%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO031-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 06:14:48 AM UTC 2025
% Result : Unsatisfiable 72.25s 72.34s
% Output : CNFRefutation 72.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 5 RR)
% Number of literals : 72 ( 71 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 157 ( 36 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
file('theBenchmark.p',prove_multiply_add_property) ).
cnf(c1,axiom,
add(X,inverse(X)) = n1,
file('theBenchmark.p',additive_inverse) ).
cnf(c2,axiom,
multiply(X,inverse(X)) = n0,
file('theBenchmark.p',multiplicative_inverse) ).
cnf(c3,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)),
file('theBenchmark.p',associativity_of_add) ).
cnf(c4,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('theBenchmark.p',associativity_of_multiply) ).
cnf(c5,axiom,
add(multiply(X,inverse(X)),Y) = Y,
file('theBenchmark.p',property3_dual) ).
cnf(c6,plain,
add(n0,X) = X,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c9,axiom,
multiply(add(X,inverse(X)),Y) = Y,
file('theBenchmark.p',property3) ).
cnf(c10,plain,
multiply(n1,X) = X,
inference(equational,[status(thm)],[c1,c9]) ).
cnf(c11,plain,
inverse(n1) = n0,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c12,plain,
add(n1,n0) = n1,
inference(equational,[status(thm)],[c1,c11]) ).
cnf(c13,axiom,
multiply(X,add(Y,add(X,Z))) = X,
file('theBenchmark.p',l2) ).
cnf(c14,plain,
add(X,n1) = n1,
inference(equational,[status(thm)],[c10,c12,c13]) ).
cnf(c15,plain,
multiply(X,n1) = X,
inference(equational,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
multiply(X,add(X,Y)) = X,
inference(equational,[status(thm)],[c6,c13]) ).
cnf(c18,plain,
multiply(n0,X) = n0,
inference(equational,[status(thm)],[c6,c16]) ).
cnf(c19,axiom,
add(X,multiply(Y,multiply(X,Z))) = X,
file('theBenchmark.p',l1) ).
cnf(c20,plain,
multiply(X,n0) = n0,
inference(equational,[status(thm)],[c6,c18,c19]) ).
cnf(c21,plain,
multiply(X,X) = X,
inference(equational,[status(thm)],[c16,c19]) ).
cnf(c23,plain,
add(X,multiply(X,Y)) = X,
inference(equational,[status(thm)],[c10,c19]) ).
cnf(c24,plain,
add(X,X) = X,
inference(equational,[status(thm)],[c16,c23]) ).
cnf(c25,plain,
add(X,multiply(Y,X)) = X,
inference(equational,[status(thm)],[c13,c19]) ).
cnf(c26,plain,
multiply(X,add(Y,X)) = X,
inference(equational,[status(thm)],[c13,c19]) ).
cnf(c27,plain,
add(X,add(Y,X)) = add(X,Y),
inference(equational,[status(thm)],[c3,c16,c25]) ).
cnf(c29,plain,
multiply(X,multiply(Y,X)) = multiply(X,Y),
inference(equational,[status(thm)],[c4,c23,c26]) ).
cnf(c32,plain,
multiply(X,multiply(inverse(X),Y)) = n0,
inference(equational,[status(thm)],[c2,c4,c18]) ).
cnf(c34,plain,
add(X,add(X,Y)) = add(X,Y),
inference(equational,[status(thm)],[c3,c24]) ).
cnf(c36,plain,
multiply(inverse(X),multiply(Y,X)) = n0,
inference(equational,[status(thm)],[c4,c20,c29,c32]) ).
cnf(c51,plain,
add(X,add(multiply(X,Y),Z)) = add(X,Z),
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c57,axiom,
multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y,
file('theBenchmark.p',l4) ).
cnf(c58,plain,
multiply(add(X,Y),multiply(add(Y,Z),Y)) = Y,
inference(equational,[status(thm)],[c4,c57]) ).
cnf(c59,plain,
multiply(add(X,Y),Y) = Y,
inference(equational,[status(thm)],[c1,c10,c58]) ).
cnf(c60,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c25,c29,c59]) ).
cnf(c61,plain,
multiply(X,multiply(Y,Z)) = multiply(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c4,c60]) ).
cnf(c62,axiom,
add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y,
file('theBenchmark.p',l3) ).
cnf(c63,plain,
add(multiply(X,Y),add(multiply(Y,Z),Y)) = Y,
inference(equational,[status(thm)],[c3,c62]) ).
cnf(c64,plain,
add(multiply(X,Y),Y) = Y,
inference(equational,[status(thm)],[c13,c24,c63]) ).
cnf(c65,plain,
add(X,Y) = add(Y,X),
inference(equational,[status(thm)],[c26,c27,c64]) ).
cnf(c67,plain,
multiply(X,multiply(Y,multiply(X,Z))) = multiply(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c19,c59]) ).
cnf(c70,plain,
multiply(add(X,Y),multiply(Z,Y)) = multiply(Z,Y),
inference(equational,[status(thm)],[c58,c67]) ).
cnf(c74,plain,
add(X,add(Y,multiply(X,Z))) = add(X,Y),
inference(equational,[status(thm)],[c51,c65]) ).
cnf(c82,plain,
multiply(add(X,Y),multiply(Z,X)) = multiply(Z,X),
inference(equational,[status(thm)],[c65,c70]) ).
cnf(c84,plain,
multiply(X,multiply(Y,add(Z,multiply(Y,X)))) = multiply(Y,X),
inference(equational,[status(thm)],[c29,c58,c60,c61,c63]) ).
cnf(c91,plain,
add(X,add(multiply(Y,multiply(X,Z)),W)) = add(X,W),
inference(equational,[status(thm)],[c3,c19]) ).
cnf(c115,plain,
add(multiply(X,Y),multiply(X,multiply(Y,Z))) = multiply(X,Y),
inference(equational,[status(thm)],[c4,c23]) ).
cnf(c117,plain,
multiply(add(X,Y),add(X,add(Y,Z))) = add(X,Y),
inference(equational,[status(thm)],[c3,c16]) ).
cnf(c118,plain,
add(X,add(multiply(Y,multiply(Z,X)),W)) = add(X,W),
inference(equational,[status(thm)],[c84,c91]) ).
cnf(c134,plain,
add(multiply(X,Y),multiply(Y,multiply(Z,X))) = multiply(X,Y),
inference(equational,[status(thm)],[c4,c60,c115]) ).
cnf(c146,plain,
add(X,add(Y,add(multiply(Z,X),W))) = add(X,add(Y,W)),
inference(equational,[status(thm)],[c3,c16,c118]) ).
cnf(c189,plain,
multiply(X,add(multiply(Y,X),multiply(X,Z))) = add(multiply(Y,X),multiply(X,Z)),
inference(equational,[status(thm)],[c60,c63,c117]) ).
cnf(c193,plain,
add(multiply(X,Y),multiply(add(Y,Z),X)) = multiply(add(Y,Z),X),
inference(equational,[status(thm)],[c16,c65,c134]) ).
cnf(c315,plain,
multiply(X,add(multiply(X,Y),multiply(Z,X))) = add(multiply(Z,X),multiply(X,Y)),
inference(equational,[status(thm)],[c65,c189]) ).
cnf(c385,axiom,
add(multiply(X,Y),add(multiply(Y,Z),multiply(Z,X))) = multiply(add(X,Y),multiply(add(Y,Z),add(Z,X))),
file('theBenchmark.p',distributivity) ).
cnf(c386,plain,
multiply(add(X,Y),multiply(add(Y,Z),add(Z,X))) = add(multiply(X,Y),add(multiply(Y,Z),multiply(Z,X))),
inference(equational,[status(thm)],[c385]) ).
cnf(c387,plain,
multiply(X,add(Y,multiply(Z,X))) = add(multiply(X,Y),multiply(Z,X)),
inference(equational,[status(thm)],[c4,c21,c60,c64,c82,c386]) ).
cnf(c388,plain,
multiply(X,add(Y,multiply(X,Z))) = add(multiply(X,Y),multiply(Z,X)),
inference(equational,[status(thm)],[c60,c387]) ).
cnf(c389,plain,
multiply(X,add(multiply(Y,X),Z)) = add(multiply(X,Z),multiply(Y,X)),
inference(equational,[status(thm)],[c65,c387]) ).
cnf(c391,plain,
multiply(add(X,Y),add(Z,X)) = add(X,multiply(add(X,Y),Z)),
inference(equational,[status(thm)],[c16,c65,c387]) ).
cnf(c392,plain,
add(multiply(X,Y),multiply(inverse(Y),X)) = add(X,multiply(inverse(Y),add(X,Y))),
inference(equational,[status(thm)],[c1,c2,c6,c10,c60,c65,c386,c391]) ).
cnf(c393,plain,
multiply(X,inverse(inverse(X))) = add(X,inverse(inverse(X))),
inference(equational,[status(thm)],[c1,c2,c6,c15,c60,c392]) ).
cnf(c394,plain,
add(X,inverse(inverse(X))) = X,
inference(equational,[status(thm)],[c23,c34,c393]) ).
cnf(c395,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c59,c393,c394]) ).
cnf(c398,plain,
multiply(inverse(X),add(Y,X)) = multiply(Y,inverse(X)),
inference(equational,[status(thm)],[c6,c36,c60,c193,c388,c392]) ).
cnf(c399,plain,
add(inverse(X),multiply(Y,X)) = add(inverse(X),Y),
inference(equational,[status(thm)],[c74,c392]) ).
cnf(c402,plain,
multiply(X,add(Y,inverse(X))) = multiply(Y,X),
inference(equational,[status(thm)],[c395,c398]) ).
cnf(c403,plain,
multiply(X,add(inverse(X),Y)) = multiply(Y,X),
inference(equational,[status(thm)],[c2,c6,c387,c399]) ).
cnf(c452,plain,
add(multiply(X,Y),multiply(X,inverse(Y))) = X,
inference(equational,[status(thm)],[c23,c60,c392,c398]) ).
cnf(c453,plain,
add(X,add(Y,multiply(Z,inverse(X)))) = add(X,add(Y,Z)),
inference(equational,[status(thm)],[c146,c452]) ).
cnf(c454,plain,
add(multiply(X,Y),multiply(Z,X)) = multiply(add(Y,Z),X),
inference(equational,[status(thm)],[c60,c387,c395,c403,c453]) ).
cnf(c464,plain,
add(multiply(X,Y),multiply(Z,Y)) = multiply(add(X,Z),Y),
inference(equational,[status(thm)],[c29,c315,c389,c402,c454]) ).
cnf(g1,plain,
multiply(a,add(b,c)) = add(multiply(b,a),multiply(c,a)),
inference(equational,[status(thm)],[c60,c464]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO031-1 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n004.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 04:24:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 72.25/72.34 % SZS status Unsatisfiable
% 72.25/72.34 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------