%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM310+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:25:52 EDT 2022
% Result : Theorem 26.59s 26.76s
% Output : CNFRefutation 26.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 80 ( 36 unt; 0 def)
% Number of atoms : 170 ( 34 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 177 ( 87 ~; 73 |; 10 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 113 ( 1 sgn 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))) ).
fof(rdn6,axiom,
rdn_translate(n6,rdn_pos(rdnn(n6))) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)) ).
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(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( ~ less(Y,X)
& Y != X ) ) ).
fof(sum_entry_point_pos_pos,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
& rdn_translate(Z,rdn_pos(RDN_Z)) )
=> sum(X,Y,Z) ) ).
fof(unique_LHS,axiom,
! [X1,X2,Y,Z] :
( ( sum(X1,Y,Z)
& sum(X2,Y,Z) )
=> X1 = X2 ) ).
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_n3_n3_n6_n0,axiom,
rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0)) ).
fof(rdn_digit_add_n6_n0_n6_n0,axiom,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)) ).
fof(sum_n2_n3_not_n6,conjecture,
~ sum(n2,n3,n6) ).
fof(subgoal_0,plain,
~ sum(n2,n3,n6),
inference(strip,[],[sum_n2_n3_not_n6]) ).
fof(negate_0_0,plain,
~ ~ sum(n2,n3,n6),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[rdn_positive_less23]) ).
fof(normalize_0_1,plain,
sum(n2,n3,n6),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_2,plain,
! [X1,X2,Y,Z] :
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z)
| X1 = X2 ),
inference(canonicalize,[],[unique_LHS]) ).
fof(normalize_0_3,plain,
! [X1,X2,Y,Z] :
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z)
| X1 = X2 ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(canonicalize,[],[rdn6]) ).
fof(normalize_0_5,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[rdn3]) ).
fof(normalize_0_6,plain,
! [RDN_X,RDN_Y,RDN_Z,X,Y,Z] :
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| sum(X,Y,Z) ),
inference(canonicalize,[],[sum_entry_point_pos_pos]) ).
fof(normalize_0_7,plain,
! [RDN_X,RDN_Y,RDN_Z,X,Y,Z] :
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| sum(X,Y,Z) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n3_n3_n6_n0]) ).
fof(normalize_0_9,plain,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n6_n0_n6_n0]) ).
fof(normalize_0_10,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_11,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_10]) ).
fof(normalize_0_12,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[rdn2]) ).
fof(normalize_0_13,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_14,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_13]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(canonicalize,[],[less_property]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ less(X,Y)
<=> ( Y = X
| less(Y,X) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ( Y != X
| ~ less(X,Y) )
& ( ~ less(X,Y)
| ~ less(Y,X) )
& ( Y = X
| less(X,Y)
| less(Y,X) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( Y != X
| ~ less(X,Y) ),
inference(conjunct,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
sum(n2,n3,n6),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_2,plain,
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z)
| X1 = X2 ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ sum(X_1378,n3,n6)
| ~ sum(n2,n3,n6)
| n2 = X_1378 ),
inference(subst,[],[refute_0_2:[bind(X1,$fot(n2)),bind(X2,$fot(X_1378)),bind(Y,$fot(n3)),bind(Z,$fot(n6))]]) ).
cnf(refute_0_4,plain,
( ~ sum(X_1378,n3,n6)
| n2 = X_1378 ),
inference(resolve,[$cnf( sum(n2,n3,n6) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ sum(n3,n3,n6)
| n2 = n3 ),
inference(subst,[],[refute_0_4:[bind(X_1378,$fot(n3))]]) ).
cnf(refute_0_6,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_7,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_8,plain,
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| sum(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n3),rdnn(n6))
| ~ rdn_translate(Y,rdn_pos(rdnn(n3)))
| ~ rdn_translate(Z,rdn_pos(rdnn(n6)))
| sum(Y,Y,Z) ),
inference(subst,[],[refute_0_8:[bind(RDN_X,$fot(rdnn(n3))),bind(RDN_Y,$fot(rdnn(n3))),bind(RDN_Z,$fot(rdnn(n6))),bind(X,$fot(Y))]]) ).
cnf(refute_0_10,plain,
rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_12,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_11]) ).
cnf(refute_0_13,plain,
( ~ rdn_digit_add(rdnn(X_68664),rdnn(X_68665),rdnn(n6),rdnn(n0))
| ~ rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_68664),rdnn(X_68665),rdnn(n6)) ),
inference(subst,[],[refute_0_12:[bind(C,$fot(n0)),bind(D1,$fot(X_68664)),bind(D2,$fot(X_68665)),bind(ID,$fot(n6)),bind(RD,$fot(n6))]]) ).
cnf(refute_0_14,plain,
( ~ rdn_digit_add(rdnn(X_68664),rdnn(X_68665),rdnn(n6),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_68664),rdnn(X_68665),rdnn(n6)) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n3),rdnn(n6)) ),
inference(subst,[],[refute_0_14:[bind(X_68664,$fot(n3)),bind(X_68665,$fot(n3))]]) ).
cnf(refute_0_16,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n3),rdnn(n6)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0)) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ rdn_translate(Y,rdn_pos(rdnn(n3)))
| ~ rdn_translate(Z,rdn_pos(rdnn(n6)))
| sum(Y,Y,Z) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n3),rdnn(n6)) )],[refute_0_16,refute_0_9]) ).
cnf(refute_0_18,plain,
( ~ rdn_translate(X_68884,rdn_pos(rdnn(n6)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| sum(n3,n3,X_68884) ),
inference(subst,[],[refute_0_17:[bind(Y,$fot(n3)),bind(Z,$fot(X_68884))]]) ).
cnf(refute_0_19,plain,
( ~ rdn_translate(X_68884,rdn_pos(rdnn(n6)))
| sum(n3,n3,X_68884) ),
inference(resolve,[$cnf( rdn_translate(n3,rdn_pos(rdnn(n3))) )],[refute_0_7,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| sum(n3,n3,n6) ),
inference(subst,[],[refute_0_19:[bind(X_68884,$fot(n6))]]) ).
cnf(refute_0_21,plain,
sum(n3,n3,n6),
inference(resolve,[$cnf( rdn_translate(n6,rdn_pos(rdnn(n6))) )],[refute_0_6,refute_0_20]) ).
cnf(refute_0_22,plain,
n2 = n3,
inference(resolve,[$cnf( sum(n3,n3,n6) )],[refute_0_21,refute_0_5]) ).
cnf(refute_0_23,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_24,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_25,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( n2 != n3
| n3 = n2 ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(n2)),bind(Y0,$fot(n3))]]) ).
cnf(refute_0_27,plain,
n3 = n2,
inference(resolve,[$cnf( $equal(n2,n3) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
rdnn(n3) = rdnn(n3),
introduced(tautology,[refl,[$fot(rdnn(n3))]]) ).
cnf(refute_0_29,plain,
( n3 != n2
| rdnn(n3) != rdnn(n3)
| rdnn(n3) = rdnn(n2) ),
introduced(tautology,[equality,[$cnf( $equal(rdnn(n3),rdnn(n3)) ),[1,0],$fot(n2)]]) ).
cnf(refute_0_30,plain,
( n3 != n2
| rdnn(n3) = rdnn(n2) ),
inference(resolve,[$cnf( $equal(rdnn(n3),rdnn(n3)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
rdnn(n3) = rdnn(n2),
inference(resolve,[$cnf( $equal(n3,n2) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
( rdnn(n3) != rdnn(n2)
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(rdnn(n2),rdnn(n2)) ),
introduced(tautology,[equality,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n3)) ),[1],$fot(rdnn(n2))]]) ).
cnf(refute_0_33,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(rdnn(n2),rdnn(n2)) ),
inference(resolve,[$cnf( $equal(rdnn(n3),rdnn(n2)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
rdn_positive_less(rdnn(n2),rdnn(n2)),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n3)) )],[refute_0_0,refute_0_33]) ).
cnf(refute_0_35,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_36,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_14]) ).
cnf(refute_0_37,plain,
( ~ rdn_positive_less(RDN_Y,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| less(Y,Y) ),
inference(subst,[],[refute_0_36:[bind(RDN_X,$fot(RDN_Y)),bind(X,$fot(Y))]]) ).
cnf(refute_0_38,plain,
( Y != X
| ~ less(X,Y) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_39,plain,
( X != X
| ~ less(X,X) ),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X))]]) ).
cnf(refute_0_40,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_41,plain,
~ less(X,X),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
~ less(Y,Y),
inference(subst,[],[refute_0_41:[bind(X,$fot(Y))]]) ).
cnf(refute_0_43,plain,
( ~ rdn_positive_less(RDN_Y,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y)) ),
inference(resolve,[$cnf( less(Y,Y) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n2))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2))) ),
inference(subst,[],[refute_0_43:[bind(RDN_Y,$fot(rdnn(n2))),bind(Y,$fot(n2))]]) ).
cnf(refute_0_45,plain,
~ rdn_positive_less(rdnn(n2),rdnn(n2)),
inference(resolve,[$cnf( rdn_translate(n2,rdn_pos(rdnn(n2))) )],[refute_0_35,refute_0_44]) ).
cnf(refute_0_46,plain,
$false,
inference(resolve,[$cnf( rdn_positive_less(rdnn(n2),rdnn(n2)) )],[refute_0_34,refute_0_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM310+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 04:51:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 26.59/26.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.59/26.76
% 26.59/26.76 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.59/26.76
%------------------------------------------------------------------------------