%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP407-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 43.78s 6.08s
% Output : CNFRefutation 43.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 14 ( 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 : 103 ( 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B))))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2,
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] : multiply(X0,inverse(multiply(inverse(X1),multiply(inverse(X2),multiply(inverse(X2),X2))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X2)),X3)),X1)),multiply(inverse(X3),multiply(inverse(X3),X3)))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3] : X0 = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X1,X2)),X0))),multiply(inverse(X3),multiply(inverse(X3),X3)))),
inference(paramodulation,[status(thm)],[f3,f9]) ).
fof(f13,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X4)),X5)),multiply(inverse(multiply(inverse(multiply(X1,X3)),X4)),X2))),multiply(inverse(X5),multiply(inverse(X5),X5)))),
inference(paramodulation,[status(thm)],[f9,f9]) ).
fof(f35,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1)))))) = X2,
inference(paramodulation,[status(thm)],[f9,f3]) ).
fof(f63,plain,
! [X0,X1,X2,X3,X4,X5] : X0 = inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),multiply(inverse(multiply(X3,X4)),X1))),multiply(inverse(X5),multiply(inverse(X5),X5)))),X0))),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f101,plain,
! [X0,X1,X2] : X0 = inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X0))),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(forward_demodulation,[status(thm)],[f11,f63]) ).
fof(f138,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f101,f35]) ).
fof(f330,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X0))),X3)) = multiply(inverse(multiply(X4,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X4,X3)),
inference(paramodulation,[status(thm)],[f101,f138]) ).
fof(f368,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,multiply(inverse(X1),X1)))))) = multiply(inverse(X1),X3),
inference(paramodulation,[status(thm)],[f138,f35]) ).
fof(f1313,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3))))),multiply(X0,inverse(multiply(inverse(multiply(X4,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X4,multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3))))))))) = X3,
inference(paramodulation,[status(thm)],[f330,f35]) ).
fof(f1411,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X2,
inference(forward_demodulation,[status(thm)],[f368,f1313]) ).
fof(f1479,plain,
! [X0,X1,X2] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X1,multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f1411,f330]) ).
fof(f1569,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f1479,f1479]) ).
fof(f1853,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1)))))) = inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f1569,f13]) ).
fof(f1878,plain,
! [X0] : multiply(multiply(inverse(X0),X0),a2) != a2,
inference(paramodulation,[status(thm)],[f1569,f4]) ).
fof(f2017,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X0),multiply(inverse(X0),X0)))),
inference(forward_demodulation,[status(thm)],[f35,f1853]) ).
fof(f2061,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,multiply(inverse(X0),X0)))),
inference(paramodulation,[status(thm)],[f138,f2017]) ).
fof(f2687,plain,
! [X0,X1,X2] : X0 = inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f1569,f2061]) ).
fof(f2862,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(X1),X2),
inference(backward_demodulation,[status(thm)],[f2687,f368]) ).
fof(f3085,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(X0),multiply(inverse(X1),X1))),
inference(backward_demodulation,[status(thm)],[f2862,f2687]) ).
fof(f3088,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X0),inverse(X1))),multiply(inverse(X0),multiply(inverse(X0),X0))) = X1,
inference(backward_demodulation,[status(thm)],[f2862,f1411]) ).
fof(f3161,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),multiply(inverse(X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f2862,f3088]) ).
fof(f6326,plain,
! [X0,X1,X2] : multiply(inverse(X0),inverse(multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2)))))) = X1,
inference(paramodulation,[status(thm)],[f3085,f3]) ).
fof(f6442,plain,
! [X0,X1,X2] : multiply(inverse(X0),inverse(multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))))) = X1,
inference(forward_demodulation,[status(thm)],[f2862,f6326]) ).
fof(f6443,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f3085,f6442]) ).
fof(f6570,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f6443,f6443]) ).
fof(f6654,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f6570,f3161]) ).
fof(f6655,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f6443,f6570]) ).
fof(f6862,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f6655,f3085]) ).
fof(f7038,plain,
! [X0,X1] : multiply(X0,inverse(multiply(inverse(X1),X1))) = X0,
inference(paramodulation,[status(thm)],[f6654,f6654]) ).
fof(f7258,plain,
! [X0,X1,X2] : multiply(inverse(X0),multiply(X0,X1)) = multiply(inverse(inverse(multiply(inverse(X2),X2))),X1),
inference(paramodulation,[status(thm)],[f7038,f2862]) ).
fof(f7285,plain,
! [X0,X1] : X0 = multiply(inverse(inverse(multiply(inverse(X1),X1))),X0),
inference(forward_demodulation,[status(thm)],[f6443,f7258]) ).
fof(f7286,plain,
! [X0,X1] : X0 = multiply(multiply(inverse(X1),X1),X0),
inference(forward_demodulation,[status(thm)],[f6862,f7285]) ).
fof(f7287,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f7286,f1878]) ).
fof(f7318,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f7287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP407-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n015.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 20:15:05 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.47 % Drodi V4.1.1
% 43.78/6.08 % Refutation found
% 43.78/6.08 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 43.78/6.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 41.91/6.21 % Elapsed time: 5.734631 seconds
% 41.91/6.21 % CPU time: 44.531361 seconds
% 41.91/6.21 % Total memory used: 629.828 MB
% 41.91/6.21 % Net memory used: 622.439 MB
%------------------------------------------------------------------------------