TSTP Solution File: HEN008-4 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : HEN008-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 12:12:49 EDT 2023
% Result : Unsatisfiable 0.06s 0.27s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 19 unt; 0 def)
% Number of atoms : 56 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 25 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 49 (; 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( divide(X,Y) != zero
| less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
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(f9,axiom,
! [X] : divide(zero,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f19,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f21,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f22,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0] : divide(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f28,plain,
! [X,Z] :
( ! [Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z) )
| less_equal(X,Z) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X2)
| less_equal(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ less_equal(divide(X0,X1),X2)
| less_equal(divide(X0,X2),X1) ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f33,plain,
less_equal(a,b),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f34,plain,
~ less_equal(divide(a,c),divide(b,c)),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2)))
| divide(divide(X0,X2),divide(X1,X2)) = divide(divide(X0,X1),X2) ),
inference(resolution,[status(thm)],[f22,f20]) ).
fof(f74,plain,
! [X0] :
( ~ less_equal(X0,a)
| less_equal(X0,b) ),
inference(resolution,[status(thm)],[f29,f33]) ).
fof(f96,plain,
! [X0] : less_equal(divide(a,X0),b),
inference(resolution,[status(thm)],[f74,f19]) ).
fof(f177,plain,
! [X0] : less_equal(divide(a,b),X0),
inference(resolution,[status(thm)],[f30,f96]) ).
fof(f232,plain,
! [X0] :
( ~ less_equal(X0,zero)
| X0 = zero ),
inference(resolution,[status(thm)],[f21,f22]) ).
fof(f337,plain,
divide(a,b) = zero,
inference(resolution,[status(thm)],[f177,f232]) ).
fof(f555,plain,
divide(divide(a,c),divide(b,c)) != zero,
inference(resolution,[status(thm)],[f18,f34]) ).
fof(f716,plain,
! [X0] :
( ~ less_equal(divide(zero,X0),divide(divide(a,X0),divide(b,X0)))
| divide(divide(a,X0),divide(b,X0)) = divide(divide(a,b),X0) ),
inference(paramodulation,[status(thm)],[f337,f40]) ).
fof(f717,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(a,X0),divide(b,X0)))
| divide(divide(a,X0),divide(b,X0)) = divide(divide(a,b),X0) ),
inference(forward_demodulation,[status(thm)],[f25,f716]) ).
fof(f718,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(a,X0),divide(b,X0)))
| divide(divide(a,X0),divide(b,X0)) = divide(zero,X0) ),
inference(forward_demodulation,[status(thm)],[f337,f717]) ).
fof(f719,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(a,X0),divide(b,X0)))
| divide(divide(a,X0),divide(b,X0)) = zero ),
inference(forward_demodulation,[status(thm)],[f25,f718]) ).
fof(f720,plain,
! [X0] : divide(divide(a,X0),divide(b,X0)) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f719,f21]) ).
fof(f849,plain,
zero != zero,
inference(backward_demodulation,[status(thm)],[f720,f555]) ).
fof(f850,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f849]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.06 % Problem : HEN008-4 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25 % Computer : n010.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 30 09:23:22 EDT 2023
% 0.06/0.25 % CPUTime :
% 0.06/0.26 % Drodi V3.5.1
% 0.06/0.27 % Refutation found
% 0.06/0.27 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.06/0.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.06/0.28 % Elapsed time: 0.020664 seconds
% 0.06/0.28 % CPU time: 0.084374 seconds
% 0.06/0.28 % Memory used: 14.068 MB
%------------------------------------------------------------------------------