TSTP Solution File: NUM736^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM736^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 10:47:21 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 : NUM736^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n019.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 12:32:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 % File : NUM736^1 : TPTP v8.1.2. Released v3.7.0.
% 0.20/0.52 % Domain : Number Theory
% 0.20/0.52 % Problem : Landau theorem 42
% 0.20/0.52 % Version : Especial.
% 0.20/0.52 % English : less (ts (num y) (den x)) (ts (num x) (den y))
% 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 : satz42 [Lan30]
% 0.20/0.52
% 0.20/0.52 % Status : Theorem
% 0.20/0.52 % : Without extensionality : Theorem
% 0.20/0.52 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.20/0.52 % Syntax : Number of formulae : 12 ( 2 unt; 9 typ; 0 def)
% 0.20/0.52 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.20/0.52 % Maximal formula atoms : 2 ( 1 avg)
% 0.20/0.52 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 24 @)
% 0.20/0.52 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.52 % Maximal formula depth : 6 ( 6 avg)
% 0.20/0.52 % Number of types : 3 ( 2 usr)
% 0.20/0.52 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.20/0.52 % Number of symbols : 7 ( 7 usr; 2 con; 0-2 aty)
% 0.20/0.52 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.20/0.52 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.52
% 0.20/0.52 % Comments :
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 thf(frac_type,type,
% 0.20/0.52 frac: $tType ).
% 0.20/0.52
% 0.20/0.52 thf(x,type,
% 0.20/0.52 x: frac ).
% 0.20/0.52
% 0.20/0.52 thf(y,type,
% 0.20/0.52 y: frac ).
% 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(more,type,
% 0.20/0.52 more: nat > nat > $o ).
% 0.20/0.52
% 0.20/0.52 thf(ts,type,
% 0.20/0.52 ts: nat > nat > nat ).
% 0.20/0.52
% 0.20/0.52 thf(num,type,
% 0.20/0.52 num: frac > nat ).
% 0.20/0.52
% 0.20/0.52 thf(den,type,
% 0.20/0.52 den: frac > nat ).
% 0.20/0.52
% 0.20/0.52 thf(m,axiom,
% 0.20/0.52 more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ).
% 0.20/0.52
% 0.20/0.52 thf(less,type,
% 0.20/0.52 less: nat > nat > $o ).
% 0.20/0.52
% 0.20/0.52 thf(satz11,axiom,
% 0.20/0.52 ! [Xx: nat,Xy: nat] :
% 0.20/0.52 ( ( more @ Xx @ Xy )
% 0.20/0.52 => ( less @ Xy @ Xx ) ) ).
% 0.20/0.52
% 0.20/0.52 thf(satz42,conjecture,
% 0.20/0.52 less @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ).
% 0.20/0.52
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.IOGFnLFoZN/cvc5---1.0.5_2184.p...
% 0.20/0.52 (declare-sort $$unsorted 0)
% 0.20/0.52 (declare-sort tptp.frac 0)
% 0.20/0.52 (declare-fun tptp.x () tptp.frac)
% 0.20/0.52 (declare-fun tptp.y () tptp.frac)
% 0.20/0.52 (declare-sort tptp.nat 0)
% 0.20/0.52 (declare-fun tptp.more (tptp.nat tptp.nat) Bool)
% 0.20/0.52 (declare-fun tptp.ts (tptp.nat tptp.nat) tptp.nat)
% 0.20/0.52 (declare-fun tptp.num (tptp.frac) tptp.nat)
% 0.20/0.52 (declare-fun tptp.den (tptp.frac) tptp.nat)
% 0.20/0.52 (assert (@ (@ tptp.more (@ (@ tptp.ts (@ tptp.num tptp.x)) (@ tptp.den tptp.y))) (@ (@ tptp.ts (@ tptp.num tptp.y)) (@ tptp.den tptp.x))))
% 0.20/0.52 (declare-fun tptp.less (tptp.nat tptp.nat) Bool)
% 0.20/0.52 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (@ (@ tptp.less Xy) Xx))))
% 0.20/0.52 (assert (not (@ (@ tptp.less (@ (@ tptp.ts (@ tptp.num tptp.y)) (@ tptp.den tptp.x))) (@ (@ tptp.ts (@ tptp.num tptp.x)) (@ tptp.den tptp.y)))))
% 0.20/0.52 (set-info :filename cvc5---1.0.5_2184)
% 0.20/0.52 (check-sat-assuming ( true ))
% 0.20/0.52 ------- get file name : TPTP file name is NUM736^1
% 0.20/0.52 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2184.smt2...
% 0.20/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.52 % SZS status Theorem for NUM736^1
% 0.20/0.52 % SZS output start Proof for NUM736^1
% 0.20/0.52 (
% 0.20/0.52 (let ((_let_1 (@ (@ tptp.ts (@ tptp.num tptp.x)) (@ tptp.den tptp.y)))) (let ((_let_2 (@ (@ tptp.ts (@ tptp.num tptp.y)) (@ tptp.den tptp.x)))) (let ((_let_3 (not (@ (@ tptp.less _let_2) _let_1)))) (let ((_let_4 (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (@ (@ tptp.less Xy) Xx))))) (let ((_let_5 (@ (@ tptp.more _let_1) _let_2))) (let ((_let_6 (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (ho_10 (ho_9 k_8 Xx) Xy)) (ho_10 (ho_9 k_11 Xy) Xx))))) (let ((_let_7 (ho_7 (ho_6 k_5 (ho_3 k_4 tptp.x)) (ho_3 k_2 tptp.y)))) (let ((_let_8 (ho_7 (ho_6 k_5 (ho_3 k_4 tptp.y)) (ho_3 k_2 tptp.x)))) (let ((_let_9 (ho_10 (ho_9 k_11 _let_8) _let_7))) (let ((_let_10 (ho_10 (ho_9 k_8 _let_7) _let_8))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_9))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xx tptp.nat) (Xy tptp.nat)) (or (not (@ (@ tptp.more Xx) Xy)) (@ (@ tptp.less Xy) Xx))) _let_6))))))) (let ((_let_14 (not _let_12))) (let ((_let_15 (forall ((u |u_(-> tptp.frac tptp.nat)|) (e tptp.nat) (i tptp.frac)) (not (forall ((v |u_(-> tptp.frac tptp.nat)|)) (not (forall ((ii tptp.frac)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_16 (forall ((x |u_(-> tptp.frac tptp.nat)|) (y |u_(-> tptp.frac tptp.nat)|)) (or (not (forall ((z tptp.frac)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_17 (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_18 (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_19 (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_20 (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_21 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_10 v ii) (ite (= i ii) e (ho_10 u ii)))))))))) (let ((_let_22 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_10 x z) (ho_10 y z)))) (= x y))))) (let ((_let_23 (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_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_24 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (_let_7 _let_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_6))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_9 _let_11 _let_14))) (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 (not _let_9))))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 _let_10)))) (PREPROCESS :args ((and _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15)))) :args ((and _let_10 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15))) :args (0)) :args (_let_14 true _let_9 false _let_10)) _let_13 :args (false true _let_12 false _let_6)) :args (_let_5 _let_4 _let_3 true)))))))))))))))))))))))))))
% 0.20/0.52 )
% 0.20/0.52 % SZS output end Proof for NUM736^1
% 0.20/0.52 % cvc5---1.0.5 exiting
% 0.20/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------