TSTP Solution File: HEN006-7 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : HEN006-7 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 12:12:48 EDT 2023
% Result : Unsatisfiable 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 31 unt; 0 def)
% Number of atoms : 112 ( 13 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 112 ( 57 ~; 55 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 123 (; 123 !; 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(f13,axiom,
! [X] : quotient(X,zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
quotient(x,y,xQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
less_equal(xQy,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
quotient(x,z,xQz),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ less_equal(xQz,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f19,plain,
! [X0,X1] :
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f20,plain,
! [X,Z] :
( ! [Y] : ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f22,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(f23,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)],[f22]) ).
fof(f24,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f25,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f27,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f28,plain,
! [Z,W] :
( ! [X,Y] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f33,plain,
! [X0] : quotient(X0,zero,X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f34,plain,
quotient(x,y,xQy),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f35,plain,
less_equal(xQy,z),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f36,plain,
quotient(x,z,xQz),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f37,plain,
~ less_equal(xQz,y),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(y,X0,X1)
| ~ quotient(x,X0,X2)
| ~ quotient(X2,X1,X3)
| ~ quotient(xQy,X0,X4)
| less_equal(X3,X4) ),
inference(resolution,[status(thm)],[f23,f34]) ).
fof(f58,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[f24,f25]) ).
fof(f75,plain,
quotient(xQy,z,zero),
inference(resolution,[status(thm)],[f35,f18]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ~ quotient(x,X0,X1)
| ~ quotient(X1,divide(y,X0),X2)
| ~ quotient(xQy,X0,X3)
| less_equal(X2,X3) ),
inference(resolution,[status(thm)],[f27,f41]) ).
fof(f92,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)],[f27,f23]) ).
fof(f93,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f27,f21]) ).
fof(f94,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[status(thm)],[f93,f58]) ).
fof(f95,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(resolution,[status(thm)],[f93,f18]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ quotient(divide(X0,X1),X0,X2)
| zero = X2 ),
inference(resolution,[status(thm)],[f29,f95]) ).
fof(f122,plain,
! [X0,X1] :
( ~ quotient(X0,zero,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f29,f33]) ).
fof(f159,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f114,f27]) ).
fof(f233,plain,
! [X0] : X0 = divide(X0,zero),
inference(resolution,[status(thm)],[f122,f27]) ).
fof(f301,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)],[f92,f27]) ).
fof(f459,plain,
! [X0,X1,X2] :
( ~ quotient(x,X0,X1)
| ~ quotient(xQy,X0,X2)
| less_equal(divide(X1,divide(y,X0)),X2) ),
inference(resolution,[status(thm)],[f90,f27]) ).
fof(f1219,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)],[f301,f27]) ).
fof(f1921,plain,
! [X0] :
( ~ quotient(xQy,z,X0)
| less_equal(divide(xQz,divide(y,z)),X0) ),
inference(resolution,[status(thm)],[f459,f36]) ).
fof(f1933,plain,
less_equal(divide(xQz,divide(y,z)),zero),
inference(resolution,[status(thm)],[f1921,f75]) ).
fof(f1936,plain,
zero = divide(xQz,divide(y,z)),
inference(resolution,[status(thm)],[f1933,f58]) ).
fof(f2893,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)],[f1219,f27]) ).
fof(f3870,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(resolution,[status(thm)],[f2893,f27]) ).
fof(f4004,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,divide(X1,X2)),X1)),
inference(paramodulation,[status(thm)],[f159,f3870]) ).
fof(f4005,plain,
! [X0,X1,X2] : less_equal(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)),
inference(forward_demodulation,[status(thm)],[f233,f4004]) ).
fof(f4197,plain,
less_equal(divide(xQz,y),divide(zero,y)),
inference(paramodulation,[status(thm)],[f1936,f4005]) ).
fof(f4198,plain,
less_equal(divide(xQz,y),zero),
inference(forward_demodulation,[status(thm)],[f94,f4197]) ).
fof(f4269,plain,
zero = divide(xQz,y),
inference(resolution,[status(thm)],[f4198,f58]) ).
fof(f4357,plain,
quotient(xQz,y,zero),
inference(paramodulation,[status(thm)],[f4269,f27]) ).
fof(f4366,plain,
less_equal(xQz,y),
inference(resolution,[status(thm)],[f4357,f19]) ).
fof(f4367,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4366,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : HEN006-7 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35 % Computer : n005.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue May 30 09:31:21 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Drodi V3.5.1
% 0.20/0.45 % Refutation found
% 0.20/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.46 % Elapsed time: 0.106759 seconds
% 0.20/0.46 % CPU time: 0.736792 seconds
% 0.20/0.46 % Memory used: 20.859 MB
%------------------------------------------------------------------------------