TSTP Solution File: HEN006-3 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : HEN006-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 20:21:44 EDT 2024
% Result : Unsatisfiable 0.11s 0.35s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 60 ( 19 unt; 0 def)
% Number of atoms : 110 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 44 ~; 44 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| divide(X,Y) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f8,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f11,plain,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f12,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f13,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(f14,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f15,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f17,plain,
less_equal(divide(a,b),d),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f18,plain,
~ less_equal(divide(a,d),b),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2)))
| divide(divide(X0,X1),X2) = divide(divide(X0,X2),divide(X1,X2)) ),
inference(resolution,[status(thm)],[f13,f15]) ).
fof(f30,plain,
divide(divide(a,b),d) = zero,
inference(resolution,[status(thm)],[f10,f17]) ).
fof(f31,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[f10,f12]) ).
fof(f33,plain,
! [X0,X1] :
( ~ less_equal(divide(divide(divide(X0,X1),X0),X1),zero)
| divide(divide(divide(X0,X1),X0),X1) = divide(divide(divide(X0,X1),X1),divide(X0,X1)) ),
inference(paramodulation,[status(thm)],[f31,f28]) ).
fof(f34,plain,
! [X0,X1] :
( ~ less_equal(divide(zero,X0),zero)
| divide(divide(divide(X1,X0),X1),X0) = divide(divide(divide(X1,X0),X0),divide(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f31,f33]) ).
fof(f35,plain,
! [X0,X1] :
( ~ less_equal(divide(zero,X0),zero)
| divide(zero,X0) = divide(divide(divide(X1,X0),X0),divide(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f31,f34]) ).
fof(f36,plain,
! [X0] :
( ~ less_equal(divide(zero,X0),zero)
| divide(zero,X0) = zero ),
inference(forward_demodulation,[status(thm)],[f31,f35]) ).
fof(f37,plain,
! [X0] : divide(zero,X0) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f36,f12]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero))
| divide(divide(X0,divide(X1,X2)),X1) = divide(divide(X0,X1),divide(divide(X1,X2),X1)) ),
inference(paramodulation,[status(thm)],[f31,f28]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero))
| divide(divide(X0,divide(X1,X2)),X1) = divide(divide(X0,X1),zero) ),
inference(forward_demodulation,[status(thm)],[f31,f43]) ).
fof(f54,plain,
! [X0,X1] : less_equal(zero,divide(X0,X1)),
inference(paramodulation,[status(thm)],[f31,f12]) ).
fof(f152,plain,
( spl0_5
<=> less_equal(zero,divide(divide(a,d),divide(b,d))) ),
introduced(split_symbol_definition) ).
fof(f154,plain,
( ~ less_equal(zero,divide(divide(a,d),divide(b,d)))
| spl0_5 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( spl0_6
<=> divide(divide(a,b),d) = divide(divide(a,d),divide(b,d)) ),
introduced(split_symbol_definition) ).
fof(f156,plain,
( divide(divide(a,b),d) = divide(divide(a,d),divide(b,d))
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( ~ less_equal(zero,divide(divide(a,d),divide(b,d)))
| divide(divide(a,b),d) = divide(divide(a,d),divide(b,d)) ),
inference(paramodulation,[status(thm)],[f30,f28]) ).
fof(f159,plain,
( ~ spl0_5
| spl0_6 ),
inference(split_clause,[status(thm)],[f158,f152,f155]) ).
fof(f193,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f54]) ).
fof(f194,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f195,plain,
( zero = divide(divide(a,d),divide(b,d))
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f30,f156]) ).
fof(f198,plain,
! [X0] :
( ~ less_equal(X0,zero)
| X0 = zero ),
inference(resolution,[status(thm)],[f14,f15]) ).
fof(f536,plain,
( spl0_19
<=> less_equal(divide(zero,b),divide(divide(divide(a,d),b),zero)) ),
introduced(split_symbol_definition) ).
fof(f538,plain,
( ~ less_equal(divide(zero,b),divide(divide(divide(a,d),b),zero))
| spl0_19 ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,plain,
( spl0_20
<=> divide(divide(divide(a,d),divide(b,d)),b) = divide(divide(divide(a,d),b),zero) ),
introduced(split_symbol_definition) ).
fof(f540,plain,
( divide(divide(divide(a,d),divide(b,d)),b) = divide(divide(divide(a,d),b),zero)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f542,plain,
( ~ less_equal(divide(zero,b),divide(divide(divide(a,d),b),zero))
| divide(divide(divide(a,d),divide(b,d)),b) = divide(divide(divide(a,d),b),zero)
| ~ spl0_6 ),
inference(paramodulation,[status(thm)],[f195,f44]) ).
fof(f543,plain,
( ~ spl0_19
| spl0_20
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f542,f536,f539,f155]) ).
fof(f588,plain,
( ~ less_equal(zero,divide(divide(divide(a,d),b),zero))
| spl0_19 ),
inference(forward_demodulation,[status(thm)],[f37,f538]) ).
fof(f589,plain,
( $false
| spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f588,f14]) ).
fof(f590,plain,
spl0_19,
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f592,plain,
( divide(zero,b) = divide(divide(divide(a,d),b),zero)
| ~ spl0_6
| ~ spl0_20 ),
inference(forward_demodulation,[status(thm)],[f195,f540]) ).
fof(f628,plain,
( spl0_28
<=> divide(zero,b) = zero ),
introduced(split_symbol_definition) ).
fof(f630,plain,
( divide(zero,b) != zero
| spl0_28 ),
inference(component_clause,[status(thm)],[f628]) ).
fof(f631,plain,
( spl0_29
<=> less_equal(divide(divide(a,d),b),zero) ),
introduced(split_symbol_definition) ).
fof(f632,plain,
( less_equal(divide(divide(a,d),b),zero)
| ~ spl0_29 ),
inference(component_clause,[status(thm)],[f631]) ).
fof(f634,plain,
( divide(zero,b) != zero
| less_equal(divide(divide(a,d),b),zero)
| ~ spl0_6
| ~ spl0_20 ),
inference(paramodulation,[status(thm)],[f592,f11]) ).
fof(f635,plain,
( ~ spl0_28
| spl0_29
| ~ spl0_6
| ~ spl0_20 ),
inference(split_clause,[status(thm)],[f634,f628,f631,f155,f539]) ).
fof(f688,plain,
( $false
| spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f630,f37]) ).
fof(f689,plain,
spl0_28,
inference(contradiction_clause,[status(thm)],[f688]) ).
fof(f697,plain,
( divide(divide(a,d),b) = zero
| ~ spl0_29 ),
inference(resolution,[status(thm)],[f632,f198]) ).
fof(f711,plain,
( less_equal(divide(a,d),b)
| ~ spl0_29 ),
inference(resolution,[status(thm)],[f697,f11]) ).
fof(f712,plain,
( $false
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[status(thm)],[f711,f18]) ).
fof(f713,plain,
~ spl0_29,
inference(contradiction_clause,[status(thm)],[f712]) ).
fof(f714,plain,
$false,
inference(sat_refutation,[status(thm)],[f159,f194,f543,f590,f635,f689,f713]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : HEN006-3 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n031.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 20:43:13 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Drodi V3.6.0
% 0.11/0.35 % Refutation found
% 0.11/0.35 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.36 % Elapsed time: 0.026265 seconds
% 0.17/0.36 % CPU time: 0.119682 seconds
% 0.17/0.36 % Total memory used: 10.017 MB
% 0.17/0.36 % Net memory used: 9.800 MB
%------------------------------------------------------------------------------