%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM322+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 08:52:02 AM UTC 2026
% Result : Theorem 0.14s 5.82s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 10 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 21 ( 1 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('NUM005+0.ax',rdn5) ).
fof(rdnn5,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('NUM005+0.ax',rdnn5) ).
fof(sum_entry_point_posx_negx,axiom,
! [POS_X,NEG_X,RDN_X] :
( ( rdn_translate(NEG_X,rdn_neg(RDN_X))
& rdn_translate(POS_X,rdn_pos(RDN_X)) )
=> sum(POS_X,NEG_X,n0) ),
file('NUM005+2.ax',sum_entry_point_posx_negx) ).
fof(sum_n5_nn5_what,conjecture,
? [X] : sum(n5,nn5,X),
file('theBenchmark.p',sum_n5_nn5_what) ).
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_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_291_1,plain,
! [POS_X,NEG_X,RDN_X] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X)) ),
inference(fof_nnf,[status(thm)],[sum_entry_point_posx_negx]) ).
fof(f_291_2,plain,
! [U_69,U_68,U_67] :
( sum(U_69,U_68,n0)
| ~ rdn_translate(U_68,rdn_neg(U_67))
| ~ rdn_translate(U_69,rdn_pos(U_67)) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
! [U_69,U_68] :
( ! [U_67] :
( ~ rdn_translate(U_68,rdn_neg(U_67))
| ~ rdn_translate(U_69,rdn_pos(U_67)) )
| sum(U_69,U_68,n0) ),
inference(miniscope,[status(thm)],[f_291_2]) ).
cnf(f_291_4,plain,
( ~ rdn_translate(U_68,rdn_neg(U_67))
| ~ rdn_translate(U_69,rdn_pos(U_67))
| sum(U_69,U_68,n0) ),
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_402_1,negated_conjecture,
~ ? [X] : sum(n5,nn5,X),
inference(negate,[status(cth)],[sum_n5_nn5_what]) ).
fof(f_402_2,negated_conjecture,
! [X] : ~ sum(n5,nn5,X),
inference(fof_nnf,[status(thm)],[f_402_1]) ).
fof(f_402_3,negated_conjecture,
! [U_135] : ~ sum(n5,nn5,U_135),
inference(variable_rename,[status(thm)],[f_402_2]) ).
fof(f_402_4,negated_conjecture,
! [U_135] : ~ sum(n5,nn5,U_135),
inference(definitional_conversion,[status(esa)],[f_402_3]) ).
cnf(f_402_5,negated_conjecture,
~ sum(n5,nn5,U_135),
inference(clausify,[status(thm)],[f_402_4]) ).
cnf(t1,plain,
~ sum(n5,nn5,n0),
inference(start,[status(thm),parent(0:0)],[f_402_5]) ).
cnf(t2,plain,
( ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5)))
| sum(n5,nn5,n0) ),
inference(extension,[status(thm),parent(t1:1)],[f_291_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(extension,[status(thm),parent(t2:2)],[f_133_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(extension,[status(thm),parent(t2:3)],[f_6_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM322+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 : n002.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 18:15:39 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.14/5.82 % SZS status Theorem for theBenchmark
% 0.14/5.82 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------