%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM321+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n023.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 : Fri Jul 25 12:27:56 PM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 29 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 52 ( 23 ~; 20 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 31 ( 1 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_n5_nn2_what,plain,
? [X] : sum(n5,nn2,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n5_nn2_what) ).
fof(sum_n5_nn2_what_negated,plain,
~ ? [X] : sum(n5,nn2,X),
inference(negate_conjecture,[status(cth)],[sum_n5_nn2_what]) ).
cnf(406,plain,
~ sum(n5,nn2,X0),
inference(cnf,[status(esa)],[sum_n5_nn2_what_negated]) ).
cnf(l0,plain,
~ sum(n5,nn2,n3),
inference(instantiation,[status(thm)],[406]) ).
fof(sum_entry_point_pos_neg_2,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) ),
file('Axioms/NUM005+2.ax',sum_entry_point_pos_neg_2) ).
cnf(293,plain,
( ~ rdn_translate(X0,rdn_pos(X1))
| ~ rdn_translate(X2,rdn_neg(X3))
| ~ rdn_translate(X4,rdn_pos(X5))
| ~ rdn_positive_less(X3,X1)
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X1)
| sum(X0,X2,X4) ),
inference(cnf,[status(esa)],[sum_entry_point_pos_neg_2]) ).
cnf(l1,plain,
( ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| sum(n5,nn2,n3) ),
inference(instantiation,[status(thm)],[293]) ).
fof(rdnn2,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('Axioms/NUM005+0.ax',rdnn2) ).
cnf(129,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf,[status(esa)],[rdnn2]) ).
cnf(l11,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(instantiation,[status(thm)],[129]) ).
fof(rdn5,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('Axioms/NUM005+0.ax',rdn5) ).
cnf(5,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf,[status(esa)],[rdn5]) ).
cnf(l2,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(instantiation,[status(thm)],[5]) ).
fof(add_digit_digit_digit,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)) ),
file('Axioms/NUM005+2.ax',add_digit_digit_digit) ).
cnf(301,plain,
( ~ 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,[status(esa)],[add_digit_digit_digit]) ).
cnf(l38,plain,
( ~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)) ),
inference(instantiation,[status(thm)],[301]) ).
fof(rdn_digit_add_n5_n0_n5_n0,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).
cnf(356,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n5_n0_n5_n0]) ).
cnf(l39,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(instantiation,[status(thm)],[356]) ).
fof(rdn_digit_add_n2_n3_n5_n0,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n2_n3_n5_n0) ).
cnf(329,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n2_n3_n5_n0]) ).
cnf(l45,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(instantiation,[status(thm)],[329]) ).
fof(rdn_positive_less_transitivity,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)) ),
file('Axioms/NUM005+1.ax',rdn_positive_less_transitivity) ).
cnf(274,plain,
( ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(cnf,[status(esa)],[rdn_positive_less_transitivity]) ).
cnf(l46,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n4))
| ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| rdn_positive_less(rdnn(n2),rdnn(n5)) ),
inference(instantiation,[status(thm)],[274]) ).
fof(rdn3,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('Axioms/NUM005+0.ax',rdn3) ).
cnf(3,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf,[status(esa)],[rdn3]) ).
cnf(l4,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(instantiation,[status(thm)],[3]) ).
cnf(l48,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| rdn_positive_less(rdnn(n2),rdnn(n4)) ),
inference(instantiation,[status(thm)],[274]) ).
fof(rdn_positive_less34,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('Axioms/NUM005+1.ax',rdn_positive_less34) ).
cnf(268,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf,[status(esa)],[rdn_positive_less34]) ).
cnf(l61,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(instantiation,[status(thm)],[268]) ).
fof(rdn_positive_less45,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('Axioms/NUM005+1.ax',rdn_positive_less45) ).
cnf(269,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf,[status(esa)],[rdn_positive_less45]) ).
cnf(l51,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(instantiation,[status(thm)],[269]) ).
fof(rdn_positive_less23,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('Axioms/NUM005+1.ax',rdn_positive_less23) ).
cnf(267,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf,[status(esa)],[rdn_positive_less23]) ).
cnf(l49,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(instantiation,[status(thm)],[267]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l11,l2,l38,l39,l45,l46,l4,l48,l61,l51,l49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM321+1 : TPTP v9.0.0. Released v3.1.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n023.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 : 300
% 0.12/0.33 % DateTime : Mon Jul 21 11:35:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % launching worker at depth: 6
% 0.12/0.35 % launching worker at depth: 1
% 0.12/0.35 % launching worker at depth: 2
% 0.12/0.35 % launching worker at depth: 3
% 0.12/0.35 % launching worker at depth: 4
% 0.12/0.35 % launching worker at depth: 7
% 0.12/0.35 % launching worker at depth: 5
% 0.12/0.35 % launching worker at depth: 8
% 0.12/0.35 % launching worker at depth: 9
% 0.12/0.35 % launching worker at depth: 10
% 0.12/0.39 % launching worker at depth: 11
% 0.19/0.42 % SZS status Theorem for theBenchmark
% 0.19/0.42 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------