%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM330+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 : n008.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 08:52:03 AM UTC 2026
% Result : Theorem 127.61s 133.54s
% Output : Proof 127.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 86 ( 50 unt; 0 def)
% Number of atoms : 170 ( 23 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 161 ( 77 ~; 70 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 104 ( 0 sgn 80 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn4,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('NUM005+0.ax',rdn4) ).
fof(rdn8,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('NUM005+0.ax',rdn8) ).
fof(rdnn4,axiom,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
file('NUM005+0.ax',rdnn4) ).
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(sum_entry_point_posx_negx,axiom,
! [POS_X,NEG_X,RDN_X] :
( ( rdn_translate(NEG_X,rdn_neg(RDN_X))
& rdn_translate(POS_X,rdn_pos(RDN_X)) )
=> sum(POS_X,NEG_X,n0) ),
file('NUM005+2.ax',sum_entry_point_posx_negx) ).
fof(unique_LHS,axiom,
! [X1,X2,Y,Z] :
( ( sum(X2,Y,Z)
& sum(X1,Y,Z) )
=> X1 = X2 ),
file('NUM005+2.ax',unique_LHS) ).
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_n4_n4_n8_n0,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n4_n4_n8_n0) ).
fof(rdn_digit_add_n8_n0_n8_n0,axiom,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n8_n0_n8_n0) ).
fof(sum_n4_n4_n8,conjecture,
? [X,Y] :
( Y = n4
& X = n4
& sum(X,Y,n8) ),
file('theBenchmark.p',sum_n4_n4_n8) ).
fof(f_5_1,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(fof_nnf,[status(thm)],[rdn4]) ).
cnf(f_5_2,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_9_1,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(fof_nnf,[status(thm)],[rdn8]) ).
cnf(f_9_2,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_132_1,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(fof_nnf,[status(thm)],[rdnn4]) ).
cnf(f_132_2,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(clausify,[status(thm)],[f_132_1]) ).
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_291_1,plain,
! [POS_X,NEG_X,RDN_X] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X)) ),
inference(fof_nnf,[status(thm)],[sum_entry_point_posx_negx]) ).
fof(f_291_2,plain,
! [U_69,U_68,U_67] :
( sum(U_69,U_68,n0)
| ~ rdn_translate(U_68,rdn_neg(U_67))
| ~ rdn_translate(U_69,rdn_pos(U_67)) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
! [U_69,U_68] :
( ! [U_67] :
( ~ rdn_translate(U_68,rdn_neg(U_67))
| ~ rdn_translate(U_69,rdn_pos(U_67)) )
| sum(U_69,U_68,n0) ),
inference(miniscope,[status(thm)],[f_291_2]) ).
cnf(f_291_4,plain,
( ~ rdn_translate(U_68,rdn_neg(U_67))
| ~ rdn_translate(U_69,rdn_pos(U_67))
| sum(U_69,U_68,n0) ),
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_294_1,plain,
! [X1,X2,Y,Z] :
( X1 = X2
| ~ sum(X2,Y,Z)
| ~ sum(X1,Y,Z) ),
inference(fof_nnf,[status(thm)],[unique_LHS]) ).
fof(f_294_2,plain,
! [U_82,U_81,U_80,U_79] :
( U_82 = U_81
| ~ sum(U_81,U_80,U_79)
| ~ sum(U_82,U_80,U_79) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_82,U_81] :
( ! [U_80,U_79] :
( ~ sum(U_81,U_80,U_79)
| ~ sum(U_82,U_80,U_79) )
| U_82 = U_81 ),
inference(miniscope,[status(thm)],[f_294_2]) ).
cnf(f_294_4,plain,
( ~ sum(U_81,U_80,U_79)
| ~ sum(U_82,U_80,U_79)
| U_82 = U_81 ),
inference(clausify,[status(thm)],[f_294_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_346_1,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n4_n4_n8_n0]) ).
cnf(f_346_2,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(clausify,[status(thm)],[f_346_1]) ).
fof(f_382_1,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n8_n0_n8_n0]) ).
cnf(f_382_2,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(clausify,[status(thm)],[f_382_1]) ).
fof(f_402_1,negated_conjecture,
~ ? [X,Y] :
( Y = n4
& X = n4
& sum(X,Y,n8) ),
inference(negate,[status(cth)],[sum_n4_n4_n8]) ).
fof(f_402_2,negated_conjecture,
! [X,Y] :
( Y != n4
| X != n4
| ~ sum(X,Y,n8) ),
inference(fof_nnf,[status(thm)],[f_402_1]) ).
fof(f_402_3,negated_conjecture,
! [U_136,U_135] :
( U_135 != n4
| U_136 != n4
| ~ sum(U_136,U_135,n8) ),
inference(variable_rename,[status(thm)],[f_402_2]) ).
fof(f_402_4,negated_conjecture,
! [U_136] :
( ! [U_135] :
( U_135 != n4
| ~ sum(U_136,U_135,n8) )
| U_136 != n4 ),
inference(miniscope,[status(thm)],[f_402_3]) ).
fof(f_402_5,negated_conjecture,
! [U_135,U_136] :
( U_135 != n4
| ~ sum(U_136,U_135,n8)
| U_136 != n4 ),
inference(definitional_conversion,[status(esa)],[f_402_4]) ).
cnf(f_402_6,negated_conjecture,
( U_135 != n4
| ~ sum(U_136,U_135,n8)
| U_136 != n4 ),
inference(clausify,[status(thm)],[f_402_5]) ).
cnf(t1,plain,
( ~ sum(n4,n4,n8)
| n4 != n4
| n4 != n4 ),
inference(start,[status(thm),parent(0:0)],[f_402_6]) ).
cnf(t2,plain,
( ~ sum(n4,nn4,n0)
| ~ sum(n4,nn4,n0)
| n4 = n4 ),
inference(extension,[status(thm),parent(t1:1)],[f_294_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| sum(n4,nn4,n0) ),
inference(extension,[status(thm),parent(t2:2)],[f_291_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(extension,[status(thm),parent(t4:2)],[f_132_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(extension,[status(thm),parent(t4:3)],[f_5_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| sum(n4,nn4,n0) ),
inference(extension,[status(thm),parent(t2:3)],[f_291_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(extension,[status(thm),parent(t10:2)],[f_132_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(extension,[status(thm),parent(t10:3)],[f_5_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( ~ sum(n4,nn4,n0)
| ~ sum(n4,nn4,n0)
| n4 = n4 ),
inference(extension,[status(thm),parent(t1:2)],[f_294_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t1:2]) ).
cnf(t18,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| sum(n4,nn4,n0) ),
inference(extension,[status(thm),parent(t16:2)],[f_291_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(extension,[status(thm),parent(t18:2)],[f_132_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(extension,[status(thm),parent(t18:3)],[f_5_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| sum(n4,nn4,n0) ),
inference(extension,[status(thm),parent(t16:3)],[f_291_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t16:3]) ).
cnf(t26,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(extension,[status(thm),parent(t24:2)],[f_132_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(extension,[status(thm),parent(t24:3)],[f_5_2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8))
| ~ rdn_translate(n8,rdn_pos(rdnn(n8)))
| sum(n4,n4,n8) ),
inference(extension,[status(thm),parent(t1:3)],[f_287_4]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t1:3]) ).
cnf(t32,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(extension,[status(thm),parent(t30:2)],[f_9_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,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(extension,[status(thm),parent(t30:3)],[f_297_4]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t30:3]) ).
cnf(t36,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(extension,[status(thm),parent(t34:2)],[f_382_2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(extension,[status(thm),parent(t34:3)],[f_346_2]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
cnf(t40,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(extension,[status(thm),parent(t30:4)],[f_5_2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t30:4]) ).
cnf(l20,lemma,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(lemma,[status(cth),parent(t30:4),below(t1:3)],[t30:4]) ).
cnf(t42,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(lemma_extension,[status(thm),parent(t30:5)],[l20:1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t30:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM330+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
% 0.10/6.01 % Computer : n008.cluster.edu
% 0.10/6.01 % Model : x86_64 x86_64
% 0.10/6.01 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.01 % Memory : 8046.5625MB
% 0.10/6.01 % OS : Linux 6.8.0-71-generic
% 0.10/6.01 % CPULimit : 300
% 0.10/6.01 % WCLimit : 300
% 0.10/6.01 % DateTime : Sat Sep 19 18:14:07 UTC 2026
% 0.10/6.01 % CPUTime :
% 127.61/133.54 % SZS status Theorem for theBenchmark
% 127.61/133.54 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------