TSTP Solution File: DAT056^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : DAT056^1 : TPTP v8.1.2. Released v5.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 : Wed Aug 30 22:10:26 EDT 2023
% Result : Theorem 0.22s 0.56s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : DAT056^1 : TPTP v8.1.2. Released v5.4.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n012.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 24 14:42:56 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 % File : DAT056^1 : TPTP v8.1.2. Released v5.4.0.
% 0.22/0.51 % Domain : Data Structures
% 0.22/0.51 % Problem : List operation requiring induction
% 0.22/0.51 % Version : Especial.
% 0.22/0.51 % English :
% 0.22/0.51
% 0.22/0.51 % Refs : [Bla12] Blanchette (2012), Email to Geoff Sutcliffe
% 0.22/0.51 % Source : [Bla12]
% 0.22/0.51 % Names : easy.tptp [Bla12]
% 0.22/0.51
% 0.22/0.51 % Status : Theorem
% 0.22/0.51 % Rating : 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.33 v5.4.0
% 0.22/0.51 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 0 def)
% 0.22/0.51 % Number of atoms : 7 ( 7 equ; 0 cnn)
% 0.22/0.51 % Maximal formula atoms : 4 ( 1 avg)
% 0.22/0.51 % Number of connectives : 57 ( 0 ~; 0 |; 0 &; 54 @)
% 0.22/0.51 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.22/0.51 % Maximal formula depth : 9 ( 5 avg)
% 0.22/0.51 % Number of types : 2 ( 2 usr)
% 0.22/0.51 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.22/0.51 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.22/0.51 % Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 0.22/0.51 % SPC : TH0_THM_EQU_NAR
% 0.22/0.51
% 0.22/0.51 % Comments : Induction principle is preinstantiated with the conjecture.
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 %----Should-be-implicit typings (2)
% 0.22/0.51 thf(ty_n_tc__Foo__Olst_It__J,type,
% 0.22/0.51 lst: $tType ).
% 0.22/0.51
% 0.22/0.51 thf(ty_n_t_,type,
% 0.22/0.51 a: $tType ).
% 0.22/0.51
% 0.22/0.51 %----Explicit typings (4)
% 0.22/0.51 thf(sy_c_Foo_Oap_001t_,type,
% 0.22/0.51 ap: lst > lst > lst ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Foo_Olst_OCns_001t_,type,
% 0.22/0.51 cns: a > lst > lst ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Foo_Olst_ONl_001t_,type,
% 0.22/0.51 nl: lst ).
% 0.22/0.51
% 0.22/0.51 thf(sy_v_xs,type,
% 0.22/0.51 xs: lst ).
% 0.22/0.51
% 0.22/0.51 %----Relevant facts (3)
% 0.22/0.51 thf(fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093,axiom,
% 0.22/0.51 ! [Lst: lst] :
% 0.22/0.51 ( ! [Ys: lst,Zs: lst] :
% 0.22/0.51 ( ( ap @ nl @ ( ap @ Ys @ Zs ) )
% 0.22/0.51 = ( ap @ ( ap @ nl @ Ys ) @ Zs ) )
% 0.22/0.51 => ( ! [A: a,Lst2: lst] :
% 0.22/0.51 ( ! [Ys3: lst,Zs2: lst] :
% 0.22/0.51 ( ( ap @ Lst2 @ ( ap @ Ys3 @ Zs2 ) )
% 0.22/0.51 = ( ap @ ( ap @ Lst2 @ Ys3 ) @ Zs2 ) )
% 0.22/0.51 => ! [Ys: lst,Zs: lst] :
% 0.22/0.51 ( ( ap @ ( cns @ A @ Lst2 ) @ ( ap @ Ys @ Zs ) )
% 0.22/0.51 = ( ap @ ( ap @ ( cns @ A @ Lst2 ) @ Ys ) @ Zs ) ) )
% 0.22/0.51 => ! [Ys3: lst,Zs2: lst] :
% 0.22/0.51 ( ( ap @ Lst @ ( ap @ Ys3 @ Zs2 ) )
% 0.22/0.51 = ( ap @ ( ap @ Lst @ Ys3 ) @ Zs2 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_1p_Osimps_I2_J,axiom,
% 0.22/0.51 ! [Ys2: lst,Xs: lst,X: a] :
% 0.22/0.51 ( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
% 0.22/0.51 = ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_2p_Osimps_I1_J,axiom,
% 0.22/0.51 ! [Ys2: lst] :
% 0.22/0.51 ( ( ap @ nl @ Ys2 )
% 0.22/0.51 = Ys2 ) ).
% 0.22/0.51
% 0.22/0.51 %----Conjectures (1)
% 0.22/0.51 thf(conj_0,conjecture,
% 0.22/0.51 ! [Ys: lst,Zs: lst] :
% 0.22/0.51 ( ( ap @ xs @ ( ap @ Ys @ Zs ) )
% 0.22/0.51 = ( ap @ ( ap @ xs @ Ys ) @ Zs ) ) ).
% 0.22/0.51
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.OllUWgEEn4/cvc5---1.0.5_1680.p...
% 0.22/0.51 (declare-sort $$unsorted 0)
% 0.22/0.51 (declare-sort tptp.lst 0)
% 0.22/0.51 (declare-sort tptp.a 0)
% 0.22/0.51 (declare-fun tptp.ap (tptp.lst tptp.lst) tptp.lst)
% 0.22/0.51 (declare-fun tptp.cns (tptp.a tptp.lst) tptp.lst)
% 0.22/0.51 (declare-fun tptp.nl () tptp.lst)
% 0.22/0.51 (declare-fun tptp.xs () tptp.lst)
% 0.22/0.51 (assert (forall ((Lst tptp.lst)) (=> (forall ((Ys tptp.lst) (Zs tptp.lst)) (let ((_let_1 (@ tptp.ap tptp.nl))) (= (@ _let_1 (@ (@ tptp.ap Ys) Zs)) (@ (@ tptp.ap (@ _let_1 Ys)) Zs)))) (=> (forall ((A tptp.a) (Lst2 tptp.lst)) (=> (forall ((Ys3 tptp.lst) (Zs2 tptp.lst)) (let ((_let_1 (@ tptp.ap Lst2))) (= (@ _let_1 (@ (@ tptp.ap Ys3) Zs2)) (@ (@ tptp.ap (@ _let_1 Ys3)) Zs2)))) (forall ((Ys tptp.lst) (Zs tptp.lst)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.cns A) Lst2)))) (= (@ _let_1 (@ (@ tptp.ap Ys) Zs)) (@ (@ tptp.ap (@ _let_1 Ys)) Zs)))))) (forall ((Ys3 tptp.lst) (Zs2 tptp.lst)) (let ((_let_1 (@ tptp.ap Lst))) (= (@ _let_1 (@ (@ tptp.ap Ys3) Zs2)) (@ (@ tptp.ap (@ _let_1 Ys3)) Zs2))))))))
% 0.22/0.51 (assert (forall ((Ys2 tptp.lst) (Xs tptp.lst) (X tptp.a)) (let ((_let_1 (@ tptp.cns X))) (= (@ (@ tptp.ap (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.ap Xs) Ys2))))))
% 0.22/0.56 (assert (forall ((Ys2 tptp.lst)) (= (@ (@ tptp.ap tptp.nl) Ys2) Ys2)))
% 0.22/0.56 (assert (not (forall ((Ys tptp.lst) (Zs tptp.lst)) (let ((_let_1 (@ tptp.ap tptp.xs))) (= (@ _let_1 (@ (@ tptp.ap Ys) Zs)) (@ (@ tptp.ap (@ _let_1 Ys)) Zs))))))
% 0.22/0.56 (set-info :filename cvc5---1.0.5_1680)
% 0.22/0.56 (check-sat-assuming ( true ))
% 0.22/0.56 ------- get file name : TPTP file name is DAT056^1
% 0.22/0.56 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1680.smt2...
% 0.22/0.56 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.56 % SZS status Theorem for DAT056^1
% 0.22/0.56 % SZS output start Proof for DAT056^1
% 0.22/0.56 (
% 0.22/0.56 (let ((_let_1 (not (forall ((Ys tptp.lst) (Zs tptp.lst)) (let ((_let_1 (@ tptp.ap tptp.xs))) (= (@ _let_1 (@ (@ tptp.ap Ys) Zs)) (@ (@ tptp.ap (@ _let_1 Ys)) Zs))))))) (let ((_let_2 (forall ((Ys2 tptp.lst)) (= (@ (@ tptp.ap tptp.nl) Ys2) Ys2)))) (let ((_let_3 (forall ((Ys2 tptp.lst) (Xs tptp.lst) (X tptp.a)) (let ((_let_1 (@ tptp.cns X))) (= (@ (@ tptp.ap (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.ap Xs) Ys2))))))) (let ((_let_4 (forall ((Lst tptp.lst)) (=> (forall ((Ys tptp.lst) (Zs tptp.lst)) (let ((_let_1 (@ tptp.ap tptp.nl))) (= (@ _let_1 (@ (@ tptp.ap Ys) Zs)) (@ (@ tptp.ap (@ _let_1 Ys)) Zs)))) (=> (forall ((A tptp.a) (Lst2 tptp.lst)) (=> (forall ((Ys3 tptp.lst) (Zs2 tptp.lst)) (let ((_let_1 (@ tptp.ap Lst2))) (= (@ _let_1 (@ (@ tptp.ap Ys3) Zs2)) (@ (@ tptp.ap (@ _let_1 Ys3)) Zs2)))) (forall ((Ys tptp.lst) (Zs tptp.lst)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.cns A) Lst2)))) (= (@ _let_1 (@ (@ tptp.ap Ys) Zs)) (@ (@ tptp.ap (@ _let_1 Ys)) Zs)))))) (forall ((Ys3 tptp.lst) (Zs2 tptp.lst)) (let ((_let_1 (@ tptp.ap Lst))) (= (@ _let_1 (@ (@ tptp.ap Ys3) Zs2)) (@ (@ tptp.ap (@ _let_1 Ys3)) Zs2))))))))) (let ((_let_5 (ho_3 k_2 tptp.xs))) (let ((_let_6 (= (ho_4 (ho_3 k_2 (ho_4 _let_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) (ho_4 _let_5 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))) (let ((_let_7 (forall ((Lst tptp.lst) (Ys3 tptp.lst) (Zs2 tptp.lst)) (let ((_let_1 (ho_3 k_2 Lst))) (= (ho_4 (ho_3 k_2 (ho_4 _let_1 Ys3)) Zs2) (ho_4 _let_1 (ho_4 (ho_3 k_2 Ys3) Zs2))))))) (let ((_let_8 (forall ((Ys tptp.lst) (Zs tptp.lst)) (let ((_let_1 (ho_3 k_2 tptp.xs))) (= (ho_4 (ho_3 k_2 (ho_4 _let_1 Ys)) Zs) (ho_4 _let_1 (ho_4 (ho_3 k_2 Ys) Zs))))))) (let ((_let_9 (not _let_6))) (let ((_let_10 (not _let_8))) (let ((_let_11 (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 _let_10)))))) (let ((_let_12 (or))) (let ((_let_13 (forall ((A tptp.a) (Lst2 tptp.lst) (BOUND_VARIABLE_678 tptp.lst) (BOUND_VARIABLE_676 tptp.lst)) (let ((_let_1 (ho_3 k_2 (ho_4 (ho_6 k_5 A) Lst2)))) (or (not (forall ((Ys3 tptp.lst) (Zs2 tptp.lst)) (let ((_let_1 (ho_3 k_2 Lst2))) (= (ho_4 (ho_3 k_2 (ho_4 _let_1 Ys3)) Zs2) (ho_4 _let_1 (ho_4 (ho_3 k_2 Ys3) Zs2)))))) (= (ho_4 (ho_3 k_2 (ho_4 _let_1 BOUND_VARIABLE_676)) BOUND_VARIABLE_678) (ho_4 _let_1 (ho_4 (ho_3 k_2 BOUND_VARIABLE_676) BOUND_VARIABLE_678)))))))) (let ((_let_14 (forall ((Ys tptp.lst) (Zs tptp.lst)) (let ((_let_1 (ho_3 k_2 tptp.nl))) (= (ho_4 (ho_3 k_2 (ho_4 _let_1 Ys)) Zs) (ho_4 _let_1 (ho_4 (ho_3 k_2 Ys) Zs))))))) (let ((_let_15 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_16 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_17 (ho_3 k_2 (ho_4 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_18 (ho_4 _let_17 _let_15))) (let ((_let_19 (ho_4 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_20 (= (ho_4 (ho_3 k_2 _let_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) _let_18))) (let ((_let_21 (forall ((Ys3 tptp.lst) (Zs2 tptp.lst)) (let ((_let_1 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (= (ho_4 (ho_3 k_2 (ho_4 _let_1 Ys3)) Zs2) (ho_4 _let_1 (ho_4 (ho_3 k_2 Ys3) Zs2))))))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20))) (let ((_let_24 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_25 (ho_4 _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_26 (ho_4 (ho_3 k_2 _let_25) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_27 (ho_4 _let_24 _let_15))) (let ((_let_28 (= _let_27 _let_26))) (let ((_let_29 (= _let_18 (ho_4 _let_16 _let_27)))) (let ((_let_30 (ho_4 _let_16 _let_25))) (let ((_let_31 (= _let_19 _let_30))) (let ((_let_32 (= (ho_4 _let_16 _let_26) (ho_4 (ho_3 k_2 _let_30) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)))) (let ((_let_33 (_let_21))) (let ((_let_34 (forall ((Ys2 tptp.lst) (Xs tptp.lst) (X tptp.a)) (let ((_let_1 (ho_6 k_5 X))) (= (ho_4 _let_1 (ho_4 (ho_3 k_2 Xs) Ys2)) (ho_4 (ho_3 k_2 (ho_4 _let_1 Xs)) Ys2)))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 _let_34)))))) (let ((_let_36 (_let_34))) (let ((_let_37 ((ho_4 (ho_3 k_2 (ho_4 (ho_6 k_5 X) Xs)) Ys2)))) (let ((_let_38 (and _let_29 _let_31 _let_32 _let_28))) (let ((_let_39 (ASSUME :args (_let_29)))) (let ((_let_40 (APPLY_UF ho_4))) (let ((_let_41 (ASSUME :args (_let_28)))) (let ((_let_42 (ASSUME :args (_let_32)))) (let ((_let_43 (APPLY_UF ho_3))) (let ((_let_44 (ASSUME :args (_let_31)))) (let ((_let_45 (REFL :args (k_2)))) (let ((_let_46 (not _let_13))) (let ((_let_47 (_let_46))) (let ((_let_48 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_49 (ho_3 k_2 tptp.nl))) (let ((_let_50 (ho_4 _let_49 _let_48))) (let ((_let_51 (ho_4 _let_49 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_52 (= (ho_4 (ho_3 k_2 _let_51) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) _let_50))) (let ((_let_53 (= _let_48 _let_50))) (let ((_let_54 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_51))) (let ((_let_55 (forall ((Ys2 tptp.lst)) (= Ys2 (ho_4 (ho_3 k_2 tptp.nl) Ys2))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Ys2 tptp.lst)) (= Ys2 (@ (@ tptp.ap tptp.nl) Ys2))) _let_55))))))) (let ((_let_57 (_let_55))) (let ((_let_58 (and _let_54 _let_53))) (let ((_let_59 (ASSUME :args (_let_53)))) (let ((_let_60 (ASSUME :args (_let_54)))) (let ((_let_61 (not _let_14))) (let ((_let_62 (_let_61))) (let ((_let_63 (forall ((u |u_(-> tptp.lst tptp.lst)|) (e tptp.lst) (i tptp.lst)) (not (forall ((v |u_(-> tptp.lst tptp.lst)|)) (not (forall ((ii tptp.lst)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_64 (forall ((x |u_(-> tptp.lst tptp.lst)|) (y |u_(-> tptp.lst tptp.lst)|)) (or (not (forall ((z tptp.lst)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_65 (forall ((u |u_(-> tptp.lst tptp.lst tptp.lst)|) (e |u_(-> tptp.lst tptp.lst)|) (i tptp.lst)) (not (forall ((v |u_(-> tptp.lst tptp.lst tptp.lst)|)) (not (forall ((ii tptp.lst)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_66 (forall ((x |u_(-> tptp.lst tptp.lst tptp.lst)|) (y |u_(-> tptp.lst tptp.lst tptp.lst)|)) (or (not (forall ((z tptp.lst)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_67 (forall ((u |u_(-> tptp.a tptp.lst tptp.lst)|) (e |u_(-> tptp.lst tptp.lst)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.lst tptp.lst)|)) (not (forall ((ii tptp.a)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_68 (forall ((x |u_(-> tptp.a tptp.lst tptp.lst)|) (y |u_(-> tptp.a tptp.lst tptp.lst)|)) (or (not (forall ((z tptp.a)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_69 (or _let_61 _let_46 _let_7))) (let ((_let_70 (_let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_70) :args (tptp.xs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_70)) (MACRO_RESOLUTION_TRUST (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (not (forall ((Ys tptp.lst) (Zs tptp.lst)) (let ((_let_1 (@ tptp.ap tptp.nl))) (= (@ _let_1 (@ (@ tptp.ap Ys) Zs)) (@ (@ tptp.ap (@ _let_1 Ys)) Zs))))) (not (forall ((A tptp.a) (Lst2 tptp.lst) (BOUND_VARIABLE_678 tptp.lst) (BOUND_VARIABLE_676 tptp.lst)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.cns A) Lst2)))) (or (not (forall ((Ys3 tptp.lst) (Zs2 tptp.lst)) (let ((_let_1 (@ tptp.ap Lst2))) (= (@ _let_1 (@ (@ tptp.ap Ys3) Zs2)) (@ (@ tptp.ap (@ _let_1 Ys3)) Zs2))))) (= (@ _let_1 (@ (@ tptp.ap BOUND_VARIABLE_676) BOUND_VARIABLE_678)) (@ (@ tptp.ap (@ _let_1 BOUND_VARIABLE_676)) BOUND_VARIABLE_678)))))) (forall ((Lst tptp.lst) (Ys3 tptp.lst) (Zs2 tptp.lst)) (let ((_let_1 (@ tptp.ap Lst))) (= (@ _let_1 (@ (@ tptp.ap Ys3) Zs2)) (@ (@ tptp.ap (@ _let_1 Ys3)) Zs2))))) _let_69))))) (PREPROCESS :args ((and _let_68 _let_67 _let_66 _let_65 _let_64 _let_63)))) :args ((and _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63))) :args (0)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_62)) :args _let_62)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_14))) (REFL :args ((not _let_52))) :args _let_12)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_58)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_59 _let_60) (SCOPE (TRANS (CONG (CONG _let_45 (SYMM _let_60) :args _let_43) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) :args _let_40) (SYMM (SYMM _let_59))) :args (_let_53 _let_54))) :args (_let_54 _let_53))) :args (true _let_58)) :args ((or _let_52 (not _let_54) (not _let_53)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_PROP)) :args _let_57)) _let_56 :args (_let_54 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_48 QUANTIFIERS_INST_CBQI_PROP)) :args _let_57)) _let_56 :args (_let_53 false _let_55)) :args (_let_52 false _let_54 false _let_53)) :args (_let_14 false _let_52)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_47)) :args _let_47)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_13))) (REFL :args ((not _let_23))) :args _let_12)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_38)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_39 _let_41 _let_42 _let_44) (SCOPE (TRANS (CONG (CONG _let_45 (SYMM (SYMM _let_44)) :args _let_43) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)) :args _let_40) (SYMM _let_42) (CONG (REFL :args (_let_16)) (SYMM _let_41) :args _let_40) (SYMM _let_39)) :args (_let_29 _let_28 _let_32 _let_31))) :args (_let_29 _let_31 _let_32 _let_28))) :args (true _let_38)) :args ((or _let_20 (not _let_29) (not _let_31) (not _let_32) (not _let_28)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING _let_37)) :args _let_36)) _let_35 :args (_let_32 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING _let_37)) :args _let_36))) _let_35 :args (_let_31 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING _let_37)) :args _let_36))) _let_35 :args (_let_29 false _let_34)) (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_33) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING ((ho_4 _let_24 (ho_4 (ho_3 k_2 Ys3) Zs2))))) :args _let_33))) (CNF_OR_NEG :args (_let_23 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG (REFL :args (_let_23)) (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_12)) :args ((or _let_21 _let_23))) :args (_let_23 false _let_32 false _let_31 false _let_29 false _let_28 true _let_20 false _let_21)) :args (_let_13 false _let_23)) :args (_let_7 false _let_14 false _let_13)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_11) :args (_let_10))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_8))) (REFL :args (_let_9)) :args _let_12)) _let_11 :args (_let_9 true _let_8)) :args (false false _let_7 true _let_6)) :args (_let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.56 )
% 0.22/0.56 % SZS output end Proof for DAT056^1
% 0.22/0.56 % cvc5---1.0.5 exiting
% 0.22/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------