%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP520-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:34:35 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 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 : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C,
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(X0,multiply(multiply(inverse(multiply(X0,X1)),X2),X1)) = X2,
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,X3] : multiply(X0,multiply(X1,X2)) = multiply(multiply(inverse(multiply(inverse(multiply(X0,X2)),X3)),X1),X3),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f9,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(inverse(X1),X2),multiply(multiply(inverse(multiply(X0,X3)),X1),X3))) = X2,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f14,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X2,X1))) = X2,
inference(paramodulation,[status(thm)],[f8,f3]) ).
fof(f23,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X2,X1))),X2) = X0,
inference(paramodulation,[status(thm)],[f14,f14]) ).
fof(f38,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(X0),multiply(X1,multiply(X2,multiply(X0,X3))))),X1) = inverse(multiply(X2,X3)),
inference(paramodulation,[status(thm)],[f14,f23]) ).
fof(f54,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(paramodulation,[status(thm)],[f3,f9]) ).
fof(f86,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(multiply(inverse(multiply(inverse(X1),X2)),X0),X2),
inference(paramodulation,[status(thm)],[f3,f54]) ).
fof(f90,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(X0),multiply(X1,X2))),X1) = multiply(inverse(X2),X0),
inference(paramodulation,[status(thm)],[f54,f23]) ).
fof(f93,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(backward_demodulation,[status(thm)],[f86,f8]) ).
fof(f100,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f90,f23]) ).
fof(f104,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,multiply(X1,X2))),X1) = inverse(multiply(X0,X2)),
inference(backward_demodulation,[status(thm)],[f90,f38]) ).
fof(f134,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(backward_demodulation,[status(thm)],[f104,f90]) ).
fof(f174,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f100,f100]) ).
fof(f186,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f174,f174]) ).
fof(f187,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f100,f174]) ).
fof(f195,plain,
! [X0,X1] : inverse(multiply(inverse(X0),multiply(X1,X0))) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f187,f186]) ).
fof(f198,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X1) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f134,f195]) ).
fof(f227,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),X1) = inverse(inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f198,f198]) ).
fof(f228,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),X1) = inverse(inverse(multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f174,f198]) ).
fof(f229,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f100,f198]) ).
fof(f235,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f198,f3]) ).
fof(f241,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),X1) = multiply(inverse(inverse(X1)),X0),
inference(forward_demodulation,[status(thm)],[f227,f228]) ).
fof(f242,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = inverse(inverse(X1)),
inference(forward_demodulation,[status(thm)],[f93,f229]) ).
fof(f246,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),X1) = multiply(X1,X0),
inference(backward_demodulation,[status(thm)],[f248,f241]) ).
fof(f248,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f242,f235]) ).
fof(f264,plain,
multiply(a,b) != multiply(a,b),
inference(backward_demodulation,[status(thm)],[f273,f4]) ).
fof(f273,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f248,f246]) ).
fof(f275,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP520-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:15:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.027916 seconds
% 0.14/0.41 % CPU time: 0.059603 seconds
% 0.14/0.41 % Total memory used: 2.928 MB
% 0.14/0.41 % Net memory used: 2.830 MB
%------------------------------------------------------------------------------