%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM316+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:52:01 AM UTC 2026
% Result : Theorem 223.13s 248.34s
% Output : Proof 223.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 78 ( 57 unt; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 121 ( 58 ~; 54 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 81 ( 0 sgn 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('NUM005+0.ax',rdn2) ).
fof(rdnn3,axiom,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
file('NUM005+0.ax',rdnn3) ).
fof(rdnn5,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('NUM005+0.ax',rdnn5) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('NUM005+1.ax',rdn_positive_less23) ).
fof(rdn_positive_less34,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('NUM005+1.ax',rdn_positive_less34) ).
fof(rdn_positive_less45,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('NUM005+1.ax',rdn_positive_less45) ).
fof(rdn_positive_less_transitivity,axiom,
! [X,Y,Z] :
( ( rdn_positive_less(rdnn(Y),rdnn(Z))
& rdn_positive_less(rdnn(X),rdnn(Y)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) ),
file('NUM005+1.ax',rdn_positive_less_transitivity) ).
fof(sum_entry_point_pos_neg_1,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(Z,rdn_neg(RDN_Z))
& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)
& rdn_positive_less(RDN_X,RDN_Y)
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_translate(X,rdn_pos(RDN_X)) )
=> sum(X,Y,Z) ),
file('NUM005+2.ax',sum_entry_point_pos_neg_1) ).
fof(add_digit_digit_digit,axiom,
! [C,D1,D2,RD,ID] :
( ( rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
& rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
file('NUM005+2.ax',add_digit_digit_digit) ).
fof(rdn_digit_add_n2_n3_n5_n0,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n2_n3_n5_n0) ).
fof(rdn_digit_add_n5_n0_n5_n0,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).
fof(sum_n2_nn5_nn3,conjecture,
sum(n2,nn5,nn3),
file('theBenchmark.p',sum_n2_nn5_nn3) ).
fof(f_3_1,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(fof_nnf,[status(thm)],[rdn2]) ).
fof(f_3_2,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(definitional_conversion,[status(esa)],[f_3_1]) ).
cnf(f_3_3,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_131_1,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(fof_nnf,[status(thm)],[rdnn3]) ).
fof(f_131_2,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(definitional_conversion,[status(esa)],[f_131_1]) ).
cnf(f_131_3,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_133_1,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(fof_nnf,[status(thm)],[rdnn5]) ).
fof(f_133_2,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(definitional_conversion,[status(esa)],[f_133_1]) ).
cnf(f_133_3,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_268_1,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(fof_nnf,[status(thm)],[rdn_positive_less23]) ).
fof(f_268_2,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(definitional_conversion,[status(esa)],[f_268_1]) ).
cnf(f_268_3,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_1,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(fof_nnf,[status(thm)],[rdn_positive_less34]) ).
fof(f_269_2,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(definitional_conversion,[status(esa)],[f_269_1]) ).
cnf(f_269_3,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_1,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(fof_nnf,[status(thm)],[rdn_positive_less45]) ).
fof(f_270_2,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(definitional_conversion,[status(esa)],[f_270_1]) ).
cnf(f_270_3,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(clausify,[status(thm)],[f_270_2]) ).
fof(f_275_1,plain,
! [X,Y,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ),
inference(fof_nnf,[status(thm)],[rdn_positive_less_transitivity]) ).
fof(f_275_2,plain,
! [U_2,U_1,U_0] :
( rdn_positive_less(rdnn(U_2),rdnn(U_0))
| ~ rdn_positive_less(rdnn(U_1),rdnn(U_0))
| ~ rdn_positive_less(rdnn(U_2),rdnn(U_1)) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
! [U_1,U_0,U_2] :
( rdn_positive_less(rdnn(U_2),rdnn(U_0))
| ~ rdn_positive_less(rdnn(U_1),rdnn(U_0))
| ~ rdn_positive_less(rdnn(U_2),rdnn(U_1)) ),
inference(definitional_conversion,[status(esa)],[f_275_2]) ).
cnf(f_275_4,plain,
( rdn_positive_less(rdnn(U_2),rdnn(U_0))
| ~ rdn_positive_less(rdnn(U_1),rdnn(U_0))
| ~ rdn_positive_less(rdnn(U_2),rdnn(U_1)) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_289_1,plain,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( sum(X,Y,Z)
| ~ rdn_translate(Z,rdn_neg(RDN_Z))
| ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)
| ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ),
inference(fof_nnf,[status(thm)],[sum_entry_point_pos_neg_1]) ).
fof(f_289_2,plain,
! [U_60,U_59,U_58,U_57,U_56,U_55] :
( sum(U_60,U_59,U_58)
| ~ rdn_translate(U_58,rdn_neg(U_55))
| ~ rdn_add_with_carry(rdnn(n0),U_57,U_55,U_56)
| ~ rdn_positive_less(U_57,U_56)
| ~ rdn_translate(U_59,rdn_neg(U_56))
| ~ rdn_translate(U_60,rdn_pos(U_57)) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
! [U_60,U_59,U_58] :
( ! [U_57] :
( ! [U_56] :
( ! [U_55] :
( ~ rdn_translate(U_58,rdn_neg(U_55))
| ~ rdn_add_with_carry(rdnn(n0),U_57,U_55,U_56) )
| ~ rdn_positive_less(U_57,U_56)
| ~ rdn_translate(U_59,rdn_neg(U_56)) )
| ~ rdn_translate(U_60,rdn_pos(U_57)) )
| sum(U_60,U_59,U_58) ),
inference(miniscope,[status(thm)],[f_289_2]) ).
fof(f_289_4,plain,
! [U_58,U_59,U_57,U_55,U_56,U_60] :
( ~ rdn_translate(U_58,rdn_neg(U_55))
| ~ rdn_add_with_carry(rdnn(n0),U_57,U_55,U_56)
| ~ rdn_positive_less(U_57,U_56)
| ~ rdn_translate(U_59,rdn_neg(U_56))
| ~ rdn_translate(U_60,rdn_pos(U_57))
| sum(U_60,U_59,U_58) ),
inference(definitional_conversion,[status(esa)],[f_289_3]) ).
cnf(f_289_5,plain,
( ~ rdn_translate(U_58,rdn_neg(U_55))
| ~ rdn_add_with_carry(rdnn(n0),U_57,U_55,U_56)
| ~ rdn_positive_less(U_57,U_56)
| ~ rdn_translate(U_59,rdn_neg(U_56))
| ~ rdn_translate(U_60,rdn_pos(U_57))
| sum(U_60,U_59,U_58) ),
inference(clausify,[status(thm)],[f_289_4]) ).
fof(f_297_1,plain,
! [C,D1,D2,RD,ID] :
( rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
| ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0)) ),
inference(fof_nnf,[status(thm)],[add_digit_digit_digit]) ).
fof(f_297_2,plain,
! [U_100,U_99,U_98,U_97,U_96] :
( rdn_add_with_carry(rdnn(U_100),rdnn(U_99),rdnn(U_98),rdnn(U_97))
| ~ rdn_digit_add(rdnn(U_96),rdnn(U_100),rdnn(U_97),rdnn(n0))
| ~ rdn_digit_add(rdnn(U_99),rdnn(U_98),rdnn(U_96),rdnn(n0)) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_100,U_99,U_98,U_97] :
( ! [U_96] :
( ~ rdn_digit_add(rdnn(U_96),rdnn(U_100),rdnn(U_97),rdnn(n0))
| ~ rdn_digit_add(rdnn(U_99),rdnn(U_98),rdnn(U_96),rdnn(n0)) )
| rdn_add_with_carry(rdnn(U_100),rdnn(U_99),rdnn(U_98),rdnn(U_97)) ),
inference(miniscope,[status(thm)],[f_297_2]) ).
fof(f_297_4,plain,
! [U_98,U_97,U_100,U_99,U_96] :
( ~ rdn_digit_add(rdnn(U_96),rdnn(U_100),rdnn(U_97),rdnn(n0))
| ~ rdn_digit_add(rdnn(U_99),rdnn(U_98),rdnn(U_96),rdnn(n0))
| rdn_add_with_carry(rdnn(U_100),rdnn(U_99),rdnn(U_98),rdnn(U_97)) ),
inference(definitional_conversion,[status(esa)],[f_297_3]) ).
cnf(f_297_5,plain,
( ~ rdn_digit_add(rdnn(U_96),rdnn(U_100),rdnn(U_97),rdnn(n0))
| ~ rdn_digit_add(rdnn(U_99),rdnn(U_98),rdnn(U_96),rdnn(n0))
| rdn_add_with_carry(rdnn(U_100),rdnn(U_99),rdnn(U_98),rdnn(U_97)) ),
inference(clausify,[status(thm)],[f_297_4]) ).
fof(f_325_1,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n2_n3_n5_n0]) ).
fof(f_325_2,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(definitional_conversion,[status(esa)],[f_325_1]) ).
cnf(f_325_3,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_352_1,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n5_n0_n5_n0]) ).
fof(f_352_2,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(definitional_conversion,[status(esa)],[f_352_1]) ).
cnf(f_352_3,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(clausify,[status(thm)],[f_352_2]) ).
fof(f_402_1,negated_conjecture,
~ sum(n2,nn5,nn3),
inference(negate,[status(cth)],[sum_n2_nn5_nn3]) ).
fof(f_402_2,negated_conjecture,
~ sum(n2,nn5,nn3),
inference(definitional_conversion,[status(esa)],[f_402_1]) ).
cnf(f_402_3,negated_conjecture,
~ sum(n2,nn5,nn3),
inference(clausify,[status(thm)],[f_402_2]) ).
cnf(t1,plain,
~ sum(n2,nn5,nn3),
inference(start,[status(thm),parent(0:0)],[f_402_3]) ).
cnf(t2,plain,
( ~ rdn_translate(nn3,rdn_neg(rdnn(n3)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5)))
| sum(n2,nn5,nn3) ),
inference(extension,[status(thm),parent(t1:1)],[f_289_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(extension,[status(thm),parent(t2:2)],[f_133_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(extension,[status(thm),parent(t2:3)],[f_3_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)) ),
inference(extension,[status(thm),parent(t2:4)],[f_297_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(extension,[status(thm),parent(t8:2)],[f_325_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(extension,[status(thm),parent(t8:3)],[f_352_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( ~ rdn_positive_less(rdnn(n4),rdnn(n5))
| ~ rdn_positive_less(rdnn(n2),rdnn(n4))
| rdn_positive_less(rdnn(n2),rdnn(n5)) ),
inference(extension,[status(thm),parent(t2:5)],[f_275_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:5]) ).
cnf(t16,plain,
( ~ rdn_positive_less(rdnn(n3),rdnn(n4))
| ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(rdnn(n2),rdnn(n4)) ),
inference(extension,[status(thm),parent(t14:2)],[f_275_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(extension,[status(thm),parent(t16:2)],[f_268_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(extension,[status(thm),parent(t16:3)],[f_269_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(extension,[status(thm),parent(t14:3)],[f_270_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:3]) ).
cnf(t24,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(extension,[status(thm),parent(t2:6)],[f_131_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t2:6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM316+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/25.44 % CPULimit : 300
% 0.08/25.44 % WCLimit : 300
% 0.08/25.44 % DateTime : Sat Sep 19 18:13:40 UTC 2026
% 0.08/25.44 % CPUTime :
% 223.13/248.34 % SZS status Theorem for theBenchmark
% 223.13/248.34 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------