TSTP Solution File: NUM672^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM672^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 10:46:35 EDT 2023
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM672^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n021.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 07:58:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 % File : NUM672^1 : TPTP v8.1.2. Released v3.7.0.
% 0.20/0.52 % Domain : Number Theory
% 0.20/0.52 % Problem : Landau theorem 19c
% 0.20/0.52 % Version : Especial.
% 0.20/0.52 % English : less (pl x z) (pl y z)
% 0.20/0.52
% 0.20/0.52 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.52 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.52 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.52 % Source : [Bro09]
% 0.20/0.52 % Names : satz19c [Lan30]
% 0.20/0.52
% 0.20/0.52 % Status : Theorem
% 0.20/0.52 % : Without extensionality : Theorem
% 0.20/0.52 % Rating : 0.00 v3.7.0
% 0.20/0.52 % Syntax : Number of formulae : 12 ( 2 unt; 7 typ; 0 def)
% 0.20/0.52 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.20/0.52 % Maximal formula atoms : 2 ( 1 avg)
% 0.20/0.52 % Number of connectives : 27 ( 0 ~; 0 |; 0 &; 24 @)
% 0.20/0.52 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.52 % Maximal formula depth : 9 ( 6 avg)
% 0.20/0.52 % Number of types : 2 ( 1 usr)
% 0.20/0.52 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.20/0.52 % Number of symbols : 6 ( 6 usr; 3 con; 0-2 aty)
% 0.20/0.52 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.20/0.52 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.52
% 0.20/0.52 % Comments :
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 thf(nat_type,type,
% 0.20/0.52 nat: $tType ).
% 0.20/0.52
% 0.20/0.52 thf(x,type,
% 0.20/0.52 x: nat ).
% 0.20/0.52
% 0.20/0.52 thf(y,type,
% 0.20/0.52 y: nat ).
% 0.20/0.52
% 0.20/0.52 thf(z,type,
% 0.20/0.52 z: nat ).
% 0.20/0.52
% 0.20/0.52 thf(less,type,
% 0.20/0.52 less: nat > nat > $o ).
% 0.20/0.52
% 0.20/0.52 thf(l,axiom,
% 0.20/0.52 less @ x @ y ).
% 0.20/0.52
% 0.20/0.52 thf(pl,type,
% 0.20/0.52 pl: nat > nat > nat ).
% 0.20/0.52
% 0.20/0.52 thf(more,type,
% 0.20/0.52 more: nat > nat > $o ).
% 0.20/0.52
% 0.20/0.52 thf(satz11,axiom,
% 0.20/0.52 ! [Xx: nat,Xy: nat] :
% 0.20/0.52 ( ( more @ Xx @ Xy )
% 0.20/0.52 => ( less @ Xy @ Xx ) ) ).
% 0.20/0.52
% 0.20/0.52 thf(satz19a,axiom,
% 0.20/0.52 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.20/0.52 ( ( more @ Xx @ Xy )
% 0.20/0.52 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) ) ) ).
% 0.20/0.52
% 0.20/0.52 thf(satz12,axiom,
% 0.20/0.52 ! [Xx: nat,Xy: nat] :
% 0.20/0.52 ( ( less @ Xx @ Xy )
% 0.20/0.52 => ( more @ Xy @ Xx ) ) ).
% 0.20/0.52
% 0.20/0.52 thf(satz19c,conjecture,
% 0.20/0.52 less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ).
% 0.20/0.52
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.KcjWVKUIYm/cvc5---1.0.5_25525.p...
% 0.20/0.52 (declare-sort $$unsorted 0)
% 0.20/0.52 (declare-sort tptp.nat 0)
% 0.20/0.52 (declare-fun tptp.x () tptp.nat)
% 0.20/0.52 (declare-fun tptp.y () tptp.nat)
% 0.20/0.52 (declare-fun tptp.z () tptp.nat)
% 0.20/0.52 (declare-fun tptp.less (tptp.nat tptp.nat) Bool)
% 0.20/0.52 (assert (@ (@ tptp.less tptp.x) tptp.y))
% 0.20/0.52 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.20/0.52 (declare-fun tptp.more (tptp.nat tptp.nat) Bool)
% 0.20/0.52 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (@ (@ tptp.less Xy) Xx))))
% 0.20/0.52 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xz)))))
% 0.20/0.52 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.less Xx) Xy) (@ (@ tptp.more Xy) Xx))))
% 0.20/0.52 (assert (not (@ (@ tptp.less (@ (@ tptp.pl tptp.x) tptp.z)) (@ (@ tptp.pl tptp.y) tptp.z))))
% 0.20/0.52 (set-info :filename cvc5---1.0.5_25525)
% 0.20/0.52 (check-sat-assuming ( true ))
% 0.20/0.52 ------- get file name : TPTP file name is NUM672^1
% 0.20/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25525.smt2...
% 0.20/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.52 % SZS status Theorem for NUM672^1
% 0.20/0.52 % SZS output start Proof for NUM672^1
% 0.20/0.52 (
% 0.20/0.52 (let ((_let_1 (not (@ (@ tptp.less (@ (@ tptp.pl tptp.x) tptp.z)) (@ (@ tptp.pl tptp.y) tptp.z))))) (let ((_let_2 (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.less Xx) Xy) (@ (@ tptp.more Xy) Xx))))) (let ((_let_3 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xz)))))) (let ((_let_4 (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (@ (@ tptp.less Xy) Xx))))) (let ((_let_5 (@ (@ tptp.less tptp.x) tptp.y))) (let ((_let_6 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (or (not (ho_4 (ho_3 k_5 Xx) Xy)) (ho_4 (ho_3 k_5 (ho_8 (ho_7 k_6 Xx) Xz)) (ho_8 (ho_7 k_6 Xy) Xz)))))) (let ((_let_7 (ho_8 (ho_7 k_6 tptp.x) tptp.z))) (let ((_let_8 (ho_8 (ho_7 k_6 tptp.y) tptp.z))) (let ((_let_9 (ho_4 (ho_3 k_5 _let_8) _let_7))) (let ((_let_10 (ho_4 (ho_3 k_5 tptp.y) tptp.x))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_9))) (let ((_let_13 (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) (Xz tptp.nat)) (or (not (@ (@ tptp.more Xx) Xy)) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xz)))) _let_6))))))) (let ((_let_14 (not _let_12))) (let ((_let_15 (ho_4 (ho_3 k_2 tptp.x) tptp.y))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_10))) (let ((_let_18 (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (ho_4 (ho_3 k_2 Xx) Xy)) (ho_4 (ho_3 k_5 Xy) Xx))))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (@ (@ tptp.less Xx) Xy)) (@ (@ tptp.more Xy) Xx))) _let_18))))))) (let ((_let_20 (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_21 (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_22 (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_23 (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_24 (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_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_25 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_26 (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_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_27 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_28 (ho_4 (ho_3 k_2 _let_7) _let_8))) (let ((_let_29 (not _let_9))) (let ((_let_30 (or _let_29 _let_28))) (let ((_let_31 (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (ho_4 (ho_3 k_5 Xx) Xy)) (ho_4 (ho_3 k_2 Xy) Xx))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (@ (@ tptp.more Xx) Xy)) (@ (@ tptp.less Xy) Xx))) _let_31))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (tptp.y tptp.x tptp.z QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_6))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_9 _let_11 _let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_28 _let_29 (not _let_30)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 (not _let_28))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_8 _let_7 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 Xy) Xx) true))))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)) :args (_let_29 true _let_28 false _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_16 _let_10 (not _let_17)))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 _let_15)))) (PREPROCESS :args ((and _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20)))) :args ((and _let_15 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20))) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 Xx) Xy) false))))) :args (_let_18))) _let_19 :args (_let_17 false _let_18)) :args (_let_10 false _let_15 false _let_17)) :args (_let_14 true _let_9 false _let_10)) _let_13 :args (false true _let_12 false _let_6)) :args (_let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))
% 0.20/0.52 )
% 0.20/0.52 % SZS output end Proof for NUM672^1
% 0.20/0.52 % cvc5---1.0.5 exiting
% 0.20/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------