%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM310+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 : n021.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 12:27:54 PM UTC 2025
% Result : Theorem 4.06s 0.89s
% Output : CNFRefutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 13
% Syntax : Number of formulae : 42 ( 27 unt; 0 def)
% Number of atoms : 79 ( 4 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 68 ( 31 ~; 24 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 42 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_n2_n3_not_n6,plain,
~ sum(n2,n3,n6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n2_n3_not_n6) ).
fof(sum_n2_n3_not_n6_negated,plain,
~ ~ sum(n2,n3,n6),
inference(negate_conjecture,[status(cth)],[sum_n2_n3_not_n6]) ).
cnf(406,plain,
sum(n2,n3,n6),
inference(cnf,[status(esa)],[sum_n2_n3_not_n6_negated]) ).
cnf(l0,plain,
sum(n2,n3,n6),
inference(instantiation,[status(thm)],[406]) ).
fof(unique_RHS,plain,
! [X,Y1,Y2,Z] :
( ( sum(X,Y1,Z)
& sum(X,Y2,Z) )
=> Y1 = Y2 ),
file('Axioms/NUM005+2.ax',unique_RHS) ).
cnf(298,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X2)
| X1 = X3 ),
inference(cnf,[status(esa)],[unique_RHS]) ).
cnf(l1,plain,
( ~ sum(n2,n3,n6)
| ~ sum(n2,n4,n6)
| n3 = n4 ),
inference(instantiation,[status(thm)],[298]) ).
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(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n4),rdnn(n6))
| sum(n2,n4,n6) ),
inference(instantiation,[status(thm)],[290]) ).
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(l16,plain,
( ~ rdn_digit_add(rdnn(n2),rdnn(n4),rdnn(n6),rdnn(n0))
| ~ rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n4),rdnn(n6)) ),
inference(instantiation,[status(thm)],[301]) ).
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(l4,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(instantiation,[status(thm)],[2]) ).
fof(rdn6,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
file('Axioms/NUM005+0.ax',rdn6) ).
cnf(6,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(cnf,[status(esa)],[rdn6]) ).
cnf(l27,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(instantiation,[status(thm)],[6]) ).
fof(rdn_digit_add_n2_n4_n6_n0,plain,
rdn_digit_add(rdnn(n2),rdnn(n4),rdnn(n6),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n2_n4_n6_n0) ).
cnf(330,plain,
rdn_digit_add(rdnn(n2),rdnn(n4),rdnn(n6),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n2_n4_n6_n0]) ).
cnf(l38,plain,
rdn_digit_add(rdnn(n2),rdnn(n4),rdnn(n6),rdnn(n0)),
inference(instantiation,[status(thm)],[330]) ).
fof(rdn4,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('Axioms/NUM005+0.ax',rdn4) ).
cnf(4,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(cnf,[status(esa)],[rdn4]) ).
cnf(l15,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(instantiation,[status(thm)],[4]) ).
fof(rdn_digit_add_n6_n0_n6_n0,plain,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n6_n0_n6_n0) ).
cnf(366,plain,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n6_n0_n6_n0]) ).
cnf(l40,plain,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
inference(instantiation,[status(thm)],[366]) ).
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(l9,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(instantiation,[status(thm)],[3]) ).
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(l7,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n3)))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| less(n4,n4) ),
inference(instantiation,[status(thm)],[280]) ).
fof(less_property,plain,
! [X,Y] :
( less(X,Y)
<=> ( ~ less(Y,X)
& Y != X ) ),
file('Axioms/NUM005+1.ax',less_property) ).
cnf(283,plain,
( ~ less(X0,X1)
| ~ less(X1,X0) ),
inference(cnf,[status(esa)],[less_property]) ).
cnf(l35,plain,
( ~ less(n4,n4)
| ~ less(n4,n4) ),
inference(instantiation,[status(thm)],[283]) ).
cnf(l25,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(instantiation,[status(thm)],[4]) ).
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(l20,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(instantiation,[status(thm)],[268]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l16,l4,l27,l38,l15,l40,l9,l7,l35,l25,l20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM310+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n021.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 11:34:19 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.36 % launching worker at depth: 10
% 0.20/0.43 % launching worker at depth: 11
% 4.06/0.89 % SZS status Theorem for theBenchmark
% 4.06/0.89 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------