%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP610-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 06:44:26 AM UTC 2025
% Result : Unsatisfiable 60.19s 60.46s
% Output : CNFRefutation 60.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 3 RR)
% Number of literals : 33 ( 32 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c1,axiom,
multiply(X,Y) = inverse(double_divide(Y,X)),
file('theBenchmark.p',multiply) ).
cnf(c2,plain,
inverse(double_divide(X,Y)) = multiply(Y,X),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,axiom,
inverse(double_divide(inverse(double_divide(inverse(double_divide(X,Y)),Z)),double_divide(X,Z))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c4,plain,
multiply(double_divide(X,Y),multiply(Y,multiply(Z,X))) = Z,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
multiply(double_divide(multiply(X,Y),double_divide(Y,Z)),X) = Z,
inference(equational,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(double_divide(X,Y),multiply(Y,Z)) = double_divide(multiply(X,W),double_divide(W,Z)),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c7,plain,
multiply(multiply(double_divide(X,Y),multiply(Y,Z)),X) = Z,
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
double_divide(multiply(X,Y),double_divide(Y,multiply(Z,X))) = Z,
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c10,plain,
multiply(double_divide(X,Y),multiply(Y,Z)) = multiply(double_divide(X,W),multiply(W,Z)),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c11,plain,
inverse(multiply(double_divide(X,Y),multiply(Y,Z))) = multiply(double_divide(W,Z),multiply(X,W)),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c12,plain,
multiply(double_divide(X,Y),multiply(Z,X)) = multiply(double_divide(W,Y),multiply(Z,W)),
inference(equational,[status(thm)],[c2,c6,c11]) ).
cnf(c13,plain,
multiply(X,multiply(multiply(double_divide(Y,X),Z),Y)) = Z,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c15,plain,
multiply(double_divide(X,Y),multiply(Y,X)) = double_divide(multiply(Z,W),double_divide(W,Z)),
inference(equational,[status(thm)],[c6,c12]) ).
cnf(c16,plain,
multiply(double_divide(X,Y),multiply(Y,X)) = multiply(double_divide(Z,W),multiply(W,Z)),
inference(equational,[status(thm)],[c10,c12]) ).
cnf(c17,plain,
multiply(double_divide(X,multiply(Y,Z)),multiply(Z,X)) = inverse(Y),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c18,plain,
multiply(X,inverse(X)) = multiply(double_divide(Y,Z),multiply(Z,Y)),
inference(equational,[status(thm)],[c8,c16,c17]) ).
cnf(c20,plain,
multiply(multiply(X,inverse(X)),Y) = Y,
inference(equational,[status(thm)],[c7,c18]) ).
cnf(c22,plain,
multiply(double_divide(X,Y),X) = multiply(double_divide(Z,Y),Z),
inference(equational,[status(thm)],[c12,c20]) ).
cnf(c24,plain,
double_divide(inverse(X),X) = multiply(double_divide(Y,Z),multiply(Z,Y)),
inference(equational,[status(thm)],[c8,c15,c17]) ).
cnf(c25,plain,
double_divide(inverse(X),X) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c18,c24]) ).
cnf(c26,plain,
multiply(double_divide(inverse(X),X),Y) = Y,
inference(equational,[status(thm)],[c7,c24]) ).
cnf(c27,plain,
multiply(double_divide(X,Y),X) = inverse(Y),
inference(equational,[status(thm)],[c22,c26]) ).
cnf(c30,plain,
multiply(X,multiply(Y,inverse(X))) = Y,
inference(equational,[status(thm)],[c4,c20,c25]) ).
cnf(c32,plain,
multiply(multiply(X,Y),inverse(X)) = Y,
inference(equational,[status(thm)],[c7,c26]) ).
cnf(c33,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c17,c26]) ).
cnf(c34,plain,
multiply(X,inverse(inverse(Y))) = multiply(Y,X),
inference(equational,[status(thm)],[c2,c22,c27,c33]) ).
cnf(c37,plain,
multiply(X,multiply(Y,Z)) = multiply(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c2,c13,c30]) ).
cnf(c38,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c2,c22,c27,c32,c37]) ).
cnf(c39,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c30,c34,c38]) ).
cnf(c40,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c34,c39]) ).
cnf(g1,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(equational,[status(thm)],[c20,c40]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP610-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:33:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 60.19/60.46 % SZS status Unsatisfiable
% 60.19/60.46 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------