%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP069-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.38s
% 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 : 5 ( 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 : 116 ( 116 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(X,divide(divide(divide(divide(X,X),Y),Z),divide(divide(identity,X),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(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(identity,X0),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] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f12,plain,
! [X0,X1,X2] : divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(inverse(X0),X2))) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f13,plain,
! [X0,X1,X2] : divide(X0,divide(divide(divide(identity,X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f12]) ).
fof(f14,plain,
! [X0,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),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,f11]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f19,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f15,f11]) ).
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(f30,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,multiply(identity,X1)),
inference(paramodulation,[status(thm)],[f17,f11]) ).
fof(f33,plain,
! [X0] : divide(X0,identity) = X0,
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f34,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(inverse(inverse(X3)),X2))))) = X3,
inference(paramodulation,[status(thm)],[f14,f14]) ).
fof(f36,plain,
! [X0,X1] : divide(X0,divide(identity,divide(inverse(X0),inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f41,plain,
! [X0,X1] : divide(X0,divide(divide(inverse(X1),inverse(X0)),identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f48,plain,
! [X0] : multiply(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f33,f19]) ).
fof(f49,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(multiply(identity,X3),X2))))) = X3,
inference(forward_demodulation,[status(thm)],[f17,f34]) ).
fof(f51,plain,
! [X0,X1] : divide(X0,inverse(divide(inverse(X0),inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f36]) ).
fof(f52,plain,
! [X0,X1] : multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[status(thm)],[f11,f51]) ).
fof(f53,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f11,f52]) ).
fof(f57,plain,
! [X0,X1] : divide(X0,divide(inverse(X1),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f33,f41]) ).
fof(f58,plain,
! [X0,X1] : divide(X0,multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f11,f57]) ).
fof(f78,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f53,f53]) ).
fof(f79,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f48,f53]) ).
fof(f80,plain,
! [X0,X1] : multiply(inverse(X0),multiply(multiply(identity,X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f17,f53]) ).
fof(f83,plain,
! [X0,X1] : multiply(X0,X1) = multiply(multiply(identity,X0),X1),
inference(forward_demodulation,[status(thm)],[f17,f78]) ).
fof(f84,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f83,f80]) ).
fof(f87,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f79,f53]) ).
fof(f88,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[status(thm)],[f89,f17]) ).
fof(f89,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f48,f87]) ).
fof(f90,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f88,f23]) ).
fof(f98,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(X3,X2))))) = X3,
inference(backward_demodulation,[status(thm)],[f88,f49]) ).
fof(f99,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f88,f30]) ).
fof(f100,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f90]) ).
fof(f169,plain,
! [X0,X1] : divide(multiply(inverse(inverse(X0)),X1),X1) = X0,
inference(paramodulation,[status(thm)],[f53,f58]) ).
fof(f171,plain,
! [X0,X1] : divide(X0,multiply(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f89,f58]) ).
fof(f176,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f89,f169]) ).
fof(f182,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(paramodulation,[status(thm)],[f11,f176]) ).
fof(f191,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f99,f182]) ).
fof(f287,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f191,f171]) ).
fof(f304,plain,
! [X0,X1,X2] : inverse(divide(X0,divide(inverse(identity),divide(divide(inverse(X0),X1),divide(X2,X1))))) = X2,
inference(paramodulation,[status(thm)],[f8,f98]) ).
fof(f325,plain,
! [X0,X1,X2] : divide(divide(inverse(identity),divide(divide(inverse(X0),X1),divide(X2,X1))),X0) = X2,
inference(forward_demodulation,[status(thm)],[f287,f304]) ).
fof(f326,plain,
! [X0,X1,X2] : divide(divide(identity,divide(divide(inverse(X0),X1),divide(X2,X1))),X0) = X2,
inference(forward_demodulation,[status(thm)],[f15,f325]) ).
fof(f327,plain,
! [X0,X1,X2] : divide(inverse(divide(divide(inverse(X0),X1),divide(X2,X1))),X0) = X2,
inference(forward_demodulation,[status(thm)],[f8,f326]) ).
fof(f328,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),divide(inverse(X2),X1)),X2) = X0,
inference(forward_demodulation,[status(thm)],[f287,f327]) ).
fof(f416,plain,
! [X0,X1] : divide(inverse(X0),X1) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f11,f287]) ).
fof(f476,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f416,f11]) ).
fof(f488,plain,
! [X0,X1,X2] : divide(multiply(divide(X0,X1),multiply(X1,X2)),X2) = X0,
inference(backward_demodulation,[status(thm)],[f476,f328]) ).
fof(f906,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(divide(X0,X2),multiply(X2,X1)),
inference(paramodulation,[status(thm)],[f488,f191]) ).
fof(f1322,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(divide(X0,inverse(X1)),X2),
inference(paramodulation,[status(thm)],[f84,f906]) ).
fof(f1344,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f1351,f100]) ).
fof(f1351,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f11,f1322]) ).
fof(f1391,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP069-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:56:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.043618 seconds
% 0.14/0.41 % CPU time: 0.139667 seconds
% 0.14/0.41 % Total memory used: 18.704 MB
% 0.14/0.41 % Net memory used: 18.570 MB
%------------------------------------------------------------------------------