%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM344+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/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 12:27:59 PM UTC 2025
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 21 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 54 ( 23 ~; 20 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 15 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(exist_bigger_plus_one,plain,
? [X,Y] :
( sum(X,n1,Y)
& less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exist_bigger_plus_one) ).
fof(exist_bigger_plus_one_negated,plain,
~ ? [X,Y] :
( sum(X,n1,Y)
& less(X,Y) ),
inference(negate_conjecture,[status(cth)],[exist_bigger_plus_one]) ).
cnf(406,plain,
( ~ less(X0,X1)
| ~ sum(X0,n1,X1) ),
inference(cnf,[status(esa)],[exist_bigger_plus_one_negated]) ).
cnf(l0,plain,
( ~ less(n8,n9)
| ~ sum(n8,n1,n9) ),
inference(instantiation,[status(thm)],[406]) ).
fof(less_entry_point_pos_pos,plain,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
=> less(X,Y) ),
file('Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
cnf(280,plain,
( ~ rdn_translate(X0,rdn_pos(X1))
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_positive_less(X1,X3)
| less(X0,X2) ),
inference(cnf,[status(esa)],[less_entry_point_pos_pos]) ).
cnf(l1,plain,
( ~ rdn_translate(n8,rdn_pos(rdnn(n8)))
| ~ rdn_translate(n9,rdn_pos(rdnn(n9)))
| ~ rdn_positive_less(rdnn(n8),rdnn(n9))
| less(n8,n9) ),
inference(instantiation,[status(thm)],[280]) ).
fof(sum_entry_point_pos_pos,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) ),
file('Axioms/NUM005+2.ax',sum_entry_point_pos_pos) ).
cnf(290,plain,
( ~ rdn_translate(X0,rdn_pos(X1))
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X4,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X1,X3,X5)
| sum(X0,X2,X4) ),
inference(cnf,[status(esa)],[sum_entry_point_pos_pos]) ).
cnf(l2,plain,
( ~ rdn_translate(n8,rdn_pos(rdnn(n8)))
| ~ rdn_translate(n1,rdn_pos(rdnn(n1)))
| ~ rdn_translate(n9,rdn_pos(rdnn(n9)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n8),rdnn(n1),rdnn(n9))
| sum(n8,n1,n9) ),
inference(instantiation,[status(thm)],[290]) ).
fof(rdn_positive_less89,plain,
rdn_positive_less(rdnn(n8),rdnn(n9)),
file('Axioms/NUM005+1.ax',rdn_positive_less89) ).
cnf(273,plain,
rdn_positive_less(rdnn(n8),rdnn(n9)),
inference(cnf,[status(esa)],[rdn_positive_less89]) ).
cnf(l5,plain,
rdn_positive_less(rdnn(n8),rdnn(n9)),
inference(instantiation,[status(thm)],[273]) ).
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(l6,plain,
( ~ rdn_digit_add(rdnn(n8),rdnn(n1),rdnn(n9),rdnn(n0))
| ~ rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n8),rdnn(n1),rdnn(n9)) ),
inference(instantiation,[status(thm)],[301]) ).
fof(rdn8,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('Axioms/NUM005+0.ax',rdn8) ).
cnf(8,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(cnf,[status(esa)],[rdn8]) ).
cnf(l8,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(instantiation,[status(thm)],[8]) ).
fof(rdn1,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('Axioms/NUM005+0.ax',rdn1) ).
cnf(1,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(cnf,[status(esa)],[rdn1]) ).
cnf(l4,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(instantiation,[status(thm)],[1]) ).
fof(rdn9,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
file('Axioms/NUM005+0.ax',rdn9) ).
cnf(9,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(cnf,[status(esa)],[rdn9]) ).
cnf(l3,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(instantiation,[status(thm)],[9]) ).
cnf(l11,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(instantiation,[status(thm)],[8]) ).
fof(rdn_digit_add_n8_n1_n9_n0,plain,
rdn_digit_add(rdnn(n8),rdnn(n1),rdnn(n9),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n8_n1_n9_n0) ).
cnf(387,plain,
rdn_digit_add(rdnn(n8),rdnn(n1),rdnn(n9),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n8_n1_n9_n0]) ).
cnf(l13,plain,
rdn_digit_add(rdnn(n8),rdnn(n1),rdnn(n9),rdnn(n0)),
inference(instantiation,[status(thm)],[387]) ).
fof(rdn_digit_add_n9_n0_n9_n0,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n9_n0_n9_n0) ).
cnf(396,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n9_n0_n9_n0]) ).
cnf(l15,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
inference(instantiation,[status(thm)],[396]) ).
cnf(l9,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(instantiation,[status(thm)],[9]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l5,l6,l8,l4,l3,l11,l13,l15,l9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : NUM344+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.10 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.30 % Computer : n023.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Jul 21 11:38:49 EDT 2025
% 0.09/0.30 % CPUTime :
% 0.15/0.32 % launching worker at depth: 1
% 0.15/0.32 % launching worker at depth: 2
% 0.15/0.32 % launching worker at depth: 3
% 0.15/0.32 % launching worker at depth: 4
% 0.15/0.32 % launching worker at depth: 5
% 0.15/0.32 % launching worker at depth: 6
% 0.15/0.32 % launching worker at depth: 7
% 0.15/0.32 % launching worker at depth: 8
% 0.15/0.32 % launching worker at depth: 9
% 0.15/0.34 % launching worker at depth: 10
% 0.15/0.44 % SZS status Theorem for theBenchmark
% 0.15/0.44 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------