%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN005-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:45:18 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.56s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 20 unt; 0 def)
% Number of atoms : 52 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 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 : 33 ( 33 !; 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(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
less_equal(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ less_equal(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,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(f15,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
less_equal(a,b),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f19,plain,
less_equal(b,c),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
~ less_equal(a,c),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
divide(b,c) = zero,
inference(resolution,[status(thm)],[f11,f19]) ).
fof(f24,plain,
divide(a,b) = zero,
inference(resolution,[status(thm)],[f11,f18]) ).
fof(f32,plain,
! [X0,X1] :
( divide(X0,X1) = X0
| ~ less_equal(X0,divide(X0,X1)) ),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f41,plain,
! [X0] : divide(zero,X0) = zero,
inference(resolution,[status(thm)],[f15,f32]) ).
fof(f43,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f15,f16]) ).
fof(f62,plain,
! [X0,X1,X2] :
( divide(divide(X0,X2),divide(X1,X2)) = divide(divide(X0,X1),X2)
| ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2))) ),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f133,plain,
! [X0] :
( divide(divide(X0,c),divide(b,c)) = divide(divide(X0,b),c)
| ~ less_equal(divide(divide(X0,b),c),divide(divide(X0,c),zero)) ),
inference(paramodulation,[status(thm)],[f23,f62]) ).
fof(f189,plain,
! [X0] :
( divide(divide(X0,c),zero) = divide(divide(X0,b),c)
| ~ less_equal(divide(divide(X0,b),c),divide(divide(X0,c),zero)) ),
inference(forward_demodulation,[status(thm)],[f23,f133]) ).
fof(f285,plain,
( divide(divide(a,c),zero) = divide(divide(a,b),c)
| ~ less_equal(divide(zero,c),divide(divide(a,c),zero)) ),
inference(paramodulation,[status(thm)],[f24,f189]) ).
fof(f300,plain,
( divide(divide(a,c),zero) = divide(divide(a,b),c)
| ~ less_equal(zero,divide(divide(a,c),zero)) ),
inference(forward_demodulation,[status(thm)],[f41,f285]) ).
fof(f301,plain,
( divide(divide(a,c),zero) = divide(zero,c)
| ~ less_equal(zero,divide(divide(a,c),zero)) ),
inference(forward_demodulation,[status(thm)],[f24,f300]) ).
fof(f302,plain,
( divide(divide(a,c),zero) = zero
| ~ less_equal(zero,divide(divide(a,c),zero)) ),
inference(forward_demodulation,[status(thm)],[f41,f301]) ).
fof(f303,plain,
divide(divide(a,c),zero) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f302,f15]) ).
fof(f534,plain,
less_equal(divide(a,c),zero),
inference(resolution,[status(thm)],[f303,f12]) ).
fof(f708,plain,
zero = divide(a,c),
inference(resolution,[status(thm)],[f534,f43]) ).
fof(f714,plain,
less_equal(a,c),
inference(resolution,[status(thm)],[f708,f12]) ).
fof(f733,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f714,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN005-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.52 % Computer : n016.cluster.edu
% 0.08/0.52 % Model : x86_64 x86_64
% 0.08/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.52 % Memory : 8046.5625MB
% 0.08/0.52 % OS : Linux 6.8.0-71-generic
% 0.08/0.52 % CPULimit : 300
% 0.08/0.52 % WCLimit : 300
% 0.08/0.52 % DateTime : Sun Sep 20 20:50:22 UTC 2026
% 0.08/0.53 % CPUTime :
% 0.08/0.53 % Drodi V4.1.1
% 0.08/0.56 % Refutation found
% 0.08/0.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.59 % Elapsed time: 0.047904 seconds
% 0.15/0.59 % CPU time: 0.173343 seconds
% 0.15/0.59 % Total memory used: 45.626 MB
% 0.15/0.59 % Net memory used: 45.150 MB
%------------------------------------------------------------------------------