TSTP Solution File: RNG024-7 by Metis---2.4

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : RNG024-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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  : 600s
% DateTime : Mon Jul 18 20:35:47 EDT 2022

% Result   : Unsatisfiable 0.19s 0.38s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   40 (  23 unt;   0 nHn;  20 RR)
%            Number of literals    :   66 (  65 equ;  28 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   67 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_multiplicative_zero,axiom,
    multiply(additive_identity,X) = additive_identity ).

cnf(right_additive_inverse,axiom,
    add(X,additive_inverse(X)) = additive_identity ).

cnf(right_alternative,axiom,
    multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ).

cnf(associator,axiom,
    associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ).

cnf(distributivity_of_difference2,axiom,
    multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ).

cnf(prove_right_alternative,negated_conjecture,
    associator(x,y,y) != additive_identity ).

cnf(refute_0_0,plain,
    associator(X_25,X_27,X_27) = add(multiply(multiply(X_25,X_27),X_27),additive_inverse(multiply(X_25,multiply(X_27,X_27)))),
    inference(subst,[],[associator:[bind(X,$fot(X_25)),bind(Y,$fot(X_27)),bind(Z,$fot(X_27))]]) ).

cnf(refute_0_1,plain,
    multiply(multiply(X_25,X_27),X_27) = multiply(X_25,multiply(X_27,X_27)),
    inference(subst,[],[right_alternative:[bind(X,$fot(X_25)),bind(Y,$fot(X_27))]]) ).

cnf(refute_0_2,plain,
    ( multiply(multiply(X_25,X_27),X_27) != multiply(X_25,multiply(X_27,X_27))
    | associator(X_25,X_27,X_27) != add(multiply(multiply(X_25,X_27),X_27),additive_inverse(multiply(X_25,multiply(X_27,X_27))))
    | associator(X_25,X_27,X_27) = add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) ),
    introduced(tautology,[equality,[$cnf( $equal(associator(X_25,X_27,X_27),add(multiply(multiply(X_25,X_27),X_27),additive_inverse(multiply(X_25,multiply(X_27,X_27))))) ),[1,0],$fot(multiply(X_25,multiply(X_27,X_27)))]]) ).

cnf(refute_0_3,plain,
    ( associator(X_25,X_27,X_27) != add(multiply(multiply(X_25,X_27),X_27),additive_inverse(multiply(X_25,multiply(X_27,X_27))))
    | associator(X_25,X_27,X_27) = add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_25,X_27),X_27),multiply(X_25,multiply(X_27,X_27))) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    associator(X_25,X_27,X_27) = add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))),
    inference(resolve,[$cnf( $equal(associator(X_25,X_27,X_27),add(multiply(multiply(X_25,X_27),X_27),additive_inverse(multiply(X_25,multiply(X_27,X_27))))) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    multiply(additive_identity,multiply(X_27,X_27)) = additive_identity,
    inference(subst,[],[left_multiplicative_zero:[bind(X,$fot(multiply(X_27,X_27)))]]) ).

cnf(refute_0_6,plain,
    add(X_25,additive_inverse(X_25)) = additive_identity,
    inference(subst,[],[right_additive_inverse:[bind(X,$fot(X_25))]]) ).

cnf(refute_0_7,plain,
    multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) = multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)),
    introduced(tautology,[refl,[$fot(multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)))]]) ).

cnf(refute_0_8,plain,
    ( multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) != multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27))
    | add(X_25,additive_inverse(X_25)) != additive_identity
    | multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) = multiply(additive_identity,multiply(X_27,X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)),multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27))) ),[1,0],$fot(additive_identity)]]) ).

cnf(refute_0_9,plain,
    ( add(X_25,additive_inverse(X_25)) != additive_identity
    | multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) = multiply(additive_identity,multiply(X_27,X_27)) ),
    inference(resolve,[$cnf( $equal(multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)),multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27))) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) = multiply(additive_identity,multiply(X_27,X_27)),
    inference(resolve,[$cnf( $equal(add(X_25,additive_inverse(X_25)),additive_identity) )],[refute_0_6,refute_0_9]) ).

cnf(refute_0_11,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_12,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_13,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_15,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) != multiply(additive_identity,multiply(X_27,X_27))
    | multiply(additive_identity,multiply(X_27,X_27)) != additive_identity
    | multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) = additive_identity ),
    inference(subst,[],[refute_0_15:[bind(X0,$fot(multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)))),bind(Y0,$fot(multiply(additive_identity,multiply(X_27,X_27)))),bind(Z0,$fot(additive_identity))]]) ).

cnf(refute_0_17,plain,
    ( multiply(additive_identity,multiply(X_27,X_27)) != additive_identity
    | multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) = additive_identity ),
    inference(resolve,[$cnf( $equal(multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)),multiply(additive_identity,multiply(X_27,X_27))) )],[refute_0_10,refute_0_16]) ).

cnf(refute_0_18,plain,
    multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) = additive_identity,
    inference(resolve,[$cnf( $equal(multiply(additive_identity,multiply(X_27,X_27)),additive_identity) )],[refute_0_5,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( multiply(add(X,additive_inverse(Y)),Z) != add(multiply(X,Z),additive_inverse(multiply(Y,Z)))
    | add(multiply(X,Z),additive_inverse(multiply(Y,Z))) = multiply(add(X,additive_inverse(Y)),Z) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(add(X,additive_inverse(Y)),Z))),bind(Y0,$fot(add(multiply(X,Z),additive_inverse(multiply(Y,Z)))))]]) ).

cnf(refute_0_20,plain,
    add(multiply(X,Z),additive_inverse(multiply(Y,Z))) = multiply(add(X,additive_inverse(Y)),Z),
    inference(resolve,[$cnf( $equal(multiply(add(X,additive_inverse(Y)),Z),add(multiply(X,Z),additive_inverse(multiply(Y,Z)))) )],[distributivity_of_difference2,refute_0_19]) ).

cnf(refute_0_21,plain,
    add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) = multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)),
    inference(subst,[],[refute_0_20:[bind(X,$fot(X_25)),bind(Y,$fot(X_25)),bind(Z,$fot(multiply(X_27,X_27)))]]) ).

cnf(refute_0_22,plain,
    ( multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) != additive_identity
    | add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) != multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27))
    | add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) = additive_identity ),
    inference(subst,[],[refute_0_15:[bind(X0,$fot(add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))))),bind(Y0,$fot(multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)))),bind(Z0,$fot(additive_identity))]]) ).

cnf(refute_0_23,plain,
    ( multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)) != additive_identity
    | add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) = additive_identity ),
    inference(resolve,[$cnf( $equal(add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))),multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27))) )],[refute_0_21,refute_0_22]) ).

cnf(refute_0_24,plain,
    add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) = additive_identity,
    inference(resolve,[$cnf( $equal(multiply(add(X_25,additive_inverse(X_25)),multiply(X_27,X_27)),additive_identity) )],[refute_0_18,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) != additive_identity
    | associator(X_25,X_27,X_27) != add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27))))
    | associator(X_25,X_27,X_27) = additive_identity ),
    introduced(tautology,[equality,[$cnf( $equal(associator(X_25,X_27,X_27),add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27))))) ),[1],$fot(additive_identity)]]) ).

cnf(refute_0_26,plain,
    ( associator(X_25,X_27,X_27) != add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27))))
    | associator(X_25,X_27,X_27) = additive_identity ),
    inference(resolve,[$cnf( $equal(add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))),additive_identity) )],[refute_0_24,refute_0_25]) ).

cnf(refute_0_27,plain,
    associator(X_25,X_27,X_27) = additive_identity,
    inference(resolve,[$cnf( $equal(associator(X_25,X_27,X_27),add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27))))) )],[refute_0_4,refute_0_26]) ).

cnf(refute_0_28,plain,
    associator(x,y,y) = additive_identity,
    inference(subst,[],[refute_0_27:[bind(X_25,$fot(x)),bind(X_27,$fot(y))]]) ).

cnf(refute_0_29,plain,
    ( additive_identity != additive_identity
    | associator(x,y,y) != additive_identity
    | associator(x,y,y) = additive_identity ),
    introduced(tautology,[equality,[$cnf( $equal(associator(x,y,y),additive_identity) ),[1],$fot(additive_identity)]]) ).

cnf(refute_0_30,plain,
    ( additive_identity != additive_identity
    | associator(x,y,y) = additive_identity ),
    inference(resolve,[$cnf( $equal(associator(x,y,y),additive_identity) )],[refute_0_28,refute_0_29]) ).

cnf(refute_0_31,plain,
    additive_identity != additive_identity,
    inference(resolve,[$cnf( $equal(associator(x,y,y),additive_identity) )],[refute_0_30,prove_right_alternative]) ).

cnf(refute_0_32,plain,
    additive_identity = additive_identity,
    introduced(tautology,[refl,[$fot(additive_identity)]]) ).

cnf(refute_0_33,plain,
    $false,
    inference(resolve,[$cnf( $equal(additive_identity,additive_identity) )],[refute_0_32,refute_0_31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : RNG024-7 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n021.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  : 600
% 0.13/0.34  % DateTime : Mon May 30 12:37:28 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.38  
% 0.19/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.39  
%------------------------------------------------------------------------------