TSTP Solution File: COL014-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : COL014-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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 : Fri Jul 15 00:36:13 EDT 2022

% Result   : Unsatisfiable 0.14s 0.35s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   15 (  10 unt;   0 nHn;  11 RR)
%            Number of literals    :   22 (  21 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   15 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(l_definition,axiom,
    apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ).

cnf(prove_fixed_point,negated_conjecture,
    Y != apply(combinator,Y) ).

cnf(refute_0_0,plain,
    apply(X_4,X_4) != apply(combinator,apply(X_4,X_4)),
    inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(X_4,X_4)))]]) ).

cnf(refute_0_1,plain,
    apply(apply(l,combinator),X_4) = apply(combinator,apply(X_4,X_4)),
    inference(subst,[],[l_definition:[bind(X,$fot(combinator)),bind(Y,$fot(X_4))]]) ).

cnf(refute_0_2,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_3,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_4,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( apply(apply(l,combinator),X_4) != apply(combinator,apply(X_4,X_4))
    | apply(combinator,apply(X_4,X_4)) = apply(apply(l,combinator),X_4) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(apply(apply(l,combinator),X_4))),bind(Y0,$fot(apply(combinator,apply(X_4,X_4))))]]) ).

cnf(refute_0_6,plain,
    apply(combinator,apply(X_4,X_4)) = apply(apply(l,combinator),X_4),
    inference(resolve,[$cnf( $equal(apply(apply(l,combinator),X_4),apply(combinator,apply(X_4,X_4))) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( apply(X_4,X_4) != apply(apply(l,combinator),X_4)
    | apply(combinator,apply(X_4,X_4)) != apply(apply(l,combinator),X_4)
    | apply(X_4,X_4) = apply(combinator,apply(X_4,X_4)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(apply(X_4,X_4),apply(combinator,apply(X_4,X_4))) ),[1],$fot(apply(apply(l,combinator),X_4))]]) ).

cnf(refute_0_8,plain,
    ( apply(X_4,X_4) != apply(apply(l,combinator),X_4)
    | apply(X_4,X_4) = apply(combinator,apply(X_4,X_4)) ),
    inference(resolve,[$cnf( $equal(apply(combinator,apply(X_4,X_4)),apply(apply(l,combinator),X_4)) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    apply(X_4,X_4) != apply(apply(l,combinator),X_4),
    inference(resolve,[$cnf( $equal(apply(X_4,X_4),apply(combinator,apply(X_4,X_4))) )],[refute_0_8,refute_0_0]) ).

cnf(refute_0_10,plain,
    apply(apply(l,combinator),apply(l,combinator)) != apply(apply(l,combinator),apply(l,combinator)),
    inference(subst,[],[refute_0_9:[bind(X_4,$fot(apply(l,combinator)))]]) ).

cnf(refute_0_11,plain,
    apply(apply(l,combinator),apply(l,combinator)) = apply(apply(l,combinator),apply(l,combinator)),
    introduced(tautology,[refl,[$fot(apply(apply(l,combinator),apply(l,combinator)))]]) ).

cnf(refute_0_12,plain,
    $false,
    inference(resolve,[$cnf( $equal(apply(apply(l,combinator),apply(l,combinator)),apply(apply(l,combinator),apply(l,combinator))) )],[refute_0_11,refute_0_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : COL014-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Tue May 31 08:27:41 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  
% 0.14/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.35  
%------------------------------------------------------------------------------