%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG008-7 : 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 07:42:43 AM UTC 2025
% Result : Unsatisfiable 0.82s 1.02s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of clauses : 53 ( 53 unt; 0 nHn; 6 RR)
% Number of literals : 53 ( 52 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 : 97 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(b,a) != c,
file('theBenchmark.p',prove_commutativity) ).
cnf(c1,axiom,
multiply(X,X) = X,
file('theBenchmark.p',boolean_ring) ).
cnf(c2,axiom,
add(X,additive_identity) = X,
file('RNG005-0.ax',right_additive_identity) ).
cnf(c3,axiom,
add(additive_identity,X) = X,
file('RNG005-0.ax',left_additive_identity) ).
cnf(c4,axiom,
multiply(a,b) = c,
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c5,plain,
c = multiply(a,b),
inference(equational,[status(thm)],[c4]) ).
cnf(c6,axiom,
add(X,Y) = add(Y,X),
file('RNG005-0.ax',commutativity_for_addition) ).
cnf(c7,axiom,
add(additive_inverse(X),X) = additive_identity,
file('RNG005-0.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)],[c3,c8]) ).
cnf(c10,axiom,
add(X,add(Y,Z)) = add(add(X,Y),Z),
file('RNG005-0.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(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
file('RNG005-0.ax',associativity_for_multiplication) ).
cnf(c13,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(X,multiply(X,Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c1,c13]) ).
cnf(c15,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c16,plain,
add(X,add(additive_inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c3,c8,c11]) ).
cnf(c17,plain,
additive_inverse(additive_inverse(X)) = X,
inference(equational,[status(thm)],[c2,c8,c16]) ).
cnf(c18,plain,
add(X,add(Y,additive_inverse(X))) = Y,
inference(equational,[status(thm)],[c2,c8,c15]) ).
cnf(c19,plain,
add(additive_inverse(X),add(Y,X)) = Y,
inference(equational,[status(thm)],[c17,c18]) ).
cnf(c20,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('RNG005-0.ax',distribute1) ).
cnf(c21,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c20]) ).
cnf(c22,plain,
add(X,multiply(X,Y)) = multiply(X,add(X,Y)),
inference(equational,[status(thm)],[c1,c21]) ).
cnf(c23,plain,
multiply(X,add(X,X)) = add(X,X),
inference(equational,[status(thm)],[c1,c22]) ).
cnf(c24,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('RNG005-0.ax',distribute2) ).
cnf(c25,plain,
add(multiply(X,Y),multiply(Z,Y)) = multiply(add(X,Z),Y),
inference(equational,[status(thm)],[c24]) ).
cnf(c27,plain,
add(X,multiply(Y,X)) = multiply(add(X,Y),X),
inference(equational,[status(thm)],[c1,c25]) ).
cnf(c31,plain,
add(X,add(Y,additive_inverse(add(X,Y)))) = additive_identity,
inference(equational,[status(thm)],[c8,c11]) ).
cnf(c32,plain,
add(X,additive_inverse(add(additive_inverse(Y),X))) = Y,
inference(equational,[status(thm)],[c2,c16,c31]) ).
cnf(c33,plain,
add(X,additive_inverse(add(Y,X))) = additive_inverse(Y),
inference(equational,[status(thm)],[c17,c32]) ).
cnf(c34,plain,
add(X,additive_inverse(Y)) = additive_inverse(add(Y,additive_inverse(X))),
inference(equational,[status(thm)],[c16,c33]) ).
cnf(c36,plain,
add(additive_inverse(X),Y) = additive_inverse(add(X,additive_inverse(Y))),
inference(equational,[status(thm)],[c6,c34]) ).
cnf(c38,plain,
multiply(X,add(Y,multiply(X,Z))) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c14,c21]) ).
cnf(c41,plain,
add(multiply(X,add(X,Y)),Z) = add(X,add(multiply(X,Y),Z)),
inference(equational,[status(thm)],[c11,c22]) ).
cnf(c42,plain,
add(X,add(multiply(X,additive_identity),Y)) = add(X,Y),
inference(equational,[status(thm)],[c1,c2,c41]) ).
cnf(c43,plain,
multiply(X,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c8,c18,c42]) ).
cnf(c45,plain,
add(X,multiply(Y,add(Y,Z))) = add(Y,add(X,multiply(Y,Z))),
inference(equational,[status(thm)],[c15,c22]) ).
cnf(c50,plain,
add(X,multiply(add(Y,Z),Y)) = add(Y,add(X,multiply(Z,Y))),
inference(equational,[status(thm)],[c15,c27]) ).
cnf(c51,plain,
add(X,add(Y,multiply(additive_identity,X))) = add(Y,X),
inference(equational,[status(thm)],[c1,c2,c50]) ).
cnf(c52,plain,
multiply(additive_identity,X) = additive_identity,
inference(equational,[status(thm)],[c8,c9,c16,c36,c51]) ).
cnf(c60,plain,
multiply(X,multiply(add(Y,X),Y)) = multiply(X,add(Y,Y)),
inference(equational,[status(thm)],[c27,c38]) ).
cnf(c61,plain,
multiply(additive_inverse(X),add(X,X)) = additive_identity,
inference(equational,[status(thm)],[c31,c33,c43,c52,c60]) ).
cnf(c62,plain,
multiply(additive_inverse(X),X) = additive_inverse(X),
inference(equational,[status(thm)],[c2,c9,c19,c22,c36,c61]) ).
cnf(c63,plain,
multiply(X,additive_inverse(X)) = X,
inference(equational,[status(thm)],[c17,c62]) ).
cnf(c64,plain,
add(X,X) = additive_identity,
inference(equational,[status(thm)],[c8,c22,c43,c63]) ).
cnf(c66,plain,
add(X,add(X,Y)) = Y,
inference(equational,[status(thm)],[c2,c8,c11,c23,c50,c61,c64]) ).
cnf(c67,plain,
add(X,add(Y,X)) = Y,
inference(equational,[status(thm)],[c6,c66]) ).
cnf(c72,plain,
add(X,multiply(Y,add(Z,Y))) = add(Y,add(X,multiply(Y,Z))),
inference(equational,[status(thm)],[c6,c45]) ).
cnf(c78,plain,
add(X,multiply(add(Y,Z),Z)) = add(Z,add(X,multiply(Y,Z))),
inference(equational,[status(thm)],[c6,c50]) ).
cnf(c86,plain,
add(X,add(Y,multiply(Z,X))) = add(Y,multiply(X,add(X,Z))),
inference(equational,[status(thm)],[c11,c66,c67,c72,c78]) ).
cnf(c87,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c22,c27,c66,c86]) ).
cnf(g1,plain,
multiply(b,a) = c,
inference(equational,[status(thm)],[c5,c87]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG008-7 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 14 16:22:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.82/1.02 % SZS status Unsatisfiable
% 0.82/1.02 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------