%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP509-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:34:33 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of formulae : 47 ( 47 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 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 : 101 ( 101 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,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(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(multiply(multiply(X0,X1),X2),X3),inverse(multiply(X0,X2))),inverse(X1)) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f16,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(X2)))) = inverse(multiply(multiply(X3,X1),inverse(multiply(X3,X2)))),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f20,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3))))),inverse(X0)) = inverse(X2),
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f37,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),inverse(X0)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f3,f20]) ).
fof(f42,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(X1,X0),X2))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f3,f37]) ).
fof(f43,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))) = inverse(X1),
inference(paramodulation,[status(thm)],[f37,f37]) ).
fof(f44,plain,
! [X0,X1,X2] : multiply(X0,inverse(X1)) = inverse(multiply(multiply(X2,X1),inverse(multiply(X2,X0)))),
inference(paramodulation,[status(thm)],[f10,f37]) ).
fof(f46,plain,
! [X0,X1,X2] : multiply(multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))),inverse(X2)) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f37,f12]) ).
fof(f47,plain,
! [X0,X1,X2] : multiply(multiply(multiply(inverse(X0),X1),inverse(multiply(X2,inverse(X2)))),inverse(inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f37,f12]) ).
fof(f48,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))) = inverse(X0),
inference(paramodulation,[status(thm)],[f37,f3]) ).
fof(f55,plain,
! [X0,X1] : inverse(multiply(X0,inverse(multiply(X0,X1)))) = X1,
inference(backward_demodulation,[status(thm)],[f42,f10]) ).
fof(f58,plain,
! [X0,X1,X2] : inverse(multiply(X0,inverse(X1))) = inverse(multiply(multiply(X2,X0),inverse(multiply(X2,X1)))),
inference(backward_demodulation,[status(thm)],[f42,f16]) ).
fof(f70,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f43,f46]) ).
fof(f71,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,inverse(X1)))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f70,f48]) ).
fof(f80,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(backward_demodulation,[status(thm)],[f82,f55]) ).
fof(f81,plain,
! [X0,X1,X2] : multiply(multiply(multiply(inverse(X0),X1),multiply(X2,inverse(X2))),inverse(inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f82,f47]) ).
fof(f82,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f44,f58]) ).
fof(f98,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f80,f80]) ).
fof(f100,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f98,f98]) ).
fof(f102,plain,
! [X0,X1] : inverse(multiply(multiply(X0,X1),inverse(X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f70,f100]) ).
fof(f103,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X0,X1))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f82,f102]) ).
fof(f106,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = inverse(inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f103,f103]) ).
fof(f107,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = inverse(inverse(multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f98,f103]) ).
fof(f112,plain,
! [X0,X1,X2] : multiply(X0,inverse(inverse(multiply(multiply(inverse(X0),X1),multiply(X2,inverse(X2)))))) = X1,
inference(backward_demodulation,[status(thm)],[f115,f81]) ).
fof(f115,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = multiply(X1,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f106,f107]) ).
fof(f119,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X0),X1),inverse(inverse(multiply(X2,inverse(X2)))))) = X1,
inference(forward_demodulation,[status(thm)],[f106,f112]) ).
fof(f120,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X0),X1),multiply(X2,inverse(inverse(inverse(X2)))))) = X1,
inference(forward_demodulation,[status(thm)],[f106,f119]) ).
fof(f145,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = inverse(multiply(X1,inverse(X1))),
inference(paramodulation,[status(thm)],[f71,f103]) ).
fof(f149,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f82,f145]) ).
fof(f161,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,inverse(X1)))) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f149,f103]) ).
fof(f170,plain,
! [X0] : inverse(inverse(inverse(X0))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f172,f71]) ).
fof(f172,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f82,f161]) ).
fof(f176,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X0),X1),multiply(X2,inverse(X2)))) = X1,
inference(backward_demodulation,[status(thm)],[f170,f120]) ).
fof(f177,plain,
! [X0,X1] : multiply(X0,inverse(inverse(multiply(inverse(X0),X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f172,f176]) ).
fof(f178,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),inverse(inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f106,f177]) ).
fof(f179,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X0,inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f70,f178]) ).
fof(f186,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = multiply(X1,X0),
inference(backward_demodulation,[status(thm)],[f188,f115]) ).
fof(f188,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f103,f179]) ).
fof(f191,plain,
multiply(inverse(a1),a1) != multiply(b1,inverse(b1)),
inference(backward_demodulation,[status(thm)],[f202,f4]) ).
fof(f202,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f188,f186]) ).
fof(f205,plain,
multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)),
inference(forward_demodulation,[status(thm)],[f202,f191]) ).
fof(f206,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f205,f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP509-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:10:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.034248 seconds
% 0.13/0.39 % CPU time: 0.074593 seconds
% 0.13/0.39 % Total memory used: 3.863 MB
% 0.13/0.39 % Net memory used: 3.832 MB
%------------------------------------------------------------------------------