%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO028-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 61.06s 61.22s
% Output : CNFRefutation 61.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 3 RR)
% Number of literals : 47 ( 46 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 22 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,Y) = add(Y,X),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c2,axiom,
multiply(X,Y) = multiply(Y,X),
file('theBenchmark.p',commutativity_of_multiply) ).
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(c7,axiom,
multiply(X,add(Y,add(X,Z))) = X,
file('theBenchmark.p',l2) ).
cnf(c8,axiom,
add(X,multiply(Y,multiply(X,Z))) = X,
file('theBenchmark.p',l1) ).
cnf(c9,plain,
multiply(X,add(Y,X)) = X,
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c10,plain,
add(X,multiply(Y,X)) = X,
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c16,plain,
multiply(X,add(Y,add(Z,X))) = X,
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c17,plain,
add(X,multiply(Y,multiply(Z,X))) = X,
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c21,axiom,
multiply(add(X,Y),add(X,inverse(Y))) = X,
file('theBenchmark.p',b1) ).
cnf(c22,axiom,
add(multiply(X,Y),multiply(X,inverse(Y))) = X,
file('theBenchmark.p',b2) ).
cnf(c23,plain,
multiply(X,multiply(Y,add(Z,X))) = multiply(X,Y),
inference(equational,[status(thm)],[c4,c7,c22]) ).
cnf(c24,plain,
multiply(inverse(X),add(Y,X)) = multiply(inverse(X),Y),
inference(equational,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
add(X,add(Y,multiply(Z,X))) = add(X,Y),
inference(equational,[status(thm)],[c3,c8,c21]) ).
cnf(c26,plain,
add(inverse(X),multiply(Y,X)) = add(inverse(X),Y),
inference(equational,[status(thm)],[c22,c25]) ).
cnf(c27,plain,
add(X,add(inverse(X),Y)) = add(X,inverse(X)),
inference(equational,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
multiply(X,add(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c16,c27]) ).
cnf(c29,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(X,inverse(X)),
inference(equational,[status(thm)],[c23,c24]) ).
cnf(c30,plain,
add(X,multiply(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c17,c29]) ).
cnf(c33,plain,
multiply(add(X,Y),add(inverse(Y),X)) = X,
inference(equational,[status(thm)],[c1,c21]) ).
cnf(c34,plain,
add(multiply(X,Y),multiply(Y,inverse(X))) = Y,
inference(equational,[status(thm)],[c2,c22]) ).
cnf(c35,plain,
add(multiply(X,Y),multiply(inverse(Y),X)) = X,
inference(equational,[status(thm)],[c2,c22]) ).
cnf(c37,plain,
add(X,add(multiply(Y,X),Z)) = add(X,Z),
inference(equational,[status(thm)],[c1,c25]) ).
cnf(c38,plain,
add(X,multiply(inverse(X),Y)) = add(X,Y),
inference(equational,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
add(X,inverse(inverse(X))) = X,
inference(equational,[status(thm)],[c30,c38]) ).
cnf(c40,plain,
add(X,multiply(Y,inverse(X))) = add(X,Y),
inference(equational,[status(thm)],[c22,c37]) ).
cnf(c42,plain,
multiply(X,multiply(add(Y,X),Z)) = multiply(X,Z),
inference(equational,[status(thm)],[c2,c23]) ).
cnf(c43,plain,
multiply(X,add(inverse(X),Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c33,c42]) ).
cnf(c44,plain,
multiply(X,inverse(inverse(X))) = X,
inference(equational,[status(thm)],[c28,c43]) ).
cnf(c45,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c34,c39,c40,c44]) ).
cnf(c71,plain,
multiply(X,multiply(add(Y,add(X,Z)),W)) = multiply(X,W),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c72,plain,
multiply(X,add(inverse(add(X,Y)),Z)) = multiply(X,Z),
inference(equational,[status(thm)],[c33,c71]) ).
cnf(c76,plain,
add(X,add(multiply(Y,multiply(X,Z)),W)) = add(X,W),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c79,plain,
add(X,multiply(Y,inverse(multiply(X,Z)))) = add(X,Y),
inference(equational,[status(thm)],[c22,c76]) ).
cnf(c112,plain,
multiply(X,multiply(Y,add(inverse(X),Z))) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c4,c35,c72]) ).
cnf(c113,plain,
add(X,multiply(Y,add(X,Z))) = add(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c38,c45,c112]) ).
cnf(c114,plain,
add(X,add(Y,multiply(Z,inverse(X)))) = add(X,add(Y,Z)),
inference(equational,[status(thm)],[c3,c21,c79]) ).
cnf(c115,plain,
multiply(X,add(Y,multiply(Z,X))) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c43,c45,c114]) ).
cnf(c129,plain,
add(X,multiply(Y,add(Z,X))) = add(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c1,c113]) ).
cnf(c143,plain,
add(multiply(X,Y),multiply(Y,add(Z,X))) = multiply(Y,add(Z,X)),
inference(equational,[status(thm)],[c1,c10,c23]) ).
cnf(c145,plain,
multiply(add(X,Y),add(Z,Y)) = add(Y,multiply(add(X,Y),Z)),
inference(equational,[status(thm)],[c9,c129,c143]) ).
cnf(c149,plain,
add(multiply(X,Y),multiply(Y,Z)) = multiply(Y,add(Z,X)),
inference(equational,[status(thm)],[c10,c115,c145]) ).
cnf(c152,plain,
add(multiply(X,Y),multiply(Z,Y)) = multiply(Y,add(Z,X)),
inference(equational,[status(thm)],[c2,c149]) ).
cnf(g1,plain,
multiply(a,add(b,c)) = add(multiply(b,a),multiply(c,a)),
inference(equational,[status(thm)],[c1,c152]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : BOO028-1 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.14 % Command : run_Leo-III %s %d THM
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8042.1875MB
% 0.11/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Jul 14 04:24:49 EDT 2025
% 0.11/0.36 % CPUTime :
% 61.06/61.22 % SZS status Unsatisfiable
% 61.06/61.22 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------