%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : RNG009-7 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 173.47s 173.88s
% Output : CNFRefutation 173.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of clauses : 115 ( 115 unt; 0 nHn; 28 RR)
% Number of literals : 115 ( 114 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; 4 con; 0-2 aty)
% Number of variables : 181 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(b,a) != c,
file('theBenchmark.p',prove_commutativity) ).
cnf(c1,axiom,
add(additive_identity,X) = X,
file('RNG005-0.ax',left_additive_identity) ).
cnf(c2,axiom,
add(X,additive_identity) = X,
file('RNG005-0.ax',right_additive_identity) ).
cnf(c3,axiom,
multiply(a,b) = c,
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c4,axiom,
add(X,Y) = add(Y,X),
file('RNG005-0.ax',commutativity_for_addition) ).
cnf(c5,axiom,
add(X,additive_inverse(X)) = additive_identity,
file('RNG005-0.ax',right_additive_inverse) ).
cnf(c6,plain,
additive_inverse(additive_identity) = additive_identity,
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c7,axiom,
multiply(X,multiply(X,X)) = X,
file('theBenchmark.p',x_cubed_is_x) ).
cnf(c8,axiom,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
file('RNG005-0.ax',associativity_for_multiplication) ).
cnf(c9,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[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,plain,
multiply(a,multiply(b,X)) = multiply(c,X),
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c13,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c14,plain,
add(X,add(additive_inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c1,c5,c11]) ).
cnf(c15,plain,
additive_inverse(additive_inverse(X)) = X,
inference(equational,[status(thm)],[c2,c5,c14]) ).
cnf(c17,plain,
add(X,add(Y,additive_inverse(X))) = Y,
inference(equational,[status(thm)],[c2,c5,c13]) ).
cnf(c18,plain,
add(additive_inverse(X),add(Y,X)) = Y,
inference(equational,[status(thm)],[c15,c17]) ).
cnf(c19,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('RNG005-0.ax',distribute1) ).
cnf(c20,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c19]) ).
cnf(c23,plain,
multiply(a,add(X,b)) = add(c,multiply(a,X)),
inference(equational,[status(thm)],[c3,c4,c20]) ).
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(c28,plain,
multiply(add(a,X),b) = add(c,multiply(X,b)),
inference(equational,[status(thm)],[c3,c25]) ).
cnf(c29,plain,
add(c,multiply(additive_identity,b)) = c,
inference(equational,[status(thm)],[c2,c3,c28]) ).
cnf(c31,plain,
multiply(X,multiply(X,multiply(X,Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c7,c9]) ).
cnf(c32,plain,
multiply(a,multiply(a,c)) = c,
inference(equational,[status(thm)],[c3,c31]) ).
cnf(c35,plain,
multiply(X,add(multiply(X,X),Y)) = add(X,multiply(X,Y)),
inference(equational,[status(thm)],[c7,c20]) ).
cnf(c36,plain,
add(X,multiply(X,additive_identity)) = X,
inference(equational,[status(thm)],[c2,c7,c35]) ).
cnf(c37,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c1,c36]) ).
cnf(c38,plain,
multiply(additive_inverse(X),additive_identity) = additive_identity,
inference(equational,[status(thm)],[c5,c14,c36]) ).
cnf(c39,plain,
multiply(X,additive_identity) = additive_identity,
inference(equational,[status(thm)],[c15,c38]) ).
cnf(c40,plain,
multiply(additive_identity,multiply(additive_identity,X)) = multiply(additive_identity,X),
inference(equational,[status(thm)],[c9,c37]) ).
cnf(c41,plain,
multiply(X,add(Y,multiply(X,X))) = add(X,multiply(X,Y)),
inference(equational,[status(thm)],[c4,c7,c20]) ).
cnf(c43,plain,
add(X,add(Y,additive_inverse(add(X,Y)))) = additive_identity,
inference(equational,[status(thm)],[c5,c11]) ).
cnf(c44,plain,
multiply(additive_identity,b) = additive_identity,
inference(equational,[status(thm)],[c17,c29,c43]) ).
cnf(c48,plain,
multiply(additive_identity,multiply(b,X)) = multiply(additive_identity,X),
inference(equational,[status(thm)],[c9,c44]) ).
cnf(c49,plain,
add(X,additive_inverse(add(additive_inverse(Y),X))) = Y,
inference(equational,[status(thm)],[c2,c14,c43]) ).
cnf(c50,plain,
add(X,additive_inverse(add(Y,X))) = additive_inverse(Y),
inference(equational,[status(thm)],[c15,c49]) ).
cnf(c53,plain,
additive_inverse(add(X,additive_inverse(Y))) = add(Y,additive_inverse(X)),
inference(equational,[status(thm)],[c14,c50]) ).
cnf(c54,plain,
multiply(X,multiply(additive_identity,Y)) = multiply(additive_identity,Y),
inference(equational,[status(thm)],[c9,c39]) ).
cnf(c58,plain,
multiply(add(X,Y),multiply(X,X)) = add(X,multiply(Y,multiply(X,X))),
inference(equational,[status(thm)],[c7,c25]) ).
cnf(c59,plain,
add(X,multiply(additive_identity,multiply(X,X))) = X,
inference(equational,[status(thm)],[c2,c7,c58]) ).
cnf(c60,plain,
multiply(additive_identity,multiply(X,X)) = additive_identity,
inference(equational,[status(thm)],[c17,c43,c59]) ).
cnf(c61,plain,
multiply(additive_identity,X) = additive_identity,
inference(equational,[status(thm)],[c40,c54,c60]) ).
cnf(c63,plain,
multiply(a,multiply(a,multiply(c,X))) = multiply(c,X),
inference(equational,[status(thm)],[c12,c31]) ).
cnf(c64,plain,
multiply(c,multiply(b,multiply(b,X))) = multiply(c,X),
inference(equational,[status(thm)],[c12,c31]) ).
cnf(c76,plain,
add(X,add(Y,add(additive_inverse(X),Z))) = add(Y,Z),
inference(equational,[status(thm)],[c13,c14]) ).
cnf(c87,plain,
multiply(add(c,multiply(X,b)),Y) = multiply(add(a,X),multiply(b,Y)),
inference(equational,[status(thm)],[c9,c28]) ).
cnf(c91,plain,
multiply(add(c,multiply(a,X)),Y) = multiply(a,multiply(add(X,b),Y)),
inference(equational,[status(thm)],[c9,c23]) ).
cnf(c135,plain,
add(multiply(X,Y),add(multiply(X,Z),W)) = add(multiply(X,add(Y,Z)),W),
inference(equational,[status(thm)],[c11,c20]) ).
cnf(c136,plain,
add(multiply(X,multiply(Y,Z)),multiply(W,Z)) = multiply(add(multiply(X,Y),W),Z),
inference(equational,[status(thm)],[c9,c25]) ).
cnf(c149,plain,
add(multiply(X,Y),add(multiply(Z,Y),W)) = add(multiply(add(X,Z),Y),W),
inference(equational,[status(thm)],[c11,c25]) ).
cnf(c155,plain,
add(multiply(X,Y),multiply(Z,multiply(W,Y))) = multiply(add(X,multiply(Z,W)),Y),
inference(equational,[status(thm)],[c9,c25]) ).
cnf(c166,plain,
multiply(X,add(multiply(X,multiply(X,Y)),Z)) = multiply(X,add(Y,Z)),
inference(equational,[status(thm)],[c20,c31]) ).
cnf(c167,plain,
add(X,add(Y,add(additive_inverse(add(X,Y)),Z))) = Z,
inference(equational,[status(thm)],[c1,c11,c43]) ).
cnf(c168,plain,
add(X,add(additive_inverse(add(X,Y)),Z)) = add(additive_inverse(Y),Z),
inference(equational,[status(thm)],[c76,c167]) ).
cnf(c171,plain,
add(X,add(Y,additive_inverse(add(X,Z)))) = add(additive_inverse(Z),Y),
inference(equational,[status(thm)],[c4,c168]) ).
cnf(c183,plain,
multiply(add(X,multiply(Y,Z)),multiply(Z,Z)) = multiply(add(multiply(X,Z),Y),Z),
inference(equational,[status(thm)],[c7,c136,c155]) ).
cnf(c200,plain,
multiply(X,multiply(add(Y,multiply(X,X)),Z)) = multiply(add(X,multiply(X,Y)),Z),
inference(equational,[status(thm)],[c9,c41]) ).
cnf(c206,plain,
add(additive_inverse(multiply(X,Y)),multiply(add(Z,X),Y)) = multiply(Z,Y),
inference(equational,[status(thm)],[c2,c4,c43,c50,c149]) ).
cnf(c207,plain,
additive_inverse(multiply(additive_inverse(X),Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c2,c43,c50,c61,c206]) ).
cnf(c208,plain,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c49,c50,c207]) ).
cnf(c213,plain,
additive_inverse(multiply(add(X,additive_inverse(Y)),Z)) = multiply(add(Y,additive_inverse(X)),Z),
inference(equational,[status(thm)],[c53,c207]) ).
cnf(c214,plain,
add(additive_inverse(multiply(X,Y)),multiply(X,add(Z,Y))) = multiply(X,Z),
inference(equational,[status(thm)],[c2,c4,c5,c135]) ).
cnf(c215,plain,
additive_inverse(multiply(X,additive_inverse(Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c2,c39,c43,c50,c214]) ).
cnf(c216,plain,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c207,c208,c215]) ).
cnf(c223,plain,
multiply(add(multiply(X,multiply(Y,Y)),Z),Y) = multiply(add(X,Z),Y),
inference(equational,[status(thm)],[c7,c9,c25,c183]) ).
cnf(c227,plain,
multiply(X,add(Y,additive_inverse(multiply(X,multiply(X,Y))))) = additive_identity,
inference(equational,[status(thm)],[c5,c39,c166]) ).
cnf(c229,plain,
multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Y))))) = multiply(X,Y),
inference(equational,[status(thm)],[c7,c9]) ).
cnf(c230,plain,
multiply(b,multiply(c,multiply(c,a))) = multiply(b,a),
inference(equational,[status(thm)],[c12,c229]) ).
cnf(c231,plain,
multiply(c,multiply(a,multiply(c,multiply(a,c)))) = c,
inference(equational,[status(thm)],[c32,c63,c229]) ).
cnf(c234,plain,
add(multiply(X,Y),multiply(Z,add(Y,W))) = add(multiply(add(X,Z),Y),multiply(Z,W)),
inference(equational,[status(thm)],[c20,c149]) ).
cnf(c235,plain,
add(multiply(X,Y),additive_inverse(multiply(Z,Y))) = multiply(add(X,additive_inverse(Z)),Y),
inference(equational,[status(thm)],[c2,c38,c208,c234]) ).
cnf(c295,plain,
multiply(b,multiply(c,multiply(c,multiply(a,X)))) = multiply(b,multiply(a,X)),
inference(equational,[status(thm)],[c9,c230]) ).
cnf(c416,plain,
multiply(a,multiply(a,multiply(add(a,b),X))) = multiply(add(a,multiply(a,c)),X),
inference(equational,[status(thm)],[c91,c200]) ).
cnf(c426,plain,
multiply(a,multiply(add(b,additive_inverse(multiply(a,c))),X)) = additive_identity,
inference(equational,[status(thm)],[c4,c11,c171,c227,c235,c416]) ).
cnf(c427,plain,
multiply(add(b,additive_inverse(multiply(a,c))),a) = additive_identity,
inference(equational,[status(thm)],[c39,c229,c426]) ).
cnf(c428,plain,
multiply(a,multiply(c,a)) = multiply(b,a),
inference(equational,[status(thm)],[c2,c9,c15,c206,c208,c427]) ).
cnf(c432,plain,
multiply(a,multiply(c,multiply(a,X))) = multiply(b,multiply(a,X)),
inference(equational,[status(thm)],[c9,c428]) ).
cnf(c435,plain,
multiply(b,multiply(b,multiply(a,c))) = multiply(a,c),
inference(equational,[status(thm)],[c229,c432]) ).
cnf(c447,plain,
multiply(c,multiply(X,multiply(b,multiply(X,multiply(b,X))))) = multiply(c,X),
inference(equational,[status(thm)],[c12,c229]) ).
cnf(c464,plain,
multiply(b,multiply(c,c)) = multiply(a,c),
inference(equational,[status(thm)],[c231,c295,c432,c435]) ).
cnf(c467,plain,
multiply(add(multiply(a,c),X),c) = multiply(add(b,X),c),
inference(equational,[status(thm)],[c223,c464]) ).
cnf(c469,plain,
multiply(b,multiply(c,multiply(c,X))) = multiply(a,multiply(c,X)),
inference(equational,[status(thm)],[c9,c464]) ).
cnf(c474,plain,
multiply(a,multiply(c,multiply(c,X))) = multiply(b,multiply(c,X)),
inference(equational,[status(thm)],[c31,c469]) ).
cnf(c489,plain,
multiply(add(multiply(c,b),X),multiply(b,Y)) = multiply(add(a,X),multiply(b,Y)),
inference(equational,[status(thm)],[c64,c87,c136,c155]) ).
cnf(c490,plain,
multiply(add(a,additive_inverse(multiply(c,b))),multiply(b,X)) = additive_identity,
inference(equational,[status(thm)],[c43,c48,c50,c61,c489]) ).
cnf(c491,plain,
multiply(c,add(a,additive_inverse(multiply(c,b)))) = additive_identity,
inference(equational,[status(thm)],[c39,c447,c490]) ).
cnf(c492,plain,
multiply(c,multiply(c,b)) = multiply(c,a),
inference(equational,[status(thm)],[c2,c15,c214,c216,c491]) ).
cnf(c493,plain,
multiply(b,multiply(c,b)) = multiply(b,a),
inference(equational,[status(thm)],[c428,c474,c492]) ).
cnf(c494,plain,
multiply(c,multiply(c,a)) = multiply(c,b),
inference(equational,[status(thm)],[c31,c492]) ).
cnf(c495,plain,
multiply(b,multiply(c,a)) = multiply(a,multiply(c,b)),
inference(equational,[status(thm)],[c469,c492]) ).
cnf(c499,plain,
multiply(c,multiply(c,multiply(b,X))) = multiply(c,multiply(a,X)),
inference(equational,[status(thm)],[c9,c492]) ).
cnf(c512,plain,
multiply(add(b,multiply(X,c)),a) = multiply(add(X,a),multiply(c,a)),
inference(equational,[status(thm)],[c4,c25,c136,c428]) ).
cnf(c654,plain,
multiply(c,multiply(a,multiply(c,b))) = multiply(c,multiply(a,a)),
inference(equational,[status(thm)],[c493,c499]) ).
cnf(c813,plain,
multiply(add(b,additive_inverse(multiply(X,c))),c) = multiply(add(a,additive_inverse(X)),multiply(c,c)),
inference(equational,[status(thm)],[c9,c235,c467]) ).
cnf(c869,plain,
add(multiply(X,multiply(Y,Z)),multiply(W,multiply(V,Z))) = multiply(add(multiply(X,Y),multiply(W,V)),Z),
inference(equational,[status(thm)],[c9,c155]) ).
cnf(c879,plain,
add(multiply(X,multiply(Y,multiply(Z,W))),multiply(V,W)) = multiply(add(multiply(X,multiply(Y,Z)),V),W),
inference(equational,[status(thm)],[c9,c136]) ).
cnf(c880,plain,
multiply(add(multiply(a,c),X),multiply(a,Y)) = multiply(add(b,X),multiply(a,Y)),
inference(equational,[status(thm)],[c9,c25,c295,c464,c869,c879]) ).
cnf(c883,plain,
multiply(add(multiply(a,c),X),multiply(c,Y)) = multiply(add(b,X),multiply(c,Y)),
inference(equational,[status(thm)],[c63,c880]) ).
cnf(c959,plain,
multiply(X,multiply(add(multiply(X,multiply(X,Y)),Z),W)) = multiply(X,multiply(add(Y,Z),W)),
inference(equational,[status(thm)],[c25,c166,c879]) ).
cnf(c960,plain,
multiply(b,multiply(add(multiply(c,b),X),Y)) = multiply(b,multiply(add(a,X),Y)),
inference(equational,[status(thm)],[c230,c494,c959]) ).
cnf(c964,plain,
multiply(c,multiply(add(multiply(c,b),X),Y)) = multiply(c,multiply(add(a,X),Y)),
inference(equational,[status(thm)],[c12,c960]) ).
cnf(c1002,plain,
multiply(c,multiply(add(a,additive_inverse(multiply(c,b))),X)) = additive_identity,
inference(equational,[status(thm)],[c39,c43,c50,c61,c964]) ).
cnf(c1003,plain,
multiply(add(a,additive_inverse(multiply(c,b))),c) = additive_identity,
inference(equational,[status(thm)],[c39,c229,c1002]) ).
cnf(c1005,plain,
multiply(c,multiply(a,c)) = multiply(b,c),
inference(equational,[status(thm)],[c2,c6,c9,c17,c53,c464,c813,c1003]) ).
cnf(c1008,plain,
multiply(add(additive_inverse(a),multiply(c,b)),c) = additive_identity,
inference(equational,[status(thm)],[c4,c6,c213,c1003]) ).
cnf(c1009,plain,
multiply(c,multiply(a,a)) = multiply(b,a),
inference(equational,[status(thm)],[c2,c9,c11,c18,c495,c512,c654,c1008]) ).
cnf(c1032,plain,
multiply(add(b,additive_inverse(multiply(a,c))),multiply(c,X)) = additive_identity,
inference(equational,[status(thm)],[c43,c50,c61,c883]) ).
cnf(c1033,plain,
multiply(c,add(b,additive_inverse(multiply(a,c)))) = additive_identity,
inference(equational,[status(thm)],[c39,c229,c1032]) ).
cnf(c1034,plain,
multiply(c,b) = multiply(b,c),
inference(equational,[status(thm)],[c2,c15,c214,c216,c1005,c1033]) ).
cnf(c1035,plain,
multiply(b,a) = c,
inference(equational,[status(thm)],[c7,c12,c654,c1009,c1034]) ).
cnf(g1,plain,
multiply(b,a) = c,
inference(equational,[status(thm)],[c1035]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG009-7 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 16:23:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 173.47/173.88 % SZS status Unsatisfiable
% 173.47/173.88 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------