%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM331+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 : 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 12:27:57 PM UTC 2025
% Result : Theorem 233.56s 29.67s
% Output : CNFRefutation 233.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 33 unt; 0 def)
% Number of atoms : 87 ( 8 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 70 ( 30 ~; 27 |; 8 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(communative_sum_n6_n7,plain,
! [Z1,Z2] :
( ( sum(n6,n7,Z1)
& sum(n7,n6,Z2) )
=> Z1 = Z2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',communative_sum_n6_n7) ).
fof(communative_sum_n6_n7_negated,plain,
~ ! [Z1,Z2] :
( ( sum(n6,n7,Z1)
& sum(n7,n6,Z2) )
=> Z1 = Z2 ),
inference(negate_conjecture,[status(cth)],[communative_sum_n6_n7]) ).
cnf(406,plain,
sum(n6,n7,sK1),
inference(cnf,[status(esa)],[communative_sum_n6_n7_negated]) ).
cnf(l0,plain,
sum(n6,n7,sK1),
inference(instantiation,[status(thm)],[406]) ).
fof(unique_sum,plain,
! [X,Y,Z1,Z2] :
( ( sum(X,Y,Z1)
& sum(X,Y,Z2) )
=> Z1 = Z2 ),
file('Axioms/NUM005+2.ax',unique_sum) ).
cnf(296,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf,[status(esa)],[unique_sum]) ).
cnf(l1,plain,
( ~ sum(n6,n7,n13)
| ~ sum(n6,n7,sK1)
| n13 = sK1 ),
inference(instantiation,[status(thm)],[296]) ).
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(l240,plain,
( ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| ~ rdn_translate(n7,rdn_pos(rdnn(n7)))
| ~ rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n7),rdn(rdnn(n3),rdnn(n1)))
| sum(n6,n7,n13) ),
inference(instantiation,[status(thm)],[290]) ).
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(l243,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(instantiation,[status(thm)],[6]) ).
fof(add_digit_digit_rdn,plain,
! [C,D1,D2,ID,RD,IC1,IC2] :
( ( 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(n1),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdn(rdnn(RD),rdnn(n1))) ),
file('Axioms/NUM005+2.ax',add_digit_digit_rdn) ).
cnf(302,plain,
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X2),rdnn(X4),rdnn(X5),rdnn(X6))
| ~ rdn_digit_add(rdnn(X3),rdnn(X6),rdnn(n1),rdnn(n0))
| rdn_add_with_carry(rdnn(X4),rdnn(X0),rdnn(X1),rdn(rdnn(X5),rdnn(n1))) ),
inference(cnf,[status(esa)],[add_digit_digit_rdn]) ).
cnf(l260,plain,
( ~ rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1))
| ~ rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0))
| ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n7),rdn(rdnn(n3),rdnn(n1))) ),
inference(instantiation,[status(thm)],[302]) ).
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(l262,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
inference(instantiation,[status(thm)],[316]) ).
fof(rdn13,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
file('Axioms/NUM005+0.ax',rdn13) ).
cnf(13,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(cnf,[status(esa)],[rdn13]) ).
cnf(l241,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(instantiation,[status(thm)],[13]) ).
fof(rdn_digit_add_n6_n7_n3_n1,plain,
rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n6_n7_n3_n1) ).
cnf(373,plain,
rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)),
inference(cnf,[status(esa)],[rdn_digit_add_n6_n7_n3_n1]) ).
cnf(l271,plain,
rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)),
inference(instantiation,[status(thm)],[373]) ).
cnf(l124,plain,
( ~ sum(n7,n6,sK1)
| ~ sum(n7,n6,sK2)
| sK1 = sK2 ),
inference(instantiation,[status(thm)],[296]) ).
fof(rdn_digit_add_n3_n0_n3_n0,plain,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n3_n0_n3_n0) ).
cnf(336,plain,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n3_n0_n3_n0]) ).
cnf(l261,plain,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
inference(instantiation,[status(thm)],[336]) ).
cnf(408,plain,
sK1 != sK2,
inference(cnf,[status(esa)],[communative_sum_n6_n7_negated]) ).
cnf(l162,plain,
sK1 != sK2,
inference(instantiation,[status(thm)],[408]) ).
cnf(l44,plain,
( ~ rdn_translate(n7,rdn_pos(rdnn(n7)))
| ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| ~ rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1))))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1)))
| sum(n7,n6,n13) ),
inference(instantiation,[status(thm)],[290]) ).
cnf(l130,plain,
( ~ rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1))
| ~ rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0))
| ~ rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1))) ),
inference(instantiation,[status(thm)],[302]) ).
cnf(l321,plain,
rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
inference(instantiation,[status(thm)],[316]) ).
cnf(l53,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(instantiation,[status(thm)],[13]) ).
fof(rdn_digit_add_n7_n6_n3_n1,plain,
rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n7_n6_n3_n1) ).
cnf(382,plain,
rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)),
inference(cnf,[status(esa)],[rdn_digit_add_n7_n6_n3_n1]) ).
cnf(l132,plain,
rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)),
inference(instantiation,[status(thm)],[382]) ).
cnf(l123,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(instantiation,[status(thm)],[6]) ).
fof(rdn7,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
file('Axioms/NUM005+0.ax',rdn7) ).
cnf(7,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(cnf,[status(esa)],[rdn7]) ).
cnf(l55,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(instantiation,[status(thm)],[7]) ).
cnf(l250,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(instantiation,[status(thm)],[7]) ).
cnf(l157,plain,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
inference(instantiation,[status(thm)],[336]) ).
cnf(407,plain,
sum(n7,n6,sK2),
inference(cnf,[status(esa)],[communative_sum_n6_n7_negated]) ).
cnf(l134,plain,
sum(n7,n6,sK2),
inference(instantiation,[status(thm)],[407]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l240,l243,l260,l262,l241,l271,l124,l261,l162,l44,l130,l321,l53,l132,l123,l55,l250,l157,l134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM331+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 21 11:36:49 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.36 % launching worker at depth: 10
% 0.18/0.50 % launching worker at depth: 11
% 17.30/2.55 % launching worker at depth: 12
% 233.56/29.67 % SZS status Theorem for theBenchmark
% 233.56/29.67 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------