%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP440-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:34:13 PM UTC 2026
% Result : Unsatisfiable 53.41s 7.40s
% Output : CNFRefutation 54.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 2
% Syntax : Number of formulae : 46 ( 46 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 17 ( 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 : 191 ( 191 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = D,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2,X3] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = X3,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(X0,multiply(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3)))))),multiply(multiply(X4,X5),inverse(multiply(X6,multiply(X0,X5))))))) = X6,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f10,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),X2),inverse(multiply(X3,multiply(X4,X2))))),X3)))) = X4,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f17,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = X2,
inference(paramodulation,[status(thm)],[f10,f3]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : inverse(multiply(X0,multiply(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3)))))),multiply(multiply(X4,multiply(multiply(inverse(X0),multiply(multiply(inverse(X5),X6),inverse(multiply(X7,multiply(X8,X6))))),X7)),X8)))) = X5,
inference(paramodulation,[status(thm)],[f3,f17]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(X2,X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(X2,multiply(X6,X8)))))),
inference(paramodulation,[status(thm)],[f9,f10]) ).
fof(f1113,plain,
! [X0,X1,X2,X3] : X0 = multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(inverse(X0),multiply(X1,X3)))))),
inference(paramodulation,[status(thm)],[f17,f49]) ).
fof(f1446,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X3,multiply(X0,multiply(X4,multiply(multiply(inverse(X4),X5),inverse(multiply(inverse(X2),multiply(inverse(X1),X5)))))))))))) = X3,
inference(paramodulation,[status(thm)],[f1113,f3]) ).
fof(f1810,plain,
! [X0,X1,X2] : inverse(multiply(inverse(X0),multiply(X0,multiply(X1,inverse(multiply(X2,X1)))))) = X2,
inference(paramodulation,[status(thm)],[f1113,f1446]) ).
fof(f1994,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(X0),multiply(X0,multiply(multiply(X1,multiply(X2,inverse(multiply(X3,X2)))),X3)))) = inverse(X1),
inference(paramodulation,[status(thm)],[f1810,f1810]) ).
fof(f2021,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = multiply(X2,multiply(X6,multiply(multiply(inverse(X6),multiply(X7,inverse(multiply(X8,X7)))),X8))),
inference(paramodulation,[status(thm)],[f1810,f49]) ).
fof(f2106,plain,
! [X0,X1,X2,X3] : X0 = multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(X2,inverse(multiply(X3,X2)))),X3))),
inference(forward_demodulation,[status(thm)],[f17,f2021]) ).
fof(f2162,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = multiply(X2,multiply(X6,multiply(multiply(inverse(X6),multiply(multiply(X7,multiply(X8,inverse(multiply(X9,X8)))),X9)),inverse(X7)))),
inference(paramodulation,[status(thm)],[f1994,f49]) ).
fof(f2217,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : inverse(multiply(X0,multiply(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3)))))),multiply(multiply(X4,multiply(multiply(inverse(X0),multiply(multiply(inverse(X5),X6),inverse(multiply(X7,multiply(X8,X6))))),X7)),X8)))) = multiply(inverse(X9),multiply(X9,multiply(multiply(X5,multiply(X10,inverse(multiply(X11,X10)))),X11))),
inference(paramodulation,[status(thm)],[f1994,f21]) ).
fof(f2248,plain,
! [X0,X1,X2,X3] : X0 = multiply(inverse(X1),multiply(X1,multiply(multiply(X0,multiply(X2,inverse(multiply(X3,X2)))),X3))),
inference(forward_demodulation,[status(thm)],[f21,f2217]) ).
fof(f2251,plain,
! [X0,X1,X2,X3,X4] : X0 = multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(X2,multiply(X3,inverse(multiply(X4,X3)))),X4)),inverse(X2)))),
inference(forward_demodulation,[status(thm)],[f17,f2162]) ).
fof(f2646,plain,
! [X0,X1,X2,X3,X4,X5] : X0 = multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X0),multiply(X1,multiply(X3,multiply(multiply(inverse(X3),multiply(X4,inverse(multiply(X5,X4)))),X5)))))))),
inference(paramodulation,[status(thm)],[f2106,f1113]) ).
fof(f2667,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(X0,multiply(X1,multiply(inverse(X1),inverse(multiply(X2,multiply(X0,multiply(X3,multiply(multiply(inverse(X3),multiply(X4,inverse(multiply(X5,X4)))),X5))))))))) = X2,
inference(paramodulation,[status(thm)],[f2106,f3]) ).
fof(f2788,plain,
! [X0,X1,X2] : X0 = multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X0),X1))))),
inference(forward_demodulation,[status(thm)],[f2106,f2646]) ).
fof(f2812,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(X1,multiply(inverse(X1),inverse(multiply(X2,X0)))))) = X2,
inference(forward_demodulation,[status(thm)],[f2106,f2667]) ).
fof(f2940,plain,
! [X0,X1,X2,X3,X4] : X0 = multiply(inverse(X1),multiply(X1,multiply(multiply(X0,multiply(multiply(X2,multiply(inverse(X2),inverse(multiply(X3,X4)))),X3)),X4))),
inference(paramodulation,[status(thm)],[f2812,f2248]) ).
fof(f2941,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(X0),multiply(X0,multiply(multiply(X1,multiply(inverse(X1),inverse(multiply(X2,X3)))),X2)))) = X3,
inference(paramodulation,[status(thm)],[f2812,f1810]) ).
fof(f5418,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : X0 = multiply(inverse(X1),multiply(X1,multiply(X0,multiply(multiply(X2,multiply(inverse(X2),inverse(multiply(X3,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(X5,multiply(X6,inverse(multiply(X7,X6)))),X7)),inverse(X5))))))),X3)))),
inference(paramodulation,[status(thm)],[f2251,f2940]) ).
fof(f5637,plain,
! [X0,X1,X2,X3] : X0 = multiply(inverse(X1),multiply(X1,multiply(X0,multiply(multiply(X2,multiply(inverse(X2),inverse(X3))),X3)))),
inference(forward_demodulation,[status(thm)],[f2251,f5418]) ).
fof(f5751,plain,
! [X0,X1,X2,X3] : inverse(multiply(X0,multiply(inverse(X0),inverse(multiply(multiply(multiply(X1,multiply(inverse(X1),inverse(X2))),X2),X3))))) = X3,
inference(paramodulation,[status(thm)],[f5637,f2941]) ).
fof(f5752,plain,
! [X0,X1,X2,X3] : X0 = multiply(X0,multiply(X1,inverse(multiply(multiply(multiply(X2,multiply(inverse(X2),inverse(X3))),X3),X1)))),
inference(paramodulation,[status(thm)],[f5637,f2248]) ).
fof(f6785,plain,
! [X0,X1,X2] : inverse(multiply(inverse(X0),X0)) = multiply(multiply(X1,multiply(inverse(X1),inverse(X2))),X2),
inference(paramodulation,[status(thm)],[f5752,f2812]) ).
fof(f7619,plain,
! [X0,X1,X2] : X0 = multiply(X0,multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),X2)),X1)))),
inference(paramodulation,[status(thm)],[f6785,f5752]) ).
fof(f8618,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(inverse(multiply(inverse(X2),X2)),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = multiply(inverse(X6),X6),
inference(paramodulation,[status(thm)],[f7619,f49]) ).
fof(f8766,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(forward_demodulation,[status(thm)],[f17,f8618]) ).
fof(f9953,plain,
! [X0] : multiply(multiply(inverse(X0),X0),a2) != a2,
inference(paramodulation,[status(thm)],[f8766,f4]) ).
fof(f9956,plain,
! [X0,X1,X2] : X0 = multiply(X1,multiply(inverse(multiply(inverse(X0),X1)),multiply(inverse(X2),X2))),
inference(paramodulation,[status(thm)],[f8766,f2788]) ).
fof(f12705,plain,
! [X0,X1] : X0 = multiply(X0,multiply(inverse(X1),X1)),
inference(paramodulation,[status(thm)],[f8766,f9956]) ).
fof(f13200,plain,
! [X0,X1,X2] : X0 = multiply(inverse(X1),multiply(X1,multiply(X0,multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f12705,f5637]) ).
fof(f13411,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f12705,f13200]) ).
fof(f13937,plain,
! [X0,X1] : X0 = multiply(inverse(inverse(X0)),multiply(inverse(X1),X1)),
inference(paramodulation,[status(thm)],[f8766,f13411]) ).
fof(f14207,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f12705,f13937]) ).
fof(f14277,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f14207,f13411]) ).
fof(f14738,plain,
! [X0,X1,X2] : inverse(inverse(multiply(multiply(multiply(X0,multiply(inverse(X0),inverse(X1))),X1),X2))) = X2,
inference(backward_demodulation,[status(thm)],[f14277,f5751]) ).
fof(f14996,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,multiply(inverse(X0),inverse(X1))),X1),X2) = X2,
inference(forward_demodulation,[status(thm)],[f14207,f14738]) ).
fof(f14997,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f14277,f14996]) ).
fof(f15549,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f14997,f9953]) ).
fof(f16104,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f15549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP440-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.56 % Computer : n007.cluster.edu
% 0.11/0.56 % Model : x86_64 x86_64
% 0.11/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.56 % Memory : 8046.5625MB
% 0.11/0.56 % OS : Linux 6.8.0-71-generic
% 0.11/0.56 % CPULimit : 300
% 0.11/0.56 % WCLimit : 300
% 0.11/0.56 % DateTime : Sun Sep 20 20:11:21 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 % Drodi V4.1.1
% 53.41/7.40 % Refutation found
% 53.41/7.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 53.41/7.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.09/7.54 % Elapsed time: 6.965319 seconds
% 7.09/7.54 % CPU time: 54.899369 seconds
% 7.09/7.54 % Total memory used: 1.099 GB
% 7.09/7.54 % Net memory used: 1.080 GB
%------------------------------------------------------------------------------