TSTP Solution File: NUM294+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM294+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:25:47 EDT 2022
% Result : Theorem 4.90s 5.07s
% Output : CNFRefutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 24 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 39 ~; 30 |; 3 &)
% ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 5 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn12,axiom,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))) ).
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_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)) ).
fof(rdn_positive_less_multi_digit_low,axiom,
! [Ds,O,Db] :
( ( rdn_positive_less(rdnn(Ds),rdnn(Db))
& rdn_non_zero(O) )
=> rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ) ).
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(n12_less_something,conjecture,
? [X] : less(n12,X) ).
fof(subgoal_0,plain,
? [X] : less(n12,X),
inference(strip,[],[n12_less_something]) ).
fof(negate_0_0,plain,
~ ? [X] : less(n12,X),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(canonicalize,[],[rdn13]) ).
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,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[rdn_positive_less23]) ).
fof(normalize_0_5,plain,
! [Db,Ds,O] :
( ~ rdn_non_zero(O)
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ),
inference(canonicalize,[],[rdn_positive_less_multi_digit_low]) ).
fof(normalize_0_6,plain,
! [Db,Ds,O] :
( ~ rdn_non_zero(O)
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))),
inference(canonicalize,[],[rdn12]) ).
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(canonicalize,[],[less_entry_point_pos_pos]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,plain,
! [X] : ~ less(n12,X),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
! [X] : ~ less(n12,X),
inference(specialize,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
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_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_6,plain,
( ~ rdn_non_zero(O)
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db))
| rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ rdn_non_zero(X_784)
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(rdn(rdnn(n2),X_784),rdn(rdnn(n3),X_784)) ),
inference(subst,[],[refute_0_6:[bind(Db,$fot(n3)),bind(Ds,$fot(n2)),bind(O,$fot(X_784))]]) ).
cnf(refute_0_8,plain,
( ~ rdn_non_zero(X_784)
| rdn_positive_less(rdn(rdnn(n2),X_784),rdn(rdnn(n3),X_784)) ),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n3)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ rdn_non_zero(rdnn(n1))
| rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(n3),rdnn(n1))) ),
inference(subst,[],[refute_0_8:[bind(X_784,$fot(rdnn(n1)))]]) ).
cnf(refute_0_10,plain,
rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(n3),rdnn(n1))),
inference(resolve,[$cnf( rdn_non_zero(rdnn(n1)) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_12,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_9]) ).
cnf(refute_0_13,plain,
( ~ rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),X_8383)
| ~ rdn_translate(X_8385,rdn_pos(X_8383))
| ~ rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1))))
| less(n12,X_8385) ),
inference(subst,[],[refute_0_12:[bind(RDN_X,$fot(rdn(rdnn(n2),rdnn(n1)))),bind(RDN_Y,$fot(X_8383)),bind(X,$fot(n12)),bind(Y,$fot(X_8385))]]) ).
cnf(refute_0_14,plain,
( ~ rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),X_8383)
| ~ rdn_translate(X_8385,rdn_pos(X_8383))
| less(n12,X_8385) ),
inference(resolve,[$cnf( rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
~ less(n12,X),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_16,plain,
~ less(n12,X_8385),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_8385))]]) ).
cnf(refute_0_17,plain,
( ~ rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),X_8383)
| ~ rdn_translate(X_8385,rdn_pos(X_8383)) ),
inference(resolve,[$cnf( less(n12,X_8385) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(n3),rdnn(n1)))
| ~ rdn_translate(X_8387,rdn_pos(rdn(rdnn(n3),rdnn(n1)))) ),
inference(subst,[],[refute_0_17:[bind(X_8383,$fot(rdn(rdnn(n3),rdnn(n1)))),bind(X_8385,$fot(X_8387))]]) ).
cnf(refute_0_19,plain,
~ rdn_translate(X_8387,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(resolve,[$cnf( rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(n3),rdnn(n1))) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
~ rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(subst,[],[refute_0_19:[bind(X_8387,$fot(n13))]]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))) )],[refute_0_0,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM294+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n015.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 : 600
% 0.13/0.34 % DateTime : Fri Jul 8 00:13:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.90/5.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.90/5.07
% 4.90/5.07 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.90/5.07
%------------------------------------------------------------------------------