TSTP Solution File: HEN009-6 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : HEN009-6 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 12:12:51 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 66 ( 35 unt; 0 def)
% Number of atoms : 103 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 33 ~; 32 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 44 (; 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| divide(X,Y) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( divide(X,Y) != zero
| less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : less_equal(zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : divide(X,X) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] :
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
divide(identity,a) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
divide(identity,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
divide(identity,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f19,plain,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f20,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f21,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(f22,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f23,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f27,plain,
! [X0] : divide(X0,X0) = zero,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ less_equal(divide(X0,X1),X2)
| less_equal(divide(X0,X2),X1) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f32,plain,
divide(identity,a) = b,
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f33,plain,
divide(identity,b) = c,
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f34,plain,
divide(identity,c) = d,
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f35,plain,
b != d,
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f56,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f19,f27]) ).
fof(f57,plain,
( spl0_0
<=> zero = zero ),
introduced(split_symbol_definition) ).
fof(f59,plain,
( zero != zero
| spl0_0 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f104,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f59]) ).
fof(f105,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f121,plain,
! [X0] : less_equal(divide(b,divide(X0,a)),divide(divide(identity,X0),a)),
inference(paramodulation,[status(thm)],[f32,f21]) ).
fof(f167,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[f23,f20]) ).
fof(f168,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[f23,f22]) ).
fof(f229,plain,
! [X0,X1] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[f28,f56]) ).
fof(f433,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f229,f168]) ).
fof(f438,plain,
less_equal(divide(identity,c),b),
inference(paramodulation,[status(thm)],[f33,f229]) ).
fof(f439,plain,
less_equal(d,b),
inference(forward_demodulation,[status(thm)],[f34,f438]) ).
fof(f441,plain,
less_equal(divide(identity,b),a),
inference(paramodulation,[status(thm)],[f32,f229]) ).
fof(f442,plain,
less_equal(c,a),
inference(forward_demodulation,[status(thm)],[f33,f441]) ).
fof(f459,plain,
divide(d,b) = zero,
inference(resolution,[status(thm)],[f439,f18]) ).
fof(f469,plain,
divide(c,a) = zero,
inference(resolution,[status(thm)],[f442,f18]) ).
fof(f472,plain,
! [X0] :
( ~ less_equal(zero,X0)
| less_equal(divide(d,X0),b) ),
inference(paramodulation,[status(thm)],[f459,f28]) ).
fof(f473,plain,
! [X0] : less_equal(divide(d,X0),b),
inference(forward_subsumption_resolution,[status(thm)],[f472,f22]) ).
fof(f487,plain,
( spl0_25
<=> less_equal(d,b) ),
introduced(split_symbol_definition) ).
fof(f490,plain,
( zero != zero
| less_equal(d,b) ),
inference(paramodulation,[status(thm)],[f459,f19]) ).
fof(f491,plain,
( ~ spl0_0
| spl0_25 ),
inference(split_clause,[status(thm)],[f490,f57,f487]) ).
fof(f495,plain,
less_equal(divide(b,zero),divide(divide(identity,c),a)),
inference(paramodulation,[status(thm)],[f469,f121]) ).
fof(f496,plain,
less_equal(divide(b,zero),divide(d,a)),
inference(forward_demodulation,[status(thm)],[f34,f495]) ).
fof(f1078,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f433,f19]) ).
fof(f1150,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[status(thm)],[f1078,f167]) ).
fof(f5038,plain,
less_equal(b,divide(d,a)),
inference(forward_demodulation,[status(thm)],[f1150,f496]) ).
fof(f5042,plain,
( spl0_90
<=> less_equal(divide(d,a),b) ),
introduced(split_symbol_definition) ).
fof(f5044,plain,
( ~ less_equal(divide(d,a),b)
| spl0_90 ),
inference(component_clause,[status(thm)],[f5042]) ).
fof(f5045,plain,
( spl0_91
<=> b = divide(d,a) ),
introduced(split_symbol_definition) ).
fof(f5046,plain,
( b = divide(d,a)
| ~ spl0_91 ),
inference(component_clause,[status(thm)],[f5045]) ).
fof(f5048,plain,
( ~ less_equal(divide(d,a),b)
| b = divide(d,a) ),
inference(resolution,[status(thm)],[f5038,f23]) ).
fof(f5049,plain,
( ~ spl0_90
| spl0_91 ),
inference(split_clause,[status(thm)],[f5048,f5042,f5045]) ).
fof(f5051,plain,
( $false
| spl0_90 ),
inference(forward_subsumption_resolution,[status(thm)],[f5044,f473]) ).
fof(f5052,plain,
spl0_90,
inference(contradiction_clause,[status(thm)],[f5051]) ).
fof(f5123,plain,
( spl0_93
<=> divide(d,a) = d ),
introduced(split_symbol_definition) ).
fof(f5124,plain,
( divide(d,a) = d
| ~ spl0_93 ),
inference(component_clause,[status(thm)],[f5123]) ).
fof(f5126,plain,
( ~ less_equal(d,b)
| divide(d,a) = d
| ~ spl0_91 ),
inference(paramodulation,[status(thm)],[f5046,f167]) ).
fof(f5127,plain,
( ~ spl0_25
| spl0_93
| ~ spl0_91 ),
inference(split_clause,[status(thm)],[f5126,f487,f5123,f5045]) ).
fof(f5141,plain,
( b = d
| ~ spl0_91
| ~ spl0_93 ),
inference(forward_demodulation,[status(thm)],[f5046,f5124]) ).
fof(f5142,plain,
( $false
| ~ spl0_91
| ~ spl0_93 ),
inference(forward_subsumption_resolution,[status(thm)],[f5141,f35]) ).
fof(f5143,plain,
( ~ spl0_91
| ~ spl0_93 ),
inference(contradiction_clause,[status(thm)],[f5142]) ).
fof(f5144,plain,
$false,
inference(sat_refutation,[status(thm)],[f105,f491,f5049,f5052,f5127,f5143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN009-6 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 09:32:58 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.34 % Drodi V3.5.1
% 0.19/0.38 % Refutation found
% 0.19/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.40 % Elapsed time: 0.055654 seconds
% 0.19/0.40 % CPU time: 0.310699 seconds
% 0.19/0.40 % Memory used: 19.257 MB
%------------------------------------------------------------------------------