%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 12:45:17 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 25 unt; 0 def)
% Number of atoms : 81 ( 9 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 78 ( 40 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 93 !; 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(f10,negated_conjecture,
~ quotient(x,zero,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [X,Z] :
( less_equal(Z,X)
| ! [Y] : ~ quotient(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,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(f16,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)],[f15]) ).
fof(f17,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
~ quotient(x,zero,x),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f24,plain,
! [X0] : quotient(zero,X0,zero),
inference(resolution,[status(thm)],[f11,f17]) ).
fof(f46,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f14,f20]) ).
fof(f47,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(resolution,[status(thm)],[f46,f11]) ).
fof(f65,plain,
! [X0,X1] :
( divide(X0,X1) = X0
| ~ less_equal(X0,divide(X0,X1)) ),
inference(resolution,[status(thm)],[f18,f46]) ).
fof(f66,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f18,f17]) ).
fof(f86,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)],[f16,f20]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(divide(X0,zero),X1,X4)
| ~ quotient(X2,zero,X3)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f86,f24]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(divide(X0,zero),X1,X3)
| ~ quotient(divide(X0,X1),zero,X2) ),
inference(resolution,[status(thm)],[f99,f20]) ).
fof(f122,plain,
! [X0,X1,X2] :
( less_equal(divide(divide(X0,X1),zero),X2)
| ~ quotient(divide(X0,zero),X1,X2) ),
inference(resolution,[status(thm)],[f107,f20]) ).
fof(f128,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(resolution,[status(thm)],[f122,f47]) ).
fof(f138,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[status(thm)],[f128,f66]) ).
fof(f159,plain,
! [X0] : quotient(divide(X0,X0),zero,zero),
inference(paramodulation,[status(thm)],[f138,f20]) ).
fof(f165,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(resolution,[status(thm)],[f159,f12]) ).
fof(f183,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[status(thm)],[f165,f66]) ).
fof(f203,plain,
! [X0] : quotient(X0,X0,zero),
inference(paramodulation,[status(thm)],[f183,f20]) ).
fof(f207,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(resolution,[status(thm)],[f203,f122]) ).
fof(f234,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f207,f66]) ).
fof(f263,plain,
! [X0] : quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(paramodulation,[status(thm)],[f234,f20]) ).
fof(f270,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[f263,f12]) ).
fof(f315,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f270,f66]) ).
fof(f343,plain,
! [X0] : quotient(X0,divide(X0,zero),zero),
inference(paramodulation,[status(thm)],[f315,f20]) ).
fof(f350,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f343,f12]) ).
fof(f373,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[status(thm)],[f350,f65]) ).
fof(f399,plain,
! [X0] : quotient(X0,zero,X0),
inference(paramodulation,[status(thm)],[f373,f20]) ).
fof(f402,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f23,f399]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.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 20:45:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.046072 seconds
% 0.13/0.40 % CPU time: 0.159170 seconds
% 0.13/0.40 % Total memory used: 44.801 MB
% 0.13/0.40 % Net memory used: 44.195 MB
%------------------------------------------------------------------------------