%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG024-6 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.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 07:42:45 AM UTC 2025
% Result : Unsatisfiable 1.02s 1.20s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 4 RR)
% Number of literals : 20 ( 19 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
associator(x,y,y) != additive_identity,
file('theBenchmark.p',prove_right_alternative) ).
cnf(c1,axiom,
add(additive_identity,X) = X,
file('RNG003-0.ax',left_additive_identity) ).
cnf(c2,axiom,
add(X,additive_identity) = X,
file('RNG003-0.ax',right_additive_identity) ).
cnf(c3,axiom,
additive_inverse(additive_inverse(X)) = X,
file('RNG003-0.ax',additive_inverse_additive_inverse) ).
cnf(c6,axiom,
add(X,Y) = add(Y,X),
file('RNG003-0.ax',commutativity_for_addition) ).
cnf(c7,axiom,
add(additive_inverse(X),X) = additive_identity,
file('RNG003-0.ax',left_additive_inverse) ).
cnf(c8,plain,
add(X,additive_inverse(X)) = additive_identity,
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
additive_inverse(additive_identity) = additive_identity,
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c10,axiom,
add(X,add(Y,Z)) = add(add(X,Y),Z),
file('RNG003-0.ax',associativity_for_addition) ).
cnf(c11,plain,
add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)),
file('RNG003-0.ax',right_alternative) ).
cnf(c15,plain,
add(X,add(additive_inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c1,c8,c11]) ).
cnf(c24,plain,
add(X,add(Y,additive_inverse(add(X,Y)))) = additive_identity,
inference(equational,[status(thm)],[c8,c11]) ).
cnf(c25,plain,
add(X,additive_inverse(add(additive_inverse(Y),X))) = Y,
inference(equational,[status(thm)],[c2,c15,c24]) ).
cnf(c26,plain,
add(X,additive_inverse(add(Y,X))) = additive_inverse(Y),
inference(equational,[status(thm)],[c3,c25]) ).
cnf(c27,plain,
add(X,additive_inverse(Y)) = additive_inverse(add(Y,additive_inverse(X))),
inference(equational,[status(thm)],[c15,c26]) ).
cnf(c60,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))),
file('RNG003-0.ax',associator) ).
cnf(c61,plain,
associator(X,Y,Z) = additive_inverse(add(multiply(X,multiply(Y,Z)),additive_inverse(multiply(multiply(X,Y),Z)))),
inference(equational,[status(thm)],[c27,c60]) ).
cnf(g1,plain,
associator(x,y,y) = additive_identity,
inference(equational,[status(thm)],[c8,c9,c12,c61]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : RNG024-6 : TPTP v9.0.0. Released v1.0.0.
% 0.08/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n005.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 16:24:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.02/1.20 % SZS status Unsatisfiable
% 1.02/1.20 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------