%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM328+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 : n002.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 4.24s 4.73s
% Output : Proof 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 46 unt; 0 def)
% Number of atoms : 172 ( 36 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 170 ( 76 ~; 73 |; 17 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 106 ( 1 sgn 70 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('NUM005+0.ax',rdn0) ).
fof(rdn9,axiom,
rdn_translate(n9,rdn_pos(rdnn(n9))),
file('NUM005+0.ax',rdn9) ).
fof(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('NUM005+1.ax',less_property) ).
fof(less_or_equal,axiom,
! [X,Y] :
( less_or_equal(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('NUM005+1.ax',less_or_equal) ).
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_n9_n0_n9_n0,axiom,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
file('NUM005+2.ax',rdn_digit_add_n9_n0_n9_n0) ).
fof(sum_something_anotherthing_firstthing,conjecture,
? [X,Y] : sum(X,Y,X),
file('theBenchmark.p',sum_something_anotherthing_firstthing) ).
fof(f_1_1,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(fof_nnf,[status(thm)],[rdn0]) ).
cnf(f_1_2,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(clausify,[status(thm)],[f_1_1]) ).
fof(f_10_1,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(fof_nnf,[status(thm)],[rdn9]) ).
cnf(f_10_2,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_284_1,plain,
! [X,Y] :
( ( less(X,Y)
| Y = X
| less(Y,X) )
& ( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(fof_nnf,[status(thm)],[less_property]) ).
fof(f_284_2,plain,
! [U_29,U_28] :
( ( less(U_29,U_28)
| U_28 = U_29
| less(U_28,U_29) )
& ( ( U_28 != U_29
& ~ less(U_28,U_29) )
| ~ less(U_29,U_28) ) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
( ! [U_33,U_31] :
( less(U_33,U_31)
| U_31 = U_33
| less(U_31,U_33) )
& ! [U_32,U_30] :
( ( U_30 != U_32
& ~ less(U_30,U_32) )
| ~ less(U_32,U_30) ) ),
inference(miniscope,[status(thm)],[f_284_2]) ).
cnf(f_284_4,plain,
( ~ less(U_30,U_32)
| ~ less(U_32,U_30) ),
inference(clausify,[status(thm)],[f_284_3]) ).
cnf(f_284_6,plain,
( less(U_33,U_31)
| U_31 = U_33
| less(U_31,U_33) ),
inference(clausify,[status(thm)],[f_284_3]) ).
fof(f_285_1,plain,
! [X,Y] :
( ( less_or_equal(X,Y)
| ( X != Y
& ~ less(X,Y) ) )
& ( X = Y
| less(X,Y)
| ~ less_or_equal(X,Y) ) ),
inference(fof_nnf,[status(thm)],[less_or_equal]) ).
fof(f_285_2,plain,
! [U_35,U_34] :
( ( less_or_equal(U_35,U_34)
| ( U_35 != U_34
& ~ less(U_35,U_34) ) )
& ( U_35 = U_34
| less(U_35,U_34)
| ~ less_or_equal(U_35,U_34) ) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
( ! [U_39,U_37] :
( less_or_equal(U_39,U_37)
| ( U_39 != U_37
& ~ less(U_39,U_37) ) )
& ! [U_38,U_36] :
( U_38 = U_36
| less(U_38,U_36)
| ~ less_or_equal(U_38,U_36) ) ),
inference(miniscope,[status(thm)],[f_285_2]) ).
cnf(f_285_4,plain,
( U_38 = U_36
| less(U_38,U_36)
| ~ less_or_equal(U_38,U_36) ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_6,plain,
( U_39 != U_37
| less_or_equal(U_39,U_37) ),
inference(clausify,[status(thm)],[f_285_3]) ).
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_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_392_1,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
inference(fof_nnf,[status(thm)],[rdn_digit_add_n9_n0_n9_n0]) ).
cnf(f_392_2,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
inference(clausify,[status(thm)],[f_392_1]) ).
fof(f_402_1,negated_conjecture,
~ ? [X,Y] : sum(X,Y,X),
inference(negate,[status(cth)],[sum_something_anotherthing_firstthing]) ).
fof(f_402_2,negated_conjecture,
! [X,Y] : ~ sum(X,Y,X),
inference(fof_nnf,[status(thm)],[f_402_1]) ).
fof(f_402_3,negated_conjecture,
! [U_136,U_135] : ~ sum(U_136,U_135,U_136),
inference(variable_rename,[status(thm)],[f_402_2]) ).
fof(f_402_4,negated_conjecture,
! [U_136,U_135] : ~ sum(U_136,U_135,U_136),
inference(definitional_conversion,[status(esa)],[f_402_3]) ).
cnf(f_402_5,negated_conjecture,
~ sum(U_136,U_135,U_136),
inference(clausify,[status(thm)],[f_402_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_4,axiom,
( rdnn(Eq_x_0) = rdnn(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( rdn_add_with_carry(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ rdn_add_with_carry(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
( ~ less(rdnn(n0),rdnn(n0))
| ~ less(rdnn(n0),rdnn(n0)) ),
inference(start,[status(thm),parent(0:0)],[f_284_4]) ).
cnf(t2,plain,
( rdnn(n0) = rdnn(n0)
| ~ less_or_equal(rdnn(n0),rdnn(n0))
| less(rdnn(n0),rdnn(n0)) ),
inference(extension,[status(thm),parent(t1:1)],[f_285_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( rdnn(n0) != rdnn(n0)
| less_or_equal(rdnn(n0),rdnn(n0)) ),
inference(extension,[status(thm),parent(t2:2)],[f_285_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( less(rdnn(n0),rdnn(n0))
| less(rdnn(n0),rdnn(n0))
| rdnn(n0) = rdnn(n0) ),
inference(extension,[status(thm),parent(t4:2)],[f_284_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
$false,
inference(reduction,[status(thm),parent(t6:2)],[t6:2,t1:1]) ).
cnf(t9,plain,
$false,
inference(reduction,[status(thm),parent(t6:3)],[t6:3,t1:1]) ).
cnf(t10,plain,
( rdnn(n9) != rdnn(n9)
| rdn_add_with_carry(rdnn(n0),rdnn(n9),rdnn(n0),rdnn(n9))
| rdnn(n9) != rdnn(n9)
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n9),rdnn(n0),rdnn(n9))
| rdnn(n0) != rdnn(n0)
| rdnn(n0) != rdnn(n0) ),
inference(extension,[status(thm),parent(t2:3)],[equality_15]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t10:2)],[t10:2,t2:3]) ).
cnf(t13,plain,
( ~ rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0))
| ~ rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(n9),rdnn(n0),rdnn(n9)) ),
inference(extension,[status(thm),parent(t10:3)],[f_297_4]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t10:3]) ).
cnf(t15,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
inference(extension,[status(thm),parent(t13:2)],[f_392_2]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
inference(extension,[status(thm),parent(t13:3)],[f_392_2]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t13:3]) ).
cnf(t19,plain,
( n9 != n9
| rdnn(n9) = rdnn(n9) ),
inference(extension,[status(thm),parent(t10:4)],[equality_4]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t10:4]) ).
cnf(t21,plain,
n9 = n9,
inference(extension,[status(thm),parent(t19:2)],[equality_1]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(l11,lemma,
rdnn(n9) = rdnn(n9),
inference(lemma,[status(cth),parent(t10:4),below(t2:3)],[t10:4]) ).
cnf(t23,plain,
( ~ rdn_translate(n9,rdn_pos(rdnn(n9)))
| ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| ~ rdn_translate(n9,rdn_pos(rdnn(n9)))
| sum(n9,n0,n9)
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n9),rdnn(n0),rdnn(n9)) ),
inference(extension,[status(thm),parent(t10:5)],[f_287_4]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t10:5]) ).
cnf(t25,plain,
~ sum(n9,n0,n9),
inference(extension,[status(thm),parent(t23:2)],[f_402_5]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t23:2]) ).
cnf(t27,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(extension,[status(thm),parent(t23:3)],[f_10_2]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t23:3]) ).
cnf(t29,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(extension,[status(thm),parent(t23:4)],[f_1_2]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t23:4]) ).
cnf(t31,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(extension,[status(thm),parent(t23:5)],[f_10_2]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t23:5]) ).
cnf(t33,plain,
rdnn(n9) = rdnn(n9),
inference(lemma_extension,[status(thm),parent(t10:6)],[l11:1]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t10:6]) ).
cnf(l1,lemma,
less(rdnn(n0),rdnn(n0)),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t35,plain,
less(rdnn(n0),rdnn(n0)),
inference(lemma_extension,[status(thm),parent(t1:2)],[l1:1]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t1:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM328+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
% 0.09/0.58 % Computer : n002.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Sat Sep 19 18:15:50 UTC 2026
% 0.09/0.58 % CPUTime :
% 4.24/4.73 % SZS status Theorem for theBenchmark
% 4.24/4.73 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------