TSTP Solution File: NUM754^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM754^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 10:47:39 EDT 2023
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM754^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.17/0.35 % Computer : n001.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Fri Aug 25 12:51:59 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 % File : NUM754^1 : TPTP v8.1.2. Released v3.7.0.
% 0.20/0.53 % Domain : Number Theory
% 0.20/0.53 % Problem : Landau theorem 62h
% 0.20/0.53 % Version : Especial.
% 0.20/0.53 % English : moref (pf z x) (pf u y)
% 0.20/0.53
% 0.20/0.53 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.53 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.53 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.53 % Source : [Bro09]
% 0.20/0.53 % Names : satz62h [Lan30]
% 0.20/0.53
% 0.20/0.53 % Status : Theorem
% 0.20/0.53 % : Without extensionality : Theorem
% 0.20/0.53 % Rating : 0.09 v8.1.0, 0.17 v7.5.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.17 v5.5.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.20/0.53 % Syntax : Number of formulae : 14 ( 4 unt; 8 typ; 0 def)
% 0.20/0.53 % Number of atoms : 11 ( 0 equ; 0 cnn)
% 0.20/0.53 % Maximal formula atoms : 4 ( 1 avg)
% 0.20/0.53 % Number of connectives : 39 ( 0 ~; 0 |; 0 &; 34 @)
% 0.20/0.53 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.53 % Maximal formula depth : 11 ( 7 avg)
% 0.20/0.53 % Number of types : 2 ( 1 usr)
% 0.20/0.53 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.20/0.53 % Number of symbols : 7 ( 7 usr; 4 con; 0-2 aty)
% 0.20/0.53 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.20/0.53 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.53
% 0.20/0.53 % Comments :
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 thf(frac_type,type,
% 0.20/0.53 frac: $tType ).
% 0.20/0.53
% 0.20/0.53 thf(x,type,
% 0.20/0.53 x: frac ).
% 0.20/0.53
% 0.20/0.53 thf(y,type,
% 0.20/0.53 y: frac ).
% 0.20/0.53
% 0.20/0.53 thf(z,type,
% 0.20/0.53 z: frac ).
% 0.20/0.53
% 0.20/0.53 thf(u,type,
% 0.20/0.53 u: frac ).
% 0.20/0.53
% 0.20/0.53 thf(eq,type,
% 0.20/0.53 eq: frac > frac > $o ).
% 0.20/0.53
% 0.20/0.53 thf(e,axiom,
% 0.20/0.53 eq @ x @ y ).
% 0.20/0.53
% 0.20/0.53 thf(moref,type,
% 0.20/0.53 moref: frac > frac > $o ).
% 0.20/0.53
% 0.20/0.53 thf(m,axiom,
% 0.20/0.53 moref @ z @ u ).
% 0.20/0.53
% 0.20/0.53 thf(pf,type,
% 0.20/0.53 pf: frac > frac > frac ).
% 0.20/0.53
% 0.20/0.53 thf(satz44,axiom,
% 0.20/0.53 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.20/0.53 ( ( moref @ Xx @ Xy )
% 0.20/0.53 => ( ( eq @ Xx @ Xz )
% 0.20/0.53 => ( ( eq @ Xy @ Xu )
% 0.20/0.53 => ( moref @ Xz @ Xu ) ) ) ) ).
% 0.20/0.53
% 0.20/0.53 thf(satz62g,axiom,
% 0.20/0.53 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.20/0.53 ( ( eq @ Xx @ Xy )
% 0.20/0.53 => ( ( moref @ Xz @ Xu )
% 0.20/0.53 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.20/0.53
% 0.20/0.53 thf(satz58,axiom,
% 0.20/0.53 ! [Xx: frac,Xy: frac] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ) ).
% 0.20/0.53
% 0.20/0.53 thf(satz62h,conjecture,
% 0.20/0.53 moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ).
% 0.20/0.53
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.q40e4enHgd/cvc5---1.0.5_31516.p...
% 0.20/0.53 (declare-sort $$unsorted 0)
% 0.20/0.53 (declare-sort tptp.frac 0)
% 0.20/0.53 (declare-fun tptp.x () tptp.frac)
% 0.20/0.53 (declare-fun tptp.y () tptp.frac)
% 0.20/0.53 (declare-fun tptp.z () tptp.frac)
% 0.20/0.53 (declare-fun tptp.u () tptp.frac)
% 0.20/0.53 (declare-fun tptp.eq (tptp.frac tptp.frac) Bool)
% 0.20/0.53 (assert (@ (@ tptp.eq tptp.x) tptp.y))
% 0.20/0.53 (declare-fun tptp.moref (tptp.frac tptp.frac) Bool)
% 0.20/0.53 (assert (@ (@ tptp.moref tptp.z) tptp.u))
% 0.20/0.53 (declare-fun tptp.pf (tptp.frac tptp.frac) tptp.frac)
% 0.20/0.53 (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))))))
% 0.20/0.53 (assert (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac) (Xu tptp.frac)) (=> (@ (@ tptp.eq Xx) Xy) (=> (@ (@ tptp.moref Xz) Xu) (@ (@ tptp.moref (@ (@ tptp.pf Xx) Xz)) (@ (@ tptp.pf Xy) Xu))))))
% 0.20/0.53 (assert (forall ((Xx tptp.frac) (Xy tptp.frac)) (@ (@ tptp.eq (@ (@ tptp.pf Xx) Xy)) (@ (@ tptp.pf Xy) Xx))))
% 0.20/0.53 (assert (not (@ (@ tptp.moref (@ (@ tptp.pf tptp.z) tptp.x)) (@ (@ tptp.pf tptp.u) tptp.y))))
% 0.20/0.53 (set-info :filename cvc5---1.0.5_31516)
% 0.20/0.53 (check-sat-assuming ( true ))
% 0.20/0.53 ------- get file name : TPTP file name is NUM754^1
% 0.20/0.53 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31516.smt2...
% 0.20/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Theorem for NUM754^1
% 0.20/0.53 % SZS output start Proof for NUM754^1
% 0.20/0.53 (
% 0.20/0.53 (let ((_let_1 (not (@ (@ tptp.moref (@ (@ tptp.pf tptp.z) tptp.x)) (@ (@ tptp.pf tptp.u) tptp.y))))) (let ((_let_2 (forall ((Xx tptp.frac) (Xy tptp.frac)) (@ (@ tptp.eq (@ (@ tptp.pf Xx) Xy)) (@ (@ tptp.pf Xy) Xx))))) (let ((_let_3 (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac) (Xu tptp.frac)) (=> (@ (@ tptp.eq Xx) Xy) (=> (@ (@ tptp.moref Xz) Xu) (@ (@ tptp.moref (@ (@ tptp.pf Xx) Xz)) (@ (@ tptp.pf Xy) Xu))))))) (let ((_let_4 (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_5 (@ (@ tptp.moref tptp.z) tptp.u))) (let ((_let_6 (@ (@ tptp.eq tptp.x) tptp.y))) (let ((_let_7 (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_5 Xz) Xu)) (ho_4 (ho_3 k_5 (ho_8 (ho_7 k_6 Xx) Xz)) (ho_8 (ho_7 k_6 Xy) Xu)))))) (let ((_let_8 (ho_8 (ho_7 k_6 tptp.y) tptp.u))) (let ((_let_9 (ho_8 (ho_7 k_6 tptp.x) tptp.z))) (let ((_let_10 (ho_4 (ho_3 k_5 _let_9) _let_8))) (let ((_let_11 (ho_4 (ho_3 k_5 tptp.z) tptp.u))) (let ((_let_12 (not _let_11))) (let ((_let_13 (ho_4 (ho_3 k_2 tptp.x) tptp.y))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_10))) (let ((_let_16 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 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.moref Xz) Xu)) (@ (@ tptp.moref (@ (@ tptp.pf Xx) Xz)) (@ (@ tptp.pf Xy) Xu)))) _let_7))))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (ho_8 (ho_7 k_6 tptp.u) tptp.y))) (let ((_let_19 (ho_8 (ho_7 k_6 tptp.z) tptp.x))) (let ((_let_20 (ho_4 (ho_3 k_5 _let_19) _let_18))) (let ((_let_21 (ho_4 (ho_3 k_2 _let_8) _let_18))) (let ((_let_22 (not _let_21))) (let ((_let_23 (ho_4 (ho_3 k_2 _let_9) _let_19))) (let ((_let_24 (not _let_23))) (let ((_let_25 (not _let_10))) (let ((_let_26 (or _let_25 _let_24 _let_22 _let_20))) (let ((_let_27 (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_28 (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) (Xu tptp.frac)) (or (not (@ (@ tptp.moref Xx) Xy)) (not (@ (@ tptp.eq Xx) Xz)) (not (@ (@ tptp.eq Xy) Xu)) (@ (@ tptp.moref Xz) Xu))) _let_27))))))) (let ((_let_29 (forall ((Xx tptp.frac) (Xy tptp.frac)) (ho_4 (ho_3 k_2 (ho_8 (ho_7 k_6 Xx) Xy)) (ho_8 (ho_7 k_6 Xy) Xx))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_29)))))) (let ((_let_31 (_let_29))) (let ((_let_32 ((ho_8 (ho_7 k_6 Xy) Xx)))) (let ((_let_33 (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_34 (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_35 (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_36 (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_37 (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_38 (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_39 (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_40 (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_16 :args (tptp.x tptp.y tptp.z tptp.u QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_7))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_14 _let_12 _let_10 _let_17))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_6)) (PREPROCESS :args ((= _let_6 _let_13)))) (PREPROCESS :args ((and _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33)))) :args ((and _let_13 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33))) :args (0)) (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 _let_11)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_20 _let_22 _let_24 _let_25 (not _let_26)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 (not _let_20))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.y tptp.u QUANTIFIERS_INST_E_MATCHING _let_32)) :args _let_31)) _let_30 :args (_let_21 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.x tptp.z QUANTIFIERS_INST_E_MATCHING _let_32)) :args _let_31)) _let_30 :args (_let_23 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_9 _let_8 _let_19 _let_18 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 Xx) Xz) false)) (not (= (ho_4 (ho_3 k_2 Xy) Xu) false))))) :args (_let_27))) _let_28 :args (_let_26 false _let_27)) :args (_let_25 true _let_20 false _let_21 false _let_23 false _let_26)) :args (_let_17 false _let_13 false _let_11 true _let_10)) _let_16 :args (false true _let_15 false _let_7)) :args (_let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.54 )
% 0.20/0.54 % SZS output end Proof for NUM754^1
% 0.20/0.54 % cvc5---1.0.5 exiting
% 0.20/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------