TSTP Solution File: HEN007-3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : HEN007-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 26 unt; 0 def)
% Number of atoms : 74 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 27 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 73 (; 73 !; 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(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)),
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(a,b),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f18,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f19,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[f15,f12]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2)))
| divide(divide(X0,X2),divide(X1,X2)) = divide(divide(X0,X1),X2) ),
inference(resolution,[status(thm)],[f13,f15]) ).
fof(f29,plain,
! [X0] : divide(zero,X0) = zero,
inference(resolution,[status(thm)],[f14,f19]) ).
fof(f30,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[f14,f15]) ).
fof(f31,plain,
! [X0,X1] :
( ~ less_equal(divide(divide(X0,zero),X1),divide(divide(X0,X1),zero))
| divide(divide(X0,X1),divide(zero,X1)) = divide(divide(X0,zero),X1) ),
inference(paramodulation,[status(thm)],[f29,f28]) ).
fof(f32,plain,
! [X0,X1] :
( ~ less_equal(divide(divide(X0,zero),X1),divide(divide(X0,X1),zero))
| divide(divide(X0,X1),zero) = divide(divide(X0,zero),X1) ),
inference(forward_demodulation,[status(thm)],[f29,f31]) ).
fof(f95,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[f10,f12]) ).
fof(f96,plain,
divide(a,b) = zero,
inference(resolution,[status(thm)],[f10,f17]) ).
fof(f144,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(X0,X0),zero))
| divide(divide(X0,X0),zero) = divide(divide(X0,zero),X0) ),
inference(paramodulation,[status(thm)],[f95,f32]) ).
fof(f145,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(X0,X0),zero))
| divide(divide(X0,X0),zero) = zero ),
inference(forward_demodulation,[status(thm)],[f95,f144]) ).
fof(f146,plain,
! [X0] : divide(divide(X0,X0),zero) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f145,f14]) ).
fof(f200,plain,
! [X0,X1,X2] :
( ~ less_equal(divide(zero,X0),divide(divide(divide(X1,X2),X0),divide(X1,X0)))
| divide(divide(divide(X1,X2),X0),divide(X1,X0)) = divide(divide(divide(X1,X2),X1),X0) ),
inference(paramodulation,[status(thm)],[f95,f28]) ).
fof(f201,plain,
! [X0,X1,X2] :
( ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2)))
| divide(divide(divide(X0,X1),X2),divide(X0,X2)) = divide(divide(divide(X0,X1),X0),X2) ),
inference(forward_demodulation,[status(thm)],[f29,f200]) ).
fof(f202,plain,
! [X0,X1,X2] :
( ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2)))
| divide(divide(divide(X0,X1),X2),divide(X0,X2)) = divide(zero,X2) ),
inference(forward_demodulation,[status(thm)],[f95,f201]) ).
fof(f203,plain,
! [X0,X1,X2] :
( ~ less_equal(zero,divide(divide(divide(X0,X1),X2),divide(X0,X2)))
| divide(divide(divide(X0,X1),X2),divide(X0,X2)) = zero ),
inference(forward_demodulation,[status(thm)],[f29,f202]) ).
fof(f204,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),X2),divide(X0,X2)) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f203,f14]) ).
fof(f296,plain,
! [X0] :
( ~ less_equal(divide(divide(X0,a),b),divide(divide(X0,b),zero))
| divide(divide(X0,b),divide(a,b)) = divide(divide(X0,a),b) ),
inference(paramodulation,[status(thm)],[f96,f28]) ).
fof(f297,plain,
! [X0] :
( ~ less_equal(divide(divide(X0,a),b),divide(divide(X0,b),zero))
| divide(divide(X0,b),zero) = divide(divide(X0,a),b) ),
inference(forward_demodulation,[status(thm)],[f96,f296]) ).
fof(f359,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(resolution,[status(thm)],[f146,f11]) ).
fof(f435,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[status(thm)],[f359,f30]) ).
fof(f448,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(X0,divide(X0,zero)),zero))
| divide(divide(X0,divide(X0,zero)),zero) = divide(divide(X0,zero),divide(X0,zero)) ),
inference(paramodulation,[status(thm)],[f435,f32]) ).
fof(f449,plain,
! [X0] :
( ~ less_equal(zero,divide(divide(X0,divide(X0,zero)),zero))
| divide(divide(X0,divide(X0,zero)),zero) = zero ),
inference(forward_demodulation,[status(thm)],[f435,f448]) ).
fof(f450,plain,
! [X0] : divide(divide(X0,divide(X0,zero)),zero) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f449,f14]) ).
fof(f693,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f450,f11]) ).
fof(f762,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f693,f30]) ).
fof(f1729,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f762,f11]) ).
fof(f1884,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[status(thm)],[f1729,f19]) ).
fof(f1956,plain,
! [X0] :
( ~ less_equal(divide(divide(X0,a),b),divide(divide(X0,b),zero))
| divide(X0,b) = divide(divide(X0,a),b) ),
inference(backward_demodulation,[status(thm)],[f1884,f297]) ).
fof(f1957,plain,
! [X0] :
( ~ less_equal(divide(divide(X0,a),b),divide(X0,b))
| divide(X0,b) = divide(divide(X0,a),b) ),
inference(forward_demodulation,[status(thm)],[f1884,f1956]) ).
fof(f2573,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),X2),divide(X0,X2)),
inference(resolution,[status(thm)],[f204,f11]) ).
fof(f2739,plain,
! [X0] : divide(X0,b) = divide(divide(X0,a),b),
inference(backward_subsumption_resolution,[status(thm)],[f1957,f2573]) ).
fof(f3292,plain,
! [X0] : less_equal(divide(X0,b),divide(X0,a)),
inference(paramodulation,[status(thm)],[f2739,f12]) ).
fof(f3293,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f18,f3292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : HEN007-3 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:33:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.20/0.51 % Refutation found
% 0.20/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.52 % Elapsed time: 0.174213 seconds
% 0.20/0.52 % CPU time: 1.275917 seconds
% 0.20/0.52 % Memory used: 41.785 MB
%------------------------------------------------------------------------------