%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO023-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.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 06:14:47 AM UTC 2025
% Result : Unsatisfiable 65.05s 65.25s
% Output : CNFRefutation 65.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 8
% Syntax : Number of clauses : 105 ( 105 unt; 0 nHn; 4 RR)
% Number of literals : 105 ( 104 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; 4 con; 0-3 aty)
% Number of variables : 210 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(a,multiply(b,c)) != multiply(add(a,b),add(a,c)),
file('theBenchmark.p',prove_add_multiply_property) ).
cnf(c1,axiom,
pixley(X,X,Y) = Y,
file('theBenchmark.p',pixley1) ).
cnf(c2,axiom,
pixley(X,Y,Y) = X,
file('theBenchmark.p',pixley2) ).
cnf(c3,axiom,
pixley(X,Y,X) = X,
file('theBenchmark.p',pixley3) ).
cnf(c4,axiom,
add(X,inverse(X)) = n1,
file('theBenchmark.p',additive_inverse) ).
cnf(c5,axiom,
multiply(add(X,Y),Y) = Y,
file('theBenchmark.p',multiply_add) ).
cnf(c6,plain,
multiply(n1,inverse(X)) = inverse(X),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c7,axiom,
multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)),
file('theBenchmark.p',multiply_add_property) ).
cnf(c8,plain,
add(multiply(X,Y),multiply(Z,Y)) = multiply(Y,add(X,Z)),
inference(equational,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X,add(add(Y,X),Z)) = add(X,multiply(Z,X)),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
multiply(X,add(Y,add(Z,X))) = add(multiply(Y,X),X),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c11,plain,
add(multiply(X,inverse(Y)),inverse(Y)) = multiply(inverse(Y),add(X,n1)),
inference(equational,[status(thm)],[c4,c10]) ).
cnf(c12,plain,
add(inverse(X),inverse(X)) = multiply(inverse(X),add(n1,n1)),
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c15,plain,
multiply(multiply(X,add(Y,Z)),multiply(Z,X)) = multiply(Z,X),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c16,plain,
multiply(multiply(X,n1),multiply(inverse(Y),X)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c18,plain,
multiply(n1,add(inverse(X),inverse(X))) = multiply(inverse(X),add(n1,n1)),
inference(equational,[status(thm)],[c5,c12,c16]) ).
cnf(c19,plain,
multiply(add(X,Y),add(multiply(Z,Y),Y)) = add(multiply(Z,Y),Y),
inference(equational,[status(thm)],[c5,c10,c15]) ).
cnf(c20,plain,
multiply(add(X,Y),add(Y,Y)) = add(Y,Y),
inference(equational,[status(thm)],[c5,c19]) ).
cnf(c25,plain,
add(add(X,X),multiply(Y,add(X,X))) = multiply(add(X,X),add(add(Z,X),Y)),
inference(equational,[status(thm)],[c8,c20]) ).
cnf(c26,plain,
add(multiply(X,add(Y,Y)),add(Y,Y)) = multiply(add(Y,Y),add(X,add(Z,Y))),
inference(equational,[status(thm)],[c8,c20]) ).
cnf(c28,plain,
multiply(add(X,multiply(Y,Z)),multiply(Z,add(Y,Y))) = multiply(Z,add(Y,Y)),
inference(equational,[status(thm)],[c8,c15,c19]) ).
cnf(c29,axiom,
pixley(X,Y,Z) = add(multiply(X,inverse(Y)),add(multiply(X,Z),multiply(inverse(Y),Z))),
file('theBenchmark.p',pixley_defn) ).
cnf(c30,plain,
add(multiply(X,inverse(Y)),multiply(Z,add(X,inverse(Y)))) = pixley(X,Y,Z),
inference(equational,[status(thm)],[c8,c29]) ).
cnf(c31,plain,
add(multiply(X,inverse(X)),multiply(Y,n1)) = Y,
inference(equational,[status(thm)],[c1,c4,c30]) ).
cnf(c32,plain,
multiply(X,multiply(X,n1)) = multiply(X,n1),
inference(equational,[status(thm)],[c5,c31]) ).
cnf(c33,plain,
add(inverse(n1),multiply(X,n1)) = X,
inference(equational,[status(thm)],[c6,c31]) ).
cnf(c34,plain,
add(inverse(n1),n1) = add(X,n1),
inference(equational,[status(thm)],[c5,c33]) ).
cnf(c35,plain,
multiply(X,add(inverse(n1),n1)) = add(X,multiply(n1,X)),
inference(equational,[status(thm)],[c9,c34]) ).
cnf(c37,plain,
multiply(X,multiply(n1,add(X,X))) = multiply(n1,add(X,X)),
inference(equational,[status(thm)],[c8,c20,c33]) ).
cnf(c41,plain,
add(inverse(X),multiply(Y,add(n1,inverse(X)))) = pixley(n1,X,Y),
inference(equational,[status(thm)],[c6,c30]) ).
cnf(c43,plain,
add(multiply(X,inverse(Y)),add(X,inverse(Y))) = pixley(X,Y,add(Z,add(X,inverse(Y)))),
inference(equational,[status(thm)],[c5,c30]) ).
cnf(c44,plain,
multiply(add(X,n1),add(inverse(n1),n1)) = add(inverse(n1),n1),
inference(equational,[status(thm)],[c19,c34]) ).
cnf(c45,plain,
multiply(add(X,n1),add(Y,n1)) = add(inverse(n1),n1),
inference(equational,[status(thm)],[c34,c44]) ).
cnf(c46,plain,
add(multiply(X,multiply(Y,n1)),multiply(Y,n1)) = multiply(multiply(Y,n1),add(X,Y)),
inference(equational,[status(thm)],[c10,c31]) ).
cnf(c47,plain,
multiply(multiply(X,n1),add(X,X)) = multiply(n1,add(X,X)),
inference(equational,[status(thm)],[c8,c32,c46]) ).
cnf(c48,plain,
add(multiply(X,n1),multiply(Y,multiply(X,n1))) = multiply(multiply(X,n1),add(X,Y)),
inference(equational,[status(thm)],[c9,c31]) ).
cnf(c49,plain,
pixley(n1,X,add(Y,add(n1,inverse(X)))) = add(inverse(X),add(n1,inverse(X))),
inference(equational,[status(thm)],[c6,c43]) ).
cnf(c54,plain,
multiply(pixley(X,Y,Z),multiply(Z,add(X,inverse(Y)))) = multiply(Z,add(X,inverse(Y))),
inference(equational,[status(thm)],[c5,c30]) ).
cnf(c55,plain,
multiply(X,multiply(X,add(X,inverse(Y)))) = multiply(X,add(X,inverse(Y))),
inference(equational,[status(thm)],[c3,c54]) ).
cnf(c56,plain,
multiply(X,multiply(Y,add(X,inverse(Y)))) = multiply(Y,add(X,inverse(Y))),
inference(equational,[status(thm)],[c2,c54]) ).
cnf(c57,plain,
multiply(add(X,X),add(Y,multiply(X,n1))) = multiply(add(X,X),add(Y,n1)),
inference(equational,[status(thm)],[c8,c47]) ).
cnf(c59,plain,
multiply(add(X,X),add(inverse(n1),n1)) = X,
inference(equational,[status(thm)],[c5,c33,c57]) ).
cnf(c60,plain,
add(inverse(n1),n1) = n1,
inference(equational,[status(thm)],[c45,c59]) ).
cnf(c61,plain,
add(X,n1) = n1,
inference(equational,[status(thm)],[c34,c60]) ).
cnf(c63,plain,
multiply(add(X,X),n1) = X,
inference(equational,[status(thm)],[c59,c60]) ).
cnf(c64,plain,
add(inverse(n1),X) = add(X,X),
inference(equational,[status(thm)],[c33,c63]) ).
cnf(c65,plain,
add(X,multiply(n1,X)) = multiply(X,n1),
inference(equational,[status(thm)],[c35,c60]) ).
cnf(c69,plain,
add(multiply(X,inverse(X)),Y) = add(Y,Y),
inference(equational,[status(thm)],[c31,c63]) ).
cnf(c70,plain,
multiply(n1,add(X,X)) = X,
inference(equational,[status(thm)],[c8,c31,c69]) ).
cnf(c71,plain,
multiply(X,X) = X,
inference(equational,[status(thm)],[c37,c70]) ).
cnf(c72,plain,
multiply(inverse(X),n1) = inverse(X),
inference(equational,[status(thm)],[c18,c61,c70]) ).
cnf(c73,plain,
add(add(X,X),X) = X,
inference(equational,[status(thm)],[c63,c65,c70]) ).
cnf(c74,plain,
add(X,X) = X,
inference(equational,[status(thm)],[c9,c71,c73]) ).
cnf(c76,plain,
multiply(X,n1) = X,
inference(equational,[status(thm)],[c63,c74]) ).
cnf(c77,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c8,c74]) ).
cnf(c78,plain,
add(inverse(n1),X) = X,
inference(equational,[status(thm)],[c64,c74]) ).
cnf(c81,plain,
add(multiply(inverse(n1),X),X) = X,
inference(equational,[status(thm)],[c5,c10,c64,c74]) ).
cnf(c82,plain,
multiply(X,add(Y,X)) = X,
inference(equational,[status(thm)],[c26,c74,c78,c81]) ).
cnf(c83,plain,
add(multiply(X,Y),Y) = Y,
inference(equational,[status(thm)],[c26,c74,c82]) ).
cnf(c85,plain,
multiply(X,add(X,Y)) = add(X,multiply(Y,X)),
inference(equational,[status(thm)],[c25,c74,c81]) ).
cnf(c89,plain,
add(X,add(Y,X)) = add(Y,X),
inference(equational,[status(thm)],[c57,c61,c74,c76,c83]) ).
cnf(c90,plain,
multiply(inverse(X),add(X,Y)) = multiply(inverse(X),Y),
inference(equational,[status(thm)],[c8,c69,c74]) ).
cnf(c91,plain,
pixley(X,Y,inverse(X)) = inverse(Y),
inference(equational,[status(thm)],[c4,c8,c30,c72,c90]) ).
cnf(c92,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c2,c91]) ).
cnf(c93,plain,
add(inverse(X),X) = n1,
inference(equational,[status(thm)],[c4,c92]) ).
cnf(c96,plain,
add(n1,inverse(X)) = n1,
inference(equational,[status(thm)],[c3,c49,c89,c93]) ).
cnf(c97,plain,
add(n1,X) = n1,
inference(equational,[status(thm)],[c92,c96]) ).
cnf(c103,plain,
add(multiply(X,Y),X) = X,
inference(equational,[status(thm)],[c77,c83]) ).
cnf(c105,plain,
add(X,multiply(Y,X)) = X,
inference(equational,[status(thm)],[c8,c47,c74,c76,c85,c97]) ).
cnf(c106,plain,
add(add(X,Y),Y) = add(X,Y),
inference(equational,[status(thm)],[c57,c61,c74,c76,c105]) ).
cnf(c107,plain,
multiply(X,multiply(X,Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c28,c74,c105]) ).
cnf(c109,plain,
multiply(multiply(X,Y),add(Y,Z)) = multiply(X,Y),
inference(equational,[status(thm)],[c9,c105]) ).
cnf(c110,plain,
add(inverse(X),Y) = pixley(n1,X,Y),
inference(equational,[status(thm)],[c41,c76,c109]) ).
cnf(c111,plain,
multiply(X,pixley(n1,Y,X)) = X,
inference(equational,[status(thm)],[c3,c57,c74,c76,c110]) ).
cnf(c112,plain,
multiply(multiply(X,Y),add(Z,Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c10,c83,c105]) ).
cnf(c114,plain,
add(add(add(X,Y),Z),Y) = add(add(X,Y),Z),
inference(equational,[status(thm)],[c25,c74,c105]) ).
cnf(c115,plain,
add(add(X,Y),X) = add(X,Y),
inference(equational,[status(thm)],[c33,c76,c78,c114]) ).
cnf(c121,plain,
add(add(X,Y),multiply(Z,X)) = add(X,Y),
inference(equational,[status(thm)],[c105,c109]) ).
cnf(c153,plain,
pixley(n1,inverse(X),Y) = add(X,Y),
inference(equational,[status(thm)],[c92,c110]) ).
cnf(c180,plain,
add(multiply(X,add(Y,Z)),multiply(Z,X)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c8,c106]) ).
cnf(c193,plain,
add(multiply(X,Y),multiply(multiply(Z,Y),X)) = multiply(X,Y),
inference(equational,[status(thm)],[c48,c76,c85,c105,c180]) ).
cnf(c194,plain,
multiply(multiply(X,Y),multiply(X,add(Z,Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c8,c20,c74,c77,c180]) ).
cnf(c195,plain,
multiply(X,multiply(Y,add(Z,X))) = multiply(X,Y),
inference(equational,[status(thm)],[c8,c77,c103,c193,c194]) ).
cnf(c196,plain,
multiply(X,multiply(Y,add(X,Z))) = multiply(X,Y),
inference(equational,[status(thm)],[c115,c195]) ).
cnf(c197,plain,
multiply(X,add(Y,inverse(X))) = multiply(Y,X),
inference(equational,[status(thm)],[c56,c196]) ).
cnf(c288,plain,
pixley(n1,X,multiply(Y,add(Z,inverse(X)))) = pixley(add(Z,inverse(X)),X,Y),
inference(equational,[status(thm)],[c5,c30,c106,c110]) ).
cnf(c289,plain,
pixley(n1,X,multiply(Y,X)) = add(Y,inverse(X)),
inference(equational,[status(thm)],[c2,c197,c288]) ).
cnf(c354,plain,
add(X,multiply(Y,inverse(X))) = add(Y,X),
inference(equational,[status(thm)],[c92,c153,c289]) ).
cnf(c370,plain,
multiply(add(X,Y),add(multiply(Z,X),W)) = add(multiply(Z,X),multiply(W,add(X,Y))),
inference(equational,[status(thm)],[c8,c109]) ).
cnf(c371,plain,
multiply(X,add(multiply(Y,X),Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c8,c48,c76,c85,c105,c370]) ).
cnf(c372,plain,
multiply(add(X,Y),add(X,Z)) = add(X,multiply(Z,add(X,Y))),
inference(equational,[status(thm)],[c55,c71,c85,c105,c370]) ).
cnf(c373,plain,
add(X,multiply(inverse(X),Y)) = add(X,Y),
inference(equational,[status(thm)],[c4,c76,c90,c372]) ).
cnf(c374,plain,
add(X,Y) = add(Y,X),
inference(equational,[status(thm)],[c77,c354,c373]) ).
cnf(c378,plain,
pixley(n1,X,multiply(X,Y)) = pixley(n1,X,Y),
inference(equational,[status(thm)],[c92,c110,c373]) ).
cnf(c380,plain,
add(X,inverse(Y)) = pixley(n1,Y,X),
inference(equational,[status(thm)],[c77,c289,c378]) ).
cnf(c383,plain,
multiply(X,add(Y,multiply(Z,X))) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c8,c107,c371]) ).
cnf(c408,plain,
multiply(add(X,Y),add(Z,multiply(W,X))) = add(multiply(Z,add(X,Y)),multiply(W,X)),
inference(equational,[status(thm)],[c8,c109]) ).
cnf(c409,plain,
multiply(add(X,Y),add(Z,X)) = add(X,multiply(Z,add(X,Y))),
inference(equational,[status(thm)],[c55,c71,c111,c374,c380,c408]) ).
cnf(c410,plain,
add(X,multiply(Y,add(X,Z))) = add(X,multiply(Z,add(X,Y))),
inference(equational,[status(thm)],[c121,c372,c408]) ).
cnf(c411,plain,
add(X,multiply(Y,add(X,Z))) = add(X,multiply(Z,Y)),
inference(equational,[status(thm)],[c112,c383,c410]) ).
cnf(c412,plain,
add(X,add(Y,multiply(Z,X))) = add(X,Y),
inference(equational,[status(thm)],[c85,c105,c409,c411]) ).
cnf(c414,plain,
add(multiply(X,Y),multiply(Y,Z)) = multiply(Y,add(X,Z)),
inference(equational,[status(thm)],[c8,c46,c76,c82,c411]) ).
cnf(c419,plain,
add(X,multiply(Y,add(Z,X))) = add(X,multiply(Z,Y)),
inference(equational,[status(thm)],[c412,c414]) ).
cnf(g1,plain,
add(a,multiply(b,c)) = multiply(add(a,b),add(a,c)),
inference(equational,[status(thm)],[c372,c374,c419]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : BOO023-1 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n010.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 04:23:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 65.05/65.25 % SZS status Unsatisfiable
% 65.05/65.25 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------