TSTP Solution File: BOO005-2 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : BOO005-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.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 : Thu Jul 14 23:44:25 EDT 2022

% Result   : Unsatisfiable 0.63s 0.81s
% Output   : CNFRefutation 0.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   34 (  21 unt;   0 nHn;  18 RR)
%            Number of literals    :   53 (  52 equ;  21 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   39 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(distributivity2,axiom,
    add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ).

cnf(additive_inverse1,axiom,
    add(X,inverse(X)) = multiplicative_identity ).

cnf(multiplicative_id1,axiom,
    multiply(X,multiplicative_identity) = X ).

cnf(multiplicative_id2,axiom,
    multiply(multiplicative_identity,X) = X ).

cnf(prove_a_plus_1_is_a,negated_conjecture,
    add(a,multiplicative_identity) != multiplicative_identity ).

cnf(refute_0_0,plain,
    add(X_20,multiply(X_21,inverse(X_20))) = multiply(add(X_20,X_21),add(X_20,inverse(X_20))),
    inference(subst,[],[distributivity2:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(inverse(X_20)))]]) ).

cnf(refute_0_1,plain,
    add(X_20,inverse(X_20)) = multiplicative_identity,
    inference(subst,[],[additive_inverse1:[bind(X,$fot(X_20))]]) ).

cnf(refute_0_2,plain,
    ( add(X_20,multiply(X_21,inverse(X_20))) != multiply(add(X_20,X_21),add(X_20,inverse(X_20)))
    | add(X_20,inverse(X_20)) != multiplicative_identity
    | add(X_20,multiply(X_21,inverse(X_20))) = multiply(add(X_20,X_21),multiplicative_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,inverse(X_20))),multiply(add(X_20,X_21),add(X_20,inverse(X_20)))) ),[1,1],$fot(multiplicative_identity)]]) ).

cnf(refute_0_3,plain,
    ( add(X_20,multiply(X_21,inverse(X_20))) != multiply(add(X_20,X_21),add(X_20,inverse(X_20)))
    | add(X_20,multiply(X_21,inverse(X_20))) = multiply(add(X_20,X_21),multiplicative_identity) ),
    inference(resolve,[$cnf( $equal(add(X_20,inverse(X_20)),multiplicative_identity) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    add(X_20,multiply(X_21,inverse(X_20))) = multiply(add(X_20,X_21),multiplicative_identity),
    inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,inverse(X_20))),multiply(add(X_20,X_21),add(X_20,inverse(X_20)))) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    multiply(add(X_20,X_21),multiplicative_identity) = add(X_20,X_21),
    inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_20,X_21)))]]) ).

cnf(refute_0_6,plain,
    ( multiply(add(X_20,X_21),multiplicative_identity) != add(X_20,X_21)
    | add(X_20,multiply(X_21,inverse(X_20))) != multiply(add(X_20,X_21),multiplicative_identity)
    | add(X_20,multiply(X_21,inverse(X_20))) = add(X_20,X_21) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,inverse(X_20))),multiply(add(X_20,X_21),multiplicative_identity)) ),[1],$fot(add(X_20,X_21))]]) ).

cnf(refute_0_7,plain,
    ( add(X_20,multiply(X_21,inverse(X_20))) != multiply(add(X_20,X_21),multiplicative_identity)
    | add(X_20,multiply(X_21,inverse(X_20))) = add(X_20,X_21) ),
    inference(resolve,[$cnf( $equal(multiply(add(X_20,X_21),multiplicative_identity),add(X_20,X_21)) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    add(X_20,multiply(X_21,inverse(X_20))) = add(X_20,X_21),
    inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,inverse(X_20))),multiply(add(X_20,X_21),multiplicative_identity)) )],[refute_0_4,refute_0_7]) ).

cnf(refute_0_9,plain,
    add(X_52,multiply(multiplicative_identity,inverse(X_52))) = add(X_52,multiplicative_identity),
    inference(subst,[],[refute_0_8:[bind(X_20,$fot(X_52)),bind(X_21,$fot(multiplicative_identity))]]) ).

cnf(refute_0_10,plain,
    multiply(multiplicative_identity,inverse(X_52)) = inverse(X_52),
    inference(subst,[],[multiplicative_id2:[bind(X,$fot(inverse(X_52)))]]) ).

cnf(refute_0_11,plain,
    ( multiply(multiplicative_identity,inverse(X_52)) != inverse(X_52)
    | add(X_52,multiply(multiplicative_identity,inverse(X_52))) != add(X_52,multiplicative_identity)
    | add(X_52,inverse(X_52)) = add(X_52,multiplicative_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_52,multiply(multiplicative_identity,inverse(X_52))),add(X_52,multiplicative_identity)) ),[0,1],$fot(inverse(X_52))]]) ).

cnf(refute_0_12,plain,
    ( add(X_52,multiply(multiplicative_identity,inverse(X_52))) != add(X_52,multiplicative_identity)
    | add(X_52,inverse(X_52)) = add(X_52,multiplicative_identity) ),
    inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(X_52)),inverse(X_52)) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    add(X_52,inverse(X_52)) = add(X_52,multiplicative_identity),
    inference(resolve,[$cnf( $equal(add(X_52,multiply(multiplicative_identity,inverse(X_52))),add(X_52,multiplicative_identity)) )],[refute_0_9,refute_0_12]) ).

cnf(refute_0_14,plain,
    add(X_52,inverse(X_52)) = multiplicative_identity,
    inference(subst,[],[additive_inverse1:[bind(X,$fot(X_52))]]) ).

cnf(refute_0_15,plain,
    ( add(X_52,inverse(X_52)) != add(X_52,multiplicative_identity)
    | add(X_52,inverse(X_52)) != multiplicative_identity
    | multiplicative_identity = add(X_52,multiplicative_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_52,inverse(X_52)),add(X_52,multiplicative_identity)) ),[0],$fot(multiplicative_identity)]]) ).

cnf(refute_0_16,plain,
    ( add(X_52,inverse(X_52)) != add(X_52,multiplicative_identity)
    | multiplicative_identity = add(X_52,multiplicative_identity) ),
    inference(resolve,[$cnf( $equal(add(X_52,inverse(X_52)),multiplicative_identity) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    multiplicative_identity = add(X_52,multiplicative_identity),
    inference(resolve,[$cnf( $equal(add(X_52,inverse(X_52)),add(X_52,multiplicative_identity)) )],[refute_0_13,refute_0_16]) ).

cnf(refute_0_18,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_19,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_20,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( multiplicative_identity != add(X_52,multiplicative_identity)
    | add(X_52,multiplicative_identity) = multiplicative_identity ),
    inference(subst,[],[refute_0_20:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_52,multiplicative_identity)))]]) ).

cnf(refute_0_22,plain,
    add(X_52,multiplicative_identity) = multiplicative_identity,
    inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_52,multiplicative_identity)) )],[refute_0_17,refute_0_21]) ).

cnf(refute_0_23,plain,
    add(a,multiplicative_identity) = multiplicative_identity,
    inference(subst,[],[refute_0_22:[bind(X_52,$fot(a))]]) ).

cnf(refute_0_24,plain,
    ( add(a,multiplicative_identity) != multiplicative_identity
    | multiplicative_identity != multiplicative_identity
    | add(a,multiplicative_identity) = multiplicative_identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(add(a,multiplicative_identity),multiplicative_identity) ),[0],$fot(multiplicative_identity)]]) ).

cnf(refute_0_25,plain,
    ( multiplicative_identity != multiplicative_identity
    | add(a,multiplicative_identity) = multiplicative_identity ),
    inference(resolve,[$cnf( $equal(add(a,multiplicative_identity),multiplicative_identity) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    multiplicative_identity != multiplicative_identity,
    inference(resolve,[$cnf( $equal(add(a,multiplicative_identity),multiplicative_identity) )],[refute_0_25,prove_a_plus_1_is_a]) ).

cnf(refute_0_27,plain,
    multiplicative_identity = multiplicative_identity,
    introduced(tautology,[refl,[$fot(multiplicative_identity)]]) ).

cnf(refute_0_28,plain,
    $false,
    inference(resolve,[$cnf( $equal(multiplicative_identity,multiplicative_identity) )],[refute_0_27,refute_0_26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : BOO005-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n017.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 : Wed Jun  1 15:20:27 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.63/0.81  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.63/0.81  
% 0.63/0.81  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.63/0.81  
%------------------------------------------------------------------------------