%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO016-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 06:14:46 AM UTC 2025
% Result : Unsatisfiable 0.71s 0.86s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 9 RR)
% Number of literals : 30 ( 29 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(x,z) != x,
file('theBenchmark.p',prove_sum) ).
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(c5,axiom,
multiply(x,y) = z,
file('theBenchmark.p',x_times_y) ).
cnf(c6,plain,
z = multiply(x,y),
inference(equational,[status(thm)],[c5]) ).
cnf(c8,axiom,
multiply(X,Y) = multiply(Y,X),
file('BOO003-0.ax',commutativity_of_multiply) ).
cnf(c9,axiom,
multiply(inverse(X),X) = additive_identity,
file('BOO003-0.ax',multiplicative_inverse2) ).
cnf(c10,plain,
multiply(X,inverse(X)) = additive_identity,
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
inverse(multiplicative_identity) = additive_identity,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c12,axiom,
add(X,inverse(X)) = multiplicative_identity,
file('BOO003-0.ax',additive_inverse1) ).
cnf(c13,plain,
multiplicative_identity = inverse(additive_identity),
inference(equational,[status(thm)],[c4,c12]) ).
cnf(c14,plain,
inverse(inverse(additive_identity)) = additive_identity,
inference(equational,[status(thm)],[c11,c13]) ).
cnf(c17,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('BOO003-0.ax',distributivity4) ).
cnf(c18,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('BOO003-0.ax',distributivity3) ).
cnf(c19,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('BOO003-0.ax',distributivity2) ).
cnf(c20,plain,
add(add(multiply(X,X),multiply(X,Y)),add(multiply(Z,X),multiply(Z,Y))) = add(X,multiply(Z,Y)),
inference(equational,[status(thm)],[c17,c18,c19]) ).
cnf(c21,axiom,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
file('BOO003-0.ax',distributivity1) ).
cnf(c22,plain,
add(add(multiply(X,Y),multiply(X,Z)),add(multiply(Z,Y),multiply(Z,Z))) = add(multiply(X,Y),Z),
inference(equational,[status(thm)],[c17,c18,c21]) ).
cnf(c23,plain,
add(multiply(X,X),Y) = add(X,multiply(Y,Y)),
inference(equational,[status(thm)],[c20,c22]) ).
cnf(c25,plain,
add(X,multiply(additive_identity,additive_identity)) = multiply(X,X),
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c29,plain,
add(multiply(X,Y),multiply(additive_identity,Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c3,c18]) ).
cnf(c30,plain,
multiply(additive_identity,inverse(X)) = additive_identity,
inference(equational,[status(thm)],[c4,c10,c29]) ).
cnf(c31,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c14,c30]) ).
cnf(c32,plain,
multiply(X,X) = X,
inference(equational,[status(thm)],[c3,c25,c31]) ).
cnf(c37,plain,
add(multiply(X,additive_identity),multiply(X,Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c4,c17]) ).
cnf(c38,plain,
multiply(X,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c3,c10,c37]) ).
cnf(c40,plain,
add(X,multiply(Y,X)) = X,
inference(equational,[status(thm)],[c3,c20,c32,c38]) ).
cnf(g1,plain,
add(x,z) = x,
inference(equational,[status(thm)],[c6,c8,c40]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO016-2 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n009.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 04:23:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.71/0.86 % SZS status Unsatisfiable
% 0.71/0.86 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------