%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP510-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:34:34 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.76s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 2
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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/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(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1,
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] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,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(f15,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)],[f9,f9]) ).
fof(f19,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)],[f11,f11]) ).
fof(f36,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),inverse(X0)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f3,f19]) ).
fof(f41,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(X1,X0),X2))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f3,f36]) ).
fof(f42,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))) = inverse(X1),
inference(paramodulation,[status(thm)],[f36,f36]) ).
fof(f43,plain,
! [X0,X1,X2] : multiply(X0,inverse(X1)) = inverse(multiply(multiply(X2,X1),inverse(multiply(X2,X0)))),
inference(paramodulation,[status(thm)],[f9,f36]) ).
fof(f45,plain,
! [X0,X1,X2] : multiply(multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))),inverse(X2)) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f36,f11]) ).
fof(f46,plain,
! [X0,X1,X2] : multiply(multiply(multiply(inverse(X0),X1),inverse(multiply(X2,inverse(X2)))),inverse(inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f36,f11]) ).
fof(f47,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))) = inverse(X0),
inference(paramodulation,[status(thm)],[f36,f3]) ).
fof(f54,plain,
! [X0,X1] : inverse(multiply(X0,inverse(multiply(X0,X1)))) = X1,
inference(backward_demodulation,[status(thm)],[f41,f9]) ).
fof(f57,plain,
! [X0,X1,X2] : inverse(multiply(X0,inverse(X1))) = inverse(multiply(multiply(X2,X0),inverse(multiply(X2,X1)))),
inference(backward_demodulation,[status(thm)],[f41,f15]) ).
fof(f69,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f42,f45]) ).
fof(f70,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,inverse(X1)))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f69,f47]) ).
fof(f79,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(backward_demodulation,[status(thm)],[f81,f54]) ).
fof(f80,plain,
! [X0,X1,X2] : multiply(multiply(multiply(inverse(X0),X1),multiply(X2,inverse(X2))),inverse(inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f81,f46]) ).
fof(f81,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f43,f57]) ).
fof(f97,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f79,f79]) ).
fof(f99,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f97,f97]) ).
fof(f101,plain,
! [X0,X1] : inverse(multiply(multiply(X0,X1),inverse(X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f69,f99]) ).
fof(f102,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X0,X1))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f81,f101]) ).
fof(f105,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = inverse(inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f102,f102]) ).
fof(f106,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = inverse(inverse(multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f97,f102]) ).
fof(f111,plain,
! [X0,X1,X2] : multiply(X0,inverse(inverse(multiply(multiply(inverse(X0),X1),multiply(X2,inverse(X2)))))) = X1,
inference(backward_demodulation,[status(thm)],[f114,f80]) ).
fof(f114,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = multiply(X1,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f105,f106]) ).
fof(f118,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X0),X1),inverse(inverse(multiply(X2,inverse(X2)))))) = X1,
inference(forward_demodulation,[status(thm)],[f105,f111]) ).
fof(f119,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X0),X1),multiply(X2,inverse(inverse(inverse(X2)))))) = X1,
inference(forward_demodulation,[status(thm)],[f105,f118]) ).
fof(f144,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = inverse(multiply(X1,inverse(X1))),
inference(paramodulation,[status(thm)],[f70,f102]) ).
fof(f148,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f81,f144]) ).
fof(f160,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,inverse(X1)))) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f148,f102]) ).
fof(f169,plain,
! [X0] : inverse(inverse(inverse(X0))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f171,f70]) ).
fof(f171,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f81,f160]) ).
fof(f175,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X0),X1),multiply(X2,inverse(X2)))) = X1,
inference(backward_demodulation,[status(thm)],[f169,f119]) ).
fof(f176,plain,
! [X0,X1] : multiply(X0,inverse(inverse(multiply(inverse(X0),X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f171,f175]) ).
fof(f177,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),inverse(inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f105,f176]) ).
fof(f178,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X0,inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f69,f177]) ).
fof(f185,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = multiply(X1,X0),
inference(backward_demodulation,[status(thm)],[f187,f114]) ).
fof(f187,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f102,f178]) ).
fof(f189,plain,
multiply(multiply(b2,inverse(b2)),a2) != a2,
inference(backward_demodulation,[status(thm)],[f201,f4]) ).
fof(f201,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f187,f185]) ).
fof(f203,plain,
multiply(a2,multiply(b2,inverse(b2))) != a2,
inference(forward_demodulation,[status(thm)],[f201,f189]) ).
fof(f204,plain,
inverse(inverse(a2)) != a2,
inference(forward_demodulation,[status(thm)],[f171,f203]) ).
fof(f205,plain,
a2 != a2,
inference(forward_demodulation,[status(thm)],[f187,f204]) ).
fof(f206,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP510-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.73 % Computer : n002.cluster.edu
% 0.07/0.73 % Model : x86_64 x86_64
% 0.07/0.73 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.73 % Memory : 8046.5625MB
% 0.07/0.73 % OS : Linux 6.8.0-71-generic
% 0.07/0.73 % CPULimit : 300
% 0.07/0.73 % WCLimit : 300
% 0.07/0.73 % DateTime : Sun Sep 20 20:18:04 UTC 2026
% 0.07/0.74 % CPUTime :
% 0.07/0.74 % Drodi V4.1.1
% 0.07/0.76 % Refutation found
% 0.07/0.76 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.77 % Elapsed time: 0.027093 seconds
% 0.07/0.77 % CPU time: 0.071421 seconds
% 0.07/0.77 % Total memory used: 3.751 MB
% 0.07/0.77 % Net memory used: 3.719 MB
%------------------------------------------------------------------------------