TSTP Solution File: NUM699^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM699^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 10:46:57 EDT 2023
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM699^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 11:32:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.48 %----Proving TH0
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 % File : NUM699^1 : TPTP v8.1.2. Released v3.7.0.
% 0.19/0.52 % Domain : Number Theory
% 0.19/0.52 % Problem : Landau theorem 25c
% 0.19/0.52 % Version : Especial.
% 0.19/0.52 % English : lessis (suc y) x
% 0.19/0.52
% 0.19/0.52 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.19/0.52 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.19/0.52 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.52 % Source : [Bro09]
% 0.19/0.52 % Names : satz25c [Lan30]
% 0.19/0.52
% 0.19/0.52 % Status : Theorem
% 0.19/0.52 % : Without extensionality : Theorem
% 0.19/0.52 % Rating : 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.19/0.52 % Syntax : Number of formulae : 12 ( 3 unt; 8 typ; 0 def)
% 0.19/0.52 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.19/0.52 % Maximal formula atoms : 2 ( 1 avg)
% 0.19/0.52 % Number of connectives : 15 ( 0 ~; 0 |; 0 &; 14 @)
% 0.19/0.52 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.52 % Maximal formula depth : 8 ( 4 avg)
% 0.19/0.52 % Number of types : 2 ( 1 usr)
% 0.19/0.52 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.52 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.19/0.52 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.19/0.52 % SPC : TH0_THM_EQU_NAR
% 0.19/0.52
% 0.19/0.52 % Comments :
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 thf(nat_type,type,
% 0.19/0.52 nat: $tType ).
% 0.19/0.52
% 0.19/0.52 thf(x,type,
% 0.19/0.52 x: nat ).
% 0.19/0.52
% 0.19/0.52 thf(y,type,
% 0.19/0.52 y: nat ).
% 0.19/0.52
% 0.19/0.52 thf(less,type,
% 0.19/0.52 less: nat > nat > $o ).
% 0.19/0.52
% 0.19/0.52 thf(l,axiom,
% 0.19/0.52 less @ y @ x ).
% 0.19/0.52
% 0.19/0.52 thf(lessis,type,
% 0.19/0.52 lessis: nat > nat > $o ).
% 0.19/0.52
% 0.19/0.52 thf(suc,type,
% 0.19/0.52 suc: nat > nat ).
% 0.19/0.52
% 0.19/0.52 thf(pl,type,
% 0.19/0.52 pl: nat > nat > nat ).
% 0.19/0.52
% 0.19/0.52 thf(n_1,type,
% 0.19/0.52 n_1: nat ).
% 0.19/0.52
% 0.19/0.52 thf(satz25b,axiom,
% 0.19/0.52 ! [Xx: nat,Xy: nat] :
% 0.19/0.52 ( ( less @ Xy @ Xx )
% 0.19/0.52 => ( lessis @ ( pl @ Xy @ n_1 ) @ Xx ) ) ).
% 0.19/0.52
% 0.19/0.52 thf(satz4a,axiom,
% 0.19/0.52 ! [Xx: nat] :
% 0.19/0.52 ( ( pl @ Xx @ n_1 )
% 0.19/0.52 = ( suc @ Xx ) ) ).
% 0.19/0.52
% 0.19/0.52 thf(satz25c,conjecture,
% 0.19/0.52 lessis @ ( suc @ y ) @ x ).
% 0.19/0.52
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.DG9S4Ddw3v/cvc5---1.0.5_22856.p...
% 0.19/0.52 (declare-sort $$unsorted 0)
% 0.19/0.52 (declare-sort tptp.nat 0)
% 0.19/0.52 (declare-fun tptp.x () tptp.nat)
% 0.19/0.52 (declare-fun tptp.y () tptp.nat)
% 0.19/0.52 (declare-fun tptp.less (tptp.nat tptp.nat) Bool)
% 0.19/0.52 (assert (@ (@ tptp.less tptp.y) tptp.x))
% 0.19/0.52 (declare-fun tptp.lessis (tptp.nat tptp.nat) Bool)
% 0.19/0.52 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.19/0.52 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.19/0.52 (declare-fun tptp.n_1 () tptp.nat)
% 0.19/0.52 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.less Xy) Xx) (@ (@ tptp.lessis (@ (@ tptp.pl Xy) tptp.n_1)) Xx))))
% 0.19/0.52 (assert (forall ((Xx tptp.nat)) (= (@ (@ tptp.pl Xx) tptp.n_1) (@ tptp.suc Xx))))
% 0.19/0.52 (assert (not (@ (@ tptp.lessis (@ tptp.suc tptp.y)) tptp.x)))
% 0.19/0.52 (set-info :filename cvc5---1.0.5_22856)
% 0.19/0.52 (check-sat-assuming ( true ))
% 0.19/0.52 ------- get file name : TPTP file name is NUM699^1
% 0.19/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22856.smt2...
% 0.19/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.19/0.52 % SZS status Theorem for NUM699^1
% 0.19/0.52 % SZS output start Proof for NUM699^1
% 0.19/0.52 (
% 0.19/0.52 (let ((_let_1 (not (@ (@ tptp.lessis (@ tptp.suc tptp.y)) tptp.x)))) (let ((_let_2 (forall ((Xx tptp.nat)) (= (@ (@ tptp.pl Xx) tptp.n_1) (@ tptp.suc Xx))))) (let ((_let_3 (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.less Xy) Xx) (@ (@ tptp.lessis (@ (@ tptp.pl Xy) tptp.n_1)) Xx))))) (let ((_let_4 (@ (@ tptp.less tptp.y) tptp.x))) (let ((_let_5 (ho_7 k_9 tptp.y))) (let ((_let_6 (ho_4 (ho_3 k_8 _let_5) tptp.x))) (let ((_let_7 (ho_7 (ho_6 k_5 tptp.y) tptp.n_1))) (let ((_let_8 (= _let_5 _let_7))) (let ((_let_9 (ho_4 (ho_3 k_8 _let_7) tptp.x))) (let ((_let_10 (not _let_6))) (let ((_let_11 (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 _let_10)))))) (let ((_let_12 (forall ((Xx tptp.nat)) (= (ho_7 k_9 Xx) (ho_7 (ho_6 k_5 Xx) tptp.n_1))))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_12)))))) (let ((_let_14 (ho_4 (ho_3 k_2 tptp.y) tptp.x))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_9))) (let ((_let_17 (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (ho_4 (ho_3 k_2 Xy) Xx)) (ho_4 (ho_3 k_8 (ho_7 (ho_6 k_5 Xy) tptp.n_1)) Xx))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (@ (@ tptp.less Xy) Xx)) (@ (@ tptp.lessis (@ (@ tptp.pl Xy) tptp.n_1)) Xx))) _let_17))))))) (let ((_let_19 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_20 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_21 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_22 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_23 (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_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_24 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_25 (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_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_26 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_27 (not _let_8))) (let ((_let_28 (not _let_9))) (let ((_let_29 (and _let_10 _let_8))) (let ((_let_30 (_let_10 _let_8))) (let ((_let_31 (ASSUME :args (_let_8)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_29)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_11 _let_31) (SCOPE (FALSE_ELIM (TRANS (CONG (CONG (REFL :args (k_8)) (SYMM _let_31) :args (APPLY_UF ho_3)) (REFL :args (tptp.x)) :args (APPLY_UF ho_4)) (FALSE_INTRO _let_11))) :args _let_30)) :args _let_30)) :args (true _let_29)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_6))) (REFL :args (_let_27)) (REFL :args (_let_28)) :args (or))) :args ((or _let_6 _let_28 _let_27))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_9 (not _let_16)))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_14)))) (PREPROCESS :args ((and _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19)))) :args ((and _let_14 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19))) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 Xy) Xx) false))))) :args (_let_17))) _let_18 :args (_let_16 false _let_17)) :args (_let_9 false _let_14 false _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_7 k_9 Xx)))) :args (_let_12))) _let_13 :args (_let_8 false _let_12)) _let_11 :args (false false _let_9 false _let_8 true _let_6)) :args (_let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))
% 0.19/0.52 )
% 0.19/0.52 % SZS output end Proof for NUM699^1
% 0.19/0.52 % cvc5---1.0.5 exiting
% 0.19/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------