TSTP Solution File: NUM688^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM688^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.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 10:46:45 EDT 2023
% Result : Theorem 0.21s 0.54s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM688^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.16/0.35 % Computer : n006.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri Aug 25 09:02:07 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.54 %------------------------------------------------------------------------------
% 0.21/0.54 % File : NUM688^1 : TPTP v8.1.2. Released v3.7.0.
% 0.21/0.54 % Domain : Number Theory
% 0.21/0.54 % Problem : Landau theorem 22b
% 0.21/0.54 % Version : Especial.
% 0.21/0.54 % English : more (pl x z) (pl y u)
% 0.21/0.54
% 0.21/0.54 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.54 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.54 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.54 % Source : [Bro09]
% 0.21/0.54 % Names : satz22b [Lan30]
% 0.21/0.54 % : satz35b [Lan30]
% 0.21/0.54
% 0.21/0.54 % Status : Theorem
% 0.21/0.54 % : Without extensionality : Theorem
% 0.21/0.54 % Rating : 0.15 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 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
% 0.21/0.54 % Syntax : Number of formulae : 13 ( 2 unt; 7 typ; 0 def)
% 0.21/0.54 % Number of atoms : 10 ( 2 equ; 0 cnn)
% 0.21/0.54 % Maximal formula atoms : 3 ( 1 avg)
% 0.21/0.54 % Number of connectives : 37 ( 3 ~; 0 |; 0 &; 28 @)
% 0.21/0.54 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.21/0.54 % Maximal formula depth : 11 ( 7 avg)
% 0.21/0.54 % Number of types : 2 ( 1 usr)
% 0.21/0.54 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.21/0.54 % Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% 0.21/0.54 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.21/0.54 % SPC : TH0_THM_EQU_NAR
% 0.21/0.54
% 0.21/0.54 % Comments :
% 0.21/0.54 %------------------------------------------------------------------------------
% 0.21/0.54 thf(nat_type,type,
% 0.21/0.54 nat: $tType ).
% 0.21/0.54
% 0.21/0.54 thf(x,type,
% 0.21/0.54 x: nat ).
% 0.21/0.54
% 0.21/0.54 thf(y,type,
% 0.21/0.54 y: nat ).
% 0.21/0.54
% 0.21/0.54 thf(z,type,
% 0.21/0.54 z: nat ).
% 0.21/0.54
% 0.21/0.54 thf(u,type,
% 0.21/0.54 u: nat ).
% 0.21/0.54
% 0.21/0.54 thf(more,type,
% 0.21/0.54 more: nat > nat > $o ).
% 0.21/0.54
% 0.21/0.54 thf(m,axiom,
% 0.21/0.54 more @ x @ y ).
% 0.21/0.54
% 0.21/0.54 thf(n,axiom,
% 0.21/0.54 ( ~ ( more @ z @ u )
% 0.21/0.54 => ( z = u ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(pl,type,
% 0.21/0.54 pl: nat > nat > nat ).
% 0.21/0.54
% 0.21/0.54 thf(et,axiom,
% 0.21/0.54 ! [Xa: $o] :
% 0.21/0.54 ( ~ ~ Xa
% 0.21/0.54 => Xa ) ).
% 0.21/0.54
% 0.21/0.54 thf(satz19h,axiom,
% 0.21/0.54 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.21/0.54 ( ( Xx = Xy )
% 0.21/0.54 => ( ( more @ Xz @ Xu )
% 0.21/0.54 => ( more @ ( pl @ Xz @ Xx ) @ ( pl @ Xu @ Xy ) ) ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(satz21,axiom,
% 0.21/0.54 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.21/0.54 ( ( more @ Xx @ Xy )
% 0.21/0.54 => ( ( more @ Xz @ Xu )
% 0.21/0.54 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(satz22b,conjecture,
% 0.21/0.54 more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ).
% 0.21/0.54
% 0.21/0.54 %------------------------------------------------------------------------------
% 0.21/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.G8E3HbAsKl/cvc5---1.0.5_5513.p...
% 0.21/0.54 (declare-sort $$unsorted 0)
% 0.21/0.54 (declare-sort tptp.nat 0)
% 0.21/0.54 (declare-fun tptp.x () tptp.nat)
% 0.21/0.54 (declare-fun tptp.y () tptp.nat)
% 0.21/0.54 (declare-fun tptp.z () tptp.nat)
% 0.21/0.54 (declare-fun tptp.u () tptp.nat)
% 0.21/0.54 (declare-fun tptp.more (tptp.nat tptp.nat) Bool)
% 0.21/0.54 (assert (@ (@ tptp.more tptp.x) tptp.y))
% 0.21/0.54 (assert (=> (not (@ (@ tptp.more tptp.z) tptp.u)) (= tptp.z tptp.u)))
% 0.21/0.54 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.21/0.54 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.21/0.54 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (=> (= Xx Xy) (=> (@ (@ tptp.more Xz) Xu) (@ (@ tptp.more (@ (@ tptp.pl Xz) Xx)) (@ (@ tptp.pl Xu) Xy))))))
% 0.21/0.54 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (=> (@ (@ tptp.more Xz) Xu) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xu))))))
% 0.21/0.54 (assert (not (@ (@ tptp.more (@ (@ tptp.pl tptp.x) tptp.z)) (@ (@ tptp.pl tptp.y) tptp.u))))
% 0.21/0.54 (set-info :filename cvc5---1.0.5_5513)
% 0.21/0.54 (check-sat-assuming ( true ))
% 0.21/0.54 ------- get file name : TPTP file name is NUM688^1
% 0.21/0.54 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5513.smt2...
% 0.21/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.54 % SZS status Theorem for NUM688^1
% 0.21/0.54 % SZS output start Proof for NUM688^1
% 0.21/0.54 (
% 0.21/0.54 (let ((_let_1 (not (@ (@ tptp.more (@ (@ tptp.pl tptp.x) tptp.z)) (@ (@ tptp.pl tptp.y) tptp.u))))) (let ((_let_2 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (=> (@ (@ tptp.more Xz) Xu) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xu))))))) (let ((_let_3 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (=> (= Xx Xy) (=> (@ (@ tptp.more Xz) Xu) (@ (@ tptp.more (@ (@ tptp.pl Xz) Xx)) (@ (@ tptp.pl Xu) Xy))))))) (let ((_let_4 (= tptp.z tptp.u))) (let ((_let_5 (=> (not (@ (@ tptp.more tptp.z) tptp.u)) _let_4))) (let ((_let_6 (@ (@ tptp.more tptp.x) tptp.y))) (let ((_let_7 (forall ((Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (or (not (ho_4 (ho_3 k_2 Xz) Xu)) (ho_4 (ho_3 k_2 (ho_7 (ho_6 k_5 Xz) Xy)) (ho_7 (ho_6 k_5 Xu) Xy)))))) (let ((_let_8 (ho_6 k_5 tptp.y))) (let ((_let_9 (ho_3 k_2 (ho_7 (ho_6 k_5 tptp.x) tptp.z)))) (let ((_let_10 (ho_4 _let_9 (ho_7 _let_8 tptp.z)))) (let ((_let_11 (ho_4 (ho_3 k_2 tptp.x) tptp.y))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10))) (let ((_let_14 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (or (not (@ (@ tptp.more Xz) Xu)) (@ (@ tptp.more (@ (@ tptp.pl Xz) Xy)) (@ (@ tptp.pl Xu) Xy)))) _let_7))))))) (let ((_let_15 (not _let_13))) (let ((_let_16 (ho_4 _let_9 (ho_7 _let_8 tptp.u)))) (let ((_let_17 (not _let_10))) (let ((_let_18 (ho_4 (ho_3 k_2 tptp.z) tptp.u))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_12 _let_19 _let_16))) (let ((_let_21 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (or (not (ho_4 (ho_3 k_2 Xx) Xy)) (not (ho_4 (ho_3 k_2 Xz) Xu)) (ho_4 (ho_3 k_2 (ho_7 (ho_6 k_5 Xx) Xz)) (ho_7 (ho_6 k_5 Xy) Xu)))))) (let ((_let_22 (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) (Xz tptp.nat) (Xu tptp.nat)) (or (not (@ (@ tptp.more Xx) Xy)) (not (@ (@ tptp.more Xz) Xu)) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xu)))) _let_21))))))) (let ((_let_23 (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_24 (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_25 (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_26 (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_27 (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_28 (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_29 (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_30 (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_31 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_6)) (PREPROCESS :args ((= _let_6 _let_11)))) (PREPROCESS :args ((and _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23)))) :args ((and _let_11 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23))) :args (0)))) (let ((_let_32 (not _let_16))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 _let_32)))))) (let ((_let_34 (or))) (let ((_let_35 (_let_4))) (let ((_let_36 (not _let_4))) (let ((_let_37 (and _let_4 _let_32))) (let ((_let_38 (ASSUME :args _let_35))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_14 :args (tptp.z tptp.x tptp.y QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_7))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_13)) :args ((or _let_12 _let_10 _let_15))) _let_31 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_37)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_33 _let_38) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (_let_9)) (CONG (REFL :args (_let_8)) (SYMM (SYMM _let_38)) :args (APPLY_UF ho_7)) :args (APPLY_UF ho_4)) (FALSE_INTRO _let_33))) :args (_let_32 _let_4))) :args (_let_4 _let_32))) :args (true _let_37)) (CONG (REFL :args (_let_36)) (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_16))) (REFL :args (_let_17)) :args _let_34)) :args ((or _let_16 _let_36 _let_17))) _let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 (=> _let_19 _let_4)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) (REFL :args _let_35) :args _let_34)) :args ((or _let_4 _let_18))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_16 _let_12 (not _let_20)))) _let_33 _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (tptp.x tptp.y tptp.z tptp.u QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_21))) _let_22 :args (_let_20 false _let_21)) :args (_let_19 true _let_16 false _let_11 false _let_20)) :args (_let_4 true _let_18)) :args (_let_17 true _let_16 false _let_4)) :args (_let_15 false _let_11 true _let_10)) _let_14 :args (false true _let_13 false _let_7)) :args (_let_6 _let_5 (forall ((Xa Bool)) (=> (not (not Xa)) Xa)) _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))
% 0.21/0.54 )
% 0.21/0.54 % SZS output end Proof for NUM688^1
% 0.21/0.54 % cvc5---1.0.5 exiting
% 0.21/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------