TSTP Solution File: ITP209^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP209^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 03:19:35 EDT 2023
% Result : Theorem 0.22s 0.57s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ITP209^1 : TPTP v8.1.2. Released v8.1.0.
% 0.08/0.15 % Command : do_cvc5 %s %d
% 0.14/0.37 % Computer : n017.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sun Aug 27 11:09:11 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.22/0.52 %----Proving TH0
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 % File : ITP209^1 : TPTP v8.1.2. Released v8.1.0.
% 0.22/0.52 % Domain : Interactive Theorem Proving
% 0.22/0.52 % Problem : Sledgehammer problem Syntax_Match 00088_002922
% 0.22/0.52 % Version : [Des22] axioms.
% 0.22/0.52 % English :
% 0.22/0.52
% 0.22/0.52 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.22/0.52 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.22/0.52 % Source : [Des22]
% 0.22/0.52 % Names : 0023_Syntax_Match_00088_002922 [Des22]
% 0.22/0.52
% 0.22/0.52 % Status : Theorem
% 0.22/0.52 % Rating : 0.08 v8.1.0
% 0.22/0.52 % Syntax : Number of formulae : 17 ( 6 unt; 6 typ; 0 def)
% 0.22/0.52 % Number of atoms : 20 ( 13 equ; 0 cnn)
% 0.22/0.52 % Maximal formula atoms : 3 ( 1 avg)
% 0.22/0.52 % Number of connectives : 93 ( 0 ~; 0 |; 1 &; 86 @)
% 0.22/0.52 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.22/0.52 % Maximal formula depth : 7 ( 4 avg)
% 0.22/0.52 % Number of types : 2 ( 1 usr)
% 0.22/0.52 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.22/0.52 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.22/0.52 % Number of variables : 35 ( 1 ^; 34 !; 0 ?; 35 :)
% 0.22/0.52 % SPC : TH0_THM_EQU_NAR
% 0.22/0.52
% 0.22/0.52 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.22/0.52 % from the van Emde Boas Trees session in the Archive of Formal
% 0.22/0.52 % proofs -
% 0.22/0.52 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.22/0.52 % 2022-02-17 14:22:46.636
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 % Could-be-implicit typings (1)
% 0.22/0.52 thf(ty_n_tf__a,type,
% 0.22/0.52 a: $tType ).
% 0.22/0.52
% 0.22/0.52 % Explicit typings (5)
% 0.22/0.52 thf(sy_c_Syntax__Match_Oac__operator_001tf__a,type,
% 0.22/0.52 syntax_ac_operator_a: ( a > a > a ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(sy_v_a,type,
% 0.22/0.52 a2: a ).
% 0.22/0.52
% 0.22/0.52 thf(sy_v_b,type,
% 0.22/0.52 b: a ).
% 0.22/0.52
% 0.22/0.52 thf(sy_v_c,type,
% 0.22/0.52 c: a ).
% 0.22/0.52
% 0.22/0.52 thf(sy_v_f,type,
% 0.22/0.52 f: a > a > a ).
% 0.22/0.52
% 0.22/0.52 % Relevant facts (10)
% 0.22/0.52 thf(fact_0_ac__operator__axioms,axiom,
% 0.22/0.52 syntax_ac_operator_a @ f ).
% 0.22/0.52
% 0.22/0.52 % ac_operator_axioms
% 0.22/0.52 thf(fact_1_commute,axiom,
% 0.22/0.52 ! [A: a,B: a] :
% 0.22/0.52 ( ( f @ A @ B )
% 0.22/0.52 = ( f @ B @ A ) ) ).
% 0.22/0.52
% 0.22/0.52 % commute
% 0.22/0.52 thf(fact_2_left__commute,axiom,
% 0.22/0.52 ! [A: a,B: a,C: a] :
% 0.22/0.52 ( ( f @ A @ ( f @ B @ C ) )
% 0.22/0.52 = ( f @ B @ ( f @ A @ C ) ) ) ).
% 0.22/0.52
% 0.22/0.52 % left_commute
% 0.22/0.52 thf(fact_3_right__assoc,axiom,
% 0.22/0.52 ! [A: a,B: a,C: a] :
% 0.22/0.52 ( ( f @ ( f @ A @ B ) @ C )
% 0.22/0.52 = ( f @ A @ ( f @ B @ C ) ) ) ).
% 0.22/0.52
% 0.22/0.52 % right_assoc
% 0.22/0.52 thf(fact_4_ac__operator_Ointro,axiom,
% 0.22/0.52 ! [F: a > a > a] :
% 0.22/0.52 ( ! [A2: a,B2: a,C2: a] :
% 0.22/0.52 ( ( F @ ( F @ A2 @ B2 ) @ C2 )
% 0.22/0.52 = ( F @ A2 @ ( F @ B2 @ C2 ) ) )
% 0.22/0.52 => ( ! [A2: a,B2: a] :
% 0.22/0.52 ( ( F @ A2 @ B2 )
% 0.22/0.52 = ( F @ B2 @ A2 ) )
% 0.22/0.52 => ( syntax_ac_operator_a @ F ) ) ) ).
% 0.22/0.52
% 0.22/0.52 % ac_operator.intro
% 0.22/0.52 thf(fact_5_ac__operator_Ocommute,axiom,
% 0.22/0.52 ! [F: a > a > a,A: a,B: a] :
% 0.22/0.52 ( ( syntax_ac_operator_a @ F )
% 0.22/0.52 => ( ( F @ A @ B )
% 0.22/0.52 = ( F @ B @ A ) ) ) ).
% 0.22/0.52
% 0.22/0.52 % ac_operator.commute
% 0.22/0.52 thf(fact_6_ac__operator_Oleft__assoc,axiom,
% 0.22/0.52 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.22/0.52 ( ( syntax_ac_operator_a @ F )
% 0.22/0.52 => ( ( F @ A @ ( F @ B @ C ) )
% 0.22/0.52 = ( F @ ( F @ A @ B ) @ C ) ) ) ).
% 0.22/0.52
% 0.22/0.52 % ac_operator.left_assoc
% 0.22/0.52 thf(fact_7_ac__operator_Oright__assoc,axiom,
% 0.22/0.52 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.22/0.52 ( ( syntax_ac_operator_a @ F )
% 0.22/0.52 => ( ( F @ ( F @ A @ B ) @ C )
% 0.22/0.52 = ( F @ A @ ( F @ B @ C ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 % ac_operator.right_assoc
% 0.22/0.52 thf(fact_8_ac__operator_Oleft__commute,axiom,
% 0.22/0.52 ! [F: a > a > a,A: a,B: a,C: a] :
% 0.22/0.52 ( ( syntax_ac_operator_a @ F )
% 0.22/0.52 => ( ( F @ A @ ( F @ B @ C ) )
% 0.22/0.52 = ( F @ B @ ( F @ A @ C ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 % ac_operator.left_commute
% 0.22/0.52 thf(fact_9_ac__operator__def,axiom,
% 0.22/0.52 ( syntax_ac_operator_a
% 0.22/0.52 = ( ^ [F2: a > a > a] :
% 0.22/0.52 ( ! [A3: a,B3: a,C3: a] :
% 0.22/0.52 ( ( F2 @ ( F2 @ A3 @ B3 ) @ C3 )
% 0.22/0.52 = ( F2 @ A3 @ ( F2 @ B3 @ C3 ) ) )
% 0.22/0.52 & ! [A3: a,B3: a] :
% 0.22/0.52 ( ( F2 @ A3 @ B3 )
% 0.22/0.52 = ( F2 @ B3 @ A3 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 % ac_operator_def
% 0.22/0.52
% 0.22/0.52 % Conjectures (1)
% 0.22/0.52 thf(conj_0,conjecture,
% 0.22/0.52 ( ( f @ ( f @ a2 @ b ) @ c )
% 0.22/0.52 = ( f @ ( f @ a2 @ c ) @ b ) ) ).
% 0.22/0.57
% 0.22/0.57 %------------------------------------------------------------------------------
% 0.22/0.57 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.bvryXwyf8f/cvc5---1.0.5_5272.p...
% 0.22/0.57 (declare-sort $$unsorted 0)
% 0.22/0.57 (declare-sort tptp.a 0)
% 0.22/0.57 (declare-fun tptp.syntax_ac_operator_a ((-> tptp.a tptp.a tptp.a)) Bool)
% 0.22/0.57 (declare-fun tptp.a2 () tptp.a)
% 0.22/0.57 (declare-fun tptp.b () tptp.a)
% 0.22/0.57 (declare-fun tptp.c () tptp.a)
% 0.22/0.57 (declare-fun tptp.f (tptp.a tptp.a) tptp.a)
% 0.22/0.57 (assert (@ tptp.syntax_ac_operator_a tptp.f))
% 0.22/0.57 (assert (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.f A) B) (@ (@ tptp.f B) A))))
% 0.22/0.57 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.f A))) (let ((_let_2 (@ tptp.f B))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.22/0.57 (assert (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.f A))) (= (@ (@ tptp.f (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.f B) C))))))
% 0.22/0.57 (assert (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (forall ((A2 tptp.a) (B2 tptp.a) (C2 tptp.a)) (let ((_let_1 (@ F A2))) (= (@ (@ F (@ _let_1 B2)) C2) (@ _let_1 (@ (@ F B2) C2))))) (=> (forall ((A2 tptp.a) (B2 tptp.a)) (= (@ (@ F A2) B2) (@ (@ F B2) A2))) (@ tptp.syntax_ac_operator_a F)))))
% 0.22/0.57 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (=> (@ tptp.syntax_ac_operator_a F) (= (@ (@ F A) B) (@ (@ F B) A)))))
% 0.22/0.57 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ F A))) (=> (@ tptp.syntax_ac_operator_a F) (= (@ _let_1 (@ (@ F B) C)) (@ (@ F (@ _let_1 B)) C))))))
% 0.22/0.57 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ F A))) (=> (@ tptp.syntax_ac_operator_a F) (= (@ (@ F (@ _let_1 B)) C) (@ _let_1 (@ (@ F B) C)))))))
% 0.22/0.57 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ F A))) (let ((_let_2 (@ F B))) (=> (@ tptp.syntax_ac_operator_a F) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C))))))))
% 0.22/0.57 (assert (= tptp.syntax_ac_operator_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (and (forall ((A3 tptp.a) (B3 tptp.a) (C3 tptp.a)) (let ((_let_1 (@ F2 A3))) (= (@ (@ F2 (@ _let_1 B3)) C3) (@ _let_1 (@ (@ F2 B3) C3))))) (forall ((A3 tptp.a) (B3 tptp.a)) (= (@ (@ F2 A3) B3) (@ (@ F2 B3) A3)))))))
% 0.22/0.57 (assert (let ((_let_1 (@ tptp.f tptp.a2))) (not (= (@ (@ tptp.f (@ _let_1 tptp.b)) tptp.c) (@ (@ tptp.f (@ _let_1 tptp.c)) tptp.b)))))
% 0.22/0.57 (set-info :filename cvc5---1.0.5_5272)
% 0.22/0.57 (check-sat-assuming ( true ))
% 0.22/0.57 ------- get file name : TPTP file name is ITP209^1
% 0.22/0.57 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5272.smt2...
% 0.22/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.57 % SZS status Theorem for ITP209^1
% 0.22/0.57 % SZS output start Proof for ITP209^1
% 0.22/0.57 (
% 0.22/0.57 (let ((_let_1 (@ tptp.f tptp.a2))) (let ((_let_2 (not (= (@ (@ tptp.f (@ _let_1 tptp.b)) tptp.c) (@ (@ tptp.f (@ _let_1 tptp.c)) tptp.b))))) (let ((_let_3 (= tptp.syntax_ac_operator_a (lambda ((F2 (-> tptp.a tptp.a tptp.a))) (and (forall ((A3 tptp.a) (B3 tptp.a) (C3 tptp.a)) (let ((_let_1 (@ F2 A3))) (= (@ (@ F2 (@ _let_1 B3)) C3) (@ _let_1 (@ (@ F2 B3) C3))))) (forall ((A3 tptp.a) (B3 tptp.a)) (= (@ (@ F2 A3) B3) (@ (@ F2 B3) A3)))))))) (let ((_let_4 (@ tptp.syntax_ac_operator_a tptp.f))) (let ((_let_5 (forall ((A3 tptp.a) (B3 tptp.a) (C3 tptp.a)) (let ((_let_1 (ho_3 k_2 A3))) (= (ho_4 _let_1 (ho_4 (ho_3 k_2 B3) C3)) (ho_4 (ho_3 k_2 (ho_4 _let_1 B3)) C3)))))) (let ((_let_6 (ho_3 k_2 tptp.b))) (let ((_let_7 (ho_4 _let_6 tptp.a2))) (let ((_let_8 (ho_3 k_2 tptp.a2))) (let ((_let_9 (ho_4 _let_8 tptp.c))) (let ((_let_10 (ho_4 _let_6 _let_9))) (let ((_let_11 (= _let_10 (ho_4 (ho_3 k_2 _let_7) tptp.c)))) (let ((_let_12 (forall ((u |u_(-> tptp.a tptp.a)|) (e tptp.a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_13 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_14 (forall ((u |u_(-> tptp.a tptp.a tptp.a)|) (e |u_(-> tptp.a tptp.a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_15 (forall ((x |u_(-> tptp.a tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_16 (forall ((A3 tptp.a) (B3 tptp.a)) (= (ho_4 (ho_3 k_2 B3) A3) (ho_4 (ho_3 k_2 A3) B3))))) (let ((_let_17 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO (ASSUME :args (_let_3)) :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (forall ((A3 tptp.a) (B3 tptp.a) (C3 tptp.a)) (let ((_let_1 (@ tptp.f A3))) (= (@ (@ tptp.f (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.f B3) C3))))) (forall ((A3 tptp.a) (B3 tptp.a)) (= (@ (@ tptp.f A3) B3) (@ (@ tptp.f B3) A3)))) (and _let_5 _let_16)))))) (PREPROCESS :args ((and _let_15 _let_14 _let_13 _let_12)))) :args ((and _let_5 _let_16 _let_15 _let_14 _let_13 _let_12))))) (let ((_let_18 (ho_4 (ho_3 k_2 _let_9) tptp.b))) (let ((_let_19 (= _let_18 _let_10))) (let ((_let_20 (ho_4 _let_8 tptp.b))) (let ((_let_21 (= _let_20 _let_7))) (let ((_let_22 (= _let_18 (ho_4 (ho_3 k_2 _let_20) tptp.c)))) (let ((_let_23 (not _let_11))) (let ((_let_24 (AND_ELIM _let_17 :args (1)))) (let ((_let_25 (_let_16))) (let ((_let_26 ((ho_4 (ho_3 k_2 B3) A3)))) (let ((_let_27 (ASSUME :args _let_25))) (let ((_let_28 (not _let_22))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_28)))))) (let ((_let_30 (and _let_28 _let_21 _let_19))) (let ((_let_31 (ASSUME :args (_let_21)))) (let ((_let_32 (ASSUME :args (_let_19)))) (let ((_let_33 (_let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_33) :args (tptp.b tptp.a2 tptp.c QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_33)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_30)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_32 _let_29 _let_31) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_32) (CONG (CONG (REFL :args (k_2)) (SYMM _let_31) :args (APPLY_UF ho_3)) (REFL :args (tptp.c)) :args (APPLY_UF ho_4)) :args (=)) (FALSE_INTRO _let_29))) :args (_let_19 _let_28 _let_21))) :args (_let_28 _let_21 _let_19))) :args (true _let_30)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_22))) (REFL :args ((not _let_21))) (REFL :args ((not _let_19))) (REFL :args (_let_23)) :args (or))) _let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.b tptp.a2 QUANTIFIERS_INST_E_MATCHING _let_26)) :args _let_25)) _let_24 :args (_let_21 false _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.b _let_9 QUANTIFIERS_INST_E_MATCHING _let_26)) :args _let_25)) _let_24 :args (_let_19 false _let_16)) :args (_let_23 true _let_22 false _let_21 false _let_19)) (AND_ELIM _let_17 :args (0)) :args (false true _let_11 false _let_5)) :args (_let_4 (forall ((A tptp.a) (B tptp.a)) (= (@ (@ tptp.f A) B) (@ (@ tptp.f B) A))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.f A))) (let ((_let_2 (@ tptp.f B))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ tptp.f A))) (= (@ (@ tptp.f (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.f B) C))))) (forall ((F (-> tptp.a tptp.a tptp.a))) (=> (forall ((A2 tptp.a) (B2 tptp.a) (C2 tptp.a)) (let ((_let_1 (@ F A2))) (= (@ (@ F (@ _let_1 B2)) C2) (@ _let_1 (@ (@ F B2) C2))))) (=> (forall ((A2 tptp.a) (B2 tptp.a)) (= (@ (@ F A2) B2) (@ (@ F B2) A2))) (@ tptp.syntax_ac_operator_a F)))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a)) (=> (@ tptp.syntax_ac_operator_a F) (= (@ (@ F A) B) (@ (@ F B) A)))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ F A))) (=> (@ tptp.syntax_ac_operator_a F) (= (@ _let_1 (@ (@ F B) C)) (@ (@ F (@ _let_1 B)) C))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ F A))) (=> (@ tptp.syntax_ac_operator_a F) (= (@ (@ F (@ _let_1 B)) C) (@ _let_1 (@ (@ F B) C)))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (A tptp.a) (B tptp.a) (C tptp.a)) (let ((_let_1 (@ F A))) (let ((_let_2 (@ F B))) (=> (@ tptp.syntax_ac_operator_a F) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C))))))) _let_3 _let_2 true))))))))))))))))))))))))))))))))))))
% 0.22/0.58 )
% 0.22/0.58 % SZS output end Proof for ITP209^1
% 0.22/0.58 % cvc5---1.0.5 exiting
% 0.22/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------