%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM292+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% 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 : 600s
% DateTime : Mon Jul 18 12:25:46 EDT 2022
% Result : Theorem 5.35s 5.54s
% Output : CNFRefutation 5.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 19 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 29 ~; 26 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 8 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))) ).
fof(rdn13,axiom,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))) ).
fof(rdn_digit1,axiom,
rdn_non_zero_digit(rdnn(n1)) ).
fof(rdn_extra_digits_positive_less,axiom,
! [D,Db,Ob] :
( rdn_non_zero(Ob)
=> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ) ).
fof(rdn_non_zero_by_digit,axiom,
! [X] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ) ).
fof(less_entry_point_pos_pos,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
=> less(X,Y) ) ).
fof(n2_less_n13,conjecture,
less(n2,n13) ).
fof(subgoal_0,plain,
less(n2,n13),
inference(strip,[],[n2_less_n13]) ).
fof(negate_0_0,plain,
~ less(n2,n13),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[rdn2]) ).
fof(normalize_0_1,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(canonicalize,[],[rdn_digit1]) ).
fof(normalize_0_2,plain,
! [X] :
( ~ rdn_non_zero_digit(rdnn(X))
| rdn_non_zero(rdnn(X)) ),
inference(canonicalize,[],[rdn_non_zero_by_digit]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ rdn_non_zero_digit(rdnn(X))
| rdn_non_zero(rdnn(X)) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [D,Db,Ob] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
inference(canonicalize,[],[rdn_extra_digits_positive_less]) ).
fof(normalize_0_5,plain,
! [D,Db,Ob] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(canonicalize,[],[rdn13]) ).
fof(normalize_0_7,plain,
! [RDN_X,RDN_Y,X,Y] :
( ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(X,Y) ),
inference(canonicalize,[],[less_entry_point_pos_pos]) ).
fof(normalize_0_8,plain,
! [RDN_X,RDN_Y,X,Y] :
( ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(X,Y) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
~ less(n2,n13),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_2,plain,
( ~ rdn_non_zero_digit(rdnn(X))
| rdn_non_zero(rdnn(X)) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ rdn_non_zero_digit(rdnn(n1))
| rdn_non_zero(rdnn(n1)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(n1))]]) ).
cnf(refute_0_4,plain,
rdn_non_zero(rdnn(n1)),
inference(resolve,[$cnf( rdn_non_zero_digit(rdnn(n1)) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_6,plain,
( ~ rdn_non_zero(rdnn(n1))
| rdn_positive_less(rdnn(X_83),rdn(rdnn(X_84),rdnn(n1))) ),
inference(subst,[],[refute_0_5:[bind(D,$fot(X_83)),bind(Db,$fot(X_84)),bind(Ob,$fot(rdnn(n1)))]]) ).
cnf(refute_0_7,plain,
rdn_positive_less(rdnn(X_83),rdn(rdnn(X_84),rdnn(n1))),
inference(resolve,[$cnf( rdn_non_zero(rdnn(n1)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
rdn_positive_less(rdnn(X_83),rdn(rdnn(n3),rdnn(n1))),
inference(subst,[],[refute_0_7:[bind(X_84,$fot(n3))]]) ).
cnf(refute_0_9,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_10,plain,
( ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
( ~ rdn_positive_less(X_9813,rdn(rdnn(n3),rdnn(n1)))
| ~ rdn_translate(X_9815,rdn_pos(X_9813))
| ~ rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| less(X_9815,n13) ),
inference(subst,[],[refute_0_10:[bind(RDN_X,$fot(X_9813)),bind(RDN_Y,$fot(rdn(rdnn(n3),rdnn(n1)))),bind(X,$fot(X_9815)),bind(Y,$fot(n13))]]) ).
cnf(refute_0_12,plain,
( ~ rdn_positive_less(X_9813,rdn(rdnn(n3),rdnn(n1)))
| ~ rdn_translate(X_9815,rdn_pos(X_9813))
| less(X_9815,n13) ),
inference(resolve,[$cnf( rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ rdn_positive_less(rdnn(X_83),rdn(rdnn(n3),rdnn(n1)))
| ~ rdn_translate(X_9822,rdn_pos(rdnn(X_83)))
| less(X_9822,n13) ),
inference(subst,[],[refute_0_12:[bind(X_9813,$fot(rdnn(X_83))),bind(X_9815,$fot(X_9822))]]) ).
cnf(refute_0_14,plain,
( ~ rdn_translate(X_9822,rdn_pos(rdnn(X_83)))
| less(X_9822,n13) ),
inference(resolve,[$cnf( rdn_positive_less(rdnn(X_83),rdn(rdnn(n3),rdnn(n1))) )],[refute_0_8,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| less(n2,n13) ),
inference(subst,[],[refute_0_14:[bind(X_83,$fot(n2)),bind(X_9822,$fot(n2))]]) ).
cnf(refute_0_16,plain,
less(n2,n13),
inference(resolve,[$cnf( rdn_translate(n2,rdn_pos(rdnn(n2))) )],[refute_0_0,refute_0_15]) ).
cnf(refute_0_17,plain,
~ less(n2,n13),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( less(n2,n13) )],[refute_0_16,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM292+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jul 6 18:44:13 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.35/5.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.35/5.54
% 5.35/5.54 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.35/5.54
%------------------------------------------------------------------------------