%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP415-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:33:39 PM UTC 2026
% Result : Unsatisfiable 37.49s 5.20s
% Output : CNFRefutation 37.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 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 : 16 ( 4 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 : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,A)),multiply(B,inverse(C)))),inverse(multiply(inverse(A),A)))))) = C,
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] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))) = X2,
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,X4] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2))),inverse(multiply(inverse(X0),X0)))))) = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X3),X3))))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f13,plain,
! [X0,X1,X2] : X0 = multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X0))))),inverse(multiply(inverse(X1),X1))))),
inference(paramodulation,[status(thm)],[f3,f11]) ).
fof(f35,plain,
! [X0,X1,X2] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2))),inverse(multiply(inverse(X0),X0))))))) = X2,
inference(paramodulation,[status(thm)],[f11,f3]) ).
fof(f76,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0)))))) = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(inverse(multiply(inverse(multiply(inverse(multiply(X5,X1)),multiply(X5,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1)))))))),inverse(multiply(inverse(X3),X3))))),
inference(paramodulation,[status(thm)],[f13,f11]) ).
fof(f80,plain,
! [X0,X1,X2,X3] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0)))))) = multiply(inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1))),
inference(forward_demodulation,[status(thm)],[f13,f76]) ).
fof(f120,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(multiply(X1,inverse(X2))))))),inverse(multiply(inverse(X1),X1))) = X2,
inference(paramodulation,[status(thm)],[f80,f3]) ).
fof(f121,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(multiply(X1,X2)))))),inverse(multiply(inverse(X1),X1)))) = X2,
inference(paramodulation,[status(thm)],[f80,f35]) ).
fof(f136,plain,
! [X0,X1,X2] : X0 = multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X0)),inverse(multiply(inverse(X2),X2)))))))),
inference(paramodulation,[status(thm)],[f80,f13]) ).
fof(f169,plain,
! [X0,X1,X2,X3] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X0)),X3)),inverse(multiply(inverse(X0),X0))))))) = multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))))),
inference(paramodulation,[status(thm)],[f136,f136]) ).
fof(f431,plain,
! [X0,X1,X2,X3] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X3))))))),X0)),X3)),inverse(multiply(inverse(X0),X0)))))) = multiply(inverse(X2),X2),
inference(paramodulation,[status(thm)],[f120,f3]) ).
fof(f1530,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(multiply(inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))))),X2)),inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0)))))))) = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f80,f431]) ).
fof(f1676,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0)))))))) = multiply(inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f35,f1530]) ).
fof(f5114,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X0),inverse(multiply(inverse(X2),X2))))))))),
inference(paramodulation,[status(thm)],[f169,f136]) ).
fof(f5416,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)],[f1676,f5114]) ).
fof(f7758,plain,
! [X0,X1,X2,X3] : multiply(inverse(X0),X0) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X3))))))),inverse(multiply(inverse(X2),X2)))),X3),
inference(paramodulation,[status(thm)],[f120,f5416]) ).
fof(f8178,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(forward_demodulation,[status(thm)],[f121,f7758]) ).
fof(f8227,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f4,f8178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP415-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:15:06 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 37.49/5.20 % Refutation found
% 37.49/5.20 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 37.49/5.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.67/5.30 % Elapsed time: 4.910056 seconds
% 13.67/5.30 % CPU time: 38.545544 seconds
% 13.67/5.30 % Total memory used: 1.152 GB
% 13.67/5.30 % Net memory used: 1.146 GB
%------------------------------------------------------------------------------