%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM344+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 : n020.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 08:52:05 AM UTC 2026
% Result : Theorem 222.23s 222.58s
% Output : Proof 222.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 43 unt; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 135 ( 65 ~; 59 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 102 ( 0 sgn 81 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn1,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('NUM005+0.ax',rdn1) ).
fof(rdn6,axiom,
rdn_translate(n6,rdn_pos(rdnn(n6))),
file('NUM005+0.ax',rdn6) ).
fof(rdn7,axiom,
rdn_translate(n7,rdn_pos(rdnn(n7))),
file('NUM005+0.ax',rdn7) ).
fof(rdn_positive_less67,axiom,
rdn_positive_less(rdnn(n6),rdnn(n7)),
file('NUM005+1.ax',rdn_positive_less67) ).
fof(less_entry_point_pos_pos,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_positive_less(RDN_X,RDN_Y)
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_pos(RDN_X)) )
=> less(X,Y) ),
file('NUM005+1.ax',less_entry_point_pos_pos) ).
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(rdn_digit_add_n6_n1_n7_n0,axiom,
rdn_digit_add(rdnn(n6),rdnn(n1),rdnn(n7),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n6_n1_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(exist_bigger_plus_one,conjecture,
? [X,Y] :
( less(X,Y)
& sum(X,n1,Y) ),
file('theBenchmark.p',exist_bigger_plus_one) ).
fof(f_2_1,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(fof_nnf,[status(thm)],[rdn1]) ).
fof(f_2_2,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_7_1,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(fof_nnf,[status(thm)],[rdn6]) ).
fof(f_7_2,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(definitional_conversion,[status(esa)],[f_7_1]) ).
cnf(f_7_3,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(fof_nnf,[status(thm)],[rdn7]) ).
fof(f_8_2,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_272_1,plain,
rdn_positive_less(rdnn(n6),rdnn(n7)),
inference(fof_nnf,[status(thm)],[rdn_positive_less67]) ).
fof(f_272_2,plain,
rdn_positive_less(rdnn(n6),rdnn(n7)),
inference(definitional_conversion,[status(esa)],[f_272_1]) ).
cnf(f_272_3,plain,
rdn_positive_less(rdnn(n6),rdnn(n7)),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_281_1,plain,
! [X,Y,RDN_X,RDN_Y] :
( less(X,Y)
| ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ),
inference(fof_nnf,[status(thm)],[less_entry_point_pos_pos]) ).
fof(f_281_2,plain,
! [U_19,U_18,U_17,U_16] :
( less(U_19,U_18)
| ~ rdn_positive_less(U_17,U_16)
| ~ rdn_translate(U_18,rdn_pos(U_16))
| ~ rdn_translate(U_19,rdn_pos(U_17)) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
! [U_19,U_18] :
( ! [U_17] :
( ! [U_16] :
( ~ rdn_positive_less(U_17,U_16)
| ~ rdn_translate(U_18,rdn_pos(U_16)) )
| ~ rdn_translate(U_19,rdn_pos(U_17)) )
| less(U_19,U_18) ),
inference(miniscope,[status(thm)],[f_281_2]) ).
fof(f_281_4,plain,
! [U_17,U_16,U_18,U_19] :
( ~ rdn_positive_less(U_17,U_16)
| ~ rdn_translate(U_18,rdn_pos(U_16))
| ~ rdn_translate(U_19,rdn_pos(U_17))
| less(U_19,U_18) ),
inference(definitional_conversion,[status(esa)],[f_281_3]) ).
cnf(f_281_5,plain,
( ~ rdn_positive_less(U_17,U_16)
| ~ rdn_translate(U_18,rdn_pos(U_16))
| ~ rdn_translate(U_19,rdn_pos(U_17))
| less(U_19,U_18) ),
inference(clausify,[status(thm)],[f_281_4]) ).
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_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_99,U_100,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(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_363_1,plain,
rdn_digit_add(rdnn(n6),rdnn(n1),rdnn(n7),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n6_n1_n7_n0]) ).
fof(f_363_2,plain,
rdn_digit_add(rdnn(n6),rdnn(n1),rdnn(n7),rdnn(n0)),
inference(definitional_conversion,[status(esa)],[f_363_1]) ).
cnf(f_363_3,plain,
rdn_digit_add(rdnn(n6),rdnn(n1),rdnn(n7),rdnn(n0)),
inference(clausify,[status(thm)],[f_363_2]) ).
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]) ).
fof(f_372_2,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(definitional_conversion,[status(esa)],[f_372_1]) ).
cnf(f_372_3,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_402_1,negated_conjecture,
~ ? [X,Y] :
( less(X,Y)
& sum(X,n1,Y) ),
inference(negate,[status(cth)],[exist_bigger_plus_one]) ).
fof(f_402_2,negated_conjecture,
! [X,Y] :
( ~ less(X,Y)
| ~ sum(X,n1,Y) ),
inference(fof_nnf,[status(thm)],[f_402_1]) ).
fof(f_402_3,negated_conjecture,
! [U_136,U_135] :
( ~ less(U_136,U_135)
| ~ sum(U_136,n1,U_135) ),
inference(variable_rename,[status(thm)],[f_402_2]) ).
fof(f_402_4,negated_conjecture,
! [U_136,U_135] :
( ~ less(U_136,U_135)
| ~ sum(U_136,n1,U_135) ),
inference(definitional_conversion,[status(esa)],[f_402_3]) ).
cnf(f_402_5,negated_conjecture,
( ~ less(U_136,U_135)
| ~ sum(U_136,n1,U_135) ),
inference(clausify,[status(thm)],[f_402_4]) ).
cnf(t1,plain,
( ~ sum(n6,n1,n7)
| ~ less(n6,n7) ),
inference(start,[status(thm),parent(0:0)],[f_402_5]) ).
cnf(t2,plain,
( ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| ~ rdn_translate(n7,rdn_pos(rdnn(n7)))
| ~ rdn_positive_less(rdnn(n6),rdnn(n7))
| less(n6,n7) ),
inference(extension,[status(thm),parent(t1:1)],[f_281_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
rdn_positive_less(rdnn(n6),rdnn(n7)),
inference(extension,[status(thm),parent(t2:2)],[f_272_3]) ).
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(t2:3)],[f_8_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(extension,[status(thm),parent(t2:4)],[f_7_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n1),rdnn(n7))
| ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| ~ rdn_translate(n1,rdn_pos(rdnn(n1)))
| ~ rdn_translate(n7,rdn_pos(rdnn(n7)))
| sum(n6,n1,n7) ),
inference(extension,[status(thm),parent(t1:2)],[f_287_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(extension,[status(thm),parent(t10:2)],[f_8_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(extension,[status(thm),parent(t10:3)],[f_2_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(extension,[status(thm),parent(t10:4)],[f_7_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:4]) ).
cnf(t18,plain,
( ~ rdn_digit_add(rdnn(n6),rdnn(n1),rdnn(n7),rdnn(n0))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n1),rdnn(n7)) ),
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(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(extension,[status(thm),parent(t18:2)],[f_372_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
rdn_digit_add(rdnn(n6),rdnn(n1),rdnn(n7),rdnn(n0)),
inference(extension,[status(thm),parent(t18:3)],[f_363_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM344+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
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 18:15:34 UTC 2026
% 0.07/0.35 % CPUTime :
% 222.23/222.58 % SZS status Theorem for theBenchmark
% 222.23/222.58 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------