TSTP Solution File: NUM337+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM337+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 12:26:01 EDT 2022
% Result : Theorem 41.23s 41.45s
% Output : CNFRefutation 41.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 24 unt; 0 def)
% Number of atoms : 131 ( 15 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 132 ( 62 ~; 53 |; 8 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 100 ( 0 sgn 63 !; 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(minus_entry_point,axiom,
! [X,Y,Z] :
( sum(Y,Z,X)
<=> difference(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_n3_n2_n5_n0,axiom,
rdn_digit_add(rdnn(n3),rdnn(n2),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(diff_n5_only_n3_n2,conjecture,
! [X] :
( difference(n5,X,n2)
=> X = n3 ) ).
fof(subgoal_0,plain,
! [X] :
( difference(n5,X,n2)
=> X = n3 ),
inference(strip,[],[diff_n5_only_n3_n2]) ).
fof(negate_0_0,plain,
~ ! [X] :
( difference(n5,X,n2)
=> X = n3 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( X != n3
& difference(n5,X,n2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_X != n3
& difference(n5,skolemFOFtoCNF_X,n2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
difference(n5,skolemFOFtoCNF_X,n2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ difference(X,Y,Z)
<=> ~ sum(Y,Z,X) ),
inference(canonicalize,[],[minus_entry_point]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] :
( ~ difference(X,Y,Z)
<=> ~ sum(Y,Z,X) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ( ~ difference(X,Y,Z)
| sum(Y,Z,X) )
& ( ~ sum(Y,Z,X)
| difference(X,Y,Z) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ difference(X,Y,Z)
| sum(Y,Z,X) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X1,X2,Y,Z] :
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z)
| X1 = X2 ),
inference(canonicalize,[],[unique_LHS]) ).
fof(normalize_0_8,plain,
! [X1,X2,Y,Z] :
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z)
| X1 = X2 ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[rdn2]) ).
fof(normalize_0_10,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[rdn5]) ).
fof(normalize_0_11,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[rdn3]) ).
fof(normalize_0_12,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n3_n2_n5_n0]) ).
fof(normalize_0_13,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n5_n0_n5_n0]) ).
fof(normalize_0_14,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_15,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_14]) ).
fof(normalize_0_16,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_17,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_16]) ).
fof(normalize_0_18,plain,
skolemFOFtoCNF_X != n3,
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
difference(n5,skolemFOFtoCNF_X,n2),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ difference(X,Y,Z)
| sum(Y,Z,X) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ difference(n5,skolemFOFtoCNF_X,n2)
| sum(skolemFOFtoCNF_X,n2,n5) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(n5)),bind(Y,$fot(skolemFOFtoCNF_X)),bind(Z,$fot(n2))]]) ).
cnf(refute_0_3,plain,
sum(skolemFOFtoCNF_X,n2,n5),
inference(resolve,[$cnf( difference(n5,skolemFOFtoCNF_X,n2) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z)
| X1 = X2 ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ sum(X_1384,n2,n5)
| ~ sum(skolemFOFtoCNF_X,n2,n5)
| skolemFOFtoCNF_X = X_1384 ),
inference(subst,[],[refute_0_4:[bind(X1,$fot(skolemFOFtoCNF_X)),bind(X2,$fot(X_1384)),bind(Y,$fot(n2)),bind(Z,$fot(n5))]]) ).
cnf(refute_0_6,plain,
( ~ sum(X_1384,n2,n5)
| skolemFOFtoCNF_X = X_1384 ),
inference(resolve,[$cnf( sum(skolemFOFtoCNF_X,n2,n5) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ sum(n3,n2,n5)
| skolemFOFtoCNF_X = n3 ),
inference(subst,[],[refute_0_6:[bind(X_1384,$fot(n3))]]) ).
cnf(refute_0_8,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_13,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_15]) ).
cnf(refute_0_14,plain,
( ~ rdn_digit_add(rdnn(X_66668),rdnn(X_66669),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_66668),rdnn(X_66669),rdnn(n5)) ),
inference(subst,[],[refute_0_13:[bind(C,$fot(n0)),bind(D1,$fot(X_66668)),bind(D2,$fot(X_66669)),bind(ID,$fot(n5)),bind(RD,$fot(n5))]]) ).
cnf(refute_0_15,plain,
( ~ rdn_digit_add(rdnn(X_66668),rdnn(X_66669),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_66668),rdnn(X_66669),rdnn(n5)) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5)) ),
inference(subst,[],[refute_0_15:[bind(X_66668,$fot(n3)),bind(X_66669,$fot(n2))]]) ).
cnf(refute_0_17,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)) )],[refute_0_11,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| sum(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_19,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5))
| ~ rdn_translate(X_115282,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_115283,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_115284,rdn_pos(rdnn(n5)))
| sum(X_115282,X_115283,X_115284) ),
inference(subst,[],[refute_0_18:[bind(RDN_X,$fot(rdnn(n3))),bind(RDN_Y,$fot(rdnn(n2))),bind(RDN_Z,$fot(rdnn(n5))),bind(X,$fot(X_115282)),bind(Y,$fot(X_115283)),bind(Z,$fot(X_115284))]]) ).
cnf(refute_0_20,plain,
( ~ rdn_translate(X_115282,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_115283,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_115284,rdn_pos(rdnn(n5)))
| sum(X_115282,X_115283,X_115284) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5)) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ rdn_translate(X_115561,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_115562,rdn_pos(rdnn(n5)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| sum(n3,X_115561,X_115562) ),
inference(subst,[],[refute_0_20:[bind(X_115282,$fot(n3)),bind(X_115283,$fot(X_115561)),bind(X_115284,$fot(X_115562))]]) ).
cnf(refute_0_22,plain,
( ~ rdn_translate(X_115561,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_115562,rdn_pos(rdnn(n5)))
| sum(n3,X_115561,X_115562) ),
inference(resolve,[$cnf( rdn_translate(n3,rdn_pos(rdnn(n3))) )],[refute_0_10,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ rdn_translate(X_115563,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sum(n3,X_115563,n5) ),
inference(subst,[],[refute_0_22:[bind(X_115561,$fot(X_115563)),bind(X_115562,$fot(n5))]]) ).
cnf(refute_0_24,plain,
( ~ rdn_translate(X_115563,rdn_pos(rdnn(n2)))
| sum(n3,X_115563,n5) ),
inference(resolve,[$cnf( rdn_translate(n5,rdn_pos(rdnn(n5))) )],[refute_0_9,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| sum(n3,n2,n5) ),
inference(subst,[],[refute_0_24:[bind(X_115563,$fot(n2))]]) ).
cnf(refute_0_26,plain,
sum(n3,n2,n5),
inference(resolve,[$cnf( rdn_translate(n2,rdn_pos(rdnn(n2))) )],[refute_0_8,refute_0_25]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_X = n3,
inference(resolve,[$cnf( sum(n3,n2,n5) )],[refute_0_26,refute_0_7]) ).
cnf(refute_0_28,plain,
skolemFOFtoCNF_X != n3,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,n3) )],[refute_0_27,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM337+1 : TPTP v8.1.0. Released v3.1.0.
% 0.08/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n029.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 : Thu Jul 7 21:46:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 41.23/41.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.23/41.45
% 41.23/41.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 41.23/41.45
%------------------------------------------------------------------------------