TSTP Solution File: NUM691^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM691^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 10:46:50 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 : NUM691^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 11:17:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 % File : NUM691^1 : TPTP v8.1.2. Released v3.7.0.
% 0.20/0.52 % Domain : Number Theory
% 0.20/0.52 % Problem : Landau theorem 23
% 0.20/0.52 % Version : Especial.
% 0.20/0.52 % English : ~(more (pl x z) (pl y u)) -> pl x z = pl y u
% 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 : satz23 [Lan30]
% 0.20/0.52
% 0.20/0.52 % Status : Theorem
% 0.20/0.52 % : Without extensionality : Theorem
% 0.20/0.52 % Rating : 0.15 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.20/0.52 % Syntax : Number of formulae : 13 ( 0 unt; 7 typ; 0 def)
% 0.20/0.52 % Number of atoms : 14 ( 5 equ; 0 cnn)
% 0.20/0.52 % Maximal formula atoms : 4 ( 2 avg)
% 0.20/0.52 % Number of connectives : 51 ( 7 ~; 0 |; 0 &; 34 @)
% 0.20/0.52 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.20/0.52 % Maximal formula depth : 11 ( 7 avg)
% 0.20/0.52 % Number of types : 2 ( 1 usr)
% 0.20/0.52 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.52 % Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% 0.20/0.52 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.20/0.52 % SPC : TH0_THM_EQU_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(u,type,
% 0.20/0.52 u: 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(m,axiom,
% 0.20/0.52 ( ~ ( more @ x @ y )
% 0.20/0.52 => ( x = y ) ) ).
% 0.20/0.52
% 0.20/0.52 thf(n,axiom,
% 0.20/0.52 ( ~ ( more @ z @ u )
% 0.20/0.52 => ( z = u ) ) ).
% 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(et,axiom,
% 0.20/0.52 ! [Xa: $o] :
% 0.20/0.52 ( ~ ~ Xa
% 0.20/0.52 => Xa ) ).
% 0.20/0.52
% 0.20/0.52 thf(satz22a,axiom,
% 0.20/0.52 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.20/0.52 ( ( ~ ( more @ Xx @ Xy )
% 0.20/0.52 => ( Xx = Xy ) )
% 0.20/0.52 => ( ( more @ Xz @ Xu )
% 0.20/0.52 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) ).
% 0.20/0.52
% 0.20/0.52 thf(satz22b,axiom,
% 0.20/0.52 ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
% 0.20/0.52 ( ( more @ Xx @ Xy )
% 0.20/0.52 => ( ( ~ ( more @ Xz @ Xu )
% 0.20/0.52 => ( Xz = Xu ) )
% 0.20/0.52 => ( more @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xu ) ) ) ) ).
% 0.20/0.52
% 0.20/0.52 thf(satz23,conjecture,
% 0.20/0.52 ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
% 0.20/0.52 => ( ( pl @ x @ z )
% 0.20/0.52 = ( pl @ y @ u ) ) ) ).
% 0.20/0.52
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.6Gl4wWWVNP/cvc5---1.0.5_2181.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.u () tptp.nat)
% 0.20/0.52 (declare-fun tptp.more (tptp.nat tptp.nat) Bool)
% 0.20/0.52 (assert (=> (not (@ (@ tptp.more tptp.x) tptp.y)) (= tptp.x tptp.y)))
% 0.20/0.52 (assert (=> (not (@ (@ tptp.more tptp.z) tptp.u)) (= tptp.z tptp.u)))
% 0.20/0.52 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.20/0.52 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.20/0.52 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (=> (=> (not (@ (@ tptp.more Xx) Xy)) (= Xx Xy)) (=> (@ (@ tptp.more Xz) Xu) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xu))))))
% 0.20/0.52 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (=> (=> (not (@ (@ tptp.more Xz) Xu)) (= Xz Xu)) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xu))))))
% 0.20/0.52 (assert (let ((_let_1 (@ (@ tptp.pl tptp.y) tptp.u))) (let ((_let_2 (@ (@ tptp.pl tptp.x) tptp.z))) (not (=> (not (@ (@ tptp.more _let_2) _let_1)) (= _let_2 _let_1))))))
% 0.20/0.52 (set-info :filename cvc5---1.0.5_2181)
% 0.20/0.52 (check-sat-assuming ( true ))
% 0.20/0.52 ------- get file name : TPTP file name is NUM691^1
% 0.20/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2181.smt2...
% 0.20/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.52 % SZS status Theorem for NUM691^1
% 0.20/0.52 % SZS output start Proof for NUM691^1
% 0.20/0.52 (
% 0.20/0.52 (let ((_let_1 (@ (@ tptp.pl tptp.y) tptp.u))) (let ((_let_2 (@ (@ tptp.pl tptp.x) tptp.z))) (let ((_let_3 (not (@ (@ tptp.more _let_2) _let_1)))) (let ((_let_4 (not (=> _let_3 (= _let_2 _let_1))))) (let ((_let_5 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (=> (=> (not (@ (@ tptp.more Xz) Xu)) (= Xz Xu)) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xu))))))) (let ((_let_6 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (=> (=> (not (@ (@ tptp.more Xx) Xy)) (= Xx Xy)) (=> (@ (@ tptp.more Xz) Xu) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xu))))))) (let ((_let_7 (= tptp.z tptp.u))) (let ((_let_8 (=> (not (@ (@ tptp.more tptp.z) tptp.u)) _let_7))) (let ((_let_9 (= tptp.x tptp.y))) (let ((_let_10 (=> (not (@ (@ tptp.more tptp.x) tptp.y)) _let_9))) (let ((_let_11 (ho_6 k_5 tptp.y))) (let ((_let_12 (ho_7 _let_11 tptp.u))) (let ((_let_13 (ho_7 (ho_6 k_5 tptp.x) tptp.z))) (let ((_let_14 (= _let_13 _let_12))) (let ((_let_15 (ho_3 k_2 _let_13))) (let ((_let_16 (ho_4 _let_15 _let_12))) (let ((_let_17 (not _let_16))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> _let_3 (= _let_1 _let_2))) (not (=> _let_17 _let_14))))))))) (let ((_let_19 (ho_4 (ho_3 k_2 tptp.x) tptp.y))) (let ((_let_20 (not _let_9))) (let ((_let_21 (not _let_19))) (let ((_let_22 (and _let_21 _let_20))) (let ((_let_23 (ho_4 _let_15 (ho_7 _let_11 tptp.z)))) (let ((_let_24 (or _let_21 _let_23))) (let ((_let_25 (ho_4 (ho_3 k_2 tptp.z) tptp.u))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_22 _let_26 _let_16))) (let ((_let_28 (not _let_22))) (let ((_let_29 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (or (not (ho_4 (ho_3 k_2 Xx) Xy)) (and (not (ho_4 (ho_3 k_2 Xz) Xu)) (not (= 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_30 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 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)) (and (not (@ (@ tptp.more Xz) Xu)) (not (= Xz Xu))) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xu)))) _let_29))))))) (let ((_let_31 (NOT_IMPLIES_ELIM1 _let_18))) (let ((_let_32 (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (or (and (not (ho_4 (ho_3 k_2 Xx) Xy)) (not (= 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_33 (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat) (Xu tptp.nat)) (or (and (not (@ (@ tptp.more Xx) Xy)) (not (= Xx Xy))) (not (@ (@ tptp.more Xz) Xu)) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xu)))) _let_32))))))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (tptp.x tptp.y tptp.z tptp.u QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_32))) _let_33 :args (_let_27 false _let_32)))) (let ((_let_35 (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_26 _let_16 _let_22 (not _let_27)))))) (let ((_let_36 (or))) (let ((_let_37 (_let_7))) (let ((_let_38 (REORDERING (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_8)) (PREPROCESS :args ((= _let_8 (=> _let_26 _let_7)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) (REFL :args _let_37) :args _let_36)) :args ((or _let_7 _let_25))))) (let ((_let_39 (not _let_23))) (let ((_let_40 (not _let_7))) (let ((_let_41 (ASSUME :args (_let_17)))) (let ((_let_42 (APPLY_UF ho_7))) (let ((_let_43 (ASSUME :args _let_37))) (let ((_let_44 (CONG (REFL :args (_let_11)) (SYMM (SYMM _let_43)) :args _let_42))) (let ((_let_45 (ASSUME :args (_let_23)))) (let ((_let_46 (_let_9))) (let ((_let_47 (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_48 (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_49 (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_50 (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_51 (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_52 (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_53 (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_54 (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_55 (=> _let_21 _let_9))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (IMPLIES_ELIM (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_10)) (PREPROCESS :args ((= _let_10 _let_55)))) (PREPROCESS :args ((and _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47)))) :args ((and _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47))) :args (0))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_19))) (REFL :args _let_46) :args _let_36)) :args ((or _let_9 _let_19))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_41 _let_43 _let_45) :args (_let_7 _let_17 _let_23)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_45)) (CONG (REFL :args (_let_15)) _let_44 :args (APPLY_UF ho_4)) (FALSE_INTRO _let_41))) :args (_let_17 _let_7 _let_23)) :args ((not (and _let_7 _let_17 _let_23)) SB_LITERAL))) (CONG (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) (REFL :args (_let_39)) :args _let_36)) :args ((or _let_16 _let_40 _let_39))) _let_31 _let_38 _let_35 _let_34 _let_31 (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_21 _let_23 (not _let_24)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.x tptp.y tptp.z tptp.z QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_29)))) _let_30 :args (_let_24 false _let_29)) (REORDERING (CNF_AND_POS :args (_let_22 0)) :args ((or _let_21 _let_28))) :args (_let_21 true _let_16 false _let_7 true _let_25 false _let_27 true _let_16 false _let_23 false _let_24 true _let_22)) :args (_let_9 true _let_19)))) (let ((_let_57 (and _let_9 _let_7))) (let ((_let_58 (ASSUME :args _let_46))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_57)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_43 _let_58) (SCOPE (TRANS (CONG (CONG (REFL :args (k_5)) (SYMM (SYMM _let_58)) :args (APPLY_UF ho_6)) (REFL :args (tptp.z)) :args _let_42) _let_44) :args (_let_7 _let_9))) :args (_let_9 _let_7))) :args (true _let_57)) :args ((or _let_14 _let_20 _let_40))) (MACRO_RESOLUTION_TRUST _let_38 (MACRO_RESOLUTION_TRUST _let_35 _let_31 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_22 1)) :args ((or _let_20 _let_28))) _let_56 :args (_let_28 false _let_9)) _let_34 :args (_let_26 true _let_16 true _let_22 false _let_27)) :args (_let_7 true _let_25)) _let_56 (NOT_IMPLIES_ELIM2 _let_18) :args (false false _let_7 false _let_9 true _let_14)) :args (_let_10 _let_8 (forall ((Xa Bool)) (=> (not (not Xa)) Xa)) _let_6 _let_5 _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.52 )
% 0.20/0.52 % SZS output end Proof for NUM691^1
% 0.20/0.52 % cvc5---1.0.5 exiting
% 0.20/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------