TSTP Solution File: NUM346+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM346+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 12:26:04 EDT 2022
% Result : Theorem 42.31s 42.47s
% Output : CNFRefutation 42.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 71 ( 31 unt; 0 def)
% Number of atoms : 155 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 158 ( 74 ~; 68 |; 9 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 102 ( 0 sgn 60 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))) ).
fof(rdn4,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))) ).
fof(rdn_positive_less45,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)) ).
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(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_sum,axiom,
! [X,Y,Z1,Z2] :
( ( sum(X,Y,Z1)
& sum(X,Y,Z2) )
=> Z1 = Z2 ) ).
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_n3_greater_n4,conjecture,
! [X] :
( sum(n2,n3,X)
=> less(n4,X) ) ).
fof(subgoal_0,plain,
! [X] :
( sum(n2,n3,X)
=> less(n4,X) ),
inference(strip,[],[sum_n2_n3_greater_n4]) ).
fof(negate_0_0,plain,
~ ! [X] :
( sum(n2,n3,X)
=> less(n4,X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( ~ less(n4,X)
& sum(n2,n3,X) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ less(n4,skolemFOFtoCNF_X)
& sum(n2,n3,skolemFOFtoCNF_X) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ less(n4,skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
sum(n2,n3,skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [X,Y,Z1,Z2] :
( ~ sum(X,Y,Z1)
| ~ sum(X,Y,Z2)
| Z1 = Z2 ),
inference(canonicalize,[],[unique_sum]) ).
fof(normalize_0_5,plain,
! [X,Y,Z1,Z2] :
( ~ sum(X,Y,Z1)
| ~ sum(X,Y,Z2)
| Z1 = Z2 ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[rdn2]) ).
fof(normalize_0_7,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[rdn3]) ).
fof(normalize_0_8,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[rdn5]) ).
fof(normalize_0_9,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n2_n3_n5_n0]) ).
fof(normalize_0_10,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n5_n0_n5_n0]) ).
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(canonicalize,[],[add_digit_digit_digit]) ).
fof(normalize_0_12,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_11]) ).
fof(normalize_0_13,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_14,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_13]) ).
fof(normalize_0_15,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(canonicalize,[],[rdn4]) ).
fof(normalize_0_16,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_17,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_16]) ).
fof(normalize_0_18,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(canonicalize,[],[rdn_positive_less45]) ).
cnf(refute_0_0,plain,
~ less(n4,skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
sum(n2,n3,skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ sum(X,Y,Z1)
| ~ sum(X,Y,Z2)
| Z1 = Z2 ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ sum(n2,n3,X_1787)
| ~ sum(n2,n3,skolemFOFtoCNF_X)
| skolemFOFtoCNF_X = X_1787 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(n2)),bind(Y,$fot(n3)),bind(Z1,$fot(skolemFOFtoCNF_X)),bind(Z2,$fot(X_1787))]]) ).
cnf(refute_0_4,plain,
( ~ sum(n2,n3,X_1787)
| skolemFOFtoCNF_X = X_1787 ),
inference(resolve,[$cnf( sum(n2,n3,skolemFOFtoCNF_X) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ sum(n2,n3,n5)
| skolemFOFtoCNF_X = n5 ),
inference(subst,[],[refute_0_4:[bind(X_1787,$fot(n5))]]) ).
cnf(refute_0_6,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_9,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,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_12]) ).
cnf(refute_0_12,plain,
( ~ rdn_digit_add(rdnn(X_65309),rdnn(X_65310),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_65309),rdnn(X_65310),rdnn(n5)) ),
inference(subst,[],[refute_0_11:[bind(C,$fot(n0)),bind(D1,$fot(X_65309)),bind(D2,$fot(X_65310)),bind(ID,$fot(n5)),bind(RD,$fot(n5))]]) ).
cnf(refute_0_13,plain,
( ~ rdn_digit_add(rdnn(X_65309),rdnn(X_65310),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_65309),rdnn(X_65310),rdnn(n5)) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,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_13:[bind(X_65309,$fot(n2)),bind(X_65310,$fot(n3))]]) ).
cnf(refute_0_15,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| sum(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_17,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| ~ rdn_translate(X_116352,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_116353,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_116354,rdn_pos(rdnn(n5)))
| sum(X_116352,X_116353,X_116354) ),
inference(subst,[],[refute_0_16:[bind(RDN_X,$fot(rdnn(n2))),bind(RDN_Y,$fot(rdnn(n3))),bind(RDN_Z,$fot(rdnn(n5))),bind(X,$fot(X_116352)),bind(Y,$fot(X_116353)),bind(Z,$fot(X_116354))]]) ).
cnf(refute_0_18,plain,
( ~ rdn_translate(X_116352,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_116353,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_116354,rdn_pos(rdnn(n5)))
| sum(X_116352,X_116353,X_116354) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ rdn_translate(X_116741,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_116742,rdn_pos(rdnn(n3)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sum(X_116741,X_116742,n5) ),
inference(subst,[],[refute_0_18:[bind(X_116352,$fot(X_116741)),bind(X_116353,$fot(X_116742)),bind(X_116354,$fot(n5))]]) ).
cnf(refute_0_20,plain,
( ~ rdn_translate(X_116741,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_116742,rdn_pos(rdnn(n3)))
| sum(X_116741,X_116742,n5) ),
inference(resolve,[$cnf( rdn_translate(n5,rdn_pos(rdnn(n5))) )],[refute_0_8,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ rdn_translate(X_116744,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| sum(X_116744,n3,n5) ),
inference(subst,[],[refute_0_20:[bind(X_116741,$fot(X_116744)),bind(X_116742,$fot(n3))]]) ).
cnf(refute_0_22,plain,
( ~ rdn_translate(X_116744,rdn_pos(rdnn(n2)))
| sum(X_116744,n3,n5) ),
inference(resolve,[$cnf( rdn_translate(n3,rdn_pos(rdnn(n3))) )],[refute_0_7,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| sum(n2,n3,n5) ),
inference(subst,[],[refute_0_22:[bind(X_116744,$fot(n2))]]) ).
cnf(refute_0_24,plain,
sum(n2,n3,n5),
inference(resolve,[$cnf( rdn_translate(n2,rdn_pos(rdnn(n2))) )],[refute_0_6,refute_0_23]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_X = n5,
inference(resolve,[$cnf( sum(n2,n3,n5) )],[refute_0_24,refute_0_5]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_X != n5
| ~ less(n4,n5)
| less(n4,skolemFOFtoCNF_X) ),
introduced(tautology,[equality,[$cnf( ~ less(n4,skolemFOFtoCNF_X) ),[1],$fot(n5)]]) ).
cnf(refute_0_27,plain,
( ~ less(n4,n5)
| less(n4,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,n5) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
~ less(n4,n5),
inference(resolve,[$cnf( less(n4,skolemFOFtoCNF_X) )],[refute_0_27,refute_0_0]) ).
cnf(refute_0_29,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_30,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_17]) ).
cnf(refute_0_31,plain,
( ~ rdn_positive_less(rdnn(n4),X_8862)
| ~ rdn_translate(X_8864,rdn_pos(X_8862))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| less(n4,X_8864) ),
inference(subst,[],[refute_0_30:[bind(RDN_X,$fot(rdnn(n4))),bind(RDN_Y,$fot(X_8862)),bind(X,$fot(n4)),bind(Y,$fot(X_8864))]]) ).
cnf(refute_0_32,plain,
( ~ rdn_positive_less(rdnn(n4),X_8862)
| ~ rdn_translate(X_8864,rdn_pos(X_8862))
| less(n4,X_8864) ),
inference(resolve,[$cnf( rdn_translate(n4,rdn_pos(rdnn(n4))) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| less(n4,n5) ),
inference(subst,[],[refute_0_32:[bind(X_8862,$fot(rdnn(n5))),bind(X_8864,$fot(n5))]]) ).
cnf(refute_0_34,plain,
( ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| less(n4,n5) ),
inference(resolve,[$cnf( rdn_translate(n5,rdn_pos(rdnn(n5))) )],[refute_0_8,refute_0_33]) ).
cnf(refute_0_35,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_36,plain,
less(n4,n5),
inference(resolve,[$cnf( rdn_positive_less(rdnn(n4),rdnn(n5)) )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( less(n4,n5) )],[refute_0_36,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM346+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 00:08:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 42.31/42.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.31/42.47
% 42.31/42.47 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 42.31/42.48
%------------------------------------------------------------------------------