TSTP Solution File: COL033-1 by Metis---2.4

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : COL033-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 00:36:16 EDT 2022

% Result   : Unsatisfiable 136.58s 136.75s
% Output   : CNFRefutation 136.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   36 (  22 unt;   0 nHn;  24 RR)
%            Number of literals    :   56 (  55 equ;  26 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   44 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
    apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).

cnf(l_definition,axiom,
    apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ).

cnf(m_definition,axiom,
    apply(m,X) = apply(X,X) ).

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

cnf(refute_0_0,plain,
    apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) != apply(f(apply(apply(b,X_9),X_10)),apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10)))),
    inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(apply(b,X_9),X_10)))]]) ).

cnf(refute_0_1,plain,
    apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) = apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10)))),
    inference(subst,[],[b_definition:[bind(X,$fot(X_9)),bind(Y,$fot(X_10)),bind(Z,$fot(f(apply(apply(b,X_9),X_10))))]]) ).

cnf(refute_0_2,plain,
    ( apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) != apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10))))
    | apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) != apply(f(apply(apply(b,X_9),X_10)),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10)))))
    | apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) = apply(f(apply(apply(b,X_9),X_10)),apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))),apply(f(apply(apply(b,X_9),X_10)),apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))))) ),[1,1],$fot(apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10)))))]]) ).

cnf(refute_0_3,plain,
    ( apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) != apply(f(apply(apply(b,X_9),X_10)),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10)))))
    | apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) = apply(f(apply(apply(b,X_9),X_10)),apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10)))) ),
    inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10))))) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) != apply(f(apply(apply(b,X_9),X_10)),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10))))),
    inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))),apply(f(apply(apply(b,X_9),X_10)),apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))))) )],[refute_0_3,refute_0_0]) ).

cnf(refute_0_5,plain,
    ( apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10)))) != apply(f(apply(apply(b,X_9),X_10)),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10)))))
    | apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) != apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10))))
    | apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) = apply(f(apply(apply(b,X_9),X_10)),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10))))) ),
    introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10))))) ),[1],$fot(apply(f(apply(apply(b,X_9),X_10)),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10))))))]]) ).

cnf(refute_0_6,plain,
    ( apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10)))) != apply(f(apply(apply(b,X_9),X_10)),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10)))))
    | apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))) = apply(f(apply(apply(b,X_9),X_10)),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10))))) ),
    inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10))))) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10)))) != apply(f(apply(apply(b,X_9),X_10)),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10))))),
    inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_9),X_10),f(apply(apply(b,X_9),X_10))),apply(f(apply(apply(b,X_9),X_10)),apply(X_9,apply(X_10,f(apply(apply(b,X_9),X_10)))))) )],[refute_0_6,refute_0_4]) ).

cnf(refute_0_8,plain,
    apply(m,apply(l,f(apply(apply(b,m),l)))) != apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))),
    inference(subst,[],[refute_0_7:[bind(X_10,$fot(l)),bind(X_9,$fot(m))]]) ).

cnf(refute_0_9,plain,
    apply(m,apply(l,X_5)) = apply(apply(l,X_5),apply(l,X_5)),
    inference(subst,[],[m_definition:[bind(X,$fot(apply(l,X_5)))]]) ).

cnf(refute_0_10,plain,
    apply(apply(l,X_2),X_3) = apply(X_2,apply(X_3,X_3)),
    inference(subst,[],[l_definition:[bind(X,$fot(X_2)),bind(Y,$fot(X_3))]]) ).

cnf(refute_0_11,plain,
    apply(m,X_3) = apply(X_3,X_3),
    inference(subst,[],[m_definition:[bind(X,$fot(X_3))]]) ).

cnf(refute_0_12,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_13,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_14,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( apply(m,X_3) != apply(X_3,X_3)
    | apply(X_3,X_3) = apply(m,X_3) ),
    inference(subst,[],[refute_0_14:[bind(X0,$fot(apply(m,X_3))),bind(Y0,$fot(apply(X_3,X_3)))]]) ).

cnf(refute_0_16,plain,
    apply(X_3,X_3) = apply(m,X_3),
    inference(resolve,[$cnf( $equal(apply(m,X_3),apply(X_3,X_3)) )],[refute_0_11,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( apply(X_3,X_3) != apply(m,X_3)
    | apply(apply(l,X_2),X_3) != apply(X_2,apply(X_3,X_3))
    | apply(apply(l,X_2),X_3) = apply(X_2,apply(m,X_3)) ),
    introduced(tautology,[equality,[$cnf( $equal(apply(apply(l,X_2),X_3),apply(X_2,apply(X_3,X_3))) ),[1,1],$fot(apply(m,X_3))]]) ).

cnf(refute_0_18,plain,
    ( apply(apply(l,X_2),X_3) != apply(X_2,apply(X_3,X_3))
    | apply(apply(l,X_2),X_3) = apply(X_2,apply(m,X_3)) ),
    inference(resolve,[$cnf( $equal(apply(X_3,X_3),apply(m,X_3)) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    apply(apply(l,X_2),X_3) = apply(X_2,apply(m,X_3)),
    inference(resolve,[$cnf( $equal(apply(apply(l,X_2),X_3),apply(X_2,apply(X_3,X_3))) )],[refute_0_10,refute_0_18]) ).

cnf(refute_0_20,plain,
    apply(apply(l,X_5),apply(l,X_5)) = apply(X_5,apply(m,apply(l,X_5))),
    inference(subst,[],[refute_0_19:[bind(X_2,$fot(X_5)),bind(X_3,$fot(apply(l,X_5)))]]) ).

cnf(refute_0_21,plain,
    ( apply(apply(l,X_5),apply(l,X_5)) != apply(X_5,apply(m,apply(l,X_5)))
    | apply(m,apply(l,X_5)) != apply(apply(l,X_5),apply(l,X_5))
    | apply(m,apply(l,X_5)) = apply(X_5,apply(m,apply(l,X_5))) ),
    introduced(tautology,[equality,[$cnf( $equal(apply(m,apply(l,X_5)),apply(apply(l,X_5),apply(l,X_5))) ),[1],$fot(apply(X_5,apply(m,apply(l,X_5))))]]) ).

cnf(refute_0_22,plain,
    ( apply(m,apply(l,X_5)) != apply(apply(l,X_5),apply(l,X_5))
    | apply(m,apply(l,X_5)) = apply(X_5,apply(m,apply(l,X_5))) ),
    inference(resolve,[$cnf( $equal(apply(apply(l,X_5),apply(l,X_5)),apply(X_5,apply(m,apply(l,X_5)))) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    apply(m,apply(l,X_5)) = apply(X_5,apply(m,apply(l,X_5))),
    inference(resolve,[$cnf( $equal(apply(m,apply(l,X_5)),apply(apply(l,X_5),apply(l,X_5))) )],[refute_0_9,refute_0_22]) ).

cnf(refute_0_24,plain,
    apply(m,apply(l,f(apply(apply(b,m),l)))) = apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))),
    inference(subst,[],[refute_0_23:[bind(X_5,$fot(f(apply(apply(b,m),l))))]]) ).

cnf(refute_0_25,plain,
    ( apply(m,apply(l,f(apply(apply(b,m),l)))) != apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l)))))
    | apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))) = apply(m,apply(l,f(apply(apply(b,m),l)))) ),
    inference(subst,[],[refute_0_14:[bind(X0,$fot(apply(m,apply(l,f(apply(apply(b,m),l)))))),bind(Y0,$fot(apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l)))))))]]) ).

cnf(refute_0_26,plain,
    apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))) = apply(m,apply(l,f(apply(apply(b,m),l)))),
    inference(resolve,[$cnf( $equal(apply(m,apply(l,f(apply(apply(b,m),l)))),apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l)))))) )],[refute_0_24,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))) != apply(m,apply(l,f(apply(apply(b,m),l))))
    | apply(m,apply(l,f(apply(apply(b,m),l)))) != apply(m,apply(l,f(apply(apply(b,m),l))))
    | apply(m,apply(l,f(apply(apply(b,m),l)))) = apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(apply(m,apply(l,f(apply(apply(b,m),l)))),apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l)))))) ),[1],$fot(apply(m,apply(l,f(apply(apply(b,m),l)))))]]) ).

cnf(refute_0_28,plain,
    ( apply(m,apply(l,f(apply(apply(b,m),l)))) != apply(m,apply(l,f(apply(apply(b,m),l))))
    | apply(m,apply(l,f(apply(apply(b,m),l)))) = apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))) ),
    inference(resolve,[$cnf( $equal(apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))),apply(m,apply(l,f(apply(apply(b,m),l))))) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    apply(m,apply(l,f(apply(apply(b,m),l)))) != apply(m,apply(l,f(apply(apply(b,m),l)))),
    inference(resolve,[$cnf( $equal(apply(m,apply(l,f(apply(apply(b,m),l)))),apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l)))))) )],[refute_0_28,refute_0_8]) ).

cnf(refute_0_30,plain,
    apply(m,apply(l,f(apply(apply(b,m),l)))) = apply(m,apply(l,f(apply(apply(b,m),l)))),
    introduced(tautology,[refl,[$fot(apply(m,apply(l,f(apply(apply(b,m),l)))))]]) ).

cnf(refute_0_31,plain,
    $false,
    inference(resolve,[$cnf( $equal(apply(m,apply(l,f(apply(apply(b,m),l)))),apply(m,apply(l,f(apply(apply(b,m),l))))) )],[refute_0_30,refute_0_29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : COL033-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.14/0.33  % Computer : n027.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Tue May 31 06:03:17 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 136.58/136.75  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 136.58/136.75  
% 136.58/136.75  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 136.58/136.76  
%------------------------------------------------------------------------------