%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP093-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 12:32:29 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 83 ( 75 unt; 0 def)
% Number of atoms : 103 ( 102 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 30 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 155 ( 155 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(identity,divide(divide(divide(X,Y),Z),X)),Z) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = divide(X,divide(identity,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = divide(identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = divide(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(identity,divide(divide(divide(X0,X1),X2),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(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0,X1,X2] : divide(inverse(divide(divide(divide(X0,X1),X2),X0)),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,X3] : divide(inverse(divide(divide(X0,X1),inverse(divide(divide(divide(X2,X0),X3),X2)))),X1) = X3,
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f14,plain,
! [X0,X1] : divide(inverse(divide(divide(inverse(X0),X1),identity)),X1) = X0,
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : divide(inverse(multiply(divide(X0,X1),divide(divide(divide(X2,X0),X3),X2))),X1) = X3,
inference(forward_demodulation,[status(thm)],[f12,f13]) ).
fof(f16,plain,
! [X0,X1,X2] : multiply(inverse(divide(divide(divide(X0,X1),inverse(X2)),X0)),X2) = X1,
inference(paramodulation,[status(thm)],[f11,f12]) ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f22,plain,
! [X0,X1,X2] : divide(inverse(divide(divide(multiply(X0,X1),X2),X0)),X2) = inverse(X1),
inference(paramodulation,[status(thm)],[f12,f11]) ).
fof(f23,plain,
! [X0,X1,X2] : multiply(inverse(divide(multiply(divide(X0,X1),X2),X0)),X2) = X1,
inference(forward_demodulation,[status(thm)],[f12,f16]) ).
fof(f27,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,multiply(identity,X1)),
inference(paramodulation,[status(thm)],[f17,f12]) ).
fof(f78,plain,
! [X0,X1] : divide(inverse(divide(X0,identity)),X1) = divide(divide(inverse(X0),X1),identity),
inference(paramodulation,[status(thm)],[f14,f14]) ).
fof(f79,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,identity)),X1) = divide(divide(divide(X2,X0),X1),X2),
inference(paramodulation,[status(thm)],[f11,f14]) ).
fof(f87,plain,
! [X0,X1,X2,X3] : divide(inverse(multiply(X0,divide(divide(divide(X1,inverse(divide(divide(inverse(X0),X2),identity))),X3),X1))),X2) = X3,
inference(paramodulation,[status(thm)],[f14,f15]) ).
fof(f107,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,divide(inverse(divide(inverse(divide(divide(inverse(X0),X1),identity)),identity)),X2))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f79,f87]) ).
fof(f114,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f8,f9]) ).
fof(f116,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f12,f9]) ).
fof(f117,plain,
! [X0] : divide(inverse(divide(identity,identity)),inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f121,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f116,f10]) ).
fof(f122,plain,
! [X0] : multiply(inverse(divide(identity,identity)),X0) = X0,
inference(forward_demodulation,[status(thm)],[f12,f117]) ).
fof(f123,plain,
! [X0] : multiply(inverse(inverse(identity)),X0) = X0,
inference(forward_demodulation,[status(thm)],[f8,f122]) ).
fof(f124,plain,
! [X0] : multiply(multiply(identity,identity),X0) = X0,
inference(forward_demodulation,[status(thm)],[f17,f123]) ).
fof(f125,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f116,f121]) ).
fof(f126,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f116,f125]) ).
fof(f127,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(trivial_equality_resolution,[status(thm)],[f126]) ).
fof(f129,plain,
multiply(identity,identity) = inverse(identity),
inference(paramodulation,[status(thm)],[f114,f17]) ).
fof(f130,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f114,f12]) ).
fof(f132,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[status(thm)],[f134,f124]) ).
fof(f134,plain,
multiply(identity,identity) = identity,
inference(forward_demodulation,[status(thm)],[f114,f129]) ).
fof(f137,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,divide(inverse(divide(inverse(multiply(divide(inverse(X0),X1),identity)),identity)),X2))),X1) = X2,
inference(backward_demodulation,[status(thm)],[f130,f107]) ).
fof(f139,plain,
! [X0,X1] : divide(inverse(divide(X0,identity)),X1) = multiply(divide(inverse(X0),X1),identity),
inference(backward_demodulation,[status(thm)],[f130,f78]) ).
fof(f148,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f132,f27]) ).
fof(f149,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f132,f17]) ).
fof(f150,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f132,f127]) ).
fof(f157,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,divide(inverse(multiply(inverse(multiply(divide(inverse(X0),X1),identity)),identity)),X2))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f130,f137]) ).
fof(f158,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,multiply(divide(inverse(inverse(multiply(divide(inverse(X0),X1),identity))),X2),identity))),X1) = X2,
inference(backward_demodulation,[status(thm)],[f160,f157]) ).
fof(f160,plain,
! [X0,X1] : divide(inverse(multiply(X0,identity)),X1) = multiply(divide(inverse(X0),X1),identity),
inference(forward_demodulation,[status(thm)],[f130,f139]) ).
fof(f176,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(trivial_equality_resolution,[status(thm)],[f150]) ).
fof(f189,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,multiply(divide(multiply(identity,multiply(divide(inverse(X0),X1),identity)),X2),identity))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f17,f158]) ).
fof(f190,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,multiply(divide(multiply(divide(inverse(X0),X1),identity),X2),identity))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f132,f189]) ).
fof(f207,plain,
! [X0,X1,X2] : multiply(inverse(multiply(multiply(divide(inverse(X0),X1),X2),X0)),X2) = X1,
inference(paramodulation,[status(thm)],[f12,f23]) ).
fof(f211,plain,
! [X0,X1] : multiply(inverse(divide(multiply(identity,X0),X1)),X0) = X1,
inference(paramodulation,[status(thm)],[f9,f23]) ).
fof(f215,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f132,f211]) ).
fof(f271,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(paramodulation,[status(thm)],[f8,f215]) ).
fof(f280,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,multiply(divide(divide(inverse(X0),X1),X2),identity))),X1) = X2,
inference(backward_demodulation,[status(thm)],[f286,f190]) ).
fof(f286,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f149,f271]) ).
fof(f289,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,divide(divide(inverse(X0),X1),X2))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f286,f280]) ).
fof(f294,plain,
! [X0,X1] : divide(inverse(divide(identity,X0)),multiply(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f9,f22]) ).
fof(f306,plain,
! [X0,X1] : divide(inverse(inverse(X0)),multiply(X0,X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f8,f294]) ).
fof(f307,plain,
! [X0,X1] : divide(X0,multiply(X0,X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f149,f306]) ).
fof(f320,plain,
! [X0,X1] : X0 = inverse(divide(multiply(divide(X1,X0),identity),X1)),
inference(paramodulation,[status(thm)],[f23,f286]) ).
fof(f331,plain,
! [X0,X1] : X0 = inverse(divide(divide(X1,X0),X1)),
inference(forward_demodulation,[status(thm)],[f286,f320]) ).
fof(f372,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f148,f307]) ).
fof(f377,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),X1) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f307,f215]) ).
fof(f381,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f149,f372]) ).
fof(f383,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f176,f384]) ).
fof(f384,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f149,f377]) ).
fof(f398,plain,
! [X0,X1] : multiply(inverse(X0),X1) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f381,f215]) ).
fof(f418,plain,
! [X0,X1,X2] : divide(X0,multiply(multiply(divide(inverse(X1),X2),X0),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f398,f207]) ).
fof(f472,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(paramodulation,[status(thm)],[f384,f383]) ).
fof(f476,plain,
! [X0,X1] : divide(X0,multiply(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f384,f307]) ).
fof(f489,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f381,f331]) ).
fof(f646,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,inverse(X1))),X2) = multiply(divide(inverse(X0),X2),X1),
inference(paramodulation,[status(thm)],[f307,f289]) ).
fof(f672,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,X1)),X2) = multiply(divide(inverse(X0),X2),X1),
inference(forward_demodulation,[status(thm)],[f148,f646]) ).
fof(f674,plain,
! [X0,X1,X2] : divide(X0,multiply(divide(divide(X0,X1),X2),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f676,f418]) ).
fof(f676,plain,
! [X0,X1,X2] : divide(divide(X0,X1),X2) = multiply(divide(inverse(X1),X2),X0),
inference(forward_demodulation,[status(thm)],[f489,f672]) ).
fof(f758,plain,
! [X0,X1] : multiply(X0,X1) = divide(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f149,f398]) ).
fof(f865,plain,
! [X0,X1] : divide(inverse(X0),X1) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f12,f489]) ).
fof(f1017,plain,
! [X0,X1,X2] : divide(X0,multiply(inverse(X1),X2)) = multiply(X1,divide(X0,X2)),
inference(paramodulation,[status(thm)],[f476,f674]) ).
fof(f1065,plain,
! [X0,X1,X2] : divide(X0,divide(X1,X2)) = multiply(X2,divide(X0,X1)),
inference(forward_demodulation,[status(thm)],[f398,f1017]) ).
fof(f1303,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f865,f12]) ).
fof(f1324,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,divide(X0,inverse(X2))),
inference(forward_demodulation,[status(thm)],[f1065,f1303]) ).
fof(f1326,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f758,f1324]) ).
fof(f1327,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f472,f1326]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP093-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 19:56:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.44 % Refutation found
% 0.09/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.084112 seconds
% 0.09/0.45 % CPU time: 0.432144 seconds
% 0.09/0.45 % Total memory used: 73.682 MB
% 0.09/0.45 % Net memory used: 72.593 MB
%------------------------------------------------------------------------------