TSTP Solution File: NUM323+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM323+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 12:25:56 EDT 2022
% Result : Theorem 44.36s 44.54s
% Output : CNFRefutation 44.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 25 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 87 ( 43 ~; 38 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 66 ( 1 sgn 35 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))) ).
fof(rdnn5,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))) ).
fof(rdnn7,axiom,
rdn_translate(nn7,rdn_neg(rdnn(n7))) ).
fof(sum_entry_point_neg_neg,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(X,rdn_neg(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
& 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_n5_n7_n0,axiom,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)) ).
fof(rdn_digit_add_n7_n0_n7_n0,axiom,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)) ).
fof(sum_what_nn5_nn7,conjecture,
? [X] : sum(X,nn5,nn7) ).
fof(subgoal_0,plain,
? [X] : sum(X,nn5,nn7),
inference(strip,[],[sum_what_nn5_nn7]) ).
fof(negate_0_0,plain,
~ ? [X] : sum(X,nn5,nn7),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
inference(canonicalize,[],[rdnn7]) ).
fof(normalize_0_1,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(canonicalize,[],[rdnn5]) ).
fof(normalize_0_2,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(canonicalize,[],[rdnn2]) ).
fof(normalize_0_3,plain,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n2_n5_n7_n0]) ).
fof(normalize_0_4,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n7_n0_n7_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_Y,RDN_Z)
| ~ rdn_translate(X,rdn_neg(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_neg_neg]) ).
fof(normalize_0_8,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_neg(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,
! [X] : ~ sum(X,nn5,nn7),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
! [X] : ~ sum(X,nn5,nn7),
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
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(nn2,rdn_neg(rdnn(n2))),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_3,plain,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),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_69590),rdnn(X_69591),rdnn(n7),rdnn(n0))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_69590),rdnn(X_69591),rdnn(n7)) ),
inference(subst,[],[refute_0_5:[bind(C,$fot(n0)),bind(D1,$fot(X_69590)),bind(D2,$fot(X_69591)),bind(ID,$fot(n7)),bind(RD,$fot(n7))]]) ).
cnf(refute_0_7,plain,
( ~ rdn_digit_add(rdnn(X_69590),rdnn(X_69591),rdnn(n7),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_69590),rdnn(X_69591),rdnn(n7)) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n5),rdnn(n7)) ),
inference(subst,[],[refute_0_7:[bind(X_69590,$fot(n2)),bind(X_69591,$fot(n5))]]) ).
cnf(refute_0_9,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n5),rdnn(n7)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(X,rdn_neg(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(Z,rdn_neg(RDN_Z))
| sum(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n5),rdnn(n7))
| ~ rdn_translate(X_123728,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X_123729,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X_123730,rdn_neg(rdnn(n7)))
| sum(X_123728,X_123729,X_123730) ),
inference(subst,[],[refute_0_10:[bind(RDN_X,$fot(rdnn(n2))),bind(RDN_Y,$fot(rdnn(n5))),bind(RDN_Z,$fot(rdnn(n7))),bind(X,$fot(X_123728)),bind(Y,$fot(X_123729)),bind(Z,$fot(X_123730))]]) ).
cnf(refute_0_12,plain,
( ~ rdn_translate(X_123728,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X_123729,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X_123730,rdn_neg(rdnn(n7)))
| sum(X_123728,X_123729,X_123730) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n5),rdnn(n7)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ rdn_translate(X_124061,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X_124062,rdn_neg(rdnn(n7)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| sum(nn2,X_124061,X_124062) ),
inference(subst,[],[refute_0_12:[bind(X_123728,$fot(nn2)),bind(X_123729,$fot(X_124061)),bind(X_123730,$fot(X_124062))]]) ).
cnf(refute_0_14,plain,
( ~ rdn_translate(X_124061,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X_124062,rdn_neg(rdnn(n7)))
| sum(nn2,X_124061,X_124062) ),
inference(resolve,[$cnf( rdn_translate(nn2,rdn_neg(rdnn(n2))) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ rdn_translate(X_124064,rdn_neg(rdnn(n7)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5)))
| sum(nn2,nn5,X_124064) ),
inference(subst,[],[refute_0_14:[bind(X_124061,$fot(nn5)),bind(X_124062,$fot(X_124064))]]) ).
cnf(refute_0_16,plain,
( ~ rdn_translate(X_124064,rdn_neg(rdnn(n7)))
| sum(nn2,nn5,X_124064) ),
inference(resolve,[$cnf( rdn_translate(nn5,rdn_neg(rdnn(n5))) )],[refute_0_1,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ rdn_translate(nn7,rdn_neg(rdnn(n7)))
| sum(nn2,nn5,nn7) ),
inference(subst,[],[refute_0_16:[bind(X_124064,$fot(nn7))]]) ).
cnf(refute_0_18,plain,
sum(nn2,nn5,nn7),
inference(resolve,[$cnf( rdn_translate(nn7,rdn_neg(rdnn(n7))) )],[refute_0_0,refute_0_17]) ).
cnf(refute_0_19,plain,
~ sum(X,nn5,nn7),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_20,plain,
~ sum(nn2,nn5,nn7),
inference(subst,[],[refute_0_19:[bind(X,$fot(nn2))]]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( sum(nn2,nn5,nn7) )],[refute_0_18,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM323+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 : n028.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 01:32:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 44.36/44.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.36/44.54
% 44.36/44.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 44.36/44.54
%------------------------------------------------------------------------------