%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM342+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 : 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 12:27:58 PM UTC 2025
% Result : Theorem 5.48s 1.10s
% Output : CNFRefutation 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 23 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 56 ( 25 ~; 22 |; 6 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_and_difference,plain,
? [X,Y] :
( sum(X,Y,n8)
& difference(X,Y,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_and_difference) ).
fof(sum_and_difference_negated,plain,
~ ? [X,Y] :
( sum(X,Y,n8)
& difference(X,Y,n0) ),
inference(negate_conjecture,[status(cth)],[sum_and_difference]) ).
cnf(406,plain,
( ~ sum(X0,X1,n8)
| ~ difference(X0,X1,n0) ),
inference(cnf,[status(esa)],[sum_and_difference_negated]) ).
cnf(l0,plain,
( ~ sum(n4,n4,n8)
| ~ difference(n4,n4,n0) ),
inference(instantiation,[status(thm)],[406]) ).
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(l1,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n8,rdn_pos(rdnn(n8)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8))
| sum(n4,n4,n8) ),
inference(instantiation,[status(thm)],[290]) ).
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(l2,plain,
( ~ sum(n4,n0,n4)
| difference(n4,n4,n0) ),
inference(instantiation,[status(thm)],[299]) ).
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(l19,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(instantiation,[status(thm)],[8]) ).
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(l147,plain,
( ~ rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0))
| ~ rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)) ),
inference(instantiation,[status(thm)],[301]) ).
fof(rdn_digit_add_n4_n4_n8_n0,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n4_n4_n8_n0) ).
cnf(350,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n4_n4_n8_n0]) ).
cnf(l152,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(instantiation,[status(thm)],[350]) ).
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(l3,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(instantiation,[status(thm)],[4]) ).
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(l153,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(instantiation,[status(thm)],[386]) ).
cnf(l7,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(instantiation,[status(thm)],[4]) ).
cnf(l5,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4))
| sum(n4,n0,n4) ),
inference(instantiation,[status(thm)],[290]) ).
cnf(l107,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(instantiation,[status(thm)],[4]) ).
fof(rdn0,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('Axioms/NUM005+0.ax',rdn0) ).
cnf(0,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf,[status(esa)],[rdn0]) ).
cnf(l18,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(instantiation,[status(thm)],[0]) ).
cnf(l31,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(instantiation,[status(thm)],[4]) ).
cnf(l129,plain,
( ~ rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0))
| ~ rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4)) ),
inference(instantiation,[status(thm)],[301]) ).
fof(rdn_digit_add_n4_n0_n4_n0,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n4_n0_n4_n0) ).
cnf(346,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n4_n0_n4_n0]) ).
cnf(l131,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(instantiation,[status(thm)],[346]) ).
cnf(l130,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(instantiation,[status(thm)],[346]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l19,l147,l152,l3,l153,l7,l5,l107,l18,l31,l129,l131,l130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM342+1 : TPTP v9.0.0. Released v3.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/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 11:38:34 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.36 % launching worker at depth: 1
% 0.14/0.36 % launching worker at depth: 2
% 0.14/0.36 % launching worker at depth: 3
% 0.14/0.36 % launching worker at depth: 4
% 0.14/0.36 % launching worker at depth: 5
% 0.14/0.36 % launching worker at depth: 6
% 0.14/0.36 % launching worker at depth: 7
% 0.14/0.36 % launching worker at depth: 8
% 0.14/0.37 % launching worker at depth: 9
% 0.14/0.37 % launching worker at depth: 10
% 0.20/0.42 % launching worker at depth: 11
% 5.48/1.10 % SZS status Theorem for theBenchmark
% 5.48/1.10 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------