TSTP Solution File: AGT026+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : AGT026+2 : TPTP v8.1.2. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 11:58:32 EDT 2023
% Result : Theorem 10.16s 1.82s
% Output : CNFRefutation 10.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 75 ( 28 unt; 0 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 190 ( 82 ~; 80 |; 17 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 6 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-2 aty)
% Number of variables : 130 (; 126 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,N,M,P] :
( ( accept_population(A,P,N)
& less(M,N) )
=> accept_population(A,P,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
<=> 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(f635,axiom,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f661,axiom,
rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))),
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(f737,axiom,
rdn_translate(n100,rdn_pos(rdn(rdnn(n0),rdn(rdnn(n0),rdnn(n1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f893,axiom,
rdn_non_zero_digit(rdnn(n1)),
file('/export/starexec/sandbox/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/sandbox/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/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_translate(X,rdn_pos(RDN_X))
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_positive_less(RDN_X,RDN_Y) )
=> less(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f923,conjecture,
? [X,Y] : ~ accept_population(X,Y,n100),
file('/export/starexec/sandbox/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,N)
| ~ less(M,N)
| accept_population(A,P,M) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f935,plain,
! [A,M,P] :
( ! [N] :
( ~ accept_population(A,P,N)
| ~ less(M,N) )
| accept_population(A,P,M) ),
inference(miniscoping,[status(esa)],[f934]) ).
fof(f936,plain,
! [X0,X1,X2,X3] :
( ~ accept_population(X0,X1,X2)
| ~ less(X3,X2)
| accept_population(X0,X1,X3) ),
inference(cnf_transformation,[status(esa)],[f935]) ).
fof(f1011,plain,
! [A] :
( ( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0)
| accept_city(A,towna) )
& ( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
| ~ accept_city(A,towna) ) ),
inference(NNF_transformation,[status(esa)],[f16]) ).
fof(f1012,plain,
( ! [A] :
( ~ accept_population(A,atheist,n75)
| ~ accept_population(A,christian,n24)
| ~ accept_population(A,muslim,n1)
| ~ accept_population(A,native,n0)
| ~ accept_population(A,other,n0)
| accept_city(A,towna) )
& ! [A] :
( ( accept_population(A,atheist,n75)
& accept_population(A,christian,n24)
& accept_population(A,muslim,n1)
& accept_population(A,native,n0)
& accept_population(A,other,n0) )
| ~ accept_city(A,towna) ) ),
inference(miniscoping,[status(esa)],[f1011]) ).
fof(f1013,plain,
! [X0] :
( ~ accept_population(X0,atheist,n75)
| ~ accept_population(X0,christian,n24)
| ~ accept_population(X0,muslim,n1)
| ~ accept_population(X0,native,n0)
| ~ accept_population(X0,other,n0)
| accept_city(X0,towna) ),
inference(cnf_transformation,[status(esa)],[f1012]) ).
fof(f1392,plain,
accept_population(muslimcountrybhumanitarianorganization,other,n0),
inference(cnf_transformation,[status(esa)],[f362]) ).
fof(f1502,plain,
accept_population(muslimcountrybhumanitarianorganization,native,n0),
inference(cnf_transformation,[status(esa)],[f472]) ).
fof(f1503,plain,
accept_population(muslimcountrybhumanitarianorganization,muslim,n1),
inference(cnf_transformation,[status(esa)],[f473]) ).
fof(f1665,plain,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
inference(cnf_transformation,[status(esa)],[f635]) ).
fof(f1691,plain,
rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))),
inference(cnf_transformation,[status(esa)],[f661]) ).
fof(f1742,plain,
rdn_translate(n75,rdn_pos(rdn(rdnn(n5),rdnn(n7)))),
inference(cnf_transformation,[status(esa)],[f712]) ).
fof(f1767,plain,
rdn_translate(n100,rdn_pos(rdn(rdnn(n0),rdn(rdnn(n0),rdnn(n1))))),
inference(cnf_transformation,[status(esa)],[f737]) ).
fof(f1923,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(cnf_transformation,[status(esa)],[f893]) ).
fof(f1944,plain,
! [Ds,Os,Db,Ob] :
( ~ rdn_positive_less(Os,Ob)
| rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
inference(pre_NNF_transformation,[status(esa)],[f912]) ).
fof(f1945,plain,
! [Os,Ob] :
( ~ rdn_positive_less(Os,Ob)
| ! [Ds,Db] : rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
inference(miniscoping,[status(esa)],[f1944]) ).
fof(f1946,plain,
! [X0,X1,X2,X3] :
( ~ rdn_positive_less(X0,X1)
| rdn_positive_less(rdn(rdnn(X2),X0),rdn(rdnn(X3),X1)) ),
inference(cnf_transformation,[status(esa)],[f1945]) ).
fof(f1949,plain,
! [D,Db,Ob] :
( ~ rdn_non_zero(Ob)
| rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
inference(pre_NNF_transformation,[status(esa)],[f914]) ).
fof(f1950,plain,
! [Ob] :
( ~ rdn_non_zero(Ob)
| ! [D,Db] : rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
inference(miniscoping,[status(esa)],[f1949]) ).
fof(f1951,plain,
! [X0,X1,X2] :
( ~ rdn_non_zero(X0)
| rdn_positive_less(rdnn(X1),rdn(rdnn(X2),X0)) ),
inference(cnf_transformation,[status(esa)],[f1950]) ).
fof(f1952,plain,
! [X] :
( ~ rdn_non_zero_digit(rdnn(X))
| rdn_non_zero(rdnn(X)) ),
inference(pre_NNF_transformation,[status(esa)],[f915]) ).
fof(f1953,plain,
! [X0] :
( ~ rdn_non_zero_digit(rdnn(X0))
| rdn_non_zero(rdnn(X0)) ),
inference(cnf_transformation,[status(esa)],[f1952]) ).
fof(f1957,plain,
! [X,Y,RDN_X,RDN_Y] :
( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y)
| less(X,Y) ),
inference(pre_NNF_transformation,[status(esa)],[f917]) ).
fof(f1958,plain,
! [X,Y] :
( ! [RDN_X,RDN_Y] :
( ~ rdn_translate(X,rdn_pos(RDN_X))
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_positive_less(RDN_X,RDN_Y) )
| less(X,Y) ),
inference(miniscoping,[status(esa)],[f1957]) ).
fof(f1959,plain,
! [X0,X1,X2,X3] :
( ~ rdn_translate(X0,rdn_pos(X1))
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_positive_less(X1,X3)
| less(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f1958]) ).
fof(f1979,plain,
! [X,Y] : accept_population(X,Y,n100),
inference(pre_NNF_transformation,[status(esa)],[f924]) ).
fof(f1980,plain,
! [X0,X1] : accept_population(X0,X1,n100),
inference(cnf_transformation,[status(esa)],[f1979]) ).
fof(f2835,plain,
( spl0_144
<=> accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
introduced(split_symbol_definition) ).
fof(f2837,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| spl0_144 ),
inference(component_clause,[status(thm)],[f2835]) ).
fof(f2841,plain,
( $false
| spl0_144 ),
inference(forward_subsumption_resolution,[status(thm)],[f2837,f1392]) ).
fof(f2842,plain,
spl0_144,
inference(contradiction_clause,[status(thm)],[f2841]) ).
fof(f3508,plain,
( spl0_273
<=> accept_city(muslimcountrybhumanitarianorganization,towna) ),
introduced(split_symbol_definition) ).
fof(f3509,plain,
( accept_city(muslimcountrybhumanitarianorganization,towna)
| ~ spl0_273 ),
inference(component_clause,[status(thm)],[f3508]) ).
fof(f3567,plain,
( spl0_287
<=> accept_population(muslimcountrybhumanitarianorganization,atheist,n75) ),
introduced(split_symbol_definition) ).
fof(f3569,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| spl0_287 ),
inference(component_clause,[status(thm)],[f3567]) ).
fof(f3570,plain,
( spl0_288
<=> accept_population(muslimcountrybhumanitarianorganization,christian,n24) ),
introduced(split_symbol_definition) ).
fof(f3572,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| spl0_288 ),
inference(component_clause,[status(thm)],[f3570]) ).
fof(f3588,plain,
( spl0_289
<=> accept_population(muslimcountrybhumanitarianorganization,native,n0) ),
introduced(split_symbol_definition) ).
fof(f3590,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| spl0_289 ),
inference(component_clause,[status(thm)],[f3588]) ).
fof(f3591,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| accept_city(muslimcountrybhumanitarianorganization,towna) ),
inference(resolution,[status(thm)],[f1503,f1013]) ).
fof(f3592,plain,
( ~ spl0_287
| ~ spl0_288
| ~ spl0_289
| ~ spl0_144
| spl0_273 ),
inference(split_clause,[status(thm)],[f3591,f3567,f3570,f3588,f2835,f3508]) ).
fof(f3622,plain,
( $false
| spl0_289 ),
inference(forward_subsumption_resolution,[status(thm)],[f3590,f1502]) ).
fof(f3623,plain,
spl0_289,
inference(contradiction_clause,[status(thm)],[f3622]) ).
fof(f5254,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rdn_translate(X0,rdn_pos(X1))
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_positive_less(X1,X3)
| ~ accept_population(X4,X5,X2)
| accept_population(X4,X5,X0) ),
inference(resolution,[status(thm)],[f1959,f936]) ).
fof(f5260,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2)))
| ~ rdn_translate(X3,rdn_pos(rdn(rdnn(X4),X5)))
| ~ accept_population(X6,X7,X3)
| accept_population(X6,X7,X0)
| ~ rdn_positive_less(X2,X5) ),
inference(resolution,[status(thm)],[f5254,f1946]) ).
fof(f5284,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
| ~ rdn_translate(X3,rdn_pos(rdn(rdnn(X4),rdn(rdnn(X5),X6))))
| ~ accept_population(X7,X8,X3)
| accept_population(X7,X8,X0)
| ~ rdn_non_zero(X6) ),
inference(resolution,[status(thm)],[f5260,f1951]) ).
fof(f5364,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
| ~ rdn_translate(X3,rdn_pos(rdn(rdnn(X4),rdn(rdnn(X5),rdnn(X6)))))
| ~ accept_population(X7,X8,X3)
| accept_population(X7,X8,X0)
| ~ rdn_non_zero_digit(rdnn(X6)) ),
inference(resolution,[status(thm)],[f5284,f1953]) ).
fof(f5386,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
| ~ rdn_translate(X3,rdn_pos(rdn(rdnn(X4),rdn(rdnn(X5),rdnn(n1)))))
| ~ accept_population(X6,X7,X3)
| accept_population(X6,X7,X0) ),
inference(resolution,[status(thm)],[f5364,f1923]) ).
fof(f5414,plain,
! [X0,X1,X2,X3,X4] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
| ~ accept_population(X3,X4,n100)
| accept_population(X3,X4,X0) ),
inference(resolution,[status(thm)],[f5386,f1767]) ).
fof(f5415,plain,
! [X0,X1,X2,X3,X4] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(X2))))
| accept_population(X3,X4,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f5414,f1980]) ).
fof(f5480,plain,
! [X0,X1] : accept_population(X0,X1,n75),
inference(resolution,[status(thm)],[f5415,f1742]) ).
fof(f5538,plain,
! [X0,X1] : accept_population(X0,X1,n24),
inference(resolution,[status(thm)],[f5415,f1691]) ).
fof(f5553,plain,
( $false
| spl0_287 ),
inference(backward_subsumption_resolution,[status(thm)],[f3569,f5480]) ).
fof(f5554,plain,
spl0_287,
inference(contradiction_clause,[status(thm)],[f5553]) ).
fof(f5781,plain,
( $false
| spl0_288 ),
inference(backward_subsumption_resolution,[status(thm)],[f3572,f5538]) ).
fof(f5782,plain,
spl0_288,
inference(contradiction_clause,[status(thm)],[f5781]) ).
fof(f5855,plain,
( $false
| ~ spl0_273 ),
inference(forward_subsumption_resolution,[status(thm)],[f3509,f1665]) ).
fof(f5856,plain,
~ spl0_273,
inference(contradiction_clause,[status(thm)],[f5855]) ).
fof(f5857,plain,
$false,
inference(sat_refutation,[status(thm)],[f2842,f3592,f3623,f5554,f5782,f5856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.28 % Problem : AGT026+2 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.06/0.28 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.50 % Computer : n029.cluster.edu
% 0.06/0.50 % Model : x86_64 x86_64
% 0.06/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.50 % Memory : 8042.1875MB
% 0.06/0.50 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.50 % CPULimit : 300
% 0.06/0.50 % WCLimit : 300
% 0.06/0.50 % DateTime : Tue May 30 11:06:37 EDT 2023
% 0.06/0.50 % CPUTime :
% 0.06/0.51 % Drodi V3.5.1
% 10.16/1.82 % Refutation found
% 10.16/1.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.16/1.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.16/1.85 % Elapsed time: 1.343021 seconds
% 10.16/1.85 % CPU time: 10.515640 seconds
% 10.16/1.85 % Memory used: 161.604 MB
%------------------------------------------------------------------------------