%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : AGT020+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 11:47:14 AM UTC 2026
% Result : Theorem 94.68s 12.59s
% Output : CNFRefutation 94.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 19
% Syntax : Number of formulae : 79 ( 31 unt; 0 def)
% Number of atoms : 211 ( 23 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 227 ( 95 ~; 101 |; 24 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-2 aty)
% Number of variables : 96 ( 92 !; 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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f362,axiom,
accept_population(muslimcountrybhumanitarianorganization,other,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f472,axiom,
accept_population(muslimcountrybhumanitarianorganization,native,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f473,axiom,
accept_population(muslimcountrybhumanitarianorganization,muslim,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f475,axiom,
accept_population(muslimcountrybhumanitarianorganization,atheist,n78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f635,axiom,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f712,axiom,
rdn_translate(n75,rdn_pos(rdn(rdnn(n5),rdnn(n7)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f715,axiom,
rdn_translate(n78,rdn_pos(rdn(rdnn(n8),rdnn(n7)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f899,axiom,
rdn_non_zero_digit(rdnn(n7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f907,axiom,
rdn_positive_less(rdnn(n5),rdnn(n6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f908,axiom,
rdn_positive_less(rdnn(n6),rdnn(n7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f909,axiom,
rdn_positive_less(rdnn(n7),rdnn(n8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f911,axiom,
! [X,Y,Z] :
( ( rdn_positive_less(rdnn(Y),rdnn(Z))
& rdn_positive_less(rdnn(X),rdnn(Y)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f913,axiom,
! [Ds,O,Db] :
( ( rdn_non_zero(O)
& rdn_positive_less(rdnn(Ds),rdnn(Db)) )
=> rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f915,axiom,
! [X] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f920,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f923,conjecture,
? [X,Y] : ~ accept_population(X,christian,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f924,negated_conjecture,
~ ? [X,Y] : ~ accept_population(X,christian,Y),
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(X2,X3,X0)
| ~ accept_population(X2,X3,X1)
| ~ less(X0,X1) ),
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_population(X0,muslim,n1)
| ~ accept_population(X0,other,n0)
| ~ accept_population(X0,atheist,n75)
| ~ accept_population(X0,christian,n24)
| ~ accept_population(X0,native,n0)
| accept_city(X0,towna) ),
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(f1505,plain,
accept_population(muslimcountrybhumanitarianorganization,atheist,n78),
inference(cnf_transformation,[status(thm)],[f475]) ).
fof(f1665,plain,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
inference(cnf_transformation,[status(thm)],[f635]) ).
fof(f1742,plain,
rdn_translate(n75,rdn_pos(rdn(rdnn(n5),rdnn(n7)))),
inference(cnf_transformation,[status(thm)],[f712]) ).
fof(f1745,plain,
rdn_translate(n78,rdn_pos(rdn(rdnn(n8),rdnn(n7)))),
inference(cnf_transformation,[status(thm)],[f715]) ).
fof(f1929,plain,
rdn_non_zero_digit(rdnn(n7)),
inference(cnf_transformation,[status(thm)],[f899]) ).
fof(f1937,plain,
rdn_positive_less(rdnn(n5),rdnn(n6)),
inference(cnf_transformation,[status(thm)],[f907]) ).
fof(f1938,plain,
rdn_positive_less(rdnn(n6),rdnn(n7)),
inference(cnf_transformation,[status(thm)],[f908]) ).
fof(f1939,plain,
rdn_positive_less(rdnn(n7),rdnn(n8)),
inference(cnf_transformation,[status(thm)],[f909]) ).
fof(f1941,plain,
! [X,Y,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ),
inference(pre_NNF_transformation,[status(thm)],[f911]) ).
fof(f1942,plain,
! [X,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ! [Y] :
( ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ) ),
inference(miniscoping,[status(thm)],[f1941]) ).
fof(f1943,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X2),rdnn(X1))
| ~ rdn_positive_less(rdnn(X2),rdnn(X0))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(cnf_transformation,[status(thm)],[f1942]) ).
fof(f1947,plain,
! [Ds,O,Db] :
( rdn_positive_less(rdn(rdnn(Ds),O),rdn(rdnn(Db),O))
| ~ rdn_non_zero(O)
| ~ rdn_positive_less(rdnn(Ds),rdnn(Db)) ),
inference(pre_NNF_transformation,[status(thm)],[f913]) ).
fof(f1948,plain,
! [X0,X1,X2] :
( ~ rdn_non_zero(X2)
| rdn_positive_less(rdn(rdnn(X0),X2),rdn(rdnn(X1),X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(cnf_transformation,[status(thm)],[f1947]) ).
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_digit(rdnn(X0))
| rdn_non_zero(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] :
( ~ rdn_translate(X2,rdn_pos(X0))
| ~ rdn_translate(X3,rdn_pos(X1))
| less(X2,X3)
| ~ rdn_positive_less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1958]) ).
fof(f1966,plain,
! [X,Y] :
( ( Y = X
| less(Y,X)
| less(X,Y) )
& ( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f920]) ).
fof(f1967,plain,
( ! [X,Y] :
( Y = X
| less(Y,X)
| less(X,Y) )
& ! [X,Y] :
( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1966]) ).
fof(f1968,plain,
! [X0,X1] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1967]) ).
fof(f1970,plain,
! [X0,X1] :
( less(X1,X0)
| less(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f1967]) ).
fof(f1979,plain,
! [X,Y] : accept_population(X,christian,Y),
inference(pre_NNF_transformation,[status(thm)],[f924]) ).
fof(f1980,plain,
! [X0,X1] : accept_population(X0,christian,X1),
inference(cnf_transformation,[status(thm)],[f1979]) ).
fof(f1992,plain,
rdn_non_zero(rdnn(n7)),
inference(resolution,[status(thm)],[f1953,f1929]) ).
fof(f2287,plain,
! [X0,X1,X2,X3] :
( ~ rdn_positive_less(X2,X3)
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_pos(X2))
| ~ less(X0,X1) ),
inference(resolution,[status(thm)],[f1959,f1968]) ).
fof(f2546,plain,
! [X0] :
( ~ accept_population(X0,other,n0)
| accept_city(X0,towna)
| ~ accept_population(X0,muslim,n1)
| ~ accept_population(X0,atheist,n75)
| ~ accept_population(X0,native,n0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1013,f1980]) ).
fof(f2633,plain,
! [X0,X1,X2,X3] :
( ~ accept_population(X0,X1,X3)
| X3 = X2
| less(X3,X2)
| accept_population(X0,X1,X2) ),
inference(resolution,[status(thm)],[f936,f1970]) ).
fof(f2867,plain,
! [X0] :
( X0 = n78
| accept_population(muslimcountrybhumanitarianorganization,atheist,X0)
| less(n78,X0) ),
inference(resolution,[status(thm)],[f2633,f1505]) ).
fof(f3085,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| accept_city(muslimcountrybhumanitarianorganization,towna)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| n75 = n78
| less(n78,n75) ),
inference(resolution,[status(thm)],[f2867,f2546]) ).
fof(f3097,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| less(n78,n75)
| accept_city(muslimcountrybhumanitarianorganization,towna)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| n75 = n78 ),
inference(forward_subsumption_resolution,[status(thm)],[f3085,f1502]) ).
fof(f3361,plain,
( less(n78,n75)
| n78 = n75
| accept_city(muslimcountrybhumanitarianorganization,towna)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3097,f1392]) ).
fof(f3362,plain,
( less(n78,n75)
| n78 = n75
| accept_city(muslimcountrybhumanitarianorganization,towna) ),
inference(resolution,[status(thm)],[f3361,f1503]) ).
fof(f3377,plain,
( n75 = n78
| less(n78,n75) ),
inference(forward_subsumption_resolution,[status(thm)],[f3362,f1665]) ).
fof(f3380,plain,
! [X0,X1] :
( ~ rdn_translate(n78,rdn_pos(X1))
| ~ rdn_translate(n75,rdn_pos(X0))
| n75 = n78
| ~ rdn_positive_less(X0,X1) ),
inference(resolution,[status(thm)],[f3377,f2287]) ).
fof(f3435,plain,
! [X0] :
( ~ rdn_translate(n75,rdn_pos(X0))
| ~ rdn_positive_less(X0,rdn(rdnn(n8),rdnn(n7)))
| n75 = n78 ),
inference(resolution,[status(thm)],[f3380,f1745]) ).
fof(f3516,plain,
( n78 = n75
| ~ rdn_positive_less(rdn(rdnn(n5),rdnn(n7)),rdn(rdnn(n8),rdnn(n7))) ),
inference(resolution,[status(thm)],[f3435,f1742]) ).
fof(f3537,plain,
( ~ rdn_non_zero(rdnn(n7))
| ~ rdn_positive_less(rdnn(n5),rdnn(n8))
| n78 = n75 ),
inference(resolution,[status(thm)],[f3516,f1948]) ).
fof(f3539,plain,
( ~ rdn_positive_less(rdnn(n5),rdnn(n8))
| n78 = n75 ),
inference(forward_subsumption_resolution,[status(thm)],[f3537,f1992]) ).
fof(f3540,plain,
! [X0] :
( ~ rdn_positive_less(rdnn(X0),rdnn(n8))
| n75 = n78
| ~ rdn_positive_less(rdnn(n5),rdnn(X0)) ),
inference(resolution,[status(thm)],[f3539,f1943]) ).
fof(f3651,plain,
( ~ rdn_positive_less(rdnn(n6),rdnn(n8))
| n75 = n78 ),
inference(resolution,[status(thm)],[f3540,f1937]) ).
fof(f3656,plain,
! [X0] :
( n75 = n78
| ~ rdn_positive_less(rdnn(X0),rdnn(n8))
| ~ rdn_positive_less(rdnn(n6),rdnn(X0)) ),
inference(resolution,[status(thm)],[f3651,f1943]) ).
fof(f3699,plain,
( n75 = n78
| ~ rdn_positive_less(rdnn(n7),rdnn(n8)) ),
inference(resolution,[status(thm)],[f3656,f1938]) ).
fof(f3701,plain,
n78 = n75,
inference(forward_subsumption_resolution,[status(thm)],[f3699,f1939]) ).
fof(f3746,plain,
accept_population(muslimcountrybhumanitarianorganization,atheist,n75),
inference(backward_demodulation,[status(thm)],[f3701,f1505]) ).
fof(f3773,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| accept_city(muslimcountrybhumanitarianorganization,towna)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0) ),
inference(resolution,[status(thm)],[f3746,f2546]) ).
fof(f3776,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| accept_city(muslimcountrybhumanitarianorganization,towna)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3773,f1502]) ).
fof(f3927,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| accept_city(muslimcountrybhumanitarianorganization,towna) ),
inference(forward_subsumption_resolution,[status(thm)],[f3776,f1392]) ).
fof(f3928,plain,
accept_city(muslimcountrybhumanitarianorganization,towna),
inference(resolution,[status(thm)],[f3927,f1503]) ).
fof(f3937,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3928,f1665]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : AGT020+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37 % Computer : n001.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 12:55:44 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.17/0.42 % Drodi V4.1.1
% 94.68/12.59 % Refutation found
% 94.68/12.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 94.68/12.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.74/12.67 % Elapsed time: 12.273618 seconds
% 14.74/12.67 % CPU time: 96.576701 seconds
% 14.74/12.67 % Total memory used: 408.213 MB
% 14.74/12.67 % Net memory used: 393.576 MB
%------------------------------------------------------------------------------