TSTP Solution File: HEN007-2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : HEN007-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 24 unt; 0 def)
% Number of atoms : 79 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 36 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 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 : 77 (; 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
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(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,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,W1,Z,W2] :
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z)
| ~ quotient(X,Z,W2)
| less_equal(W2,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
quotient(z,y,zQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
quotient(z,x,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X,Z] :
( ! [Y] : ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f29,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f30,plain,
! [Z,W] :
( ! [X,Y] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f35,plain,
! [X0] : quotient(X0,zero,X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f36,plain,
! [X,Z] :
( ! [Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z) )
| less_equal(X,Z) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X2)
| less_equal(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [Y,W2] :
( ! [X,Z] :
( ! [W1] :
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z) )
| ~ quotient(X,Z,W2) )
| less_equal(W2,Y) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4] :
( ~ quotient(X0,X1,X2)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X3,X4)
| less_equal(X4,X1) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
less_equal(x,y),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f41,plain,
quotient(z,y,zQy),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f42,plain,
quotient(z,x,zQx),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f43,plain,
~ less_equal(zQy,zQx),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f114,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f35,f23]) ).
fof(f143,plain,
! [X0,X1,X2,X3] :
( ~ less_equal(divide(X0,X1),X2)
| ~ quotient(X0,X2,X3)
| less_equal(X3,X1) ),
inference(resolution,[status(thm)],[f29,f39]) ).
fof(f163,plain,
! [X0] :
( ~ quotient(z,x,X0)
| zQx = X0 ),
inference(resolution,[status(thm)],[f31,f42]) ).
fof(f166,plain,
! [X0,X1] :
( ~ quotient(X0,zero,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f31,f35]) ).
fof(f167,plain,
! [X0,X1,X2] :
( ~ quotient(X0,X1,X2)
| divide(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f31,f29]) ).
fof(f229,plain,
zQx = divide(z,x),
inference(resolution,[status(thm)],[f163,f29]) ).
fof(f298,plain,
! [X0] : X0 = divide(X0,zero),
inference(resolution,[status(thm)],[f166,f29]) ).
fof(f429,plain,
! [X0,X1,X2] :
( ~ quotient(X0,divide(X0,X1),X2)
| less_equal(X2,X1) ),
inference(resolution,[status(thm)],[f143,f114]) ).
fof(f827,plain,
! [X0,X1] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[f429,f29]) ).
fof(f847,plain,
! [X0,X1,X2] :
( ~ less_equal(X0,X1)
| less_equal(divide(X2,divide(X2,X0)),X1) ),
inference(resolution,[status(thm)],[f827,f37]) ).
fof(f865,plain,
less_equal(divide(z,zQx),x),
inference(paramodulation,[status(thm)],[f229,f827]) ).
fof(f893,plain,
quotient(divide(z,zQx),x,zero),
inference(resolution,[status(thm)],[f865,f20]) ).
fof(f1078,plain,
divide(divide(z,zQx),x) = zero,
inference(resolution,[status(thm)],[f893,f167]) ).
fof(f1653,plain,
! [X0] : less_equal(divide(X0,divide(X0,x)),y),
inference(resolution,[status(thm)],[f847,f40]) ).
fof(f1670,plain,
less_equal(divide(divide(z,zQx),zero),y),
inference(paramodulation,[status(thm)],[f1078,f1653]) ).
fof(f1671,plain,
less_equal(divide(z,zQx),y),
inference(forward_demodulation,[status(thm)],[f298,f1670]) ).
fof(f1683,plain,
! [X0] :
( ~ quotient(z,y,X0)
| less_equal(X0,zQx) ),
inference(resolution,[status(thm)],[f1671,f143]) ).
fof(f1780,plain,
less_equal(zQy,zQx),
inference(resolution,[status(thm)],[f1683,f41]) ).
fof(f1781,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1780,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN007-2 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 30 09:29:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Drodi V3.5.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.057273 seconds
% 0.13/0.40 % CPU time: 0.336970 seconds
% 0.13/0.40 % Memory used: 13.644 MB
%------------------------------------------------------------------------------