TSTP Solution File: NUM312+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM312+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 : 300s
% DateTime : Wed May 31 12:24:50 EDT 2023
% Result : Theorem 15.80s 2.38s
% Output : CNFRefutation 15.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 16 unt; 0 def)
% Number of atoms : 81 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 80 ( 36 ~; 32 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 72 (; 71 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f287,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f294,axiom,
! [X1,X2,Y,Z] :
( ( sum(X1,Y,Z)
& sum(X2,Y,Z) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f297,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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
! [X] :
( sum(X,n3,n5)
=> X = n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ! [X] :
( sum(X,n3,n5)
=> X = n2 ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f407,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f409,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f716,plain,
! [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) ),
inference(pre_NNF_transformation,[status(esa)],[f287]) ).
fof(f717,plain,
! [X,Y,Z] :
( ! [RDN_Z] :
( ! [RDN_X,RDN_Y] :
( ~ 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) ),
inference(miniscoping,[status(esa)],[f716]) ).
fof(f718,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X0,rdn_pos(X1))
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_add_with_carry(rdnn(n0),X1,X3,X4)
| ~ rdn_translate(X5,rdn_pos(X4))
| sum(X0,X2,X5) ),
inference(cnf_transformation,[status(esa)],[f717]) ).
fof(f737,plain,
! [X1,X2,Y,Z] :
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z)
| X1 = X2 ),
inference(pre_NNF_transformation,[status(esa)],[f294]) ).
fof(f738,plain,
! [X1,X2] :
( ! [Y,Z] :
( ~ sum(X1,Y,Z)
| ~ sum(X2,Y,Z) )
| X1 = X2 ),
inference(miniscoping,[status(esa)],[f737]) ).
fof(f739,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X1,X2)
| X0 = X3 ),
inference(cnf_transformation,[status(esa)],[f738]) ).
fof(f747,plain,
! [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)) ),
inference(pre_NNF_transformation,[status(esa)],[f297]) ).
fof(f748,plain,
! [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)) ),
inference(miniscoping,[status(esa)],[f747]) ).
fof(f749,plain,
! [X0,X1,X2,X3,X4] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
| rdn_add_with_carry(rdnn(X3),rdnn(X0),rdnn(X1),rdnn(X4)) ),
inference(cnf_transformation,[status(esa)],[f748]) ).
fof(f784,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[status(esa)],[f325]) ).
fof(f811,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[status(esa)],[f352]) ).
fof(f861,plain,
? [X] :
( sum(X,n3,n5)
& X != n2 ),
inference(pre_NNF_transformation,[status(esa)],[f403]) ).
fof(f862,plain,
( sum(sk0_0,n3,n5)
& sk0_0 != n2 ),
inference(skolemization,[status(esa)],[f861]) ).
fof(f863,plain,
sum(sk0_0,n3,n5),
inference(cnf_transformation,[status(esa)],[f862]) ).
fof(f864,plain,
sk0_0 != n2,
inference(cnf_transformation,[status(esa)],[f862]) ).
fof(f868,plain,
! [X0] :
( ~ sum(X0,n3,n5)
| X0 = sk0_0 ),
inference(resolution,[status(thm)],[f739,f863]) ).
fof(f5333,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n5)) ),
inference(resolution,[status(thm)],[f749,f811]) ).
fof(f5398,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolution,[status(thm)],[f5333,f784]) ).
fof(f5452,plain,
! [X0,X1,X2] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n5)))
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f5398,f718]) ).
fof(f6161,plain,
! [X0,X1] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| sum(X0,n3,X1) ),
inference(resolution,[status(thm)],[f5452,f407]) ).
fof(f6397,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| sum(X0,n3,n5) ),
inference(resolution,[status(thm)],[f6161,f409]) ).
fof(f6398,plain,
sum(n2,n3,n5),
inference(resolution,[status(thm)],[f6397,f406]) ).
fof(f6399,plain,
n2 = sk0_0,
inference(resolution,[status(thm)],[f6398,f868]) ).
fof(f6400,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6399,f864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM312+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35 % Computer : n004.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue May 30 09:45:22 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Drodi V3.5.1
% 15.80/2.38 % Refutation found
% 15.80/2.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 15.80/2.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.80/2.45 % Elapsed time: 2.088947 seconds
% 15.80/2.45 % CPU time: 16.218348 seconds
% 15.80/2.45 % Memory used: 177.216 MB
%------------------------------------------------------------------------------