%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG008-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 07:42:42 AM UTC 2025
% Result : Unsatisfiable 0.75s 0.90s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 5 RR)
% Number of literals : 32 ( 31 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(b,a) != c,
file('theBenchmark.p',prove_commutativity) ).
cnf(c2,axiom,
multiply(X,X) = X,
file('theBenchmark.p',boolean_ring) ).
cnf(c3,axiom,
add(additive_identity,X) = X,
file('RNG002-0.ax',left_identity) ).
cnf(c4,axiom,
additive_inverse(additive_inverse(X)) = X,
file('RNG002-0.ax',additive_inverse_additive_inverse) ).
cnf(c7,axiom,
multiply(a,b) = c,
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c8,plain,
c = multiply(a,b),
inference(equational,[status(thm)],[c7]) ).
cnf(c9,axiom,
add(X,Y) = add(Y,X),
file('RNG002-0.ax',commutative_addition) ).
cnf(c11,axiom,
add(additive_inverse(X),X) = additive_identity,
file('RNG002-0.ax',left_additive_inverse) ).
cnf(c12,plain,
add(X,additive_inverse(X)) = additive_identity,
inference(equational,[status(thm)],[c9,c11]) ).
cnf(c13,axiom,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
file('RNG002-0.ax',multiply_additive_inverse2) ).
cnf(c14,plain,
additive_inverse(multiply(X,Y)) = multiply(additive_inverse(X),Y),
inference(equational,[status(thm)],[c13]) ).
cnf(c15,axiom,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
file('RNG002-0.ax',multiply_additive_inverse1) ).
cnf(c16,plain,
multiply(X,additive_inverse(Y)) = multiply(additive_inverse(X),Y),
inference(equational,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
multiply(X,additive_inverse(X)) = additive_inverse(X),
inference(equational,[status(thm)],[c2,c14,c16]) ).
cnf(c18,plain,
additive_inverse(X) = X,
inference(equational,[status(thm)],[c2,c4,c14,c17]) ).
cnf(c20,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('RNG002-0.ax',associative_multiplication) ).
cnf(c21,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)),
file('RNG002-0.ax',associative_addition) ).
cnf(c22,plain,
add(X,add(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c12,c18,c21]) ).
cnf(c23,plain,
multiply(X,multiply(X,Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c2,c20]) ).
cnf(c24,plain,
add(X,add(Y,X)) = Y,
inference(equational,[status(thm)],[c9,c22]) ).
cnf(c25,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c9,c21]) ).
cnf(c26,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('RNG002-0.ax',distribute1) ).
cnf(c27,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('RNG002-0.ax',distribute2) ).
cnf(c29,plain,
add(X,add(Y,add(X,Z))) = add(Y,Z),
inference(equational,[status(thm)],[c22,c25]) ).
cnf(c30,plain,
add(X,add(Y,add(Z,X))) = add(Y,Z),
inference(equational,[status(thm)],[c24,c25]) ).
cnf(c33,plain,
add(X,add(Y,add(multiply(Y,X),multiply(X,Y)))) = add(X,Y),
inference(equational,[status(thm)],[c2,c9,c21,c25,c26,c27]) ).
cnf(c34,plain,
add(X,multiply(X,multiply(Y,X))) = add(X,multiply(X,Y)),
inference(equational,[status(thm)],[c9,c20,c23,c29,c33]) ).
cnf(c35,plain,
multiply(X,multiply(Y,X)) = multiply(X,Y),
inference(equational,[status(thm)],[c22,c34]) ).
cnf(c36,plain,
add(X,multiply(X,Y)) = add(X,multiply(Y,X)),
inference(equational,[status(thm)],[c2,c9,c20,c30,c33,c35]) ).
cnf(c37,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c22,c36]) ).
cnf(g1,plain,
multiply(b,a) = c,
inference(equational,[status(thm)],[c8,c37]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : RNG008-4 : TPTP v9.0.0. Released v1.0.0.
% 0.01/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n002.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 16:22:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.75/0.90 % SZS status Unsatisfiable
% 0.75/0.90 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------