%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN006-7 : 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 12:45:20 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.56s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 56 ( 26 unt; 0 def)
% Number of atoms : 112 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 58 ~; 56 |; 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 112 ( 112 !; 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(f13,axiom,
! [X] : quotient(X,zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
quotient(x,y,xQy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
less_equal(xQy,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
quotient(x,z,xQz),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ less_equal(xQz,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1] :
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1] :
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X,Z] :
( less_equal(Z,X)
| ! [Y] : ~ quotient(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1,X2] :
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,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(f23,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)],[f22]) ).
fof(f24,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f33,plain,
! [X0] : quotient(X0,zero,X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f34,plain,
quotient(x,y,xQy),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
less_equal(xQy,z),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f36,plain,
quotient(x,z,xQz),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f37,plain,
~ less_equal(xQz,y),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f24,f25]) ).
fof(f62,plain,
quotient(xQy,z,zero),
inference(resolution,[status(thm)],[f35,f18]) ).
fof(f73,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)],[f27,f23]) ).
fof(f74,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(resolution,[status(thm)],[f27,f21]) ).
fof(f76,plain,
! [X0] :
( xQy = X0
| ~ quotient(x,y,X0) ),
inference(resolution,[status(thm)],[f29,f34]) ).
fof(f84,plain,
xQy = divide(x,y),
inference(resolution,[status(thm)],[f76,f27]) ).
fof(f88,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[status(thm)],[f74,f47]) ).
fof(f89,plain,
! [X0,X1] : quotient(divide(X0,X1),X0,zero),
inference(resolution,[status(thm)],[f74,f18]) ).
fof(f152,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)],[f73,f27]) ).
fof(f171,plain,
! [X0,X1,X2,X3,X4,X5] :
( less_equal(X3,X5)
| ~ quotient(divide(X0,divide(X1,X4)),X1,X5)
| ~ quotient(X2,zero,X3)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[f89,f73]) ).
fof(f634,plain,
! [X0,X1,X2] :
( less_equal(X1,X2)
| ~ quotient(divide(x,X0),z,X2)
| ~ quotient(xQz,divide(X0,z),X1) ),
inference(resolution,[status(thm)],[f152,f36]) ).
fof(f723,plain,
! [X0,X1] :
( less_equal(divide(xQz,divide(X0,z)),X1)
| ~ quotient(divide(x,X0),z,X1) ),
inference(resolution,[status(thm)],[f634,f27]) ).
fof(f735,plain,
! [X0] :
( less_equal(divide(xQz,divide(y,z)),X0)
| ~ quotient(xQy,z,X0) ),
inference(paramodulation,[status(thm)],[f84,f723]) ).
fof(f745,plain,
less_equal(divide(xQz,divide(y,z)),zero),
inference(resolution,[status(thm)],[f735,f62]) ).
fof(f876,plain,
! [X0,X1,X2,X3,X4] :
( less_equal(X2,X4)
| ~ quotient(divide(X0,divide(X1,X3)),X1,X4)
| ~ quotient(divide(X0,X1),zero,X2) ),
inference(resolution,[status(thm)],[f171,f27]) ).
fof(f905,plain,
! [X0,X1,X2,X3] :
( less_equal(divide(X0,X1),X3)
| ~ quotient(divide(X0,divide(X1,X2)),X1,X3) ),
inference(resolution,[status(thm)],[f876,f33]) ).
fof(f927,plain,
! [X0,X1,X2] : less_equal(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)),
inference(resolution,[status(thm)],[f905,f27]) ).
fof(f1884,plain,
zero = divide(xQz,divide(y,z)),
inference(resolution,[status(thm)],[f745,f47]) ).
fof(f1964,plain,
! [X0,X1,X2] :
( divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1)
| ~ less_equal(divide(divide(X0,divide(X1,X2)),X1),divide(X0,X1)) ),
inference(resolution,[status(thm)],[f927,f25]) ).
fof(f2038,plain,
( divide(xQz,y) = divide(divide(xQz,divide(y,z)),y)
| ~ less_equal(divide(zero,y),divide(xQz,y)) ),
inference(paramodulation,[status(thm)],[f1884,f1964]) ).
fof(f2083,plain,
( divide(xQz,y) = divide(divide(xQz,divide(y,z)),y)
| ~ less_equal(zero,divide(xQz,y)) ),
inference(forward_demodulation,[status(thm)],[f88,f2038]) ).
fof(f2084,plain,
( divide(xQz,y) = divide(zero,y)
| ~ less_equal(zero,divide(xQz,y)) ),
inference(forward_demodulation,[status(thm)],[f1884,f2083]) ).
fof(f2085,plain,
( divide(xQz,y) = zero
| ~ less_equal(zero,divide(xQz,y)) ),
inference(forward_demodulation,[status(thm)],[f88,f2084]) ).
fof(f2086,plain,
divide(xQz,y) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f2085,f24]) ).
fof(f2204,plain,
quotient(xQz,y,zero),
inference(paramodulation,[status(thm)],[f2086,f27]) ).
fof(f2815,plain,
less_equal(xQz,y),
inference(resolution,[status(thm)],[f2204,f19]) ).
fof(f2831,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2815,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN006-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.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 20:45:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.56 % Refutation found
% 0.10/0.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.57 % Elapsed time: 0.201416 seconds
% 0.10/0.57 % CPU time: 1.338389 seconds
% 0.10/0.57 % Total memory used: 61.106 MB
% 0.10/0.57 % Net memory used: 57.457 MB
%------------------------------------------------------------------------------