TSTP Solution File: NUM644^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM644^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 10:46:05 EDT 2023
% Result : Timeout 299.41s 300.16s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM644^1 : TPTP v8.1.2. Released v3.7.0.
% 0.06/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 14:36:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 %----Proving TH0
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : NUM644^1 : TPTP v8.1.2. Released v3.7.0.
% 0.19/0.48 % Domain : Number Theory
% 0.19/0.48 % Problem : Landau theorem 6
% 0.19/0.48 % Version : Especial.
% 0.19/0.48 % English : pl x y = pl y x
% 0.19/0.48
% 0.19/0.48 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.19/0.48 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.19/0.48 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.48 % Source : [Bro09]
% 0.19/0.48 % Names : satz6 [Lan30]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % : Without extensionality : Theorem
% 0.19/0.48 % Rating : 0.92 v8.1.0, 0.91 v7.5.0, 1.00 v3.7.0
% 0.19/0.48 % Syntax : Number of formulae : 17 ( 7 unt; 9 typ; 0 def)
% 0.19/0.48 % Number of atoms : 11 ( 5 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 4 ( 1 avg)
% 0.19/0.48 % Number of connectives : 44 ( 0 ~; 0 |; 0 &; 39 @)
% 0.19/0.48 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 9 ( 4 avg)
% 0.19/0.48 % Number of types : 3 ( 2 usr)
% 0.19/0.48 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.19/0.48 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.19/0.48 % SPC : TH0_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments :
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(nat_type,type,
% 0.19/0.48 nat: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(x,type,
% 0.19/0.48 x: nat ).
% 0.19/0.48
% 0.19/0.48 thf(y,type,
% 0.19/0.48 y: nat ).
% 0.19/0.48
% 0.19/0.48 thf(pl,type,
% 0.19/0.48 pl: nat > nat > nat ).
% 0.19/0.48
% 0.19/0.48 thf(set_type,type,
% 0.19/0.48 set: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(esti,type,
% 0.19/0.48 esti: nat > set > $o ).
% 0.19/0.48
% 0.19/0.48 thf(setof,type,
% 0.19/0.48 setof: ( nat > $o ) > set ).
% 0.19/0.48
% 0.19/0.48 thf(estie,axiom,
% 0.19/0.48 ! [Xp: nat > $o,Xs: nat] :
% 0.19/0.48 ( ( esti @ Xs @ ( setof @ Xp ) )
% 0.19/0.48 => ( Xp @ Xs ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(n_1,type,
% 0.19/0.48 n_1: nat ).
% 0.19/0.48
% 0.19/0.48 thf(suc,type,
% 0.19/0.48 suc: nat > nat ).
% 0.19/0.48
% 0.19/0.48 thf(ax5,axiom,
% 0.19/0.48 ! [Xs: set] :
% 0.19/0.48 ( ( esti @ n_1 @ Xs )
% 0.19/0.48 => ( ! [Xx: nat] :
% 0.19/0.48 ( ( esti @ Xx @ Xs )
% 0.19/0.48 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 0.19/0.48 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(estii,axiom,
% 0.19/0.48 ! [Xp: nat > $o,Xs: nat] :
% 0.19/0.48 ( ( Xp @ Xs )
% 0.19/0.48 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(satz4a,axiom,
% 0.19/0.48 ! [Xx: nat] :
% 0.19/0.48 ( ( pl @ Xx @ n_1 )
% 0.19/0.48 = ( suc @ Xx ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(satz4c,axiom,
% 0.19/0.48 ! [Xx: nat] :
% 0.19/0.48 ( ( pl @ n_1 @ Xx )
% 0.19/0.48 = ( suc @ Xx ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(satz4f,axiom,
% 0.19/0.48 ! [Xx: nat,Xy: nat] :
% 0.19/0.48 ( ( suc @ ( pl @ Xx @ Xy ) )
% 0.19/0.48 = ( pl @ Xx @ ( suc @ Xy ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(satz4d,axiom,
% 0.19/0.48 ! [Xx: nat,Xy: nat] :
% 0.19/0.48 ( ( pl @ ( suc @ Xx ) @ Xy )
% 0.19/0.48 = ( suc @ ( pl @ Xx @ Xy ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(satz6,conjecture,
% 0.19/0.48 ( ( pl @ x @ y )
% 0.19/0.48 = ( pl @ y @ x ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.EaZ2fDPD1l/cvc5---1.0.5_14714.p...
% 0.19/0.48 (declare-sort $$unsorted 0)
% 0.19/0.48 (declare-sort tptp.nat 0)
% 0.19/0.48 (declare-fun tptp.x () tptp.nat)
% 0.19/0.48 (declare-fun tptp.y () tptp.nat)
% 0.19/0.48 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.19/0.48 (declare-sort tptp.set 0)
% 0.19/0.48 (declare-fun tptp.esti (tptp.nat tptp.set) Bool)
% 0.19/0.48 (declare-fun tptp.setof ((-> tptp.nat Bool)) tptp.set)
% 0.19/0.48 (assert (forall ((Xp (-> tptp.nat Bool)) (Xs tptp.nat)) (=> (@ (@ tptp.esti Xs) (@ tptp.setof Xp)) (@ Xp Xs))))
% 0.19/0.48 (declare-fun tptp.n_1 () tptp.nat)
% 0.19/0.48 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.19/0.48 (assert (forall ((Xs tptp.set)) (=> (@ (@ tptp.esti tptp.n_1) Xs) (=> (forall ((Xx tptp.nat)) (=> (@ (@ tptp.esti Xx) Xs) (@ (@ tptp.esti (@ tptp.suc Xx)) Xs))) (forall ((Xx tptp.nat)) (@ (@ tptp.esti Xx) Xs))))))
% 0.19/0.48 (assert (forall ((Xp (-> tptp.nat Bool)) (Xs tptp.nat)) (=> (@ Xp Xs) (@ (@ tptp.esti Xs) (@ tptp.setof Xp)))))
% 0.19/0.48 (assert (forall ((Xx tptp.nat)) (= (@ (@ tptp.pl Xx) tptp.n_1) (@ tptp.suc Xx))))
% 0.19/0.48 (assert (forall ((Xx tptp.nat)) (= (@ (@ tptp.pl tptp.n_1) Xx) (@ tptp.suc Xx))))
% 0.19/0.48 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (let ((_let_1 (@ tptp.pl Xx))) (= (@ tptp.suc (@ _let_1 Xy)) (@ _let_1 (@ tptp.suc Xy))))))
% 0.19/0.48 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (= (@ (@ tptp.pl (@ tptp.suc Xx)) Xy) (@ tptp.suc (@ (@ tptp.pl Xx) Xy)))))
% 0.19/0.48 (ass/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 15884 Alarm clock ( read result; case "$result" in
% 299.41/300.16 unsat)
% 299.41/300.16 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.41/300.16 ;;
% 299.41/300.16 sat)
% 299.41/300.16 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.41/300.16 ;;
% 299.41/300.16 esac; exit 1 )
% 299.41/300.17 Alarm clock
% 299.41/300.17 % cvc5---1.0.5 exiting
% 299.41/300.18 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------