%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG016-6 : TPTP v9.0.0. Released v1.0.0.
% 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 07:42:44 AM UTC 2025
% Result : Unsatisfiable 1.29s 1.44s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 3 RR)
% Number of literals : 19 ( 18 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 : 36 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(add(x,additive_inverse(y)),z) != add(multiply(x,z),additive_inverse(multiply(y,z))),
file('theBenchmark.p',prove_distributivity) ).
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(c4,axiom,
multiply(additive_identity,X) = additive_identity,
file('RNG003-0.ax',left_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(c14,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c16,plain,
add(X,add(Y,additive_inverse(X))) = Y,
inference(equational,[status(thm)],[c2,c8,c14]) ).
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(c53,plain,
add(multiply(add(X,Y),Z),W) = add(multiply(X,Z),add(multiply(Y,Z),W)),
inference(equational,[status(thm)],[c11,c21]) ).
cnf(c64,plain,
add(multiply(X,Y),add(multiply(additive_inverse(X),Y),Z)) = Z,
inference(equational,[status(thm)],[c1,c4,c8,c53]) ).
cnf(c65,plain,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c16,c64]) ).
cnf(c92,plain,
add(multiply(X,Y),additive_inverse(multiply(Z,Y))) = multiply(add(X,additive_inverse(Z)),Y),
inference(equational,[status(thm)],[c21,c65]) ).
cnf(g1,plain,
multiply(add(x,additive_inverse(y)),z) = add(multiply(x,z),additive_inverse(multiply(y,z))),
inference(equational,[status(thm)],[c92]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG016-6 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % 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 16:23:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.29/1.44 % SZS status Unsatisfiable
% 1.29/1.44 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------