%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN006-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:45:19 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 19 unt; 0 def)
% Number of atoms : 55 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( less_equal(X,Y)
| divide(X,Y) != zero ),
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] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[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(thm)],[f4]) ).
fof(f14,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
less_equal(divide(a,b),d),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
~ less_equal(divide(a,d),b),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f21,plain,
! [X0,X1] :
( X0 = divide(X0,X1)
| ~ less_equal(X0,divide(X0,X1)) ),
inference(resolution,[status(thm)],[f12,f15]) ).
fof(f22,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[f12,f10]) ).
fof(f23,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[status(thm)],[f14,f21]) ).
fof(f24,plain,
! [X0] :
( X0 = zero
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f14,f15]) ).
fof(f26,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),X2) = divide(divide(X0,X2),divide(X1,X2))
| ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2))) ),
inference(resolution,[status(thm)],[f13,f15]) ).
fof(f61,plain,
divide(divide(a,b),d) = zero,
inference(resolution,[status(thm)],[f17,f10]) ).
fof(f94,plain,
! [X0,X1,X2] :
( divide(divide(X0,divide(X1,X2)),X1) = divide(divide(X0,X1),divide(divide(X1,X2),X1))
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero)) ),
inference(paramodulation,[status(thm)],[f22,f26]) ).
fof(f134,plain,
! [X0,X1,X2] :
( divide(divide(X0,divide(X1,X2)),X1) = divide(divide(X0,X1),zero)
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero)) ),
inference(forward_demodulation,[status(thm)],[f22,f94]) ).
fof(f142,plain,
( divide(divide(a,b),d) = divide(divide(a,d),divide(b,d))
| ~ less_equal(zero,divide(divide(a,d),divide(b,d))) ),
inference(paramodulation,[status(thm)],[f61,f26]) ).
fof(f154,plain,
( zero = divide(divide(a,d),divide(b,d))
| ~ less_equal(zero,divide(divide(a,d),divide(b,d))) ),
inference(forward_demodulation,[status(thm)],[f61,f142]) ).
fof(f155,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(forward_subsumption_resolution,[status(thm)],[f154,f14]) ).
fof(f792,plain,
( divide(divide(divide(a,d),divide(b,d)),b) = divide(divide(divide(a,d),b),zero)
| ~ less_equal(divide(zero,b),divide(divide(divide(a,d),b),zero)) ),
inference(paramodulation,[status(thm)],[f155,f134]) ).
fof(f822,plain,
( divide(divide(divide(a,d),divide(b,d)),b) = divide(divide(divide(a,d),b),zero)
| ~ less_equal(zero,divide(divide(divide(a,d),b),zero)) ),
inference(forward_demodulation,[status(thm)],[f23,f792]) ).
fof(f823,plain,
( divide(zero,b) = divide(divide(divide(a,d),b),zero)
| ~ less_equal(zero,divide(divide(divide(a,d),b),zero)) ),
inference(forward_demodulation,[status(thm)],[f155,f822]) ).
fof(f824,plain,
( zero = divide(divide(divide(a,d),b),zero)
| ~ less_equal(zero,divide(divide(divide(a,d),b),zero)) ),
inference(forward_demodulation,[status(thm)],[f23,f823]) ).
fof(f825,plain,
zero = divide(divide(divide(a,d),b),zero),
inference(forward_subsumption_resolution,[status(thm)],[f824,f14]) ).
fof(f1733,plain,
less_equal(divide(divide(a,d),b),zero),
inference(resolution,[status(thm)],[f825,f11]) ).
fof(f2007,plain,
divide(divide(a,d),b) = zero,
inference(resolution,[status(thm)],[f1733,f24]) ).
fof(f2013,plain,
less_equal(divide(a,d),b),
inference(resolution,[status(thm)],[f2007,f11]) ).
fof(f2054,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2013,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:45:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.47 % Refutation found
% 0.12/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.49 % Elapsed time: 0.134378 seconds
% 0.12/0.49 % CPU time: 0.776255 seconds
% 0.12/0.49 % Total memory used: 62.053 MB
% 0.12/0.49 % Net memory used: 61.101 MB
%------------------------------------------------------------------------------