%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP066-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:32:26 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 58 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 108 ( 108 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(identity,divide(X,divide(Y,divide(divide(divide(X,X),X),Z)))),Z) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = divide(X,divide(identity,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = divide(identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = divide(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(identity,divide(X0,divide(X1,divide(divide(divide(X0,X0),X0),X2)))),X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = divide(identity,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = divide(X0,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(divide(divide(X0,X0),X0),X2)))),X2) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f13,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f9,f11]) ).
fof(f14,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(inverse(X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f8,f13]) ).
fof(f15,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f19,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f15,f12]) ).
fof(f22,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(backward_demodulation,[status(thm)],[f18,f10]) ).
fof(f23,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(trivial_equality_resolution,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] : divide(inverse(inverse(divide(X0,divide(inverse(identity),X1)))),X1) = X0,
inference(paramodulation,[status(thm)],[f8,f14]) ).
fof(f31,plain,
! [X0,X1] : divide(inverse(divide(X0,divide(X1,identity))),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f35,plain,
! [X0,X1] : divide(multiply(identity,divide(X0,divide(inverse(identity),X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f17,f25]) ).
fof(f36,plain,
! [X0,X1] : divide(multiply(identity,divide(X0,divide(identity,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f15,f35]) ).
fof(f37,plain,
! [X0,X1] : divide(multiply(identity,divide(X0,inverse(X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f36]) ).
fof(f38,plain,
! [X0,X1] : divide(multiply(identity,multiply(X0,X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f12,f37]) ).
fof(f41,plain,
! [X0,X1] : multiply(inverse(divide(X0,divide(X1,identity))),X0) = X1,
inference(forward_demodulation,[status(thm)],[f12,f31]) ).
fof(f64,plain,
! [X0] : divide(multiply(identity,divide(X0,identity)),identity) = X0,
inference(paramodulation,[status(thm)],[f19,f38]) ).
fof(f88,plain,
! [X0,X1] : multiply(inverse(X0),multiply(identity,multiply(X0,divide(X1,identity)))) = X1,
inference(paramodulation,[status(thm)],[f38,f41]) ).
fof(f91,plain,
! [X0] : multiply(inverse(identity),divide(X0,identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f41]) ).
fof(f92,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = multiply(identity,multiply(X1,identity)),
inference(paramodulation,[status(thm)],[f38,f41]) ).
fof(f93,plain,
! [X0,X1,X2] : multiply(inverse(divide(X0,X1)),X0) = inverse(divide(X2,divide(X1,divide(inverse(X2),identity)))),
inference(paramodulation,[status(thm)],[f14,f41]) ).
fof(f97,plain,
! [X0,X1] : divide(multiply(identity,X0),X1) = inverse(divide(X1,divide(X0,identity))),
inference(paramodulation,[status(thm)],[f41,f38]) ).
fof(f102,plain,
! [X0] : divide(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f103,f64]) ).
fof(f103,plain,
! [X0] : multiply(identity,divide(X0,identity)) = X0,
inference(forward_demodulation,[status(thm)],[f15,f91]) ).
fof(f104,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = multiply(identity,divide(X1,identity)),
inference(forward_demodulation,[status(thm)],[f19,f92]) ).
fof(f106,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f103,f104]) ).
fof(f107,plain,
! [X0,X1] : X0 = inverse(divide(X1,divide(X0,divide(inverse(X1),identity)))),
inference(forward_demodulation,[status(thm)],[f106,f93]) ).
fof(f112,plain,
! [X0,X1] : X0 = inverse(divide(X1,divide(X0,inverse(X1)))),
inference(backward_demodulation,[status(thm)],[f102,f107]) ).
fof(f113,plain,
! [X0,X1] : divide(multiply(identity,X0),X1) = inverse(divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f102,f97]) ).
fof(f114,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[status(thm)],[f102,f103]) ).
fof(f116,plain,
! [X0,X1] : multiply(inverse(X0),multiply(identity,multiply(X0,X1))) = X1,
inference(backward_demodulation,[status(thm)],[f102,f88]) ).
fof(f119,plain,
! [X0,X1] : X0 = inverse(divide(X1,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12,f112]) ).
fof(f122,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f114,f23]) ).
fof(f129,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f114,f113]) ).
fof(f131,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f114,f116]) ).
fof(f133,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f122]) ).
fof(f138,plain,
! [X0,X1,X2] : divide(divide(divide(X0,divide(inverse(X1),X2)),X1),X2) = X0,
inference(backward_demodulation,[status(thm)],[f129,f14]) ).
fof(f141,plain,
! [X0,X1] : X0 = divide(multiply(X0,X1),X1),
inference(backward_demodulation,[status(thm)],[f129,f119]) ).
fof(f161,plain,
! [X0] : X0 = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f102,f141]) ).
fof(f187,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(paramodulation,[status(thm)],[f18,f131]) ).
fof(f194,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f161,f187]) ).
fof(f199,plain,
! [X0,X1,X2] : divide(multiply(divide(X0,divide(inverse(inverse(X1)),X2)),X1),X2) = X0,
inference(paramodulation,[status(thm)],[f12,f138]) ).
fof(f219,plain,
! [X0,X1,X2] : divide(multiply(divide(X0,divide(X1,X2)),X1),X2) = X0,
inference(forward_demodulation,[status(thm)],[f194,f199]) ).
fof(f246,plain,
! [X0,X1] : divide(inverse(X0),X1) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f12,f129]) ).
fof(f251,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f129,f12]) ).
fof(f342,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f246,f12]) ).
fof(f392,plain,
! [X0,X1,X2] : divide(multiply(X0,X1),X2) = multiply(X0,divide(X1,X2)),
inference(paramodulation,[status(thm)],[f141,f219]) ).
fof(f425,plain,
! [X0,X1,X2] : divide(multiply(X0,X1),X2) = divide(X0,divide(X2,X1)),
inference(forward_demodulation,[status(thm)],[f251,f392]) ).
fof(f690,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f12,f425]) ).
fof(f717,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f722,f133]) ).
fof(f722,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f342,f690]) ).
fof(f751,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f717]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP066-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:02:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.41 % Elapsed time: 0.036903 seconds
% 0.15/0.41 % CPU time: 0.125942 seconds
% 0.15/0.41 % Total memory used: 22.441 MB
% 0.15/0.41 % Net memory used: 22.313 MB
%------------------------------------------------------------------------------