%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:45:19 PM UTC 2026
% Result : Unsatisfiable 1.23s 0.64s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 20 unt; 0 def)
% Number of atoms : 85 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 46 ~; 44 |; 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : less_equal(zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
quotient(x,y,xQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
less_equal(xQy,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
quotient(x,z,xQz),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ less_equal(xQz,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X,Z] :
( less_equal(Z,X)
| ! [Y] : ~ quotient(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1,X2] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,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(f24,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)],[f23]) ).
fof(f25,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f35,plain,
! [X,Z] :
( less_equal(X,Z)
| ! [Y] :
( ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f36,plain,
! [X0,X1,X2] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
quotient(x,y,xQy),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f38,plain,
less_equal(xQy,z),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
quotient(x,z,xQz),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
~ less_equal(xQz,y),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X3,X4)
| ~ quotient(xQy,X0,X4)
| ~ quotient(X2,X1,X3)
| ~ quotient(x,X0,X2)
| ~ quotient(y,X0,X1) ),
inference(resolution,[status(thm)],[f24,f37]) ).
fof(f50,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f25,f26]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( less_equal(X2,X3)
| ~ quotient(xQy,X0,X3)
| ~ quotient(X1,divide(y,X0),X2)
| ~ quotient(x,X0,X1) ),
inference(resolution,[status(thm)],[f28,f44]) ).
fof(f78,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f28,f22]) ).
fof(f88,plain,
quotient(xQy,z,zero),
inference(resolution,[status(thm)],[f19,f38]) ).
fof(f612,plain,
! [X0,X1,X2] :
( less_equal(divide(X1,divide(y,X0)),X2)
| ~ quotient(xQy,X0,X2)
| ~ quotient(x,X0,X1) ),
inference(resolution,[status(thm)],[f75,f28]) ).
fof(f5086,plain,
! [X0] :
( less_equal(divide(xQz,divide(y,z)),X0)
| ~ quotient(xQy,z,X0) ),
inference(resolution,[status(thm)],[f612,f39]) ).
fof(f5098,plain,
less_equal(divide(xQz,divide(y,z)),zero),
inference(resolution,[status(thm)],[f5086,f88]) ).
fof(f5101,plain,
zero = divide(xQz,divide(y,z)),
inference(resolution,[status(thm)],[f5098,f50]) ).
fof(f5154,plain,
quotient(xQz,divide(y,z),zero),
inference(paramodulation,[status(thm)],[f5101,f28]) ).
fof(f5228,plain,
less_equal(xQz,divide(y,z)),
inference(resolution,[status(thm)],[f5154,f20]) ).
fof(f5254,plain,
! [X0] :
( less_equal(xQz,X0)
| ~ less_equal(divide(y,z),X0) ),
inference(resolution,[status(thm)],[f5228,f36]) ).
fof(f5273,plain,
less_equal(xQz,y),
inference(resolution,[status(thm)],[f5254,f78]) ).
fof(f5276,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5273,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:43:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 1.23/0.64 % Refutation found
% 1.23/0.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.23/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.23/0.67 % Elapsed time: 0.291415 seconds
% 1.23/0.67 % CPU time: 2.060515 seconds
% 1.23/0.67 % Total memory used: 68.675 MB
% 1.23/0.67 % Net memory used: 63.412 MB
%------------------------------------------------------------------------------