%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG009-5 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 07:42:43 AM UTC 2025
% Result : Unsatisfiable 93.42s 93.51s
% Output : CNFRefutation 93.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 5 RR)
% Number of literals : 65 ( 64 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 137 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_commutativity) ).
cnf(c1,axiom,
add(X,additive_identity) = X,
file('theBenchmark.p',right_identity) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('theBenchmark.p',commutative_addition) ).
cnf(c3,plain,
add(additive_identity,X) = X,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,axiom,
add(X,additive_inverse(X)) = additive_identity,
file('theBenchmark.p',right_additive_inverse) ).
cnf(c5,plain,
additive_inverse(additive_identity) = additive_identity,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c6,axiom,
multiply(X,multiply(X,X)) = X,
file('theBenchmark.p',x_cubed_is_x) ).
cnf(c7,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('theBenchmark.p',associative_multiplication) ).
cnf(c8,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)),
file('theBenchmark.p',associative_addition) ).
cnf(c9,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c10,plain,
add(X,add(additive_inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c3,c4,c8]) ).
cnf(c11,plain,
additive_inverse(additive_inverse(X)) = X,
inference(equational,[status(thm)],[c1,c4,c10]) ).
cnf(c12,plain,
add(X,add(Y,additive_inverse(X))) = Y,
inference(equational,[status(thm)],[c1,c4,c9]) ).
cnf(c14,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('theBenchmark.p',distribute1) ).
cnf(c15,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c14]) ).
cnf(c16,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('theBenchmark.p',distribute2) ).
cnf(c17,plain,
add(multiply(X,Y),multiply(Z,Y)) = multiply(add(X,Z),Y),
inference(equational,[status(thm)],[c16]) ).
cnf(c20,plain,
multiply(X,multiply(X,multiply(X,Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c21,plain,
multiply(X,add(Y,multiply(X,X))) = add(X,multiply(X,Y)),
inference(equational,[status(thm)],[c2,c6,c15]) ).
cnf(c22,plain,
add(X,multiply(X,additive_identity)) = X,
inference(equational,[status(thm)],[c3,c6,c21]) ).
cnf(c23,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c24,plain,
multiply(additive_inverse(X),additive_identity) = additive_identity,
inference(equational,[status(thm)],[c4,c10,c22]) ).
cnf(c25,plain,
multiply(X,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c11,c24]) ).
cnf(c26,plain,
multiply(additive_identity,multiply(additive_identity,X)) = multiply(additive_identity,X),
inference(equational,[status(thm)],[c7,c23]) ).
cnf(c29,plain,
add(X,add(Y,additive_inverse(add(X,Y)))) = additive_identity,
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c30,plain,
add(X,additive_inverse(add(additive_inverse(Y),X))) = Y,
inference(equational,[status(thm)],[c1,c10,c29]) ).
cnf(c31,plain,
add(X,additive_inverse(add(Y,X))) = additive_inverse(Y),
inference(equational,[status(thm)],[c11,c30]) ).
cnf(c33,plain,
multiply(X,multiply(additive_identity,Y)) = multiply(additive_identity,Y),
inference(equational,[status(thm)],[c7,c25]) ).
cnf(c37,plain,
multiply(add(X,Y),multiply(Y,Y)) = add(Y,multiply(X,multiply(Y,Y))),
inference(equational,[status(thm)],[c2,c6,c17]) ).
cnf(c38,plain,
add(X,multiply(additive_identity,multiply(X,X))) = X,
inference(equational,[status(thm)],[c3,c6,c37]) ).
cnf(c39,plain,
multiply(additive_identity,multiply(X,X)) = additive_identity,
inference(equational,[status(thm)],[c12,c29,c38]) ).
cnf(c40,plain,
multiply(additive_identity,X) = additive_identity,
inference(equational,[status(thm)],[c26,c33,c39]) ).
cnf(c41,plain,
multiply(add(X,Y),multiply(X,X)) = add(X,multiply(Y,multiply(X,X))),
inference(equational,[status(thm)],[c6,c17]) ).
cnf(c44,plain,
add(X,multiply(additive_inverse(X),multiply(X,X))) = additive_identity,
inference(equational,[status(thm)],[c29,c31,c39,c41]) ).
cnf(c67,plain,
add(multiply(X,multiply(Y,Z)),multiply(W,Z)) = multiply(add(multiply(X,Y),W),Z),
inference(equational,[status(thm)],[c7,c17]) ).
cnf(c73,plain,
add(multiply(X,Y),multiply(Z,multiply(W,Y))) = multiply(add(X,multiply(Z,W)),Y),
inference(equational,[status(thm)],[c7,c17]) ).
cnf(c74,plain,
add(multiply(X,Y),add(multiply(Z,Y),W)) = add(multiply(add(X,Z),Y),W),
inference(equational,[status(thm)],[c8,c17]) ).
cnf(c75,plain,
add(multiply(X,Y),add(multiply(X,Z),W)) = add(multiply(X,add(Y,Z)),W),
inference(equational,[status(thm)],[c8,c15]) ).
cnf(c81,plain,
multiply(X,add(multiply(X,multiply(X,Y)),Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c15,c20]) ).
cnf(c82,plain,
multiply(X,add(Y,multiply(X,multiply(X,Z)))) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c15,c20]) ).
cnf(c109,plain,
add(additive_inverse(multiply(X,Y)),multiply(add(Z,X),Y)) = multiply(Z,Y),
inference(equational,[status(thm)],[c1,c2,c29,c31,c74]) ).
cnf(c110,plain,
additive_inverse(multiply(additive_inverse(X),Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c1,c29,c31,c40,c109]) ).
cnf(c111,plain,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c30,c31,c110]) ).
cnf(c115,plain,
add(additive_inverse(multiply(X,Y)),multiply(X,add(Z,Y))) = multiply(X,Z),
inference(equational,[status(thm)],[c1,c2,c29,c31,c75]) ).
cnf(c116,plain,
additive_inverse(multiply(X,additive_inverse(Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c1,c25,c29,c31,c115]) ).
cnf(c117,plain,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c30,c31,c116]) ).
cnf(c126,plain,
multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Y))))) = multiply(X,Y),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c135,plain,
multiply(add(multiply(X,Y),Z),multiply(Y,Y)) = multiply(add(X,multiply(Z,Y)),Y),
inference(equational,[status(thm)],[c6,c67,c73]) ).
cnf(c137,plain,
multiply(add(X,additive_inverse(multiply(X,multiply(Y,Y)))),Y) = additive_identity,
inference(equational,[status(thm)],[c7,c39,c44,c111,c126,c135]) ).
cnf(c149,plain,
add(X,multiply(add(additive_inverse(X),Y),multiply(X,X))) = multiply(Y,multiply(X,X)),
inference(equational,[status(thm)],[c10,c41]) ).
cnf(c256,plain,
multiply(add(additive_inverse(X),Y),multiply(X,X)) = add(additive_inverse(X),multiply(Y,multiply(X,X))),
inference(equational,[status(thm)],[c11,c41,c111,c117]) ).
cnf(c406,plain,
add(multiply(X,multiply(Y,multiply(Z,W))),multiply(V,W)) = multiply(add(multiply(X,multiply(Y,Z)),V),W),
inference(equational,[status(thm)],[c7,c67]) ).
cnf(c424,plain,
multiply(X,multiply(add(Y,multiply(X,multiply(X,Z))),W)) = multiply(X,multiply(add(Y,Z),W)),
inference(equational,[status(thm)],[c7,c82]) ).
cnf(c427,plain,
multiply(X,multiply(add(multiply(X,multiply(X,Y)),Z),W)) = multiply(X,multiply(add(Y,Z),W)),
inference(equational,[status(thm)],[c17,c81,c406]) ).
cnf(c462,plain,
multiply(X,multiply(add(Y,additive_inverse(multiply(X,multiply(X,Y)))),Z)) = additive_identity,
inference(equational,[status(thm)],[c25,c29,c31,c40,c427]) ).
cnf(c463,plain,
multiply(add(X,additive_inverse(multiply(Y,multiply(Y,X)))),Y) = additive_identity,
inference(equational,[status(thm)],[c25,c126,c462]) ).
cnf(c464,plain,
multiply(X,multiply(X,multiply(Y,X))) = multiply(Y,X),
inference(equational,[status(thm)],[c1,c7,c11,c109,c111,c463]) ).
cnf(c466,plain,
multiply(X,add(Y,additive_inverse(multiply(Y,multiply(X,X))))) = additive_identity,
inference(equational,[status(thm)],[c1,c5,c25,c137,c463]) ).
cnf(c467,plain,
multiply(X,multiply(Y,multiply(X,X))) = multiply(X,Y),
inference(equational,[status(thm)],[c1,c11,c115,c117,c466]) ).
cnf(c468,plain,
multiply(add(X,multiply(Y,multiply(Y,Z))),Y) = multiply(add(X,Z),Y),
inference(equational,[status(thm)],[c424,c464]) ).
cnf(c469,plain,
multiply(X,multiply(Y,Y)) = multiply(Y,multiply(Y,X)),
inference(equational,[status(thm)],[c7,c10,c20,c149,c256,c467,c468]) ).
cnf(c474,plain,
multiply(X,multiply(Y,multiply(Y,Z))) = multiply(Y,multiply(Y,multiply(X,Z))),
inference(equational,[status(thm)],[c7,c469]) ).
cnf(c475,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c6,c7,c464,c467,c474]) ).
cnf(g1,plain,
multiply(a,b) = multiply(b,a),
inference(equational,[status(thm)],[c475]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG009-5 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n008.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 16:23:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 93.42/93.51 % SZS status Unsatisfiable
% 93.42/93.51 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------