%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG007-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 0.63s 0.84s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 3 RR)
% Number of literals : 15 ( 14 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(a,a) != additive_identity,
file('theBenchmark.p',prove_inverse) ).
cnf(c2,axiom,
multiply(X,X) = X,
file('theBenchmark.p',boolean_ring) ).
cnf(c4,axiom,
additive_inverse(additive_inverse(X)) = X,
file('RNG002-0.ax',additive_inverse_additive_inverse) ).
cnf(c7,axiom,
add(X,Y) = add(Y,X),
file('RNG002-0.ax',commutative_addition) ).
cnf(c9,axiom,
add(additive_inverse(X),X) = additive_identity,
file('RNG002-0.ax',left_additive_inverse) ).
cnf(c10,plain,
add(X,additive_inverse(X)) = additive_identity,
inference(equational,[status(thm)],[c7,c9]) ).
cnf(c11,axiom,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
file('RNG002-0.ax',multiply_additive_inverse1) ).
cnf(c12,plain,
additive_inverse(multiply(X,Y)) = multiply(X,additive_inverse(Y)),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,axiom,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
file('RNG002-0.ax',multiply_additive_inverse2) ).
cnf(c14,plain,
multiply(additive_inverse(X),Y) = multiply(X,additive_inverse(Y)),
inference(equational,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
multiply(X,additive_inverse(X)) = additive_inverse(X),
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c16,plain,
additive_inverse(X) = X,
inference(equational,[status(thm)],[c4,c14,c15]) ).
cnf(c17,plain,
add(X,X) = additive_identity,
inference(equational,[status(thm)],[c10,c16]) ).
cnf(g1,plain,
add(a,a) = additive_identity,
inference(equational,[status(thm)],[c17]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG007-4 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 14 16:22:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.63/0.84 % SZS status Unsatisfiable
% 0.63/0.84 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------