%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP430-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 06:44:02 AM UTC 2025
% Result : Unsatisfiable 8.57s 8.76s
% Output : CNFRefutation 8.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 3 RR)
% Number of literals : 57 ( 56 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 3 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 : 172 ( 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(X,inverse(multiply(Y,multiply(multiply(multiply(Z,inverse(Z)),inverse(multiply(W,Y))),X)))) = W,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(X,inverse(multiply(multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,W))),multiply(V,inverse(V))),multiply(Z,X)))) = W,
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(Z,inverse(Z))),multiply(W,X)))) = multiply(multiply(multiply(V,inverse(V)),inverse(multiply(Y,W))),multiply(U,inverse(U))),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(X,inverse(multiply(multiply(Y,inverse(multiply(multiply(Z,multiply(W,inverse(W))),multiply(V,Y)))),multiply(Z,X)))) = V,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
multiply(X,inverse(multiply(Y,multiply(Z,X)))) = multiply(multiply(W,inverse(W)),inverse(multiply(Y,multiply(Z,multiply(V,inverse(V)))))),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(X,multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
multiply(X,inverse(multiply(inverse(Y),multiply(multiply(Z,inverse(Z)),X)))) = Y,
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c9,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(Z,inverse(Z))),multiply(W,X)))) = multiply(V,inverse(multiply(multiply(Y,multiply(U,inverse(U))),multiply(W,V)))),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c11,plain,
multiply(inverse(X),inverse(multiply(Y,multiply(Z,inverse(Z))))) = multiply(multiply(W,inverse(W)),inverse(multiply(Y,multiply(X,multiply(V,inverse(V)))))),
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c12,plain,
multiply(inverse(X),inverse(multiply(Y,multiply(Z,inverse(Z))))) = multiply(W,inverse(multiply(Y,multiply(X,W)))),
inference(equational,[status(thm)],[c5,c11]) ).
cnf(c15,plain,
multiply(multiply(X,inverse(X)),multiply(Y,inverse(Y))) = multiply(Z,inverse(multiply(multiply(W,multiply(V,inverse(V))),multiply(inverse(W),Z)))),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c16,plain,
multiply(X,inverse(multiply(multiply(multiply(Y,inverse(Y)),multiply(Z,inverse(Z))),multiply(W,X)))) = inverse(W),
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c17,plain,
inverse(inverse(multiply(X,inverse(X)))) = multiply(multiply(Y,inverse(Y)),multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
inverse(multiply(X,inverse(X))) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c8,c16,c17]) ).
cnf(c19,plain,
inverse(inverse(multiply(X,inverse(X)))) = inverse(inverse(multiply(Y,inverse(Y)))),
inference(equational,[status(thm)],[c7,c17]) ).
cnf(c24,plain,
multiply(inverse(X),inverse(inverse(inverse(multiply(Y,inverse(Y)))))) = multiply(Z,inverse(multiply(multiply(W,inverse(W)),multiply(X,Z)))),
inference(equational,[status(thm)],[c12,c17]) ).
cnf(c26,plain,
multiply(X,inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),multiply(Z,X)))) = inverse(Z),
inference(equational,[status(thm)],[c9,c16,c17]) ).
cnf(c30,plain,
inverse(inverse(multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))))) = inverse(inverse(multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c18,c19]) ).
cnf(c35,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(Y),inverse(inverse(multiply(Z,inverse(Z))))))) = Y,
inference(equational,[status(thm)],[c8,c17]) ).
cnf(c36,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(Y)),multiply(Z,inverse(Z))) = inverse(inverse(multiply(inverse(Y),inverse(inverse(multiply(W,inverse(W))))))),
inference(equational,[status(thm)],[c3,c16,c35]) ).
cnf(c41,plain,
inverse(inverse(multiply(inverse(multiply(X,Y)),inverse(inverse(multiply(Z,inverse(Z))))))) = multiply(W,inverse(multiply(multiply(X,multiply(V,inverse(V))),multiply(Y,W)))),
inference(equational,[status(thm)],[c3,c7,c36]) ).
cnf(c46,plain,
inverse(multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(inverse(multiply(Z,inverse(Z)))))))) = Y,
inference(equational,[status(thm)],[c1,c26]) ).
cnf(c52,plain,
multiply(multiply(multiply(X,inverse(X)),Y),multiply(Z,inverse(Z))) = inverse(inverse(multiply(Y,inverse(inverse(multiply(W,inverse(W))))))),
inference(equational,[status(thm)],[c36,c46]) ).
cnf(c56,plain,
inverse(inverse(multiply(inverse(multiply(multiply(X,inverse(X)),Y)),inverse(inverse(multiply(Z,inverse(Z))))))) = inverse(Y),
inference(equational,[status(thm)],[c16,c41]) ).
cnf(c59,plain,
inverse(inverse(multiply(X,multiply(Y,multiply(Z,inverse(Z)))))) = inverse(inverse(multiply(X,multiply(Y,multiply(W,inverse(W)))))),
inference(equational,[status(thm)],[c5,c56]) ).
cnf(c63,plain,
inverse(multiply(inverse(multiply(multiply(X,inverse(X)),Y)),inverse(inverse(multiply(Z,inverse(Z)))))) = Y,
inference(equational,[status(thm)],[c8,c56]) ).
cnf(c64,plain,
multiply(multiply(X,inverse(X)),Y) = multiply(multiply(Z,inverse(Z)),Y),
inference(equational,[status(thm)],[c35,c63]) ).
cnf(c75,plain,
inverse(inverse(multiply(X,inverse(inverse(multiply(Y,inverse(Y))))))) = inverse(inverse(multiply(X,multiply(multiply(Z,inverse(Z)),multiply(W,inverse(W)))))),
inference(equational,[status(thm)],[c17,c59]) ).
cnf(c76,plain,
multiply(X,multiply(inverse(multiply(Y,inverse(Y))),inverse(inverse(multiply(Z,inverse(Z)))))) = multiply(X,multiply(W,inverse(W))),
inference(equational,[status(thm)],[c6,c19]) ).
cnf(c78,plain,
multiply(inverse(X),inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),multiply(Z,inverse(Z))))) = inverse(X),
inference(equational,[status(thm)],[c11,c26]) ).
cnf(c79,plain,
multiply(X,inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),multiply(Z,inverse(Z))))) = X,
inference(equational,[status(thm)],[c46,c78]) ).
cnf(c80,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c2,c16,c79]) ).
cnf(c82,plain,
multiply(inverse(inverse(inverse(multiply(X,inverse(X))))),Y) = multiply(multiply(Z,inverse(Z)),Y),
inference(equational,[status(thm)],[c64,c80]) ).
cnf(c87,plain,
multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(Y,inverse(Y))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c7,c79]) ).
cnf(c88,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = X,
inference(equational,[status(thm)],[c79,c87]) ).
cnf(c89,plain,
multiply(X,inverse(inverse(inverse(inverse(multiply(Y,inverse(Y))))))) = X,
inference(equational,[status(thm)],[c82,c88]) ).
cnf(c96,plain,
multiply(inverse(X),multiply(Y,inverse(Y))) = multiply(Z,inverse(multiply(multiply(W,inverse(W)),multiply(X,Z)))),
inference(equational,[status(thm)],[c24,c80]) ).
cnf(c97,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(Y,inverse(Y)))) = inverse(multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c18,c79]) ).
cnf(c102,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(Y,Z))) = multiply(inverse(Z),inverse(multiply(Y,multiply(W,inverse(W))))),
inference(equational,[status(thm)],[c12,c88]) ).
cnf(c103,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(Y,Z))) = multiply(W,inverse(multiply(Y,multiply(Z,W)))),
inference(equational,[status(thm)],[c12,c102]) ).
cnf(c104,plain,
inverse(multiply(X,inverse(X))) = multiply(Y,inverse(multiply(Z,multiply(inverse(Z),Y)))),
inference(equational,[status(thm)],[c18,c88,c103]) ).
cnf(c105,plain,
inverse(multiply(X,multiply(inverse(X),Y))) = multiply(inverse(Y),multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c88,c96,c104]) ).
cnf(c106,plain,
inverse(multiply(X,inverse(X))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c87,c88,c105]) ).
cnf(c107,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c76,c88,c106]) ).
cnf(c108,plain,
inverse(inverse(multiply(X,inverse(X)))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c88,c97,c105,c106]) ).
cnf(c109,plain,
multiply(multiply(X,inverse(X)),Y) = inverse(inverse(Y)),
inference(equational,[status(thm)],[c52,c89,c107,c108]) ).
cnf(c110,plain,
inverse(inverse(multiply(X,inverse(X)))) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c106,c108]) ).
cnf(c111,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(equational,[status(thm)],[c46,c88,c109,c110]) ).
cnf(c112,plain,
multiply(inverse(inverse(X)),inverse(X)) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c88,c104,c106]) ).
cnf(c113,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference(equational,[status(thm)],[c2,c26,c109,c111,c112]) ).
cnf(c114,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c111,c113]) ).
cnf(c115,plain,
multiply(inverse(X),X) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c30,c88,c114]) ).
cnf(c117,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c75,c107,c109,c114,c115]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c117]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GRP430-1 : TPTP v9.0.0. Released v2.6.0.
% 0.02/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:27:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 8.57/8.76 % SZS status Unsatisfiable
% 8.57/8.76 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------