%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO022-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 2.74s 2.93s
% Output : CNFRefutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 6 RR)
% Number of literals : 47 ( 46 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 : 78 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('theBenchmark.p',prove_associativity_of_multiply) ).
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,
multiply(add(X,Y),Y) = Y,
file('theBenchmark.p',multiply_add) ).
cnf(c4,axiom,
add(multiply(X,Y),Y) = Y,
file('theBenchmark.p',add_multiply) ).
cnf(c5,plain,
multiply(X,X) = X,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c6,plain,
add(X,X) = X,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c7,plain,
add(n0,inverse(X)) = inverse(X),
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c8,plain,
inverse(n0) = n1,
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c10,plain,
add(n0,n1) = n1,
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c15,axiom,
add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)),
file('theBenchmark.p',add_multiply_property) ).
cnf(c16,plain,
multiply(add(X,Y),add(Z,Y)) = add(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c15]) ).
cnf(c17,plain,
add(X,Y) = add(Y,X),
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c19,plain,
add(X,multiply(Y,X)) = X,
inference(equational,[status(thm)],[c3,c6,c16]) ).
cnf(c20,plain,
add(inverse(X),n0) = inverse(X),
inference(equational,[status(thm)],[c2,c19]) ).
cnf(c23,plain,
multiply(add(X,Y),X) = X,
inference(equational,[status(thm)],[c3,c17]) ).
cnf(c24,plain,
multiply(n1,X) = X,
inference(equational,[status(thm)],[c1,c23]) ).
cnf(c25,plain,
multiply(X,add(Y,X)) = add(X,multiply(X,Y)),
inference(equational,[status(thm)],[c6,c16]) ).
cnf(c31,axiom,
multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)),
file('theBenchmark.p',multiply_add_property) ).
cnf(c32,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c6,c31]) ).
cnf(c33,plain,
multiply(X,n1) = X,
inference(equational,[status(thm)],[c4,c10,c24,c31]) ).
cnf(c34,plain,
add(X,multiply(X,Y)) = X,
inference(equational,[status(thm)],[c4,c5,c25,c31]) ).
cnf(c35,plain,
add(X,n0) = X,
inference(equational,[status(thm)],[c2,c34]) ).
cnf(c36,plain,
add(n0,X) = X,
inference(equational,[status(thm)],[c17,c35]) ).
cnf(c42,plain,
add(X,add(Y,X)) = add(Y,X),
inference(equational,[status(thm)],[c3,c17,c34]) ).
cnf(c46,plain,
add(X,add(X,Y)) = add(Y,X),
inference(equational,[status(thm)],[c17,c42]) ).
cnf(c47,plain,
add(inverse(X),multiply(Y,X)) = add(Y,inverse(X)),
inference(equational,[status(thm)],[c1,c16,c33]) ).
cnf(c49,plain,
add(X,inverse(inverse(X))) = inverse(inverse(X)),
inference(equational,[status(thm)],[c2,c20,c47]) ).
cnf(c50,plain,
multiply(X,inverse(inverse(X))) = X,
inference(equational,[status(thm)],[c23,c32,c49]) ).
cnf(c52,plain,
multiply(X,inverse(Y)) = multiply(inverse(Y),add(X,Y)),
inference(equational,[status(thm)],[c2,c31,c35]) ).
cnf(c53,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c1,c33,c50,c52]) ).
cnf(c54,plain,
n0 = inverse(n1),
inference(equational,[status(thm)],[c8,c53]) ).
cnf(c57,plain,
add(inverse(n1),X) = X,
inference(equational,[status(thm)],[c36,c54]) ).
cnf(c63,plain,
multiply(X,inverse(Y)) = multiply(inverse(Y),add(Y,X)),
inference(equational,[status(thm)],[c2,c31,c54,c57]) ).
cnf(c64,plain,
add(inverse(X),multiply(X,Y)) = add(Y,inverse(X)),
inference(equational,[status(thm)],[c1,c16,c24]) ).
cnf(c65,plain,
add(X,multiply(Y,inverse(X))) = add(X,add(X,add(X,Y))),
inference(equational,[status(thm)],[c46,c53,c63,c64]) ).
cnf(c66,plain,
add(X,add(X,add(X,Y))) = add(Y,X),
inference(equational,[status(thm)],[c42,c46,c52,c53,c64,c65]) ).
cnf(c76,plain,
add(X,add(X,Y)) = add(X,Y),
inference(equational,[status(thm)],[c17,c46]) ).
cnf(c160,plain,
multiply(X,Y) = add(multiply(Y,X),multiply(multiply(Z,Y),X)),
inference(equational,[status(thm)],[c4,c31,c66,c76]) ).
cnf(c170,plain,
multiply(X,add(Y,multiply(Z,X))) = add(multiply(Z,X),multiply(X,Y)),
inference(equational,[status(thm)],[c16,c19]) ).
cnf(c249,plain,
add(multiply(X,Y),multiply(Y,multiply(Z,X))) = multiply(Y,X),
inference(equational,[status(thm)],[c32,c160]) ).
cnf(c250,plain,
multiply(multiply(X,Y),multiply(Z,Y)) = multiply(multiply(X,Y),Z),
inference(equational,[status(thm)],[c170,c249]) ).
cnf(c254,plain,
multiply(multiply(X,Y),Z) = multiply(multiply(Z,Y),X),
inference(equational,[status(thm)],[c32,c250]) ).
cnf(c256,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Z,Y)),
inference(equational,[status(thm)],[c32,c254]) ).
cnf(c257,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c32,c256]) ).
cnf(g1,plain,
multiply(multiply(a,b),c) = multiply(a,multiply(b,c)),
inference(equational,[status(thm)],[c257]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : BOO022-1 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n014.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 04:23:49 EDT 2025
% 0.11/0.32 % CPUTime :
% 2.74/2.93 % SZS status Unsatisfiable
% 2.74/2.93 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------