%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP002-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 06:43:15 AM UTC 2025
% Result : Unsatisfiable 26.47s 26.61s
% Output : CNFRefutation 26.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 13 RR)
% Number of literals : 39 ( 38 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(k,inverse(b)) != identity,
file('theBenchmark.p',prove_k_times_inverse_b_is_e) ).
cnf(c1,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c2,axiom,
multiply(X,identity) = X,
file('theBenchmark.p',right_identity) ).
cnf(c3,axiom,
multiply(a,b) = c,
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c4,plain,
c = multiply(a,b),
inference(equational,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(h,b) = j,
file('theBenchmark.p',h_times_b_is_j) ).
cnf(c6,plain,
j = multiply(h,b),
inference(equational,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiply(X,inverse(X)) = identity,
file('theBenchmark.p',right_inverse) ).
cnf(c9,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c10,axiom,
multiply(d,inverse(b)) = h,
file('theBenchmark.p',d_times_inverse_b_is_h) ).
cnf(c11,plain,
h = multiply(d,inverse(b)),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
multiply(c,inverse(a)) = d,
file('theBenchmark.p',c_times_inverse_a_is_d) ).
cnf(c13,plain,
d = multiply(multiply(a,b),inverse(a)),
inference(equational,[status(thm)],[c4,c12]) ).
cnf(c14,axiom,
multiply(j,inverse(h)) = k,
file('theBenchmark.p',j_times_inverse_h_is_k) ).
cnf(c15,plain,
k = multiply(multiply(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)),b),inverse(multiply(multiply(multiply(a,b),inverse(a)),inverse(b)))),
inference(equational,[status(thm)],[c6,c11,c13,c14]) ).
cnf(c16,axiom,
multiply(X,multiply(X,X)) = identity,
file('theBenchmark.p',x_cubed_is_identity) ).
cnf(c17,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c18,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c1,c7,c17]) ).
cnf(c19,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c2,c7,c18]) ).
cnf(c20,plain,
multiply(inverse(X),inverse(X)) = X,
inference(equational,[status(thm)],[c2,c16,c18]) ).
cnf(c21,plain,
multiply(X,X) = inverse(X),
inference(equational,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c1,c9,c17]) ).
cnf(c23,plain,
multiply(X,multiply(X,multiply(X,Y))) = Y,
inference(equational,[status(thm)],[c1,c16,c17]) ).
cnf(c24,plain,
multiply(inverse(X),Y) = multiply(X,multiply(X,Y)),
inference(equational,[status(thm)],[c22,c23]) ).
cnf(c25,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(equational,[status(thm)],[c7,c17]) ).
cnf(c26,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c2,c21,c23,c25]) ).
cnf(c27,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
inference(equational,[status(thm)],[c18,c26]) ).
cnf(c28,plain,
multiply(X,multiply(X,inverse(Y))) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c23,c26]) ).
cnf(c29,plain,
multiply(X,inverse(multiply(Y,multiply(Y,X)))) = Y,
inference(equational,[status(thm)],[c2,c18,c24,c25]) ).
cnf(c30,plain,
multiply(X,multiply(X,Y)) = inverse(multiply(Y,multiply(Y,X))),
inference(equational,[status(thm)],[c23,c29]) ).
cnf(c32,plain,
multiply(X,multiply(Y,multiply(X,Y))) = inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c17,c21]) ).
cnf(c33,plain,
multiply(X,inverse(multiply(Y,inverse(X)))) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c22,c24,c27,c30]) ).
cnf(c35,plain,
multiply(X,inverse(multiply(Y,multiply(Z,X)))) = inverse(multiply(Y,Z)),
inference(equational,[status(thm)],[c17,c26]) ).
cnf(c37,plain,
inverse(multiply(X,inverse(multiply(Y,Z)))) = multiply(Y,multiply(Z,inverse(X))),
inference(equational,[status(thm)],[c17,c27]) ).
cnf(c39,plain,
multiply(X,inverse(multiply(Y,inverse(Z)))) = inverse(multiply(Y,inverse(multiply(X,Z)))),
inference(equational,[status(thm)],[c27,c37]) ).
cnf(c50,plain,
multiply(X,inverse(multiply(X,multiply(X,Y)))) = multiply(Y,multiply(X,multiply(X,Y))),
inference(equational,[status(thm)],[c18,c24,c32]) ).
cnf(c62,plain,
multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))) = multiply(Y,multiply(Y,multiply(X,multiply(X,Z)))),
inference(equational,[status(thm)],[c17,c24,c28]) ).
cnf(g1,plain,
multiply(k,inverse(b)) = identity,
inference(equational,[status(thm)],[c2,c7,c9,c15,c17,c19,c20,c21,c22,c23,c24,c26,c27,c33,c35,c39,c50,c62]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP002-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 14 08:04:49 EDT 2025
% 0.13/0.33 % CPUTime :
% 26.47/26.61 % SZS status Unsatisfiable
% 26.47/26.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------