%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO008-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.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 06:14:43 AM UTC 2025
% Result : Unsatisfiable 2.24s 2.48s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 4 RR)
% Number of literals : 55 ( 54 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 : 106 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
file('theBenchmark.p',prove_associativity) ).
cnf(c1,axiom,
multiply(X,multiplicative_identity) = X,
file('BOO003-0.ax',multiplicative_id1) ).
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,
add(X,Y) = add(Y,X),
file('BOO003-0.ax',commutativity_of_add) ).
cnf(c6,axiom,
multiply(X,Y) = multiply(Y,X),
file('BOO003-0.ax',commutativity_of_multiply) ).
cnf(c7,axiom,
multiply(inverse(X),X) = additive_identity,
file('BOO003-0.ax',multiplicative_inverse2) ).
cnf(c8,plain,
multiply(X,inverse(X)) = additive_identity,
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
inverse(multiplicative_identity) = additive_identity,
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c10,axiom,
add(X,inverse(X)) = multiplicative_identity,
file('BOO003-0.ax',additive_inverse1) ).
cnf(c12,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('BOO003-0.ax',distributivity3) ).
cnf(c13,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('BOO003-0.ax',distributivity4) ).
cnf(c14,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('BOO003-0.ax',distributivity2) ).
cnf(c15,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)],[c12,c13,c14]) ).
cnf(c16,axiom,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
file('BOO003-0.ax',distributivity1) ).
cnf(c17,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)],[c12,c13,c16]) ).
cnf(c18,plain,
add(multiply(X,X),Y) = add(X,multiply(Y,Y)),
inference(equational,[status(thm)],[c15,c17]) ).
cnf(c23,plain,
add(X,multiply(Y,Y)) = add(Y,multiply(X,X)),
inference(equational,[status(thm)],[c5,c18]) ).
cnf(c24,plain,
add(multiply(X,additive_identity),multiply(X,Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c25,plain,
multiply(X,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c3,c8,c24]) ).
cnf(c26,plain,
multiply(X,X) = X,
inference(equational,[status(thm)],[c3,c4,c23,c25]) ).
cnf(c27,plain,
multiply(additive_identity,X) = additive_identity,
inference(equational,[status(thm)],[c6,c25]) ).
cnf(c28,plain,
add(X,multiply(X,Y)) = X,
inference(equational,[status(thm)],[c3,c4,c15,c26,c27]) ).
cnf(c32,plain,
add(X,multiply(Y,X)) = X,
inference(equational,[status(thm)],[c6,c28]) ).
cnf(c33,plain,
add(multiply(X,Y),multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c2,c10,c12]) ).
cnf(c34,plain,
multiply(X,inverse(inverse(X))) = inverse(inverse(X)),
inference(equational,[status(thm)],[c3,c8,c33]) ).
cnf(c36,plain,
add(multiply(X,Y),multiply(X,inverse(Y))) = X,
inference(equational,[status(thm)],[c1,c10,c13]) ).
cnf(c37,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c4,c8,c34,c36]) ).
cnf(c38,plain,
add(X,multiply(Y,inverse(X))) = add(X,Y),
inference(equational,[status(thm)],[c15,c36]) ).
cnf(c39,plain,
add(multiply(X,Y),inverse(Y)) = add(X,inverse(Y)),
inference(equational,[status(thm)],[c17,c36]) ).
cnf(c41,plain,
add(inverse(X),multiply(Y,X)) = add(inverse(X),Y),
inference(equational,[status(thm)],[c37,c38]) ).
cnf(c42,plain,
add(multiply(X,Y),inverse(X)) = add(Y,inverse(X)),
inference(equational,[status(thm)],[c6,c39]) ).
cnf(c53,plain,
add(X,add(X,Y)) = add(X,Y),
inference(equational,[status(thm)],[c2,c15,c26,c28]) ).
cnf(c54,plain,
add(X,add(Y,X)) = add(X,Y),
inference(equational,[status(thm)],[c5,c53]) ).
cnf(c63,plain,
add(multiply(X,Y),add(Y,inverse(X))) = add(Y,inverse(X)),
inference(equational,[status(thm)],[c42,c53]) ).
cnf(c76,plain,
add(multiply(X,Y),multiply(X,multiply(Y,Z))) = multiply(X,Y),
inference(equational,[status(thm)],[c13,c28]) ).
cnf(c77,plain,
multiply(X,multiply(inverse(X),Y)) = additive_identity,
inference(equational,[status(thm)],[c4,c8,c76]) ).
cnf(c95,plain,
add(X,inverse(multiply(inverse(X),Y))) = inverse(multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c3,c5,c41,c77]) ).
cnf(c115,plain,
add(add(multiply(X,Y),multiply(Z,Y)),inverse(Y)) = add(add(X,Z),inverse(Y)),
inference(equational,[status(thm)],[c12,c39]) ).
cnf(c116,plain,
add(add(X,Y),inverse(X)) = multiplicative_identity,
inference(equational,[status(thm)],[c10,c26,c32,c115]) ).
cnf(c124,plain,
add(add(X,inverse(Y)),inverse(multiply(Y,X))) = multiplicative_identity,
inference(equational,[status(thm)],[c63,c116]) ).
cnf(c127,plain,
add(add(X,Y),inverse(multiply(inverse(Y),X))) = multiplicative_identity,
inference(equational,[status(thm)],[c37,c124]) ).
cnf(c128,plain,
inverse(multiply(X,inverse(add(X,Y)))) = multiplicative_identity,
inference(equational,[status(thm)],[c6,c53,c95,c127]) ).
cnf(c129,plain,
multiply(X,inverse(add(X,Y))) = additive_identity,
inference(equational,[status(thm)],[c9,c37,c128]) ).
cnf(c251,plain,
add(add(X,Y),inverse(Z)) = add(inverse(Z),add(multiply(X,Z),multiply(Y,Z))),
inference(equational,[status(thm)],[c5,c115]) ).
cnf(c252,plain,
add(add(X,Y),Z) = add(add(X,Z),add(X,Y)),
inference(equational,[status(thm)],[c4,c37,c38,c129,c251]) ).
cnf(c257,plain,
add(inverse(X),add(multiply(Y,X),multiply(Z,X))) = add(inverse(X),add(Y,Z)),
inference(equational,[status(thm)],[c54,c115]) ).
cnf(c258,plain,
add(add(X,Y),add(X,Z)) = add(add(X,Y),Z),
inference(equational,[status(thm)],[c4,c37,c38,c129,c257]) ).
cnf(c259,plain,
add(add(X,Y),Z) = add(add(X,Z),Y),
inference(equational,[status(thm)],[c53,c252,c258]) ).
cnf(c260,plain,
add(add(X,Y),Z) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c5,c259]) ).
cnf(c262,plain,
add(X,add(Y,Z)) = add(Z,add(X,Y)),
inference(equational,[status(thm)],[c5,c259,c260]) ).
cnf(c263,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c5,c262]) ).
cnf(g1,plain,
add(a,add(b,c)) = add(add(a,b),c),
inference(equational,[status(thm)],[c260,c263]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO008-2 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n013.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 04:22:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 2.24/2.48 % SZS status Unsatisfiable
% 2.24/2.48 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------