TSTP Solution File: NUM704^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM704^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 10:47:03 EDT 2023
% Result : Timeout 299.68s 300.17s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM704^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n029.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 12:40:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 %----Proving TH0
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 % File : NUM704^1 : TPTP v8.1.2. Released v3.7.0.
% 0.21/0.49 % Domain : Number Theory
% 0.21/0.49 % Problem : Landau theorem 27
% 0.21/0.49 % Version : Especial.
% 0.21/0.49 % English : ~(forall x:nat.~(~((forall x_0_0:nat.p x_0_0 -> ~(less x x_0_0) ->
% 0.21/0.49 % x = x_0_0) -> ~(p x))))
% 0.21/0.49
% 0.21/0.49 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.49 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.49 % Source : [Bro09]
% 0.21/0.49 % Names : satz27 [Lan30]
% 0.21/0.49
% 0.21/0.49 % Status : Theorem
% 0.21/0.49 % : Without extensionality : Theorem
% 0.21/0.49 % Rating : 1.00 v3.7.0
% 0.21/0.49 % Syntax : Number of formulae : 21 ( 5 unt; 10 typ; 0 def)
% 0.21/0.49 % Number of atoms : 21 ( 5 equ; 0 cnn)
% 0.21/0.49 % Maximal formula atoms : 4 ( 1 avg)
% 0.21/0.49 % Number of connectives : 70 ( 13 ~; 0 |; 0 &; 43 @)
% 0.21/0.49 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.21/0.49 % Maximal formula depth : 12 ( 7 avg)
% 0.21/0.49 % Number of types : 3 ( 2 usr)
% 0.21/0.49 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.21/0.49 % Number of symbols : 9 ( 8 usr; 1 con; 0-2 aty)
% 0.21/0.49 % Number of variables : 19 ( 0 ^; 19 !; 0 ?; 19 :)
% 0.21/0.49 % SPC : TH0_THM_EQU_NAR
% 0.21/0.49
% 0.21/0.49 % Comments :
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 thf(nat_type,type,
% 0.21/0.49 nat: $tType ).
% 0.21/0.49
% 0.21/0.49 thf(p,type,
% 0.21/0.49 p: nat > $o ).
% 0.21/0.49
% 0.21/0.49 thf(s,axiom,
% 0.21/0.49 ~ ! [Xx: nat] :
% 0.21/0.49 ~ ( p @ Xx ) ).
% 0.21/0.49
% 0.21/0.49 thf(less,type,
% 0.21/0.49 less: nat > nat > $o ).
% 0.21/0.49
% 0.21/0.49 thf(et,axiom,
% 0.21/0.49 ! [Xa: $o] :
% 0.21/0.49 ( ~ ~ Xa
% 0.21/0.49 => Xa ) ).
% 0.21/0.49
% 0.21/0.49 thf(more,type,
% 0.21/0.49 more: nat > nat > $o ).
% 0.21/0.49
% 0.21/0.49 thf(satz10g,axiom,
% 0.21/0.49 ! [Xx: nat,Xy: nat] :
% 0.21/0.49 ( ( more @ Xx @ Xy )
% 0.21/0.49 => ~ ( ~ ( less @ Xx @ Xy )
% 0.21/0.49 => ( Xx = Xy ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(pl,type,
% 0.21/0.49 pl: nat > nat > nat ).
% 0.21/0.49
% 0.21/0.49 thf(n_1,type,
% 0.21/0.49 n_1: nat ).
% 0.21/0.49
% 0.21/0.49 thf(satz18,axiom,
% 0.21/0.49 ! [Xx: nat,Xy: nat] : ( more @ ( pl @ Xx @ Xy ) @ Xx ) ).
% 0.21/0.49
% 0.21/0.49 thf(set_type,type,
% 0.21/0.49 set: $tType ).
% 0.21/0.49
% 0.21/0.49 thf(esti,type,
% 0.21/0.49 esti: nat > set > $o ).
% 0.21/0.49
% 0.21/0.49 thf(setof,type,
% 0.21/0.49 setof: ( nat > $o ) > set ).
% 0.21/0.49
% 0.21/0.49 thf(estie,axiom,
% 0.21/0.49 ! [Xp: nat > $o,Xs: nat] :
% 0.21/0.49 ( ( esti @ Xs @ ( setof @ Xp ) )
% 0.21/0.49 => ( Xp @ Xs ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(suc,type,
% 0.21/0.49 suc: nat > nat ).
% 0.21/0.49
% 0.21/0.49 thf(ax5,axiom,
% 0.21/0.49 ! [Xs: set] :
% 0.21/0.49 ( ( esti @ n_1 @ Xs )
% 0.21/0.49 => ( ! [Xx: nat] :
% 0.21/0.49 ( ( esti @ Xx @ Xs )
% 0.21/0.49 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 0.21/0.49 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(estii,axiom,
% 0.21/0.49 ! [Xp: nat > $o,Xs: nat] :
% 0.21/0.49 ( ( Xp @ Xs )
% 0.21/0.49 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(satz24a,axiom,
% 0.21/0.49 ! [Xx: nat] :
% 0.21/0.49 ( ~ ( less @ n_1 @ Xx )
% 0.21/0.49 => ( n_1 = Xx ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(satz25b,axiom,
% 0.21/0.49 ! [Xx: nat,Xy: nat] :
% 0.21/0.49 ( ( less @ Xy @ Xx )
% 0.21/0.49 => ( ~ ( less @ ( pl @ Xy @ n_1 ) @ Xx )
% 0.21/0.49 => ( ( pl @ Xy @ n_1 )
% 0.21/0.49 = Xx ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(satz4a,axiom,
% 0.21/0.49 ! [Xx: nat] :
% 0.21/0.49 ( ( pl @ Xx @ n_1 )
% 0.21/0.49 = ( suc @ Xx ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(satz27,conjecture,
% 0.21/0.49 ~ ! [Xx: nat] :
% 0.21/0.49 ~ ~ ( ! [Xx_0_0: nat] :
% 0.21/0.49 ( ( p @ Xx_0_0 )
% 0.21/0.49 => ( ~ ( less @ Xx @ Xx_0_0 )
% 0.21/0.49 => ( Xx = Xx_0_0 ) ) )
% 0.21/0.49 => ~ ( p @ Xx ) ) ).
% 0.21/0.49
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.2B4uWfVSrW/cvc5---1.0.5_22589.p...
% 0.21/0.49 (declare-sort $$unsorted 0)
% 0.21/0.49 (declare-sort tptp.nat 0)
% 0.21/0.49 (declare-fun tptp.p (tptp.nat) Bool)
% 0.21/0.49 (assert (not (forall ((Xx tptp.nat)) (not (@ tptp.p Xx)))))
% 0.21/0.49 (declare-fun tptp.less (tptp.nat tptp.nat) Bool)
% 0.21/0.49 (assert (forall ((Xa Bool)) (=> (not (not Xa)) Xa)))
% 0.21/0.49 (declare-fun tptp.more (tptp.nat tptp.nat) Bool)
% 0.21/0.49 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (=> (@ (@ tptp.more Xx) Xy) (not (=> (not (@ (@ tptp.less Xx) Xy)) (= Xx Xy))))))
% 0.21/0.49 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.21/0.49 (declare-fun tptp.n_1 () tptp.nat)
% 0.21/0.49 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (@ (@ tptp.more (@ (@ tptp.pl Xx) Xy)) Xx)))
% 0.21/0.49 (declare-sort tptp.set 0)
% 0.21/0.49 (declare-fun tptp.esti (tptp.nat tptp.set) Bool)
% 299.68/300.17 /export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 22737 Alarm clock ( read result; case "$result" in
% 299.68/300.17 unsat)
% 299.68/300.17 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.68/300.17 ;;
% 299.68/300.17 sat)
% 299.68/300.17 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.68/300.17 ;;
% 299.68/300.17 esac; exit 1 )
% 299.68/300.17 Alarm clock
% 299.68/300.17 % cvc5---1.0.5 exiting
% 299.68/300.18 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------