%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM306+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 : n025.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 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 16
% Syntax : Number of formulae : 52 ( 38 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 77 ( 33 ~; 30 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_n23_n34_n57,plain,
sum(n23,n34,n57),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_n23_n34_n57) ).
fof(sum_n23_n34_n57_negated,plain,
~ sum(n23,n34,n57),
inference(negate_conjecture,[status(cth)],[sum_n23_n34_n57]) ).
cnf(406,plain,
~ sum(n23,n34,n57),
inference(cnf,[status(esa)],[sum_n23_n34_n57_negated]) ).
cnf(l0,plain,
~ sum(n23,n34,n57),
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(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2))))
| ~ rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3))))
| ~ rdn_translate(n57,rdn_pos(rdn(rdnn(n7),rdnn(n5))))
| ~ rdn_add_with_carry(rdnn(n0),rdn(rdnn(n3),rdnn(n2)),rdn(rdnn(n4),rdnn(n3)),rdn(rdnn(n7),rdnn(n5)))
| sum(n23,n34,n57) ),
inference(instantiation,[status(thm)],[290]) ).
fof(rdn23,plain,
rdn_translate(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2)))),
file('Axioms/NUM005+0.ax',rdn23) ).
cnf(23,plain,
rdn_translate(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2)))),
inference(cnf,[status(esa)],[rdn23]) ).
cnf(l2,plain,
rdn_translate(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2)))),
inference(instantiation,[status(thm)],[23]) ).
fof(rdn57,plain,
rdn_translate(n57,rdn_pos(rdn(rdnn(n7),rdnn(n5)))),
file('Axioms/NUM005+0.ax',rdn57) ).
cnf(57,plain,
rdn_translate(n57,rdn_pos(rdn(rdnn(n7),rdnn(n5)))),
inference(cnf,[status(esa)],[rdn57]) ).
cnf(l4,plain,
rdn_translate(n57,rdn_pos(rdn(rdnn(n7),rdnn(n5)))),
inference(instantiation,[status(thm)],[57]) ).
fof(rdn34,plain,
rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3)))),
file('Axioms/NUM005+0.ax',rdn34) ).
cnf(34,plain,
rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3)))),
inference(cnf,[status(esa)],[rdn34]) ).
cnf(l11,plain,
rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3)))),
inference(instantiation,[status(thm)],[34]) ).
fof(add_rdn_rdn_rdn,plain,
! [C,D1,O1,D2,O2,RD,RO,ID,IC1,IC2,RC] :
( ( 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(RC),rdnn(n0))
& rdn_add_with_carry(rdnn(RC),O1,O2,RO)
& rdn_non_zero(O1)
& rdn_non_zero(O2)
& rdn_non_zero(RO) )
=> rdn_add_with_carry(rdnn(C),rdn(rdnn(D1),O1),rdn(rdnn(D2),O2),rdn(rdnn(RD),RO)) ),
file('Axioms/NUM005+2.ax',add_rdn_rdn_rdn) ).
cnf(304,plain,
( ~ rdn_non_zero(X0)
| ~ rdn_non_zero(X1)
| ~ rdn_non_zero(X2)
| ~ rdn_add_with_carry(rdnn(X3),X0,X1,X2)
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(X6),rdnn(X7))
| ~ rdn_digit_add(rdnn(X6),rdnn(X8),rdnn(X9),rdnn(X10))
| ~ rdn_digit_add(rdnn(X7),rdnn(X10),rdnn(X3),rdnn(n0))
| rdn_add_with_carry(rdnn(X8),rdn(rdnn(X4),X0),rdn(rdnn(X5),X1),rdn(rdnn(X9),X2)) ),
inference(cnf,[status(esa)],[add_rdn_rdn_rdn]) ).
cnf(l55,plain,
( ~ rdn_non_zero(rdnn(n2))
| ~ rdn_non_zero(rdnn(n3))
| ~ rdn_non_zero(rdnn(n5))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| ~ rdn_digit_add(rdnn(n3),rdnn(n4),rdnn(n7),rdnn(n0))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0))
| ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdn(rdnn(n3),rdnn(n2)),rdn(rdnn(n4),rdnn(n3)),rdn(rdnn(n7),rdnn(n5))) ),
inference(instantiation,[status(thm)],[304]) ).
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(l56,plain,
( ~ rdn_non_zero_digit(rdnn(n5))
| rdn_non_zero(rdnn(n5)) ),
inference(instantiation,[status(thm)],[278]) ).
fof(rdn_digit5,plain,
rdn_non_zero_digit(rdnn(n5)),
file('Axioms/NUM005+1.ax',rdn_digit5) ).
cnf(260,plain,
rdn_non_zero_digit(rdnn(n5)),
inference(cnf,[status(esa)],[rdn_digit5]) ).
cnf(l62,plain,
rdn_non_zero_digit(rdnn(n5)),
inference(instantiation,[status(thm)],[260]) ).
cnf(l58,plain,
( ~ rdn_non_zero_digit(rdnn(n2))
| rdn_non_zero(rdnn(n2)) ),
inference(instantiation,[status(thm)],[278]) ).
fof(rdn_digit2,plain,
rdn_non_zero_digit(rdnn(n2)),
file('Axioms/NUM005+1.ax',rdn_digit2) ).
cnf(257,plain,
rdn_non_zero_digit(rdnn(n2)),
inference(cnf,[status(esa)],[rdn_digit2]) ).
cnf(l59,plain,
rdn_non_zero_digit(rdnn(n2)),
inference(instantiation,[status(thm)],[257]) ).
cnf(l57,plain,
( ~ rdn_non_zero_digit(rdnn(n3))
| rdn_non_zero(rdnn(n3)) ),
inference(instantiation,[status(thm)],[278]) ).
fof(rdn_digit3,plain,
rdn_non_zero_digit(rdnn(n3)),
file('Axioms/NUM005+1.ax',rdn_digit3) ).
cnf(258,plain,
rdn_non_zero_digit(rdnn(n3)),
inference(cnf,[status(esa)],[rdn_digit3]) ).
cnf(l64,plain,
rdn_non_zero_digit(rdnn(n3)),
inference(instantiation,[status(thm)],[258]) ).
fof(rdn_digit_add_n3_n4_n7_n0,plain,
rdn_digit_add(rdnn(n3),rdnn(n4),rdnn(n7),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n3_n4_n7_n0) ).
cnf(340,plain,
rdn_digit_add(rdnn(n3),rdnn(n4),rdnn(n7),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n3_n4_n7_n0]) ).
cnf(l97,plain,
rdn_digit_add(rdnn(n3),rdnn(n4),rdnn(n7),rdnn(n0)),
inference(instantiation,[status(thm)],[340]) ).
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(l99,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(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(l108,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(instantiation,[status(thm)],[356]) ).
fof(rdn_digit_add_n7_n0_n7_n0,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
file('Axioms/NUM005+2.ax',rdn_digit_add_n7_n0_n7_n0) ).
cnf(376,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(cnf,[status(esa)],[rdn_digit_add_n7_n0_n7_n0]) ).
cnf(l98,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(instantiation,[status(thm)],[376]) ).
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(l96,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(instantiation,[status(thm)],[306]) ).
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(l112,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(instantiation,[status(thm)],[329]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l4,l11,l55,l56,l62,l58,l59,l57,l64,l97,l99,l108,l98,l96,l112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM306+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
% 0.13/0.33 % Computer : n025.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 11:33:49 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 4
% 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: 5
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.35 % launching worker at depth: 10
% 0.19/0.38 % launching worker at depth: 11
% 0.19/0.46 % SZS status Theorem for theBenchmark
% 0.19/0.46 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------