TSTP Solution File: NUM312+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM312+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 37.52s 37.71s
% Output : CNFRefutation 37.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 23 unt; 0 def)
% Number of atoms : 114 ( 15 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 53 ~; 48 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 82 ( 0 sgn 48 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))) ).
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_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_only_n2_n3_n5,conjecture,
! [X] :
( sum(X,n3,n5)
=> X = n2 ) ).
fof(subgoal_0,plain,
! [X] :
( sum(X,n3,n5)
=> X = n2 ),
inference(strip,[],[sum_only_n2_n3_n5]) ).
fof(negate_0_0,plain,
~ ! [X] :
( sum(X,n3,n5)
=> X = n2 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( X != n2
& sum(X,n3,n5) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_X != n2
& sum(skolemFOFtoCNF_X,n3,n5) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
sum(skolemFOFtoCNF_X,n3,n5),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X1,X2,Y,Z] :
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z)
| X1 = X2 ),
inference(canonicalize,[],[unique_LHS]) ).
fof(normalize_0_4,plain,
! [X1,X2,Y,Z] :
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z)
| X1 = X2 ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[rdn5]) ).
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_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n2_n3_n5_n0]) ).
fof(normalize_0_9,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n5_n0_n5_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_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_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(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
skolemFOFtoCNF_X != n2,
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
sum(skolemFOFtoCNF_X,n3,n5),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z)
| X1 = X2 ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ sum(X_1348,n3,n5)
| ~ sum(skolemFOFtoCNF_X,n3,n5)
| skolemFOFtoCNF_X = X_1348 ),
inference(subst,[],[refute_0_1:[bind(X1,$fot(skolemFOFtoCNF_X)),bind(X2,$fot(X_1348)),bind(Y,$fot(n3)),bind(Z,$fot(n5))]]) ).
cnf(refute_0_3,plain,
( ~ sum(X_1348,n3,n5)
| skolemFOFtoCNF_X = X_1348 ),
inference(resolve,[$cnf( sum(skolemFOFtoCNF_X,n3,n5) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ sum(n2,n3,n5)
| skolemFOFtoCNF_X = n2 ),
inference(subst,[],[refute_0_3:[bind(X_1348,$fot(n2))]]) ).
cnf(refute_0_5,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[normalize_0_5]) ).
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_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_9,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,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_11,plain,
( ~ rdn_digit_add(rdnn(X_66461),rdnn(X_66462),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_66461),rdnn(X_66462),rdnn(n5)) ),
inference(subst,[],[refute_0_10:[bind(C,$fot(n0)),bind(D1,$fot(X_66461)),bind(D2,$fot(X_66462)),bind(ID,$fot(n5)),bind(RD,$fot(n5))]]) ).
cnf(refute_0_12,plain,
( ~ rdn_digit_add(rdnn(X_66461),rdnn(X_66462),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_66461),rdnn(X_66462),rdnn(n5)) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,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_12:[bind(X_66461,$fot(n2)),bind(X_66462,$fot(n3))]]) ).
cnf(refute_0_14,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) )],[refute_0_8,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| sum(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_16,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| ~ rdn_translate(X_119188,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_119189,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_119190,rdn_pos(rdnn(n5)))
| sum(X_119188,X_119189,X_119190) ),
inference(subst,[],[refute_0_15:[bind(RDN_X,$fot(rdnn(n2))),bind(RDN_Y,$fot(rdnn(n3))),bind(RDN_Z,$fot(rdnn(n5))),bind(X,$fot(X_119188)),bind(Y,$fot(X_119189)),bind(Z,$fot(X_119190))]]) ).
cnf(refute_0_17,plain,
( ~ rdn_translate(X_119188,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_119189,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_119190,rdn_pos(rdnn(n5)))
| sum(X_119188,X_119189,X_119190) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ rdn_translate(X_119331,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_119333,rdn_pos(rdnn(n5)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| sum(X_119331,n3,X_119333) ),
inference(subst,[],[refute_0_17:[bind(X_119188,$fot(X_119331)),bind(X_119189,$fot(n3)),bind(X_119190,$fot(X_119333))]]) ).
cnf(refute_0_19,plain,
( ~ rdn_translate(X_119331,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_119333,rdn_pos(rdnn(n5)))
| sum(X_119331,n3,X_119333) ),
inference(resolve,[$cnf( rdn_translate(n3,rdn_pos(rdnn(n3))) )],[refute_0_7,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ rdn_translate(X_119335,rdn_pos(rdnn(n5)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| sum(n2,n3,X_119335) ),
inference(subst,[],[refute_0_19:[bind(X_119331,$fot(n2)),bind(X_119333,$fot(X_119335))]]) ).
cnf(refute_0_21,plain,
( ~ rdn_translate(X_119335,rdn_pos(rdnn(n5)))
| sum(n2,n3,X_119335) ),
inference(resolve,[$cnf( rdn_translate(n2,rdn_pos(rdnn(n2))) )],[refute_0_6,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sum(n2,n3,n5) ),
inference(subst,[],[refute_0_21:[bind(X_119335,$fot(n5))]]) ).
cnf(refute_0_23,plain,
sum(n2,n3,n5),
inference(resolve,[$cnf( rdn_translate(n5,rdn_pos(rdnn(n5))) )],[refute_0_5,refute_0_22]) ).
cnf(refute_0_24,plain,
skolemFOFtoCNF_X = n2,
inference(resolve,[$cnf( sum(n2,n3,n5) )],[refute_0_23,refute_0_4]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_X != n2,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,n2) )],[refute_0_24,refute_0_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM312+1 : TPTP v8.1.0. Released v3.1.0.
% 0.00/0.11 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jul 5 08:57:52 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 37.52/37.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.52/37.71
% 37.52/37.71 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.52/37.71
%------------------------------------------------------------------------------