TSTP Solution File: NUM665^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM665^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 10:46:26 EDT 2023
% Result : Theorem 70.16s 70.33s
% Output : Proof 70.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM665^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 07:35:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.47 %----Proving TH0
% 40.41/40.80 %------------------------------------------------------------------------------
% 40.41/40.80 % File : NUM665^1 : TPTP v8.1.2. Released v3.7.0.
% 40.41/40.80 % Domain : Number Theory
% 40.41/40.80 % Problem : Landau theorem 16c
% 40.41/40.80 % Version : Especial.
% 40.41/40.80 % English : some (lambda u.diffprop x z u)
% 40.41/40.80
% 40.41/40.80 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 40.41/40.80 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 40.41/40.80 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 40.41/40.80 % Source : [Bro09]
% 40.41/40.80 % Names : satz16c [Lan30]
% 40.41/40.80
% 40.41/40.80 % Status : Theorem
% 40.41/40.80 % : Without extensionality : Theorem
% 40.41/40.80 % Rating : 0.18 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 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
% 40.41/40.80 % Syntax : Number of formulae : 13 ( 1 unt; 8 typ; 0 def)
% 40.41/40.80 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 40.41/40.80 % Maximal formula atoms : 5 ( 2 avg)
% 40.41/40.80 % Number of connectives : 27 ( 0 ~; 0 |; 0 &; 24 @)
% 40.41/40.80 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 40.41/40.80 % Maximal formula depth : 11 ( 6 avg)
% 40.41/40.80 % Number of types : 2 ( 1 usr)
% 40.41/40.80 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 40.41/40.80 % Number of symbols : 7 ( 7 usr; 3 con; 0-3 aty)
% 40.41/40.80 % Number of variables : 9 ( 4 ^; 5 !; 0 ?; 9 :)
% 40.41/40.80 % SPC : TH0_THM_NEQ_NAR
% 40.41/40.80
% 40.41/40.80 % Comments :
% 40.41/40.80 %------------------------------------------------------------------------------
% 40.41/40.80 thf(nat_type,type,
% 40.41/40.80 nat: $tType ).
% 40.41/40.80
% 40.41/40.80 thf(x,type,
% 40.41/40.80 x: nat ).
% 40.41/40.80
% 40.41/40.80 thf(y,type,
% 40.41/40.80 y: nat ).
% 40.41/40.80
% 40.41/40.80 thf(z,type,
% 40.41/40.80 z: nat ).
% 40.41/40.80
% 40.41/40.80 thf(moreis,type,
% 40.41/40.80 moreis: nat > nat > $o ).
% 40.41/40.80
% 40.41/40.80 thf(m,axiom,
% 40.41/40.80 moreis @ x @ y ).
% 40.41/40.80
% 40.41/40.80 thf(some,type,
% 40.41/40.80 some: ( nat > $o ) > $o ).
% 40.41/40.80
% 40.41/40.80 thf(diffprop,type,
% 40.41/40.80 diffprop: nat > nat > nat > $o ).
% 40.41/40.80
% 40.41/40.80 thf(n,axiom,
% 40.41/40.80 ( some
% 40.41/40.80 @ ^ [Xu: nat] : ( diffprop @ y @ z @ Xu ) ) ).
% 40.41/40.80
% 40.41/40.80 thf(lessis,type,
% 40.41/40.80 lessis: nat > nat > $o ).
% 40.41/40.80
% 40.41/40.80 thf(satz16b,axiom,
% 40.41/40.80 ! [Xx: nat,Xy: nat,Xz: nat] :
% 40.41/40.80 ( ( some
% 40.41/40.80 @ ^ [Xv: nat] : ( diffprop @ Xy @ Xx @ Xv ) )
% 40.41/40.80 => ( ( lessis @ Xy @ Xz )
% 40.41/40.80 => ( some
% 40.41/40.80 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) ).
% 40.41/40.80
% 40.41/40.80 thf(satz13,axiom,
% 40.41/40.80 ! [Xx: nat,Xy: nat] :
% 40.41/40.80 ( ( moreis @ Xx @ Xy )
% 40.41/40.80 => ( lessis @ Xy @ Xx ) ) ).
% 40.41/40.80
% 40.41/40.80 thf(satz16c,conjecture,
% 40.41/40.80 ( some
% 40.41/40.80 @ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) ) ).
% 40.41/40.80
% 40.41/40.80 %------------------------------------------------------------------------------
% 40.41/40.80 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.647e7DFadI/cvc5---1.0.5_16621.p...
% 40.41/40.80 (declare-sort $$unsorted 0)
% 40.41/40.80 (declare-sort tptp.nat 0)
% 40.41/40.80 (declare-fun tptp.x () tptp.nat)
% 40.41/40.80 (declare-fun tptp.y () tptp.nat)
% 40.41/40.80 (declare-fun tptp.z () tptp.nat)
% 40.41/40.80 (declare-fun tptp.moreis (tptp.nat tptp.nat) Bool)
% 40.41/40.80 (assert (@ (@ tptp.moreis tptp.x) tptp.y))
% 40.41/40.80 (declare-fun tptp.some ((-> tptp.nat Bool)) Bool)
% 40.41/40.80 (declare-fun tptp.diffprop (tptp.nat tptp.nat tptp.nat) Bool)
% 40.41/40.80 (assert (@ tptp.some (lambda ((Xu tptp.nat)) (@ (@ (@ tptp.diffprop tptp.y) tptp.z) Xu))))
% 40.41/40.80 (declare-fun tptp.lessis (tptp.nat tptp.nat) Bool)
% 40.41/40.80 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (@ tptp.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xy) Xx) Xv))) (=> (@ (@ tptp.lessis Xy) Xz) (@ tptp.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xz) Xx) Xv)))))))
% 40.41/40.80 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.moreis Xx) Xy) (@ (@ tptp.lessis Xy) Xx))))
% 40.41/40.80 (assert (not (@ tptp.some (lambda ((Xu tptp.nat)) (@ (@ (@ tptp.diffprop tptp.x) tptp.z) Xu)))))
% 40.41/40.80 (set-info :filename cvc5---1.0.5_16621)
% 40.41/40.80 (check-sat-assuming ( true ))
% 40.41/40.80 ------- get file name : TPTP file name is NUM665^1
% 40.41/40.80 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16621.smt2...
% 40.41/40.80 --- Run --ho-elim --full-saturate-quant at 10...
% 40.41/40.80 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 40.41/40.80 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 40.41/40.80 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 40.41/40.80 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 40.41/40.80 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 70.16/70.33 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 70.16/70.33 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 70.16/70.33 % SZS status Theorem for NUM665^1
% 70.16/70.33 % SZS output start Proof for NUM665^1
% 70.16/70.33 (
% 70.16/70.33 (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.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xy) Xx) Xv))) (=> (@ (@ tptp.lessis Xy) Xz) (@ tptp.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xz) Xx) Xv)))))))) (let ((_let_4 (@ tptp.some (lambda ((Xu tptp.nat)) (@ (@ (@ tptp.diffprop tptp.y) tptp.z) Xu))))) (let ((_let_5 (@ (@ tptp.moreis tptp.x) tptp.y))) (let ((_let_6 (ho_16 k_15 k_6))) (let ((_let_7 (= k_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_465))) (let ((_let_8 (ho_10 (ho_9 k_12 tptp.x) tptp.z))) (let ((_let_9 (ho_16 k_15 _let_8))) (let ((_let_10 (= k_6 _let_8))) (let ((_let_11 (not _let_6))) (let ((_let_12 (not (@ tptp.some ll_5)))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (PREPROCESS :args ((= _let_1 _let_12))) (PREPROCESS :args ((= _let_12 _let_11))))))) (let ((_let_14 (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_16 k_15 z) (ho_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_465 z))))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_7))) (let ((_let_17 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_16 x z) (ho_16 y z)))) (= x y))))) (let ((_let_18 (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_19 (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_20 (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_21 (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_22 (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_23 (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_24 (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_16 v ii) (ite (= i ii) e (ho_16 u ii)))))))))) (let ((_let_25 (forall ((BOUND_VARIABLE_702 tptp.nat)) (= (ho_7 k_6 BOUND_VARIABLE_702) (ho_7 (ho_10 (ho_9 k_8 tptp.x) tptp.z) BOUND_VARIABLE_702))))) (let ((_let_26 (forall ((BOUND_VARIABLE_692 tptp.nat) (BOUND_VARIABLE_693 tptp.nat) (BOUND_VARIABLE_694 tptp.nat)) (= (ho_7 (ho_10 (ho_9 k_11 BOUND_VARIABLE_692) BOUND_VARIABLE_693) BOUND_VARIABLE_694) (ho_7 (ho_10 (ho_9 k_8 BOUND_VARIABLE_692) BOUND_VARIABLE_693) BOUND_VARIABLE_694))))) (let ((_let_27 (forall ((BOUND_VARIABLE_682 tptp.nat) (BOUND_VARIABLE_683 tptp.nat) (BOUND_VARIABLE_684 tptp.nat)) (= (ho_7 (ho_10 (ho_9 k_12 BOUND_VARIABLE_682) BOUND_VARIABLE_683) BOUND_VARIABLE_684) (ho_7 (ho_10 (ho_9 k_8 BOUND_VARIABLE_682) BOUND_VARIABLE_683) BOUND_VARIABLE_684))))) (let ((_let_28 (forall ((BOUND_VARIABLE_676 tptp.nat)) (= (ho_7 k_13 BOUND_VARIABLE_676) (ho_7 (ho_10 (ho_9 k_8 tptp.y) tptp.z) BOUND_VARIABLE_676))))) (let ((_let_29 (ho_7 (ho_10 k_14 tptp.x) tptp.y))) (let ((_let_30 (forall ((BOUND_VARIABLE_702 tptp.nat)) (= (@ (@ (@ tptp.diffprop tptp.x) tptp.z) BOUND_VARIABLE_702) (ll_5 BOUND_VARIABLE_702))))) (let ((_let_31 (forall ((BOUND_VARIABLE_692 tptp.nat) (BOUND_VARIABLE_693 tptp.nat) (BOUND_VARIABLE_694 tptp.nat)) (= (@ (@ (@ tptp.diffprop BOUND_VARIABLE_692) BOUND_VARIABLE_693) BOUND_VARIABLE_694) (ll_4 BOUND_VARIABLE_692 BOUND_VARIABLE_693 BOUND_VARIABLE_694))))) (let ((_let_32 (forall ((BOUND_VARIABLE_682 tptp.nat) (BOUND_VARIABLE_683 tptp.nat) (BOUND_VARIABLE_684 tptp.nat)) (= (@ (@ (@ tptp.diffprop BOUND_VARIABLE_682) BOUND_VARIABLE_683) BOUND_VARIABLE_684) (ll_3 BOUND_VARIABLE_682 BOUND_VARIABLE_683 BOUND_VARIABLE_684))))) (let ((_let_33 (forall ((BOUND_VARIABLE_676 tptp.nat)) (= (@ (@ (@ tptp.diffprop tptp.y) tptp.z) BOUND_VARIABLE_676) (ll_2 BOUND_VARIABLE_676))))) (let ((_let_34 (and _let_5 _let_33 _let_32 _let_31 _let_30))) (let ((_let_35 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (ASSUME :args (_let_5)) (PREPROCESS :args ((and _let_33 _let_32 _let_31 _let_30)))) :args (_let_34)) (PREPROCESS :args ((= _let_34 (and _let_29 _let_28 _let_27 _let_26 _let_25))))) (PREPROCESS :args ((and _let_17 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18)))) :args ((and _let_29 _let_28 _let_27 _let_26 _let_25 _let_17 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18))))) (let ((_let_36 (AND_ELIM _let_35 :args (5)))) (let ((_let_37 (_let_17))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 (ho_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_465 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_751))) (let ((_let_40 (ho_16 k_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_751))) (let ((_let_41 (= _let_40 _let_39))) (let ((_let_42 (= k_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_751))) (let ((_let_43 (ite _let_42 _let_29 _let_40))) (let ((_let_44 (= _let_39 _let_43))) (let ((_let_45 (ho_16 k_15 k_13))) (let ((_let_46 (= k_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1077))) (let ((_let_47 (not _let_40))) (let ((_let_48 (_let_41))) (let ((_let_49 (AND_ELIM _let_35 :args (0)))) (let ((_let_50 (not _let_29))) (let ((_let_51 (_let_43))) (let ((_let_52 (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ite (= k_13 ii) (ho_7 (ho_10 k_14 tptp.x) tptp.y) (ho_16 k_15 ii)) (ho_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_465 ii))))) (let ((_let_53 (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_16 v ii) (ite (= k_13 ii) (ho_7 (ho_10 k_14 tptp.x) tptp.y) (ho_16 k_15 ii)))))))) (let ((_let_54 (not _let_53))) (let ((_let_55 (AND_ELIM _let_35 :args (6)))) (let ((_let_56 (_let_24))) (let ((_let_57 (ASSUME :args _let_56))) (let ((_let_58 (or))) (let ((_let_59 (_let_52))) (let ((_let_60 (_let_54))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_751 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_59))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_60)) :args _let_60) (REWRITE :args ((=> _let_54 (not (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_465 ii) (ite (= k_13 ii) (ho_7 (ho_10 k_14 tptp.x) tptp.y) (ho_16 k_15 ii))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) (REFL :args _let_59) :args _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (k_15 _let_29 k_13 QUANTIFIERS_INST_ENUM)) :args _let_56)) _let_55 :args (_let_54 false _let_24)) :args (_let_52 true _let_53)) :args (_let_44 false _let_52)))) (let ((_let_62 (not _let_44))) (let ((_let_63 (not _let_43))) (let ((_let_64 (_let_44))) (let ((_let_65 (@ tptp.some ll_2))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (PREPROCESS :args ((= _let_4 _let_65))) (PREPROCESS :args ((= _let_65 _let_45))))))) (let ((_let_67 (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_16 k_15 z) (ho_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1077 z))))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_46))) (let ((_let_70 (ho_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1077 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1504))) (let ((_let_71 (ho_16 k_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1504))) (let ((_let_72 (= _let_71 _let_70))) (let ((_let_73 (= k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1504))) (let ((_let_74 (ite _let_73 _let_6 _let_71))) (let ((_let_75 (= _let_70 _let_74))) (let ((_let_76 (not _let_71))) (let ((_let_77 (_let_72))) (let ((_let_78 (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ite (= k_6 ii) (ho_16 k_15 k_6) (ho_16 k_15 ii)) (ho_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1077 ii))))) (let ((_let_79 (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_16 v ii) (ite (= k_6 ii) (ho_16 k_15 k_6) (ho_16 k_15 ii)))))))) (let ((_let_80 (not _let_79))) (let ((_let_81 (_let_78))) (let ((_let_82 (_let_80))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_81) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1504 QUANTIFIERS_INST_CBQI_PROP)) :args _let_81))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_82)) :args _let_82) (REWRITE :args ((=> _let_80 (not (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_1077 ii) (ite (= k_6 ii) (ho_16 k_15 k_6) (ho_16 k_15 ii))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_80) _let_79))) (REFL :args _let_81) :args _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (k_15 _let_6 k_6 QUANTIFIERS_INST_ENUM)) :args _let_56)) _let_55 :args (_let_80 false _let_24)) :args (_let_78 true _let_79)) :args (_let_75 false _let_78)))) (let ((_let_84 (not _let_75))) (let ((_let_85 (not _let_74))) (let ((_let_86 (_let_75))) (let ((_let_87 (_let_74))) (let ((_let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_6))))) (let ((_let_89 (FALSE_INTRO _let_13))) (let ((_let_90 (APPLY_UF ho_16))) (let ((_let_91 (ASSUME :args (_let_73)))) (let ((_let_92 (ASSUME :args (_let_71)))) (let ((_let_93 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(REFL :args ((not _let_179))) :args _let_58)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_221)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_222 _let_219 _let_192) (SCOPE (FALSE_ELIM (TRANS _let_220 (FALSE_INTRO _let_222))) :args (_let_185 _let_184 _let_183))) :args (_let_183 _let_184 _let_185))) :args (true _let_221)) (CONG _let_209 (REFL :args ((not _let_184))) (MACRO_SR_PRED_INTRO :args ((= (not _let_185) _let_178))) (REFL :args (_let_190)) :args _let_58)) _let_216 _let_192 (REORDERING (CNF_EQUIV_POS1 :args _let_191) :args ((or (not _let_177) _let_181 _let_189))) _let_188 (REORDERING (CNF_EQUIV_NEG1 :args _let_186) :args ((or _let_178 _let_177 _let_179))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_217)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_218 _let_219 _let_192) (SCOPE (TRUE_ELIM (TRANS _let_220 (TRUE_INTRO _let_218))) :args (_let_178 _let_184 _let_183))) :args (_let_183 _let_184 _let_178))) :args (true _let_217)) _let_216 _let_192 (REORDERING (CNF_EQUIV_POS2 :args _let_191) :args ((or _let_177 _let_190 _let_189))) _let_188 (CNF_EQUIV_NEG2 :args _let_186) :args ((or _let_179 _let_185) false _let_184 false _let_183 true _let_181 false _let_182 true _let_177)) :args (_let_179 false _let_184 false _let_183 false _let_181 false _let_182 false _let_177 true _let_178)) :args (_let_174 false _let_179)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_119 :args (k_6 _let_8 QUANTIFIERS_INST_ENUM)) :args _let_118)) _let_117 :args (_let_176 false _let_19)) :args (_let_10 false _let_174 false _let_176)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_104 _let_9 _let_107 (not _let_108)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_171)) :args ((or _let_50 _let_103 (not _let_171)))) _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_173 :args (tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING ((not (= (ho_7 (ho_10 k_14 Xx) Xy) false))))) :args (_let_172))) _let_173 :args (_let_171 false _let_172)) :args (_let_103 false _let_29 false _let_171)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_169)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_99 _let_162 _let_170) (SCOPE (TRUE_ELIM (TRANS (CONG _let_99 (REFL :args (_let_105)) :args _let_90) (CONG _let_100 (TRANS (SYMM _let_170) _let_162) :args _let_90) (CONG _let_99 _let_163 :args _let_90) (CONG _let_100 (REFL :args (k_13)) :args _let_90) _let_97)) :args (_let_45 _let_46 _let_112 _let_113))) :args (_let_45 _let_112 _let_46 _let_113))) :args (true _let_169)) :args ((or _let_96 _let_106 _let_165 _let_95 (not _let_113)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_147)) :args ((or _let_113 _let_146 (not _let_147)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_168)) :args _let_168)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_146) _let_145))) (REFL :args ((not _let_150))) :args _let_58)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_166)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_167 _let_162 _let_133) (SCOPE (FALSE_ELIM (TRANS _let_164 (FALSE_INTRO _let_167))) :args (_let_153 _let_112 _let_126))) :args (_let_126 _let_112 _let_153))) :args (true _let_166)) (CONG _let_136 (REFL :args (_let_165)) (MACRO_SR_PRED_INTRO :args ((= (not _let_153) _let_149))) (REFL :args (_let_158)) :args _let_58)) _let_144 _let_133 (REORDERING (CNF_EQUIV_POS1 :args _let_159) :args ((or (not _let_148) _let_151 _let_157))) _let_156 (REORDERING (CNF_EQUIV_NEG1 :args _let_154) :args ((or _let_149 _let_148 _let_150))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_160)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_161 _let_162 _let_133) (SCOPE (TRUE_ELIM (TRANS _let_164 (TRUE_INTRO _let_161))) :args (_let_149 _let_112 _let_126))) :args (_let_126 _let_112 _let_149))) :args (true _let_160)) _let_144 _let_133 (REORDERING (CNF_EQUIV_POS2 :args _let_159) :args ((or _let_148 _let_158 _let_157))) _let_156 (CNF_EQUIV_NEG2 :args _let_154) :args ((or _let_150 _let_153) false _let_112 false _let_126 true _let_151 false _let_152 true _let_148)) :args (_let_150 false _let_112 false _let_126 false _let_151 false _let_152 false _let_148 true _let_149)) :args (_let_145 false _let_150)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_119 :args (k_13 _let_105 QUANTIFIERS_INST_ENUM)) :args _let_118)) _let_117 :args (_let_147 false _let_19)) :args (_let_113 false _let_145 false _let_147)) _let_144 _let_94 _let_66 :args (_let_106 false _let_113 false _let_112 false _let_46 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (tptp.z tptp.y tptp.x QUANTIFIERS_INST_E_MATCHING ((ho_10 (ho_9 k_11 Xy) Xx) (not (= (ho_7 (ho_10 k_17 Xy) Xz) false))))) :args (_let_109))) _let_111 :args (_let_108 false _let_109)) :args (_let_9 false _let_103 false _let_106 false _let_108)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_7 (not _let_16)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_102)) :args _let_102)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) (REFL :args ((not _let_41))) :args _let_58)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_66 _let_99 _let_98 _let_101) :args (_let_45 _let_47 _let_42 _let_46)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_101)) (CONG _let_99 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_751)) :args _let_90) (CONG _let_100 (SYMM _let_98) :args _let_90) _let_97)) :args (_let_45 _let_46 _let_42 _let_47)) :args ((not (and _let_45 _let_47 _let_42 _let_46)) SB_LITERAL))) (CONG (REFL :args (_let_96)) (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_40))) (REFL :args ((not _let_42))) (REFL :args (_let_95)) :args _let_58)) _let_94 _let_66 (REORDERING (CNF_ITE_POS2 :args _let_51) :args ((or _let_40 _let_42 _let_63))) (REORDERING (CNF_EQUIV_POS1 :args _let_64) :args ((or (not _let_39) _let_43 _let_62))) _let_61 (REORDERING (CNF_EQUIV_NEG1 :args _let_48) :args ((or _let_40 _let_39 _let_41))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_64) :args ((or _let_39 _let_63 _let_62))) _let_61 (REORDERING (CNF_ITE_NEG3 :args _let_51) :args ((or _let_50 _let_47 _let_43))) _let_49 (CNF_EQUIV_NEG2 :args _let_48) :args ((or _let_41 _let_47) false _let_44 false _let_43 false _let_29 true _let_39)) :args (_let_41 false _let_46 false _let_45 false _let_42 false _let_43 false _let_44 false _let_39 true _let_40)) :args (_let_14 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (k_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_465 QUANTIFIERS_INST_ENUM)) :args _let_37)) _let_36 :args (_let_16 false _let_17)) :args (_let_7 false _let_14 false _let_16)) _let_13 :args (false false _let_10 false _let_9 false _let_7 true _let_6)) :args (_let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 70.16/70.34 )
% 70.16/70.34 % SZS output end Proof for NUM665^1
% 70.16/70.35 % cvc5---1.0.5 exiting
% 70.16/70.35 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------