%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM306+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 : n013.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 08:52:00 AM UTC 2026
% Result : Theorem 283.66s 283.95s
% Output : Proof 283.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 102 ( 75 unt; 0 def)
% Number of atoms : 197 ( 13 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 179 ( 84 ~; 81 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 123 ( 0 sgn 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn23,axiom,
rdn_translate(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2)))),
file('NUM005+0.ax',rdn23) ).
fof(rdn34,axiom,
rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3)))),
file('NUM005+0.ax',rdn34) ).
fof(rdn57,axiom,
rdn_translate(n57,rdn_pos(rdn(rdnn(n7),rdnn(n5)))),
file('NUM005+0.ax',rdn57) ).
fof(rdn_digit2,axiom,
rdn_non_zero_digit(rdnn(n2)),
file('NUM005+1.ax',rdn_digit2) ).
fof(rdn_digit3,axiom,
rdn_non_zero_digit(rdnn(n3)),
file('NUM005+1.ax',rdn_digit3) ).
fof(rdn_digit5,axiom,
rdn_non_zero_digit(rdnn(n5)),
file('NUM005+1.ax',rdn_digit5) ).
fof(rdn_non_zero_by_digit,axiom,
! [X] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ),
file('NUM005+1.ax',rdn_non_zero_by_digit) ).
fof(sum_entry_point_pos_pos,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(Z,rdn_pos(RDN_Z))
& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_pos(RDN_X)) )
=> sum(X,Y,Z) ),
file('NUM005+2.ax',sum_entry_point_pos_pos) ).
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(add_rdn_rdn_rdn,axiom,
! [C,D1,O1,D2,O2,RD,RO,ID,IC1,IC2,RC] :
( ( rdn_non_zero(RO)
& rdn_non_zero(O2)
& rdn_non_zero(O1)
& rdn_add_with_carry(rdnn(RC),O1,O2,RO)
& rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(RC),rdnn(n0))
& rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2))
& rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) )
=> rdn_add_with_carry(rdnn(C),rdn(rdnn(D1),O1),rdn(rdnn(D2),O2),rdn(rdnn(RD),RO)) ),
file('NUM005+2.ax',add_rdn_rdn_rdn) ).
fof(rdn_digit_add_n0_n0_n0_n0,axiom,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n0_n0_n0_n0) ).
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_n3_n4_n7_n0,axiom,
rdn_digit_add(rdnn(n3),rdnn(n4),rdnn(n7),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n3_n4_n7_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(rdn_digit_add_n7_n0_n7_n0,axiom,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n7_n0_n7_n0) ).
fof(sum_n23_n34_n57,conjecture,
sum(n23,n34,n57),
file('theBenchmark.p',sum_n23_n34_n57) ).
fof(f_24_1,plain,
rdn_translate(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2)))),
inference(fof_nnf,[status(thm)],[rdn23]) ).
cnf(f_24_2,plain,
rdn_translate(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2)))),
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_35_1,plain,
rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3)))),
inference(fof_nnf,[status(thm)],[rdn34]) ).
cnf(f_35_2,plain,
rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3)))),
inference(clausify,[status(thm)],[f_35_1]) ).
fof(f_58_1,plain,
rdn_translate(n57,rdn_pos(rdn(rdnn(n7),rdnn(n5)))),
inference(fof_nnf,[status(thm)],[rdn57]) ).
cnf(f_58_2,plain,
rdn_translate(n57,rdn_pos(rdn(rdnn(n7),rdnn(n5)))),
inference(clausify,[status(thm)],[f_58_1]) ).
fof(f_258_1,plain,
rdn_non_zero_digit(rdnn(n2)),
inference(fof_nnf,[status(thm)],[rdn_digit2]) ).
cnf(f_258_2,plain,
rdn_non_zero_digit(rdnn(n2)),
inference(clausify,[status(thm)],[f_258_1]) ).
fof(f_259_1,plain,
rdn_non_zero_digit(rdnn(n3)),
inference(fof_nnf,[status(thm)],[rdn_digit3]) ).
cnf(f_259_2,plain,
rdn_non_zero_digit(rdnn(n3)),
inference(clausify,[status(thm)],[f_259_1]) ).
fof(f_261_1,plain,
rdn_non_zero_digit(rdnn(n5)),
inference(fof_nnf,[status(thm)],[rdn_digit5]) ).
cnf(f_261_2,plain,
rdn_non_zero_digit(rdnn(n5)),
inference(clausify,[status(thm)],[f_261_1]) ).
fof(f_279_1,plain,
! [X] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(fof_nnf,[status(thm)],[rdn_non_zero_by_digit]) ).
fof(f_279_2,plain,
! [U_13] :
( rdn_non_zero(rdnn(U_13))
| ~ rdn_non_zero_digit(rdnn(U_13)) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
cnf(f_279_3,plain,
( rdn_non_zero(rdnn(U_13))
| ~ rdn_non_zero_digit(rdnn(U_13)) ),
inference(clausify,[status(thm)],[f_279_2]) ).
fof(f_287_1,plain,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( sum(X,Y,Z)
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ),
inference(fof_nnf,[status(thm)],[sum_entry_point_pos_pos]) ).
fof(f_287_2,plain,
! [U_48,U_47,U_46,U_45,U_44,U_43] :
( sum(U_48,U_47,U_46)
| ~ rdn_translate(U_46,rdn_pos(U_43))
| ~ rdn_add_with_carry(rdnn(n0),U_45,U_44,U_43)
| ~ rdn_translate(U_47,rdn_pos(U_44))
| ~ rdn_translate(U_48,rdn_pos(U_45)) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_48,U_47,U_46] :
( ! [U_45] :
( ! [U_44] :
( ! [U_43] :
( ~ rdn_translate(U_46,rdn_pos(U_43))
| ~ rdn_add_with_carry(rdnn(n0),U_45,U_44,U_43) )
| ~ rdn_translate(U_47,rdn_pos(U_44)) )
| ~ rdn_translate(U_48,rdn_pos(U_45)) )
| sum(U_48,U_47,U_46) ),
inference(miniscope,[status(thm)],[f_287_2]) ).
cnf(f_287_4,plain,
( ~ rdn_translate(U_46,rdn_pos(U_43))
| ~ rdn_add_with_carry(rdnn(n0),U_45,U_44,U_43)
| ~ rdn_translate(U_47,rdn_pos(U_44))
| ~ rdn_translate(U_48,rdn_pos(U_45))
| sum(U_48,U_47,U_46) ),
inference(clausify,[status(thm)],[f_287_3]) ).
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]) ).
cnf(f_297_4,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_3]) ).
fof(f_300_1,plain,
! [C,D1,O1,D2,O2,RD,RO,ID,IC1,IC2,RC] :
( rdn_add_with_carry(rdnn(C),rdn(rdnn(D1),O1),rdn(rdnn(D2),O2),rdn(rdnn(RD),RO))
| ~ rdn_non_zero(RO)
| ~ rdn_non_zero(O2)
| ~ rdn_non_zero(O1)
| ~ rdn_add_with_carry(rdnn(RC),O1,O2,RO)
| ~ rdn_digit_add(rdnn(IC1),rdnn(IC2),rdnn(RC),rdnn(n0))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(IC2))
| ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(IC1)) ),
inference(fof_nnf,[status(thm)],[add_rdn_rdn_rdn]) ).
fof(f_300_2,plain,
! [U_128,U_127,U_126,U_125,U_124,U_123,U_122,U_121,U_120,U_119,U_118] :
( rdn_add_with_carry(rdnn(U_128),rdn(rdnn(U_127),U_126),rdn(rdnn(U_125),U_124),rdn(rdnn(U_123),U_122))
| ~ rdn_non_zero(U_122)
| ~ rdn_non_zero(U_124)
| ~ rdn_non_zero(U_126)
| ~ rdn_add_with_carry(rdnn(U_118),U_126,U_124,U_122)
| ~ rdn_digit_add(rdnn(U_120),rdnn(U_119),rdnn(U_118),rdnn(n0))
| ~ rdn_digit_add(rdnn(U_121),rdnn(U_128),rdnn(U_123),rdnn(U_119))
| ~ rdn_digit_add(rdnn(U_127),rdnn(U_125),rdnn(U_121),rdnn(U_120)) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_128,U_127,U_126,U_125,U_124,U_123,U_122] :
( ! [U_121,U_120] :
( ! [U_119] :
( ! [U_118] :
( ~ rdn_add_with_carry(rdnn(U_118),U_126,U_124,U_122)
| ~ rdn_digit_add(rdnn(U_120),rdnn(U_119),rdnn(U_118),rdnn(n0)) )
| ~ rdn_digit_add(rdnn(U_121),rdnn(U_128),rdnn(U_123),rdnn(U_119)) )
| ~ rdn_digit_add(rdnn(U_127),rdnn(U_125),rdnn(U_121),rdnn(U_120)) )
| ~ rdn_non_zero(U_122)
| ~ rdn_non_zero(U_124)
| ~ rdn_non_zero(U_126)
| rdn_add_with_carry(rdnn(U_128),rdn(rdnn(U_127),U_126),rdn(rdnn(U_125),U_124),rdn(rdnn(U_123),U_122)) ),
inference(miniscope,[status(thm)],[f_300_2]) ).
cnf(f_300_4,plain,
( ~ rdn_add_with_carry(rdnn(U_118),U_126,U_124,U_122)
| ~ rdn_digit_add(rdnn(U_120),rdnn(U_119),rdnn(U_118),rdnn(n0))
| ~ rdn_digit_add(rdnn(U_121),rdnn(U_128),rdnn(U_123),rdnn(U_119))
| ~ rdn_digit_add(rdnn(U_127),rdnn(U_125),rdnn(U_121),rdnn(U_120))
| ~ rdn_non_zero(U_122)
| ~ rdn_non_zero(U_124)
| ~ rdn_non_zero(U_126)
| rdn_add_with_carry(rdnn(U_128),rdn(rdnn(U_127),U_126),rdn(rdnn(U_125),U_124),rdn(rdnn(U_123),U_122)) ),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_302_1,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n0_n0_n0_n0]) ).
cnf(f_302_2,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(clausify,[status(thm)],[f_302_1]) ).
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]) ).
cnf(f_325_2,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(clausify,[status(thm)],[f_325_1]) ).
fof(f_336_1,plain,
rdn_digit_add(rdnn(n3),rdnn(n4),rdnn(n7),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n3_n4_n7_n0]) ).
cnf(f_336_2,plain,
rdn_digit_add(rdnn(n3),rdnn(n4),rdnn(n7),rdnn(n0)),
inference(clausify,[status(thm)],[f_336_1]) ).
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]) ).
cnf(f_352_2,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(clausify,[status(thm)],[f_352_1]) ).
fof(f_372_1,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n7_n0_n7_n0]) ).
cnf(f_372_2,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(clausify,[status(thm)],[f_372_1]) ).
fof(f_402_1,negated_conjecture,
~ sum(n23,n34,n57),
inference(negate,[status(cth)],[sum_n23_n34_n57]) ).
cnf(f_402_2,negated_conjecture,
~ sum(n23,n34,n57),
inference(clausify,[status(thm)],[f_402_1]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_17,axiom,
( rdn_digit_add(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ rdn_digit_add(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ sum(n23,n34,n57),
inference(start,[status(thm),parent(0:0)],[f_402_2]) ).
cnf(t2,plain,
( ~ rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3))))
| ~ rdn_add_with_carry(rdnn(n0),rdn(rdnn(n3),rdnn(n2)),rdn(rdnn(n4),rdnn(n3)),rdn(rdnn(n7),rdnn(n5)))
| ~ rdn_translate(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2))))
| ~ rdn_translate(n57,rdn_pos(rdn(rdnn(n7),rdnn(n5))))
| sum(n23,n34,n57) ),
inference(extension,[status(thm),parent(t1:1)],[f_287_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
rdn_translate(n57,rdn_pos(rdn(rdnn(n7),rdnn(n5)))),
inference(extension,[status(thm),parent(t2:2)],[f_58_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
rdn_translate(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2)))),
inference(extension,[status(thm),parent(t2:3)],[f_24_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ rdn_digit_add(rdnn(n3),rdnn(n4),rdnn(n7),rdnn(n0))
| ~ rdn_non_zero(rdnn(n3))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))
| ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0))
| ~ rdn_non_zero(rdnn(n2))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0))
| ~ rdn_non_zero(rdnn(n5))
| rdn_add_with_carry(rdnn(n0),rdn(rdnn(n3),rdnn(n2)),rdn(rdnn(n4),rdnn(n3)),rdn(rdnn(n7),rdnn(n5))) ),
inference(extension,[status(thm),parent(t2:4)],[f_300_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
( ~ rdn_non_zero_digit(rdnn(n5))
| rdn_non_zero(rdnn(n5)) ),
inference(extension,[status(thm),parent(t8:2)],[f_279_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
rdn_non_zero_digit(rdnn(n5)),
inference(extension,[status(thm),parent(t10:2)],[f_261_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( rdnn(n0) != rdnn(n0)
| rdnn(n0) != rdnn(n0)
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0))
| rdnn(n7) != rdnn(n7)
| rdnn(n7) != rdnn(n7)
| rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)) ),
inference(extension,[status(thm),parent(t8:3)],[equality_17]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:3]) ).
cnf(t16,plain,
rdnn(n7) = rdnn(n7),
inference(extension,[status(thm),parent(t14:2)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
rdnn(n7) = rdnn(n7),
inference(extension,[status(thm),parent(t14:3)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(extension,[status(thm),parent(t14:4)],[f_372_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:4]) ).
cnf(t22,plain,
rdnn(n0) = rdnn(n0),
inference(extension,[status(thm),parent(t14:5)],[equality_1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:5]) ).
cnf(t24,plain,
rdnn(n0) = rdnn(n0),
inference(extension,[status(thm),parent(t14:6)],[equality_1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t14:6]) ).
cnf(t26,plain,
( ~ rdn_non_zero_digit(rdnn(n2))
| rdn_non_zero(rdnn(n2)) ),
inference(extension,[status(thm),parent(t8:4)],[f_279_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t8:4]) ).
cnf(t28,plain,
rdn_non_zero_digit(rdnn(n2)),
inference(extension,[status(thm),parent(t26:2)],[f_258_2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(extension,[status(thm),parent(t8:5)],[f_302_2]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t8:5]) ).
cnf(t32,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(t8:6)],[f_297_4]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t8:6]) ).
cnf(t34,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(extension,[status(thm),parent(t32:2)],[f_325_2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(extension,[status(thm),parent(t32:3)],[f_352_2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
cnf(t38,plain,
( ~ rdn_non_zero_digit(rdnn(n3))
| rdn_non_zero(rdnn(n3)) ),
inference(extension,[status(thm),parent(t8:7)],[f_279_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t8:7]) ).
cnf(t40,plain,
rdn_non_zero_digit(rdnn(n3)),
inference(extension,[status(thm),parent(t38:2)],[f_259_2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
rdn_digit_add(rdnn(n3),rdnn(n4),rdnn(n7),rdnn(n0)),
inference(extension,[status(thm),parent(t8:8)],[f_336_2]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t8:8]) ).
cnf(t44,plain,
rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3)))),
inference(extension,[status(thm),parent(t2:5)],[f_35_2]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM306+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 18:10:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 283.66/283.95 % SZS status Theorem for theBenchmark
% 283.66/283.95 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------