%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 17 unt; 0 def)
% Number of atoms : 71 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 76 ( 39 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 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 : 83 ( 83 !; 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(f11,axiom,
! [X] : quotient(zero,X,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ quotient(x,x,zero),
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(f26,plain,
! [X0] : quotient(zero,X0,zero),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
~ quotient(x,x,zero),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f50,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f16,f22]) ).
fof(f51,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(resolution,[status(thm)],[f50,f13]) ).
fof(f70,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f20,f19]) ).
fof(f90,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)],[f18,f22]) ).
fof(f96,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)],[f90,f26]) ).
fof(f129,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)],[f96,f22]) ).
fof(f135,plain,
! [X0,X1,X2] :
( less_equal(divide(divide(X0,X1),zero),X2)
| ~ quotient(divide(X0,zero),X1,X2) ),
inference(resolution,[status(thm)],[f129,f22]) ).
fof(f141,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(resolution,[status(thm)],[f135,f51]) ).
fof(f151,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[status(thm)],[f141,f70]) ).
fof(f184,plain,
! [X0] : quotient(divide(X0,X0),zero,zero),
inference(paramodulation,[status(thm)],[f151,f22]) ).
fof(f190,plain,
! [X0] : less_equal(divide(X0,X0),zero),
inference(resolution,[status(thm)],[f184,f14]) ).
fof(f203,plain,
! [X0] : zero = divide(X0,X0),
inference(resolution,[status(thm)],[f190,f70]) ).
fof(f224,plain,
! [X0] : quotient(X0,X0,zero),
inference(paramodulation,[status(thm)],[f203,f22]) ).
fof(f228,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f27,f224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n003.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 20 20:47:00 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.43 % Elapsed time: 0.049249 seconds
% 0.08/0.43 % CPU time: 0.169117 seconds
% 0.08/0.43 % Total memory used: 44.732 MB
% 0.08/0.43 % Net memory used: 44.223 MB
%------------------------------------------------------------------------------