TSTP Solution File: NUM651^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM651^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 10:46:10 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
% 0.00/0.13 % Problem : NUM651^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n029.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 : Fri Aug 25 16:20:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.49 %----Proving TH0
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 % File : NUM651^1 : TPTP v8.1.2. Released v3.7.0.
% 0.22/0.50 % Domain : Number Theory
% 0.22/0.50 % Problem : Landau theorem 9b
% 0.22/0.50 % Version : Especial.
% 0.22/0.50 % English : ~((x = y -> ~(~(forall x_0:nat.~(x = pl y x_0)))) ->
% 0.22/0.50 % ~(~((~(forall x_0:nat.~(x = pl y x_0)) ->
% 0.22/0.50 % ~(~(forall x_0:nat.~(y = pl x x_0)))) ->
% 0.22/0.50 % ~(~(forall x_0:nat.~(y = pl x x_0)) -> ~(x = y)))))
% 0.22/0.50
% 0.22/0.50 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.22/0.50 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.22/0.50 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.50 % Source : [Bro09]
% 0.22/0.50 % Names : satz9b [Lan30]
% 0.22/0.50
% 0.22/0.50 % Status : Theorem
% 0.22/0.50 % : Without extensionality : Theorem
% 0.22/0.50 % Rating : 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.22/0.50 % Syntax : Number of formulae : 9 ( 3 unt; 4 typ; 0 def)
% 0.22/0.50 % Number of atoms : 9 ( 9 equ; 0 cnn)
% 0.22/0.50 % Maximal formula atoms : 6 ( 1 avg)
% 0.22/0.50 % Number of connectives : 46 ( 18 ~; 0 |; 0 &; 22 @)
% 0.22/0.50 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.22/0.50 % Maximal formula depth : 11 ( 5 avg)
% 0.22/0.50 % Number of types : 2 ( 1 usr)
% 0.22/0.50 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.22/0.50 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.22/0.50 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.22/0.50 % SPC : TH0_THM_EQU_NAR
% 0.22/0.50
% 0.22/0.50 % Comments :
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 thf(nat_type,type,
% 0.22/0.50 nat: $tType ).
% 0.22/0.50
% 0.22/0.50 thf(x,type,
% 0.22/0.50 x: nat ).
% 0.22/0.50
% 0.22/0.50 thf(y,type,
% 0.22/0.50 y: nat ).
% 0.22/0.50
% 0.22/0.50 thf(pl,type,
% 0.22/0.50 pl: nat > nat > nat ).
% 0.22/0.50
% 0.22/0.50 thf(satz7,axiom,
% 0.22/0.50 ! [Xx: nat,Xy: nat] :
% 0.22/0.50 ( Xy
% 0.22/0.50 != ( pl @ Xx @ Xy ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(satz6,axiom,
% 0.22/0.50 ! [Xx: nat,Xy: nat] :
% 0.22/0.50 ( ( pl @ Xx @ Xy )
% 0.22/0.50 = ( pl @ Xy @ Xx ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(et,axiom,
% 0.22/0.50 ! [Xa: $o] :
% 0.22/0.50 ( ~ ~ Xa
% 0.22/0.50 => Xa ) ).
% 0.22/0.50
% 0.22/0.50 thf(satz5,axiom,
% 0.22/0.50 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.22/0.50 ( ( pl @ ( pl @ Xx @ Xy ) @ Xz )
% 0.22/0.50 = ( pl @ Xx @ ( pl @ Xy @ Xz ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(satz9b,conjecture,
% 0.22/0.50 ~ ( ( ( x = y )
% 0.22/0.50 => ~ ~ ! [Xx_0: nat] :
% 0.22/0.50 ( x
% 0.22/0.50 != ( pl @ y @ Xx_0 ) ) )
% 0.22/0.50 => ~ ~ ( ( ~ ! [Xx_0: nat] :
% 0.22/0.50 ( x
% 0.22/0.50 != ( pl @ y @ Xx_0 ) )
% 0.22/0.50 => ~ ~ ! [Xx_0: nat] :
% 0.22/0.50 ( y
% 0.22/0.50 != ( pl @ x @ Xx_0 ) ) )
% 0.22/0.50 => ~ ( ~ ! [Xx_0: nat] :
% 0.22/0.50 ( y
% 0.22/0.50 != ( pl @ x @ Xx_0 ) )
% 0.22/0.50 => ( x != y ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.qpAY7rFXG6/cvc5---1.0.5_24898.p...
% 0.22/0.50 (declare-sort $$unsorted 0)
% 0.22/0.50 (declare-sort tptp.nat 0)
% 0.22/0.50 (declare-fun tptp.x () tptp.nat)
% 0.22/0.50 (declare-fun tptp.y () tptp.nat)
% 0.22/0.50 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.22/0.50 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (not (= Xy (@ (@ tptp.pl Xx) Xy)))))
% 0.22/0.50 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (= (@ (@ tptp.pl Xx) Xy) (@ (@ tptp.pl Xy) Xx))))
% 0.22/0.50 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.22/0.50 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (let ((_let_1 (@ tptp.pl Xx))) (= (@ (@ tptp.pl (@ _let_1 Xy)) Xz) (@ _let_1 (@ (@ tptp.pl Xy) Xz))))))
% 0.22/0.50 (assert (let ((_let_1 (= tptp.x tptp.y))) (not (not (=> (=> _let_1 (not (not (forall ((Xx_0 tptp.nat)) (not (= tptp.x (@ (@ tptp.pl tptp.y) Xx_0))))))) (not (not (=> (=> (not (forall ((Xx_0 tptp.nat)) (not (= tptp.x (@ (@ tptp.pl tptp.y) Xx_0))))) (not (not (forall ((Xx_0 tptp.nat)) (not (= tptp.y (@ (@ tptp.pl tptp.x) Xx_0))))))) (not (=> (not (forall ((Xx_0 tptp.nat)) (not (= tptp.y (@ (@ tptp.pl tptp.x) Xx_0))))) (not _let_1)))))))))))
% 0.22/0.50 (set-info :filename cvc5---1.0.5_24898)
% 0.22/0.50 (check-sat-assuming ( true ))
% 0.22/0.50 ------- get file name : TPTP file name is NUM651^1
% 0.22/0.56 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24898.smt2...
% 0.22/0.56 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.56 % SZS status Theorem for NUM651^1
% 0.22/0.56 % SZS output start Proof for NUM651^1
% 0.22/0.56 (
% 0.22/0.56 (let ((_let_1 (= tptp.x tptp.y))) (let ((_let_2 (not _let_1))) (let ((_let_3 (not (=> (not (forall ((Xx_0 tptp.nat)) (not (= tptp.y (@ (@ tptp.pl tptp.x) Xx_0))))) _let_2)))) (let ((_let_4 (forall ((Xx_0 tptp.nat)) (not (= tptp.y (@ (@ tptp.pl tptp.x) Xx_0)))))) (let ((_let_5 (not (forall ((Xx_0 tptp.nat)) (not (= tptp.x (@ (@ tptp.pl tptp.y) Xx_0))))))) (let ((_let_6 (forall ((Xx_0 tptp.nat)) (not (= tptp.x (@ (@ tptp.pl tptp.y) Xx_0)))))) (let ((_let_7 (not (not (=> (=> _let_1 (not (not _let_6))) (not (not (=> (=> _let_5 (not (not _let_4))) _let_3)))))))) (let ((_let_8 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (let ((_let_1 (@ tptp.pl Xx))) (= (@ (@ tptp.pl (@ _let_1 Xy)) Xz) (@ _let_1 (@ (@ tptp.pl Xy) Xz))))))) (let ((_let_9 (forall ((Xx tptp.nat) (Xy tptp.nat)) (= (@ (@ tptp.pl Xx) Xy) (@ (@ tptp.pl Xy) Xx))))) (let ((_let_10 (forall ((Xx tptp.nat) (Xy tptp.nat)) (not (= Xy (@ (@ tptp.pl Xx) Xy)))))) (let ((_let_11 (forall ((Xx tptp.nat) (Xy tptp.nat)) (not (= Xy (ho_4 (ho_3 k_2 Xx) Xy)))))) (let ((_let_12 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (ho_4 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_14 (ho_4 (ho_3 k_2 _let_13) tptp.y))) (let ((_let_15 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (= _let_14 (ho_4 (ho_3 k_2 _let_15) _let_14)))) (let ((_let_17 (forall ((u |u_(-> tptp.nat tptp.nat)|) (e tptp.nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_18 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_19 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_20 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_10)) (PREPROCESS :args ((= _let_10 _let_11)))))) (let ((_let_22 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_21 (PREPROCESS :args ((and _let_20 _let_19 _let_18 _let_17)))) :args ((and _let_11 _let_20 _let_19 _let_18 _let_17))) :args (0)))) (let ((_let_23 (ho_3 k_2 tptp.y))) (let ((_let_24 (ho_4 _let_23 _let_13))) (let ((_let_25 (= _let_24 _let_14))) (let ((_let_26 (= _let_15 _let_13))) (let ((_let_27 (ho_4 _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_28 (= _let_24 (ho_4 (ho_3 k_2 _let_27) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_29 (= tptp.y (ho_4 (ho_3 k_2 tptp.x) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_30 (= tptp.x _let_27))) (let ((_let_31 (forall ((Xx tptp.nat) (Xy tptp.nat)) (= (ho_4 (ho_3 k_2 Xy) Xx) (ho_4 (ho_3 k_2 Xx) Xy))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_9)) (PREPROCESS :args ((= _let_9 _let_31)))))) (let ((_let_33 (_let_31))) (let ((_let_34 ((ho_4 (ho_3 k_2 Xy) Xx)))) (let ((_let_35 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (let ((_let_1 (ho_3 k_2 Xx))) (= (ho_4 _let_1 (ho_4 (ho_3 k_2 Xy) Xz)) (ho_4 (ho_3 k_2 (ho_4 _let_1 Xy)) Xz)))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_8)) (PREPROCESS :args ((= _let_8 _let_35)))))) (let ((_let_37 (forall ((Xx_0 tptp.nat)) (not (= tptp.y (ho_4 (ho_3 k_2 tptp.x) Xx_0)))))) (let ((_let_38 (forall ((Xx_0 tptp.nat)) (not (= tptp.x (ho_4 (ho_3 k_2 tptp.y) Xx_0)))))) (let ((_let_39 (not _let_38))) (let ((_let_40 (=> _let_39 _let_37))) (let ((_let_41 (not _let_37))) (let ((_let_42 (forall ((Xx_0 tptp.nat)) (not (= tptp.y (ho_4 (ho_3 k_2 tptp.x) Xx_0)))))) (let ((_let_43 (not _let_42))) (let ((_let_44 (=> _let_43 _let_2))) (let ((_let_45 (not _let_44))) (let ((_let_46 (=> _let_40 _let_45))) (let ((_let_47 (not _let_40))) (let ((_let_48 (forall ((Xx_0 tptp.nat)) (not (= tptp.x (ho_4 (ho_3 k_2 tptp.y) Xx_0)))))) (let ((_let_49 (=> _let_1 _let_48))) (let ((_let_50 (ho_4 _let_12 tptp.y))) (let ((_let_51 (= _let_27 _let_50))) (let ((_let_52 (= _let_50 (ho_4 _let_12 _let_50)))) (let ((_let_53 (_let_11))) (let ((_let_54 (and _let_1 _let_30 _let_51))) (let ((_let_55 (APPLY_UF ho_4))) (let ((_let_56 (ASSUME :args (_let_51)))) (let ((_let_57 (_let_30))) (let ((_let_58 (ASSUME :args _let_57))) (let ((_let_59 (SYMM (SYMM _let_58)))) (let ((_let_60 (ASSUME :args (_let_1)))) (let ((_let_61 (SYMM _let_60))) (let ((_let_62 (or))) (let ((_let_63 (not _let_48))) (let ((_let_64 (_let_63))) (let ((_let_65 (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_64)) :args _let_64) (REWRITE :args ((=> _let_63 (not (not _let_30))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_48))) (REFL :args _let_57) :args _let_62)))) (let ((_let_66 (_let_49))) (let ((_let_67 (EQUIV_ELIM2 (SYMM (ALPHA_EQUIV :args (_let_48 (= Xx_0 Xx_0))))))) (let ((_let_68 (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (=> (=> _let_1 _let_6) (=> (=> _let_5 _let_4) _let_3)) (=> _let_49 _let_46))))))) :args ((or _let_46 (not _let_49)))))) (let ((_let_69 (_let_40))) (let ((_let_70 (REORDERING (CNF_IMPLIES_NEG1 :args _let_69) :args ((or _let_39 _let_40))))) (let ((_let_71 (REORDERING (CNF_IMPLIES_POS :args (_let_46)) :args ((or _let_45 _let_47 (not _let_46)))))) (let ((_let_72 (_let_44))) (let ((_let_73 (_let_29))) (let ((_let_74 (_let_41))) (let ((_let_75 (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_74)) :args _let_74) (REWRITE :args ((=> _let_41 (not (not _let_29))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_37))) (REFL :args _let_73) :args _let_62)))) (let ((_let_76 (and _let_1 _let_29))) (let ((_let_77 (_let_1 _let_29))) (let ((_let_78 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_79 (APPLY_UF ho_3))) (let ((_let_80 (SYMM _let_61))) (let ((_let_81 (REFL :args (k_2)))) (let ((_let_82 (ASSUME :args _let_73))) (let ((_let_83 (SYMM (SYMM _let_82)))) (let ((_let_84 (_let_48))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_84) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_84)) (RESOLUTION (CNF_AND_NEG :args (_let_76)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_60 _let_82) (SCOPE (TRANS _let_80 _let_83 (CONG (CONG _let_81 _let_80 :args _let_79) _let_78 :args _let_55)) :args _let_77)) :args _let_77)) :args (true _let_76)) _let_75 (EQUIV_ELIM2 (SYMM (ALPHA_EQUIV :args (_let_37 (= Xx_0 Xx_0))))) (REORDERING (CNF_IMPLIES_NEG1 :args _let_72) :args ((or _let_43 _let_44))) _let_71 _let_70 _let_68 _let_67 (CNF_IMPLIES_NEG2 :args _let_66) _let_65 (RESOLUTION (CNF_AND_NEG :args (_let_54)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_56 _let_58 _let_60) (SCOPE (CONG (REFL :args (_let_12)) (TRANS _let_61 _let_59 (SYMM (SYMM _let_56))) :args _let_55) :args (_let_51 _let_30 _let_1))) :args (_let_1 _let_30 _let_51))) :args (true _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_50 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_53)) _let_22 :args ((not _let_52) false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.y QUANTIFIERS_INST_E_MATCHING _let_34)) :args _let_33)) _let_32 :args (_let_51 false _let_31)) :args (_let_2 false (= tptp.x (ho_4 _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) false _let_29 true _let_37 true _let_42 true _let_44 false _let_40 false _let_46 false _let_38 false _let_49 false _let_48 true _let_30 true _let_52 false _let_51)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST _let_71 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_IMPLIES_NEG2 :args _let_72) (CONG (REFL :args _let_72) (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) :args _let_62)) :args ((or _let_1 _let_44))) _let_85 :args (_let_44 true _let_1)) (MACRO_RESOLUTION_TRUST _let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_NEG1 :args _let_66) :args ((or _let_1 _let_49))) _let_85 :args (_let_49 true _let_1)) :args (_let_46 false _let_49)) :args (_let_47 false _let_44 false _let_46)))) (let ((_let_87 (and _let_30 _let_29 _let_28 _let_26 _let_25))) (let ((_let_88 (ASSUME :args (_let_25)))) (let ((_let_89 (ASSUME :args (_let_28)))) (let ((_let_90 (ASSUME :args (_let_26)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_15 _let_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_53)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_87)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_90 _let_88 _let_89 _let_58 _let_82) (SCOPE (CONG (CONG _let_81 (SYMM _let_90) :args _let_79) (TRANS _let_83 (CONG (CONG _let_81 _let_59 :args _let_79) _let_78 :args _let_55) (SYMM _let_89) (SYMM (SYMM _let_88))) :args _let_55) :args (_let_26 _let_25 _let_28 _let_30 _let_29))) :args (_let_30 _let_29 _let_28 _let_26 _let_25))) :args (true _let_87)) (MACRO_RESOLUTION_TRUST _let_65 (MACRO_RESOLUTION_TRUST _let_67 (MACRO_RESOLUTION_TRUST _let_70 _let_86 :args (_let_39 true _let_40)) :args (_let_63 true _let_38)) :args (_let_30 true _let_48)) (MACRO_RESOLUTION_TRUST _let_75 (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args _let_69) _let_86 :args (_let_41 true _let_40)) :args (_let_29 true _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((ho_4 (ho_3 k_2 (ho_4 (ho_3 k_2 Xx) Xy)) Xz)))) :args (_let_35))) _let_36 :args (_let_28 false _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_PROP)) :args _let_33)) _let_32 :args (_let_26 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_13 tptp.y QUANTIFIERS_INST_E_MATCHING _let_34)) :args _let_33)) _let_32 :args (_let_25 false _let_31)) :args (_let_16 false _let_30 false _let_29 false _let_28 false _let_26 false _let_25)) _let_22 :args (false false _let_16 false _let_11)) :args (_let_10 _let_9 (forall ((Xa Bool)) (=> (not (not Xa)) Xa)) _let_8 _let_7 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.56 )
% 0.22/0.56 % SZS output end Proof for NUM651^1
% 0.22/0.56 % cvc5---1.0.5 exiting
% 0.22/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------