TSTP Solution File: NUM830^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 10:48:19 EDT 2023
% Result : Theorem 0.23s 0.57s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n011.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 : Fri Aug 25 16:27:38 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.51 %----Proving TH0
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 % File : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.23/0.53 % Domain : Number Theory (Induction on naturals)
% 0.23/0.53 % Problem : TPS problem from PA-THMS
% 0.23/0.53 % Version : Especial.
% 0.23/0.53 % English :
% 0.23/0.53
% 0.23/0.53 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.23/0.53 % Source : [Bro09]
% 0.23/0.53 % Names : tps_0798 [Bro09]
% 0.23/0.53
% 0.23/0.53 % Status : Theorem
% 0.23/0.53 % Rating : 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0
% 0.23/0.53 % Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% 0.23/0.53 % Number of atoms : 17 ( 9 equ; 0 cnn)
% 0.23/0.53 % Maximal formula atoms : 5 ( 3 avg)
% 0.23/0.53 % Number of connectives : 33 ( 0 ~; 0 |; 3 &; 29 @)
% 0.23/0.53 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.23/0.53 % Maximal formula depth : 5 ( 2 avg)
% 0.23/0.53 % Number of types : 2 ( 1 usr)
% 0.23/0.53 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.23/0.53 % Number of symbols : 9 ( 8 usr; 5 con; 0-2 aty)
% 0.23/0.53 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.23/0.53 % SPC : TH0_THM_EQU_NAR
% 0.23/0.53
% 0.23/0.53 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.23/0.53 % project in the Department of Mathematical Sciences at Carnegie
% 0.23/0.53 % Mellon University. Distributed under the Creative Commons copyleft
% 0.23/0.53 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.23/0.53 % :
% 0.23/0.53 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.23/0.53 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 thf(n_type,type,
% 0.23/0.53 n: $tType ).
% 0.23/0.53
% 0.23/0.53 thf(c0_type,type,
% 0.23/0.53 c0: n ).
% 0.23/0.53
% 0.23/0.53 thf(cS_type,type,
% 0.23/0.53 cS: n > n ).
% 0.23/0.53
% 0.23/0.53 thf(c_plus_type,type,
% 0.23/0.53 c_plus: n > n > n ).
% 0.23/0.53
% 0.23/0.53 thf(c_star_type,type,
% 0.23/0.53 c_star: n > n > n ).
% 0.23/0.53
% 0.23/0.53 thf(cPA_1_type,type,
% 0.23/0.53 cPA_1: $o ).
% 0.23/0.53
% 0.23/0.53 thf(cPA_2_type,type,
% 0.23/0.53 cPA_2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(cPA_3_type,type,
% 0.23/0.53 cPA_3: $o ).
% 0.23/0.53
% 0.23/0.53 thf(cPA_4_type,type,
% 0.23/0.53 cPA_4: $o ).
% 0.23/0.53
% 0.23/0.53 thf(cPA_1_def,definition,
% 0.23/0.53 ( cPA_1
% 0.23/0.53 = ( ! [Xx: n] :
% 0.23/0.53 ( ( c_plus @ Xx @ c0 )
% 0.23/0.53 = Xx ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(cPA_2_def,definition,
% 0.23/0.53 ( cPA_2
% 0.23/0.53 = ( ! [Xx: n,Xy: n] :
% 0.23/0.53 ( ( c_plus @ Xx @ ( cS @ Xy ) )
% 0.23/0.53 = ( cS @ ( c_plus @ Xx @ Xy ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(cPA_3_def,definition,
% 0.23/0.53 ( cPA_3
% 0.23/0.53 = ( ! [Xx: n] :
% 0.23/0.53 ( ( c_star @ Xx @ c0 )
% 0.23/0.53 = c0 ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(cPA_4_def,definition,
% 0.23/0.53 ( cPA_4
% 0.23/0.53 = ( ! [Xx: n,Xy: n] :
% 0.23/0.53 ( ( c_star @ Xx @ ( cS @ Xy ) )
% 0.23/0.53 = ( c_plus @ ( c_star @ Xx @ Xy ) @ Xx ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(cPA_THM1,conjecture,
% 0.23/0.53 ( ( cPA_1
% 0.23/0.53 & cPA_2
% 0.23/0.53 & cPA_3
% 0.23/0.53 & cPA_4 )
% 0.23/0.53 => ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
% 0.23/0.53 = ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.KfF2CNISZV/cvc5---1.0.5_19496.p...
% 0.23/0.53 (declare-sort $$unsorted 0)
% 0.23/0.53 (declare-sort tptp.n 0)
% 0.23/0.53 (declare-fun tptp.c0 () tptp.n)
% 0.23/0.53 (declare-fun tptp.cS (tptp.n) tptp.n)
% 0.23/0.53 (declare-fun tptp.c_plus (tptp.n tptp.n) tptp.n)
% 0.23/0.53 (declare-fun tptp.c_star (tptp.n tptp.n) tptp.n)
% 0.23/0.53 (declare-fun tptp.cPA_1 () Bool)
% 0.23/0.53 (declare-fun tptp.cPA_2 () Bool)
% 0.23/0.53 (declare-fun tptp.cPA_3 () Bool)
% 0.23/0.53 (declare-fun tptp.cPA_4 () Bool)
% 0.23/0.53 (assert (= tptp.cPA_1 (forall ((Xx tptp.n)) (= (@ (@ tptp.c_plus Xx) tptp.c0) Xx))))
% 0.23/0.53 (assert (= tptp.cPA_2 (forall ((Xx tptp.n) (Xy tptp.n)) (let ((_let_1 (@ tptp.c_plus Xx))) (= (@ _let_1 (@ tptp.cS Xy)) (@ tptp.cS (@ _let_1 Xy)))))))
% 0.23/0.53 (assert (= tptp.cPA_3 (forall ((Xx tptp.n)) (= (@ (@ tptp.c_star Xx) tptp.c0) tptp.c0))))
% 0.23/0.53 (assert (= tptp.cPA_4 (forall ((Xx tptp.n) (Xy tptp.n)) (let ((_let_1 (@ tptp.c_star Xx))) (= (@ _let_1 (@ tptp.cS Xy)) (@ (@ tptp.c_plus (@ _let_1 Xy)) Xx))))))
% 0.23/0.53 (assert (let ((_let_1 (@ tptp.cS (@ tptp.cS tptp.c0)))) (not (=> (and tptp.cPA_1 tptp.cPA_2 tptp.cPA_3 tptp.cPA_4) (= (@ (@ tptp.c_star _let_1) _let_1) (@ (@ tptp.c_plus _let_1) _let_1))))))
% 0.23/0.57 (set-info :filename cvc5---1.0.5_19496)
% 0.23/0.57 (check-sat-assuming ( true ))
% 0.23/0.57 ------- get file name : TPTP file name is NUM830^5
% 0.23/0.57 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19496.smt2...
% 0.23/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.57 % SZS status Theorem for NUM830^5
% 0.23/0.57 % SZS output start Proof for NUM830^5
% 0.23/0.57 (
% 0.23/0.57 (let ((_let_1 (@ tptp.cS (@ tptp.cS tptp.c0)))) (let ((_let_2 (= (@ (@ tptp.c_star _let_1) _let_1) (@ (@ tptp.c_plus _let_1) _let_1)))) (let ((_let_3 (not (=> (and tptp.cPA_1 tptp.cPA_2 tptp.cPA_3 tptp.cPA_4) _let_2)))) (let ((_let_4 (forall ((Xx tptp.n) (Xy tptp.n)) (let ((_let_1 (@ tptp.c_star Xx))) (= (@ _let_1 (@ tptp.cS Xy)) (@ (@ tptp.c_plus (@ _let_1 Xy)) Xx)))))) (let ((_let_5 (= tptp.cPA_4 _let_4))) (let ((_let_6 (= tptp.cPA_3 (forall ((Xx tptp.n)) (= (@ (@ tptp.c_star Xx) tptp.c0) tptp.c0))))) (let ((_let_7 (forall ((Xx tptp.n) (Xy tptp.n)) (let ((_let_1 (@ tptp.c_plus Xx))) (= (@ _let_1 (@ tptp.cS Xy)) (@ tptp.cS (@ _let_1 Xy))))))) (let ((_let_8 (= tptp.cPA_2 _let_7))) (let ((_let_9 (= tptp.cPA_1 (forall ((Xx tptp.n)) (= (@ (@ tptp.c_plus Xx) tptp.c0) Xx))))) (let ((_let_10 (ho_3 k_2 tptp.c0))) (let ((_let_11 (ho_3 k_2 _let_10))) (let ((_let_12 (ho_5 k_6 _let_11))) (let ((_let_13 (ho_3 _let_12 _let_11))) (let ((_let_14 (ho_5 k_4 _let_11))) (let ((_let_15 (ho_3 _let_14 _let_11))) (let ((_let_16 (= _let_15 _let_13))) (let ((_let_17 (ho_3 _let_14 tptp.c0))) (let ((_let_18 (= _let_11 _let_17))) (let ((_let_19 (ho_3 _let_14 _let_10))) (let ((_let_20 (= _let_15 (ho_3 k_2 _let_19)))) (let ((_let_21 (ho_3 _let_12 tptp.c0))) (let ((_let_22 (= tptp.c0 _let_21))) (let ((_let_23 (ho_3 _let_12 _let_10))) (let ((_let_24 (ho_5 k_4 _let_23))) (let ((_let_25 (ho_3 _let_24 _let_11))) (let ((_let_26 (= _let_13 _let_25))) (let ((_let_27 (ho_3 _let_24 tptp.c0))) (let ((_let_28 (= _let_23 _let_27))) (let ((_let_29 (= _let_19 (ho_3 k_2 _let_17)))) (let ((_let_30 (ho_3 _let_24 _let_10))) (let ((_let_31 (= _let_25 (ho_3 k_2 _let_30)))) (let ((_let_32 (ho_5 k_4 _let_21))) (let ((_let_33 (ho_3 _let_32 _let_11))) (let ((_let_34 (= _let_23 _let_33))) (let ((_let_35 (ho_3 _let_32 tptp.c0))) (let ((_let_36 (= _let_21 _let_35))) (let ((_let_37 (= _let_30 (ho_3 k_2 _let_27)))) (let ((_let_38 (ho_3 _let_32 _let_10))) (let ((_let_39 (= _let_33 (ho_3 k_2 _let_38)))) (let ((_let_40 (= _let_38 (ho_3 k_2 _let_35)))) (let ((_let_41 (forall ((Xx tptp.n) (Xy tptp.n)) (let ((_let_1 (ho_5 k_6 Xx))) (= (ho_3 (ho_5 k_4 (ho_3 _let_1 Xy)) Xx) (ho_3 _let_1 (ho_3 k_2 Xy))))))) (let ((_let_42 (forall ((Xx tptp.n)) (= tptp.c0 (ho_3 (ho_5 k_6 Xx) tptp.c0))))) (let ((_let_43 (forall ((Xx tptp.n) (Xy tptp.n)) (let ((_let_1 (ho_5 k_4 Xx))) (= (ho_3 k_2 (ho_3 _let_1 Xy)) (ho_3 _let_1 (ho_3 k_2 Xy))))))) (let ((_let_44 (forall ((Xx tptp.n)) (= Xx (ho_3 (ho_5 k_4 Xx) tptp.c0))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (ASSUME :args (_let_5)) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_8)) (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT)))) :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> (and (forall ((Xx tptp.n)) (= Xx (@ (@ tptp.c_plus Xx) tptp.c0))) _let_7 (forall ((Xx tptp.n)) (= tptp.c0 (@ (@ tptp.c_star Xx) tptp.c0))) _let_4) _let_2)) (not (=> (and _let_44 _let_43 _let_42 _let_41) _let_16))))))))) (let ((_let_46 (NOT_IMPLIES_ELIM1 _let_45))) (let ((_let_47 (AND_ELIM _let_46 :args (0)))) (let ((_let_48 (_let_44))) (let ((_let_49 ((ho_5 k_4 Xx)))) (let ((_let_50 (ASSUME :args _let_48))) (let ((_let_51 (AND_ELIM _let_46 :args (1)))) (let ((_let_52 (_let_43))) (let ((_let_53 ((ho_3 (ho_5 k_4 Xx) (ho_3 k_2 Xy))))) (let ((_let_54 (ASSUME :args _let_52))) (let ((_let_55 (_let_42))) (let ((_let_56 (AND_ELIM _let_46 :args (3)))) (let ((_let_57 (_let_41))) (let ((_let_58 ((ho_3 (ho_5 k_6 Xx) (ho_3 k_2 Xy))))) (let ((_let_59 (ASSUME :args _let_57))) (let ((_let_60 (and _let_18 _let_20 _let_22 _let_26 _let_28 _let_29 _let_31 _let_34 _let_36 _let_37 _let_39 _let_40))) (let ((_let_61 (ASSUME :args (_let_26)))) (let ((_let_62 (ASSUME :args (_let_31)))) (let ((_let_63 (APPLY_UF ho_3))) (let ((_let_64 (ASSUME :args (_let_37)))) (let ((_let_65 (ASSUME :args (_let_28)))) (let ((_let_66 (ASSUME :args (_let_34)))) (let ((_let_67 (ASSUME :args (_let_39)))) (let ((_let_68 (ASSUME :args (_let_40)))) (let ((_let_69 (ASSUME :args (_let_36)))) (let ((_let_70 (ASSUME :args (_let_22)))) (let ((_let_71 (REFL :args (k_2)))) (let ((_let_72 (ASSUME :args (_let_18)))) (let ((_let_73 (ASSUME :args (_let_29)))) (let ((_let_74 (ASSUME :args (_let_20)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_60)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_61 _let_62 _let_64 _let_65 _let_66 _let_67 _let_68 _let_69 _let_70 _let_72 _let_73 _let_74) (SCOPE (TRANS (SYMM (SYMM _let_74)) (CONG _let_71 (TRANS (SYMM (SYMM _let_73)) (CONG _let_71 (TRANS (SYMM _let_72) (CONG _let_71 (TRANS (CONG _let_71 (TRANS (SYMM (SYMM _let_70)) (SYMM (SYMM _let_69))) :args _let_63) (SYMM _let_68)) :args _let_63) (SYMM _let_67) (SYMM _let_66) (SYMM (SYMM _let_65))) :args _let_63) (SYMM _let_64)) :args _let_63) (SYMM _let_62) (SYMM _let_61)) :args (_let_26 _let_31 _let_37 _let_28 _let_34 _let_39 _let_40 _let_36 _let_22 _let_18 _let_29 _let_20))) :args (_let_18 _let_20 _let_22 _let_26 _let_28 _let_29 _let_31 _let_34 _let_36 _let_37 _let_39 _let_40))) :args (true _let_60)) :args ((or _let_16 (not _let_18) (not _let_20) (not _let_22) (not _let_26) (not _let_28) (not _let_29) (not _let_31) (not _let_34) (not _let_36) (not _let_37) (not _let_39) (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_21 tptp.c0 QUANTIFIERS_INST_CBQI_PROP)) :args _let_52))) _let_51 :args (_let_40 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_21 _let_10 QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52))) _let_51 :args (_let_39 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_23 tptp.c0 QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52))) _let_51 :args (_let_37 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_36 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_11 tptp.c0 QUANTIFIERS_INST_E_MATCHING _let_58)) :args _let_57))) _let_56 :args (_let_34 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_23 _let_10 QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52))) _let_51 :args (_let_31 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_11 tptp.c0 QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52))) _let_51 :args (_let_29 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_28 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_11 _let_10 QUANTIFIERS_INST_E_MATCHING _let_58)) :args _let_57))) _let_56 :args (_let_26 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_55) :args (_let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_5 k_6 Xx)))) :args _let_55)) (AND_ELIM _let_46 :args (2)) :args (_let_22 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_11 _let_10 QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52))) _let_51 :args (_let_20 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_49)) :args _let_48)) _let_47 :args (_let_18 false _let_44)) (NOT_IMPLIES_ELIM2 _let_45) :args (false false _let_40 false _let_39 false _let_37 false _let_36 false _let_34 false _let_31 false _let_29 false _let_28 false _let_26 false _let_22 false _let_20 false _let_18 true _let_16)) :args (_let_9 _let_8 _let_6 _let_5 _let_3 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.57 )
% 0.23/0.57 % SZS output end Proof for NUM830^5
% 0.23/0.57 % cvc5---1.0.5 exiting
% 0.23/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------