TSTP Solution File: NUM686^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 10:46:42 EDT 2023
% Result : Timeout 299.89s 300.17s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 13:44:21 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 % File : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% 0.20/0.49 % Domain : Number Theory
% 0.20/0.49 % Problem : Landau theorem 21
% 0.20/0.49 % Version : Especial.
% 0.20/0.49 % English : some (lambda u_0.diffprop (pl x z) (pl y u) u_0)
% 0.20/0.49
% 0.20/0.49 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.49 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.49 % Source : [Bro09]
% 0.20/0.49 % Names : satz21 [Lan30]
% 0.20/0.49
% 0.20/0.49 % Status : Theorem
% 0.20/0.49 % : Without extensionality : Theorem
% 0.20/0.49 % Rating : 0.38 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0, 0.80 v4.1.0, 0.67 v3.7.0
% 0.20/0.49 % Syntax : Number of formulae : 14 ( 1 unt; 8 typ; 0 def)
% 0.20/0.49 % Number of atoms : 17 ( 1 equ; 0 cnn)
% 0.20/0.49 % Maximal formula atoms : 6 ( 2 avg)
% 0.20/0.49 % Number of connectives : 47 ( 0 ~; 0 |; 0 &; 44 @)
% 0.20/0.49 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.49 % Maximal formula depth : 12 ( 8 avg)
% 0.20/0.49 % Number of types : 2 ( 1 usr)
% 0.20/0.49 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.20/0.49 % Number of symbols : 8 ( 7 usr; 4 con; 0-3 aty)
% 0.20/0.49 % Number of variables : 16 ( 8 ^; 8 !; 0 ?; 16 :)
% 0.20/0.49 % SPC : TH0_THM_EQU_NAR
% 0.20/0.49
% 0.20/0.49 % Comments :
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 thf(nat_type,type,
% 0.20/0.49 nat: $tType ).
% 0.20/0.49
% 0.20/0.49 thf(x,type,
% 0.20/0.49 x: nat ).
% 0.20/0.49
% 0.20/0.49 thf(y,type,
% 0.20/0.49 y: nat ).
% 0.20/0.49
% 0.20/0.49 thf(z,type,
% 0.20/0.49 z: nat ).
% 0.20/0.49
% 0.20/0.49 thf(u,type,
% 0.20/0.49 u: nat ).
% 0.20/0.49
% 0.20/0.49 thf(some,type,
% 0.20/0.49 some: ( nat > $o ) > $o ).
% 0.20/0.49
% 0.20/0.49 thf(diffprop,type,
% 0.20/0.49 diffprop: nat > nat > nat > $o ).
% 0.20/0.49
% 0.20/0.49 thf(m,axiom,
% 0.20/0.49 ( some
% 0.20/0.49 @ ^ [Xu: nat] : ( diffprop @ x @ y @ Xu ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(n,axiom,
% 0.20/0.49 ( some
% 0.20/0.49 @ ^ [Xu_0: nat] : ( diffprop @ z @ u @ Xu_0 ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(pl,type,
% 0.20/0.49 pl: nat > nat > nat ).
% 0.20/0.49
% 0.20/0.49 thf(satz15,axiom,
% 0.20/0.49 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.20/0.49 ( ( some
% 0.20/0.49 @ ^ [Xv: nat] : ( diffprop @ Xy @ Xx @ Xv ) )
% 0.20/0.49 => ( ( some
% 0.20/0.49 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xy @ Xv ) )
% 0.20/0.49 => ( some
% 0.20/0.49 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(satz19a,axiom,
% 0.20/0.49 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.20/0.49 ( ( some
% 0.20/0.49 @ ^ [Xu: nat] : ( diffprop @ Xx @ Xy @ Xu ) )
% 0.20/0.49 => ( some
% 0.20/0.49 @ ^ [Xu: nat] : ( diffprop @ ( pl @ Xx @ Xz ) @ ( pl @ Xy @ Xz ) @ Xu ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(satz6,axiom,
% 0.20/0.49 ! [Xx: nat,Xy: nat] :
% 0.20/0.49 ( ( pl @ Xx @ Xy )
% 0.20/0.49 = ( pl @ Xy @ Xx ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(satz21,conjecture,
% 0.20/0.49 ( some
% 0.20/0.49 @ ^ [Xu_0: nat] : ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) @ Xu_0 ) ) ).
% 0.20/0.49
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.jDWhe4eALI/cvc5---1.0.5_13242.p...
% 0.20/0.49 (declare-sort $$unsorted 0)
% 0.20/0.49 (declare-sort tptp.nat 0)
% 0.20/0.49 (declare-fun tptp.x () tptp.nat)
% 0.20/0.49 (declare-fun tptp.y () tptp.nat)
% 0.20/0.49 (declare-fun tptp.z () tptp.nat)
% 0.20/0.49 (declare-fun tptp.u () tptp.nat)
% 0.20/0.49 (declare-fun tptp.some ((-> tptp.nat Bool)) Bool)
% 0.20/0.49 (declare-fun tptp.diffprop (tptp.nat tptp.nat tptp.nat) Bool)
% 0.20/0.49 (assert (@ tptp.some (lambda ((Xu tptp.nat)) (@ (@ (@ tptp.diffprop tptp.x) tptp.y) Xu))))
% 0.20/0.49 (assert (@ tptp.some (lambda ((Xu_0 tptp.nat)) (@ (@ (@ tptp.diffprop tptp.z) tptp.u) Xu_0))))
% 0.20/0.49 (declare-fun tptp.pl (tptp.nat tptp.nat) tptp.nat)
% 0.20/0.49 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (@ tptp.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xy) Xx) Xv))) (=> (@ tptp.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xz) Xy) Xv))) (@ tptp.some (lambda ((Xv tptp.nat)) (@ (@ (@ tptp.diffprop Xz) Xx) Xv)))))))
% 0.20/0.49 (assert (forall ((Xx tptp.nat) (Xy tptp.nat) (Xz tptp.nat)) (=> (@ tptp.some (lambda ((Xu tptp.nat)) (@ (@ (@ tptp.diffprop Xx) Xy) Xu))) (@ tptp.some (lambda ((Xu tptp.nat)) (@ (@ (@ tptp.diffprop (@ (@ tptp.pl Xx) Xz)) (@ (@ tptp.pl Xy) Xz)) Xu))))))
% 0.20/0.49 (assert (forall ((Xx tptp.nat) (Xy tptp.nat)) (= (@ (@ tptp.pl Xx) Xy) (@ (@ tptp.pl/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 13429 Alarm clock ( read result; case "$result" in
% 299.89/300.17 unsat)
% 299.89/300.17 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.89/300.17 ;;
% 299.89/300.17 sat)
% 299.89/300.17 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.89/300.17 ;;
% 299.89/300.17 esac; exit 1 )
% 299.89/300.18 Alarm clock
% 299.89/300.18 % cvc5---1.0.5 exiting
% 299.89/300.18 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------