%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP586-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),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(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),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(X0,multiply(X1,inverse(double_divide(double_divide(X0,X1),inverse(X2))))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f4]) ).
fof(f12,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,multiply(inverse(X2),double_divide(X0,X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f11]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(multiply(X1,multiply(inverse(X2),double_divide(X0,X1))),multiply(inverse(X3),X2))) = X3,
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f15,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(inverse(X1),double_divide(X2,X0))),X2) = inverse(X1),
inference(paramodulation,[status(thm)],[f12,f5]) ).
fof(f39,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f57,plain,
! [X0,X1] : multiply(inverse(X0),multiply(inverse(X1),X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f39,f5]) ).
fof(f61,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(multiply(inverse(X0),X1))) = X1,
inference(paramodulation,[status(thm)],[f57,f39]) ).
fof(f69,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(inverse(X1))) = multiply(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f57,f61]) ).
fof(f94,plain,
! [X0,X1,X2] : double_divide(inverse(X0),inverse(multiply(X1,X2))) = multiply(inverse(double_divide(X2,X1)),X0),
inference(paramodulation,[status(thm)],[f5,f69]) ).
fof(f101,plain,
! [X0,X1,X2] : double_divide(inverse(X0),inverse(multiply(X1,X2))) = multiply(multiply(X1,X2),X0),
inference(forward_demodulation,[status(thm)],[f5,f94]) ).
fof(f293,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(backward_demodulation,[status(thm)],[f101,f61]) ).
fof(f319,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(X0),double_divide(X1,inverse(X1))),
inference(paramodulation,[status(thm)],[f15,f293]) ).
fof(f334,plain,
! [X0,X1,X2] : double_divide(inverse(X0),inverse(X1)) = multiply(multiply(multiply(inverse(X2),X1),X2),X0),
inference(paramodulation,[status(thm)],[f293,f101]) ).
fof(f344,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(X1)) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f293,f334]) ).
fof(f455,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(double_divide(X1,inverse(X1)))) = X0,
inference(paramodulation,[status(thm)],[f319,f39]) ).
fof(f467,plain,
! [X0,X1] : multiply(double_divide(X0,inverse(X0)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f344,f455]) ).
fof(f477,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(paramodulation,[status(thm)],[f344,f467]) ).
fof(f702,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f477,f6]) ).
fof(f735,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f702]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP586-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n020.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sun Sep 20 20:18:32 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.037761 seconds
% 0.13/0.39 % CPU time: 0.138023 seconds
% 0.13/0.39 % Total memory used: 7.472 MB
% 0.13/0.39 % Net memory used: 7.418 MB
%------------------------------------------------------------------------------