TSTP Solution File: NUM331+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM331+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:25:59 EDT 2022
% Result : Theorem 79.99s 80.20s
% Output : CNFRefutation 79.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 87 ( 37 unt; 0 def)
% Number of atoms : 196 ( 34 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 206 ( 97 ~; 90 |; 13 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 57 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn6,axiom,
rdn_translate(n6,rdn_pos(rdnn(n6))) ).
fof(rdn7,axiom,
rdn_translate(n7,rdn_pos(rdnn(n7))) ).
fof(rdn13,axiom,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))) ).
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_rdn,axiom,
! [C,D1,D2,ID,RD,IC1,IC2] :
( ( rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1))
& rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2))
& rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(n1),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdn(rdnn(RD),rdnn(n1))) ) ).
fof(rdn_digit_add_n1_n0_n1_n0,axiom,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)) ).
fof(rdn_digit_add_n3_n0_n3_n0,axiom,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)) ).
fof(rdn_digit_add_n6_n7_n3_n1,axiom,
rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)) ).
fof(rdn_digit_add_n7_n6_n3_n1,axiom,
rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)) ).
fof(communative_sum_n6_n7,conjecture,
! [Z1,Z2] :
( ( sum(n6,n7,Z1)
& sum(n7,n6,Z2) )
=> Z1 = Z2 ) ).
fof(subgoal_0,plain,
! [Z1,Z2] :
( ( sum(n6,n7,Z1)
& sum(n7,n6,Z2) )
=> Z1 = Z2 ),
inference(strip,[],[communative_sum_n6_n7]) ).
fof(negate_0_0,plain,
~ ! [Z1,Z2] :
( ( sum(n6,n7,Z1)
& sum(n7,n6,Z2) )
=> Z1 = Z2 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [Z1,Z2] :
( Z1 != Z2
& sum(n6,n7,Z1)
& sum(n7,n6,Z2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_Z1 != skolemFOFtoCNF_Z2
& sum(n6,n7,skolemFOFtoCNF_Z1)
& sum(n7,n6,skolemFOFtoCNF_Z2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
sum(n7,n6,skolemFOFtoCNF_Z2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z1,Z2] :
( ~ sum(X,Y,Z1)
| ~ sum(X,Y,Z2)
| Z1 = Z2 ),
inference(canonicalize,[],[unique_sum]) ).
fof(normalize_0_4,plain,
! [X,Y,Z1,Z2] :
( ~ sum(X,Y,Z1)
| ~ sum(X,Y,Z2)
| Z1 = Z2 ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(canonicalize,[],[rdn6]) ).
fof(normalize_0_6,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(canonicalize,[],[rdn7]) ).
fof(normalize_0_7,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(canonicalize,[],[rdn13]) ).
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_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_9,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_8]) ).
fof(normalize_0_10,plain,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n3_n0_n3_n0]) ).
fof(normalize_0_11,plain,
rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)),
inference(canonicalize,[],[rdn_digit_add_n7_n6_n3_n1]) ).
fof(normalize_0_12,plain,
! [C,D1,D2,IC1,IC2,ID,RD] :
( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1))
| ~ rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2))
| rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdn(rdnn(RD),rdnn(n1))) ),
inference(canonicalize,[],[add_digit_digit_rdn]) ).
fof(normalize_0_13,plain,
! [C,D1,D2,IC1,IC2,ID,RD] :
( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1))
| ~ rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2))
| rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdn(rdnn(RD),rdnn(n1))) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n1_n0_n1_n0]) ).
fof(normalize_0_15,plain,
skolemFOFtoCNF_Z1 != skolemFOFtoCNF_Z2,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_16,plain,
sum(n6,n7,skolemFOFtoCNF_Z1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_17,plain,
rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)),
inference(canonicalize,[],[rdn_digit_add_n6_n7_n3_n1]) ).
cnf(refute_0_0,plain,
sum(n7,n6,skolemFOFtoCNF_Z2),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ sum(X,Y,Z1)
| ~ sum(X,Y,Z2)
| Z1 = Z2 ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ sum(n7,n6,X_1517)
| ~ sum(n7,n6,skolemFOFtoCNF_Z2)
| skolemFOFtoCNF_Z2 = X_1517 ),
inference(subst,[],[refute_0_1:[bind(X,$fot(n7)),bind(Y,$fot(n6)),bind(Z1,$fot(skolemFOFtoCNF_Z2)),bind(Z2,$fot(X_1517))]]) ).
cnf(refute_0_3,plain,
( ~ sum(n7,n6,X_1517)
| skolemFOFtoCNF_Z2 = X_1517 ),
inference(resolve,[$cnf( sum(n7,n6,skolemFOFtoCNF_Z2) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ sum(n7,n6,n13)
| skolemFOFtoCNF_Z2 = n13 ),
inference(subst,[],[refute_0_3:[bind(X_1517,$fot(n13))]]) ).
cnf(refute_0_5,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_6,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(canonicalize,[],[normalize_0_7]) ).
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_9]) ).
cnf(refute_0_9,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1)))
| ~ rdn_translate(X,rdn_pos(rdnn(n7)))
| ~ rdn_translate(Y,rdn_pos(rdnn(n6)))
| ~ rdn_translate(Z,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| sum(X,Y,Z) ),
inference(subst,[],[refute_0_8:[bind(RDN_X,$fot(rdnn(n7))),bind(RDN_Y,$fot(rdnn(n6))),bind(RDN_Z,$fot(rdn(rdnn(n3),rdnn(n1))))]]) ).
cnf(refute_0_10,plain,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1))
| ~ rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2))
| rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdn(rdnn(RD),rdnn(n1))) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_13,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(X_186333),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(n3),rdnn(X_186329),rdnn(X_186335),rdnn(X_186333))
| ~ rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1))
| rdn_add_with_carry(rdnn(X_186329),rdnn(n7),rdnn(n6),rdn(rdnn(X_186335),rdnn(n1))) ),
inference(subst,[],[refute_0_12:[bind(C,$fot(X_186329)),bind(D1,$fot(n7)),bind(D2,$fot(n6)),bind(IC1,$fot(n1)),bind(IC2,$fot(X_186333)),bind(ID,$fot(n3)),bind(RD,$fot(X_186335))]]) ).
cnf(refute_0_14,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(X_186333),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(n3),rdnn(X_186329),rdnn(X_186335),rdnn(X_186333))
| rdn_add_with_carry(rdnn(X_186329),rdnn(n7),rdnn(n6),rdn(rdnn(X_186335),rdnn(n1))) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1))) ),
inference(subst,[],[refute_0_14:[bind(X_186329,$fot(n0)),bind(X_186333,$fot(n0)),bind(X_186335,$fot(n3))]]) ).
cnf(refute_0_16,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1))) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_18,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1))),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
( ~ rdn_translate(X,rdn_pos(rdnn(n7)))
| ~ rdn_translate(Y,rdn_pos(rdnn(n6)))
| ~ rdn_translate(Z,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| sum(X,Y,Z) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1))) )],[refute_0_18,refute_0_9]) ).
cnf(refute_0_20,plain,
( ~ rdn_translate(X_188436,rdn_pos(rdnn(n7)))
| ~ rdn_translate(X_188437,rdn_pos(rdnn(n6)))
| ~ rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| sum(X_188436,X_188437,n13) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_188436)),bind(Y,$fot(X_188437)),bind(Z,$fot(n13))]]) ).
cnf(refute_0_21,plain,
( ~ rdn_translate(X_188436,rdn_pos(rdnn(n7)))
| ~ rdn_translate(X_188437,rdn_pos(rdnn(n6)))
| sum(X_188436,X_188437,n13) ),
inference(resolve,[$cnf( rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))) )],[refute_0_7,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ rdn_translate(X_188440,rdn_pos(rdnn(n6)))
| ~ rdn_translate(n7,rdn_pos(rdnn(n7)))
| sum(n7,X_188440,n13) ),
inference(subst,[],[refute_0_21:[bind(X_188436,$fot(n7)),bind(X_188437,$fot(X_188440))]]) ).
cnf(refute_0_23,plain,
( ~ rdn_translate(X_188440,rdn_pos(rdnn(n6)))
| sum(n7,X_188440,n13) ),
inference(resolve,[$cnf( rdn_translate(n7,rdn_pos(rdnn(n7))) )],[refute_0_6,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| sum(n7,n6,n13) ),
inference(subst,[],[refute_0_23:[bind(X_188440,$fot(n6))]]) ).
cnf(refute_0_25,plain,
sum(n7,n6,n13),
inference(resolve,[$cnf( rdn_translate(n6,rdn_pos(rdnn(n6))) )],[refute_0_5,refute_0_24]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_Z2 = n13,
inference(resolve,[$cnf( sum(n7,n6,n13) )],[refute_0_25,refute_0_4]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_Z1 != skolemFOFtoCNF_Z2,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_28,plain,
sum(n6,n7,skolemFOFtoCNF_Z1),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_29,plain,
( ~ sum(n6,n7,X_1517)
| ~ sum(n6,n7,skolemFOFtoCNF_Z1)
| skolemFOFtoCNF_Z1 = X_1517 ),
inference(subst,[],[refute_0_1:[bind(X,$fot(n6)),bind(Y,$fot(n7)),bind(Z1,$fot(skolemFOFtoCNF_Z1)),bind(Z2,$fot(X_1517))]]) ).
cnf(refute_0_30,plain,
( ~ sum(n6,n7,X_1517)
| skolemFOFtoCNF_Z1 = X_1517 ),
inference(resolve,[$cnf( sum(n6,n7,skolemFOFtoCNF_Z1) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ sum(n6,n7,n13)
| skolemFOFtoCNF_Z1 = n13 ),
inference(subst,[],[refute_0_30:[bind(X_1517,$fot(n13))]]) ).
cnf(refute_0_32,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n7),rdn(rdnn(n3),rdnn(n1)))
| ~ rdn_translate(X,rdn_pos(rdnn(n6)))
| ~ rdn_translate(Y,rdn_pos(rdnn(n7)))
| ~ rdn_translate(Z,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| sum(X,Y,Z) ),
inference(subst,[],[refute_0_8:[bind(RDN_X,$fot(rdnn(n6))),bind(RDN_Y,$fot(rdnn(n7))),bind(RDN_Z,$fot(rdn(rdnn(n3),rdnn(n1))))]]) ).
cnf(refute_0_33,plain,
rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_34,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(X_186333),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(n3),rdnn(X_186329),rdnn(X_186335),rdnn(X_186333))
| ~ rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1))
| rdn_add_with_carry(rdnn(X_186329),rdnn(n6),rdnn(n7),rdn(rdnn(X_186335),rdnn(n1))) ),
inference(subst,[],[refute_0_12:[bind(C,$fot(X_186329)),bind(D1,$fot(n6)),bind(D2,$fot(n7)),bind(IC1,$fot(n1)),bind(IC2,$fot(X_186333)),bind(ID,$fot(n3)),bind(RD,$fot(X_186335))]]) ).
cnf(refute_0_35,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(X_186333),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(n3),rdnn(X_186329),rdnn(X_186335),rdnn(X_186333))
| rdn_add_with_carry(rdnn(X_186329),rdnn(n6),rdnn(n7),rdn(rdnn(X_186335),rdnn(n1))) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n7),rdn(rdnn(n3),rdnn(n1))) ),
inference(subst,[],[refute_0_35:[bind(X_186329,$fot(n0)),bind(X_186333,$fot(n0)),bind(X_186335,$fot(n3))]]) ).
cnf(refute_0_37,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n7),rdn(rdnn(n3),rdnn(n1))) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)) )],[refute_0_10,refute_0_36]) ).
cnf(refute_0_38,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n7),rdn(rdnn(n3),rdnn(n1))),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)) )],[refute_0_17,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ rdn_translate(X,rdn_pos(rdnn(n6)))
| ~ rdn_translate(Y,rdn_pos(rdnn(n7)))
| ~ rdn_translate(Z,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| sum(X,Y,Z) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n7),rdn(rdnn(n3),rdnn(n1))) )],[refute_0_38,refute_0_32]) ).
cnf(refute_0_40,plain,
( ~ rdn_translate(X_188333,rdn_pos(rdnn(n6)))
| ~ rdn_translate(X_188334,rdn_pos(rdnn(n7)))
| ~ rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| sum(X_188333,X_188334,n13) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_188333)),bind(Y,$fot(X_188334)),bind(Z,$fot(n13))]]) ).
cnf(refute_0_41,plain,
( ~ rdn_translate(X_188333,rdn_pos(rdnn(n6)))
| ~ rdn_translate(X_188334,rdn_pos(rdnn(n7)))
| sum(X_188333,X_188334,n13) ),
inference(resolve,[$cnf( rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))) )],[refute_0_7,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ rdn_translate(X_188337,rdn_pos(rdnn(n7)))
| ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| sum(n6,X_188337,n13) ),
inference(subst,[],[refute_0_41:[bind(X_188333,$fot(n6)),bind(X_188334,$fot(X_188337))]]) ).
cnf(refute_0_43,plain,
( ~ rdn_translate(X_188337,rdn_pos(rdnn(n7)))
| sum(n6,X_188337,n13) ),
inference(resolve,[$cnf( rdn_translate(n6,rdn_pos(rdnn(n6))) )],[refute_0_5,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ rdn_translate(n7,rdn_pos(rdnn(n7)))
| sum(n6,n7,n13) ),
inference(subst,[],[refute_0_43:[bind(X_188337,$fot(n7))]]) ).
cnf(refute_0_45,plain,
sum(n6,n7,n13),
inference(resolve,[$cnf( rdn_translate(n7,rdn_pos(rdnn(n7))) )],[refute_0_6,refute_0_44]) ).
cnf(refute_0_46,plain,
skolemFOFtoCNF_Z1 = n13,
inference(resolve,[$cnf( sum(n6,n7,n13) )],[refute_0_45,refute_0_31]) ).
cnf(refute_0_47,plain,
( n13 != skolemFOFtoCNF_Z2
| skolemFOFtoCNF_Z1 != n13
| skolemFOFtoCNF_Z1 = skolemFOFtoCNF_Z2 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Z1,n13) ),[1],$fot(skolemFOFtoCNF_Z2)]]) ).
cnf(refute_0_48,plain,
( n13 != skolemFOFtoCNF_Z2
| skolemFOFtoCNF_Z1 = skolemFOFtoCNF_Z2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z1,n13) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
n13 != skolemFOFtoCNF_Z2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z1,skolemFOFtoCNF_Z2) )],[refute_0_48,refute_0_27]) ).
cnf(refute_0_50,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_51,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_52,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( skolemFOFtoCNF_Z2 != n13
| n13 = skolemFOFtoCNF_Z2 ),
inference(subst,[],[refute_0_52:[bind(X0,$fot(skolemFOFtoCNF_Z2)),bind(Y0,$fot(n13))]]) ).
cnf(refute_0_54,plain,
skolemFOFtoCNF_Z2 != n13,
inference(resolve,[$cnf( $equal(n13,skolemFOFtoCNF_Z2) )],[refute_0_53,refute_0_49]) ).
cnf(refute_0_55,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z2,n13) )],[refute_0_26,refute_0_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM331+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.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 : Wed Jul 6 04:51:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 79.99/80.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 79.99/80.20
% 79.99/80.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 79.99/80.20
%------------------------------------------------------------------------------