%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 12:45:18 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 27 unt; 0 def)
% Number of atoms : 92 ( 13 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 90 ( 46 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 98 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
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,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
less_equal(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X,Z] :
( less_equal(Z,X)
| ! [Y] : ~ quotient(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [V4,V5] :
( less_equal(V4,V5)
| ! [V1,Z] :
( ~ quotient(V1,Z,V5)
| ! [V2,V3] :
( ~ quotient(V3,V2,V4)
| ! [X] :
( ~ quotient(X,Z,V3)
| ! [Y] :
( ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( less_equal(X6,X7)
| ~ quotient(X2,X3,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X3,X5)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
less_equal(x,y),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
less_equal(y,z),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
~ less_equal(x,z),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f19,f20]) ).
fof(f34,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( less_equal(X5,X6)
| ~ quotient(divide(X3,X0),X1,X6)
| ~ quotient(X4,X2,X5)
| ~ quotient(X3,X1,X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f22,f18]) ).
fof(f35,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f22,f16]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4,X5] :
( less_equal(X4,X5)
| ~ quotient(divide(X0,X3),X1,X5)
| ~ quotient(X2,divide(X3,X1),X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f34,f22]) ).
fof(f37,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[status(thm)],[f35,f30]) ).
fof(f46,plain,
quotient(y,z,zero),
inference(resolution,[status(thm)],[f13,f26]) ).
fof(f47,plain,
quotient(x,y,zero),
inference(resolution,[status(thm)],[f13,f25]) ).
fof(f72,plain,
! [X0,X1,X2] :
( divide(X0,X1) = X2
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f24,f22]) ).
fof(f86,plain,
divide(x,y) = zero,
inference(resolution,[status(thm)],[f72,f47]) ).
fof(f87,plain,
divide(y,z) = zero,
inference(resolution,[status(thm)],[f72,f46]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(divide(X0,X2),X1,X4)
| ~ quotient(divide(X0,X1),divide(X2,X1),X3) ),
inference(resolution,[status(thm)],[f36,f22]) ).
fof(f171,plain,
! [X0,X1,X2,X3] :
( less_equal(divide(divide(X0,X2),divide(X1,X2)),X3)
| ~ quotient(divide(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f96,f22]) ).
fof(f188,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(resolution,[status(thm)],[f171,f22]) ).
fof(f395,plain,
! [X0] : less_equal(divide(divide(x,X0),divide(y,X0)),divide(zero,X0)),
inference(paramodulation,[status(thm)],[f86,f188]) ).
fof(f422,plain,
! [X0] : less_equal(divide(divide(x,X0),divide(y,X0)),zero),
inference(forward_demodulation,[status(thm)],[f37,f395]) ).
fof(f651,plain,
! [X0] : zero = divide(divide(x,X0),divide(y,X0)),
inference(resolution,[status(thm)],[f422,f30]) ).
fof(f672,plain,
zero = divide(divide(x,z),zero),
inference(paramodulation,[status(thm)],[f87,f651]) ).
fof(f720,plain,
quotient(divide(x,z),zero,zero),
inference(paramodulation,[status(thm)],[f672,f22]) ).
fof(f729,plain,
less_equal(divide(x,z),zero),
inference(resolution,[status(thm)],[f720,f14]) ).
fof(f740,plain,
zero = divide(x,z),
inference(resolution,[status(thm)],[f729,f30]) ).
fof(f766,plain,
quotient(x,z,zero),
inference(paramodulation,[status(thm)],[f740,f22]) ).
fof(f785,plain,
less_equal(x,z),
inference(resolution,[status(thm)],[f766,f14]) ).
fof(f796,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f785,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n014.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 20:45:34 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.049822 seconds
% 0.12/0.40 % CPU time: 0.175182 seconds
% 0.12/0.40 % Total memory used: 41.158 MB
% 0.12/0.40 % Net memory used: 40.662 MB
%------------------------------------------------------------------------------