%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG025-6 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.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 07:42:46 AM UTC 2025
% Result : Unsatisfiable 116.48s 116.84s
% Output : CNFRefutation 116.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 3 RR)
% Number of literals : 52 ( 51 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; 3 con; 0-3 aty)
% Number of variables : 117 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
associator(x,y,x) != additive_identity,
file('theBenchmark.p',prove_flexible_law) ).
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(c4,axiom,
multiply(additive_identity,X) = additive_identity,
file('RNG003-0.ax',left_multiplicative_zero) ).
cnf(c5,axiom,
multiply(X,additive_identity) = additive_identity,
file('RNG003-0.ax',right_multiplicative_zero) ).
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(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(c13,axiom,
multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)),
file('RNG003-0.ax',left_alternative) ).
cnf(c14,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c15,plain,
add(X,add(additive_inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c1,c8,c11]) ).
cnf(c16,plain,
add(X,add(Y,additive_inverse(X))) = Y,
inference(equational,[status(thm)],[c2,c8,c14]) ).
cnf(c18,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('RNG003-0.ax',distribute1) ).
cnf(c19,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c18]) ).
cnf(c20,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('RNG003-0.ax',distribute2) ).
cnf(c21,plain,
add(multiply(X,Y),multiply(Z,Y)) = multiply(add(X,Z),Y),
inference(equational,[status(thm)],[c20]) ).
cnf(c28,plain,
add(X,add(Y,additive_inverse(add(X,Y)))) = additive_identity,
inference(equational,[status(thm)],[c8,c11]) ).
cnf(c29,plain,
add(X,additive_inverse(add(additive_inverse(Y),X))) = Y,
inference(equational,[status(thm)],[c2,c15,c28]) ).
cnf(c30,plain,
add(X,additive_inverse(add(Y,X))) = additive_inverse(Y),
inference(equational,[status(thm)],[c3,c29]) ).
cnf(c31,plain,
additive_inverse(add(X,additive_inverse(Y))) = add(Y,additive_inverse(X)),
inference(equational,[status(thm)],[c15,c30]) ).
cnf(c35,plain,
additive_inverse(add(additive_inverse(X),Y)) = add(X,additive_inverse(Y)),
inference(equational,[status(thm)],[c6,c31]) ).
cnf(c65,plain,
add(multiply(X,multiply(X,Y)),multiply(Z,Y)) = multiply(add(multiply(X,X),Z),Y),
inference(equational,[status(thm)],[c13,c21]) ).
cnf(c66,plain,
add(multiply(X,Y),add(multiply(X,Z),W)) = add(multiply(X,add(Y,Z)),W),
inference(equational,[status(thm)],[c11,c19]) ).
cnf(c67,plain,
add(multiply(X,Y),add(multiply(Z,Y),W)) = add(multiply(add(X,Z),Y),W),
inference(equational,[status(thm)],[c11,c21]) ).
cnf(c92,plain,
add(additive_inverse(multiply(X,Y)),multiply(X,add(Z,Y))) = multiply(X,Z),
inference(equational,[status(thm)],[c2,c6,c28,c30,c66]) ).
cnf(c93,plain,
additive_inverse(multiply(X,additive_inverse(Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c2,c5,c28,c30,c92]) ).
cnf(c94,plain,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c29,c30,c93]) ).
cnf(c120,plain,
additive_inverse(multiply(X,add(Y,additive_inverse(Z)))) = multiply(X,add(Z,additive_inverse(Y))),
inference(equational,[status(thm)],[c31,c94]) ).
cnf(c124,plain,
add(additive_inverse(multiply(X,Y)),multiply(add(Z,X),Y)) = multiply(Z,Y),
inference(equational,[status(thm)],[c2,c6,c8,c67]) ).
cnf(c125,plain,
additive_inverse(multiply(additive_inverse(X),Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c2,c4,c28,c30,c124]) ).
cnf(c126,plain,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c93,c94,c125]) ).
cnf(c133,plain,
additive_inverse(multiply(add(X,additive_inverse(Y)),Z)) = multiply(add(Y,additive_inverse(X)),Z),
inference(equational,[status(thm)],[c31,c126]) ).
cnf(c145,plain,
additive_inverse(multiply(add(additive_inverse(X),Y),Z)) = multiply(add(X,additive_inverse(Y)),Z),
inference(equational,[status(thm)],[c6,c133]) ).
cnf(c187,plain,
add(additive_inverse(multiply(X,Y)),multiply(X,add(Y,Z))) = multiply(X,Z),
inference(equational,[status(thm)],[c6,c29,c92]) ).
cnf(c188,plain,
add(additive_inverse(multiply(X,Y)),multiply(X,Z)) = multiply(X,add(Z,additive_inverse(Y))),
inference(equational,[status(thm)],[c29,c35,c187]) ).
cnf(c189,plain,
add(multiply(X,Y),additive_inverse(multiply(X,Z))) = multiply(X,add(Y,additive_inverse(Z))),
inference(equational,[status(thm)],[c120,c125,c126,c188]) ).
cnf(c190,plain,
add(additive_inverse(multiply(X,Y)),multiply(add(X,Z),Y)) = multiply(Z,Y),
inference(equational,[status(thm)],[c6,c29,c124]) ).
cnf(c191,plain,
add(additive_inverse(multiply(X,Y)),multiply(Z,Y)) = multiply(add(additive_inverse(X),Z),Y),
inference(equational,[status(thm)],[c15,c190]) ).
cnf(c192,plain,
add(multiply(X,Y),additive_inverse(multiply(Z,Y))) = multiply(add(X,additive_inverse(Z)),Y),
inference(equational,[status(thm)],[c3,c94,c145,c191]) ).
cnf(c200,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))),
file('RNG003-0.ax',associator) ).
cnf(c201,plain,
add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) = associator(X,Y,Z),
inference(equational,[status(thm)],[c200]) ).
cnf(c732,plain,
add(multiply(X,multiply(X,Y)),multiply(Z,multiply(Y,Y))) = multiply(add(multiply(X,X),multiply(Z,Y)),Y),
inference(equational,[status(thm)],[c12,c65]) ).
cnf(c733,plain,
multiply(multiply(X,add(X,Y)),Y) = multiply(X,multiply(add(X,Y),Y)),
inference(equational,[status(thm)],[c19,c21,c732]) ).
cnf(c744,plain,
multiply(multiply(X,Y),add(Y,X)) = multiply(X,multiply(Y,add(Y,X))),
inference(equational,[status(thm)],[c3,c30,c94,c126,c733]) ).
cnf(c746,plain,
multiply(multiply(X,Y),X) = multiply(X,multiply(Y,X)),
inference(equational,[status(thm)],[c11,c12,c16,c187,c188,c189,c744]) ).
cnf(c747,plain,
associator(X,Y,X) = additive_identity,
inference(equational,[status(thm)],[c4,c8,c192,c201,c746]) ).
cnf(g1,plain,
associator(x,y,x) = additive_identity,
inference(equational,[status(thm)],[c747]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : RNG025-6 : TPTP v9.0.0. Released v1.0.0.
% 0.05/0.10 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n013.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Jul 14 16:24:19 EDT 2025
% 0.10/0.31 % CPUTime :
% 116.48/116.84 % SZS status Unsatisfiable
% 116.48/116.84 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------