%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM334+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 : n007.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 120.77s 121.08s
% Output : Proof 120.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 33 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 90 ( 42 ~; 38 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 73 ( 0 sgn 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('NUM005+0.ax',rdn2) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('NUM005+0.ax',rdn5) ).
fof(rdn7,axiom,
rdn_translate(n7,rdn_pos(rdnn(n7))),
file('NUM005+0.ax',rdn7) ).
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(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_n5_n2_n7_n0,axiom,
rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n5_n2_n7_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(diff_n7_n5_n2,conjecture,
difference(n7,n5,n2),
file('theBenchmark.p',diff_n7_n5_n2) ).
fof(f_3_1,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(fof_nnf,[status(thm)],[rdn2]) ).
cnf(f_3_2,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_6_1,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(fof_nnf,[status(thm)],[rdn5]) ).
cnf(f_6_2,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_8_1,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(fof_nnf,[status(thm)],[rdn7]) ).
cnf(f_8_2,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(clausify,[status(thm)],[f_8_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_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]) ).
cnf(f_296_4,plain,
( difference(U_94,U_92,U_90)
| ~ sum(U_92,U_90,U_94) ),
inference(clausify,[status(thm)],[f_296_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_354_1,plain,
rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n5_n2_n7_n0]) ).
cnf(f_354_2,plain,
rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
inference(clausify,[status(thm)],[f_354_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,
~ difference(n7,n5,n2),
inference(negate,[status(cth)],[diff_n7_n5_n2]) ).
fof(f_402_2,negated_conjecture,
~ difference(n7,n5,n2),
inference(definitional_conversion,[status(esa)],[f_402_1]) ).
cnf(f_402_3,negated_conjecture,
~ difference(n7,n5,n2),
inference(clausify,[status(thm)],[f_402_2]) ).
cnf(t1,plain,
~ difference(n7,n5,n2),
inference(start,[status(thm),parent(0:0)],[f_402_3]) ).
cnf(t2,plain,
( ~ sum(n5,n2,n7)
| difference(n7,n5,n2) ),
inference(extension,[status(thm),parent(t1:1)],[f_296_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n2),rdnn(n7))
| ~ rdn_translate(n7,rdn_pos(rdnn(n7)))
| sum(n5,n2,n7) ),
inference(extension,[status(thm),parent(t2:2)],[f_287_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(extension,[status(thm),parent(t4:2)],[f_8_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n5),rdnn(n2),rdnn(n7)) ),
inference(extension,[status(thm),parent(t4:3)],[f_297_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(extension,[status(thm),parent(t8:2)],[f_372_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
inference(extension,[status(thm),parent(t8:3)],[f_354_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(extension,[status(thm),parent(t4:4)],[f_3_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:4]) ).
cnf(t16,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(extension,[status(thm),parent(t4:5)],[f_6_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t4:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM334+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
% 0.09/0.38 % Computer : n007.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 19 18:11:21 UTC 2026
% 0.09/0.38 % CPUTime :
% 120.77/121.08 % SZS status Theorem for theBenchmark
% 120.77/121.08 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------