%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN010-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:45:23 PM UTC 2026
% Result : Unsatisfiable 2.66s 0.80s
% Output : CNFRefutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 9
% Syntax : Number of formulae : 79 ( 39 unt; 0 def)
% Number of atoms : 124 ( 123 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 93 ( 48 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 189 ( 189 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : divide(divide(X,Y),X) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Z,Y] : divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : divide(zero,X) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( X = Y
| divide(Y,X) != zero
| divide(X,Y) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : divide(X,identity) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( divide(X,Z) = zero
| divide(Y,Z) != zero
| divide(X,Y) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] :
( divide(divide(X,Z),Y) = zero
| divide(divide(X,Y),Z) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,Z] :
( divide(divide(X,Z),divide(Y,Z)) = zero
| divide(X,Y) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0] : divide(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1] :
( X0 = X1
| divide(X1,X0) != zero
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0] : divide(X0,identity) = zero,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X,Z] :
( divide(X,Z) = zero
| ! [Y] :
( divide(Y,Z) != zero
| divide(X,Y) != zero ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1,X2] :
( divide(X0,X2) = zero
| divide(X1,X2) != zero
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( divide(divide(X0,X2),X1) = zero
| divide(divide(X0,X1),X2) != zero ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
! [X,Y] :
( ! [Z] : divide(divide(X,Z),divide(Y,Z)) = zero
| divide(X,Y) != zero ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f19,plain,
! [X0,X1,X2] :
( divide(divide(X0,X2),divide(X1,X2)) = zero
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0,X1] :
( divide(X0,X1) = X0
| divide(X0,divide(X0,X1)) != zero ),
inference(resolution,[status(thm)],[f13,f10]) ).
fof(f29,plain,
! [X0] :
( zero = X0
| divide(X0,zero) != zero ),
inference(resolution,[status(thm)],[f13,f12]) ).
fof(f51,plain,
! [X0,X1,X2] :
( divide(divide(X0,X2),X1) = zero
| divide(X0,X1) != zero ),
inference(resolution,[status(thm)],[f16,f10]) ).
fof(f62,plain,
! [X0,X1,X2] :
( divide(divide(X0,X2),divide(X1,X2)) = divide(divide(X0,X1),X2)
| divide(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2))) != zero ),
inference(resolution,[status(thm)],[f11,f13]) ).
fof(f78,plain,
! [X0,X1] : divide(divide(divide(X0,X1),divide(identity,X1)),divide(zero,X1)) = zero,
inference(paramodulation,[status(thm)],[f14,f11]) ).
fof(f92,plain,
! [X0,X1] : divide(divide(divide(X0,X1),divide(identity,X1)),zero) = zero,
inference(forward_demodulation,[status(thm)],[f12,f78]) ).
fof(f96,plain,
! [X0,X1] : zero = divide(divide(X0,X1),divide(identity,X1)),
inference(resolution,[status(thm)],[f92,f29]) ).
fof(f155,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),X2),X0) = zero,
inference(resolution,[status(thm)],[f51,f10]) ).
fof(f346,plain,
! [X0,X1] : divide(divide(X0,X0),X1) = zero,
inference(resolution,[status(thm)],[f17,f10]) ).
fof(f348,plain,
! [X0,X1] : divide(divide(X0,divide(identity,X1)),X1) = zero,
inference(resolution,[status(thm)],[f17,f96]) ).
fof(f383,plain,
! [X0,X1] : divide(divide(X0,X0),X1) = divide(X0,X0),
inference(resolution,[status(thm)],[f346,f28]) ).
fof(f429,plain,
! [X0] : zero = divide(X0,X0),
inference(forward_demodulation,[status(thm)],[f346,f383]) ).
fof(f451,plain,
! [X0,X1] : divide(divide(X0,divide(X0,X1)),X1) = zero,
inference(resolution,[status(thm)],[f429,f17]) ).
fof(f501,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f451,f29]) ).
fof(f559,plain,
! [X0,X1,X2,X3] : divide(divide(divide(divide(X0,X1),divide(X2,X1)),X3),divide(divide(divide(X0,X2),X1),X3)) = zero,
inference(resolution,[status(thm)],[f19,f11]) ).
fof(f563,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),X2),divide(X0,X2)) = zero,
inference(resolution,[status(thm)],[f19,f10]) ).
fof(f723,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),divide(divide(X1,X2),X1)) = divide(divide(X0,divide(X1,X2)),X1)
| divide(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero)) != zero ),
inference(paramodulation,[status(thm)],[f10,f62]) ).
fof(f871,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),zero) = divide(divide(X0,divide(X1,X2)),X1)
| divide(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero)) != zero ),
inference(forward_demodulation,[status(thm)],[f10,f723]) ).
fof(f918,plain,
! [X0,X1,X2] :
( divide(divide(X0,X2),divide(divide(X1,divide(identity,X2)),X2)) = divide(divide(X0,divide(X1,divide(identity,X2))),X2)
| divide(divide(divide(X0,divide(X1,divide(identity,X2))),X2),divide(divide(X0,X2),zero)) != zero ),
inference(paramodulation,[status(thm)],[f348,f62]) ).
fof(f945,plain,
! [X0,X1,X2] :
( divide(divide(X0,X2),zero) = divide(divide(X0,divide(X1,divide(identity,X2))),X2)
| divide(divide(divide(X0,divide(X1,divide(identity,X2))),X2),divide(divide(X0,X2),zero)) != zero ),
inference(forward_demodulation,[status(thm)],[f348,f918]) ).
fof(f1740,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[status(thm)],[f501,f28]) ).
fof(f1791,plain,
! [X0,X1] :
( divide(divide(X0,divide(X1,zero)),divide(X1,divide(X1,zero))) = divide(divide(X0,X1),divide(X1,zero))
| divide(divide(divide(X0,X1),divide(X1,zero)),divide(divide(X0,divide(X1,zero)),zero)) != zero ),
inference(paramodulation,[status(thm)],[f501,f62]) ).
fof(f1829,plain,
! [X0,X1,X2] :
( divide(X0,X2) = divide(divide(X0,divide(X1,divide(identity,X2))),X2)
| divide(divide(divide(X0,divide(X1,divide(identity,X2))),X2),divide(divide(X0,X2),zero)) != zero ),
inference(backward_demodulation,[status(thm)],[f1740,f945]) ).
fof(f1832,plain,
! [X0,X1,X2] :
( divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1)
| divide(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero)) != zero ),
inference(backward_demodulation,[status(thm)],[f1740,f871]) ).
fof(f1879,plain,
! [X0,X1] :
( divide(divide(X0,divide(X1,zero)),divide(X1,divide(X1,zero))) = divide(divide(X0,X1),divide(X1,zero))
| divide(divide(divide(X0,X1),X1),divide(divide(X0,divide(X1,zero)),zero)) != zero ),
inference(forward_demodulation,[status(thm)],[f1740,f1791]) ).
fof(f1880,plain,
! [X0,X1] :
( divide(divide(X0,divide(X1,zero)),divide(X1,divide(X1,zero))) = divide(divide(X0,X1),divide(X1,zero))
| divide(divide(divide(X0,X1),X1),divide(X0,divide(X1,zero))) != zero ),
inference(forward_demodulation,[status(thm)],[f1740,f1879]) ).
fof(f1881,plain,
! [X0,X1] :
( divide(divide(X0,divide(X1,zero)),divide(X1,divide(X1,zero))) = divide(divide(X0,X1),divide(X1,zero))
| divide(divide(divide(X0,X1),X1),divide(X0,X1)) != zero ),
inference(forward_demodulation,[status(thm)],[f1740,f1880]) ).
fof(f1882,plain,
! [X0,X1] :
( divide(divide(X0,divide(X1,zero)),divide(X1,divide(X1,zero))) = divide(divide(X0,X1),divide(X1,zero))
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f10,f1881]) ).
fof(f1883,plain,
! [X0,X1] :
( divide(divide(X0,X1),divide(X1,divide(X1,zero))) = divide(divide(X0,X1),divide(X1,zero))
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f1740,f1882]) ).
fof(f1884,plain,
! [X0,X1] :
( divide(divide(X0,X1),zero) = divide(divide(X0,X1),divide(X1,zero))
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f501,f1883]) ).
fof(f1885,plain,
! [X0,X1] :
( divide(X0,X1) = divide(divide(X0,X1),divide(X1,zero))
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f1740,f1884]) ).
fof(f1886,plain,
! [X0,X1] :
( divide(X0,X1) = divide(divide(X0,X1),X1)
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f1740,f1885]) ).
fof(f1889,plain,
! [X0,X1] : divide(X0,X1) = divide(divide(X0,X1),X1),
inference(trivial_equality_resolution,[status(thm)],[f1886]) ).
fof(f1931,plain,
! [X0,X1,X2] :
( divide(X0,X2) = divide(divide(X0,divide(X1,divide(identity,X2))),X2)
| divide(divide(divide(X0,divide(X1,divide(identity,X2))),X2),divide(X0,X2)) != zero ),
inference(forward_demodulation,[status(thm)],[f1740,f1829]) ).
fof(f1932,plain,
! [X0,X1,X2] :
( divide(X0,X1) = divide(divide(X0,divide(X2,divide(identity,X1))),X1)
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f563,f1931]) ).
fof(f1934,plain,
! [X0,X1,X2] : divide(X0,X1) = divide(divide(X0,divide(X2,divide(identity,X1))),X1),
inference(trivial_equality_resolution,[status(thm)],[f1932]) ).
fof(f1939,plain,
! [X0,X1,X2] :
( divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1)
| divide(divide(divide(X0,divide(X1,X2)),X1),divide(X0,X1)) != zero ),
inference(forward_demodulation,[status(thm)],[f1740,f1832]) ).
fof(f1940,plain,
! [X0,X1,X2] :
( divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1)
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f563,f1939]) ).
fof(f1941,plain,
! [X0,X1,X2] : divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1),
inference(trivial_equality_resolution,[status(thm)],[f1940]) ).
fof(f2141,plain,
! [X0,X1,X2] :
( divide(divide(divide(X0,X1),X1),divide(X2,X1)) = divide(divide(divide(X0,X1),X2),X1)
| divide(divide(divide(divide(X0,X1),X2),X1),divide(divide(X0,X1),divide(X2,X1))) != zero ),
inference(paramodulation,[status(thm)],[f1889,f62]) ).
fof(f2181,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),divide(X2,X1)) = divide(divide(divide(X0,X1),X2),X1)
| divide(divide(divide(divide(X0,X1),X2),X1),divide(divide(X0,X1),divide(X2,X1))) != zero ),
inference(forward_demodulation,[status(thm)],[f1889,f2141]) ).
fof(f2261,plain,
! [X0,X1,X2,X3] : divide(divide(divide(X0,X1),X2),divide(X0,divide(X1,X3))) = zero,
inference(paramodulation,[status(thm)],[f1941,f155]) ).
fof(f2270,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(X0,divide(X1,X2))) = zero,
inference(paramodulation,[status(thm)],[f1941,f10]) ).
fof(f2303,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),divide(X2,X1)) = divide(divide(divide(X0,X1),X2),X1)
| zero != zero ),
inference(backward_demodulation,[status(thm)],[f2261,f2181]) ).
fof(f2308,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(X2,X1)) = divide(divide(divide(X0,X1),X2),X1),
inference(trivial_equality_resolution,[status(thm)],[f2303]) ).
fof(f3379,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),X2),divide(divide(divide(X0,X2),X1),X2)) = zero,
inference(paramodulation,[status(thm)],[f1941,f559]) ).
fof(f3556,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,X2),X1)
| zero != zero ),
inference(backward_demodulation,[status(thm)],[f3557,f62]) ).
fof(f3557,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2))) = zero,
inference(forward_demodulation,[status(thm)],[f2308,f3379]) ).
fof(f3863,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,X2),X1),
inference(trivial_equality_resolution,[status(thm)],[f3556]) ).
fof(f6172,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(X2,X1)) = divide(divide(divide(X0,X1),X2),X1),
inference(paramodulation,[status(thm)],[f1889,f3863]) ).
fof(f6247,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),X2),divide(divide(X0,X2),X1)) = zero,
inference(paramodulation,[status(thm)],[f3863,f2270]) ).
fof(f6314,plain,
! [X0,X1,X2] : divide(divide(X0,X1),X2) = divide(divide(divide(X0,X2),X1),X2),
inference(forward_demodulation,[status(thm)],[f3863,f6172]) ).
fof(f6783,plain,
! [X0,X1,X2] :
( divide(divide(divide(X0,X1),X2),X1) = divide(divide(X0,X1),X2)
| divide(divide(divide(X0,X1),X2),divide(divide(X0,X2),X1)) != zero ),
inference(paramodulation,[status(thm)],[f6314,f28]) ).
fof(f6864,plain,
! [X0,X1,X2] :
( divide(divide(divide(X0,X1),X2),X1) = divide(divide(X0,X1),X2)
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f6247,f6783]) ).
fof(f6865,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),X2) = divide(divide(X0,X2),X1)
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f6314,f6864]) ).
fof(f6866,plain,
! [X0,X1,X2] : divide(divide(X0,X1),X2) = divide(divide(X0,X2),X1),
inference(trivial_equality_resolution,[status(thm)],[f6865]) ).
fof(f6876,plain,
! [X0,X1,X2] : divide(X0,X1) = divide(divide(X0,X1),divide(X2,divide(identity,X1))),
inference(paramodulation,[status(thm)],[f1934,f6866]) ).
fof(f7109,plain,
divide(identity,a) != divide(identity,a),
inference(backward_demodulation,[status(thm)],[f6876,f20]) ).
fof(f7257,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f7109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:45:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 2.66/0.80 % Refutation found
% 2.66/0.80 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.66/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.52/0.82 % Elapsed time: 0.447327 seconds
% 1.52/0.82 % CPU time: 3.253682 seconds
% 1.52/0.82 % Total memory used: 134.767 MB
% 1.52/0.82 % Net memory used: 130.797 MB
%------------------------------------------------------------------------------