%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP520-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:44:14 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 3 RR)
% Number of literals : 15 ( 14 equ; 1 neg)
% Maximal clause size : 1 ( 1 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 : 33 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c1,axiom,
multiply(X,multiply(multiply(inverse(multiply(X,Y)),Z),Y)) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),W),Z) = multiply(X,multiply(W,Y)),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,Y))) = Z,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(multiply(inverse(X),Y),multiply(Z,multiply(X,W))) = multiply(Z,multiply(Y,W)),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c7,plain,
multiply(multiply(inverse(X),Y),Z) = multiply(inverse(multiply(X,W)),multiply(Y,multiply(Z,W))),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c8,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c9,plain,
multiply(multiply(inverse(X),Y),X) = Y,
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c10,plain,
multiply(inverse(X),multiply(Y,X)) = Y,
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c11,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
multiply(X,multiply(Y,Z)) = multiply(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c16,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference(equational,[status(thm)],[c10,c11,c12]) ).
cnf(c18,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c12,c16]) ).
cnf(g1,plain,
multiply(a,b) = multiply(b,a),
inference(equational,[status(thm)],[c18]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : GRP520-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.04/0.09 % Command : run_Leo-III %s %d THM
% 0.09/0.28 % Computer : n005.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon Jul 14 08:31:04 EDT 2025
% 0.09/0.28 % CPUTime :
% 0.14/0.44 % SZS status Unsatisfiable
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------