%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP075-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:32:27 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 71 ( 65 unt; 0 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 18 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 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 : 131 ( 131 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z,U] : double_divide(double_divide(double_divide(X,double_divide(Y,identity)),double_divide(double_divide(Z,double_divide(U,double_divide(U,identity))),double_divide(X,identity))),Y) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = double_divide(X,inverse(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,X3] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),double_divide(X0,identity))),X1) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = double_divide(X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = double_divide(X0,inverse(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) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),inverse(X0))),X1) = X2,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),inverse(X0))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f8,f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(double_divide(X2,double_divide(X3,inverse(X3))),inverse(X0))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f8,f13]) ).
fof(f15,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(double_divide(X2,identity),inverse(X0))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f9,f14]) ).
fof(f16,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(inverse(X2),inverse(X0))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f8,f15]) ).
fof(f17,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f18,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f19,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f20,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f17,f10]) ).
fof(f24,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(inverse(X0),inverse(X1))),X1) = X0,
inference(paramodulation,[status(thm)],[f9,f16]) ).
fof(f26,plain,
! [X0,X1] : double_divide(double_divide(double_divide(inverse(X0),inverse(X1)),identity),X1) = X0,
inference(paramodulation,[status(thm)],[f9,f16]) ).
fof(f34,plain,
! [X0,X1] : double_divide(inverse(double_divide(inverse(X0),inverse(X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f26]) ).
fof(f35,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f11,f34]) ).
fof(f41,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,multiply(identity,X1)),double_divide(inverse(X2),inverse(X0))),inverse(X1)) = X2,
inference(paramodulation,[status(thm)],[f18,f16]) ).
fof(f56,plain,
! [X0] : double_divide(inverse(identity),inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f17,f35]) ).
fof(f60,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(X0),multiply(X1,X2)),X0) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f11,f35]) ).
fof(f68,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f56]) ).
fof(f75,plain,
! [X0] : multiply(inverse(X0),inverse(identity)) = inverse(X0),
inference(paramodulation,[status(thm)],[f56,f11]) ).
fof(f76,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f68,f56]) ).
fof(f78,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(backward_demodulation,[status(thm)],[f68,f20]) ).
fof(f89,plain,
! [X0] : multiply(inverse(X0),identity) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f68,f75]) ).
fof(f91,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(trivial_equality_resolution,[status(thm)],[f78]) ).
fof(f97,plain,
! [X0] : double_divide(multiply(inverse(X0),identity),X0) = identity,
inference(paramodulation,[status(thm)],[f68,f35]) ).
fof(f100,plain,
! [X0,X1] : double_divide(double_divide(double_divide(identity,inverse(X0)),double_divide(inverse(X1),identity)),X0) = X1,
inference(paramodulation,[status(thm)],[f68,f16]) ).
fof(f104,plain,
! [X0] : double_divide(inverse(X0),X0) = identity,
inference(forward_demodulation,[status(thm)],[f89,f97]) ).
fof(f110,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),identity)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f76,f100]) ).
fof(f111,plain,
! [X0,X1] : double_divide(double_divide(X0,inverse(inverse(X1))),X0) = X1,
inference(forward_demodulation,[status(thm)],[f8,f110]) ).
fof(f112,plain,
! [X0,X1] : double_divide(double_divide(X0,multiply(identity,X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f18,f111]) ).
fof(f138,plain,
! [X0,X1] : double_divide(double_divide(double_divide(X0,inverse(X1)),identity),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f104,f16]) ).
fof(f145,plain,
! [X0,X1] : double_divide(inverse(double_divide(X0,inverse(X1))),X1) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f8,f138]) ).
fof(f146,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f148,f35]) ).
fof(f147,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f148,f60]) ).
fof(f148,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X1),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f11,f145]) ).
fof(f155,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f168,f91]) ).
fof(f161,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(backward_demodulation,[status(thm)],[f168,f112]) ).
fof(f165,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,X1),double_divide(inverse(X2),inverse(X0))),inverse(X1)) = X2,
inference(backward_demodulation,[status(thm)],[f168,f41]) ).
fof(f168,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f18,f146]) ).
fof(f170,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f155]) ).
fof(f186,plain,
! [X0,X1] : double_divide(identity,double_divide(X0,X1)) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f19,f161]) ).
fof(f187,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f161,f161]) ).
fof(f193,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f161,f11]) ).
fof(f196,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),X0) = X1,
inference(backward_demodulation,[status(thm)],[f186,f24]) ).
fof(f203,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f148,f196]) ).
fof(f291,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f187,f11]) ).
fof(f414,plain,
! [X0,X1] : double_divide(inverse(X0),X1) = inverse(double_divide(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f193,f148]) ).
fof(f423,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f148,f291]) ).
fof(f435,plain,
! [X0,X1] : double_divide(inverse(X0),X1) = multiply(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f11,f414]) ).
fof(f445,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f147,f423]) ).
fof(f553,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(X1)) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f203,f435]) ).
fof(f575,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,X1),multiply(X2,X0)),inverse(X1)) = X2,
inference(backward_demodulation,[status(thm)],[f553,f165]) ).
fof(f646,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = double_divide(double_divide(X1,X0),inverse(X2)),
inference(paramodulation,[status(thm)],[f11,f445]) ).
fof(f663,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),double_divide(X1,X2)),X2) = X0,
inference(backward_demodulation,[status(thm)],[f646,f575]) ).
fof(f727,plain,
! [X0,X1,X2] : multiply(multiply(inverse(X0),double_divide(X1,X2)),X2) = double_divide(X0,X1),
inference(paramodulation,[status(thm)],[f291,f663]) ).
fof(f756,plain,
! [X0,X1,X2] : multiply(double_divide(X0,inverse(double_divide(X1,X2))),X2) = double_divide(X0,X1),
inference(forward_demodulation,[status(thm)],[f445,f727]) ).
fof(f757,plain,
! [X0,X1,X2] : multiply(double_divide(X0,multiply(X1,X2)),X1) = double_divide(X0,X2),
inference(forward_demodulation,[status(thm)],[f11,f756]) ).
fof(f799,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(double_divide(multiply(X1,X2),X0),X2),
inference(paramodulation,[status(thm)],[f161,f757]) ).
fof(f1521,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = inverse(double_divide(multiply(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f799,f291]) ).
fof(f1569,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f1584,f170]) ).
fof(f1584,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f11,f1521]) ).
fof(f1630,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP075-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 19:52:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.094845 seconds
% 0.14/0.46 % CPU time: 0.424936 seconds
% 0.14/0.46 % Total memory used: 75.050 MB
% 0.14/0.46 % Net memory used: 74.474 MB
%------------------------------------------------------------------------------