TSTP Solution File: NUM342+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM342+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:26:03 EDT 2022
% Result : Theorem 25.86s 26.10s
% Output : CNFRefutation 25.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 25 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 123 ( 60 ~; 50 |; 8 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 90 ( 0 sgn 52 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))) ).
fof(rdn4,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))) ).
fof(rdn8,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))) ).
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_n4_n0_n4_n0,axiom,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)) ).
fof(rdn_digit_add_n4_n4_n8_n0,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)) ).
fof(rdn_digit_add_n8_n0_n8_n0,axiom,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)) ).
fof(sum_and_difference,conjecture,
? [X,Y] :
( sum(X,Y,n8)
& difference(X,Y,n0) ) ).
fof(subgoal_0,plain,
? [X,Y] :
( sum(X,Y,n8)
& difference(X,Y,n0) ),
inference(strip,[],[sum_and_difference]) ).
fof(negate_0_0,plain,
~ ? [X,Y] :
( sum(X,Y,n8)
& difference(X,Y,n0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ difference(X,Y,n0)
| ~ sum(X,Y,n8) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ difference(X,Y,n0)
| ~ sum(X,Y,n8) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(canonicalize,[],[rdn4]) ).
fof(normalize_0_3,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(canonicalize,[],[rdn8]) ).
fof(normalize_0_4,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_5,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_4]) ).
fof(normalize_0_6,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n4_n4_n8_n0]) ).
fof(normalize_0_7,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n8_n0_n8_n0]) ).
fof(normalize_0_8,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_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(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ difference(X,Y,Z)
<=> ~ sum(Y,Z,X) ),
inference(canonicalize,[],[minus_entry_point]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ difference(X,Y,Z)
<=> ~ sum(Y,Z,X) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ( ~ difference(X,Y,Z)
| sum(Y,Z,X) )
& ( ~ sum(Y,Z,X)
| difference(X,Y,Z) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ sum(Y,Z,X)
| difference(X,Y,Z) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(canonicalize,[],[rdn0]) ).
fof(normalize_0_15,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(canonicalize,[],[rdn_digit_add_n4_n0_n4_n0]) ).
cnf(refute_0_0,plain,
( ~ difference(X,Y,n0)
| ~ sum(X,Y,n8) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ difference(n4,n4,n0)
| ~ sum(n4,n4,n8) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(n4)),bind(Y,$fot(n4))]]) ).
cnf(refute_0_2,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_3,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,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_5]) ).
cnf(refute_0_5,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8))
| ~ rdn_translate(Y,rdn_pos(rdnn(n4)))
| ~ rdn_translate(Z,rdn_pos(rdnn(n8)))
| sum(Y,Y,Z) ),
inference(subst,[],[refute_0_4:[bind(RDN_X,$fot(rdnn(n4))),bind(RDN_Y,$fot(rdnn(n4))),bind(RDN_Z,$fot(rdnn(n8))),bind(X,$fot(Y))]]) ).
cnf(refute_0_6,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,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_9]) ).
cnf(refute_0_9,plain,
( ~ rdn_digit_add(rdnn(X_68694),rdnn(X_68695),rdnn(n8),rdnn(n0))
| ~ rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_68694),rdnn(X_68695),rdnn(n8)) ),
inference(subst,[],[refute_0_8:[bind(C,$fot(n0)),bind(D1,$fot(X_68694)),bind(D2,$fot(X_68695)),bind(ID,$fot(n8)),bind(RD,$fot(n8))]]) ).
cnf(refute_0_10,plain,
( ~ rdn_digit_add(rdnn(X_68694),rdnn(X_68695),rdnn(n8),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X_68694),rdnn(X_68695),rdnn(n8)) ),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)) ),
inference(subst,[],[refute_0_10:[bind(X_68694,$fot(n4)),bind(X_68695,$fot(n4))]]) ).
cnf(refute_0_12,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ rdn_translate(Y,rdn_pos(rdnn(n4)))
| ~ rdn_translate(Z,rdn_pos(rdnn(n8)))
| sum(Y,Y,Z) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)) )],[refute_0_12,refute_0_5]) ).
cnf(refute_0_14,plain,
( ~ rdn_translate(X_69002,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n8,rdn_pos(rdnn(n8)))
| sum(X_69002,X_69002,n8) ),
inference(subst,[],[refute_0_13:[bind(Y,$fot(X_69002)),bind(Z,$fot(n8))]]) ).
cnf(refute_0_15,plain,
( ~ rdn_translate(X_69002,rdn_pos(rdnn(n4)))
| sum(X_69002,X_69002,n8) ),
inference(resolve,[$cnf( rdn_translate(n8,rdn_pos(rdnn(n8))) )],[refute_0_3,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| sum(n4,n4,n8) ),
inference(subst,[],[refute_0_15:[bind(X_69002,$fot(n4))]]) ).
cnf(refute_0_17,plain,
sum(n4,n4,n8),
inference(resolve,[$cnf( rdn_translate(n4,rdn_pos(rdnn(n4))) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
~ difference(n4,n4,n0),
inference(resolve,[$cnf( sum(n4,n4,n8) )],[refute_0_17,refute_0_1]) ).
cnf(refute_0_19,plain,
( ~ sum(Y,Z,X)
| difference(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_20,plain,
( ~ sum(n4,n0,n4)
| difference(n4,n4,n0) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(n4)),bind(Y,$fot(n4)),bind(Z,$fot(n0))]]) ).
cnf(refute_0_21,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_22,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_23,plain,
( ~ rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4)) ),
inference(subst,[],[refute_0_8:[bind(C,$fot(n0)),bind(D1,$fot(n4)),bind(D2,$fot(n0)),bind(ID,$fot(n4)),bind(RD,$fot(n4))]]) ).
cnf(refute_0_24,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4)),
inference(resolve,[$cnf( rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4))
| ~ rdn_translate(X_32623,rdn_pos(rdnn(n0)))
| ~ rdn_translate(X_32624,rdn_pos(rdnn(n4)))
| sum(X_32624,X_32623,X_32624) ),
inference(subst,[],[refute_0_4:[bind(RDN_X,$fot(rdnn(n4))),bind(RDN_Y,$fot(rdnn(n0))),bind(RDN_Z,$fot(rdnn(n4))),bind(X,$fot(X_32624)),bind(Y,$fot(X_32623)),bind(Z,$fot(X_32624))]]) ).
cnf(refute_0_26,plain,
( ~ rdn_translate(X_32623,rdn_pos(rdnn(n0)))
| ~ rdn_translate(X_32624,rdn_pos(rdnn(n4)))
| sum(X_32624,X_32623,X_32624) ),
inference(resolve,[$cnf( rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ rdn_translate(X_32637,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| sum(X_32637,n0,X_32637) ),
inference(subst,[],[refute_0_26:[bind(X_32623,$fot(n0)),bind(X_32624,$fot(X_32637))]]) ).
cnf(refute_0_28,plain,
( ~ rdn_translate(X_32637,rdn_pos(rdnn(n4)))
| sum(X_32637,n0,X_32637) ),
inference(resolve,[$cnf( rdn_translate(n0,rdn_pos(rdnn(n0))) )],[refute_0_21,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| sum(n4,n0,n4) ),
inference(subst,[],[refute_0_28:[bind(X_32637,$fot(n4))]]) ).
cnf(refute_0_30,plain,
sum(n4,n0,n4),
inference(resolve,[$cnf( rdn_translate(n4,rdn_pos(rdnn(n4))) )],[refute_0_2,refute_0_29]) ).
cnf(refute_0_31,plain,
difference(n4,n4,n0),
inference(resolve,[$cnf( sum(n4,n0,n4) )],[refute_0_30,refute_0_20]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( difference(n4,n4,n0) )],[refute_0_31,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM342+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 : n008.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 09:35:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 25.86/26.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.86/26.10
% 25.86/26.10 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.95/26.10
%------------------------------------------------------------------------------