%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO010-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.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 06:14:44 AM UTC 2025
% Result : Unsatisfiable 0.62s 0.85s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 3 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(a,multiply(a,b)) != a,
file('theBenchmark.p',prove_a_plus_ab_is_a) ).
cnf(c1,axiom,
multiply(X,multiplicative_identity) = X,
file('BOO003-0.ax',multiplicative_id1) ).
cnf(c2,axiom,
multiply(multiplicative_identity,X) = X,
file('BOO003-0.ax',multiplicative_id2) ).
cnf(c3,axiom,
add(X,additive_identity) = X,
file('BOO003-0.ax',additive_id1) ).
cnf(c4,axiom,
add(additive_identity,X) = X,
file('BOO003-0.ax',additive_id2) ).
cnf(c6,axiom,
multiply(X,Y) = multiply(Y,X),
file('BOO003-0.ax',commutativity_of_multiply) ).
cnf(c7,axiom,
multiply(inverse(X),X) = additive_identity,
file('BOO003-0.ax',multiplicative_inverse2) ).
cnf(c8,plain,
multiply(X,inverse(X)) = additive_identity,
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c12,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('BOO003-0.ax',distributivity3) ).
cnf(c13,plain,
add(multiply(X,Y),multiply(Z,Y)) = multiply(add(X,Z),Y),
inference(equational,[status(thm)],[c12]) ).
cnf(c14,plain,
add(X,multiply(Y,X)) = multiply(add(multiplicative_identity,Y),X),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c24,plain,
add(X,multiply(X,Y)) = multiply(add(multiplicative_identity,Y),X),
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c33,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('BOO003-0.ax',distributivity4) ).
cnf(c34,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c33]) ).
cnf(c37,plain,
multiply(X,add(inverse(X),Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c4,c8,c34]) ).
cnf(c39,plain,
multiply(X,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c3,c8,c37]) ).
cnf(c45,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('BOO003-0.ax',distributivity2) ).
cnf(c49,plain,
multiply(X,add(X,Y)) = X,
inference(equational,[status(thm)],[c3,c6,c39,c45]) ).
cnf(c50,plain,
add(multiplicative_identity,X) = multiplicative_identity,
inference(equational,[status(thm)],[c2,c49]) ).
cnf(g1,plain,
add(a,multiply(a,b)) = a,
inference(equational,[status(thm)],[c1,c6,c24,c50]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO010-2 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 04:22:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.62/0.85 % SZS status Unsatisfiable
% 0.62/0.85 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------