%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM301+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 : n003.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 08:51:59 AM UTC 2026
% Result : Theorem 38.96s 39.29s
% Output : Proof 39.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 28 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 67 ( 34 ~; 28 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 3 sgn 39 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('NUM005+0.ax',rdnn2) ).
fof(rdnn99,axiom,
rdn_translate(nn99,rdn_neg(rdn(rdnn(n9),rdnn(n9)))),
file('NUM005+0.ax',rdnn99) ).
fof(rdn_digit9,axiom,
rdn_non_zero_digit(rdnn(n9)),
file('NUM005+1.ax',rdn_digit9) ).
fof(rdn_extra_digits_positive_less,axiom,
! [D,Db,Ob] :
( rdn_non_zero(Ob)
=> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
file('NUM005+1.ax',rdn_extra_digits_positive_less) ).
fof(rdn_non_zero_by_digit,axiom,
! [X] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ),
file('NUM005+1.ax',rdn_non_zero_by_digit) ).
fof(less_entry_point_neg_neg,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_positive_less(RDN_Y,RDN_X)
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> less(X,Y) ),
file('NUM005+1.ax',less_entry_point_neg_neg) ).
fof(something_less_nn2,conjecture,
? [X] : less(X,nn2),
file('theBenchmark.p',something_less_nn2) ).
fof(f_130_1,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(fof_nnf,[status(thm)],[rdnn2]) ).
fof(f_130_2,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(definitional_conversion,[status(esa)],[f_130_1]) ).
cnf(f_130_3,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_227_1,plain,
rdn_translate(nn99,rdn_neg(rdn(rdnn(n9),rdnn(n9)))),
inference(fof_nnf,[status(thm)],[rdnn99]) ).
fof(f_227_2,plain,
rdn_translate(nn99,rdn_neg(rdn(rdnn(n9),rdnn(n9)))),
inference(definitional_conversion,[status(esa)],[f_227_1]) ).
cnf(f_227_3,plain,
rdn_translate(nn99,rdn_neg(rdn(rdnn(n9),rdnn(n9)))),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_265_1,plain,
rdn_non_zero_digit(rdnn(n9)),
inference(fof_nnf,[status(thm)],[rdn_digit9]) ).
fof(f_265_2,plain,
rdn_non_zero_digit(rdnn(n9)),
inference(definitional_conversion,[status(esa)],[f_265_1]) ).
cnf(f_265_3,plain,
rdn_non_zero_digit(rdnn(n9)),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_278_1,plain,
! [D,Db,Ob] :
( rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob))
| ~ rdn_non_zero(Ob) ),
inference(fof_nnf,[status(thm)],[rdn_extra_digits_positive_less]) ).
fof(f_278_2,plain,
! [U_12,U_11,U_10] :
( rdn_positive_less(rdnn(U_12),rdn(rdnn(U_11),U_10))
| ~ rdn_non_zero(U_10) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
! [U_10,U_11,U_12] :
( rdn_positive_less(rdnn(U_12),rdn(rdnn(U_11),U_10))
| ~ rdn_non_zero(U_10) ),
inference(definitional_conversion,[status(esa)],[f_278_2]) ).
cnf(f_278_4,plain,
( rdn_positive_less(rdnn(U_12),rdn(rdnn(U_11),U_10))
| ~ rdn_non_zero(U_10) ),
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_1,plain,
! [X] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(fof_nnf,[status(thm)],[rdn_non_zero_by_digit]) ).
fof(f_279_2,plain,
! [U_13] :
( rdn_non_zero(rdnn(U_13))
| ~ rdn_non_zero_digit(rdnn(U_13)) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_13] :
( rdn_non_zero(rdnn(U_13))
| ~ rdn_non_zero_digit(rdnn(U_13)) ),
inference(definitional_conversion,[status(esa)],[f_279_2]) ).
cnf(f_279_4,plain,
( rdn_non_zero(rdnn(U_13))
| ~ rdn_non_zero_digit(rdnn(U_13)) ),
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_283_1,plain,
! [X,Y,RDN_X,RDN_Y] :
( less(X,Y)
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(fof_nnf,[status(thm)],[less_entry_point_neg_neg]) ).
fof(f_283_2,plain,
! [U_27,U_26,U_25,U_24] :
( less(U_27,U_26)
| ~ rdn_positive_less(U_24,U_25)
| ~ rdn_translate(U_26,rdn_neg(U_24))
| ~ rdn_translate(U_27,rdn_neg(U_25)) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_27,U_26] :
( ! [U_25] :
( ! [U_24] :
( ~ rdn_positive_less(U_24,U_25)
| ~ rdn_translate(U_26,rdn_neg(U_24)) )
| ~ rdn_translate(U_27,rdn_neg(U_25)) )
| less(U_27,U_26) ),
inference(miniscope,[status(thm)],[f_283_2]) ).
fof(f_283_4,plain,
! [U_26,U_25,U_24,U_27] :
( ~ rdn_positive_less(U_24,U_25)
| ~ rdn_translate(U_26,rdn_neg(U_24))
| ~ rdn_translate(U_27,rdn_neg(U_25))
| less(U_27,U_26) ),
inference(definitional_conversion,[status(esa)],[f_283_3]) ).
cnf(f_283_5,plain,
( ~ rdn_positive_less(U_24,U_25)
| ~ rdn_translate(U_26,rdn_neg(U_24))
| ~ rdn_translate(U_27,rdn_neg(U_25))
| less(U_27,U_26) ),
inference(clausify,[status(thm)],[f_283_4]) ).
fof(f_402_1,negated_conjecture,
~ ? [X] : less(X,nn2),
inference(negate,[status(cth)],[something_less_nn2]) ).
fof(f_402_2,negated_conjecture,
! [X] : ~ less(X,nn2),
inference(fof_nnf,[status(thm)],[f_402_1]) ).
fof(f_402_3,negated_conjecture,
! [U_135] : ~ less(U_135,nn2),
inference(variable_rename,[status(thm)],[f_402_2]) ).
fof(f_402_4,negated_conjecture,
! [U_135] : ~ less(U_135,nn2),
inference(definitional_conversion,[status(esa)],[f_402_3]) ).
cnf(f_402_5,negated_conjecture,
~ less(U_135,nn2),
inference(clausify,[status(thm)],[f_402_4]) ).
cnf(t1,plain,
~ less(nn99,nn2),
inference(start,[status(thm),parent(0:0)],[f_402_5]) ).
cnf(t2,plain,
( ~ rdn_translate(nn99,rdn_neg(rdn(rdnn(n9),rdnn(n9))))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n2),rdn(rdnn(n9),rdnn(n9)))
| less(nn99,nn2) ),
inference(extension,[status(thm),parent(t1:1)],[f_283_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ rdn_non_zero(rdnn(n9))
| rdn_positive_less(rdnn(n2),rdn(rdnn(n9),rdnn(n9))) ),
inference(extension,[status(thm),parent(t2:2)],[f_278_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ rdn_non_zero_digit(rdnn(n9))
| rdn_non_zero(rdnn(n9)) ),
inference(extension,[status(thm),parent(t4:2)],[f_279_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
rdn_non_zero_digit(rdnn(n9)),
inference(extension,[status(thm),parent(t6:2)],[f_265_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(extension,[status(thm),parent(t2:3)],[f_130_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
rdn_translate(nn99,rdn_neg(rdn(rdnn(n9),rdnn(n9)))),
inference(extension,[status(thm),parent(t2:4)],[f_227_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM301+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
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 18:12:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 38.96/39.29 % SZS status Theorem for theBenchmark
% 38.96/39.29 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------