_let_20 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_10 x z) (ho_10 y z)))) (= x y))))) (let ((_let_21 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_22 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_23 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_15 v ii) (ite (= i ii) e (ho_15 u ii)))))))))) (let ((_let_24 (forall ((BOUND_VARIABLE_700 tptp.nat)) (= (ho_7 k_6 BOUND_VARIABLE_700) (ho_7 (ho_10 (ho_9 k_8 tptp.x) tptp.z) BOUND_VARIABLE_700))))) (let ((_let_25 (forall ((BOUND_VARIABLE_690 tptp.nat) (BOUND_VARIABLE_691 tptp.nat) (BOUND_VARIABLE_692 tptp.nat)) (= (ho_7 (ho_10 (ho_9 k_11 BOUND_VARIABLE_690) BOUND_VARIABLE_691) BOUND_VARIABLE_692) (ho_7 (ho_10 (ho_9 k_8 BOUND_VARIABLE_690) BOUND_VARIABLE_691) BOUND_VARIABLE_692))))) (let ((_let_26 (forall ((BOUND_VARIABLE_680 tptp.nat) (BOUND_VARIABLE_681 tptp.nat) (BOUND_VARIABLE_682 tptp.nat)) (= (ho_7 (ho_10 (ho_9 k_12 BOUND_VARIABLE_680) BOUND_VARIABLE_681) BOUND_VARIABLE_682) (ho_7 (ho_10 (ho_9 k_8 BOUND_VARIABLE_680) BOUND_VARIABLE_681) BOUND_VARIABLE_682))))) (let ((_let_27 (forall ((BOUND_VARIABLE_674 tptp.nat)) (= (ho_7 k_13 BOUND_VARIABLE_674) (ho_7 (ho_10 (ho_9 k_8 tptp.x) tptp.y) BOUND_VARIABLE_674))))) (let ((_let_28 (ho_15 k_14 k_13))) (let ((_let_29 (forall ((BOUND_VARIABLE_700 tptp.nat)) (= (@ (@ (@ tptp.diffprop tptp.x) tptp.z) BOUND_VARIABLE_700) (ll_5 BOUND_VARIABLE_700))))) (let ((_let_30 (forall ((BOUND_VARIABLE_690 tptp.nat) (BOUND_VARIABLE_691 tptp.nat) (BOUND_VARIABLE_692 tptp.nat)) (= (@ (@ (@ tptp.diffprop BOUND_VARIABLE_690) BOUND_VARIABLE_691) BOUND_VARIABLE_692) (ll_4 BOUND_VARIABLE_690 BOUND_VARIABLE_691 BOUND_VARIABLE_692))))) (let ((_let_31 (forall ((BOUND_VARIABLE_680 tptp.nat) (BOUND_VARIABLE_681 tptp.nat) (BOUND_VARIABLE_682 tptp.nat)) (= (@ (@ (@ tptp.diffprop BOUND_VARIABLE_680) BOUND_VARIABLE_681) BOUND_VARIABLE_682) (ll_3 BOUND_VARIABLE_680 BOUND_VARIABLE_681 BOUND_VARIABLE_682))))) (let ((_let_32 (forall ((BOUND_VARIABLE_674 tptp.nat)) (= (@ (@ (@ tptp.diffprop tptp.x) tptp.y) BOUND_VARIABLE_674) (ll_2 BOUND_VARIABLE_674))))) (let ((_let_33 (@ tptp.some ll_2))) (let ((_let_34 (and _let_33 _let_32 _let_31 _let_30 _let_29))) (let ((_let_35 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 _let_33)))) (PREPROCESS :args ((and _let_32 _let_31 _let_30 _let_29)))) :args (_let_34)) (PREPROCESS :args ((= _let_34 (and _let_28 _let_27 _let_26 _let_25 _let_24))))) (PREPROCESS :args ((and _let_16 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17)))) :args ((and _let_28 _let_27 _let_26 _let_25 _let_24 _let_16 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17))))) (let ((_let_36 (AND_ELIM _let_35 :args (5)))) (let ((_let_37 (_let_16))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_110 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261))) (let ((_let_40 (ho_15 k_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261))) (let ((_let_41 (= _let_40 _let_39))) (let ((_let_42 (= k_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261))) (let ((_let_43 (ite _let_42 _let_28 _let_40))) (let ((_let_44 (= _let_39 _let_43))) (let ((_let_45 (not _let_40))) (let ((_let_46 (_let_41))) (let ((_let_47 (AND_ELIM _let_35 :args (0)))) (let ((_let_48 (not _let_28))) (let ((_let_49 (_let_43))) (let ((_let_50 (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ite (= k_13 ii) (ho_15 k_14 k_13) (ho_15 k_14 ii)) (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_110 ii))))) (let ((_let_51 (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_15 v ii) (ite (= k_13 ii) (ho_15 k_14 k_13) (ho_15 k_14 ii)))))))) (let ((_let_52 (not _let_51))) (let ((_let_53 (AND_ELIM _let_35 :args (6)))) (let ((_let_54 (_let_23))) (let ((_let_55 (ASSUME :args _let_54))) (let ((_let_56 (or))) (let ((_let_57 (_let_50))) (let ((_let_58 (_let_52))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_57) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_57))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58) (REWRITE :args ((=> _let_52 (not (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_110 ii) (ite (= k_13 ii) (ho_15 k_14 k_13) (ho_15 k_14 ii))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) (REFL :args _let_57) :args _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (k_14 _let_28 k_13 QUANTIFIERS_INST_ENUM)) :args _let_54)) _let_53 :args (_let_52 false _let_23)) :args (_let_50 true _let_51)) :args (_let_44 false _let_50)))) (let ((_let_60 (not _let_44))) (let ((_let_61 (not _let_43))) (let ((_let_62 (_let_44))) (let ((_let_63 (REFL :args (_let_48)))) (let ((_let_64 (ASSUME :args (_let_28)))) (let ((_let_65 (TRUE_INTRO _let_64))) (let ((_let_66 (APPLY_UF ho_15))) (let ((_let_67 (ASSUME :args (_let_42)))) (let ((_let_68 (REFL :args (k_14)))) (let ((_let_69 (ASSUME :args (_let_45)))) (let ((_let_70 (_let_14))) (let ((_let_71 (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 k_6))) (let ((_let_72 (= k_6 k_13))) (let ((_let_73 (ite _let_72 _let_28 _let_71))) (let ((_let_74 (= _let_7 _let_73))) (let ((_let_75 (not _let_7))) (let ((_let_76 (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ite (= k_13 ii) (ho_15 k_14 k_13) (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 ii)) (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1144 ii))))) (let ((_let_77 (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_15 v ii) (ite (= k_13 ii) (ho_15 k_14 k_13) (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 ii)))))))) (let ((_let_78 (not _let_77))) (let ((_let_79 (_let_76))) (let ((_let_80 (_let_78))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_80)) :args _let_80) (REWRITE :args ((=> _let_78 (not (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1144 ii) (ite (= k_13 ii) (ho_15 k_14 k_13) (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 ii))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_77))) (REFL :args _let_79) :args _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 _let_28 k_13 QUANTIFIERS_INST_ENUM)) :args _let_54)) _let_53 :args (_let_78 false _let_23)) :args (_let_76 true _let_77)))) (let ((_let_82 (ASSUME :args _let_79))) (let ((_let_83 (not _let_73))) (let ((_let_84 (ho_15 k_14 k_6))) (let ((_let_85 (not _let_72))) (let ((_let_86 (not _let_84))) (let ((_let_87 (not (@ tptp.some ll_5)))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (PREPROCESS :args ((= _let_1 _let_87))) (PREPROCESS :args ((= _let_87 _let_86))))))) (let ((_let_89 (ASSUME :args (_let_72)))) (let ((_let_90 (and _let_85 _let_84))) (let ((_let_91 (= _let_71 _let_90))) (let ((_let_92 (not _let_71))) (let ((_let_93 (forall ((ii |u_(-> tptp.nat Bool)|)) (= (and (not (= k_13 ii)) (ho_15 k_14 ii)) (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 ii))))) (let ((_let_94 (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_15 v ii) (and (not (= k_13 ii)) (ho_15 k_14 ii)))))))) (let ((_let_95 (not _let_94))) (let ((_let_96 (_let_93))) (let ((_let_97 (_let_95))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_97)) :args _let_97) (REWRITE :args ((=> _let_95 (not (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 ii) (and (not (= k_13 ii)) (ho_15 k_14 ii))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_94))) (REFL :args _let_96) :args _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_55 :args (k_14 false k_13 QUANTIFIERS_INST_ENUM)) :args _let_54))) _let_53 :args (_let_95 false _let_23)) :args (_let_93 true _let_94)))) (let ((_let_99 ((ho_15 k_14 ii)))) (let ((_let_100 (ASSUME :args _let_96))) (let ((_let_101 (not _let_90))) (let ((_let_102 (ho_10 (ho_9 k_11 tptp.x) tptp.y))) (let ((_let_103 (ho_15 k_14 _let_102))) (let ((_let_104 (not _let_103))) (let ((_let_105 (ho_7 (ho_10 k_17 tptp.z) tptp.y))) (let ((_let_106 (not _let_105))) (let ((_let_107 (or _let_106 _let_104 _let_9))) (let ((_let_108 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_let_187 _let_180)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_202)) (CONG _let_68 (SYMM _let_201) :args _let_66) _let_65)) :args (_let_28 _let_180 _let_187)) :args ((not (and _let_28 _let_187 _let_180)) SB_LITERAL))) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_187) _let_178))) (REFL :args (_let_181)) :args _let_56)) _let_47 (REORDERING (CNF_ITE_POS2 :args _let_194) :args ((or _let_180 _let_183 _let_191))) (REORDERING (CNF_EQUIV_POS2 :args _let_198) :args ((or _let_182 _let_193 _let_196))) _let_195 (REORDERING (CNF_EQUIV_POS1 :args _let_192) :args ((or (not _let_177) _let_184 _let_190))) _let_189 (REORDERING (CNF_AND_POS :args (_let_182 1)) :args ((or _let_178 _let_197))) (REORDERING (CNF_EQUIV_NEG1 :args _let_188) :args ((or _let_178 _let_177 _let_179))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_200) (CONG (REFL :args _let_200) (MACRO_SR_PRED_INTRO :args ((= (not _let_181) _let_180))) (REFL :args _let_199) :args _let_56)) :args ((or _let_187 _let_180 _let_182))) (REORDERING (CNF_EQUIV_POS1 :args _let_198) :args ((or _let_183 _let_197 _let_196))) _let_195 (REORDERING (CNF_ITE_NEG1 :args _let_194) :args ((or _let_48 _let_181 _let_184))) _let_47 (REORDERING (CNF_ITE_NEG3 :args _let_194) :args ((or _let_48 _let_184 _let_193))) _let_47 (REORDERING (CNF_EQUIV_POS2 :args _let_192) :args ((or _let_177 _let_191 _let_190))) _let_189 (CNF_EQUIV_NEG2 :args _let_188) :args ((or _let_179 _let_187) true _let_182 false _let_186 true _let_180 false _let_28 true _let_183 false _let_28 true _let_184 false _let_185 true _let_177)) :args (_let_179 false _let_28 false _let_180 true _let_183 false _let_186 false _let_184 false _let_185 true _let_182 false _let_177 true _let_178)) :args (_let_174 false _let_179)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (k_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1144 QUANTIFIERS_INST_ENUM)) :args _let_37)) _let_36 :args (_let_176 false _let_16)) :args (_let_10 false _let_174 false _let_176)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_106 _let_104 _let_9 (not _let_107)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_171)) :args ((or _let_170 _let_105 (not _let_171)))) (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_169)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_173 :args (tptp.y tptp.z QUANTIFIERS_INST_E_MATCHING ((not (= (ho_7 (ho_10 k_16 Xx) Xy) false))))) :args (_let_172))) _let_173 :args (_let_171 false _let_172)) :args (_let_105 false _let_169 false _let_171)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_64 _let_167 _let_168) :args (_let_28 _let_104 _let_111)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_168)) (CONG _let_68 (SYMM _let_167) :args _let_66) _let_65)) :args (_let_28 _let_111 _let_104)) :args ((not (and _let_28 _let_104 _let_111)) SB_LITERAL))) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_104) _let_103))) (REFL :args ((not _let_111))) :args _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_111 _let_113 (not _let_114)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_166)) :args _let_166)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_113) _let_112))) (REFL :args ((not _let_120))) :args _let_56)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_164)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_165 _let_162 _let_134) (SCOPE (FALSE_ELIM (TRANS _let_163 (FALSE_INTRO _let_165))) :args (_let_127 _let_126 _let_125))) :args (_let_125 _let_126 _let_127))) :args (true _let_164)) (CONG _let_151 (REFL :args ((not _let_126))) (MACRO_SR_PRED_INTRO :args ((= (not _let_127) _let_119))) (REFL :args (_let_132)) :args _let_56)) _let_159 _let_134 (REORDERING (CNF_EQUIV_POS1 :args _let_133) :args ((or (not _let_118) _let_123 _let_131))) _let_130 (REORDERING (CNF_EQUIV_NEG1 :args _let_128) :args ((or _let_119 _let_118 _let_120))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_160)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_161 _let_162 _let_134) (SCOPE (TRUE_ELIM (TRANS _let_163 (TRUE_INTRO _let_161))) :args (_let_119 _let_126 _let_125))) :args (_let_125 _let_126 _let_119))) :args (true _let_160)) _let_159 _let_134 (REORDERING (CNF_EQUIV_POS2 :args _let_133) :args ((or _let_118 _let_132 _let_131))) _let_130 (CNF_EQUIV_NEG2 :args _let_128) :args ((or _let_120 _let_127) false _let_126 false _let_125 true _let_123 false _let_124 true _let_118)) :args (_let_120 false _let_126 false _let_125 false _let_123 false _let_124 false _let_118 true _let_119)) :args (_let_112 false _let_120)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (k_13 _let_102 QUANTIFIERS_INST_ENUM)) :args _let_116)) _let_115 :args (_let_114 false _let_18)) :args (_let_111 false _let_112 false _let_114)) _let_47 :args (_let_103 false _let_111 false _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (tptp.z tptp.y tptp.x QUANTIFIERS_INST_E_MATCHING ((not (= (ho_7 (ho_10 k_17 Xx) Xy) false)) (ho_9 k_11 Xz)))) :args (_let_108))) _let_110 :args (_let_107 false _let_108)) :args (_let_9 false _let_105 false _let_103 false _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_74)) :args ((or _let_73 _let_75 (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_ITE_POS2 :args (_let_73)) :args ((or _let_71 _let_72 _let_83))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_91)) :args ((or _let_90 _let_92 (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_90 1)) :args ((or _let_84 _let_101))) _let_88 :args (_let_101 true _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_100 :args (k_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_99)) :args _let_96))) _let_98 :args (_let_91 false _let_93)) :args (_let_92 true _let_90 false _let_91)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_64 _let_89 _let_88) :args (_let_28 _let_86 _let_72)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_88)) (CONG _let_68 (SYMM (SYMM _let_89)) :args _let_66) _let_65)) :args (_let_28 _let_72 _let_86)) :args ((not (and _let_28 _let_86 _let_72)) SB_LITERAL))) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_86) _let_84))) (REFL :args (_let_85)) :args _let_56)) :args ((or _let_84 _let_48 _let_85))) _let_88 _let_47 :args (_let_85 true _let_84 false _let_28)) :args (_let_83 true _let_71 true _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_82 :args (k_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 ii)))) :args _let_79))) _let_81 :args (_let_74 false _let_76)) :args (_let_75 true _let_73 false _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_14 _let_6 (not _let_15)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_70)) :args _let_70)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) (REFL :args ((not _let_41))) :args _let_56)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_64 _let_67 _let_69) :args (_let_28 _let_45 _let_42)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_69)) (CONG _let_68 (SYMM _let_67) :args _let_66) _let_65)) :args (_let_28 _let_42 _let_45)) :args ((not (and _let_28 _let_45 _let_42)) SB_LITERAL))) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_40))) (REFL :args ((not _let_42))) :args _let_56)) _let_47 (REORDERING (CNF_ITE_POS2 :args _let_49) :args ((or _let_40 _let_42 _let_61))) (REORDERING (CNF_EQUIV_POS1 :args _let_62) :args ((or (not _let_39) _let_43 _let_60))) _let_59 (REORDERING (CNF_EQUIV_NEG1 :args _let_46) :args ((or _let_40 _let_39 _let_41))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_62) :args ((or _let_39 _let_61 _let_60))) _let_59 (REORDERING (CNF_ITE_NEG3 :args _let_49) :args ((or _let_48 _let_45 _let_43))) _let_47 (CNF_EQUIV_NEG2 :args _let_46) :args ((or _let_41 _let_45) false _let_44 false _let_43 false _let_28 true _let_39)) :args (_let_41 false _let_28 false _let_42 false _let_43 false _let_44 false _let_39 true _let_40)) :args (_let_13 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (k_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_110 QUANTIFIERS_INST_ENUM)) :args _let_37)) _let_36 :args (_let_15 false _let_16)) :args (_let_6 false _let_13 false _let_15)) :args (false false _let_12 false _let_11 false _let_10 false _let_9 true _let_7 false _let_6)) :args (_let_5 _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 7.11/7.31 )
% 7.11/7.31 % SZS output end Proof for NUM666^1
% 7.11/7.31 % cvc5---1.0.5 exiting
% 7.11/7.31 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------