%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM324+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 : n029.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 0.21s 0.53s
% Output : CNFRefutation 0.21s
% 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 : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 31 ( 1 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_what_nn5_nn3,plain,
? [X] : sum(X,nn5,nn3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_what_nn5_nn3) ).
fof(sum_what_nn5_nn3_negated,plain,
~ ? [X] : sum(X,nn5,nn3),
inference(negate_conjecture,[status(cth)],[sum_what_nn5_nn3]) ).
cnf(406,plain,
~ sum(X0,nn5,nn3),
inference(cnf,[status(esa)],[sum_what_nn5_nn3_negated]) ).
cnf(l0,plain,
~ sum(n2,nn5,nn3),
inference(instantiation,[status(thm)],[406]) ).
fof(sum_entry_point_pos_neg_1,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_X,RDN_Y)
& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)
& rdn_translate(Z,rdn_neg(RDN_Z)) )
=> sum(X,Y,Z) ),
file('Axioms/NUM005+2.ax',sum_entry_point_pos_neg_1) ).
cnf(292,plain,
( ~ rdn_translate(X0,rdn_pos(X1))
| ~ rdn_translate(X2,rdn_neg(X3))
| ~ rdn_translate(X4,rdn_neg(X5))
| ~ rdn_positive_less(X1,X3)
| ~ rdn_add_with_carry(rdnn(n0),X1,X5,X3)
| sum(X0,X2,X4) ),
inference(cnf,[status(esa)],[sum_entry_point_pos_neg_1]) ).
cnf(l1,plain,
( ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5)))
| ~ rdn_translate(nn3,rdn_neg(rdnn(n3)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| sum(n2,nn5,nn3) ),
inference(instantiation,[status(thm)],[292]) ).
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(l83,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(rdnn3,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
file('Axioms/NUM005+0.ax',rdnn3) ).
cnf(130,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(cnf,[status(esa)],[rdnn3]) ).
cnf(l5,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(instantiation,[status(thm)],[130]) ).
fof(rdnn5,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('Axioms/NUM005+0.ax',rdnn5) ).
cnf(132,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf,[status(esa)],[rdnn5]) ).
cnf(l3,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(instantiation,[status(thm)],[132]) ).
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(l36,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(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(l38,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(instantiation,[status(thm)],[269]) ).
fof(rdn2,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('Axioms/NUM005+0.ax',rdn2) ).
cnf(2,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf,[status(esa)],[rdn2]) ).
cnf(l2,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(instantiation,[status(thm)],[2]) ).
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(l84,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(instantiation,[status(thm)],[329]) ).
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(l85,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(instantiation,[status(thm)],[356]) ).
cnf(l45,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_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(l55,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(instantiation,[status(thm)],[267]) ).
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(l56,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(instantiation,[status(thm)],[268]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l83,l5,l3,l36,l38,l2,l84,l85,l45,l55,l56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM324+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Jul 21 11:36:04 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.21/0.35 % launching worker at depth: 3
% 0.21/0.35 % launching worker at depth: 1
% 0.21/0.35 % launching worker at depth: 2
% 0.21/0.35 % launching worker at depth: 4
% 0.21/0.35 % launching worker at depth: 5
% 0.21/0.35 % launching worker at depth: 6
% 0.21/0.35 % launching worker at depth: 7
% 0.21/0.35 % launching worker at depth: 8
% 0.21/0.35 % launching worker at depth: 9
% 0.21/0.36 % launching worker at depth: 10
% 0.21/0.40 % launching worker at depth: 11
% 0.21/0.53 % SZS status Theorem for theBenchmark
% 0.21/0.53 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------