%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM303+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 : n026.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 200.26s 200.53s
% Output : Proof 200.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 22 unt; 0 def)
% Number of atoms : 81 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 77 ( 35 ~; 30 |; 9 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 2 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn21,axiom,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
file('NUM005+0.ax',rdn21) ).
fof(rdn31,axiom,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
file('NUM005+0.ax',rdn31) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('NUM005+1.ax',rdn_positive_less23) ).
fof(rdn_positive_less_multi_digit_high,axiom,
! [Ds,Os,Db,Ob] :
( rdn_positive_less(Os,Ob)
=> rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
file('NUM005+1.ax',rdn_positive_less_multi_digit_high) ).
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(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('NUM005+1.ax',less_property) ).
fof(n31_not_n12,conjecture,
n31 != n21,
file('theBenchmark.p',n31_not_n12) ).
fof(f_22_1,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(fof_nnf,[status(thm)],[rdn21]) ).
cnf(f_22_2,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_32_1,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(fof_nnf,[status(thm)],[rdn31]) ).
cnf(f_32_2,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(clausify,[status(thm)],[f_32_1]) ).
fof(f_268_1,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(fof_nnf,[status(thm)],[rdn_positive_less23]) ).
cnf(f_268_2,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(clausify,[status(thm)],[f_268_1]) ).
fof(f_276_1,plain,
! [Ds,Os,Db,Ob] :
( rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob))
| ~ rdn_positive_less(Os,Ob) ),
inference(fof_nnf,[status(thm)],[rdn_positive_less_multi_digit_high]) ).
fof(f_276_2,plain,
! [U_6,U_5,U_4,U_3] :
( rdn_positive_less(rdn(rdnn(U_6),U_5),rdn(rdnn(U_4),U_3))
| ~ rdn_positive_less(U_5,U_3) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
( rdn_positive_less(rdn(rdnn(U_6),U_5),rdn(rdnn(U_4),U_3))
| ~ rdn_positive_less(U_5,U_3) ),
inference(clausify,[status(thm)],[f_276_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]) ).
cnf(f_281_4,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_3]) ).
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_5,plain,
( U_30 != U_32
| ~ less(U_32,U_30) ),
inference(clausify,[status(thm)],[f_284_3]) ).
fof(f_402_1,negated_conjecture,
n31 = n21,
inference(negate,[status(cth)],[n31_not_n12]) ).
cnf(f_402_2,negated_conjecture,
n31 = n21,
inference(clausify,[status(thm)],[f_402_1]) ).
cnf(t1,plain,
n31 = n21,
inference(start,[status(thm),parent(0:0)],[f_402_2]) ).
cnf(t2,plain,
( ~ less(n21,n31)
| n31 != n21 ),
inference(extension,[status(thm),parent(t1:1)],[f_284_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3))))
| ~ rdn_positive_less(rdn(rdnn(n1),rdnn(n2)),rdn(rdnn(n1),rdnn(n3)))
| ~ rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2))))
| less(n21,n31) ),
inference(extension,[status(thm),parent(t2:2)],[f_281_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(extension,[status(thm),parent(t4:2)],[f_22_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| rdn_positive_less(rdn(rdnn(n1),rdnn(n2)),rdn(rdnn(n1),rdnn(n3))) ),
inference(extension,[status(thm),parent(t4:3)],[f_276_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(extension,[status(thm),parent(t8:2)],[f_268_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(extension,[status(thm),parent(t4:4)],[f_32_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM303+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
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 18:14:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 200.26/200.53 % SZS status Theorem for theBenchmark
% 200.26/200.53 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------