%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO003-4 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.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 06:14:42 AM UTC 2025
% Result : Unsatisfiable 0.39s 0.61s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 5 RR)
% Number of literals : 21 ( 20 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,a) != a,
file('theBenchmark.p',prove_a_times_a_is_a) ).
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(c9,axiom,
multiply(X,inverse(X)) = additive_identity,
file('BOO004-0.ax',multiplicative_inverse1) ).
cnf(c10,plain,
additive_identity = inverse(multiplicative_identity),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c12,plain,
add(inverse(multiplicative_identity),X) = X,
inference(equational,[status(thm)],[c6,c10]) ).
cnf(c13,plain,
add(X,inverse(multiplicative_identity)) = X,
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c14,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('BOO004-0.ax',distributivity1) ).
cnf(c15,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('BOO004-0.ax',distributivity2) ).
cnf(c16,plain,
multiply(multiply(add(X,X),add(X,Y)),add(multiply(X,Y),Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c3,c14,c15]) ).
cnf(c17,plain,
multiply(X,add(inverse(X),Y)) = multiply(add(X,X),Y),
inference(equational,[status(thm)],[c2,c7,c9,c10,c12,c16]) ).
cnf(c20,plain,
multiply(inverse(multiplicative_identity),add(X,X)) = inverse(multiplicative_identity),
inference(equational,[status(thm)],[c1,c4,c9,c10,c17]) ).
cnf(c21,plain,
multiply(inverse(multiplicative_identity),inverse(multiplicative_identity)) = inverse(multiplicative_identity),
inference(equational,[status(thm)],[c1,c10,c20]) ).
cnf(c22,plain,
multiply(X,X) = X,
inference(equational,[status(thm)],[c13,c14,c21]) ).
cnf(g1,plain,
multiply(a,a) = a,
inference(equational,[status(thm)],[c22]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO003-4 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n005.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 04:21:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.39/0.61 % SZS status Unsatisfiable
% 0.39/0.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------