%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO012-4 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 06:14:45 AM UTC 2025
% Result : Unsatisfiable 0.47s 0.64s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 5 RR)
% Number of literals : 35 ( 34 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
inverse(inverse(x)) != x,
file('theBenchmark.p',prove_inverse_is_an_involution) ).
cnf(c1,axiom,
add(X,additive_identity) = X,
file('BOO004-0.ax',additive_id1) ).
cnf(c2,axiom,
multiply(X,multiplicative_identity) = X,
file('BOO004-0.ax',multiplicative_id1) ).
cnf(c3,axiom,
add(X,Y) = add(Y,X),
file('BOO004-0.ax',commutativity_of_add) ).
cnf(c4,axiom,
multiply(X,Y) = multiply(Y,X),
file('BOO004-0.ax',commutativity_of_multiply) ).
cnf(c5,plain,
multiply(multiplicative_identity,X) = X,
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
add(additive_identity,X) = X,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c7,axiom,
add(X,inverse(X)) = multiplicative_identity,
file('BOO004-0.ax',additive_inverse1) ).
cnf(c8,plain,
inverse(additive_identity) = multiplicative_identity,
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,axiom,
multiply(X,inverse(X)) = additive_identity,
file('BOO004-0.ax',multiplicative_inverse1) ).
cnf(c11,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('BOO004-0.ax',distributivity1) ).
cnf(c12,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('BOO004-0.ax',distributivity2) ).
cnf(c13,plain,
multiply(multiply(add(X,X),add(X,Y)),add(multiply(X,Y),Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c3,c11,c12]) ).
cnf(c14,plain,
multiply(X,add(inverse(X),Y)) = multiply(add(X,X),Y),
inference(equational,[status(thm)],[c2,c6,c7,c9,c13]) ).
cnf(c15,plain,
multiply(add(X,X),additive_identity) = additive_identity,
inference(equational,[status(thm)],[c1,c9,c14]) ).
cnf(c16,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c1,c15]) ).
cnf(c17,plain,
multiply(X,X) = X,
inference(equational,[status(thm)],[c1,c11,c16]) ).
cnf(c21,plain,
multiply(additive_identity,add(multiplicative_identity,X)) = multiply(additive_identity,X),
inference(equational,[status(thm)],[c6,c8,c14]) ).
cnf(c22,plain,
multiply(add(X,Y),add(X,multiplicative_identity)) = add(X,Y),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c23,plain,
add(X,multiplicative_identity) = multiplicative_identity,
inference(equational,[status(thm)],[c5,c7,c22]) ).
cnf(c24,plain,
add(X,X) = X,
inference(equational,[status(thm)],[c2,c14,c23]) ).
cnf(c25,plain,
add(multiplicative_identity,X) = multiplicative_identity,
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c26,plain,
multiply(additive_identity,X) = additive_identity,
inference(equational,[status(thm)],[c2,c21,c25]) ).
cnf(c28,plain,
multiply(X,add(X,Y)) = X,
inference(equational,[status(thm)],[c1,c11,c26]) ).
cnf(c32,plain,
multiply(X,inverse(inverse(X))) = X,
inference(equational,[status(thm)],[c2,c7,c14,c24]) ).
cnf(c33,plain,
multiply(add(X,Y),add(X,Z)) = add(multiply(Y,Z),X),
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c34,plain,
multiply(add(X,Y),add(X,inverse(Y))) = X,
inference(equational,[status(thm)],[c1,c9,c11]) ).
cnf(c35,plain,
add(X,inverse(inverse(X))) = X,
inference(equational,[status(thm)],[c5,c7,c34]) ).
cnf(c36,plain,
multiply(X,inverse(inverse(inverse(X)))) = additive_identity,
inference(equational,[status(thm)],[c9,c14,c24,c35]) ).
cnf(c38,plain,
multiply(X,add(inverse(inverse(X)),Y)) = X,
inference(equational,[status(thm)],[c13,c17,c24,c28,c32,c35]) ).
cnf(c42,plain,
multiply(add(X,Y),add(Y,Z)) = add(multiply(X,Z),Y),
inference(equational,[status(thm)],[c3,c33]) ).
cnf(c44,plain,
add(multiply(X,Y),inverse(inverse(X))) = X,
inference(equational,[status(thm)],[c35,c38,c42]) ).
cnf(c45,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c6,c36,c44]) ).
cnf(g1,plain,
inverse(inverse(x)) = x,
inference(equational,[status(thm)],[c45]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO012-4 : TPTP v9.0.0. Released v1.1.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n003.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 04:22:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.47/0.64 % SZS status Unsatisfiable
% 0.47/0.64 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------