TSTP Solution File: NUM332+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM332+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 37.54s 37.73s
% Output : CNFRefutation 37.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of formulae : 142 ( 63 unt; 0 def)
% Number of atoms : 311 ( 37 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 313 ( 144 ~; 138 |; 24 &)
% ( 0 <=>; 7 =>; 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 : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 174 ( 0 sgn 78 !; 4 ?)
% 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(rdn6,axiom,
rdn_translate(n6,rdn_pos(rdnn(n6))) ).
fof(rdn9,axiom,
rdn_translate(n9,rdn_pos(rdnn(n9))) ).
fof(rdn11,axiom,
rdn_translate(n11,rdn_pos(rdn(rdnn(n1),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_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(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_n2_n3_n5_n0,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) ).
fof(rdn_digit_add_n2_n9_n1_n1,axiom,
rdn_digit_add(rdnn(n2),rdnn(n9),rdnn(n1),rdnn(n1)) ).
fof(rdn_digit_add_n3_n6_n9_n0,axiom,
rdn_digit_add(rdnn(n3),rdnn(n6),rdnn(n9),rdnn(n0)) ).
fof(rdn_digit_add_n5_n0_n5_n0,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) ).
fof(rdn_digit_add_n5_n6_n1_n1,axiom,
rdn_digit_add(rdnn(n5),rdnn(n6),rdnn(n1),rdnn(n1)) ).
fof(rdn_digit_add_n9_n0_n9_n0,axiom,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)) ).
fof(associative_sum,conjecture,
! [Z1,Z2,Z3,Z4] :
( ( sum(n2,n3,Z1)
& sum(Z1,n6,Z2)
& sum(n3,n6,Z3)
& sum(n2,Z3,Z4) )
=> Z2 = Z4 ) ).
fof(subgoal_0,plain,
! [Z1,Z2,Z3,Z4] :
( ( sum(n2,n3,Z1)
& sum(Z1,n6,Z2)
& sum(n3,n6,Z3)
& sum(n2,Z3,Z4) )
=> Z2 = Z4 ),
inference(strip,[],[associative_sum]) ).
fof(negate_0_0,plain,
~ ! [Z1,Z2,Z3,Z4] :
( ( sum(n2,n3,Z1)
& sum(Z1,n6,Z2)
& sum(n3,n6,Z3)
& sum(n2,Z3,Z4) )
=> Z2 = Z4 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [Z1,Z2,Z3,Z4] :
( Z2 != Z4
& sum(Z1,n6,Z2)
& sum(n2,Z3,Z4)
& sum(n2,n3,Z1)
& sum(n3,n6,Z3) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_Z2 != skolemFOFtoCNF_Z4
& sum(n2,n3,skolemFOFtoCNF_Z1)
& sum(n2,skolemFOFtoCNF_Z3,skolemFOFtoCNF_Z4)
& sum(n3,n6,skolemFOFtoCNF_Z3)
& sum(skolemFOFtoCNF_Z1,n6,skolemFOFtoCNF_Z2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
sum(skolemFOFtoCNF_Z1,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,
sum(n2,n3,skolemFOFtoCNF_Z1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[rdn2]) ).
fof(normalize_0_7,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[rdn5]) ).
fof(normalize_0_8,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[rdn3]) ).
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(n6,rdn_pos(rdnn(n6))),
inference(canonicalize,[],[rdn6]) ).
fof(normalize_0_16,plain,
rdn_translate(n11,rdn_pos(rdn(rdnn(n1),rdnn(n1)))),
inference(canonicalize,[],[rdn11]) ).
fof(normalize_0_17,plain,
rdn_digit_add(rdnn(n5),rdnn(n6),rdnn(n1),rdnn(n1)),
inference(canonicalize,[],[rdn_digit_add_n5_n6_n1_n1]) ).
fof(normalize_0_18,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_19,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_18]) ).
fof(normalize_0_20,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n1_n0_n1_n0]) ).
fof(normalize_0_21,plain,
skolemFOFtoCNF_Z2 != skolemFOFtoCNF_Z4,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_22,plain,
sum(n2,skolemFOFtoCNF_Z3,skolemFOFtoCNF_Z4),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_23,plain,
sum(n3,n6,skolemFOFtoCNF_Z3),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_24,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(canonicalize,[],[rdn9]) ).
fof(normalize_0_25,plain,
rdn_digit_add(rdnn(n3),rdnn(n6),rdnn(n9),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n3_n6_n9_n0]) ).
fof(normalize_0_26,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n9_n0_n9_n0]) ).
fof(normalize_0_27,plain,
rdn_digit_add(rdnn(n2),rdnn(n9),rdnn(n1),rdnn(n1)),
inference(canonicalize,[],[rdn_digit_add_n2_n9_n1_n1]) ).
cnf(refute_0_0,plain,
sum(skolemFOFtoCNF_Z1,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(skolemFOFtoCNF_Z1,n6,X_1253)
| ~ sum(skolemFOFtoCNF_Z1,n6,skolemFOFtoCNF_Z2)
| skolemFOFtoCNF_Z2 = X_1253 ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_Z1)),bind(Y,$fot(n6)),bind(Z1,$fot(skolemFOFtoCNF_Z2)),bind(Z2,$fot(X_1253))]]) ).
cnf(refute_0_3,plain,
( ~ sum(skolemFOFtoCNF_Z1,n6,X_1253)
| skolemFOFtoCNF_Z2 = X_1253 ),
inference(resolve,[$cnf( sum(skolemFOFtoCNF_Z1,n6,skolemFOFtoCNF_Z2) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
sum(n2,n3,skolemFOFtoCNF_Z1),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ sum(n2,n3,X_1253)
| ~ sum(n2,n3,skolemFOFtoCNF_Z1)
| skolemFOFtoCNF_Z1 = X_1253 ),
inference(subst,[],[refute_0_1:[bind(X,$fot(n2)),bind(Y,$fot(n3)),bind(Z1,$fot(skolemFOFtoCNF_Z1)),bind(Z2,$fot(X_1253))]]) ).
cnf(refute_0_6,plain,
( ~ sum(n2,n3,X_1253)
| skolemFOFtoCNF_Z1 = X_1253 ),
inference(resolve,[$cnf( sum(n2,n3,skolemFOFtoCNF_Z1) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ sum(n2,n3,n5)
| skolemFOFtoCNF_Z1 = n5 ),
inference(subst,[],[refute_0_6:[bind(X_1253,$fot(n5))]]) ).
cnf(refute_0_8,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_9,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_10,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_12,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_13,plain,
( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
| rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_14,plain,
( ~ rdn_digit_add(rdnn(X_66240),rdnn(X_66241),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_66240),rdnn(X_66241),rdnn(n5)) ),
inference(subst,[],[refute_0_13:[bind(C,$fot(n0)),bind(D1,$fot(X_66240)),bind(D2,$fot(X_66241)),bind(ID,$fot(n5)),bind(RD,$fot(n5))]]) ).
cnf(refute_0_15,plain,
( ~ rdn_digit_add(rdnn(X_66240),rdnn(X_66241),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_66240),rdnn(X_66241),rdnn(n5)) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)) ),
inference(subst,[],[refute_0_15:[bind(X_66240,$fot(n2)),bind(X_66241,$fot(n3))]]) ).
cnf(refute_0_17,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) )],[refute_0_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_14]) ).
cnf(refute_0_19,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| ~ rdn_translate(X_100335,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_100336,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_100337,rdn_pos(rdnn(n5)))
| sum(X_100335,X_100336,X_100337) ),
inference(subst,[],[refute_0_18:[bind(RDN_X,$fot(rdnn(n2))),bind(RDN_Y,$fot(rdnn(n3))),bind(RDN_Z,$fot(rdnn(n5))),bind(X,$fot(X_100335)),bind(Y,$fot(X_100336)),bind(Z,$fot(X_100337))]]) ).
cnf(refute_0_20,plain,
( ~ rdn_translate(X_100335,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_100336,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_100337,rdn_pos(rdnn(n5)))
| sum(X_100335,X_100336,X_100337) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ rdn_translate(X_100670,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_100672,rdn_pos(rdnn(n5)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| sum(X_100670,n3,X_100672) ),
inference(subst,[],[refute_0_20:[bind(X_100335,$fot(X_100670)),bind(X_100336,$fot(n3)),bind(X_100337,$fot(X_100672))]]) ).
cnf(refute_0_22,plain,
( ~ rdn_translate(X_100670,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_100672,rdn_pos(rdnn(n5)))
| sum(X_100670,n3,X_100672) ),
inference(resolve,[$cnf( rdn_translate(n3,rdn_pos(rdnn(n3))) )],[refute_0_10,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ rdn_translate(X_100673,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sum(X_100673,n3,n5) ),
inference(subst,[],[refute_0_22:[bind(X_100670,$fot(X_100673)),bind(X_100672,$fot(n5))]]) ).
cnf(refute_0_24,plain,
( ~ rdn_translate(X_100673,rdn_pos(rdnn(n2)))
| sum(X_100673,n3,n5) ),
inference(resolve,[$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(n2,n3,n5) ),
inference(subst,[],[refute_0_24:[bind(X_100673,$fot(n2))]]) ).
cnf(refute_0_26,plain,
sum(n2,n3,n5),
inference(resolve,[$cnf( rdn_translate(n2,rdn_pos(rdnn(n2))) )],[refute_0_8,refute_0_25]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_Z1 = n5,
inference(resolve,[$cnf( sum(n2,n3,n5) )],[refute_0_26,refute_0_7]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_Z1 != n5
| ~ sum(n5,n6,X_1253)
| sum(skolemFOFtoCNF_Z1,n6,X_1253) ),
introduced(tautology,[equality,[$cnf( ~ sum(skolemFOFtoCNF_Z1,n6,X_1253) ),[0],$fot(n5)]]) ).
cnf(refute_0_29,plain,
( ~ sum(n5,n6,X_1253)
| sum(skolemFOFtoCNF_Z1,n6,X_1253) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z1,n5) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ sum(n5,n6,X_1253)
| skolemFOFtoCNF_Z2 = X_1253 ),
inference(resolve,[$cnf( sum(skolemFOFtoCNF_Z1,n6,X_1253) )],[refute_0_29,refute_0_3]) ).
cnf(refute_0_31,plain,
( ~ sum(n5,n6,n11)
| skolemFOFtoCNF_Z2 = n11 ),
inference(subst,[],[refute_0_30:[bind(X_1253,$fot(n11))]]) ).
cnf(refute_0_32,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_33,plain,
rdn_translate(n11,rdn_pos(rdn(rdnn(n1),rdnn(n1)))),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_34,plain,
rdn_digit_add(rdnn(n5),rdnn(n6),rdnn(n1),rdnn(n1)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_35,plain,
( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1))
| ~ rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2))
| rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdn(rdnn(RD),rdnn(n1))) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_36,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n6),rdnn(n1),rdnn(n1))
| rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n6),rdn(rdnn(n1),rdnn(n1))) ),
inference(subst,[],[refute_0_35:[bind(C,$fot(n0)),bind(D1,$fot(n5)),bind(D2,$fot(n6)),bind(IC1,$fot(n1)),bind(IC2,$fot(n0)),bind(ID,$fot(n1)),bind(RD,$fot(n1))]]) ).
cnf(refute_0_37,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n6),rdn(rdnn(n1),rdnn(n1))) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n5),rdnn(n6),rdnn(n1),rdnn(n1)) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_39,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n6),rdn(rdnn(n1),rdnn(n1))),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)) )],[refute_0_38,refute_0_37]) ).
cnf(refute_0_40,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n6),rdn(rdnn(n1),rdnn(n1)))
| ~ rdn_translate(X_100335,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_100336,rdn_pos(rdnn(n6)))
| ~ rdn_translate(X_100337,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| sum(X_100335,X_100336,X_100337) ),
inference(subst,[],[refute_0_18:[bind(RDN_X,$fot(rdnn(n5))),bind(RDN_Y,$fot(rdnn(n6))),bind(RDN_Z,$fot(rdn(rdnn(n1),rdnn(n1)))),bind(X,$fot(X_100335)),bind(Y,$fot(X_100336)),bind(Z,$fot(X_100337))]]) ).
cnf(refute_0_41,plain,
( ~ rdn_translate(X_100335,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_100336,rdn_pos(rdnn(n6)))
| ~ rdn_translate(X_100337,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| sum(X_100335,X_100336,X_100337) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n6),rdn(rdnn(n1),rdnn(n1))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ rdn_translate(X_101268,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_101269,rdn_pos(rdnn(n6)))
| ~ rdn_translate(n11,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| sum(X_101268,X_101269,n11) ),
inference(subst,[],[refute_0_41:[bind(X_100335,$fot(X_101268)),bind(X_100336,$fot(X_101269)),bind(X_100337,$fot(n11))]]) ).
cnf(refute_0_43,plain,
( ~ rdn_translate(X_101268,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_101269,rdn_pos(rdnn(n6)))
| sum(X_101268,X_101269,n11) ),
inference(resolve,[$cnf( rdn_translate(n11,rdn_pos(rdn(rdnn(n1),rdnn(n1)))) )],[refute_0_33,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ rdn_translate(X_101272,rdn_pos(rdnn(n6)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sum(n5,X_101272,n11) ),
inference(subst,[],[refute_0_43:[bind(X_101268,$fot(n5)),bind(X_101269,$fot(X_101272))]]) ).
cnf(refute_0_45,plain,
( ~ rdn_translate(X_101272,rdn_pos(rdnn(n6)))
| sum(n5,X_101272,n11) ),
inference(resolve,[$cnf( rdn_translate(n5,rdn_pos(rdnn(n5))) )],[refute_0_9,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| sum(n5,n6,n11) ),
inference(subst,[],[refute_0_45:[bind(X_101272,$fot(n6))]]) ).
cnf(refute_0_47,plain,
sum(n5,n6,n11),
inference(resolve,[$cnf( rdn_translate(n6,rdn_pos(rdnn(n6))) )],[refute_0_32,refute_0_46]) ).
cnf(refute_0_48,plain,
skolemFOFtoCNF_Z2 = n11,
inference(resolve,[$cnf( sum(n5,n6,n11) )],[refute_0_47,refute_0_31]) ).
cnf(refute_0_49,plain,
skolemFOFtoCNF_Z2 != skolemFOFtoCNF_Z4,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_50,plain,
sum(n2,skolemFOFtoCNF_Z3,skolemFOFtoCNF_Z4),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_51,plain,
( ~ sum(n2,skolemFOFtoCNF_Z3,X_1253)
| ~ sum(n2,skolemFOFtoCNF_Z3,skolemFOFtoCNF_Z4)
| skolemFOFtoCNF_Z4 = X_1253 ),
inference(subst,[],[refute_0_1:[bind(X,$fot(n2)),bind(Y,$fot(skolemFOFtoCNF_Z3)),bind(Z1,$fot(skolemFOFtoCNF_Z4)),bind(Z2,$fot(X_1253))]]) ).
cnf(refute_0_52,plain,
( ~ sum(n2,skolemFOFtoCNF_Z3,X_1253)
| skolemFOFtoCNF_Z4 = X_1253 ),
inference(resolve,[$cnf( sum(n2,skolemFOFtoCNF_Z3,skolemFOFtoCNF_Z4) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
sum(n3,n6,skolemFOFtoCNF_Z3),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_54,plain,
( ~ sum(n3,n6,X_1253)
| ~ sum(n3,n6,skolemFOFtoCNF_Z3)
| skolemFOFtoCNF_Z3 = X_1253 ),
inference(subst,[],[refute_0_1:[bind(X,$fot(n3)),bind(Y,$fot(n6)),bind(Z1,$fot(skolemFOFtoCNF_Z3)),bind(Z2,$fot(X_1253))]]) ).
cnf(refute_0_55,plain,
( ~ sum(n3,n6,X_1253)
| skolemFOFtoCNF_Z3 = X_1253 ),
inference(resolve,[$cnf( sum(n3,n6,skolemFOFtoCNF_Z3) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ sum(n3,n6,n9)
| skolemFOFtoCNF_Z3 = n9 ),
inference(subst,[],[refute_0_55:[bind(X_1253,$fot(n9))]]) ).
cnf(refute_0_57,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_58,plain,
rdn_digit_add(rdnn(n3),rdnn(n6),rdnn(n9),rdnn(n0)),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_59,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_60,plain,
( ~ rdn_digit_add(rdnn(X_66240),rdnn(X_66241),rdnn(n9),rdnn(n0))
| ~ rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_66240),rdnn(X_66241),rdnn(n9)) ),
inference(subst,[],[refute_0_13:[bind(C,$fot(n0)),bind(D1,$fot(X_66240)),bind(D2,$fot(X_66241)),bind(ID,$fot(n9)),bind(RD,$fot(n9))]]) ).
cnf(refute_0_61,plain,
( ~ rdn_digit_add(rdnn(X_66240),rdnn(X_66241),rdnn(n9),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_66240),rdnn(X_66241),rdnn(n9)) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ rdn_digit_add(rdnn(n3),rdnn(n6),rdnn(n9),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n6),rdnn(n9)) ),
inference(subst,[],[refute_0_61:[bind(X_66240,$fot(n3)),bind(X_66241,$fot(n6))]]) ).
cnf(refute_0_63,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n6),rdnn(n9)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n3),rdnn(n6),rdnn(n9),rdnn(n0)) )],[refute_0_58,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n6),rdnn(n9))
| ~ rdn_translate(X_100335,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_100336,rdn_pos(rdnn(n6)))
| ~ rdn_translate(X_100337,rdn_pos(rdnn(n9)))
| sum(X_100335,X_100336,X_100337) ),
inference(subst,[],[refute_0_18:[bind(RDN_X,$fot(rdnn(n3))),bind(RDN_Y,$fot(rdnn(n6))),bind(RDN_Z,$fot(rdnn(n9))),bind(X,$fot(X_100335)),bind(Y,$fot(X_100336)),bind(Z,$fot(X_100337))]]) ).
cnf(refute_0_65,plain,
( ~ rdn_translate(X_100335,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_100336,rdn_pos(rdnn(n6)))
| ~ rdn_translate(X_100337,rdn_pos(rdnn(n9)))
| sum(X_100335,X_100336,X_100337) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n6),rdnn(n9)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ rdn_translate(X_100845,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_100847,rdn_pos(rdnn(n9)))
| ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| sum(X_100845,n6,X_100847) ),
inference(subst,[],[refute_0_65:[bind(X_100335,$fot(X_100845)),bind(X_100336,$fot(n6)),bind(X_100337,$fot(X_100847))]]) ).
cnf(refute_0_67,plain,
( ~ rdn_translate(X_100845,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X_100847,rdn_pos(rdnn(n9)))
| sum(X_100845,n6,X_100847) ),
inference(resolve,[$cnf( rdn_translate(n6,rdn_pos(rdnn(n6))) )],[refute_0_32,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ rdn_translate(X_100849,rdn_pos(rdnn(n9)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| sum(n3,n6,X_100849) ),
inference(subst,[],[refute_0_67:[bind(X_100845,$fot(n3)),bind(X_100847,$fot(X_100849))]]) ).
cnf(refute_0_69,plain,
( ~ rdn_translate(X_100849,rdn_pos(rdnn(n9)))
| sum(n3,n6,X_100849) ),
inference(resolve,[$cnf( rdn_translate(n3,rdn_pos(rdnn(n3))) )],[refute_0_10,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ rdn_translate(n9,rdn_pos(rdnn(n9)))
| sum(n3,n6,n9) ),
inference(subst,[],[refute_0_69:[bind(X_100849,$fot(n9))]]) ).
cnf(refute_0_71,plain,
sum(n3,n6,n9),
inference(resolve,[$cnf( rdn_translate(n9,rdn_pos(rdnn(n9))) )],[refute_0_57,refute_0_70]) ).
cnf(refute_0_72,plain,
skolemFOFtoCNF_Z3 = n9,
inference(resolve,[$cnf( sum(n3,n6,n9) )],[refute_0_71,refute_0_56]) ).
cnf(refute_0_73,plain,
( skolemFOFtoCNF_Z3 != n9
| ~ sum(n2,n9,X_1253)
| sum(n2,skolemFOFtoCNF_Z3,X_1253) ),
introduced(tautology,[equality,[$cnf( ~ sum(n2,skolemFOFtoCNF_Z3,X_1253) ),[1],$fot(n9)]]) ).
cnf(refute_0_74,plain,
( ~ sum(n2,n9,X_1253)
| sum(n2,skolemFOFtoCNF_Z3,X_1253) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z3,n9) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ sum(n2,n9,X_1253)
| skolemFOFtoCNF_Z4 = X_1253 ),
inference(resolve,[$cnf( sum(n2,skolemFOFtoCNF_Z3,X_1253) )],[refute_0_74,refute_0_52]) ).
cnf(refute_0_76,plain,
( ~ sum(n2,n9,n11)
| skolemFOFtoCNF_Z4 = n11 ),
inference(subst,[],[refute_0_75:[bind(X_1253,$fot(n11))]]) ).
cnf(refute_0_77,plain,
rdn_digit_add(rdnn(n2),rdnn(n9),rdnn(n1),rdnn(n1)),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_78,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(n2),rdnn(n9),rdnn(n1),rdnn(n1))
| rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n9),rdn(rdnn(n1),rdnn(n1))) ),
inference(subst,[],[refute_0_35:[bind(C,$fot(n0)),bind(D1,$fot(n2)),bind(D2,$fot(n9)),bind(IC1,$fot(n1)),bind(IC2,$fot(n0)),bind(ID,$fot(n1)),bind(RD,$fot(n1))]]) ).
cnf(refute_0_79,plain,
( ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n9),rdn(rdnn(n1),rdnn(n1))) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n2),rdnn(n9),rdnn(n1),rdnn(n1)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n9),rdn(rdnn(n1),rdnn(n1))),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)) )],[refute_0_38,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n9),rdn(rdnn(n1),rdnn(n1)))
| ~ rdn_translate(X_100335,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_100336,rdn_pos(rdnn(n9)))
| ~ rdn_translate(X_100337,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| sum(X_100335,X_100336,X_100337) ),
inference(subst,[],[refute_0_18:[bind(RDN_X,$fot(rdnn(n2))),bind(RDN_Y,$fot(rdnn(n9))),bind(RDN_Z,$fot(rdn(rdnn(n1),rdnn(n1)))),bind(X,$fot(X_100335)),bind(Y,$fot(X_100336)),bind(Z,$fot(X_100337))]]) ).
cnf(refute_0_82,plain,
( ~ rdn_translate(X_100335,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_100336,rdn_pos(rdnn(n9)))
| ~ rdn_translate(X_100337,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| sum(X_100335,X_100336,X_100337) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n9),rdn(rdnn(n1),rdnn(n1))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( ~ rdn_translate(X_101235,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_101236,rdn_pos(rdnn(n9)))
| ~ rdn_translate(n11,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| sum(X_101235,X_101236,n11) ),
inference(subst,[],[refute_0_82:[bind(X_100335,$fot(X_101235)),bind(X_100336,$fot(X_101236)),bind(X_100337,$fot(n11))]]) ).
cnf(refute_0_84,plain,
( ~ rdn_translate(X_101235,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_101236,rdn_pos(rdnn(n9)))
| sum(X_101235,X_101236,n11) ),
inference(resolve,[$cnf( rdn_translate(n11,rdn_pos(rdn(rdnn(n1),rdnn(n1)))) )],[refute_0_33,refute_0_83]) ).
cnf(refute_0_85,plain,
( ~ rdn_translate(X_101239,rdn_pos(rdnn(n9)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| sum(n2,X_101239,n11) ),
inference(subst,[],[refute_0_84:[bind(X_101235,$fot(n2)),bind(X_101236,$fot(X_101239))]]) ).
cnf(refute_0_86,plain,
( ~ rdn_translate(X_101239,rdn_pos(rdnn(n9)))
| sum(n2,X_101239,n11) ),
inference(resolve,[$cnf( rdn_translate(n2,rdn_pos(rdnn(n2))) )],[refute_0_8,refute_0_85]) ).
cnf(refute_0_87,plain,
( ~ rdn_translate(n9,rdn_pos(rdnn(n9)))
| sum(n2,n9,n11) ),
inference(subst,[],[refute_0_86:[bind(X_101239,$fot(n9))]]) ).
cnf(refute_0_88,plain,
sum(n2,n9,n11),
inference(resolve,[$cnf( rdn_translate(n9,rdn_pos(rdnn(n9))) )],[refute_0_57,refute_0_87]) ).
cnf(refute_0_89,plain,
skolemFOFtoCNF_Z4 = n11,
inference(resolve,[$cnf( sum(n2,n9,n11) )],[refute_0_88,refute_0_76]) ).
cnf(refute_0_90,plain,
( skolemFOFtoCNF_Z2 != n11
| skolemFOFtoCNF_Z4 != n11
| skolemFOFtoCNF_Z2 = skolemFOFtoCNF_Z4 ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z4) ),[1],$fot(n11)]]) ).
cnf(refute_0_91,plain,
( skolemFOFtoCNF_Z2 != n11
| skolemFOFtoCNF_Z2 = skolemFOFtoCNF_Z4 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z4,n11) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
skolemFOFtoCNF_Z2 != n11,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z2,skolemFOFtoCNF_Z4) )],[refute_0_91,refute_0_49]) ).
cnf(refute_0_93,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z2,n11) )],[refute_0_48,refute_0_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM332+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 : n025.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 : Thu Jul 7 00:42:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 37.54/37.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.54/37.73
% 37.54/37.73 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.54/37.74
%------------------------------------------------------------------------------