%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP512-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% 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 : 3 ( 3 ~; 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(a,b) != multiply(b,a),
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(a,b) != multiply(b,a),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f10,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(f14,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)],[f8,f8]) ).
fof(f18,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)],[f10,f10]) ).
fof(f35,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),inverse(X0)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f3,f18]) ).
fof(f40,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(X1,X0),X2))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f3,f35]) ).
fof(f41,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))) = inverse(X1),
inference(paramodulation,[status(thm)],[f35,f35]) ).
fof(f42,plain,
! [X0,X1,X2] : multiply(X0,inverse(X1)) = inverse(multiply(multiply(X2,X1),inverse(multiply(X2,X0)))),
inference(paramodulation,[status(thm)],[f8,f35]) ).
fof(f44,plain,
! [X0,X1,X2] : multiply(multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))),inverse(X2)) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f35,f10]) ).
fof(f45,plain,
! [X0,X1,X2] : multiply(multiply(multiply(inverse(X0),X1),inverse(multiply(X2,inverse(X2)))),inverse(inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f35,f10]) ).
fof(f46,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))) = inverse(X0),
inference(paramodulation,[status(thm)],[f35,f3]) ).
fof(f53,plain,
! [X0,X1] : inverse(multiply(X0,inverse(multiply(X0,X1)))) = X1,
inference(backward_demodulation,[status(thm)],[f40,f8]) ).
fof(f56,plain,
! [X0,X1,X2] : inverse(multiply(X0,inverse(X1))) = inverse(multiply(multiply(X2,X0),inverse(multiply(X2,X1)))),
inference(backward_demodulation,[status(thm)],[f40,f14]) ).
fof(f68,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f41,f44]) ).
fof(f69,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,inverse(X1)))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f68,f46]) ).
fof(f78,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(backward_demodulation,[status(thm)],[f80,f53]) ).
fof(f79,plain,
! [X0,X1,X2] : multiply(multiply(multiply(inverse(X0),X1),multiply(X2,inverse(X2))),inverse(inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f80,f45]) ).
fof(f80,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f42,f56]) ).
fof(f96,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f78,f78]) ).
fof(f98,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f96,f96]) ).
fof(f100,plain,
! [X0,X1] : inverse(multiply(multiply(X0,X1),inverse(X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f68,f98]) ).
fof(f101,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X0,X1))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f80,f100]) ).
fof(f104,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = inverse(inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f101,f101]) ).
fof(f105,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = inverse(inverse(multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f96,f101]) ).
fof(f110,plain,
! [X0,X1,X2] : multiply(X0,inverse(inverse(multiply(multiply(inverse(X0),X1),multiply(X2,inverse(X2)))))) = X1,
inference(backward_demodulation,[status(thm)],[f113,f79]) ).
fof(f113,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = multiply(X1,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f104,f105]) ).
fof(f117,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X0),X1),inverse(inverse(multiply(X2,inverse(X2)))))) = X1,
inference(forward_demodulation,[status(thm)],[f104,f110]) ).
fof(f118,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X0),X1),multiply(X2,inverse(inverse(inverse(X2)))))) = X1,
inference(forward_demodulation,[status(thm)],[f104,f117]) ).
fof(f143,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = inverse(multiply(X1,inverse(X1))),
inference(paramodulation,[status(thm)],[f69,f101]) ).
fof(f147,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f80,f143]) ).
fof(f159,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,inverse(X1)))) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f147,f101]) ).
fof(f168,plain,
! [X0] : inverse(inverse(inverse(X0))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f170,f69]) ).
fof(f170,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f80,f159]) ).
fof(f174,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X0),X1),multiply(X2,inverse(X2)))) = X1,
inference(backward_demodulation,[status(thm)],[f168,f118]) ).
fof(f175,plain,
! [X0,X1] : multiply(X0,inverse(inverse(multiply(inverse(X0),X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f170,f174]) ).
fof(f176,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),inverse(inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f104,f175]) ).
fof(f177,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X0,inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f68,f176]) ).
fof(f184,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = multiply(X1,X0),
inference(backward_demodulation,[status(thm)],[f186,f113]) ).
fof(f186,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f101,f177]) ).
fof(f189,plain,
multiply(a,b) != multiply(a,b),
inference(backward_demodulation,[status(thm)],[f200,f4]) ).
fof(f200,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f186,f184]) ).
fof(f203,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP512-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n018.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 20:17:28 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.49 % Refutation found
% 0.18/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.54 % Elapsed time: 0.073265 seconds
% 0.18/0.54 % CPU time: 0.084607 seconds
% 0.18/0.54 % Total memory used: 2.554 MB
% 0.18/0.54 % Net memory used: 2.522 MB
%------------------------------------------------------------------------------