%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM321+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:25:55 EDT 2022
% Result : Theorem 57.41s 57.59s
% Output : CNFRefutation 57.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 37 unt; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 66 ~; 59 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 87 ( 3 sgn 44 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))) ).
fof(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)) ).
fof(rdn_positive_less34,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)) ).
fof(rdn_positive_less45,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)) ).
fof(rdn_positive_less_transitivity,axiom,
! [X,Y,Z] :
( ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) ) ).
fof(sum_entry_point_pos_neg_2,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X)
& rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)
& rdn_translate(Z,rdn_pos(RDN_Z)) )
=> sum(X,Y,Z) ) ).
fof(add_digit_digit_digit,axiom,
! [C,D1,D2,RD,ID] :
( ( rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))
& rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ) ).
fof(rdn_digit_add_n2_n3_n5_n0,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) ).
fof(rdn_digit_add_n5_n0_n5_n0,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) ).
fof(sum_n5_nn2_what,conjecture,
? [X] : sum(n5,nn2,X) ).
fof(subgoal_0,plain,
? [X] : sum(n5,nn2,X),
inference(strip,[],[sum_n5_nn2_what]) ).
fof(negate_0_0,plain,
~ ? [X] : sum(n5,nn2,X),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[rdn3]) ).
fof(normalize_0_1,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(canonicalize,[],[rdnn2]) ).
fof(normalize_0_2,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[rdn5]) ).
fof(normalize_0_3,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n2_n3_n5_n0]) ).
fof(normalize_0_4,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n5_n0_n5_n0]) ).
fof(normalize_0_5,plain,
! [C,D1,D2,ID,RD] :
( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
| rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
inference(canonicalize,[],[add_digit_digit_digit]) ).
fof(normalize_0_6,plain,
! [C,D1,D2,ID,RD] :
( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
| rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [RDN_X,RDN_Y,RDN_Z,X,Y,Z] :
( ~ rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| sum(X,Y,Z) ),
inference(canonicalize,[],[sum_entry_point_pos_neg_2]) ).
fof(normalize_0_8,plain,
! [RDN_X,RDN_Y,RDN_Z,X,Y,Z] :
( ~ rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| sum(X,Y,Z) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[rdn_positive_less23]) ).
fof(normalize_0_10,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(canonicalize,[],[rdn_positive_less34]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(canonicalize,[],[rdn_positive_less_transitivity]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(canonicalize,[],[rdn_positive_less45]) ).
fof(normalize_0_14,plain,
! [X] : ~ sum(n5,nn2,X),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_15,plain,
! [X] : ~ sum(n5,nn2,X),
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_2,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_3,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_5,plain,
( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
| rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
( ~ rdn_digit_add(rdnn(X_66245),rdnn(X_66246),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_66245),rdnn(X_66246),rdnn(n5)) ),
inference(subst,[],[refute_0_5:[bind(C,$fot(n0)),bind(D1,$fot(X_66245)),bind(D2,$fot(X_66246)),bind(ID,$fot(n5)),bind(RD,$fot(n5))]]) ).
cnf(refute_0_7,plain,
( ~ rdn_digit_add(rdnn(X_66245),rdnn(X_66246),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_66245),rdnn(X_66246),rdnn(n5)) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)) ),
inference(subst,[],[refute_0_7:[bind(X_66245,$fot(n2)),bind(X_66246,$fot(n3))]]) ).
cnf(refute_0_9,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| sum(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_translate(X_142194,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_142195,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X_142196,rdn_pos(rdnn(n3)))
| sum(X_142194,X_142195,X_142196) ),
inference(subst,[],[refute_0_10:[bind(RDN_X,$fot(rdnn(n5))),bind(RDN_Y,$fot(rdnn(n2))),bind(RDN_Z,$fot(rdnn(n3))),bind(X,$fot(X_142194)),bind(Y,$fot(X_142195)),bind(Z,$fot(X_142196))]]) ).
cnf(refute_0_12,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_translate(X_142194,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_142195,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X_142196,rdn_pos(rdnn(n3)))
| sum(X_142194,X_142195,X_142196) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_14,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_15,plain,
( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
( ~ rdn_positive_less(rdnn(X_537),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| rdn_positive_less(rdnn(X_537),rdnn(n4)) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_537)),bind(Y,$fot(n3)),bind(Z,$fot(n4))]]) ).
cnf(refute_0_17,plain,
( ~ rdn_positive_less(rdnn(X_537),rdnn(n3))
| rdn_positive_less(rdnn(X_537),rdnn(n4)) ),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n3),rdnn(n4)) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(rdnn(n2),rdnn(n4)) ),
inference(subst,[],[refute_0_17:[bind(X_537,$fot(n2))]]) ).
cnf(refute_0_19,plain,
rdn_positive_less(rdnn(n2),rdnn(n4)),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n3)) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_21,plain,
( ~ rdn_positive_less(rdnn(X_537),rdnn(n4))
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| rdn_positive_less(rdnn(X_537),rdnn(n5)) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_537)),bind(Y,$fot(n4)),bind(Z,$fot(n5))]]) ).
cnf(refute_0_22,plain,
( ~ rdn_positive_less(rdnn(X_537),rdnn(n4))
| rdn_positive_less(rdnn(X_537),rdnn(n5)) ),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n4),rdnn(n5)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n4))
| rdn_positive_less(rdnn(n2),rdnn(n5)) ),
inference(subst,[],[refute_0_22:[bind(X_537,$fot(n2))]]) ).
cnf(refute_0_24,plain,
rdn_positive_less(rdnn(n2),rdnn(n5)),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n4)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ rdn_translate(X_142194,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_142195,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X_142196,rdn_pos(rdnn(n3)))
| sum(X_142194,X_142195,X_142196) ),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n5)) )],[refute_0_24,refute_0_12]) ).
cnf(refute_0_26,plain,
( ~ rdn_translate(X_142378,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X_142379,rdn_pos(rdnn(n3)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sum(n5,X_142378,X_142379) ),
inference(subst,[],[refute_0_25:[bind(X_142194,$fot(n5)),bind(X_142195,$fot(X_142378)),bind(X_142196,$fot(X_142379))]]) ).
cnf(refute_0_27,plain,
( ~ rdn_translate(X_142378,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X_142379,rdn_pos(rdnn(n3)))
| sum(n5,X_142378,X_142379) ),
inference(resolve,[$cnf( rdn_translate(n5,rdn_pos(rdnn(n5))) )],[refute_0_2,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ rdn_translate(X_142381,rdn_pos(rdnn(n3)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| sum(n5,nn2,X_142381) ),
inference(subst,[],[refute_0_27:[bind(X_142378,$fot(nn2)),bind(X_142379,$fot(X_142381))]]) ).
cnf(refute_0_29,plain,
( ~ rdn_translate(X_142381,rdn_pos(rdnn(n3)))
| sum(n5,nn2,X_142381) ),
inference(resolve,[$cnf( rdn_translate(nn2,rdn_neg(rdnn(n2))) )],[refute_0_1,refute_0_28]) ).
cnf(refute_0_30,plain,
~ sum(n5,nn2,X),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_31,plain,
~ sum(n5,nn2,X_142381),
inference(subst,[],[refute_0_30:[bind(X,$fot(X_142381))]]) ).
cnf(refute_0_32,plain,
~ rdn_translate(X_142381,rdn_pos(rdnn(n3))),
inference(resolve,[$cnf( sum(n5,nn2,X_142381) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
~ rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(subst,[],[refute_0_32:[bind(X_142381,$fot(n3))]]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( rdn_translate(n3,rdn_pos(rdnn(n3))) )],[refute_0_0,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM321+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.35 % Computer : n013.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 600
% 0.11/0.35 % DateTime : Wed Jul 6 06:07:29 EDT 2022
% 0.11/0.35 % CPUTime :
% 0.11/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 57.41/57.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 57.41/57.59
% 57.41/57.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 57.41/57.59
%------------------------------------------------------------------------------