%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM323+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 08:52:02 AM UTC 2026
% Result : Theorem 126.13s 131.44s
% Output : Proof 126.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 34 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 72 ( 36 ~; 30 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 61 ( 1 sgn 47 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('NUM005+0.ax',rdnn2) ).
fof(rdnn5,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('NUM005+0.ax',rdnn5) ).
fof(rdnn7,axiom,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
file('NUM005+0.ax',rdnn7) ).
fof(sum_entry_point_neg_neg,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_Y,RDN_Z)
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> sum(X,Y,Z) ),
file('NUM005+2.ax',sum_entry_point_neg_neg) ).
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_n5_n7_n0,axiom,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n2_n5_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(sum_what_nn5_nn7,conjecture,
? [X] : sum(X,nn5,nn7),
file('theBenchmark.p',sum_what_nn5_nn7) ).
fof(f_130_1,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(fof_nnf,[status(thm)],[rdnn2]) ).
cnf(f_130_2,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(clausify,[status(thm)],[f_130_1]) ).
fof(f_133_1,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(fof_nnf,[status(thm)],[rdnn5]) ).
cnf(f_133_2,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(clausify,[status(thm)],[f_133_1]) ).
fof(f_135_1,plain,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
inference(fof_nnf,[status(thm)],[rdnn7]) ).
cnf(f_135_2,plain,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
inference(clausify,[status(thm)],[f_135_1]) ).
fof(f_288_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_Y,RDN_Z)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(fof_nnf,[status(thm)],[sum_entry_point_neg_neg]) ).
fof(f_288_2,plain,
! [U_54,U_53,U_52,U_51,U_50,U_49] :
( sum(U_54,U_53,U_52)
| ~ rdn_translate(U_52,rdn_neg(U_49))
| ~ rdn_add_with_carry(rdnn(n0),U_51,U_50,U_49)
| ~ rdn_translate(U_53,rdn_neg(U_50))
| ~ rdn_translate(U_54,rdn_neg(U_51)) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_54,U_53,U_52] :
( ! [U_51] :
( ! [U_50] :
( ! [U_49] :
( ~ rdn_translate(U_52,rdn_neg(U_49))
| ~ rdn_add_with_carry(rdnn(n0),U_51,U_50,U_49) )
| ~ rdn_translate(U_53,rdn_neg(U_50)) )
| ~ rdn_translate(U_54,rdn_neg(U_51)) )
| sum(U_54,U_53,U_52) ),
inference(miniscope,[status(thm)],[f_288_2]) ).
cnf(f_288_4,plain,
( ~ rdn_translate(U_52,rdn_neg(U_49))
| ~ rdn_add_with_carry(rdnn(n0),U_51,U_50,U_49)
| ~ rdn_translate(U_53,rdn_neg(U_50))
| ~ rdn_translate(U_54,rdn_neg(U_51))
| sum(U_54,U_53,U_52) ),
inference(clausify,[status(thm)],[f_288_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_327_1,plain,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n2_n5_n7_n0]) ).
cnf(f_327_2,plain,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(clausify,[status(thm)],[f_327_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,
~ ? [X] : sum(X,nn5,nn7),
inference(negate,[status(cth)],[sum_what_nn5_nn7]) ).
fof(f_402_2,negated_conjecture,
! [X] : ~ sum(X,nn5,nn7),
inference(fof_nnf,[status(thm)],[f_402_1]) ).
fof(f_402_3,negated_conjecture,
! [U_135] : ~ sum(U_135,nn5,nn7),
inference(variable_rename,[status(thm)],[f_402_2]) ).
fof(f_402_4,negated_conjecture,
! [U_135] : ~ sum(U_135,nn5,nn7),
inference(definitional_conversion,[status(esa)],[f_402_3]) ).
cnf(f_402_5,negated_conjecture,
~ sum(U_135,nn5,nn7),
inference(clausify,[status(thm)],[f_402_4]) ).
cnf(t1,plain,
~ sum(nn2,nn5,nn7),
inference(start,[status(thm),parent(0:0)],[f_402_5]) ).
cnf(t2,plain,
( ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5)))
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n5),rdnn(n7))
| ~ rdn_translate(nn7,rdn_neg(rdnn(n7)))
| sum(nn2,nn5,nn7) ),
inference(extension,[status(thm),parent(t1:1)],[f_288_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
inference(extension,[status(thm),parent(t2:2)],[f_135_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n5),rdnn(n7)) ),
inference(extension,[status(thm),parent(t2:3)],[f_297_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(extension,[status(thm),parent(t6:2)],[f_372_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(extension,[status(thm),parent(t6:3)],[f_327_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(extension,[status(thm),parent(t2:4)],[f_133_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(extension,[status(thm),parent(t2:5)],[f_130_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM323+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
% 0.09/5.38 % Computer : n011.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 19 18:13:02 UTC 2026
% 0.09/5.38 % CPUTime :
% 126.13/131.44 % SZS status Theorem for theBenchmark
% 126.13/131.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------