%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO008-4 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 06:14:44 AM UTC 2025
% Result : Unsatisfiable 1.17s 1.35s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 4 RR)
% Number of literals : 44 ( 43 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 : 79 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
file('theBenchmark.p',prove_associativity) ).
cnf(c1,axiom,
add(X,additive_identity) = X,
file('BOO004-0.ax',additive_id1) ).
cnf(c2,axiom,
multiply(X,multiplicative_identity) = X,
file('BOO004-0.ax',multiplicative_id1) ).
cnf(c3,axiom,
add(X,Y) = add(Y,X),
file('BOO004-0.ax',commutativity_of_add) ).
cnf(c4,axiom,
multiply(X,Y) = multiply(Y,X),
file('BOO004-0.ax',commutativity_of_multiply) ).
cnf(c5,plain,
multiply(multiplicative_identity,X) = X,
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
add(additive_identity,X) = X,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c7,axiom,
add(X,inverse(X)) = multiplicative_identity,
file('BOO004-0.ax',additive_inverse1) ).
cnf(c9,axiom,
multiply(X,inverse(X)) = additive_identity,
file('BOO004-0.ax',multiplicative_inverse1) ).
cnf(c10,plain,
additive_identity = inverse(multiplicative_identity),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c12,plain,
add(inverse(multiplicative_identity),X) = X,
inference(equational,[status(thm)],[c6,c10]) ).
cnf(c13,plain,
add(X,inverse(multiplicative_identity)) = X,
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c14,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('BOO004-0.ax',distributivity1) ).
cnf(c15,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('BOO004-0.ax',distributivity2) ).
cnf(c16,plain,
multiply(multiply(add(X,X),add(X,Y)),add(multiply(X,Y),Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c3,c14,c15]) ).
cnf(c17,plain,
multiply(X,add(inverse(X),Y)) = multiply(add(X,X),Y),
inference(equational,[status(thm)],[c2,c7,c9,c10,c12,c16]) ).
cnf(c20,plain,
multiply(inverse(multiplicative_identity),add(X,X)) = inverse(multiplicative_identity),
inference(equational,[status(thm)],[c1,c4,c9,c10,c17]) ).
cnf(c23,plain,
multiply(add(X,Y),add(X,multiplicative_identity)) = add(X,Y),
inference(equational,[status(thm)],[c2,c14]) ).
cnf(c24,plain,
add(X,multiplicative_identity) = multiplicative_identity,
inference(equational,[status(thm)],[c5,c7,c23]) ).
cnf(c25,plain,
add(X,X) = X,
inference(equational,[status(thm)],[c2,c17,c24]) ).
cnf(c27,plain,
multiply(inverse(multiplicative_identity),X) = inverse(multiplicative_identity),
inference(equational,[status(thm)],[c20,c25]) ).
cnf(c29,plain,
multiply(X,add(X,Y)) = X,
inference(equational,[status(thm)],[c13,c14,c27]) ).
cnf(c33,plain,
multiply(X,inverse(inverse(X))) = X,
inference(equational,[status(thm)],[c2,c7,c17,c25]) ).
cnf(c34,plain,
multiply(add(X,Y),add(X,Z)) = add(multiply(Y,Z),X),
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c35,plain,
multiply(add(X,Y),add(X,inverse(Y))) = X,
inference(equational,[status(thm)],[c9,c10,c13,c14]) ).
cnf(c36,plain,
add(X,inverse(inverse(X))) = X,
inference(equational,[status(thm)],[c5,c7,c35]) ).
cnf(c39,plain,
multiply(X,add(inverse(inverse(X)),Y)) = X,
inference(equational,[status(thm)],[c16,c25,c29,c33]) ).
cnf(c41,plain,
multiply(add(X,Y),add(Y,Z)) = add(multiply(X,Z),Y),
inference(equational,[status(thm)],[c3,c34]) ).
cnf(c43,plain,
multiply(add(X,Y),add(inverse(Y),X)) = X,
inference(equational,[status(thm)],[c3,c35]) ).
cnf(c44,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c2,c3,c7,c36,c43]) ).
cnf(c48,plain,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
inference(equational,[status(thm)],[c3,c41]) ).
cnf(c89,plain,
multiply(add(X,Y),add(add(X,Z),Y)) = add(X,Y),
inference(equational,[status(thm)],[c39,c44,c48]) ).
cnf(c90,plain,
add(inverse(X),add(X,Y)) = multiplicative_identity,
inference(equational,[status(thm)],[c3,c5,c7,c89]) ).
cnf(c91,plain,
add(X,add(X,Y)) = add(X,Y),
inference(equational,[status(thm)],[c2,c3,c43,c90]) ).
cnf(c92,plain,
add(X,add(Y,X)) = add(X,Y),
inference(equational,[status(thm)],[c3,c91]) ).
cnf(c143,plain,
multiply(add(X,Y),add(Z,Y)) = multiply(add(X,Y),add(Y,add(inverse(X),Z))),
inference(equational,[status(thm)],[c17,c25,c41,c48]) ).
cnf(c144,plain,
add(add(X,Y),add(X,Z)) = add(Z,add(X,Y)),
inference(equational,[status(thm)],[c5,c44,c90,c143]) ).
cnf(c147,plain,
add(X,add(Y,Z)) = add(add(Z,Y),add(Z,X)),
inference(equational,[status(thm)],[c3,c144]) ).
cnf(c149,plain,
add(add(X,Y),add(X,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c91,c144]) ).
cnf(c150,plain,
add(X,add(Y,Z)) = add(Z,add(X,Y)),
inference(equational,[status(thm)],[c147,c149]) ).
cnf(c152,plain,
add(add(X,Y),Z) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c92,c149]) ).
cnf(c153,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c3,c150]) ).
cnf(g1,plain,
add(a,add(b,c)) = add(add(a,b),c),
inference(equational,[status(thm)],[c152,c153]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO008-4 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 04:22:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.17/1.35 % SZS status Unsatisfiable
% 1.17/1.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------