%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO013-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 06:14:45 AM UTC 2025
% Result : Unsatisfiable 0.79s 0.94s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 13 RR)
% Number of literals : 31 ( 30 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
b != c,
file('theBenchmark.p',prove_b_is_a) ).
cnf(c1,axiom,
multiply(X,multiplicative_identity) = X,
file('BOO003-0.ax',multiplicative_id1) ).
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) = multiplicative_identity,
file('theBenchmark.p',b_and_multiplicative_identity) ).
cnf(c6,plain,
multiplicative_identity = add(a,b),
inference(equational,[status(thm)],[c5]) ).
cnf(c7,axiom,
add(a,c) = multiplicative_identity,
file('theBenchmark.p',c_and_multiplicative_identity) ).
cnf(c8,plain,
add(a,b) = add(a,c),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,axiom,
multiply(a,b) = additive_identity,
file('theBenchmark.p',b_a_additive_identity) ).
cnf(c10,plain,
additive_identity = multiply(a,b),
inference(equational,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(a,c) = additive_identity,
file('theBenchmark.p',c_a_additive_identity) ).
cnf(c12,plain,
multiply(a,b) = multiply(a,c),
inference(equational,[status(thm)],[c10,c11]) ).
cnf(c13,axiom,
add(X,Y) = add(Y,X),
file('BOO003-0.ax',commutativity_of_add) ).
cnf(c14,axiom,
multiply(X,Y) = multiply(Y,X),
file('BOO003-0.ax',commutativity_of_multiply) ).
cnf(c22,plain,
multiply(add(a,c),X) = X,
inference(equational,[status(thm)],[c1,c6,c8,c14]) ).
cnf(c23,plain,
add(multiply(a,c),X) = X,
inference(equational,[status(thm)],[c3,c10,c12,c13]) ).
cnf(c24,plain,
add(X,multiply(a,c)) = X,
inference(equational,[status(thm)],[c4,c10,c12,c13]) ).
cnf(c25,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('BOO003-0.ax',distributivity2) ).
cnf(c34,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('BOO003-0.ax',distributivity3) ).
cnf(c35,plain,
multiply(multiply(add(X,Y),add(X,X)),add(multiply(Y,X),Z)) = multiply(add(Y,Z),X),
inference(equational,[status(thm)],[c13,c14,c25,c34]) ).
cnf(c36,axiom,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
file('BOO003-0.ax',distributivity1) ).
cnf(c37,plain,
multiply(add(a,X),add(b,X)) = X,
inference(equational,[status(thm)],[c12,c23,c36]) ).
cnf(c51,plain,
multiply(add(X,a),add(b,X)) = X,
inference(equational,[status(thm)],[c13,c37]) ).
cnf(c52,plain,
multiply(b,X) = multiply(add(a,X),b),
inference(equational,[status(thm)],[c12,c23,c35,c51]) ).
cnf(c55,plain,
multiply(add(a,X),b) = multiply(X,b),
inference(equational,[status(thm)],[c14,c52]) ).
cnf(c56,plain,
multiply(c,b) = b,
inference(equational,[status(thm)],[c22,c55]) ).
cnf(c58,plain,
multiply(add(X,a),add(X,c)) = X,
inference(equational,[status(thm)],[c24,c25]) ).
cnf(c63,plain,
multiply(c,X) = multiply(add(a,X),c),
inference(equational,[status(thm)],[c23,c35,c58]) ).
cnf(c64,plain,
b = c,
inference(equational,[status(thm)],[c8,c22,c56,c63]) ).
cnf(g1,plain,
b = c,
inference(equational,[status(thm)],[c64]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : BOO013-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n004.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 :
% 0.79/0.94 % SZS status Unsatisfiable
% 0.79/0.94 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------