TSTP Solution File: HEN011-4 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : HEN011-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 : Tue Apr 30 20:21:50 EDT 2024
% Result : Unsatisfiable 16.28s 2.45s
% Output : CNFRefutation 16.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 70 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 32 ~; 30 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f6,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| X = Y ),
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(f14,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| less_equal(divide(Z,Y),divide(Z,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X] : divide(identity,divide(identity,divide(identity,X))) = divide(identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f22,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(f24,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f30,plain,
! [X,Z] :
( ! [Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z) )
| less_equal(X,Z) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X2)
| less_equal(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,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,
! [X,Y] :
( ~ less_equal(X,Y)
| ! [Z] : less_equal(divide(Z,Y),divide(Z,X)) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ less_equal(X0,X1)
| less_equal(divide(X2,X1),divide(X2,X0)) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f37,plain,
! [X0] : divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f39,plain,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f95,plain,
( spl0_0
<=> less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a)))) ),
introduced(split_symbol_definition) ).
fof(f97,plain,
( ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a))))
| spl0_0 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( spl0_1
<=> less_equal(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,b)))) ),
introduced(split_symbol_definition) ).
fof(f100,plain,
( ~ less_equal(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,b))))
| spl0_1 ),
inference(component_clause,[status(thm)],[f98]) ).
fof(f101,plain,
( ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a))))
| ~ less_equal(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,b)))) ),
inference(resolution,[status(thm)],[f24,f39]) ).
fof(f102,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f101,f95,f98]) ).
fof(f1114,plain,
! [X0,X1] : less_equal(divide(divide(identity,X0),divide(X1,divide(identity,divide(identity,X0)))),divide(divide(identity,X1),divide(identity,divide(identity,X0)))),
inference(paramodulation,[status(thm)],[f37,f22]) ).
fof(f1156,plain,
! [X0,X1] : less_equal(divide(divide(identity,X0),divide(divide(identity,divide(identity,X1)),X0)),divide(divide(identity,X1),X0)),
inference(paramodulation,[status(thm)],[f37,f22]) ).
fof(f2349,plain,
! [X0] :
( ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),X0)
| ~ less_equal(X0,divide(divide(identity,b),divide(identity,divide(identity,a))))
| spl0_0 ),
inference(resolution,[status(thm)],[f97,f31]) ).
fof(f2403,plain,
( ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,divide(identity,divide(identity,a))),divide(divide(identity,divide(identity,b)),divide(identity,divide(identity,a)))))
| spl0_0 ),
inference(resolution,[status(thm)],[f2349,f1156]) ).
fof(f2404,plain,
( ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,a),divide(divide(identity,divide(identity,b)),divide(identity,divide(identity,a)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f37,f2403]) ).
fof(f2542,plain,
( ~ less_equal(divide(divide(identity,b),divide(divide(identity,a),divide(identity,divide(identity,b)))),divide(identity,divide(identity,a)))
| spl0_1 ),
inference(resolution,[status(thm)],[f100,f32]) ).
fof(f2879,plain,
! [X0] :
( ~ less_equal(divide(divide(identity,b),divide(divide(identity,a),divide(identity,divide(identity,b)))),X0)
| ~ less_equal(X0,divide(identity,divide(identity,a)))
| spl0_1 ),
inference(resolution,[status(thm)],[f2542,f31]) ).
fof(f3697,plain,
( ~ less_equal(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,b))),divide(identity,divide(identity,a)))
| spl0_1 ),
inference(resolution,[status(thm)],[f2879,f1114]) ).
fof(f3698,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f3697,f21]) ).
fof(f3699,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f3698]) ).
fof(f10550,plain,
( ~ less_equal(divide(divide(identity,divide(identity,b)),divide(identity,divide(identity,a))),divide(identity,divide(identity,b)))
| spl0_0 ),
inference(resolution,[status(thm)],[f2404,f34]) ).
fof(f10551,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f10550,f21]) ).
fof(f10552,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f10551]) ).
fof(f10553,plain,
$false,
inference(sat_refutation,[status(thm)],[f102,f3699,f10552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : HEN011-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 20:00:47 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.37 % Drodi V3.6.0
% 16.28/2.45 % Refutation found
% 16.28/2.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 16.28/2.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 16.94/2.52 % Elapsed time: 2.151065 seconds
% 16.94/2.52 % CPU time: 16.842616 seconds
% 16.94/2.52 % Total memory used: 292.622 MB
% 16.94/2.52 % Net memory used: 278.131 MB
%------------------------------------------------------------------------------