%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP424-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:33:50 PM UTC 2026
% Result : Unsatisfiable 0.36s 0.51s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X2),X2))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),X2)))),multiply(X3,inverse(X2))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f37,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X0),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X1,inverse(X2))),
inference(paramodulation,[status(thm)],[f3,f11]) ).
fof(f38,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),X2)))),multiply(X3,inverse(X2))),
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,inverse(X3))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(X3),X3)))),X3)))),multiply(X2,inverse(X3)))))),multiply(X4,inverse(multiply(X2,inverse(X3))))),
inference(paramodulation,[status(thm)],[f37,f38]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,inverse(X3))))) = multiply(inverse(multiply(X4,inverse(X1))),multiply(X4,inverse(multiply(X2,inverse(X3))))),
inference(forward_demodulation,[status(thm)],[f37,f108]) ).
fof(f182,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),X5)))),multiply(X4,inverse(X5)))),inverse(multiply(inverse(X5),X5)))))),
inference(paramodulation,[status(thm)],[f3,f159]) ).
fof(f246,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(X2))),
inference(forward_demodulation,[status(thm)],[f3,f182]) ).
fof(f260,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(X0),multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),X2)))),multiply(X1,inverse(X2)))),inverse(X3))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),X2)))),multiply(X4,inverse(X3))),
inference(paramodulation,[status(thm)],[f3,f246]) ).
fof(f414,plain,
! [X0,X1,X2] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f3,f260]) ).
fof(f510,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f414,f414]) ).
fof(f600,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f4,f510]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP424-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sun Sep 20 20:12:52 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.36/0.51 % Refutation found
% 0.36/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.36/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.36/0.52 % Elapsed time: 0.215364 seconds
% 0.36/0.52 % CPU time: 1.593913 seconds
% 0.36/0.52 % Total memory used: 126.282 MB
% 0.36/0.52 % Net memory used: 125.960 MB
%------------------------------------------------------------------------------