TSTP Solution File: SEV021^6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV021^6 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 19:21:21 EDT 2023
% Result : Theorem 37.62s 37.99s
% Output : Proof 37.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV021^6 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 03:19:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TH0
% 20.38/20.68 %------------------------------------------------------------------------------
% 20.38/20.68 % File : SEV021^6 : TPTP v8.1.2. Released v5.5.0.
% 20.38/20.68 % Domain : Set Theory (Relations)
% 20.38/20.68 % Problem : TPS problem from EQUIVALENCE-RELATIONS-THMS
% 20.38/20.68 % Version : Especial.
% 20.38/20.68 % English :
% 20.38/20.68
% 20.38/20.68 % Refs : [Sul12] Sultana (2012), Email to Geoff Sutcliffe
% 20.38/20.68 % Source : [Sul12]
% 20.38/20.68 % Names :
% 20.38/20.68
% 20.38/20.68 % Status : Theorem
% 20.38/20.68 % Rating : 0.46 v8.1.0, 0.55 v7.5.0, 0.57 v7.4.0, 0.89 v7.2.0, 0.88 v7.0.0, 1.00 v6.3.0, 0.80 v6.2.0, 0.86 v6.1.0, 1.00 v5.5.0
% 20.38/20.68 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 20.38/20.68 % Number of atoms : 13 ( 3 equ; 0 cnn)
% 20.38/20.68 % Maximal formula atoms : 8 ( 6 avg)
% 20.38/20.68 % Number of connectives : 38 ( 0 ~; 0 |; 11 &; 20 @)
% 20.38/20.68 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 20.38/20.68 % Maximal formula depth : 15 ( 8 avg)
% 20.38/20.68 % Number of types : 2 ( 1 usr)
% 20.38/20.68 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 20.38/20.68 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 20.38/20.68 % Number of variables : 17 ( 3 ^; 10 !; 4 ?; 17 :)
% 20.38/20.68 % SPC : TH0_THM_EQU_NAR
% 20.38/20.68
% 20.38/20.68 % Comments : .
% 20.38/20.68 % : The conjecture is of the form A => B, where A is not needed to
% 20.38/20.68 % prove B. A is an easily provable property of equality.
% 20.38/20.68 % : This version has the relation Q instantiated.
% 20.38/20.68 %------------------------------------------------------------------------------
% 20.38/20.68 thf(a_type,type,
% 20.38/20.68 a: $tType ).
% 20.38/20.68
% 20.38/20.68 thf(cP,type,
% 20.38/20.68 cP: ( a > $o ) > $o ).
% 20.38/20.68
% 20.38/20.68 thf(cQ,type,
% 20.38/20.68 cQ: a > a > $o ).
% 20.38/20.68
% 20.38/20.68 thf(cQ_def,definition,
% 20.38/20.68 ( cQ
% 20.38/20.68 = ( ^ [X: a,Y: a] :
% 20.38/20.68 ? [S: a > $o] :
% 20.38/20.68 ( ( cP @ S )
% 20.38/20.68 & ( S @ X )
% 20.38/20.68 & ( S @ Y ) ) ) ) ).
% 20.38/20.68
% 20.38/20.68 thf(cTHM262_D_EXT2_pme,conjecture,
% 20.38/20.68 ( ! [Xq1: a > $o,Xq2: a > $o] :
% 20.38/20.68 ( ( ( Xq1 = Xq2 )
% 20.38/20.68 & ( cP @ Xq1 ) )
% 20.38/20.68 => ( cP @ Xq2 ) )
% 20.38/20.68 => ( ( ! [Xp: a > $o] :
% 20.38/20.68 ( ( cP @ Xp )
% 20.38/20.68 => ? [Xz: a] : ( Xp @ Xz ) )
% 20.38/20.68 & ! [Xx: a] :
% 20.38/20.68 ? [Xp: a > $o] :
% 20.38/20.68 ( ( cP @ Xp )
% 20.38/20.68 & ( Xp @ Xx ) )
% 20.38/20.68 & ! [Xx: a,Xy: a,Xp: a > $o,Xq: a > $o] :
% 20.38/20.68 ( ( ( cP @ Xp )
% 20.38/20.68 & ( cP @ Xq )
% 20.38/20.68 & ( Xp @ Xx )
% 20.38/20.68 & ( Xq @ Xx )
% 20.38/20.68 & ( Xp @ Xy ) )
% 20.38/20.68 => ( Xq @ Xy ) ) )
% 20.38/20.68 => ( ( ^ [Xs: a > $o] :
% 20.38/20.68 ( ? [Xz: a] : ( Xs @ Xz )
% 20.38/20.68 & ! [Xx: a] :
% 20.38/20.68 ( ( Xs @ Xx )
% 20.38/20.68 => ! [Xy: a] :
% 20.38/20.68 ( ( Xs @ Xy )
% 20.38/20.68 <=> ( cQ @ Xx @ Xy ) ) ) ) )
% 20.38/20.68 = cP ) ) ) ).
% 20.38/20.68
% 20.38/20.68 %------------------------------------------------------------------------------
% 20.38/20.68 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ACLf5t1cYX/cvc5---1.0.5_29286.p...
% 20.38/20.68 (declare-sort $$unsorted 0)
% 20.38/20.68 (declare-sort tptp.a 0)
% 20.38/20.68 (declare-fun tptp.cP ((-> tptp.a Bool)) Bool)
% 20.38/20.68 (declare-fun tptp.cQ (tptp.a tptp.a) Bool)
% 20.38/20.68 (assert (= tptp.cQ (lambda ((X tptp.a) (Y tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ tptp.cP S) (@ S X) (@ S Y))))))
% 20.38/20.68 (assert (not (=> (forall ((Xq1 (-> tptp.a Bool)) (Xq2 (-> tptp.a Bool))) (=> (and (= Xq1 Xq2) (@ tptp.cP Xq1)) (@ tptp.cP Xq2))) (=> (and (forall ((Xp (-> tptp.a Bool))) (=> (@ tptp.cP Xp) (exists ((Xz tptp.a)) (@ Xp Xz)))) (forall ((Xx tptp.a)) (exists ((Xp (-> tptp.a Bool))) (and (@ tptp.cP Xp) (@ Xp Xx)))) (forall ((Xx tptp.a) (Xy tptp.a) (Xp (-> tptp.a Bool)) (Xq (-> tptp.a Bool))) (=> (and (@ tptp.cP Xp) (@ tptp.cP Xq) (@ Xp Xx) (@ Xq Xx) (@ Xp Xy)) (@ Xq Xy)))) (= (lambda ((Xs (-> tptp.a Bool))) (and (exists ((Xz tptp.a)) (@ Xs Xz)) (forall ((Xx tptp.a)) (=> (@ Xs Xx) (forall ((Xy tptp.a)) (= (@ Xs Xy) (@ (@ tptp.cQ Xx) Xy))))))) tptp.cP)))))
% 20.38/20.68 (set-info :filename cvc5---1.0.5_29286)
% 20.38/20.68 (check-sat-assuming ( true ))
% 20.38/20.68 ------- get file name : TPTP file name is SEV021^6
% 20.38/20.68 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29286.smt2...
% 20.38/20.68 --- Run --ho-elim --full-saturate-quant at 10...
% 20.38/20.68 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 20.38/20.68 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 37.62/37.99 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 37.62/37.99 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 37.62/37.99 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 37.62/37.99 % SZS status Theorem for SEV021^6
% 37.62/37.99 % SZS output start Proof for SEV021^6
% 37.62/37.99 (
% 37.62/37.99 (let ((_let_1 (not (=> (forall ((Xq1 (-> tptp.a Bool)) (Xq2 (-> tptp.a Bool))) (=> (and (= Xq1 Xq2) (@ tptp.cP Xq1)) (@ tptp.cP Xq2))) (=> (and (forall ((Xp (-> tptp.a Bool))) (=> (@ tptp.cP Xp) (exists ((Xz tptp.a)) (@ Xp Xz)))) (forall ((Xx tptp.a)) (exists ((Xp (-> tptp.a Bool))) (and (@ tptp.cP Xp) (@ Xp Xx)))) (forall ((Xx tptp.a) (Xy tptp.a) (Xp (-> tptp.a Bool)) (Xq (-> tptp.a Bool))) (=> (and (@ tptp.cP Xp) (@ tptp.cP Xq) (@ Xp Xx) (@ Xq Xx) (@ Xp Xy)) (@ Xq Xy)))) (= (lambda ((Xs (-> tptp.a Bool))) (and (exists ((Xz tptp.a)) (@ Xs Xz)) (forall ((Xx tptp.a)) (=> (@ Xs Xx) (forall ((Xy tptp.a)) (= (@ Xs Xy) (@ (@ tptp.cQ Xx) Xy))))))) tptp.cP)))))) (let ((_let_2 (= tptp.cQ (lambda ((X tptp.a) (Y tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ tptp.cP S) (@ S X) (@ S Y))))))) (let ((_let_3 (forall ((S (-> tptp.a Bool))) (or (not (@ tptp.cP S)) (not (@ S SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_389)) (not (@ S SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_390)))))) (let ((_let_4 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_390))) (let ((_let_5 (not _let_4))) (let ((_let_6 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_389))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.cP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_7 _let_5))) (let ((_let_11 (not _let_3))) (let ((_let_12 (= _let_11 _let_4))) (let ((_let_13 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_394 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_390))) (let ((_let_14 (not _let_13))) (let ((_let_15 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_394 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_389))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.cP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_394))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16 _let_14))) (let ((_let_20 (or _let_18 _let_9 _let_16 _let_7 _let_14 _let_4))) (let ((_let_21 (or _let_7 _let_12))) (let ((_let_22 (forall ((Xx tptp.a) (BOUND_VARIABLE_719 tptp.a)) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 Xx)) (= (not (forall ((S (-> tptp.a Bool))) (or (not (@ tptp.cP S)) (not (@ S Xx)) (not (@ S BOUND_VARIABLE_719))))) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 BOUND_VARIABLE_719)))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (forall ((S (-> tptp.a Bool))) (or (not (@ tptp.cP S)) (not (@ S SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) (not (@ S k_380)))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 k_380))) (let ((_let_27 (= _let_26 _let_25))) (let ((_let_28 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27))) (let ((_let_31 (not _let_22))) (let ((_let_32 (not _let_30))) (let ((_let_33 (k_3 k_380))) (let ((_let_34 (= _let_33 _let_26))) (let ((_let_35 (= _let_33 _let_25))) (let ((_let_36 (not _let_27))) (let ((_let_37 (not _let_33))) (let ((_let_38 (= k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_39 (not _let_34))) (let ((_let_40 (tptp.cP k_3))) (let ((_let_41 (not _let_38))) (let ((_let_42 (lambdaF_2 k_3))) (let ((_let_43 (= _let_40 _let_42))) (let ((_let_44 (forall ((Xz tptp.a)) (not (@ k_3 Xz))))) (let ((_let_45 (not _let_44))) (let ((_let_46 (not _let_40))) (let ((_let_47 (or _let_46 _let_45))) (let ((_let_48 (forall ((S (-> tptp.a Bool))) (or (not (@ tptp.cP S)) (not (@ S SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)) (not (@ S SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20)))))) (let ((_let_49 (forall ((Xx tptp.a) (BOUND_VARIABLE_719 tptp.a)) (or (not (@ k_3 Xx)) (= (not (forall ((S (-> tptp.a Bool))) (or (not (@ tptp.cP S)) (not (@ S Xx)) (not (@ S BOUND_VARIABLE_719))))) (@ k_3 BOUND_VARIABLE_719)))))) (let ((_let_50 (forall ((Xz tptp.a)) (not (@ k_3 Xz))))) (let ((_let_51 (not _let_50))) (let ((_let_52 (and _let_51 _let_49))) (let ((_let_53 (= _let_42 _let_52))) (let ((_let_54 (k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_55 (not _let_54))) (let ((_let_56 (k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_46 _let_57 _let_55))) (let ((_let_59 (not _let_48))) (let ((_let_60 (= _let_59 _let_54))) (let ((_let_61 (or _let_57 _let_60))) (let ((_let_62 (= tptp.cP lambdaF_2))) (let ((_let_63 (not _let_43))) (let ((_let_64 (not))) (let ((_let_65 (=>))) (let ((_let_66 (=))) (let ((_let_67 (forall ((Xx tptp.a) (Xy tptp.a) (Xp (-> tptp.a Bool)) (Xq (-> tptp.a Bool))) (or (not (@ tptp.cP Xp)) (not (@ tptp.cP Xq)) (not (@ Xp Xx)) (not (@ Xq Xx)) (not (@ Xp Xy)) (@ Xq Xy))))) (let ((_let_68 (forall ((Xp (-> tptp.a Bool))) (or (not (@ tptp.cP Xp)) (not (forall ((Xz tptp.a)) (not (@ Xp Xz)))))))) (let ((_let_69 (and _let_68 (forall ((Xx tptp.a)) (not (forall ((Xp (-> tptp.a Bool))) (or (not (@ tptp.cP Xp)) (not (@ Xp Xx)))))) _let_67))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args ((not (=> _let_69 (= tptp.cP (lambda ((Xs (-> tptp.a Bool))) (and (not (forall ((Xz tptp.a)) (not (@ Xs Xz)))) (forall ((Xx tptp.a) (BOUND_VARIABLE_719 tptp.a)) (or (not (@ Xs Xx)) (= (@ Xs BOUND_VARIABLE_719) (@ (@ tptp.cQ Xx) BOUND_VARIABLE_719))))))))) SB_DEFAULT SBA_FIXPOINT)) (CONG (CONG (REFL :args (_let_69)) (CONG (REFL :args (tptp.cP)) (MACRO_SR_PRED_INTRO :args ((= (lambda ((Xs (-> tptp.a Bool))) (and (not (forall ((Xz tptp.a)) (not (@ Xs Xz)))) (forall ((Xx tptp.a) (BOUND_VARIABLE_719 tptp.a)) (or (not (@ Xs Xx)) (= (@ Xs BOUND_VARIABLE_719) (not (forall ((S (-> tptp.a Bool))) (or (not (@ tptp.cP S)) (not (@ S Xx)) (not (@ S BOUND_VARIABLE_719)))))))))) lambdaF_2))) :args _let_66) :args _let_65) :args _let_64))))) (let ((_let_71 (NOT_IMPLIES_ELIM2 _let_70))) (let ((_let_72 (THEORY_LEMMA :args ((or _let_62 _let_63) THEORY_UF)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST _let_72 _let_71 :args (_let_63 true _let_62)))) (let ((_let_74 (_let_43))) (let ((_let_75 (CNF_EQUIV_NEG2 :args _let_74))) (let ((_let_76 (NOT_IMPLIES_ELIM1 _let_70))) (let ((_let_77 (AND_ELIM _let_76 :args (0)))) (let ((_let_78 (or))) (let ((_let_79 (CONG (THEORY_PREPROCESS :args ((= (@ tptp.cP k_3) _let_40))) :args _let_64))) (let ((_let_80 (_let_68))) (let ((_let_81 (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_80) :args (k_3 QUANTIFIERS_INST_ENUM)) :args _let_80) (CONG (REFL :args _let_80) (CONG _let_79 (REFL :args (_let_45)) :args _let_78) :args _let_65))))) (let ((_let_82 (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_45 (not _let_47)))))) (let ((_let_83 (forall ((Xs (-> tptp.a Bool))) (= (and (not (forall ((Xz tptp.a)) (not (@ Xs Xz)))) (forall ((Xx tptp.a) (BOUND_VARIABLE_719 tptp.a)) (or (not (@ Xs Xx)) (= (@ Xs BOUND_VARIABLE_719) (not (forall ((S (-> tptp.a Bool))) (or (not (@ tptp.cP S)) (not (@ S Xx)) (not (@ S BOUND_VARIABLE_719))))))))) (lambdaF_2 Xs))))) (let ((_let_84 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_85 (not _let_84))) (let ((_let_86 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_87 (not _let_86))) (let ((_let_88 (tptp.cP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or _let_89 _let_87 _let_85))) (let ((_let_91 (or _let_89 _let_46 _let_87 _let_57 _let_85 _let_54))) (let ((_let_92 (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_50 (= Xz Xz)))))) (let ((_let_93 ((forall ((Xs (-> tptp.a Bool))) (= (lambdaF_2 Xs) (@ (lambda ((Xs (-> tptp.a Bool))) (and (not (forall ((Xz tptp.a)) (not (@ Xs Xz)))) (forall ((Xx tptp.a) (BOUND_VARIABLE_719 tptp.a)) (or (not (@ Xs Xx)) (= (@ Xs BOUND_VARIABLE_719) (not (forall ((S (-> tptp.a Bool))) (or (not (@ tptp.cP S)) (not (@ S Xx)) (not (@ S BOUND_VARIABLE_719)))))))))) Xs)))))) (let ((_let_94 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_93) (REWRITE :args _let_93)))) (let ((_let_95 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_94 :args (k_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_2 Xs)))) :args (_let_83)))))) (let ((_let_96 (not _let_53))) (let ((_let_97 (not _let_52))) (let ((_let_98 (_let_53))) (let ((_let_99 (REORDERING (CNF_EQUIV_POS2 :args _let_98) :args ((or _let_42 _let_97 _let_96))))) (let ((_let_100 (not _let_49))) (let ((_let_101 (_let_100))) (let ((_let_102 (REFL :args _let_101))) (let ((_let_103 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))))) (let ((_let_104 (_let_52))) (let ((_let_105 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_104) (CONG (REFL :args _let_104) _let_103 _let_102 :args _let_78)) :args ((or _let_50 _let_52 _let_100))))) (let ((_let_106 (THEORY_PREPROCESS :args ((= (@ k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) _let_54))))) (let ((_let_107 (_let_59))) (let ((_let_108 (REFL :args _let_107))) (let ((_let_109 (CONG (THEORY_PREPROCESS :args ((= (@ k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19) _let_56))) :args _let_64))) (let ((_let_110 (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_101)) :args _let_101) (CONG _let_102 (CONG (CONG _let_109 (CONG _let_108 _let_106 :args _let_66) :args _let_78) :args _let_64) :args _let_65))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_49))) (REFL :args ((not _let_61))) :args _let_78)))) (let ((_let_111 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG (REFL :args (_let_61)) (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_78)) :args ((or _let_56 _let_61))))) (let ((_let_112 (CNF_OR_NEG :args (_let_61 1)))) (let ((_let_113 (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_48))))) (let ((_let_114 (_let_60))) (let ((_let_115 (CONG (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) _let_84))) :args _let_64))) (let ((_let_116 (CONG (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19) _let_86))) :args _let_64))) (let ((_let_117 (CONG (THEORY_PREPROCESS :args ((= (@ tptp.cP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21) _let_88))) :args _let_64))) (let ((_let_118 (REFL :args (_let_90)))) (let ((_let_119 (AND_ELIM _let_76 :args (2)))) (let ((_let_120 (_let_67))) (let ((_let_121 (REFL :args _let_120))) (let ((_let_122 (ASSUME :args _let_120))) (let ((_let_123 (MACRO_RESOLUTION_TRUST _let_95 _let_94 :args (_let_53 false _let_83)))) (let ((_let_124 (_let_48))) (let ((_let_125 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_114) :args ((or _let_59 _let_54 _let_60))) (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_46 _let_57 _let_55 (not _let_58)))) _let_112 _let_111 _let_110 _let_105 (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_124) :args (k_3 QUANTIFIERS_INST_E_MATCHING)) :args _let_124) (CONG (REFL :args _let_124) (CONG _let_79 _let_109 (CONG _let_106 :args _let_64) :args _let_78) :args _let_65))) _let_92 _let_99 _let_123 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args 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_let_61 true _let_49 false _let_58 true _let_50 true _let_52 false _let_53 false _let_48 true _let_44 false _let_47 true _let_42 true _let_43)))) (let ((_let_126 (or _let_9 _let_29))) (let ((_let_127 (forall ((S (-> tptp.a Bool))) (or (not (@ tptp.cP S)) (not (@ S SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))))) (let ((_let_128 (not _let_126))) (let ((_let_129 (not _let_127))) (let ((_let_130 (k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_131 (= _let_130 _let_129))) (let ((_let_132 (not _let_130))) (let ((_let_133 (or _let_132 _let_131))) (let ((_let_134 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_98) :args ((or (not _let_42) _let_52 _let_96))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_74) :args ((or _let_40 _let_42 _let_43))) _let_125 _let_73 :args (_let_42 true _let_40 true _let_43)) _let_123 :args (_let_52 false _let_42 false _let_53)))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_52 1)) :args ((or _let_49 _let_97))) _let_134 :args (_let_49 false _let_52)))) (let ((_let_136 (_let_129))) (let ((_let_137 (REFL :args _let_136))) (let ((_let_138 (@ k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_139 (THEORY_PREPROCESS :args ((= _let_138 _let_130))))) (let ((_let_140 (CONG _let_139 :args _let_64))) (let ((_let_141 (_let_49))) (let ((_let_142 (REFL :args _let_141))) (let ((_let_143 ((not (= (@ k_3 Xx) false)) (@ k_3 BOUND_VARIABLE_719)))) (let ((_let_144 (ASSUME :args _let_141))) (let ((_let_145 (_let_51))) (let ((_let_146 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_145)) :args _let_145) (TRANS (REWRITE :args ((=> _let_51 (not (not _let_138))))) (CONG (REFL :args _let_145) _let_139 :args _let_65)))) (CONG _let_103 (REFL :args (_let_130)) :args _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_52 0)) :args ((or _let_51 _let_97))) _let_134 :args (_let_51 false _let_52)) :args (_let_130 true _let_50)))) (let ((_let_147 (CONG (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) _let_28))) :args _let_64))) (let ((_let_148 (CONG (THEORY_PREPROCESS :args ((= (@ tptp.cP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) _let_8))) :args _let_64))) (let ((_let_149 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_136)) :args _let_136) (CONG _let_137 (CONG (CONG _let_148 _let_147 :args _let_78) :args _let_64) :args _let_65))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_129) _let_127))) (REFL :args (_let_128)) :args _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_131)) :args ((or _let_132 _let_129 (not _let_131)))) _let_146 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_133)) :args ((or _let_132 _let_131 (not _let_133)))) _let_146 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_144 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING _let_143)) :args _let_141)) (CONG _let_142 (CONG _let_140 (CONG _let_139 _let_137 :args _let_66) :args _let_78) :args _let_65))) _let_135 :args (_let_133 false _let_49)) :args (_let_131 false _let_130 false _let_133)) :args (_let_129 false _let_130 false _let_131)) :args (_let_128 true _let_127)))) (let ((_let_150 (REFL :args (_let_126)))) (let ((_let_151 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_126 0)) (CONG _let_150 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_78)) :args ((or _let_8 _let_126))) _let_149 :args (_let_8 true _let_126)))) (let ((_let_152 (ASSUME :args (_let_46)))) (let ((_let_153 (ASSUME :args (_let_38)))) (let ((_let_154 (ASSUME :args (_let_8)))) (let ((_let_155 (MACRO_RESOLUTION_TRUST (THEORY_LEMMA :args ((or _let_38 _let_39) THEORY_UF)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_152 _let_153 _let_154) :args (_let_46 _let_8 _let_38)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_154)) (CONG (SYMM _let_153) :args (APPLY_UF tptp.cP)) (FALSE_INTRO _let_152))) :args (_let_46 _let_38 _let_8)) :args ((not (and _let_46 _let_8 _let_38)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_40))) (REFL :args (_let_9)) (REFL :args (_let_41)) :args _let_78)) _let_151 _let_125 :args (_let_41 false _let_8 true _let_40)) :args (_let_39 true _let_38)))) (let ((_let_156 (_let_34))) (let ((_let_157 (or _let_132 _let_35))) (let ((_let_158 (REFL :args (_let_25)))) (let ((_let_159 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_157)) :args ((or _let_132 _let_35 (not _let_157)))) _let_146 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_144 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 k_380 QUANTIFIERS_INST_E_MATCHING _let_143)) :args _let_141)) (CONG _let_142 (CONG _let_140 (CONG (THEORY_PREPROCESS :args ((= (@ k_3 k_380) _let_33))) _let_158 :args _let_66) :args _let_78) :args _let_65))) _let_135 :args (_let_157 false _let_49)) :args (_let_35 false _let_130 false _let_157)))) (let ((_let_160 (not _let_35))) (let ((_let_161 (_let_35))) (let ((_let_162 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))))) (let ((_let_163 (_let_27))) (let ((_let_164 (_let_22))) (let ((_let_165 (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_390) _let_4))))) (let ((_let_166 (_let_11))) (let ((_let_167 (REFL :args _let_166))) (let ((_let_168 (CONG (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_389) _let_6))) :args _let_64))) (let ((_let_169 (_let_31))) (let ((_let_170 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_169)) :args _let_169) (CONG (REFL :args _let_169) (CONG (CONG _let_168 (CONG _let_167 _let_165 :args _let_66) :args _let_78) :args _let_64) :args _let_65))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_22))) (REFL :args (_let_23)) :args _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_164) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 k_380 QUANTIFIERS_INST_E_MATCHING ((not (= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 Xx) false)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 BOUND_VARIABLE_719)))) :args _let_164)) (CONG (REFL :args _let_164) (CONG _let_147 (CONG (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 k_380) _let_26))) _let_158 :args _let_66) :args _let_78) :args _let_65))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_27 _let_32))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_126 1)) (CONG _let_150 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_78)) :args ((or _let_28 _let_126))) _let_149 :args (_let_28 true _let_126)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_163) :args ((or (not _let_26) _let_25 _let_36))) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_161) (CONG (REFL :args (_let_160)) (REFL :args (_let_33)) _let_162 :args _let_78)) :args ((or _let_33 _let_24 _let_160))) _let_159 (REORDERING (CNF_EQUIV_NEG1 :args _let_156) :args ((or _let_33 _let_26 _let_34))) _let_155 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_163) (CONG (REFL :args (_let_36)) (REFL :args (_let_26)) _let_162 :args _let_78)) :args ((or _let_26 _let_24 _let_36))) (REORDERING (CNF_EQUIV_POS1 :args _let_161) :args ((or _let_37 _let_25 _let_160))) _let_159 (CNF_EQUIV_NEG2 :args _let_156) _let_155 :args ((or _let_37 _let_36) true _let_24 false _let_35 true _let_26 true _let_34)) :args (_let_36 false _let_24 false _let_35 false _let_26 true _let_34 true _let_33)) :args (_let_32 false _let_28 true _let_27)) :args (_let_31 true _let_30)) :args (_let_23 true _let_22)))) (let ((_let_171 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_21 1)) _let_170 :args ((not _let_12) true _let_21)))) (let ((_let_172 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_3))))) (let ((_let_173 (_let_12))) (let ((_let_174 (CONG (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_394 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_390) _let_13))) :args _let_64))) (let ((_let_175 (CONG (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_394 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_389) _let_15))) :args _let_64))) (let ((_let_176 (CONG (THEORY_PREPROCESS :args ((= (@ tptp.cP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_394) _let_17))) :args _let_64))) (let ((_let_177 (REFL :args (_let_19)))) (let ((_let_178 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG (REFL :args (_let_21)) (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) :args _let_78)) :args ((or _let_6 _let_21))) _let_170 :args (_let_6 true _let_21)))) (let ((_let_179 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_9 _let_4 _let_7 _let_14 _let_16 _let_18 (not _let_20)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_122 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_389 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_390 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_394 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING)) :args _let_120) (CONG _let_121 (CONG _let_176 _let_148 _let_175 _let_168 _let_174 _let_165 :args _let_78) :args _let_65))) _let_119 :args (_let_20 false _let_67)) _let_178 _let_151 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 2)) (CONG _let_177 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_78)) :args ((or _let_13 _let_19))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 1)) (CONG _let_177 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_78)) :args ((or _let_15 _let_19))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 0)) (CONG _let_177 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_78)) :args ((or _let_17 _let_19))) (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_166)) :args _let_166) (CONG _let_167 (CONG (CONG _let_176 _let_175 _let_174 :args _let_78) :args _let_64) :args _let_65))) (CONG _let_172 (REFL :args ((not _let_19))) :args _let_78)) (REORDERING (EQ_RESOLVE (CNF_EQUIV_NEG2 :args _let_173) (CONG (REFL :args _let_173) _let_172 (REFL :args (_let_5)) :args _let_78)) :args ((or _let_3 _let_12 _let_5))) _let_171 :args (_let_3 false _let_20 false _let_6 false _let_8 false _let_13 false _let_15 false _let_17 true _let_19 true _let_4 true _let_12)))) (let ((_let_180 (not _let_10))) (let ((_let_181 (_let_3))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_181) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING)) :args _let_181) (CONG (REFL :args _let_181) (CONG _let_148 _let_168 (CONG _let_165 :args _let_64) :args _let_78) :args _let_65))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_9 _let_7 _let_5 _let_180))) _let_151 _let_178 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_173) :args ((or _let_11 _let_4 _let_12))) _let_179 _let_171 :args (_let_4 false _let_3 true _let_12)) :args (_let_180 false _let_8 false _let_6 false _let_4)) _let_179 :args (false true _let_10 false _let_3)) :args (_let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 37.62/38.00 )
% 37.62/38.00 % SZS output end Proof for SEV021^6
% 37.62/38.00 % cvc5---1.0.5 exiting
% 37.62/38.00 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------