%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM339+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 : n024.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 12:27:58 PM UTC 2025
% Result : Theorem 36.95s 5.00s
% Output : CNFRefutation 36.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 19
% Syntax : Number of formulae : 71 ( 43 unt; 0 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 112 ( 49 ~; 46 |; 10 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 63 ( 4 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(show_lower_boundary,plain,
? [X] : difference(nn127,n1,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',show_lower_boundary) ).
fof(show_lower_boundary_negated,plain,
~ ? [X] : difference(nn127,n1,X),
inference(negate_conjecture,[status(cth)],[show_lower_boundary]) ).
cnf(406,plain,
~ difference(nn127,n1,X0),
inference(cnf,[status(esa)],[show_lower_boundary_negated]) ).
cnf(l0,plain,
~ difference(nn127,n1,nn128),
inference(instantiation,[status(thm)],[406]) ).
fof(minus_entry_point,plain,
! [X,Y,Z] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ),
file('Axioms/NUM005+2.ax',minus_entry_point) ).
cnf(299,plain,
( ~ sum(X0,X1,X2)
| difference(X2,X0,X1) ),
inference(cnf,[status(esa)],[minus_entry_point]) ).
cnf(l1,plain,
( ~ sum(n1,nn128,nn127)
| difference(nn127,n1,nn128) ),
inference(instantiation,[status(thm)],[299]) ).
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(l2,plain,
( ~ rdn_translate(n1,rdn_pos(rdnn(n1)))
| ~ rdn_translate(nn128,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1)))))
| ~ rdn_translate(nn127,rdn_neg(rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1)))))
| ~ rdn_positive_less(rdnn(n1),rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n1),rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))),rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))
| sum(n1,nn128,nn127) ),
inference(instantiation,[status(thm)],[292]) ).
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(l16,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(instantiation,[status(thm)],[1]) ).
fof(add_digit_rdn_rdn,plain,
! [C,D1,D2,O2,RD,RO,ID,IC1,IC2,NC] :
( ( rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1))
& rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2))
& rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(NC),rdnn(n0))
& rdn_add_with_carry(rdnn(NC),rdnn(n0),O2,RO)
& rdn_non_zero(O2)
& rdn_non_zero(RO) )
=> rdn_add_with_carry(rdnn(C),rdnn(D1),rdn(rdnn(D2),O2),rdn(rdnn(RD),RO)) ),
file('Axioms/NUM005+2.ax',add_digit_rdn_rdn) ).
cnf(303,plain,
( ~ rdn_non_zero(X0)
| ~ rdn_non_zero(X1)
| ~ rdn_add_with_carry(rdnn(X2),rdnn(n0),X0,X1)
| ~ rdn_digit_add(rdnn(X3),rdnn(X4),rdnn(X5),rdnn(X6))
| ~ rdn_digit_add(rdnn(X5),rdnn(X7),rdnn(X8),rdnn(X9))
| ~ rdn_digit_add(rdnn(X6),rdnn(X9),rdnn(X2),rdnn(n0))
| rdn_add_with_carry(rdnn(X7),rdnn(X3),rdn(rdnn(X4),X0),rdn(rdnn(X8),X1)) ),
inference(cnf,[status(esa)],[add_digit_rdn_rdn]) ).
cnf(l1210,plain,
( ~ rdn_non_zero(rdn(rdnn(n2),rdnn(n1)))
| ~ rdn_non_zero(rdn(rdnn(n2),rdnn(n1)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(n2),rdnn(n1)))
| ~ rdn_digit_add(rdnn(n1),rdnn(n7),rdnn(n8),rdnn(n0))
| ~ rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0))
| ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n1),rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))),rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1)))) ),
inference(instantiation,[status(thm)],[303]) ).
fof(rdn_extra_digits_positive_less,plain,
! [D,Db,Ob] :
( rdn_non_zero(Ob)
=> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
file('Axioms/NUM005+1.ax',rdn_extra_digits_positive_less) ).
cnf(277,plain,
( ~ rdn_non_zero(X0)
| rdn_positive_less(rdnn(X1),rdn(rdnn(X2),X0)) ),
inference(cnf,[status(esa)],[rdn_extra_digits_positive_less]) ).
cnf(l962,plain,
( ~ rdn_non_zero(rdn(rdnn(n2),rdnn(n1)))
| rdn_positive_less(rdnn(n1),rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1)))) ),
inference(instantiation,[status(thm)],[277]) ).
fof(rdn_non_zero_by_structure,plain,
! [D,O] :
( rdn_non_zero(O)
=> rdn_non_zero(rdn(rdnn(D),O)) ),
file('Axioms/NUM005+1.ax',rdn_non_zero_by_structure) ).
cnf(279,plain,
( ~ rdn_non_zero(X0)
| rdn_non_zero(rdn(rdnn(X1),X0)) ),
inference(cnf,[status(esa)],[rdn_non_zero_by_structure]) ).
cnf(l1215,plain,
( ~ rdn_non_zero(rdnn(n1))
| rdn_non_zero(rdn(rdnn(n2),rdnn(n1))) ),
inference(instantiation,[status(thm)],[279]) ).
cnf(l1230,plain,
( ~ rdn_non_zero(rdnn(n1))
| ~ rdn_non_zero(rdnn(n1))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n1),rdnn(n1))
| ~ rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(n2),rdnn(n0))
| ~ rdn_digit_add(rdnn(n2),rdnn(n0),rdnn(n2),rdnn(n0))
| ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n0),rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(n2),rdnn(n1))) ),
inference(instantiation,[status(thm)],[303]) ).
fof(rdnn127,plain,
rdn_translate(nn127,rdn_neg(rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))))),
file('Axioms/NUM005+0.ax',rdnn127) ).
cnf(254,plain,
rdn_translate(nn127,rdn_neg(rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))))),
inference(cnf,[status(esa)],[rdnn127]) ).
cnf(l911,plain,
rdn_translate(nn127,rdn_neg(rdn(rdnn(n7),rdn(rdnn(n2),rdnn(n1))))),
inference(instantiation,[status(thm)],[254]) ).
fof(rdn_non_zero_by_digit,plain,
! [X] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ),
file('Axioms/NUM005+1.ax',rdn_non_zero_by_digit) ).
cnf(278,plain,
( ~ rdn_non_zero_digit(rdnn(X0))
| rdn_non_zero(rdnn(X0)) ),
inference(cnf,[status(esa)],[rdn_non_zero_by_digit]) ).
cnf(l1235,plain,
( ~ rdn_non_zero_digit(rdnn(n1))
| rdn_non_zero(rdnn(n1)) ),
inference(instantiation,[status(thm)],[278]) ).
cnf(l964,plain,
( ~ rdn_non_zero(rdnn(n1))
| rdn_non_zero(rdn(rdnn(n2),rdnn(n1))) ),
inference(instantiation,[status(thm)],[279]) ).
cnf(l1232,plain,
( ~ rdn_non_zero_digit(rdnn(n1))
| rdn_non_zero(rdnn(n1)) ),
inference(instantiation,[status(thm)],[278]) ).
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(l1240,plain,
( ~ rdn_digit_add(rdnn(n0),rdnn(n1),rdnn(n1),rdnn(n0))
| ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n1),rdnn(n1)) ),
inference(instantiation,[status(thm)],[301]) ).
fof(rdn_digit_add_n0_n2_n2_n0,plain,
rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(n2),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n0_n2_n2_n0) ).
cnf(308,plain,
rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(n2),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n0_n2_n2_n0]) ).
cnf(l1270,plain,
rdn_digit_add(rdnn(n0),rdnn(n2),rdnn(n2),rdnn(n0)),
inference(instantiation,[status(thm)],[308]) ).
fof(rdn_digit1,plain,
rdn_non_zero_digit(rdnn(n1)),
file('Axioms/NUM005+1.ax',rdn_digit1) ).
cnf(256,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(cnf,[status(esa)],[rdn_digit1]) ).
cnf(l1238,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(instantiation,[status(thm)],[256]) ).
cnf(l1020,plain,
( ~ rdn_non_zero_digit(rdnn(n1))
| rdn_non_zero(rdnn(n1)) ),
inference(instantiation,[status(thm)],[278]) ).
fof(rdn_digit_add_n8_n0_n8_n0,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n8_n0_n8_n0) ).
cnf(386,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n8_n0_n8_n0]) ).
cnf(l1211,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(instantiation,[status(thm)],[386]) ).
fof(rdn_digit_add_n0_n1_n1_n0,plain,
rdn_digit_add(rdnn(n0),rdnn(n1),rdnn(n1),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n0_n1_n1_n0) ).
cnf(307,plain,
rdn_digit_add(rdnn(n0),rdnn(n1),rdnn(n1),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n0_n1_n1_n0]) ).
cnf(l1247,plain,
rdn_digit_add(rdnn(n0),rdnn(n1),rdnn(n1),rdnn(n0)),
inference(instantiation,[status(thm)],[307]) ).
fof(rdn_digit_add_n0_n0_n0_n0,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n0_n0_n0_n0) ).
cnf(306,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n0_n0_n0_n0]) ).
cnf(l1450,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(instantiation,[status(thm)],[306]) ).
cnf(l1213,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(instantiation,[status(thm)],[306]) ).
fof(rdnn128,plain,
rdn_translate(nn128,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))),
file('Axioms/NUM005+0.ax',rdnn128) ).
cnf(255,plain,
rdn_translate(nn128,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))),
inference(cnf,[status(esa)],[rdnn128]) ).
cnf(l6,plain,
rdn_translate(nn128,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))),
inference(instantiation,[status(thm)],[255]) ).
cnf(l1223,plain,
( ~ rdn_non_zero_digit(rdnn(n1))
| rdn_non_zero(rdnn(n1)) ),
inference(instantiation,[status(thm)],[278]) ).
fof(rdn_digit_add_n1_n0_n1_n0,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n1_n0_n1_n0) ).
cnf(316,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n1_n0_n1_n0]) ).
cnf(l1269,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
inference(instantiation,[status(thm)],[316]) ).
fof(rdn_digit_add_n2_n0_n2_n0,plain,
rdn_digit_add(rdnn(n2),rdnn(n0),rdnn(n2),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n2_n0_n2_n0) ).
cnf(326,plain,
rdn_digit_add(rdnn(n2),rdnn(n0),rdnn(n2),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n2_n0_n2_n0]) ).
cnf(l1243,plain,
rdn_digit_add(rdnn(n2),rdnn(n0),rdnn(n2),rdnn(n0)),
inference(instantiation,[status(thm)],[326]) ).
cnf(l1224,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(instantiation,[status(thm)],[256]) ).
cnf(l1089,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(instantiation,[status(thm)],[256]) ).
cnf(l1250,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(instantiation,[status(thm)],[256]) ).
fof(rdn_digit_add_n1_n7_n8_n0,plain,
rdn_digit_add(rdnn(n1),rdnn(n7),rdnn(n8),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n1_n7_n8_n0) ).
cnf(323,plain,
rdn_digit_add(rdnn(n1),rdnn(n7),rdnn(n8),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n1_n7_n8_n0]) ).
cnf(l1227,plain,
rdn_digit_add(rdnn(n1),rdnn(n7),rdnn(n8),rdnn(n0)),
inference(instantiation,[status(thm)],[323]) ).
cnf(l1214,plain,
( ~ rdn_non_zero(rdnn(n1))
| rdn_non_zero(rdn(rdnn(n2),rdnn(n1))) ),
inference(instantiation,[status(thm)],[279]) ).
cnf(l1217,plain,
( ~ rdn_non_zero_digit(rdnn(n1))
| rdn_non_zero(rdnn(n1)) ),
inference(instantiation,[status(thm)],[278]) ).
cnf(l1284,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(instantiation,[status(thm)],[256]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l16,l1210,l962,l1215,l1230,l911,l1235,l964,l1232,l1240,l1270,l1238,l1020,l1211,l1247,l1450,l1213,l6,l1223,l1269,l1243,l1224,l1089,l1250,l1227,l1214,l1217,l1284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM339+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n024.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 11:38:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.34 % launching worker at depth: 2
% 0.19/0.34 % launching worker at depth: 4
% 0.19/0.34 % launching worker at depth: 1
% 0.19/0.34 % launching worker at depth: 3
% 0.19/0.34 % launching worker at depth: 5
% 0.19/0.34 % launching worker at depth: 6
% 0.19/0.34 % launching worker at depth: 7
% 0.19/0.34 % launching worker at depth: 8
% 0.19/0.35 % launching worker at depth: 9
% 0.19/0.35 % launching worker at depth: 10
% 0.19/0.35 % launching worker at depth: 11
% 0.19/0.56 % launching worker at depth: 12
% 33.96/4.62 % launching worker at depth: 13
% 36.95/5.00 % SZS status Theorem for theBenchmark
% 36.95/5.00 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------