TSTP Solution File: NUM751^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM751^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 10:47:36 EDT 2023
% Result : Theorem 0.21s 0.55s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM751^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n008.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 12:28:17 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.55 %------------------------------------------------------------------------------
% 0.21/0.55 % File : NUM751^1 : TPTP v8.1.2. Released v3.7.0.
% 0.21/0.55 % Domain : Number Theory
% 0.21/0.55 % Problem : Landau theorem 62d
% 0.21/0.55 % Version : Especial.
% 0.21/0.55 % English : moref (pf z x) (pf z y)
% 0.21/0.55
% 0.21/0.55 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.55 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.55 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.55 % Source : [Bro09]
% 0.21/0.55 % Names : satz62d [Lan30]
% 0.21/0.55 % : satz72d [Lan30]
% 0.21/0.55
% 0.21/0.55 % Status : Theorem
% 0.21/0.55 % : Without extensionality : Theorem
% 0.21/0.55 % 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, 0.20 v5.4.0, 0.25 v4.1.0, 0.00 v3.7.0
% 0.21/0.55 % Syntax : Number of formulae : 12 ( 3 unt; 7 typ; 0 def)
% 0.21/0.55 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.21/0.55 % Maximal formula atoms : 4 ( 1 avg)
% 0.21/0.55 % Number of connectives : 34 ( 0 ~; 0 |; 0 &; 30 @)
% 0.21/0.55 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.21/0.55 % Maximal formula depth : 10 ( 7 avg)
% 0.21/0.55 % Number of types : 2 ( 1 usr)
% 0.21/0.55 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.21/0.55 % Number of symbols : 6 ( 6 usr; 3 con; 0-2 aty)
% 0.21/0.55 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.21/0.55 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.55
% 0.21/0.55 % Comments :
% 0.21/0.55 %------------------------------------------------------------------------------
% 0.21/0.55 thf(frac_type,type,
% 0.21/0.55 frac: $tType ).
% 0.21/0.55
% 0.21/0.55 thf(x,type,
% 0.21/0.55 x: frac ).
% 0.21/0.55
% 0.21/0.55 thf(y,type,
% 0.21/0.55 y: frac ).
% 0.21/0.55
% 0.21/0.55 thf(z,type,
% 0.21/0.55 z: frac ).
% 0.21/0.55
% 0.21/0.55 thf(moref,type,
% 0.21/0.55 moref: frac > frac > $o ).
% 0.21/0.55
% 0.21/0.55 thf(m,axiom,
% 0.21/0.55 moref @ x @ y ).
% 0.21/0.55
% 0.21/0.55 thf(pf,type,
% 0.21/0.55 pf: frac > frac > frac ).
% 0.21/0.55
% 0.21/0.55 thf(eq,type,
% 0.21/0.55 eq: frac > frac > $o ).
% 0.21/0.55
% 0.21/0.55 thf(satz44,axiom,
% 0.21/0.55 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.21/0.55 ( ( moref @ Xx @ Xy )
% 0.21/0.55 => ( ( eq @ Xx @ Xz )
% 0.21/0.55 => ( ( eq @ Xy @ Xu )
% 0.21/0.55 => ( moref @ Xz @ Xu ) ) ) ) ).
% 0.21/0.55
% 0.21/0.55 thf(satz62a,axiom,
% 0.21/0.55 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.21/0.55 ( ( moref @ Xx @ Xy )
% 0.21/0.55 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 0.21/0.55
% 0.21/0.55 thf(satz58,axiom,
% 0.21/0.55 ! [Xx: frac,Xy: frac] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ) ).
% 0.21/0.55
% 0.21/0.55 thf(satz62d,conjecture,
% 0.21/0.55 moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) ).
% 0.21/0.55
% 0.21/0.55 %------------------------------------------------------------------------------
% 0.21/0.55 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.0wp0OMY05H/cvc5---1.0.5_7095.p...
% 0.21/0.55 (declare-sort $$unsorted 0)
% 0.21/0.55 (declare-sort tptp.frac 0)
% 0.21/0.55 (declare-fun tptp.x () tptp.frac)
% 0.21/0.55 (declare-fun tptp.y () tptp.frac)
% 0.21/0.55 (declare-fun tptp.z () tptp.frac)
% 0.21/0.55 (declare-fun tptp.moref (tptp.frac tptp.frac) Bool)
% 0.21/0.55 (assert (@ (@ tptp.moref tptp.x) tptp.y))
% 0.21/0.55 (declare-fun tptp.pf (tptp.frac tptp.frac) tptp.frac)
% 0.21/0.55 (declare-fun tptp.eq (tptp.frac tptp.frac) Bool)
% 0.21/0.55 (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))))))
% 0.21/0.55 (assert (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac)) (=> (@ (@ tptp.moref Xx) Xy) (@ (@ tptp.moref (@ (@ tptp.pf Xx) Xz)) (@ (@ tptp.pf Xy) Xz)))))
% 0.21/0.55 (assert (forall ((Xx tptp.frac) (Xy tptp.frac)) (@ (@ tptp.eq (@ (@ tptp.pf Xx) Xy)) (@ (@ tptp.pf Xy) Xx))))
% 0.21/0.55 (assert (let ((_let_1 (@ tptp.pf tptp.z))) (not (@ (@ tptp.moref (@ _let_1 tptp.x)) (@ _let_1 tptp.y)))))
% 0.21/0.55 (set-info :filename cvc5---1.0.5_7095)
% 0.21/0.55 (check-sat-assuming ( true ))
% 0.21/0.55 ------- get file name : TPTP file name is NUM751^1
% 0.21/0.55 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7095.smt2...
% 0.21/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.55 % SZS status Theorem for NUM751^1
% 0.21/0.55 % SZS output start Proof for NUM751^1
% 0.21/0.55 (
% 0.21/0.55 (let ((_let_1 (@ tptp.pf tptp.z))) (let ((_let_2 (not (@ (@ tptp.moref (@ _let_1 tptp.x)) (@ _let_1 tptp.y))))) (let ((_let_3 (forall ((Xx tptp.frac) (Xy tptp.frac)) (@ (@ tptp.eq (@ (@ tptp.pf Xx) Xy)) (@ (@ tptp.pf Xy) Xx))))) (let ((_let_4 (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac)) (=> (@ (@ tptp.moref Xx) Xy) (@ (@ tptp.moref (@ (@ tptp.pf Xx) Xz)) (@ (@ tptp.pf Xy) Xz)))))) (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.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 Xx) Xz)) (not (ho_4 (ho_3 k_5 Xy) Xu)) (ho_4 (ho_3 k_2 Xz) Xu))))) (let ((_let_8 (ho_7 k_6 tptp.z))) (let ((_let_9 (ho_8 _let_8 tptp.y))) (let ((_let_10 (ho_8 _let_8 tptp.x))) (let ((_let_11 (ho_4 (ho_3 k_2 _let_10) _let_9))) (let ((_let_12 (ho_8 (ho_7 k_6 tptp.y) tptp.z))) (let ((_let_13 (ho_4 (ho_3 k_5 _let_12) _let_9))) (let ((_let_14 (not _let_13))) (let ((_let_15 (ho_8 (ho_7 k_6 tptp.x) tptp.z))) (let ((_let_16 (ho_4 (ho_3 k_5 _let_15) _let_10))) (let ((_let_17 (not _let_16))) (let ((_let_18 (ho_4 (ho_3 k_2 _let_15) _let_12))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17 _let_14 _let_11))) (let ((_let_21 (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_7))))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (ho_4 (ho_3 k_2 tptp.x) tptp.y))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_18))) (let ((_let_26 (forall ((Xx tptp.frac) (Xy tptp.frac) (Xz tptp.frac)) (or (not (ho_4 (ho_3 k_2 Xx) Xy)) (ho_4 (ho_3 k_2 (ho_8 (ho_7 k_6 Xx) Xz)) (ho_8 (ho_7 k_6 Xy) Xz)))))) (let ((_let_27 (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)) (or (not (@ (@ tptp.moref Xx) Xy)) (@ (@ tptp.moref (@ (@ tptp.pf Xx) Xz)) (@ (@ tptp.pf Xy) Xz)))) _let_26))))))) (let ((_let_28 (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_29 (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_30 (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_31 (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_32 (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_33 (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_34 (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_35 (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))))) (let ((_let_36 (forall ((Xx tptp.frac) (Xy tptp.frac)) (ho_4 (ho_3 k_5 (ho_8 (ho_7 k_6 Xx) Xy)) (ho_8 (ho_7 k_6 Xy) Xx))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 _let_36)))))) (let ((_let_38 (_let_36))) (let ((_let_39 ((ho_8 (ho_7 k_6 Xy) Xx)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_15 _let_12 _let_10 _let_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_7))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_11 _let_14 _let_17 _let_19 _let_22))) (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 (not _let_11))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.y tptp.z QUANTIFIERS_INST_E_MATCHING _let_39)) :args _let_38)) _let_37 :args (_let_13 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.x tptp.z QUANTIFIERS_INST_E_MATCHING _let_39)) :args _let_38)) _let_37 :args (_let_16 false _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_18 (not _let_25)))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_6)) (PREPROCESS :args ((= _let_6 _let_23)))) (PREPROCESS :args ((and _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28)))) :args ((and _let_23 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28))) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.x tptp.y tptp.z QUANTIFIERS_INST_E_MATCHING ((ho_8 (ho_7 k_6 Xx) Xz) (ho_8 (ho_7 k_6 Xy) Xz)))) :args (_let_26))) _let_27 :args (_let_25 false _let_26)) :args (_let_18 false _let_23 false _let_25)) :args (_let_22 true _let_11 false _let_13 false _let_16 false _let_18)) _let_21 :args (false true _let_20 false _let_7)) :args (_let_6 _let_5 _let_4 _let_3 _let_2 true))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.56 )
% 0.21/0.56 % SZS output end Proof for NUM751^1
% 0.21/0.56 % cvc5---1.0.5 exiting
% 0.21/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------