TSTP Solution File: NUM769^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM769^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 10:47:52 EDT 2023
% Result : Theorem 0.21s 0.51s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM769^1 : TPTP v8.1.2. Released v3.7.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n012.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 17:04:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 %----Proving TH0
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 % File : NUM769^1 : TPTP v8.1.2. Released v3.7.0.
% 0.21/0.51 % Domain : Number Theory
% 0.21/0.51 % Problem : Landau theorem 67d
% 0.21/0.51 % Version : Especial.
% 0.21/0.51 % English : eq x (pf y (mf x y))
% 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 : satz67d [Lan30]
% 0.21/0.51
% 0.21/0.51 % Status : Theorem
% 0.21/0.51 % : Without extensionality : Theorem
% 0.21/0.51 % Rating : 0.00 v3.7.0
% 0.21/0.51 % Syntax : Number of formulae : 11 ( 2 unt; 7 typ; 0 def)
% 0.21/0.51 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.21/0.51 % Maximal formula atoms : 2 ( 1 avg)
% 0.21/0.51 % Number of connectives : 22 ( 0 ~; 0 |; 0 &; 20 @)
% 0.21/0.51 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.51 % Maximal formula depth : 9 ( 6 avg)
% 0.21/0.51 % Number of types : 2 ( 1 usr)
% 0.21/0.51 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.21/0.51 % Number of symbols : 6 ( 6 usr; 2 con; 0-2 aty)
% 0.21/0.51 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 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(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 @ x @ y ).
% 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(pf,type,
% 0.21/0.51 pf: frac > frac > frac ).
% 0.21/0.51
% 0.21/0.51 thf(mf,type,
% 0.21/0.51 mf: frac > frac > frac ).
% 0.21/0.51
% 0.21/0.51 thf(satz38,axiom,
% 0.21/0.51 ! [Xx: frac,Xy: frac] :
% 0.21/0.51 ( ( eq @ Xx @ Xy )
% 0.21/0.51 => ( eq @ Xy @ Xx ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(satz67c,axiom,
% 0.21/0.51 ! [Xx: frac,Xy: frac] :
% 0.21/0.51 ( ( moref @ Xx @ Xy )
% 0.21/0.51 => ( eq @ ( pf @ Xy @ ( mf @ Xx @ Xy ) ) @ Xx ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(satz67d,conjecture,
% 0.21/0.51 eq @ x @ ( pf @ y @ ( mf @ x @ y ) ) ).
% 0.21/0.51
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.OouFXZLhHl/cvc5---1.0.5_25837.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.moref (tptp.frac tptp.frac) Bool)
% 0.21/0.51 (assert (@ (@ tptp.moref tptp.x) tptp.y))
% 0.21/0.51 (declare-fun tptp.eq (tptp.frac tptp.frac) Bool)
% 0.21/0.51 (declare-fun tptp.pf (tptp.frac tptp.frac) tptp.frac)
% 0.21/0.51 (declare-fun tptp.mf (tptp.frac tptp.frac) tptp.frac)
% 0.21/0.51 (assert (forall ((Xx tptp.frac) (Xy tptp.frac)) (=> (@ (@ tptp.eq Xx) Xy) (@ (@ tptp.eq Xy) Xx))))
% 0.21/0.51 (assert (forall ((Xx tptp.frac) (Xy tptp.frac)) (=> (@ (@ tptp.moref Xx) Xy) (@ (@ tptp.eq (@ (@ tptp.pf Xy) (@ (@ tptp.mf Xx) Xy))) Xx))))
% 0.21/0.51 (assert (not (@ (@ tptp.eq tptp.x) (@ (@ tptp.pf tptp.y) (@ (@ tptp.mf tptp.x) tptp.y)))))
% 0.21/0.51 (set-info :filename cvc5---1.0.5_25837)
% 0.21/0.51 (check-sat-assuming ( true ))
% 0.21/0.51 ------- get file name : TPTP file name is NUM769^1
% 0.21/0.51 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25837.smt2...
% 0.21/0.51 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.51 % SZS status Theorem for NUM769^1
% 0.21/0.51 % SZS output start Proof for NUM769^1
% 0.21/0.51 (
% 0.21/0.51 (let ((_let_1 (not (@ (@ tptp.eq tptp.x) (@ (@ tptp.pf tptp.y) (@ (@ tptp.mf tptp.x) tptp.y)))))) (let ((_let_2 (forall ((Xx tptp.frac) (Xy tptp.frac)) (=> (@ (@ tptp.moref Xx) Xy) (@ (@ tptp.eq (@ (@ tptp.pf Xy) (@ (@ tptp.mf Xx) Xy))) Xx))))) (let ((_let_3 (forall ((Xx tptp.frac) (Xy tptp.frac)) (=> (@ (@ tptp.eq Xx) Xy) (@ (@ tptp.eq Xy) Xx))))) (let ((_let_4 (@ (@ tptp.moref tptp.x) tptp.y))) (let ((_let_5 (ho_4 (ho_3 k_2 tptp.x) tptp.y))) (let ((_let_6 (ho_8 (ho_7 k_9 tptp.y) (ho_8 (ho_7 k_6 tptp.x) tptp.y)))) (let ((_let_7 (ho_4 (ho_3 k_5 _let_6) tptp.x))) (let ((_let_8 (not _let_5))) (let ((_let_9 (or _let_8 _let_7))) (let ((_let_10 (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_11 (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_12 (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_13 (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_14 (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_15 (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_16 (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_17 (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_18 (forall ((Xx tptp.frac) (Xy tptp.frac)) (or (not (ho_4 (ho_3 k_2 Xx) Xy)) (ho_4 (ho_3 k_5 (ho_8 (ho_7 k_9 Xy) (ho_8 (ho_7 k_6 Xx) Xy))) Xx))))) (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)) (or (not (@ (@ tptp.moref Xx) Xy)) (@ (@ tptp.eq (@ (@ tptp.pf Xy) (@ (@ tptp.mf Xx) Xy))) Xx))) _let_18))))))) (let ((_let_20 (ho_4 (ho_3 k_5 tptp.x) _let_6))) (let ((_let_21 (not _let_7))) (let ((_let_22 (or _let_21 _let_20))) (let ((_let_23 (forall ((Xx tptp.frac) (Xy tptp.frac)) (or (not (ho_4 (ho_3 k_5 Xx) Xy)) (ho_4 (ho_3 k_5 Xy) Xx))))) (let ((_let_24 (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)) (or (not (@ (@ tptp.eq Xx) Xy)) (@ (@ tptp.eq Xy) Xx))) _let_23))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_9)) :args ((or _let_8 _let_7 (not _let_9)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_20 _let_21 (not _let_22)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 (not _let_20))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (_let_6 tptp.x QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_5 Xy) Xx) true))))) :args (_let_23))) _let_24 :args (_let_22 false _let_23)) :args (_let_21 true _let_20 false _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 Xx) Xy) false))))) :args (_let_18))) _let_19 :args (_let_9 false _let_18)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_5)))) (PREPROCESS :args ((and _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10)))) :args ((and _let_5 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10))) :args (0)) :args (false true _let_7 false _let_9 false _let_5)) :args (_let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))
% 0.21/0.52 )
% 0.21/0.52 % SZS output end Proof for NUM769^1
% 0.21/0.52 % cvc5---1.0.5 exiting
% 0.21/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------