%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP409-1 : 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 12:33:38 PM UTC 2026
% Result : Unsatisfiable 1.58s 0.66s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 16 ( 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 : 96 ( 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(multiply(inverse(multiply(A,inverse(multiply(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(multiply(inverse(multiply(X0,inverse(multiply(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(f10,plain,
! [X0,X1,X2] : multiply(multiply(inverse(X0),multiply(multiply(inverse(multiply(X1,inverse(multiply(X0,X2)))),multiply(X1,inverse(X2))),inverse(X2))),inverse(multiply(inverse(X2),X2))) = inverse(X2),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3] : multiply(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(X1,X2)))),multiply(X3,inverse(X2))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(X3,multiply(inverse(X2),X2))))),X1),inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2)))) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f14,plain,
! [X0,X1,X2] : multiply(multiply(inverse(inverse(X0)),multiply(multiply(inverse(inverse(X0)),multiply(multiply(inverse(X1),multiply(multiply(inverse(multiply(X2,inverse(multiply(X1,X0)))),multiply(X2,inverse(X0))),inverse(X0))),inverse(X0))),inverse(X0))),inverse(multiply(inverse(X0),X0))) = inverse(X0),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f58,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,inverse(multiply(multiply(X0,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X1,inverse(X2))),
inference(paramodulation,[status(thm)],[f3,f11]) ).
fof(f59,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))),
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f110,plain,
! [X0,X1,X2,X3] : multiply(inverse(X0),multiply(multiply(inverse(multiply(X1,inverse(multiply(X0,X2)))),multiply(X1,inverse(X2))),inverse(X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),X2)))),multiply(X3,inverse(X2))),
inference(paramodulation,[status(thm)],[f10,f58]) ).
fof(f138,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(multiply(X1,inverse(multiply(inverse(X3),X3))),X3)))),multiply(X2,inverse(X3)))))),multiply(X4,inverse(multiply(X2,inverse(X3))))),
inference(paramodulation,[status(thm)],[f58,f59]) ).
fof(f201,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)],[f58,f138]) ).
fof(f229,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(X4,inverse(multiply(X5,X6)))),multiply(X4,inverse(X6))),inverse(multiply(X2,multiply(inverse(X6),X6))))),X5),inverse(multiply(inverse(multiply(inverse(X6),X6)),multiply(inverse(X6),X6))))))),
inference(paramodulation,[status(thm)],[f12,f201]) ).
fof(f308,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)],[f12,f229]) ).
fof(f351,plain,
! [X0,X1,X2,X3,X4] : X0 = multiply(inverse(multiply(X1,inverse(multiply(multiply(X0,inverse(multiply(inverse(multiply(X2,inverse(X3))),multiply(X2,inverse(X3))))),multiply(X4,inverse(X3)))))),multiply(X1,inverse(multiply(X4,inverse(X3))))),
inference(paramodulation,[status(thm)],[f308,f58]) ).
fof(f653,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(X2))))) = multiply(X0,inverse(multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(X2))))),
inference(paramodulation,[status(thm)],[f351,f3]) ).
fof(f698,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,inverse(multiply(inverse(inverse(X1)),multiply(multiply(inverse(inverse(X1)),multiply(multiply(inverse(inverse(X1)),multiply(multiply(inverse(X2),multiply(multiply(inverse(multiply(X3,inverse(multiply(X2,X1)))),multiply(X3,inverse(X1))),inverse(X1))),inverse(X1))),inverse(X1))),inverse(multiply(inverse(X1),X1)))))) = multiply(X0,inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X1),X1)))),multiply(X4,inverse(multiply(inverse(X1),X1)))))),
inference(paramodulation,[status(thm)],[f14,f653]) ).
fof(f887,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(X1)))) = multiply(X0,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),X1)))),multiply(X2,inverse(multiply(inverse(X1),X1)))))),
inference(forward_demodulation,[status(thm)],[f14,f698]) ).
fof(f924,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(X1)))) = multiply(X0,inverse(multiply(inverse(X2),multiply(multiply(inverse(multiply(X3,inverse(multiply(X2,X1)))),multiply(X3,inverse(X1))),inverse(multiply(inverse(X1),X1)))))),
inference(paramodulation,[status(thm)],[f3,f887]) ).
fof(f1029,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(X1)))) = multiply(X0,inverse(multiply(inverse(X2),X2))),
inference(forward_demodulation,[status(thm)],[f3,f924]) ).
fof(f1167,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(inverse(X1),X1))) = multiply(X0,inverse(multiply(inverse(X2),X2))),
inference(paramodulation,[status(thm)],[f1029,f1029]) ).
fof(f1351,plain,
! [X0,X1,X2,X3] : X0 = multiply(multiply(inverse(multiply(X1,inverse(multiply(X0,X2)))),multiply(X1,inverse(X2))),inverse(multiply(inverse(X3),X3))),
inference(paramodulation,[status(thm)],[f3,f1167]) ).
fof(f1997,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(inverse(X0),multiply(multiply(inverse(multiply(X1,inverse(multiply(X0,multiply(inverse(X2),X2))))),multiply(X1,inverse(multiply(inverse(X2),X2)))),inverse(multiply(inverse(X2),X2)))) = multiply(inverse(multiply(multiply(inverse(multiply(X3,inverse(multiply(X4,X5)))),multiply(X3,inverse(X5))),inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))))),X4),
inference(paramodulation,[status(thm)],[f1351,f110]) ).
fof(f2021,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(X0),X0) = multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(multiply(inverse(multiply(inverse(X4),X4)),multiply(inverse(X4),X4))))),X2),
inference(forward_demodulation,[status(thm)],[f1351,f1997]) ).
fof(f2022,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(forward_demodulation,[status(thm)],[f1351,f2021]) ).
fof(f2024,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f4,f2022]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP409-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:13:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 1.58/0.66 % Refutation found
% 1.58/0.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.58/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.58/0.70 % Elapsed time: 0.311523 seconds
% 1.58/0.70 % CPU time: 2.195375 seconds
% 1.58/0.70 % Total memory used: 121.326 MB
% 1.58/0.70 % Net memory used: 120.789 MB
%------------------------------------------------------------------------------