TSTP Solution File: COL039-1 by Metis---2.4

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : COL039-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n025.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 1.22s 1.39s
% Output   : CNFRefutation 1.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   28 (  18 unt;   0 nHn;  17 RR)
%            Number of literals    :   42 (  41 equ;  19 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   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   :   37 (   0 sgn)

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

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

cnf(o_definition,axiom,
    apply(apply(o,X),Y) = apply(Y,apply(X,Y)) ).

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

cnf(refute_0_0,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_1,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_2,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( apply(apply(o,X),Y) != apply(Y,apply(X,Y))
    | apply(Y,apply(X,Y)) = apply(apply(o,X),Y) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(apply(apply(o,X),Y))),bind(Y0,$fot(apply(Y,apply(X,Y))))]]) ).

cnf(refute_0_4,plain,
    apply(Y,apply(X,Y)) = apply(apply(o,X),Y),
    inference(resolve,[$cnf( $equal(apply(apply(o,X),Y),apply(Y,apply(X,Y))) )],[o_definition,refute_0_3]) ).

cnf(refute_0_5,plain,
    apply(f(Y),apply(Y,f(Y))) = apply(apply(o,Y),f(Y)),
    inference(subst,[],[refute_0_4:[bind(X,$fot(Y)),bind(Y,$fot(f(Y)))]]) ).

cnf(refute_0_6,plain,
    ( apply(Y,f(Y)) != apply(apply(o,Y),f(Y))
    | apply(f(Y),apply(Y,f(Y))) != apply(apply(o,Y),f(Y))
    | apply(Y,f(Y)) = apply(f(Y),apply(Y,f(Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y)))) ),[1],$fot(apply(apply(o,Y),f(Y)))]]) ).

cnf(refute_0_7,plain,
    ( apply(Y,f(Y)) != apply(apply(o,Y),f(Y))
    | apply(Y,f(Y)) = apply(f(Y),apply(Y,f(Y))) ),
    inference(resolve,[$cnf( $equal(apply(f(Y),apply(Y,f(Y))),apply(apply(o,Y),f(Y))) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    apply(Y,f(Y)) != apply(apply(o,Y),f(Y)),
    inference(resolve,[$cnf( $equal(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y)))) )],[refute_0_7,prove_fixed_point]) ).

cnf(refute_0_9,plain,
    apply(apply(X_37,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37)))) != apply(apply(o,apply(X_37,apply(apply(b,o),X_37))),f(apply(X_37,apply(apply(b,o),X_37)))),
    inference(subst,[],[refute_0_8:[bind(Y,$fot(apply(X_37,apply(apply(b,o),X_37))))]]) ).

cnf(refute_0_10,plain,
    apply(m,apply(apply(b,X_11),X_12)) = apply(apply(apply(b,X_11),X_12),apply(apply(b,X_11),X_12)),
    inference(subst,[],[m_definition:[bind(X,$fot(apply(apply(b,X_11),X_12)))]]) ).

cnf(refute_0_11,plain,
    apply(apply(apply(b,X_11),X_12),apply(apply(b,X_11),X_12)) = apply(X_11,apply(X_12,apply(apply(b,X_11),X_12))),
    inference(subst,[],[b_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(Z,$fot(apply(apply(b,X_11),X_12)))]]) ).

cnf(refute_0_12,plain,
    ( apply(apply(apply(b,X_11),X_12),apply(apply(b,X_11),X_12)) != apply(X_11,apply(X_12,apply(apply(b,X_11),X_12)))
    | apply(m,apply(apply(b,X_11),X_12)) != apply(apply(apply(b,X_11),X_12),apply(apply(b,X_11),X_12))
    | apply(m,apply(apply(b,X_11),X_12)) = apply(X_11,apply(X_12,apply(apply(b,X_11),X_12))) ),
    introduced(tautology,[equality,[$cnf( $equal(apply(m,apply(apply(b,X_11),X_12)),apply(apply(apply(b,X_11),X_12),apply(apply(b,X_11),X_12))) ),[1],$fot(apply(X_11,apply(X_12,apply(apply(b,X_11),X_12))))]]) ).

cnf(refute_0_13,plain,
    ( apply(m,apply(apply(b,X_11),X_12)) != apply(apply(apply(b,X_11),X_12),apply(apply(b,X_11),X_12))
    | apply(m,apply(apply(b,X_11),X_12)) = apply(X_11,apply(X_12,apply(apply(b,X_11),X_12))) ),
    inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_11),X_12),apply(apply(b,X_11),X_12)),apply(X_11,apply(X_12,apply(apply(b,X_11),X_12)))) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    apply(m,apply(apply(b,X_11),X_12)) = apply(X_11,apply(X_12,apply(apply(b,X_11),X_12))),
    inference(resolve,[$cnf( $equal(apply(m,apply(apply(b,X_11),X_12)),apply(apply(apply(b,X_11),X_12),apply(apply(b,X_11),X_12))) )],[refute_0_10,refute_0_13]) ).

cnf(refute_0_15,plain,
    apply(m,apply(apply(b,o),X_37)) = apply(o,apply(X_37,apply(apply(b,o),X_37))),
    inference(subst,[],[refute_0_14:[bind(X_11,$fot(o)),bind(X_12,$fot(X_37))]]) ).

cnf(refute_0_16,plain,
    ( apply(m,apply(apply(b,o),X_37)) != apply(o,apply(X_37,apply(apply(b,o),X_37)))
    | apply(o,apply(X_37,apply(apply(b,o),X_37))) = apply(m,apply(apply(b,o),X_37)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(apply(m,apply(apply(b,o),X_37)))),bind(Y0,$fot(apply(o,apply(X_37,apply(apply(b,o),X_37)))))]]) ).

cnf(refute_0_17,plain,
    apply(o,apply(X_37,apply(apply(b,o),X_37))) = apply(m,apply(apply(b,o),X_37)),
    inference(resolve,[$cnf( $equal(apply(m,apply(apply(b,o),X_37)),apply(o,apply(X_37,apply(apply(b,o),X_37)))) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( apply(apply(X_37,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37)))) != apply(apply(m,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37))))
    | apply(o,apply(X_37,apply(apply(b,o),X_37))) != apply(m,apply(apply(b,o),X_37))
    | apply(apply(X_37,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37)))) = apply(apply(o,apply(X_37,apply(apply(b,o),X_37))),f(apply(X_37,apply(apply(b,o),X_37)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(X_37,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37)))),apply(apply(o,apply(X_37,apply(apply(b,o),X_37))),f(apply(X_37,apply(apply(b,o),X_37))))) ),[1,0],$fot(apply(m,apply(apply(b,o),X_37)))]]) ).

cnf(refute_0_19,plain,
    ( apply(apply(X_37,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37)))) != apply(apply(m,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37))))
    | apply(apply(X_37,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37)))) = apply(apply(o,apply(X_37,apply(apply(b,o),X_37))),f(apply(X_37,apply(apply(b,o),X_37)))) ),
    inference(resolve,[$cnf( $equal(apply(o,apply(X_37,apply(apply(b,o),X_37))),apply(m,apply(apply(b,o),X_37))) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    apply(apply(X_37,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37)))) != apply(apply(m,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37)))),
    inference(resolve,[$cnf( $equal(apply(apply(X_37,apply(apply(b,o),X_37)),f(apply(X_37,apply(apply(b,o),X_37)))),apply(apply(o,apply(X_37,apply(apply(b,o),X_37))),f(apply(X_37,apply(apply(b,o),X_37))))) )],[refute_0_19,refute_0_9]) ).

cnf(refute_0_21,plain,
    apply(apply(m,apply(apply(b,o),m)),f(apply(m,apply(apply(b,o),m)))) != apply(apply(m,apply(apply(b,o),m)),f(apply(m,apply(apply(b,o),m)))),
    inference(subst,[],[refute_0_20:[bind(X_37,$fot(m))]]) ).

cnf(refute_0_22,plain,
    apply(apply(m,apply(apply(b,o),m)),f(apply(m,apply(apply(b,o),m)))) = apply(apply(m,apply(apply(b,o),m)),f(apply(m,apply(apply(b,o),m)))),
    introduced(tautology,[refl,[$fot(apply(apply(m,apply(apply(b,o),m)),f(apply(m,apply(apply(b,o),m)))))]]) ).

cnf(refute_0_23,plain,
    $false,
    inference(resolve,[$cnf( $equal(apply(apply(m,apply(apply(b,o),m)),f(apply(m,apply(apply(b,o),m)))),apply(apply(m,apply(apply(b,o),m)),f(apply(m,apply(apply(b,o),m))))) )],[refute_0_22,refute_0_21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : COL039-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n025.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  : 600
% 0.12/0.33  % DateTime : Tue May 31 12:01:43 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.22/1.39  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.22/1.39  
% 1.22/1.39  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.22/1.40  
%------------------------------------------------------------------------------