%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : AGT026+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 11:47:15 AM UTC 2026
% Result : Theorem 14.87s 2.49s
% Output : CNFRefutation 15.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 24 unt; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 152 ( 67 ~; 62 |; 17 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-2 aty)
% Number of variables : 104 ( 100 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,N,M,P] :
( ( less(M,N)
& accept_population(A,P,N) )
=> accept_population(A,P,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( ( accept_population(A,other,n0)
& accept_population(A,native,n0)
& accept_population(A,muslim,n1)
& accept_population(A,christian,n24)
& accept_population(A,atheist,n75) )
<=> accept_city(A,towna) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f362,axiom,
accept_population(muslimcountrybhumanitarianorganization,other,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f472,axiom,
accept_population(muslimcountrybhumanitarianorganization,native,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f473,axiom,
accept_population(muslimcountrybhumanitarianorganization,muslim,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f635,axiom,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f661,axiom,
rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f712,axiom,
rdn_translate(n75,rdn_pos(rdn(rdnn(n5),rdnn(n7)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f737,axiom,
rdn_translate(n100,rdn_pos(rdn(rdnn(n0),rdn(rdnn(n0),rdnn(n1))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f893,axiom,
rdn_non_zero_digit(rdnn(n1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f912,axiom,
! [Ds,Os,Db,Ob] :
( rdn_positive_less(Os,Ob)
=> rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f914,axiom,
! [D,Db,Ob] :
( rdn_non_zero(Ob)
=> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f915,axiom,
! [X] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f917,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('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f923,conjecture,
? [X,Y] : ~ accept_population(X,Y,n100),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f924,negated_conjecture,
~ ? [X,Y] : ~ accept_population(X,Y,n100),
inference(negated_conjecture,[status(cth)],[f923]) ).
fof(f934,plain,
! [A,N,M,P] :
( accept_population(A,P,M)
| ~ less(M,N)
| ~ accept_population(A,P,N) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f935,plain,
! [A,M,P] :
( accept_population(A,P,M)
| ! [N] :
( ~ less(M,N)
| ~ accept_population(A,P,N) ) ),
inference(miniscoping,[status(thm)],[f934]) ).
fof(f936,plain,
! [X0,X1,X2,X3] :
( accept_population(X0,X1,X3)
| ~ less(X3,X2)
| ~ accept_population(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f935]) ).
fof(f1011,plain,
! [A] :
( ( ~ accept_city(A,towna)
| ( accept_population(A,other,n0)
& accept_population(A,native,n0)
& accept_population(A,muslim,n1)
& accept_population(A,christian,n24)
& accept_population(A,atheist,n75) ) )
& ( accept_city(A,towna)
| ~ accept_population(A,other,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,atheist,n75) ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f1012,plain,
( ! [A] :
( ~ accept_city(A,towna)
| ( accept_population(A,other,n0)
& accept_population(A,native,n0)
& accept_population(A,muslim,n1)
& accept_population(A,christian,n24)
& accept_population(A,atheist,n75) ) )
& ! [A] :
( accept_city(A,towna)
| ~ accept_population(A,other,n0)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,atheist,n75) ) ),
inference(miniscoping,[status(thm)],[f1011]) ).
fof(f1013,plain,
! [X0] :
( accept_city(X0,towna)
| ~ accept_population(X0,other,n0)
| ~ accept_population(X0,native,n0)
| ~ accept_population(X0,muslim,n1)
| ~ accept_population(X0,christian,n24)
| ~ accept_population(X0,atheist,n75) ),
inference(cnf_transformation,[status(thm)],[f1012]) ).
fof(f1392,plain,
accept_population(muslimcountrybhumanitarianorganization,other,n0),
inference(cnf_transformation,[status(thm)],[f362]) ).
fof(f1502,plain,
accept_population(muslimcountrybhumanitarianorganization,native,n0),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f1503,plain,
accept_population(muslimcountrybhumanitarianorganization,muslim,n1),
inference(cnf_transformation,[status(thm)],[f473]) ).
fof(f1665,plain,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
inference(cnf_transformation,[status(thm)],[f635]) ).
fof(f1691,plain,
rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))),
inference(cnf_transformation,[status(thm)],[f661]) ).
fof(f1742,plain,
rdn_translate(n75,rdn_pos(rdn(rdnn(n5),rdnn(n7)))),
inference(cnf_transformation,[status(thm)],[f712]) ).
fof(f1767,plain,
rdn_translate(n100,rdn_pos(rdn(rdnn(n0),rdn(rdnn(n0),rdnn(n1))))),
inference(cnf_transformation,[status(thm)],[f737]) ).
fof(f1923,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(cnf_transformation,[status(thm)],[f893]) ).
fof(f1944,plain,
! [Ds,Os,Db,Ob] :
( rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob))
| ~ rdn_positive_less(Os,Ob) ),
inference(pre_NNF_transformation,[status(thm)],[f912]) ).
fof(f1945,plain,
! [Os,Ob] :
( ! [Ds,Db] : rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob))
| ~ rdn_positive_less(Os,Ob) ),
inference(miniscoping,[status(thm)],[f1944]) ).
fof(f1946,plain,
! [X0,X1,X2,X3] :
( rdn_positive_less(rdn(rdnn(X2),X0),rdn(rdnn(X3),X1))
| ~ rdn_positive_less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1945]) ).
fof(f1949,plain,
! [D,Db,Ob] :
( rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob))
| ~ rdn_non_zero(Ob) ),
inference(pre_NNF_transformation,[status(thm)],[f914]) ).
fof(f1950,plain,
! [Ob] :
( ! [D,Db] : rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob))
| ~ rdn_non_zero(Ob) ),
inference(miniscoping,[status(thm)],[f1949]) ).
fof(f1951,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X1),rdn(rdnn(X2),X0))
| ~ rdn_non_zero(X0) ),
inference(cnf_transformation,[status(thm)],[f1950]) ).
fof(f1952,plain,
! [X] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(pre_NNF_transformation,[status(thm)],[f915]) ).
fof(f1953,plain,
! [X0] :
( rdn_non_zero(rdnn(X0))
| ~ rdn_non_zero_digit(rdnn(X0)) ),
inference(cnf_transformation,[status(thm)],[f1952]) ).
fof(f1957,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(pre_NNF_transformation,[status(thm)],[f917]) ).
fof(f1958,plain,
! [X,Y] :
( less(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)) ) ),
inference(miniscoping,[status(thm)],[f1957]) ).
fof(f1959,plain,
! [X0,X1,X2,X3] :
( less(X0,X2)
| ~ rdn_positive_less(X1,X3)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[status(thm)],[f1958]) ).
fof(f1979,plain,
! [X,Y] : accept_population(X,Y,n100),
inference(pre_NNF_transformation,[status(thm)],[f924]) ).
fof(f1980,plain,
! [X0,X1] : accept_population(X0,X1,n100),
inference(cnf_transformation,[status(thm)],[f1979]) ).
fof(f2205,plain,
( accept_city(muslimcountrybhumanitarianorganization,towna)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75) ),
inference(resolution,[status(thm)],[f1502,f1013]) ).
fof(f2206,plain,
( accept_city(muslimcountrybhumanitarianorganization,towna)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75) ),
inference(forward_subsumption_resolution,[status(thm)],[f2205,f1503]) ).
fof(f2646,plain,
! [X0,X1] :
( less(X0,n100)
| ~ rdn_positive_less(X1,rdn(rdnn(n0),rdn(rdnn(n0),rdnn(n1))))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[status(thm)],[f1959,f1767]) ).
fof(f4195,plain,
! [X0,X1,X2] :
( less(X1,n100)
| ~ rdn_translate(X1,rdn_pos(rdn(rdnn(X2),X0)))
| ~ rdn_positive_less(X0,rdn(rdnn(n0),rdnn(n1))) ),
inference(resolution,[status(thm)],[f1946,f2646]) ).
fof(f4226,plain,
! [X0,X1,X2] :
( less(X0,n100)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
| ~ rdn_non_zero(rdnn(n1)) ),
inference(resolution,[status(thm)],[f1951,f4195]) ).
fof(f4232,plain,
! [X0,X1,X2] :
( ~ rdn_non_zero_digit(rdnn(n1))
| less(X0,n100)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2)))) ),
inference(resolution,[status(thm)],[f4226,f1953]) ).
fof(f4233,plain,
! [X0,X1,X2] :
( less(X0,n100)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f4232,f1923]) ).
fof(f4244,plain,
! [X0,X1,X2,X3,X4] :
( accept_population(X3,X4,X0)
| ~ accept_population(X3,X4,n100)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2)))) ),
inference(resolution,[status(thm)],[f4233,f936]) ).
fof(f4246,plain,
! [X0,X1,X2,X3,X4] :
( accept_population(X3,X4,X0)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f4244,f1980]) ).
fof(f4532,plain,
! [X0,X1] : accept_population(X0,X1,n75),
inference(resolution,[status(thm)],[f4246,f1742]) ).
fof(f4583,plain,
! [X0,X1] : accept_population(X0,X1,n24),
inference(resolution,[status(thm)],[f4246,f1691]) ).
fof(f4620,plain,
( accept_city(muslimcountrybhumanitarianorganization,towna)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24) ),
inference(backward_subsumption_resolution,[status(thm)],[f2206,f4532]) ).
fof(f4795,plain,
( accept_city(muslimcountrybhumanitarianorganization,towna)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4620,f4583]) ).
fof(f5661,plain,
accept_city(muslimcountrybhumanitarianorganization,towna),
inference(resolution,[status(thm)],[f4795,f1392]) ).
fof(f5666,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5661,f1665]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT026+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.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 : Mon Sep 21 12:55:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.43 % Drodi V4.1.1
% 14.87/2.49 % Refutation found
% 14.87/2.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.87/2.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.27/2.57 % Elapsed time: 2.178763 seconds
% 3.27/2.57 % CPU time: 16.248019 seconds
% 3.27/2.57 % Total memory used: 224.951 MB
% 3.27/2.57 % Net memory used: 220.486 MB
%------------------------------------------------------------------------------