%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP427-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n012.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 10.97s 11.14s
% Output : CNFRefutation 10.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 3 RR)
% Number of literals : 48 ( 47 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 133 ( 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(multiply(inverse(multiply(inverse(Y),multiply(inverse(X),Z))),W),inverse(multiply(Y,W))))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),Z)),W),inverse(multiply(Y,W))))) = inverse(multiply(multiply(inverse(multiply(inverse(V),multiply(inverse(inverse(X)),Z))),U),inverse(multiply(V,U)))),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),Z)),W),inverse(multiply(Y,W)))))) = Z,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(X),Z))))) = inverse(multiply(multiply(inverse(multiply(inverse(W),Y)),V),inverse(multiply(W,V)))),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c7,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(W,Z)))))) = multiply(W,inverse(multiply(multiply(inverse(multiply(inverse(V),Y)),U),inverse(multiply(V,U))))),
inference(equational,[status(thm)],[c3]) ).
cnf(c9,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(multiply(inverse(Z),W),inverse(multiply(inverse(Y),W))))))) = Z,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c10,plain,
multiply(inverse(X),multiply(X,Y)) = multiply(inverse(inverse(Z)),multiply(inverse(Z),Y)),
inference(equational,[status(thm)],[c1,c9]) ).
cnf(c11,plain,
multiply(inverse(inverse(inverse(X))),multiply(inverse(Y),multiply(Y,Z))) = multiply(inverse(W),multiply(W,multiply(inverse(X),Z))),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(inverse(X),multiply(X,multiply(inverse(Y),Z))) = multiply(inverse(W),multiply(W,multiply(inverse(Y),Z))),
inference(equational,[status(thm)],[c10,c11]) ).
cnf(c13,plain,
multiply(inverse(X),multiply(X,Y)) = multiply(inverse(Z),multiply(Z,Y)),
inference(equational,[status(thm)],[c9,c12]) ).
cnf(c19,plain,
multiply(inverse(X),multiply(inverse(Y),multiply(Y,inverse(multiply(multiply(inverse(Z),W),inverse(multiply(X,W))))))) = Z,
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c20,plain,
inverse(multiply(multiply(inverse(X),Y),inverse(multiply(Z,Y)))) = inverse(multiply(multiply(inverse(X),W),inverse(multiply(Z,W)))),
inference(equational,[status(thm)],[c1,c2,c19]) ).
cnf(c21,plain,
multiply(multiply(inverse(X),Y),inverse(multiply(Z,Y))) = multiply(multiply(inverse(X),W),inverse(multiply(Z,W))),
inference(equational,[status(thm)],[c19,c20]) ).
cnf(c23,plain,
multiply(multiply(inverse(X),multiply(X,Y)),inverse(multiply(Z,multiply(W,Y)))) = multiply(multiply(inverse(W),V),inverse(multiply(Z,V))),
inference(equational,[status(thm)],[c13,c21]) ).
cnf(c24,plain,
multiply(X,inverse(X)) = multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(Y),Z))),
inference(equational,[status(thm)],[c9,c23]) ).
cnf(c25,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c19,c24]) ).
cnf(c26,plain,
multiply(inverse(X),multiply(Y,inverse(Y))) = multiply(inverse(Z),multiply(Z,inverse(X))),
inference(equational,[status(thm)],[c13,c25]) ).
cnf(c28,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(Z,inverse(Z)))))) = Y,
inference(equational,[status(thm)],[c9,c24]) ).
cnf(c29,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(Y)))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c25,c28]) ).
cnf(c30,plain,
inverse(multiply(X,inverse(X))) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c20,c24,c25]) ).
cnf(c31,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c25,c30]) ).
cnf(c34,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))) = multiply(inverse(Z),multiply(Z,multiply(W,inverse(W)))),
inference(equational,[status(thm)],[c29,c31]) ).
cnf(c43,plain,
multiply(X,multiply(Y,inverse(multiply(multiply(inverse(multiply(inverse(X),Z)),W),inverse(multiply(inverse(Y),W)))))) = Z,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c44,plain,
multiply(X,multiply(Y,inverse(Y))) = inverse(inverse(X)),
inference(equational,[status(thm)],[c31,c43]) ).
cnf(c45,plain,
multiply(inverse(X),multiply(X,inverse(Y))) = inverse(inverse(inverse(Y))),
inference(equational,[status(thm)],[c13,c44]) ).
cnf(c48,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,inverse(Z))))) = Y,
inference(equational,[status(thm)],[c24,c43]) ).
cnf(c49,plain,
multiply(X,multiply(Y,inverse(multiply(Z,inverse(Z))))) = multiply(X,multiply(Y,inverse(multiply(W,inverse(W))))),
inference(equational,[status(thm)],[c28,c48]) ).
cnf(c51,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,Y)))) = inverse(Z),
inference(equational,[status(thm)],[c21,c48]) ).
cnf(c53,plain,
multiply(inverse(inverse(X)),inverse(inverse(inverse(multiply(Y,inverse(Y)))))) = X,
inference(equational,[status(thm)],[c19,c45,c49]) ).
cnf(c54,plain,
multiply(inverse(inverse(inverse(X))),X) = inverse(inverse(inverse(inverse(inverse(multiply(Y,inverse(Y))))))),
inference(equational,[status(thm)],[c10,c45,c53]) ).
cnf(c58,plain,
multiply(X,multiply(inverse(inverse(inverse(X))),inverse(inverse(inverse(Y))))) = inverse(Y),
inference(equational,[status(thm)],[c26,c44,c45,c51]) ).
cnf(c59,plain,
multiply(X,inverse(X)) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c53,c58]) ).
cnf(c60,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(equational,[status(thm)],[c28,c44,c45,c59]) ).
cnf(c61,plain,
inverse(inverse(multiply(X,inverse(X)))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c59]) ).
cnf(c62,plain,
multiply(inverse(X),multiply(X,Y)) = inverse(inverse(Y)),
inference(equational,[status(thm)],[c26,c44,c60]) ).
cnf(c65,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = inverse(inverse(X)),
inference(equational,[status(thm)],[c58,c59]) ).
cnf(c74,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c54,c60,c61]) ).
cnf(c75,plain,
multiply(X,inverse(multiply(inverse(Y),X))) = Y,
inference(equational,[status(thm)],[c19,c44,c60,c62,c74]) ).
cnf(c76,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference(equational,[status(thm)],[c45,c60,c75]) ).
cnf(c77,plain,
multiply(multiply(X,inverse(X)),Y) = Y,
inference(equational,[status(thm)],[c44,c60,c75]) ).
cnf(c78,plain,
multiply(inverse(X),X) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c76,c77]) ).
cnf(c79,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c65,c75,c78]) ).
cnf(c80,plain,
inverse(multiply(inverse(multiply(X,Y)),X)) = Y,
inference(equational,[status(thm)],[c3,c44,c60,c62,c74]) ).
cnf(c82,plain,
multiply(inverse(X),X) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c34,c44,c79,c80]) ).
cnf(c83,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c12,c62,c65,c79,c82]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c83]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP427-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:27:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 10.97/11.14 % SZS status Unsatisfiable
% 10.97/11.14 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------