TSTP Solution File: NUM753^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM753^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 10:47:38 EDT 2023
% Result : Theorem 0.41s 0.62s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM753^1 : TPTP v8.1.2. Released v3.7.0.
% 0.04/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 08:54:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 % File : NUM753^1 : TPTP v8.1.2. Released v3.7.0.
% 0.21/0.51 % Domain : Number Theory
% 0.21/0.51 % Problem : Landau theorem 62g
% 0.21/0.51 % Version : Especial.
% 0.21/0.51 % English : moref (pf x z) (pf y u)
% 0.21/0.51
% 0.21/0.51 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.51 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.51 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.51 % Source : [Bro09]
% 0.21/0.51 % Names : satz62g [Lan30]
% 0.21/0.51
% 0.21/0.51 % Status : Theorem
% 0.21/0.51 % : Without extensionality : Theorem
% 0.21/0.51 % Rating : 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.2.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.21/0.51 % Syntax : Number of formulae : 15 ( 4 unt; 8 typ; 0 def)
% 0.21/0.51 % Number of atoms : 13 ( 0 equ; 0 cnn)
% 0.21/0.51 % Maximal formula atoms : 4 ( 1 avg)
% 0.21/0.51 % Number of connectives : 44 ( 0 ~; 0 |; 0 &; 38 @)
% 0.21/0.51 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.21/0.51 % Maximal formula depth : 11 ( 6 avg)
% 0.21/0.51 % Number of types : 2 ( 1 usr)
% 0.21/0.51 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.21/0.51 % Number of symbols : 7 ( 7 usr; 4 con; 0-2 aty)
% 0.21/0.51 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.21/0.51 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.51
% 0.21/0.51 % Comments :
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 thf(frac_type,type,
% 0.21/0.51 frac: $tType ).
% 0.21/0.51
% 0.21/0.51 thf(x,type,
% 0.21/0.51 x: frac ).
% 0.21/0.51
% 0.21/0.51 thf(y,type,
% 0.21/0.51 y: frac ).
% 0.21/0.51
% 0.21/0.51 thf(z,type,
% 0.21/0.51 z: frac ).
% 0.21/0.51
% 0.21/0.51 thf(u,type,
% 0.21/0.51 u: frac ).
% 0.21/0.51
% 0.21/0.51 thf(eq,type,
% 0.21/0.51 eq: frac > frac > $o ).
% 0.21/0.51
% 0.21/0.51 thf(e,axiom,
% 0.21/0.51 eq @ x @ y ).
% 0.21/0.51
% 0.21/0.51 thf(moref,type,
% 0.21/0.51 moref: frac > frac > $o ).
% 0.21/0.51
% 0.21/0.51 thf(m,axiom,
% 0.21/0.51 moref @ z @ u ).
% 0.21/0.51
% 0.21/0.51 thf(pf,type,
% 0.21/0.51 pf: frac > frac > frac ).
% 0.21/0.51
% 0.21/0.51 thf(satz44,axiom,
% 0.21/0.51 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.21/0.51 ( ( moref @ Xx @ Xy )
% 0.21/0.51 => ( ( eq @ Xx @ Xz )
% 0.21/0.51 => ( ( eq @ Xy @ Xu )
% 0.21/0.51 => ( moref @ Xz @ Xu ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(satz62d,axiom,
% 0.21/0.51 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.21/0.51 ( ( moref @ Xx @ Xy )
% 0.21/0.51 => ( moref @ ( pf @ Xz @ Xx ) @ ( pf @ Xz @ Xy ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(satz37,axiom,
% 0.21/0.51 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 0.21/0.51
% 0.21/0.51 thf(satz56,axiom,
% 0.21/0.51 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.21/0.51 ( ( eq @ Xx @ Xy )
% 0.21/0.51 => ( ( eq @ Xz @ Xu )
% 0.21/0.51 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(satz62g,conjecture,
% 0.21/0.51 moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ).
% 0.21/0.51
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.n8WYIB3uVX/cvc5---1.0.5_25741.p...
% 0.21/0.51 (declare-sort $$unsorted 0)
% 0.21/0.51 (declare-sort tptp.frac 0)
% 0.21/0.51 (declare-fun tptp.x () tptp.frac)
% 0.21/0.51 (declare-fun tptp.y () tptp.frac)
% 0.21/0.51 (declare-fun tptp.z () tptp.frac)
% 0.21/0.51 (declare-fun tptp.u () tptp.frac)
% 0.21/0.51 (declare-fun tptp.eq (tptp.frac tptp.frac) Bool)
% 0.21/0.51 (assert (@ (@ tptp.eq tptp.x) tptp.y))
% 0.21/0.51 (declare-fun tptp.moref (tptp.frac tptp.frac) Bool)
% 0.21/0.51 (assert (@ (@ tptp.moref tptp.z) tptp.u))
% 0.21/0.51 (declare-fun tptp.pf (tptp.frac tptp.frac) tptp.frac)
% 0.21/0.51 (assert (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac) (Xu tptp.frac)) (=> (@ (@ tptp.moref Xx) Xy) (=> (@ (@ tptp.eq Xx) Xz) (=> (@ (@ tptp.eq Xy) Xu) (@ (@ tptp.moref Xz) Xu))))))
% 0.21/0.51 (assert (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac)) (let ((_let_1 (@ tptp.pf Xz))) (=> (@ (@ tptp.moref Xx) Xy) (@ (@ tptp.moref (@ _let_1 Xx)) (@ _let_1 Xy))))))
% 0.21/0.51 (assert (forall ((Xx tptp.frac)) (@ (@ tptp.eq Xx) Xx)))
% 0.21/0.51 (assert (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac) (Xu tptp.frac)) (=> (@ (@ tptp.eq Xx) Xy) (=> (@ (@ tptp.eq Xz) Xu) (@ (@ tptp.eq (@ (@ tptp.pf Xx) Xz)) (@ (@ tptp.pf Xy) Xu))))))
% 0.21/0.51 (assert (not (@ (@ tptp.moref (@ (@ tptp.pf tptp.x) tptp.z)) (@ (@ tptp.pf tptp.y) tptp.u))))
% 0.21/0.51 (set-info :filename cvc5---1.0.5_25741)
% 0.21/0.51 (check-sat-assuming ( true ))
% 0.21/0.51 ------- get file name : TPTP file name is NUM753^1
% 0.21/0.51 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25741.smt2...
% 0.41/0.62 --- Run --ho-elim --full-saturate-quant at 10...
% 0.41/0.62 % SZS status Theorem for NUM753^1
% 0.41/0.62 % SZS output start Proof for NUM753^1
% 0.41/0.62 (
% 0.41/0.62 (let ((_let_1 (not (@ (@ tptp.moref (@ (@ tptp.pf tptp.x) tptp.z)) (@ (@ tptp.pf tptp.y) tptp.u))))) (let ((_let_2 (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac) (Xu tptp.frac)) (=> (@ (@ tptp.eq Xx) Xy) (=> (@ (@ tptp.eq Xz) Xu) (@ (@ tptp.eq (@ (@ tptp.pf Xx) Xz)) (@ (@ tptp.pf Xy) Xu))))))) (let ((_let_3 (forall ((Xx tptp.frac)) (@ (@ tptp.eq Xx) Xx)))) (let ((_let_4 (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac)) (let ((_let_1 (@ tptp.pf Xz))) (=> (@ (@ tptp.moref Xx) Xy) (@ (@ tptp.moref (@ _let_1 Xx)) (@ _let_1 Xy))))))) (let ((_let_5 (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac) (Xu tptp.frac)) (=> (@ (@ tptp.moref Xx) Xy) (=> (@ (@ tptp.eq Xx) Xz) (=> (@ (@ tptp.eq Xy) Xu) (@ (@ tptp.moref Xz) Xu))))))) (let ((_let_6 (@ (@ tptp.moref tptp.z) tptp.u))) (let ((_let_7 (@ (@ tptp.eq tptp.x) tptp.y))) (let ((_let_8 (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac) (Xu tptp.frac)) (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_8 (ho_7 k_6 Xx) Xz)) (ho_8 (ho_7 k_6 Xy) Xu)))))) (let ((_let_9 (ho_8 (ho_7 k_6 tptp.y) tptp.u))) (let ((_let_10 (ho_7 k_6 tptp.x))) (let ((_let_11 (ho_8 _let_10 tptp.u))) (let ((_let_12 (ho_4 (ho_3 k_2 _let_11) _let_9))) (let ((_let_13 (ho_4 (ho_3 k_2 tptp.u) tptp.u))) (let ((_let_14 (not _let_13))) (let ((_let_15 (ho_3 k_2 tptp.x))) (let ((_let_16 (ho_4 _let_15 tptp.y))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_14 _let_12))) (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.frac) (Xy tptp.frac) (Xz tptp.frac) (Xu tptp.frac)) (or (not (@ (@ tptp.eq Xx) Xy)) (not (@ (@ tptp.eq Xz) Xu)) (@ (@ tptp.eq (@ (@ tptp.pf Xx) Xz)) (@ (@ tptp.pf Xy) Xu)))) _let_8))))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (ho_8 _let_10 tptp.z))) (let ((_let_22 (ho_3 k_5 _let_21))) (let ((_let_23 (ho_4 _let_22 _let_9))) (let ((_let_24 (not _let_12))) (let ((_let_25 (ho_4 (ho_3 k_2 _let_21) _let_21))) (let ((_let_26 (not _let_25))) (let ((_let_27 (ho_4 _let_22 _let_11))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26 _let_24 _let_23))) (let ((_let_30 (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac) (Xu tptp.frac)) (or (not (ho_4 (ho_3 k_5 Xx) Xy)) (not (ho_4 (ho_3 k_2 Xx) Xz)) (not (ho_4 (ho_3 k_2 Xy) Xu)) (ho_4 (ho_3 k_5 Xz) Xu))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac) (Xu tptp.frac)) (or (not (@ (@ tptp.moref Xx) Xy)) (not (@ (@ tptp.eq Xx) Xz)) (not (@ (@ tptp.eq Xy) Xu)) (@ (@ tptp.moref Xz) Xu))) _let_30))))))) (let ((_let_32 (ho_4 (ho_3 k_5 tptp.z) tptp.u))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_27))) (let ((_let_35 (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac)) (let ((_let_1 (ho_7 k_6 Xz))) (or (not (ho_4 (ho_3 k_5 Xx) Xy)) (ho_4 (ho_3 k_5 (ho_8 _let_1 Xx)) (ho_8 _let_1 Xy))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac)) (let ((_let_1 (@ tptp.pf Xz))) (or (not (@ (@ tptp.moref Xx) Xy)) (@ (@ tptp.moref (@ _let_1 Xx)) (@ _let_1 Xy))))) _let_35))))))) (let ((_let_37 (ho_4 (ho_3 k_2 tptp.z) tptp.z))) (let ((_let_38 (not _let_37))) (let ((_let_39 (ho_4 _let_15 tptp.x))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38 _let_25))) (let ((_let_42 (_let_8))) (let ((_let_43 (forall ((Xx tptp.frac)) (ho_4 (ho_3 k_2 Xx) Xx)))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 _let_43)))))) (let ((_let_45 (_let_43))) (let ((_let_46 (forall ((u |u_(-> tptp.frac Bool)|) (e Bool) (i tptp.frac)) (not (forall ((v |u_(-> tptp.frac Bool)|)) (not (forall ((ii tptp.frac)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> tptp.frac Bool)|) (y |u_(-> tptp.frac Bool)|)) (or (not (forall ((z tptp.frac)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> tptp.frac tptp.frac Bool)|) (e |u_(-> tptp.frac Bool)|) (i tptp.frac)) (not (forall ((v |u_(-> tptp.frac tptp.frac Bool)|)) (not (forall ((ii tptp.frac)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> tptp.frac tptp.frac Bool)|) (y |u_(-> tptp.frac tptp.frac Bool)|)) (or (not (forall ((z tptp.frac)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> tptp.frac tptp.frac)|) (e tptp.frac) (i tptp.frac)) (not (forall ((v |u_(-> tptp.frac tptp.frac)|)) (not (forall ((ii tptp.frac)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> tptp.frac tptp.frac)|) (y |u_(-> tptp.frac tptp.frac)|)) (or (not (forall ((z tptp.frac)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> tptp.frac tptp.frac tptp.frac)|) (e |u_(-> tptp.frac tptp.frac)|) (i tptp.frac)) (not (forall ((v |u_(-> tptp.frac tptp.frac tptp.frac)|)) (not (forall ((ii tptp.frac)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> tptp.frac tptp.frac tptp.frac)|) (y |u_(-> tptp.frac tptp.frac tptp.frac)|)) (or (not (forall ((z tptp.frac)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (tptp.x tptp.y tptp.u tptp.u QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_17 _let_14 _let_12 _let_20))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_7)) (PREPROCESS :args ((= _let_7 _let_16)))) (PREPROCESS :args ((and _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46)))) :args ((and _let_16 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46))) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.u QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_45)) _let_44 :args (_let_13 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_23 _let_26 _let_28 _let_24 (not _let_29)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 (not _let_23))))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_38 _let_25 (not _let_41)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_3 k_2 Xx)))) :args _let_45)) _let_44 :args (_let_39 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.z QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_45)) _let_44 :args (_let_37 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (tptp.x tptp.x tptp.z tptp.z QUANTIFIERS_INST_E_MATCHING ((ho_8 (ho_7 k_6 Xx) Xz) (ho_8 (ho_7 k_6 Xy) Xu)))) :args _let_42)) _let_19 :args (_let_41 false _let_8)) :args (_let_25 false _let_39 false _let_37 false _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_27 (not _let_34)))) (EQ_RESOLVE (ASSUME :args (_let_6)) (PREPROCESS :args ((= _let_6 _let_32)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.z tptp.u tptp.x QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_27 false _let_32 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_21 _let_11 _let_21 _let_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_30))) _let_31 :args (_let_29 false _let_30)) :args (_let_24 true _let_23 false _let_25 false _let_27 false _let_29)) :args (_let_20 false _let_16 false _let_13 true _let_12)) _let_19 :args (false true _let_18 false _let_8)) :args (_let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.41/0.62 )
% 0.41/0.62 % SZS output end Proof for NUM753^1
% 0.41/0.62 % cvc5---1.0.5 exiting
% 0.41/0.62 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------