%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP590-1 : TPTP v9.3.1. Released v2.6.0.
% 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 12:34:44 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(X2))))),X1) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(double_divide(X0,inverse(X1))),double_divide(X0,X2)),X2) = X1,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f12,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(inverse(X0),X1),double_divide(X1,X2)),X2) = X0,
inference(forward_demodulation,[status(thm)],[f5,f11]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(inverse(X0),multiply(multiply(inverse(X1),X2),double_divide(X2,X3))),X1),X3) = X0,
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f15,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X1),X2),double_divide(X2,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f12,f5]) ).
fof(f43,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X0),inverse(X1)) = X1,
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f61,plain,
! [X0,X1,X2] : multiply(inverse(X0),multiply(multiply(inverse(X1),multiply(inverse(X2),X2)),X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f43,f15]) ).
fof(f62,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(inverse(X0),multiply(inverse(X1),X1)),X2),inverse(X2)) = X0,
inference(paramodulation,[status(thm)],[f43,f12]) ).
fof(f63,plain,
! [X0,X1] : multiply(inverse(X0),multiply(inverse(X1),X1)) = inverse(X0),
inference(paramodulation,[status(thm)],[f43,f5]) ).
fof(f64,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X1),inverse(X1)) = X0,
inference(backward_demodulation,[status(thm)],[f63,f62]) ).
fof(f65,plain,
! [X0,X1] : multiply(inverse(X0),multiply(inverse(X1),X0)) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f63,f61]) ).
fof(f83,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(multiply(inverse(X1),X1))) = X0,
inference(paramodulation,[status(thm)],[f63,f64]) ).
fof(f84,plain,
! [X0,X1] : double_divide(inverse(multiply(inverse(X0),X0)),inverse(X1)) = X1,
inference(paramodulation,[status(thm)],[f63,f43]) ).
fof(f94,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),inverse(multiply(inverse(X2),X2))) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f5,f83]) ).
fof(f101,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(inverse(X0),inverse(X1)),X1),inverse(multiply(inverse(X2),X2))) = X0,
inference(paramodulation,[status(thm)],[f83,f12]) ).
fof(f105,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X1),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f94,f101]) ).
fof(f113,plain,
! [X0,X1] : multiply(multiply(inverse(X0),inverse(X1)),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f105,f5]) ).
fof(f132,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f83,f84]) ).
fof(f176,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f132,f113]) ).
fof(f177,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X1),X1)) = inverse(X0),
inference(paramodulation,[status(thm)],[f132,f105]) ).
fof(f187,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X1),X1),double_divide(X2,X0))) = inverse(X2),
inference(paramodulation,[status(thm)],[f132,f15]) ).
fof(f188,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(inverse(X0),X0),double_divide(X1,X2)),X2) = X1,
inference(paramodulation,[status(thm)],[f132,f12]) ).
fof(f191,plain,
! [X0] : multiply(multiply(inverse(X0),X0),a2) != a2,
inference(paramodulation,[status(thm)],[f132,f6]) ).
fof(f229,plain,
! [X0,X1] : multiply(X0,inverse(inverse(double_divide(X1,X0)))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f176,f187]) ).
fof(f231,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X0,X1))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f5,f229]) ).
fof(f232,plain,
! [X0,X1] : double_divide(inverse(inverse(double_divide(X0,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f176,f188]) ).
fof(f234,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f5,f232]) ).
fof(f237,plain,
inverse(inverse(a2)) != a2,
inference(forward_demodulation,[status(thm)],[f176,f191]) ).
fof(f272,plain,
! [X0,X1] : double_divide(inverse(inverse(X0)),inverse(X1)) = multiply(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f65,f234]) ).
fof(f313,plain,
! [X0,X1] : double_divide(inverse(inverse(X0)),X1) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f231,f234]) ).
fof(f326,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(backward_demodulation,[status(thm)],[f313,f272]) ).
fof(f345,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(inverse(X1),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f326,f83]) ).
fof(f359,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f363,f237]) ).
fof(f363,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f177,f345]) ).
fof(f397,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP590-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:22:57 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.031423 seconds
% 0.12/0.40 % CPU time: 0.073187 seconds
% 0.12/0.40 % Total memory used: 3.731 MB
% 0.12/0.40 % Net memory used: 3.688 MB
%------------------------------------------------------------------------------