TSTP Solution File: NUM705^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM705^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 10:47:04 EDT 2023
% Result : Theorem 11.34s 11.52s
% Output : Proof 11.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM705^1 : TPTP v8.1.2. Released v3.7.0.
% 0.15/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 11:58:20 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : NUM705^1 : TPTP v8.1.2. Released v3.7.0.
% 0.21/0.50 % Domain : Number Theory
% 0.21/0.50 % Problem : Landau theorem 27a
% 0.21/0.50 % Version : Especial.
% 0.21/0.50 % English : ~((forall x:nat.forall y:nat.~((forall x_0:nat.p x_0 ->
% 0.21/0.50 % lessis x x_0) -> ~(p x)) -> ~((forall x_0:nat.p x_0 ->
% 0.21/0.50 % lessis y x_0) -> ~(p y)) -> x = y) -> ~(some (lambda x.
% 0.21/0.50 % ~((forall x_0:nat.p x_0 -> lessis x x_0) -> ~(p x)))))
% 0.21/0.50
% 0.21/0.50 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.50 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.50 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.50 % Source : [Bro09]
% 0.21/0.50 % Names : satz27a [Lan30]
% 0.21/0.50
% 0.21/0.50 % Status : Theorem
% 0.21/0.50 % : Without extensionality : Theorem
% 0.21/0.50 % Rating : 0.23 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.21/0.50 % Syntax : Number of formulae : 11 ( 0 unt; 5 typ; 0 def)
% 0.21/0.50 % Number of atoms : 21 ( 2 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 11 ( 3 avg)
% 0.21/0.50 % Number of connectives : 58 ( 14 ~; 0 |; 0 &; 28 @)
% 0.21/0.50 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 13 ( 8 avg)
% 0.21/0.50 % Number of types : 2 ( 1 usr)
% 0.21/0.50 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.21/0.50 % Number of variables : 14 ( 2 ^; 12 !; 0 ?; 14 :)
% 0.21/0.50 % SPC : TH0_THM_EQU_NAR
% 0.21/0.50
% 0.21/0.50 % Comments :
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(nat_type,type,
% 0.21/0.50 nat: $tType ).
% 0.21/0.50
% 0.21/0.50 thf(p,type,
% 0.21/0.50 p: nat > $o ).
% 0.21/0.50
% 0.21/0.50 thf(some,type,
% 0.21/0.50 some: ( nat > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(s,axiom,
% 0.21/0.50 some @ p ).
% 0.21/0.50
% 0.21/0.50 thf(lessis,type,
% 0.21/0.50 lessis: nat > nat > $o ).
% 0.21/0.50
% 0.21/0.50 thf(more,type,
% 0.21/0.50 more: nat > nat > $o ).
% 0.21/0.50
% 0.21/0.50 thf(satz14,axiom,
% 0.21/0.50 ! [Xx: nat,Xy: nat] :
% 0.21/0.50 ( ( lessis @ Xx @ Xy )
% 0.21/0.50 => ( ~ ( more @ Xy @ Xx )
% 0.21/0.50 => ( Xy = Xx ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(et,axiom,
% 0.21/0.50 ! [Xa: $o] :
% 0.21/0.50 ( ~ ~ Xa
% 0.21/0.50 => Xa ) ).
% 0.21/0.50
% 0.21/0.50 thf(satz10d,axiom,
% 0.21/0.50 ! [Xx: nat,Xy: nat] :
% 0.21/0.50 ( ( lessis @ Xx @ Xy )
% 0.21/0.50 => ~ ( more @ Xx @ Xy ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(satz27,axiom,
% 0.21/0.50 ! [Xp: nat > $o] :
% 0.21/0.50 ( ( some @ Xp )
% 0.21/0.50 => ( some
% 0.21/0.50 @ ^ [Xx: nat] :
% 0.21/0.50 ~ ( ! [Xx_0: nat] :
% 0.21/0.50 ( ( Xp @ Xx_0 )
% 0.21/0.50 => ( lessis @ Xx @ Xx_0 ) )
% 0.21/0.50 => ~ ( Xp @ Xx ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(satz27a,conjecture,
% 0.21/0.50 ~ ( ! [Xx: nat,Xy: nat] :
% 0.21/0.50 ( ~ ( ! [Xx_0: nat] :
% 0.21/0.50 ( ( p @ Xx_0 )
% 0.21/0.50 => ( lessis @ Xx @ Xx_0 ) )
% 0.21/0.50 => ~ ( p @ Xx ) )
% 0.21/0.50 => ( ~ ( ! [Xx_0: nat] :
% 0.21/0.50 ( ( p @ Xx_0 )
% 0.21/0.50 => ( lessis @ Xy @ Xx_0 ) )
% 0.21/0.50 => ~ ( p @ Xy ) )
% 0.21/0.50 => ( Xx = Xy ) ) )
% 0.21/0.50 => ~ ( some
% 0.21/0.50 @ ^ [Xx: nat] :
% 0.21/0.50 ~ ( ! [Xx_0: nat] :
% 0.21/0.50 ( ( p @ Xx_0 )
% 0.21/0.50 => ( lessis @ Xx @ Xx_0 ) )
% 0.21/0.50 => ~ ( p @ Xx ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.74mBKyYRJ9/cvc5---1.0.5_28917.p...
% 0.21/0.50 (declare-sort $$unsorted 0)
% 0.21/0.50 (declare-sort tptp.nat 0)
% 0.21/0.50 (declare-fun tptp.p (tptp.nat) Bool)
% 0.21/0.50 (declare-fun tptp.some ((-> tptp.nat Bool)) Bool)
% 0.21/0.50 (assert (@ tptp.some tptp.p))
% 0.21/0.50 (declare-fun tptp.lessis (tptp.nat tptp.nat) Bool)
% 0.21/0.50 (declare-fun tptp.more (tptp.nat tptp.nat) Bool)
% 0.21/0.50 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.lessis Xx) Xy) (=> (not (@ (@ tptp.more Xy) Xx)) (= Xy Xx)))))
% 0.21/0.50 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.21/0.50 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.lessis Xx) Xy) (not (@ (@ tptp.more Xx) Xy)))))
% 0.21/0.50 (assert (forall ((Xp (-> tptp.nat Bool))) (=> (@ tptp.some Xp) (@ tptp.some (lambda ((Xx tptp.nat)) (not (=> (forall ((Xx_0 tptp.nat)) (=> (@ Xp Xx_0) (@ (@ tptp.lessis Xx) Xx_0))) (not (@ Xp Xx)))))))))
% 11.34/11.52 (assert (not (not (=> (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (not (=> (forall ((Xx_0 tptp.nat)) (=> (@ tptp.p Xx_0) (@ (@ tptp.lessis Xx) Xx_0))) (not (@ tptp.p Xx)))) (=> (not (=> (forall ((Xx_0 tptp.nat)) (=> (@ tptp.p Xx_0) (@ (@ tptp.lessis Xy) Xx_0))) (not (@ tptp.p Xy)))) (= Xx Xy)))) (not (@ tptp.some (lambda ((Xx tptp.nat)) (not (=> (forall ((Xx_0 tptp.nat)) (=> (@ tptp.p Xx_0) (@ (@ tptp.lessis Xx) Xx_0))) (not (@ tptp.p Xx)))))))))))
% 11.34/11.52 (set-info :filename cvc5---1.0.5_28917)
% 11.34/11.52 (check-sat-assuming ( true ))
% 11.34/11.52 ------- get file name : TPTP file name is NUM705^1
% 11.34/11.52 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_28917.smt2...
% 11.34/11.52 --- Run --ho-elim --full-saturate-quant at 10...
% 11.34/11.52 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 11.34/11.52 % SZS status Theorem for NUM705^1
% 11.34/11.52 % SZS output start Proof for NUM705^1
% 11.34/11.52 (
% 11.34/11.52 (let ((_let_1 (not (not (=> (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (not (=> (forall ((Xx_0 tptp.nat)) (=> (@ tptp.p Xx_0) (@ (@ tptp.lessis Xx) Xx_0))) (not (@ tptp.p Xx)))) (=> (not (=> (forall ((Xx_0 tptp.nat)) (=> (@ tptp.p Xx_0) (@ (@ tptp.lessis Xy) Xx_0))) (not (@ tptp.p Xy)))) (= Xx Xy)))) (not (@ tptp.some (lambda ((Xx tptp.nat)) (not (=> (forall ((Xx_0 tptp.nat)) (=> (@ tptp.p Xx_0) (@ (@ tptp.lessis Xx) Xx_0))) (not (@ tptp.p Xx)))))))))))) (let ((_let_2 (forall ((Xp (-> tptp.nat Bool))) (=> (@ tptp.some Xp) (@ tptp.some (lambda ((Xx tptp.nat)) (not (=> (forall ((Xx_0 tptp.nat)) (=> (@ Xp Xx_0) (@ (@ tptp.lessis Xx) Xx_0))) (not (@ Xp Xx)))))))))) (let ((_let_3 (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.lessis Xx) Xy) (not (@ (@ tptp.more Xx) Xy)))))) (let ((_let_4 (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.lessis Xx) Xy) (=> (not (@ (@ tptp.more Xy) Xx)) (= Xy Xx)))))) (let ((_let_5 (@ tptp.some tptp.p))) (let ((_let_6 (forall ((Xx_0 tptp.nat)) (or (not (ho_5 k_4 Xx_0)) (ho_5 (ho_7 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_311) Xx_0))))) (let ((_let_7 (forall ((Xx_0 tptp.nat)) (or (not (ho_5 k_4 Xx_0)) (ho_5 (ho_7 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_311) Xx_0))))) (let ((_let_8 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_311))) (let ((_let_9 (and _let_6 _let_8))) (let ((_let_10 (ho_5 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_311))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (forall ((BOUND_VARIABLE_776 tptp.nat)) (= (and (forall ((Xx_0 tptp.nat)) (or (not (ho_5 k_4 Xx_0)) (ho_5 (ho_7 k_6 BOUND_VARIABLE_776) Xx_0))) (ho_5 k_4 BOUND_VARIABLE_776)) (ho_5 k_8 BOUND_VARIABLE_776))))) (let ((_let_13 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_14 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_15 (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_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_16 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_17 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_10 v ii) (ite (= i ii) e (ho_10 u ii)))))))))) (let ((_let_18 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_10 x z) (ho_10 y z)))) (= x y))))) (let ((_let_19 (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_12 v ii) (ite (= i ii) e (ho_12 u ii)))))))))) (let ((_let_20 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_12 x z) (ho_12 y z)))) (= x y))))) (let ((_let_21 (forall ((BOUND_VARIABLE_828 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_761 tptp.nat)) (= (and (forall ((Xx_0 tptp.nat)) (or (not (ho_5 BOUND_VARIABLE_828 Xx_0)) (ho_5 (ho_7 k_6 BOUND_VARIABLE_761) Xx_0))) (ho_5 BOUND_VARIABLE_828 BOUND_VARIABLE_761)) (ho_5 (ho_10 k_9 BOUND_VARIABLE_828) BOUND_VARIABLE_761))))) (let ((_let_22 (ho_12 k_11 k_4))) (let ((_let_23 (forall ((BOUND_VARIABLE_776 tptp.nat)) (= (ll_3 BOUND_VARIABLE_776) (and (forall ((Xx_0 tptp.nat)) (or (not (@ tptp.p Xx_0)) (@ (@ tptp.lessis BOUND_VARIABLE_776) Xx_0))) (@ tptp.p BOUND_VARIABLE_776)))))) (let ((_let_24 (forall ((BOUND_VARIABLE_760 (-> tptp.nat Bool)) (BOUND_VARIABLE_761 tptp.nat)) (= (ll_2 BOUND_VARIABLE_760 BOUND_VARIABLE_761) (and (forall ((Xx_0 tptp.nat)) (or (not (@ BOUND_VARIABLE_760 Xx_0)) (@ (@ tptp.lessis BOUND_VARIABLE_761) Xx_0))) (@ BOUND_VARIABLE_760 BOUND_VARIABLE_761)))))) (let ((_let_25 (and _let_5 _let_24 _let_23))) (let ((_let_26 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (ASSUME :args (_let_5)) (PREPROCESS :args ((and _let_24 _let_23)))) :args (_let_25)) (PREPROCESS :args ((= _let_25 (and _let_22 _let_21 _let_12))))) (PREPROCESS :args ((and _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13)))) :args ((and _let_22 _let_21 _let_12 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13))))) (let ((_let_27 (_let_12))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_27) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_311 QUANTIFIERS_INST_ENUM)) :args _let_27))) (AND_ELIM _let_26 :args (2)) :args (_let_11 false _let_12)))) (let ((_let_29 (ho_10 k_9 k_4))) (let ((_let_30 (ho_5 _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_311))) (let ((_let_31 (= _let_10 _let_30))) (let ((_let_32 (and _let_7 _let_8))) (let ((_let_33 (= _let_30 _let_32))) (let ((_let_34 (forall ((z tptp.nat)) (= (ho_5 k_8 z) (ho_5 (ho_10 k_9 k_4) z))))) (let ((_let_35 (not _let_31))) (let ((_let_36 (= k_8 _let_29))) (let ((_let_37 (not _let_34))) (let ((_let_38 (or _let_37 _let_36))) (let ((_let_39 (_let_14))) (let ((_let_40 (ho_12 k_11 _let_29))) (let ((_let_41 (ho_12 k_11 k_8))) (let ((_let_42 (ite _let_36 _let_41 _let_40))) (let ((_let_43 (not _let_36))) (let ((_let_44 (ho_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_304 _let_29))) (let ((_let_45 (= _let_42 _let_44))) (let ((_let_46 (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ite (= k_8 ii) (ho_12 k_11 k_8) (ho_12 k_11 ii)) (ho_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_304 ii))))) (let ((_let_47 (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_12 v ii) (ite (= k_8 ii) (ho_12 k_11 k_8) (ho_12 k_11 ii)))))))) (let ((_let_48 (not _let_47))) (let ((_let_49 (_let_19))) (let ((_let_50 (or))) (let ((_let_51 (_let_46))) (let ((_let_52 (_let_48))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_52)) :args _let_52) (REWRITE :args ((=> _let_48 (not (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_304 ii) (ite (= k_8 ii) (ho_12 k_11 k_8) (ho_12 k_11 ii))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) (REFL :args _let_51) :args _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_49) :args (k_11 _let_41 k_8 QUANTIFIERS_INST_ENUM)) :args _let_49)) (AND_ELIM _let_26 :args (4)) :args (_let_48 false _let_19)) :args (_let_46 true _let_47)))) (let ((_let_54 (ASSUME :args _let_51))) (let ((_let_55 (= k_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_304))) (let ((_let_56 (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_12 k_11 z) (ho_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_304 z))))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55))) (let ((_let_59 (_let_20))) (let ((_let_60 (ho_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_304 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1316))) (let ((_let_61 (ho_12 k_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1316))) (let ((_let_62 (= _let_61 _let_60))) (let ((_let_63 (= k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1316))) (let ((_let_64 (ite _let_63 _let_41 _let_61))) (let ((_let_65 (= _let_60 _let_64))) (let ((_let_66 (not _let_61))) (let ((_let_67 (_let_62))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1316 QUANTIFIERS_INST_CBQI_PROP)) :args _let_51))) _let_53 :args (_let_65 false _let_46)))) (let ((_let_69 (not _let_65))) (let ((_let_70 (not _let_64))) (let ((_let_71 (_let_65))) (let ((_let_72 (_let_64))) (let ((_let_73 (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (forall ((Xx_0 tptp.nat)) (or (not (ho_5 k_4 Xx_0)) (ho_5 (ho_7 k_6 Xx) Xx_0)))) (not (ho_5 k_4 Xx)) (not (forall ((Xx_0 tptp.nat)) (or (not (ho_5 k_4 Xx_0)) (ho_5 (ho_7 k_6 Xy) Xx_0)))) (not (ho_5 k_4 Xy)) (= Xx Xy))))) (let ((_let_74 (not _let_41))) (let ((_let_75 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_76 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_77 (not _let_76))) (let ((_let_78 (forall ((Xx_0 tptp.nat)) (or (not (ho_5 k_4 Xx_0)) (ho_5 (ho_7 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) Xx_0))))) (let ((_let_79 (not _let_78))) (let ((_let_80 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_81 (not _let_80))) (let ((_let_82 (forall ((Xx_0 tptp.nat)) (or (not (ho_5 k_4 Xx_0)) (ho_5 (ho_7 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) Xx_0))))) (let ((_let_83 (not _let_82))) (let ((_let_84 (or _let_83 _let_81 _let_79 _let_77 _let_75))) (let ((_let_85 (ho_5 (ho_7 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_86 (or _let_77 _let_85))) (let ((_let_87 (ho_5 (ho_7 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_88 (or _let_81 _let_87))) (let ((_let_89 (ho_5 (ho_7 k_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_90 (not _let_85))) (let ((_let_91 (or _let_90 _let_89 _let_75))) (let ((_let_92 (not _let_89))) (let ((_let_93 (not _let_87))) (let ((_let_94 (or _let_93 _let_92))) (let ((_let_95 (REFL :args (_let_84)))) (let ((_let_96 (_let_82))) (let ((_let_97 (_let_78))) (let ((_let_98 (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (ho_5 (ho_7 k_6 Xx) Xy)) (ho_5 (ho_7 k_13 Xy) Xx) (= Xx Xy))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (@ (@ tptp.lessis Xx) Xy)) (@ (@ tptp.more Xy) Xx) (= Xx Xy))) _let_98))))))) (let ((_let_100 (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (ho_5 (ho_7 k_6 Xx) Xy)) (not (ho_5 (ho_7 k_13 Xx) Xy)))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (@ (@ tptp.lessis Xx) Xy)) (not (@ (@ tptp.more Xx) Xy)))) _let_100))))))) (let ((_let_102 (not _let_73))) (let ((_let_103 (_let_102))) (let ((_let_104 (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (forall ((Xx_0 tptp.nat)) (or (not (@ tptp.p Xx_0)) (@ (@ tptp.lessis Xx) Xx_0)))) (not (@ tptp.p Xx)) (not (forall ((Xx_0 tptp.nat)) (or (not (@ tptp.p Xx_0)) (@ (@ tptp.lessis Xy) Xx_0)))) (not (@ tptp.p Xy)) (= Xx Xy))))) (let ((_let_105 (=> _let_104 (not (@ tptp.some ll_3))))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (=> _let_104 (not (@ tptp.some (lambda ((Xx tptp.nat)) (not (=> (forall ((Xx_0 tptp.nat)) (or (not (@ tptp.p Xx_0)) (@ (@ tptp.lessis Xx) Xx_0))) (not (@ tptp.p Xx)))))))) _let_105))) (PREPROCESS :args ((= _let_105 (=> _let_73 _let_74))))))) :args ((or _let_74 _let_102))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_103)) :args _let_103)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_102) _let_73))) (REFL :args ((not _let_84))) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_92 _let_93 (not _let_94)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_100))) _let_101 :args (_let_94 false _let_100)) (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_75 _let_90 _let_89 (not _let_91)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_ENUM)) :args (_let_98))) _let_99 :args (_let_91 false _let_98)) (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_81 _let_87 (not _let_88)))) (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_77 _let_85 (not _let_86)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_97) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_ENUM)) :args _let_97)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_96) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_96)) (CNF_OR_NEG :args (_let_84 4)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 3)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_76))) :args _let_50)) :args ((or _let_76 _let_84))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 2)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_78))) :args _let_50)) :args ((or _let_78 _let_84))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 1)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_80))) :args _let_50)) :args ((or _let_80 _let_84))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 0)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_82))) :args _let_50)) :args ((or _let_82 _let_84))) :args (_let_84 false _let_94 false _let_89 false _let_91 false _let_87 false _let_85 false _let_88 false _let_86 true _let_75 false _let_76 false _let_78 false _let_80 false _let_82)) :args (_let_73 false _let_84)) :args (_let_74 false _let_73)))) (let ((_let_107 (ASSUME :args (_let_74)))) (let ((_let_108 (APPLY_UF ho_12))) (let ((_let_109 (ASSUME :args (_let_63)))) (let ((_let_110 (ASSUME :args (_let_61)))) (let ((_let_111 (_let_57))) (let ((_let_112 (not _let_22))) (let ((_let_113 (or _let_112 _let_40))) (let ((_let_114 (forall ((BOUND_VARIABLE_879 |u_(-> tptp.nat Bool)|)) (or (not (ho_12 k_11 BOUND_VARIABLE_879)) (ho_12 k_11 (ho_10 k_9 BOUND_VARIABLE_879)))))) (let ((_let_115 (forall ((Xp (-> tptp.nat Bool))) (or (not (@ tptp.some Xp)) (@ tptp.some (@ ll_2 Xp)))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xp (-> tptp.nat Bool))) (or (not (@ tptp.some Xp)) (@ tptp.some (lambda ((Xx tptp.nat)) (not (=> (forall ((Xx_0 tptp.nat)) (or (not (@ Xp Xx_0)) (@ (@ tptp.lessis Xx) Xx_0))) (not (@ Xp Xx)))))))) _let_115))) (PREPROCESS :args ((= _let_115 _let_114))))))) (let ((_let_117 (and _let_40 _let_55))) (let ((_let_118 (_let_40 _let_55))) (let ((_let_119 (ASSUME :args (_let_40)))) (let ((_let_120 (ASSUME :args (_let_55)))) (let ((_let_121 (_let_37))) (let ((_let_122 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_121)) :args _let_121)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_34))) (REFL :args (_let_35)) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_36 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_ITE_POS1 :args (_let_42)) :args ((or _let_41 _let_43 (not _let_42)))) _let_106 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_45)) :args ((or _let_42 (not _let_44) (not _let_45)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_117)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_119 _let_120) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_120) (REFL :args (_let_29)) :args _let_108) (TRUE_INTRO _let_119))) :args _let_118)) :args _let_118)) :args (true _let_117)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_112 _let_40 (not _let_113)))) (AND_ELIM _let_26 :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_116 :args (k_4 QUANTIFIERS_INST_ENUM)) :args (_let_114))) _let_116 :args (_let_113 false _let_114)) :args (_let_40 false _let_22 false _let_113)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_55 (not _let_58)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_111)) :args _let_111)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) (REFL :args ((not _let_62))) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_71) :args ((or (not _let_60) _let_64 _let_69))) _let_68 (REORDERING (CNF_ITE_POS3 :args _let_72) :args ((or _let_41 _let_61 _let_70))) _let_106 (REORDERING (CNF_EQUIV_NEG1 :args _let_67) :args ((or _let_61 _let_60 _let_62))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_107 _let_109 _let_110) :args (_let_74 _let_61 _let_63)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_110)) (CONG (REFL :args (k_11)) (SYMM _let_109) :args _let_108) (FALSE_INTRO _let_107))) :args (_let_74 _let_63 _let_61)) :args ((not (and _let_74 _let_61 _let_63)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_41))) (REFL :args (_let_66)) (REFL :args ((not _let_63))) :args _let_50)) _let_106 (REORDERING (CNF_ITE_NEG2 :args _let_72) :args ((or _let_66 _let_63 _let_64))) (REORDERING (CNF_EQUIV_POS2 :args _let_71) :args ((or _let_60 _let_70 _let_69))) _let_68 (CNF_EQUIV_NEG2 :args _let_67) :args ((or _let_62 _let_66) true _let_41 false _let_63 true _let_64 false _let_65 true _let_60)) :args (_let_62 false _let_65 true _let_64 true _let_41 false _let_60 true _let_61)) :args (_let_56 false _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (k_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_304 QUANTIFIERS_INST_ENUM)) :args _let_59)) (AND_ELIM _let_26 :args (3)) :args (_let_58 false _let_20)) :args (_let_55 false _let_56 false _let_58)) :args (_let_44 false _let_40 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_29 QUANTIFIERS_INST_CBQI_PROP)) :args _let_51)) _let_53 :args (_let_45 false _let_46)) :args (_let_42 false _let_44 false _let_45)) :args (_let_43 true _let_41 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_39) :args (k_8 _let_29 QUANTIFIERS_INST_ENUM)) :args _let_39)) (AND_ELIM _let_26 :args (9)) :args (_let_38 false _let_14)) :args (_let_37 true _let_36 false _let_38)) :args (_let_35 true _let_34)))) (let ((_let_123 (_let_31))) (let ((_let_124 (not _let_11))) (let ((_let_125 (not _let_9))) (let ((_let_126 (_let_11))) (let ((_let_127 (_let_21))) (let ((_let_128 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_127) :args (k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_311 QUANTIFIERS_INST_CBQI_PROP)) :args _let_127))) (AND_ELIM _let_26 :args (1)) :args (_let_33 false _let_21)))) (let ((_let_129 (not _let_33))) (let ((_let_130 (not _let_30))) (let ((_let_131 (_let_33))) (let ((_let_132 (not _let_32))) (let ((_let_133 (ALPHA_EQUIV :args (_let_7 (= Xx_0 Xx_0))))) (let ((_let_134 (not _let_8))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_9)) :args ((or _let_134 _let_9 (not _let_6)))) (EQUIV_ELIM1 _let_133) (REORDERING (CNF_AND_POS :args (_let_32 1)) :args ((or _let_8 _let_132))) (REORDERING (CNF_AND_POS :args (_let_32 0)) :args ((or _let_7 _let_132))) (REORDERING (CNF_EQUIV_POS1 :args _let_131) :args ((or _let_130 _let_32 _let_129))) _let_128 (REORDERING (CNF_EQUIV_POS2 :args _let_126) :args ((or _let_10 _let_125 _let_124))) _let_28 (REORDERING (CNF_EQUIV_NEG1 :args _let_123) :args ((or _let_10 _let_30 _let_31))) _let_122 :args (_let_10 false _let_6 false _let_8 false _let_7 false _let_32 false _let_33 true _let_9 false _let_11 false _let_30 true _let_31)))) (let ((_let_136 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_126) :args ((or (not _let_10) _let_9 _let_124))) _let_135 _let_28 :args (_let_9 false _let_10 false _let_11)))) (let ((_let_137 (not _let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_133) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_32)) :args ((or _let_134 _let_32 _let_137))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_9 1)) :args ((or _let_8 _let_125))) _let_136 :args (_let_8 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_131) :args ((or _let_30 _let_132 _let_129))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_123) _let_122 _let_135 :args (_let_130 true _let_31 false _let_10)) _let_128 :args (_let_132 true _let_30 false _let_33)) :args (_let_137 false _let_8 true _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_9 0)) :args ((or _let_6 _let_125))) _let_136 :args (_let_6 false _let_9)) :args (false true _let_7 false _let_6)) :args (_let_5 _let_4 (forall ((Xa Bool)) (=> (not (not Xa)) Xa)) _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.34/11.52 )
% 11.34/11.52 % SZS output end Proof for NUM705^1
% 11.34/11.52 % cvc5---1.0.5 exiting
% 11.34/11.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------