TSTP Solution File: HEN006-6 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : HEN006-6 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 12:12:47 EDT 2023
% Result : Unsatisfiable 0.16s 0.34s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 23 unt; 0 def)
% Number of atoms : 85 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 33 ~; 30 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 54 (; 54 !; 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(f10,axiom,
! [X] : divide(X,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f14,plain,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f15,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f16,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(f17,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f22,plain,
! [X0] : divide(X0,X0) = zero,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f23,plain,
less_equal(divide(a,b),d),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f24,plain,
~ less_equal(divide(a,d),b),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f25,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| X0 = divide(X0,X1) ),
inference(resolution,[status(thm)],[f18,f15]) ).
fof(f34,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)],[f16,f18]) ).
fof(f35,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[status(thm)],[f17,f25]) ).
fof(f37,plain,
! [X0,X1] :
( ~ less_equal(divide(divide(X0,zero),X1),divide(divide(X0,X1),zero))
| divide(divide(X0,zero),X1) = divide(divide(X0,X1),divide(zero,X1)) ),
inference(paramodulation,[status(thm)],[f35,f34]) ).
fof(f38,plain,
! [X0,X1] :
( ~ less_equal(divide(divide(X0,zero),X1),divide(divide(X0,X1),zero))
| divide(divide(X0,zero),X1) = divide(divide(X0,X1),zero) ),
inference(forward_demodulation,[status(thm)],[f35,f37]) ).
fof(f98,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(X0,divide(X0,zero)),zero))
| divide(divide(X0,zero),divide(X0,zero)) = divide(divide(X0,divide(X0,zero)),zero) ),
inference(paramodulation,[status(thm)],[f22,f38]) ).
fof(f99,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(X0,divide(X0,zero)),zero))
| zero = divide(divide(X0,divide(X0,zero)),zero) ),
inference(forward_demodulation,[status(thm)],[f22,f98]) ).
fof(f100,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(forward_subsumption_resolution,[status(thm)],[f99,f17]) ).
fof(f257,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f258,plain,
divide(divide(a,b),d) = zero,
inference(resolution,[status(thm)],[f13,f23]) ).
fof(f259,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[f13,f15]) ).
fof(f354,plain,
divide(divide(a,d),b) != zero,
inference(resolution,[status(thm)],[f14,f24]) ).
fof(f356,plain,
! [X0,X1] :
( divide(X0,divide(X0,X1)) != zero
| X0 = divide(X0,X1) ),
inference(resolution,[status(thm)],[f14,f25]) ).
fof(f358,plain,
( spl0_4
<=> less_equal(zero,divide(divide(a,d),divide(b,d))) ),
introduced(split_symbol_definition) ).
fof(f360,plain,
( ~ less_equal(zero,divide(divide(a,d),divide(b,d)))
| spl0_4 ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,plain,
( spl0_5
<=> divide(divide(a,b),d) = divide(divide(a,d),divide(b,d)) ),
introduced(split_symbol_definition) ).
fof(f362,plain,
( divide(divide(a,b),d) = divide(divide(a,d),divide(b,d))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,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)],[f258,f34]) ).
fof(f365,plain,
( ~ spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f364,f358,f361]) ).
fof(f416,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f360,f17]) ).
fof(f417,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f418,plain,
( zero = divide(divide(a,d),divide(b,d))
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f258,f362]) ).
fof(f579,plain,
! [X0] :
( divide(divide(X0,divide(X0,zero)),zero) != zero
| divide(X0,divide(X0,zero)) = divide(divide(X0,divide(X0,zero)),zero) ),
inference(paramodulation,[status(thm)],[f100,f356]) ).
fof(f580,plain,
! [X0] :
( zero != zero
| divide(X0,divide(X0,zero)) = divide(divide(X0,divide(X0,zero)),zero) ),
inference(forward_demodulation,[status(thm)],[f100,f579]) ).
fof(f581,plain,
! [X0] :
( zero != zero
| divide(X0,divide(X0,zero)) = zero ),
inference(forward_demodulation,[status(thm)],[f100,f580]) ).
fof(f582,plain,
! [X0] : divide(X0,divide(X0,zero)) = zero,
inference(trivial_equality_resolution,[status(esa)],[f581]) ).
fof(f597,plain,
! [X0] : X0 = divide(X0,zero),
inference(resolution,[status(thm)],[f582,f356]) ).
fof(f933,plain,
! [X0] :
( divide(divide(divide(divide(a,d),X0),divide(divide(b,d),X0)),divide(zero,X0)) = zero
| ~ spl0_5 ),
inference(paramodulation,[status(thm)],[f418,f257]) ).
fof(f934,plain,
! [X0] :
( divide(divide(divide(divide(a,d),X0),divide(divide(b,d),X0)),zero) = zero
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f35,f933]) ).
fof(f935,plain,
! [X0] :
( divide(divide(divide(a,d),X0),divide(divide(b,d),X0)) = zero
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f597,f934]) ).
fof(f1009,plain,
( divide(divide(divide(a,d),b),zero) = zero
| ~ spl0_5 ),
inference(paramodulation,[status(thm)],[f259,f935]) ).
fof(f1010,plain,
( divide(divide(a,d),b) = zero
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f597,f1009]) ).
fof(f1011,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f1010,f354]) ).
fof(f1012,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f1011]) ).
fof(f1013,plain,
$false,
inference(sat_refutation,[status(thm)],[f365,f417,f1012]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : HEN006-6 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n006.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 09:29:47 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.16/0.33 % Drodi V3.5.1
% 0.16/0.34 % Refutation found
% 0.16/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.59 % Elapsed time: 0.040982 seconds
% 0.17/0.59 % CPU time: 0.024006 seconds
% 0.17/0.59 % Memory used: 2.664 MB
%------------------------------------------------------------------------------