TSTP Solution File: NUM320+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM320+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 62.31s 62.50s
% Output : CNFRefutation 62.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 36 unt; 0 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 65 ~; 60 |; 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 : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 85 ( 1 sgn 44 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))) ).
fof(rdnn3,axiom,
rdn_translate(nn3,rdn_neg(rdnn(n3))) ).
fof(rdnn5,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))) ).
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_1,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_X,RDN_Y)
& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)
& rdn_translate(Z,rdn_neg(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_n2_nn5_what,conjecture,
? [Y] : sum(n2,nn5,Y) ).
fof(subgoal_0,plain,
? [Y] : sum(n2,nn5,Y),
inference(strip,[],[sum_n2_nn5_what]) ).
fof(negate_0_0,plain,
~ ? [Y] : sum(n2,nn5,Y),
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_translate(nn5,rdn_neg(rdnn(n5))),
inference(canonicalize,[],[rdnn5]) ).
fof(normalize_0_2,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(canonicalize,[],[rdnn3]) ).
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_X,RDN_Z,RDN_Y)
| ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(Z,rdn_neg(RDN_Z))
| sum(X,Y,Z) ),
inference(canonicalize,[],[sum_entry_point_pos_neg_1]) ).
fof(normalize_0_8,plain,
! [RDN_X,RDN_Y,RDN_Z,X,Y,Z] :
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)
| ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(Z,rdn_neg(RDN_Z))
| sum(X,Y,Z) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(canonicalize,[],[rdn_positive_less45]) ).
fof(normalize_0_10,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_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(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[rdn_positive_less23]) ).
fof(normalize_0_13,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(canonicalize,[],[rdn_positive_less34]) ).
fof(normalize_0_14,plain,
! [Y] : ~ sum(n2,nn5,Y),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_15,plain,
! [Y] : ~ sum(n2,nn5,Y),
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_2,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
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_69362),rdnn(X_69363),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_69362),rdnn(X_69363),rdnn(n5)) ),
inference(subst,[],[refute_0_5:[bind(C,$fot(n0)),bind(D1,$fot(X_69362)),bind(D2,$fot(X_69363)),bind(ID,$fot(n5)),bind(RD,$fot(n5))]]) ).
cnf(refute_0_7,plain,
( ~ rdn_digit_add(rdnn(X_69362),rdnn(X_69363),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_69362),rdnn(X_69363),rdnn(n5)) ),
inference(resolve,[$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_69362,$fot(n2)),bind(X_69363,$fot(n3))]]) ).
cnf(refute_0_9,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)
| ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(Z,rdn_neg(RDN_Z))
| sum(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_translate(X_163966,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_163967,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X_163968,rdn_neg(rdnn(n3)))
| sum(X_163966,X_163967,X_163968) ),
inference(subst,[],[refute_0_10:[bind(RDN_X,$fot(rdnn(n2))),bind(RDN_Y,$fot(rdnn(n5))),bind(RDN_Z,$fot(rdnn(n3))),bind(X,$fot(X_163966)),bind(Y,$fot(X_163967)),bind(Z,$fot(X_163968))]]) ).
cnf(refute_0_12,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_translate(X_163966,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_163967,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X_163968,rdn_neg(rdnn(n3)))
| sum(X_163966,X_163967,X_163968) ),
inference(resolve,[$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(n4),rdnn(n5)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_14,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_11]) ).
cnf(refute_0_15,plain,
( ~ rdn_positive_less(rdnn(X_625),rdnn(n4))
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| rdn_positive_less(rdnn(X_625),rdnn(n5)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_625)),bind(Y,$fot(n4)),bind(Z,$fot(n5))]]) ).
cnf(refute_0_16,plain,
( ~ rdn_positive_less(rdnn(X_625),rdnn(n4))
| rdn_positive_less(rdnn(X_625),rdnn(n5)) ),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n4),rdnn(n5)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n4))
| rdn_positive_less(rdnn(n2),rdnn(n5)) ),
inference(subst,[],[refute_0_16:[bind(X_625,$fot(n2))]]) ).
cnf(refute_0_18,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_19,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_20,plain,
( ~ rdn_positive_less(rdnn(X_625),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| rdn_positive_less(rdnn(X_625),rdnn(n4)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_625)),bind(Y,$fot(n3)),bind(Z,$fot(n4))]]) ).
cnf(refute_0_21,plain,
( ~ rdn_positive_less(rdnn(X_625),rdnn(n3))
| rdn_positive_less(rdnn(X_625),rdnn(n4)) ),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n3),rdnn(n4)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(rdnn(n2),rdnn(n4)) ),
inference(subst,[],[refute_0_21:[bind(X_625,$fot(n2))]]) ).
cnf(refute_0_23,plain,
rdn_positive_less(rdnn(n2),rdnn(n4)),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n3)) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
rdn_positive_less(rdnn(n2),rdnn(n5)),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n4)) )],[refute_0_23,refute_0_17]) ).
cnf(refute_0_25,plain,
( ~ rdn_translate(X_163966,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_163967,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X_163968,rdn_neg(rdnn(n3)))
| sum(X_163966,X_163967,X_163968) ),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n5)) )],[refute_0_24,refute_0_12]) ).
cnf(refute_0_26,plain,
( ~ rdn_translate(X_164304,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_164305,rdn_neg(rdnn(n5)))
| ~ rdn_translate(nn3,rdn_neg(rdnn(n3)))
| sum(X_164304,X_164305,nn3) ),
inference(subst,[],[refute_0_25:[bind(X_163966,$fot(X_164304)),bind(X_163967,$fot(X_164305)),bind(X_163968,$fot(nn3))]]) ).
cnf(refute_0_27,plain,
( ~ rdn_translate(X_164304,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_164305,rdn_neg(rdnn(n5)))
| sum(X_164304,X_164305,nn3) ),
inference(resolve,[$cnf( rdn_translate(nn3,rdn_neg(rdnn(n3))) )],[refute_0_2,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ rdn_translate(X_164307,rdn_pos(rdnn(n2)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5)))
| sum(X_164307,nn5,nn3) ),
inference(subst,[],[refute_0_27:[bind(X_164304,$fot(X_164307)),bind(X_164305,$fot(nn5))]]) ).
cnf(refute_0_29,plain,
( ~ rdn_translate(X_164307,rdn_pos(rdnn(n2)))
| sum(X_164307,nn5,nn3) ),
inference(resolve,[$cnf( rdn_translate(nn5,rdn_neg(rdnn(n5))) )],[refute_0_1,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| sum(n2,nn5,nn3) ),
inference(subst,[],[refute_0_29:[bind(X_164307,$fot(n2))]]) ).
cnf(refute_0_31,plain,
sum(n2,nn5,nn3),
inference(resolve,[$cnf( rdn_translate(n2,rdn_pos(rdnn(n2))) )],[refute_0_0,refute_0_30]) ).
cnf(refute_0_32,plain,
~ sum(n2,nn5,Y),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_33,plain,
~ sum(n2,nn5,nn3),
inference(subst,[],[refute_0_32:[bind(Y,$fot(nn3))]]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( sum(n2,nn5,nn3) )],[refute_0_31,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM320+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n019.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 : 600
% 0.14/0.34 % DateTime : Wed Jul 6 01:58:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 62.31/62.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.31/62.50
% 62.31/62.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 62.31/62.50
%------------------------------------------------------------------------------