TSTP Solution File: NUM317+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM317+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 12:24:51 EDT 2023
% Result : Theorem 212.31s 27.08s
% Output : CNFRefutation 213.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 50 ( 22 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 154 ( 73 ~; 71 |; 6 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 90 (; 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f270,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f275,axiom,
! [X,Y,Z] :
( ( rdn_positive_less(rdnn(X),rdnn(Y))
& rdn_positive_less(rdnn(Y),rdnn(Z)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f290,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_positive_less(RDN_Y,RDN_X)
& rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)
& rdn_translate(Z,rdn_pos(RDN_Z)) )
=> sum(X,Y,Z) ),
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,
sum(n5,nn2,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ sum(n5,nn2,n3),
inference(negated_conjecture,[status(cth)],[f402]) ).
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(f533,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[status(esa)],[f130]) ).
fof(f671,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[status(esa)],[f268]) ).
fof(f672,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[status(esa)],[f269]) ).
fof(f673,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[status(esa)],[f270]) ).
fof(f678,plain,
! [X,Y,Z] :
( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(pre_NNF_transformation,[status(esa)],[f275]) ).
fof(f679,plain,
! [X,Z] :
( ! [Y] :
( ~ rdn_positive_less(rdnn(X),rdnn(Y))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z)) )
| rdn_positive_less(rdnn(X),rdnn(Z)) ),
inference(miniscoping,[status(esa)],[f678]) ).
fof(f680,plain,
! [X0,X1,X2] :
( ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(cnf_transformation,[status(esa)],[f679]) ).
fof(f725,plain,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| sum(X,Y,Z) ),
inference(pre_NNF_transformation,[status(esa)],[f290]) ).
fof(f726,plain,
! [X,Y,Z] :
( ! [RDN_Z] :
( ! [RDN_X,RDN_Y] :
( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X) )
| ~ rdn_translate(Z,rdn_pos(RDN_Z)) )
| sum(X,Y,Z) ),
inference(miniscoping,[status(esa)],[f725]) ).
fof(f727,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X0,rdn_pos(X1))
| ~ rdn_translate(X2,rdn_neg(X3))
| ~ rdn_positive_less(X3,X1)
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X1)
| ~ rdn_translate(X5,rdn_pos(X4))
| sum(X0,X2,X5) ),
inference(cnf_transformation,[status(esa)],[f726]) ).
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,
~ sum(n5,nn2,n3),
inference(cnf_transformation,[status(esa)],[f403]) ).
fof(f12197,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(X3),rdnn(n0))
| ~ rdn_translate(X4,rdn_pos(rdnn(X3)))
| ~ rdn_translate(X5,rdn_neg(rdnn(X0)))
| ~ rdn_positive_less(rdnn(X0),rdnn(X3))
| ~ rdn_translate(X6,rdn_pos(rdnn(X1)))
| sum(X4,X5,X6) ),
inference(resolution,[status(thm)],[f749,f727]) ).
fof(f35329,plain,
! [X0,X1,X2,X3,X4] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X3,rdn_pos(rdnn(X2)))
| ~ rdn_positive_less(rdnn(n2),rdnn(X2))
| ~ rdn_translate(X4,rdn_pos(rdnn(X0)))
| sum(X3,nn2,X4) ),
inference(resolution,[status(thm)],[f12197,f533]) ).
fof(f35426,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X3,rdn_pos(rdnn(X2)))
| ~ rdn_translate(X4,rdn_pos(rdnn(X0)))
| sum(X3,nn2,X4)
| ~ rdn_positive_less(rdnn(n2),rdnn(X5))
| ~ rdn_positive_less(rdnn(X5),rdnn(X2)) ),
inference(resolution,[status(thm)],[f35329,f680]) ).
fof(f35539,plain,
! [X0,X1,X2,X3,X4] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X3,rdn_pos(rdnn(X2)))
| ~ rdn_translate(X4,rdn_pos(rdnn(X0)))
| sum(X3,nn2,X4)
| ~ rdn_positive_less(rdnn(n3),rdnn(X2)) ),
inference(resolution,[status(thm)],[f35426,f671]) ).
fof(f37079,plain,
( spl0_2751
<=> rdn_positive_less(rdnn(n3),rdnn(n5)) ),
introduced(split_symbol_definition) ).
fof(f37080,plain,
( rdn_positive_less(rdnn(n3),rdnn(n5))
| ~ spl0_2751 ),
inference(component_clause,[status(thm)],[f37079]) ).
fof(f37081,plain,
( ~ rdn_positive_less(rdnn(n3),rdnn(n5))
| spl0_2751 ),
inference(component_clause,[status(thm)],[f37079]) ).
fof(f37450,plain,
! [X0] :
( ~ rdn_positive_less(rdnn(n3),rdnn(X0))
| ~ rdn_positive_less(rdnn(X0),rdnn(n5))
| spl0_2751 ),
inference(resolution,[status(thm)],[f37081,f680]) ).
fof(f39313,plain,
( ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| spl0_2751 ),
inference(resolution,[status(thm)],[f37450,f672]) ).
fof(f39314,plain,
( $false
| spl0_2751 ),
inference(forward_subsumption_resolution,[status(thm)],[f39313,f673]) ).
fof(f39315,plain,
spl0_2751,
inference(contradiction_clause,[status(thm)],[f39314]) ).
fof(f39357,plain,
! [X0,X1,X2,X3] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n5),rdnn(n0))
| ~ rdn_translate(X2,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X3,rdn_pos(rdnn(X0)))
| sum(X2,nn2,X3)
| ~ spl0_2751 ),
inference(resolution,[status(thm)],[f37080,f35539]) ).
fof(f42391,plain,
! [X0,X1,X2] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(n5),rdnn(n0))
| ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| sum(X1,nn2,X2)
| ~ spl0_2751 ),
inference(resolution,[status(thm)],[f39357,f811]) ).
fof(f47326,plain,
! [X0,X1] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| sum(X0,nn2,X1)
| ~ spl0_2751 ),
inference(resolution,[status(thm)],[f42391,f784]) ).
fof(f51965,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
| sum(n5,nn2,X0)
| ~ spl0_2751 ),
inference(resolution,[status(thm)],[f47326,f409]) ).
fof(f61581,plain,
( sum(n5,nn2,n3)
| ~ spl0_2751 ),
inference(resolution,[status(thm)],[f51965,f407]) ).
fof(f61582,plain,
( $false
| ~ spl0_2751 ),
inference(forward_subsumption_resolution,[status(thm)],[f61581,f861]) ).
fof(f61583,plain,
~ spl0_2751,
inference(contradiction_clause,[status(thm)],[f61582]) ).
fof(f61584,plain,
$false,
inference(sat_refutation,[status(thm)],[f39315,f61583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM317+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n003.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 09:56:53 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 212.31/27.08 % Refutation found
% 212.31/27.08 % SZS status Theorem for theBenchmark: Theorem is valid
% 212.31/27.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 213.66/27.33 % Elapsed time: 26.998323 seconds
% 213.66/27.33 % CPU time: 213.611602 seconds
% 213.66/27.33 % Memory used: 677.467 MB
%------------------------------------------------------------------------------