%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM334+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:26:00 EDT 2022
% Result : Theorem 43.91s 44.17s
% Output : CNFRefutation 43.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 24 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 103 ( 50 ~; 43 |; 5 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 78 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))) ).
fof(rdn7,axiom,
rdn_translate(n7,rdn_pos(rdnn(n7))) ).
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(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_n5_n2_n7_n0,axiom,
rdn_digit_add(rdnn(n5),rdnn(n2),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(diff_n7_n5_n2,conjecture,
difference(n7,n5,n2) ).
fof(subgoal_0,plain,
difference(n7,n5,n2),
inference(strip,[],[diff_n7_n5_n2]) ).
fof(negate_0_0,plain,
~ difference(n7,n5,n2),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y,Z] :
( ~ difference(X,Y,Z)
<=> ~ sum(Y,Z,X) ),
inference(canonicalize,[],[minus_entry_point]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ~ difference(X,Y,Z)
<=> ~ sum(Y,Z,X) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ( ~ difference(X,Y,Z)
| sum(Y,Z,X) )
& ( ~ sum(Y,Z,X)
| difference(X,Y,Z) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ sum(Y,Z,X)
| difference(X,Y,Z) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(canonicalize,[],[rdn7]) ).
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_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n5_n2_n7_n0]) ).
fof(normalize_0_8,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n7_n0_n7_n0]) ).
fof(normalize_0_9,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_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(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,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_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(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
~ difference(n7,n5,n2),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( ~ sum(Y,Z,X)
| difference(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ sum(n5,n2,n7)
| difference(n7,n5,n2) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(n7)),bind(Y,$fot(n5)),bind(Z,$fot(n2))]]) ).
cnf(refute_0_2,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
| rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ rdn_digit_add(rdnn(X_67996),rdnn(X_67997),rdnn(n7),rdnn(n0))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_67996),rdnn(X_67997),rdnn(n7)) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(n0)),bind(D1,$fot(X_67996)),bind(D2,$fot(X_67997)),bind(ID,$fot(n7)),bind(RD,$fot(n7))]]) ).
cnf(refute_0_9,plain,
( ~ rdn_digit_add(rdnn(X_67996),rdnn(X_67997),rdnn(n7),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_67996),rdnn(X_67997),rdnn(n7)) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n2),rdnn(n7)) ),
inference(subst,[],[refute_0_9:[bind(X_67996,$fot(n5)),bind(X_67997,$fot(n2))]]) ).
cnf(refute_0_11,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n2),rdnn(n7)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)) )],[refute_0_5,refute_0_10]) ).
cnf(refute_0_12,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_12]) ).
cnf(refute_0_13,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n2),rdnn(n7))
| ~ rdn_translate(X_119808,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_119809,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_119810,rdn_pos(rdnn(n7)))
| sum(X_119808,X_119809,X_119810) ),
inference(subst,[],[refute_0_12:[bind(RDN_X,$fot(rdnn(n5))),bind(RDN_Y,$fot(rdnn(n2))),bind(RDN_Z,$fot(rdnn(n7))),bind(X,$fot(X_119808)),bind(Y,$fot(X_119809)),bind(Z,$fot(X_119810))]]) ).
cnf(refute_0_14,plain,
( ~ rdn_translate(X_119808,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_119809,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X_119810,rdn_pos(rdnn(n7)))
| sum(X_119808,X_119809,X_119810) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n2),rdnn(n7)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ rdn_translate(X_120407,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_120409,rdn_pos(rdnn(n7)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| sum(X_120407,n2,X_120409) ),
inference(subst,[],[refute_0_14:[bind(X_119808,$fot(X_120407)),bind(X_119809,$fot(n2)),bind(X_119810,$fot(X_120409))]]) ).
cnf(refute_0_16,plain,
( ~ rdn_translate(X_120407,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X_120409,rdn_pos(rdnn(n7)))
| sum(X_120407,n2,X_120409) ),
inference(resolve,[$cnf( rdn_translate(n2,rdn_pos(rdnn(n2))) )],[refute_0_4,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ rdn_translate(X_120411,rdn_pos(rdnn(n7)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sum(n5,n2,X_120411) ),
inference(subst,[],[refute_0_16:[bind(X_120407,$fot(n5)),bind(X_120409,$fot(X_120411))]]) ).
cnf(refute_0_18,plain,
( ~ rdn_translate(X_120411,rdn_pos(rdnn(n7)))
| sum(n5,n2,X_120411) ),
inference(resolve,[$cnf( rdn_translate(n5,rdn_pos(rdnn(n5))) )],[refute_0_3,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ rdn_translate(n7,rdn_pos(rdnn(n7)))
| sum(n5,n2,n7) ),
inference(subst,[],[refute_0_18:[bind(X_120411,$fot(n7))]]) ).
cnf(refute_0_20,plain,
sum(n5,n2,n7),
inference(resolve,[$cnf( rdn_translate(n7,rdn_pos(rdnn(n7))) )],[refute_0_2,refute_0_19]) ).
cnf(refute_0_21,plain,
difference(n7,n5,n2),
inference(resolve,[$cnf( sum(n5,n2,n7) )],[refute_0_20,refute_0_1]) ).
cnf(refute_0_22,plain,
~ difference(n7,n5,n2),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( difference(n7,n5,n2) )],[refute_0_21,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM334+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.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 17:09:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 43.91/44.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.91/44.17
% 43.91/44.17 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 43.91/44.17
%------------------------------------------------------------------------------