TSTP Solution File: NUM313+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM313+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 : Tue Apr 30 20:30:34 EDT 2024
% Result : Theorem 9.56s 1.62s
% Output : CNFRefutation 10.26s
% 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(f295,axiom,
! [X,Y1,Y2,Z] :
( ( sum(X,Y1,Z)
& sum(X,Y2,Z) )
=> Y1 = Y2 ),
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(n2,X,n5)
=> X = n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ! [X] :
( sum(n2,X,n5)
=> X = n3 ),
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(f740,plain,
! [X,Y1,Y2,Z] :
( ~ sum(X,Y1,Z)
| ~ sum(X,Y2,Z)
| Y1 = Y2 ),
inference(pre_NNF_transformation,[status(esa)],[f295]) ).
fof(f741,plain,
! [Y1,Y2] :
( ! [X,Z] :
( ~ sum(X,Y1,Z)
| ~ sum(X,Y2,Z) )
| Y1 = Y2 ),
inference(miniscoping,[status(esa)],[f740]) ).
fof(f742,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X2)
| X1 = X3 ),
inference(cnf_transformation,[status(esa)],[f741]) ).
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(n2,X,n5)
& X != n3 ),
inference(pre_NNF_transformation,[status(esa)],[f403]) ).
fof(f862,plain,
( sum(n2,sk0_0,n5)
& sk0_0 != n3 ),
inference(skolemization,[status(esa)],[f861]) ).
fof(f863,plain,
sum(n2,sk0_0,n5),
inference(cnf_transformation,[status(esa)],[f862]) ).
fof(f864,plain,
sk0_0 != n3,
inference(cnf_transformation,[status(esa)],[f862]) ).
fof(f869,plain,
! [X0] :
( ~ sum(n2,X0,n5)
| X0 = sk0_0 ),
inference(resolution,[status(thm)],[f742,f863]) ).
fof(f5738,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(f5794,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolution,[status(thm)],[f5738,f784]) ).
fof(f5830,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)],[f5794,f718]) ).
fof(f6192,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)],[f5830,f407]) ).
fof(f6286,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| sum(X0,n3,n5) ),
inference(resolution,[status(thm)],[f6192,f409]) ).
fof(f6287,plain,
sum(n2,n3,n5),
inference(resolution,[status(thm)],[f6286,f406]) ).
fof(f6292,plain,
n3 = sk0_0,
inference(resolution,[status(thm)],[f6287,f869]) ).
fof(f6293,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6292,f864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM313+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n007.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 20:40:47 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.6.0
% 9.56/1.62 % Refutation found
% 9.56/1.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.56/1.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.26/1.67 % Elapsed time: 1.335485 seconds
% 10.26/1.67 % CPU time: 10.369961 seconds
% 10.26/1.67 % Total memory used: 190.287 MB
% 10.26/1.67 % Net memory used: 187.079 MB
%------------------------------------------------------------------------------