%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:32:28 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 70 ( 63 unt; 0 def)
% Number of atoms : 82 ( 81 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 21 ~; 12 |; 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 : 115 ( 115 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(double_divide(identity,X),double_divide(double_divide(double_divide(Y,Z),double_divide(identity,identity)),double_divide(X,Z))) = Y,
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] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),double_divide(identity,identity)),double_divide(X0,X2))) = X1,
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,X2] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),inverse(identity)),double_divide(X0,X2))) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f13,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f14,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f16,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f13,f10]) ).
fof(f17,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f14,f16]) ).
fof(f45,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(double_divide(double_divide(X0,X1),inverse(identity)),double_divide(identity,X1))) = X0,
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f48,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(identity,inverse(identity)),double_divide(X0,inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f49,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(inverse(X1),inverse(identity)),double_divide(X0,identity))) = X1,
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f58,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X0,inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f48]) ).
fof(f59,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(inverse(X1),inverse(identity)),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f49]) ).
fof(f68,plain,
! [X0] : double_divide(inverse(identity),double_divide(identity,double_divide(identity,inverse(X0)))) = X0,
inference(paramodulation,[status(thm)],[f8,f58]) ).
fof(f69,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f58]) ).
fof(f71,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(double_divide(X1,double_divide(identity,double_divide(X0,inverse(X2)))),inverse(identity)),X2)) = X1,
inference(paramodulation,[status(thm)],[f58,f11]) ).
fof(f76,plain,
! [X0] : double_divide(double_divide(identity,X0),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f69]) ).
fof(f79,plain,
double_divide(identity,inverse(identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f76]) ).
fof(f83,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(double_divide(X1,inverse(identity)),inverse(identity)),X0)) = X1,
inference(paramodulation,[status(thm)],[f76,f11]) ).
fof(f84,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(X1,inverse(identity)),double_divide(X0,inverse(identity)))) = double_divide(identity,X1),
inference(paramodulation,[status(thm)],[f76,f11]) ).
fof(f92,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(backward_demodulation,[status(thm)],[f105,f17]) ).
fof(f94,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(double_divide(X1,double_divide(identity,double_divide(X0,inverse(X2)))),identity),X2)) = X1,
inference(backward_demodulation,[status(thm)],[f105,f71]) ).
fof(f95,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(identity,inverse(X0)))) = X0,
inference(backward_demodulation,[status(thm)],[f105,f68]) ).
fof(f101,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(inverse(X1),identity),inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f105,f59]) ).
fof(f103,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(double_divide(double_divide(X0,X1),identity),double_divide(identity,X1))) = X0,
inference(backward_demodulation,[status(thm)],[f105,f45]) ).
fof(f105,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f79]) ).
fof(f107,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(double_divide(X1,identity),inverse(identity)),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f105,f83]) ).
fof(f108,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(inverse(X1),inverse(identity)),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f107]) ).
fof(f109,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(inverse(X1),identity),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f105,f108]) ).
fof(f110,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(inverse(inverse(X1)),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f109]) ).
fof(f111,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(X1,identity),double_divide(X0,inverse(identity)))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f105,f84]) ).
fof(f112,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(inverse(X1),double_divide(X0,inverse(identity)))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f8,f111]) ).
fof(f113,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(inverse(X1),double_divide(X0,identity))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f105,f112]) ).
fof(f114,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(inverse(X1),inverse(X0))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f8,f113]) ).
fof(f134,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2 ),
inference(trivial_equality_resolution,[status(thm)],[f92]) ).
fof(f136,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(inverse(double_divide(X1,double_divide(identity,double_divide(X0,inverse(X2))))),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f94]) ).
fof(f137,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(multiply(double_divide(identity,double_divide(X0,inverse(X1))),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f12,f136]) ).
fof(f149,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(inverse(inverse(X1)),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f101]) ).
fof(f150,plain,
! [X0] : double_divide(identity,double_divide(identity,X0)) = X0,
inference(backward_demodulation,[status(thm)],[f151,f95]) ).
fof(f151,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f114,f149]) ).
fof(f156,plain,
! [X0,X1] : double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(identity,X1))) = X0,
inference(forward_demodulation,[status(thm)],[f105,f103]) ).
fof(f157,plain,
! [X0,X1] : double_divide(identity,double_divide(inverse(double_divide(X0,X1)),double_divide(identity,X1))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f156]) ).
fof(f158,plain,
! [X0,X1] : double_divide(identity,double_divide(multiply(X0,X1),double_divide(identity,X0))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f157]) ).
fof(f164,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(multiply(double_divide(identity,double_divide(X0,inverse(X1))),X2),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f150,f137]) ).
fof(f165,plain,
! [X0,X1] : double_divide(X0,double_divide(inverse(inverse(X1)),X0)) = X1,
inference(backward_demodulation,[status(thm)],[f150,f110]) ).
fof(f214,plain,
! [X0] : double_divide(identity,X0) = inverse(X0),
inference(paramodulation,[status(thm)],[f151,f150]) ).
fof(f223,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f214,f151]) ).
fof(f230,plain,
! [X0,X1] : inverse(double_divide(multiply(X0,X1),double_divide(identity,X0))) = X1,
inference(backward_demodulation,[status(thm)],[f214,f158]) ).
fof(f231,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(multiply(inverse(double_divide(X0,inverse(X1))),X2),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f214,f164]) ).
fof(f256,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f223,f134]) ).
fof(f258,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f223,f165]) ).
fof(f264,plain,
! [X0,X1] : multiply(double_divide(identity,X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f12,f230]) ).
fof(f265,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f214,f264]) ).
fof(f266,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(multiply(multiply(inverse(X1),X0),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f12,f231]) ).
fof(f279,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f256]) ).
fof(f311,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f258,f258]) ).
fof(f345,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f311,f12]) ).
fof(f551,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(multiply(X1,X2),X0)) = X2,
inference(paramodulation,[status(thm)],[f265,f266]) ).
fof(f1028,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = inverse(double_divide(multiply(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f551,f345]) ).
fof(f1093,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f1108,f279]) ).
fof(f1108,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f12,f1028]) ).
fof(f1131,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1093]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.40 % Computer : n009.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sun Sep 20 19:56:42 UTC 2026
% 0.16/0.40 % CPUTime :
% 0.20/0.43 % Drodi V4.1.1
% 0.20/0.51 % Refutation found
% 0.20/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.57 % Elapsed time: 0.146941 seconds
% 0.20/0.57 % CPU time: 0.495692 seconds
% 0.20/0.57 % Total memory used: 53.907 MB
% 0.20/0.57 % Net memory used: 53.331 MB
%------------------------------------------------------------------------------