TSTP Solution File: HEN005-1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : HEN005-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 12:12:46 EDT 2023
% Result : Unsatisfiable 0.05s 0.27s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 26 unt; 0 def)
% Number of atoms : 113 ( 16 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 110 ( 55 ~; 53 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 97 (; 97 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : less_equal(zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z,W] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W)
| Z = W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
less_equal(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f14,plain,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f15,plain,
! [X,Z] :
( ! [Y] : ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f17,plain,
! [V4,V5] :
( ! [V1,Z] :
( ! [V2,V3] :
( ! [X] :
( ! [Y] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2) )
| ~ quotient(X,Z,V3) )
| ~ quotient(V3,V2,V4) )
| ~ quotient(V1,Z,V5) )
| less_equal(V4,V5) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X5,X4,X6)
| ~ quotient(X2,X3,X7)
| less_equal(X6,X7) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f20,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f22,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f23,plain,
! [Z,W] :
( ! [X,Y] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
less_equal(x,y),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f26,plain,
less_equal(y,z),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f27,plain,
~ less_equal(x,z),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f44,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[f19,f20]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X3,X1,X4)
| ~ quotient(X4,X2,X5)
| ~ quotient(divide(X3,X0),X1,X6)
| less_equal(X5,X6) ),
inference(resolution,[status(thm)],[f22,f18]) ).
fof(f47,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f22,f16]) ).
fof(f48,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[status(thm)],[f47,f44]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X2,divide(X3,X1),X4)
| ~ quotient(divide(X0,X3),X1,X5)
| less_equal(X4,X5) ),
inference(resolution,[status(thm)],[f46,f22]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(divide(X0,X1),divide(X2,X1),X3)
| ~ quotient(divide(X0,X2),X1,X4)
| less_equal(X3,X4) ),
inference(resolution,[status(thm)],[f68,f22]) ).
fof(f74,plain,
quotient(y,z,zero),
inference(resolution,[status(thm)],[f13,f26]) ).
fof(f75,plain,
quotient(x,y,zero),
inference(resolution,[status(thm)],[f13,f25]) ).
fof(f104,plain,
! [X0] :
( ~ quotient(x,y,X0)
| zero = X0 ),
inference(resolution,[status(thm)],[f24,f75]) ).
fof(f105,plain,
! [X0] :
( ~ quotient(y,z,X0)
| zero = X0 ),
inference(resolution,[status(thm)],[f24,f74]) ).
fof(f116,plain,
zero = divide(x,y),
inference(resolution,[status(thm)],[f104,f22]) ).
fof(f128,plain,
zero = divide(y,z),
inference(resolution,[status(thm)],[f105,f22]) ).
fof(f216,plain,
! [X0,X1,X2,X3] :
( ~ quotient(divide(X0,X1),X2,X3)
| less_equal(divide(divide(X0,X2),divide(X1,X2)),X3) ),
inference(resolution,[status(thm)],[f71,f22]) ).
fof(f234,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(resolution,[status(thm)],[f216,f22]) ).
fof(f444,plain,
! [X0] : less_equal(divide(divide(x,X0),divide(y,X0)),divide(zero,X0)),
inference(paramodulation,[status(thm)],[f116,f234]) ).
fof(f445,plain,
! [X0] : less_equal(divide(divide(x,X0),divide(y,X0)),zero),
inference(forward_demodulation,[status(thm)],[f48,f444]) ).
fof(f662,plain,
! [X0] : zero = divide(divide(x,X0),divide(y,X0)),
inference(resolution,[status(thm)],[f445,f44]) ).
fof(f683,plain,
zero = divide(divide(x,z),zero),
inference(paramodulation,[status(thm)],[f128,f662]) ).
fof(f744,plain,
quotient(divide(x,z),zero,zero),
inference(paramodulation,[status(thm)],[f683,f22]) ).
fof(f746,plain,
less_equal(divide(x,z),zero),
inference(resolution,[status(thm)],[f744,f14]) ).
fof(f760,plain,
( spl0_12
<=> less_equal(zero,divide(x,z)) ),
introduced(split_symbol_definition) ).
fof(f762,plain,
( ~ less_equal(zero,divide(x,z))
| spl0_12 ),
inference(component_clause,[status(thm)],[f760]) ).
fof(f763,plain,
( spl0_13
<=> divide(x,z) = zero ),
introduced(split_symbol_definition) ).
fof(f764,plain,
( divide(x,z) = zero
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f763]) ).
fof(f766,plain,
( ~ less_equal(zero,divide(x,z))
| divide(x,z) = zero ),
inference(resolution,[status(thm)],[f746,f20]) ).
fof(f767,plain,
( ~ spl0_12
| spl0_13 ),
inference(split_clause,[status(thm)],[f766,f760,f763]) ).
fof(f768,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f762,f19]) ).
fof(f769,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f768]) ).
fof(f815,plain,
( quotient(x,z,zero)
| ~ spl0_13 ),
inference(paramodulation,[status(thm)],[f764,f22]) ).
fof(f818,plain,
( less_equal(x,z)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f815,f14]) ).
fof(f819,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f818,f27]) ).
fof(f820,plain,
~ spl0_13,
inference(contradiction_clause,[status(thm)],[f819]) ).
fof(f821,plain,
$false,
inference(sat_refutation,[status(thm)],[f767,f769,f820]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : HEN005-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.05/0.25 % Computer : n029.cluster.edu
% 0.05/0.25 % Model : x86_64 x86_64
% 0.05/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.25 % Memory : 8042.1875MB
% 0.05/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.05/0.25 % CPULimit : 300
% 0.05/0.25 % WCLimit : 300
% 0.05/0.25 % DateTime : Tue May 30 09:48:36 EDT 2023
% 0.05/0.25 % CPUTime :
% 0.05/0.26 % Drodi V3.5.1
% 0.05/0.27 % Refutation found
% 0.05/0.27 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.05/0.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.49 % Elapsed time: 0.026354 seconds
% 0.09/0.49 % CPU time: 0.065694 seconds
% 0.09/0.49 % Memory used: 3.156 MB
%------------------------------------------------------------------------------