%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP509-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 06:44:13 AM UTC 2025
% Result : Unsatisfiable 0.41s 0.59s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 3 RR)
% Number of literals : 20 ( 19 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 : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c1,axiom,
multiply(multiply(multiply(X,Y),Z),inverse(multiply(X,Z))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(X,inverse(multiply(multiply(Y,X),inverse(multiply(Y,Z))))) = Z,
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(multiply(X,Y),inverse(multiply(Z,Y))) = inverse(multiply(multiply(W,Z),inverse(multiply(W,X)))),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c6,plain,
multiply(X,inverse(multiply(multiply(Y,X),inverse(Z)))) = inverse(multiply(multiply(W,Y),inverse(multiply(W,Z)))),
inference(equational,[status(thm)],[c2]) ).
cnf(c10,plain,
multiply(X,multiply(Y,inverse(multiply(multiply(X,Y),inverse(Z))))) = Z,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c11,plain,
multiply(multiply(X,Y),multiply(Z,inverse(Y))) = multiply(X,Z),
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c12,plain,
multiply(multiply(X,multiply(Y,Z)),W) = multiply(X,multiply(multiply(Y,W),Z)),
inference(equational,[status(thm)],[c1,c11]) ).
cnf(c13,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c11,c12]) ).
cnf(c14,plain,
multiply(X,multiply(Y,multiply(Z,W))) = multiply(X,multiply(Y,multiply(W,Z))),
inference(equational,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
multiply(X,multiply(Y,multiply(Z,inverse(Y)))) = multiply(X,Z),
inference(equational,[status(thm)],[c11,c13]) ).
cnf(c16,plain,
inverse(multiply(X,multiply(Y,inverse(multiply(X,multiply(Y,Z)))))) = Z,
inference(equational,[status(thm)],[c1,c3,c13]) ).
cnf(c17,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c14,c16]) ).
cnf(c18,plain,
multiply(X,multiply(Y,inverse(X))) = Y,
inference(equational,[status(thm)],[c15,c16]) ).
cnf(c19,plain,
multiply(X,multiply(Y,Z)) = multiply(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c13,c17]) ).
cnf(c20,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c17,c18]) ).
cnf(c22,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c18,c19]) ).
cnf(c23,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c20,c22]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c17,c23]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP509-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.13 % Command : run_Leo-III %s %d THM
% 0.12/0.35 % Computer : n008.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Jul 14 08:30:49 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.41/0.59 % SZS status Unsatisfiable
% 0.41/0.59 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------