%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO014-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 06:14:46 AM UTC 2025
% Result : Unsatisfiable 3.60s 3.80s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of clauses : 69 ( 69 unt; 0 nHn; 8 RR)
% Number of literals : 69 ( 68 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 125 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
inverse(c) != d,
file('theBenchmark.p',prove_c_inverse_is_d) ).
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(a,b) = c,
file('theBenchmark.p',a_plus_b_is_c) ).
cnf(c6,plain,
c = add(a,b),
inference(equational,[status(thm)],[c5]) ).
cnf(c7,axiom,
add(X,Y) = add(Y,X),
file('BOO003-0.ax',commutativity_of_add) ).
cnf(c8,axiom,
multiply(X,Y) = multiply(Y,X),
file('BOO003-0.ax',commutativity_of_multiply) ).
cnf(c9,axiom,
add(X,inverse(X)) = multiplicative_identity,
file('BOO003-0.ax',additive_inverse1) ).
cnf(c11,axiom,
multiply(inverse(X),X) = additive_identity,
file('BOO003-0.ax',multiplicative_inverse2) ).
cnf(c12,plain,
multiply(X,inverse(X)) = additive_identity,
inference(equational,[status(thm)],[c8,c11]) ).
cnf(c13,plain,
inverse(multiplicative_identity) = additive_identity,
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c14,axiom,
multiply(inverse(a),inverse(b)) = d,
file('theBenchmark.p',a_inverse_times_b_inverse_is_d) ).
cnf(c15,plain,
d = multiply(inverse(b),inverse(a)),
inference(equational,[status(thm)],[c8,c14]) ).
cnf(c16,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('BOO003-0.ax',distributivity3) ).
cnf(c17,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('BOO003-0.ax',distributivity4) ).
cnf(c18,axiom,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
file('BOO003-0.ax',distributivity1) ).
cnf(c19,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)],[c16,c17,c18]) ).
cnf(c20,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('BOO003-0.ax',distributivity2) ).
cnf(c21,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)],[c16,c17,c20]) ).
cnf(c22,plain,
add(X,multiply(Y,Y)) = add(multiply(X,X),Y),
inference(equational,[status(thm)],[c19,c21]) ).
cnf(c28,plain,
add(multiply(X,X),Y) = add(multiply(Y,Y),X),
inference(equational,[status(thm)],[c7,c22]) ).
cnf(c29,plain,
add(multiply(X,additive_identity),multiply(X,Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c4,c17]) ).
cnf(c30,plain,
multiply(X,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c3,c12,c29]) ).
cnf(c31,plain,
multiply(X,X) = X,
inference(equational,[status(thm)],[c3,c4,c28,c30]) ).
cnf(c32,plain,
multiply(additive_identity,X) = additive_identity,
inference(equational,[status(thm)],[c8,c30]) ).
cnf(c33,plain,
add(X,multiply(X,Y)) = X,
inference(equational,[status(thm)],[c4,c7,c19,c31,c32]) ).
cnf(c37,plain,
add(X,multiply(Y,X)) = X,
inference(equational,[status(thm)],[c8,c33]) ).
cnf(c38,plain,
add(multiply(X,Y),multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c2,c9,c16]) ).
cnf(c39,plain,
multiply(X,inverse(inverse(X))) = inverse(inverse(X)),
inference(equational,[status(thm)],[c3,c12,c38]) ).
cnf(c41,plain,
add(multiply(X,Y),multiply(X,inverse(Y))) = X,
inference(equational,[status(thm)],[c1,c9,c17]) ).
cnf(c42,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c4,c12,c39,c41]) ).
cnf(c43,plain,
add(X,multiply(Y,inverse(X))) = add(X,Y),
inference(equational,[status(thm)],[c21,c41]) ).
cnf(c44,plain,
add(multiply(X,Y),inverse(Y)) = add(X,inverse(Y)),
inference(equational,[status(thm)],[c19,c41]) ).
cnf(c45,plain,
add(X,multiply(inverse(X),Y)) = add(X,Y),
inference(equational,[status(thm)],[c8,c43]) ).
cnf(c47,plain,
add(multiply(X,Y),inverse(X)) = add(Y,inverse(X)),
inference(equational,[status(thm)],[c8,c44]) ).
cnf(c49,plain,
add(inverse(X),multiply(X,Y)) = add(inverse(X),Y),
inference(equational,[status(thm)],[c42,c45]) ).
cnf(c83,plain,
add(multiply(X,Y),multiply(X,multiply(Y,Z))) = multiply(X,Y),
inference(equational,[status(thm)],[c17,c33]) ).
cnf(c84,plain,
multiply(X,multiply(inverse(X),Y)) = additive_identity,
inference(equational,[status(thm)],[c4,c12,c83]) ).
cnf(c88,plain,
multiply(inverse(X),multiply(X,Y)) = additive_identity,
inference(equational,[status(thm)],[c42,c84]) ).
cnf(c91,plain,
multiply(multiply(X,Y),inverse(X)) = additive_identity,
inference(equational,[status(thm)],[c8,c88]) ).
cnf(c95,plain,
multiply(X,inverse(multiply(inverse(X),Y))) = X,
inference(equational,[status(thm)],[c4,c41,c84]) ).
cnf(c99,plain,
multiply(X,inverse(multiply(Y,inverse(X)))) = X,
inference(equational,[status(thm)],[c8,c95]) ).
cnf(c108,plain,
add(inverse(X),inverse(multiply(X,Y))) = inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c7,c38,c42,c47,c95]) ).
cnf(c110,plain,
multiply(inverse(X),inverse(multiply(Y,X))) = inverse(X),
inference(equational,[status(thm)],[c42,c99]) ).
cnf(c131,plain,
add(add(multiply(X,Y),multiply(Z,Y)),inverse(Y)) = add(add(X,Z),inverse(Y)),
inference(equational,[status(thm)],[c16,c44]) ).
cnf(c132,plain,
add(add(X,Y),inverse(X)) = multiplicative_identity,
inference(equational,[status(thm)],[c9,c31,c37,c131]) ).
cnf(c140,plain,
add(add(X,inverse(Y)),inverse(multiply(Y,X))) = multiplicative_identity,
inference(equational,[status(thm)],[c47,c132]) ).
cnf(c142,plain,
add(add(inverse(X),Y),inverse(multiply(X,Y))) = multiplicative_identity,
inference(equational,[status(thm)],[c7,c140]) ).
cnf(c160,plain,
add(multiply(X,Y),multiply(X,multiply(Z,inverse(Y)))) = add(multiply(X,Y),multiply(X,Z)),
inference(equational,[status(thm)],[c17,c43]) ).
cnf(c176,plain,
add(multiply(X,Y),multiply(multiply(Z,inverse(X)),Y)) = add(multiply(X,Y),multiply(Z,Y)),
inference(equational,[status(thm)],[c16,c43]) ).
cnf(c177,plain,
add(X,multiply(Y,inverse(multiply(Y,inverse(X))))) = X,
inference(equational,[status(thm)],[c3,c12,c99,c176]) ).
cnf(c178,plain,
add(X,multiply(Y,inverse(multiply(inverse(X),Y)))) = X,
inference(equational,[status(thm)],[c8,c177]) ).
cnf(c180,plain,
multiply(multiply(X,Y),multiply(Y,Z)) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c4,c42,c88,c176]) ).
cnf(c181,plain,
add(inverse(X),multiply(Y,inverse(multiply(X,Y)))) = inverse(X),
inference(equational,[status(thm)],[c42,c178]) ).
cnf(c185,plain,
inverse(multiply(X,multiply(Y,inverse(multiply(X,Y))))) = multiplicative_identity,
inference(equational,[status(thm)],[c108,c142,c181]) ).
cnf(c186,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = additive_identity,
inference(equational,[status(thm)],[c13,c42,c185]) ).
cnf(c191,plain,
multiply(multiply(X,Y),multiply(Z,X)) = multiply(multiply(X,Y),Z),
inference(equational,[status(thm)],[c4,c42,c91,c160]) ).
cnf(c194,plain,
multiply(multiply(X,Y),multiply(Z,Y)) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c8,c180]) ).
cnf(c195,plain,
multiply(multiply(X,Y),Z) = multiply(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c8,c191,c194]) ).
cnf(c224,plain,
add(multiply(X,multiply(Y,Z)),multiply(X,multiply(inverse(Y),Z))) = multiply(X,Z),
inference(equational,[status(thm)],[c16,c38,c195]) ).
cnf(c225,plain,
multiply(X,inverse(multiply(X,Y))) = multiply(X,inverse(Y)),
inference(equational,[status(thm)],[c4,c110,c186,c224]) ).
cnf(c226,plain,
inverse(multiply(X,Y)) = add(inverse(X),inverse(Y)),
inference(equational,[status(thm)],[c49,c108,c225]) ).
cnf(c239,plain,
inverse(add(inverse(X),inverse(Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c42,c226]) ).
cnf(c240,plain,
inverse(add(X,inverse(Y))) = multiply(inverse(X),Y),
inference(equational,[status(thm)],[c42,c239]) ).
cnf(c313,plain,
inverse(add(X,Y)) = multiply(inverse(X),inverse(Y)),
inference(equational,[status(thm)],[c42,c240]) ).
cnf(g1,plain,
inverse(c) = d,
inference(equational,[status(thm)],[c6,c7,c15,c313]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO014-2 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n009.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 04:23:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 3.60/3.80 % SZS status Unsatisfiable
% 3.60/3.80 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------