%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM337+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:52:04 AM UTC 2026
% Result : Theorem 208.07s 208.39s
% Output : Proof 208.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 40 unt; 0 def)
% Number of atoms : 155 ( 19 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 146 ( 67 ~; 60 |; 13 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 120 ( 0 sgn 98 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('NUM005+0.ax',rdn2) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('NUM005+0.ax',rdn3) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('NUM005+0.ax',rdn5) ).
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(unique_LHS,axiom,
! [X1,X2,Y,Z] :
( ( sum(X2,Y,Z)
& sum(X1,Y,Z) )
=> X1 = X2 ),
file('NUM005+2.ax',unique_LHS) ).
fof(minus_entry_point,axiom,
! [X,Y,Z] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ),
file('NUM005+2.ax',minus_entry_point) ).
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_n3_n2_n5_n0,axiom,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n3_n2_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(diff_n5_only_n3_n2,conjecture,
! [X] :
( difference(n5,X,n2)
=> X = n3 ),
file('theBenchmark.p',diff_n5_only_n3_n2) ).
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_4_1,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(fof_nnf,[status(thm)],[rdn3]) ).
fof(f_4_2,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(definitional_conversion,[status(esa)],[f_4_1]) ).
cnf(f_4_3,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_6_1,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(fof_nnf,[status(thm)],[rdn5]) ).
fof(f_6_2,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(definitional_conversion,[status(esa)],[f_6_1]) ).
cnf(f_6_3,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(clausify,[status(thm)],[f_6_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]) ).
fof(f_287_4,plain,
! [U_44,U_43,U_45,U_46,U_47,U_48] :
( ~ 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(definitional_conversion,[status(esa)],[f_287_3]) ).
cnf(f_287_5,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_4]) ).
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]) ).
fof(f_294_4,plain,
! [U_81,U_80,U_79,U_82] :
( ~ sum(U_81,U_80,U_79)
| ~ sum(U_82,U_80,U_79)
| U_82 = U_81 ),
inference(definitional_conversion,[status(esa)],[f_294_3]) ).
cnf(f_294_5,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_4]) ).
fof(f_296_1,plain,
! [X,Y,Z] :
( ( sum(Y,Z,X)
| ~ difference(X,Y,Z) )
& ( difference(X,Y,Z)
| ~ sum(Y,Z,X) ) ),
inference(fof_nnf,[status(thm)],[minus_entry_point]) ).
fof(f_296_2,plain,
! [U_89,U_88,U_87] :
( ( sum(U_88,U_87,U_89)
| ~ difference(U_89,U_88,U_87) )
& ( difference(U_89,U_88,U_87)
| ~ sum(U_88,U_87,U_89) ) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
( ! [U_95,U_93,U_91] :
( sum(U_93,U_91,U_95)
| ~ difference(U_95,U_93,U_91) )
& ! [U_94,U_92,U_90] :
( difference(U_94,U_92,U_90)
| ~ sum(U_92,U_90,U_94) ) ),
inference(miniscope,[status(thm)],[f_296_2]) ).
fof(f_296_4,plain,
( ! [U_95,U_93,U_91] :
( sum(U_93,U_91,U_95)
| ~ difference(U_95,U_93,U_91) )
& ! [U_94,U_92,U_90] :
( difference(U_94,U_92,U_90)
| ~ sum(U_92,U_90,U_94) ) ),
inference(definitional_conversion,[status(esa)],[f_296_3]) ).
cnf(f_296_6,plain,
( sum(U_93,U_91,U_95)
| ~ difference(U_95,U_93,U_91) ),
inference(clausify,[status(thm)],[f_296_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_97,U_98,U_99,U_96,U_100] :
( ~ 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_334_1,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n3_n2_n5_n0]) ).
fof(f_334_2,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(definitional_conversion,[status(esa)],[f_334_1]) ).
cnf(f_334_3,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(clausify,[status(thm)],[f_334_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,
~ ! [X] :
( difference(n5,X,n2)
=> X = n3 ),
inference(negate,[status(cth)],[diff_n5_only_n3_n2]) ).
fof(f_402_2,negated_conjecture,
? [X] :
( X != n3
& difference(n5,X,n2) ),
inference(fof_nnf,[status(thm)],[f_402_1]) ).
fof(f_402_3,negated_conjecture,
? [U_135] :
( U_135 != n3
& difference(n5,U_135,n2) ),
inference(variable_rename,[status(thm)],[f_402_2]) ).
fof(f_402_4,negated_conjecture,
( sK1 != n3
& difference(n5,sK1,n2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_135,sK1)],[f_402_3]) ).
fof(f_402_5,negated_conjecture,
( sK1 != n3
& difference(n5,sK1,n2) ),
inference(definitional_conversion,[status(esa)],[f_402_4]) ).
cnf(f_402_6,negated_conjecture,
difference(n5,sK1,n2),
inference(clausify,[status(thm)],[f_402_5]) ).
cnf(f_402_7,negated_conjecture,
sK1 != n3,
inference(clausify,[status(thm)],[f_402_5]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
sK1 != n3,
inference(start,[status(thm),parent(0:0)],[f_402_7]) ).
cnf(t2,plain,
( n3 != sK1
| sK1 = n3 ),
inference(extension,[status(thm),parent(t1:1)],[equality_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ sum(n3,n2,n5)
| ~ sum(sK1,n2,n5)
| n3 = sK1 ),
inference(extension,[status(thm),parent(t2:2)],[f_294_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ difference(n5,sK1,n2)
| sum(sK1,n2,n5) ),
inference(extension,[status(thm),parent(t4:2)],[f_296_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
difference(n5,sK1,n2),
inference(extension,[status(thm),parent(t6:2)],[f_402_6]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sum(n3,n2,n5) ),
inference(extension,[status(thm),parent(t4:3)],[f_287_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(extension,[status(thm),parent(t10:2)],[f_6_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(extension,[status(thm),parent(t10:3)],[f_4_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(extension,[status(thm),parent(t10:4)],[f_3_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:4]) ).
cnf(t18,plain,
( ~ rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n3),rdnn(n2),rdnn(n5)) ),
inference(extension,[status(thm),parent(t10:5)],[f_297_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t10:5]) ).
cnf(t20,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(extension,[status(thm),parent(t18:2)],[f_352_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(extension,[status(thm),parent(t18:3)],[f_334_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM337+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 18:13:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 208.07/208.39 % SZS status Theorem for theBenchmark
% 208.07/208.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------