%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN008-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:45:21 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 39 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 17 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 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 : 30 ( 30 !; 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(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(f9,axiom,
! [X] : divide(zero,X) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,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(f21,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0] : divide(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f33,plain,
less_equal(a,b),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f34,plain,
~ less_equal(divide(a,c),divide(b,c)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f39,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)],[f20,f22]) ).
fof(f284,plain,
divide(a,b) = zero,
inference(resolution,[status(thm)],[f17,f33]) ).
fof(f291,plain,
! [X0] :
( divide(divide(a,b),X0) = divide(divide(a,X0),divide(b,X0))
| ~ less_equal(divide(zero,X0),divide(divide(a,X0),divide(b,X0))) ),
inference(paramodulation,[status(thm)],[f284,f39]) ).
fof(f306,plain,
! [X0] :
( divide(divide(a,b),X0) = divide(divide(a,X0),divide(b,X0))
| ~ less_equal(zero,divide(divide(a,X0),divide(b,X0))) ),
inference(forward_demodulation,[status(thm)],[f25,f291]) ).
fof(f307,plain,
! [X0] :
( divide(zero,X0) = divide(divide(a,X0),divide(b,X0))
| ~ less_equal(zero,divide(divide(a,X0),divide(b,X0))) ),
inference(forward_demodulation,[status(thm)],[f284,f306]) ).
fof(f308,plain,
! [X0] :
( zero = divide(divide(a,X0),divide(b,X0))
| ~ less_equal(zero,divide(divide(a,X0),divide(b,X0))) ),
inference(forward_demodulation,[status(thm)],[f25,f307]) ).
fof(f309,plain,
! [X0] : zero = divide(divide(a,X0),divide(b,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f308,f21]) ).
fof(f373,plain,
divide(divide(a,c),divide(b,c)) != zero,
inference(resolution,[status(thm)],[f18,f34]) ).
fof(f385,plain,
zero != zero,
inference(forward_demodulation,[status(thm)],[f309,f373]) ).
fof(f386,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f385]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:48:52 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.060210 seconds
% 0.12/0.42 % CPU time: 0.269955 seconds
% 0.12/0.42 % Total memory used: 70.029 MB
% 0.12/0.42 % Net memory used: 69.525 MB
%------------------------------------------------------------------------------