TSTP Solution File: COL044-1 by Metis---2.4

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : COL044-1 : 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 00:36:17 EDT 2022

% Result   : Unsatisfiable 12.64s 12.85s
% Output   : CNFRefutation 12.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   39 (  24 unt;   0 nHn;  21 RR)
%            Number of literals    :   60 (  59 equ;  26 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   80 (   0 sgn)

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

cnf(n_definition,axiom,
    apply(apply(apply(n,X),Y),Z) = apply(apply(apply(X,Z),Y),Z) ).

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(n,b),Y),Z) = apply(apply(apply(b,Z),Y),Z),
    inference(subst,[],[n_definition:[bind(X,$fot(b))]]) ).

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

cnf(refute_0_2,plain,
    ( apply(apply(apply(b,Z),Y),Z) != apply(Z,apply(Y,Z))
    | apply(apply(apply(n,b),Y),Z) != apply(apply(apply(b,Z),Y),Z)
    | apply(apply(apply(n,b),Y),Z) = apply(Z,apply(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(n,b),Y),Z),apply(apply(apply(b,Z),Y),Z)) ),[1],$fot(apply(Z,apply(Y,Z)))]]) ).

cnf(refute_0_3,plain,
    ( apply(apply(apply(n,b),Y),Z) != apply(apply(apply(b,Z),Y),Z)
    | apply(apply(apply(n,b),Y),Z) = apply(Z,apply(Y,Z)) ),
    inference(resolve,[$cnf( $equal(apply(apply(apply(b,Z),Y),Z),apply(Z,apply(Y,Z))) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    apply(apply(apply(n,b),Y),Z) = apply(Z,apply(Y,Z)),
    inference(resolve,[$cnf( $equal(apply(apply(apply(n,b),Y),Z),apply(apply(apply(b,Z),Y),Z)) )],[refute_0_0,refute_0_3]) ).

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

cnf(refute_0_6,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_7,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_8,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( apply(apply(apply(n,b),Y),f(Y)) != apply(f(Y),apply(Y,f(Y)))
    | apply(f(Y),apply(Y,f(Y))) = apply(apply(apply(n,b),Y),f(Y)) ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(apply(apply(apply(n,b),Y),f(Y)))),bind(Y0,$fot(apply(f(Y),apply(Y,f(Y)))))]]) ).

cnf(refute_0_10,plain,
    apply(f(Y),apply(Y,f(Y))) = apply(apply(apply(n,b),Y),f(Y)),
    inference(resolve,[$cnf( $equal(apply(apply(apply(n,b),Y),f(Y)),apply(f(Y),apply(Y,f(Y)))) )],[refute_0_5,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( apply(Y,f(Y)) != apply(apply(apply(n,b),Y),f(Y))
    | apply(f(Y),apply(Y,f(Y))) != apply(apply(apply(n,b),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(apply(n,b),Y),f(Y)))]]) ).

cnf(refute_0_12,plain,
    ( apply(Y,f(Y)) != apply(apply(apply(n,b),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(apply(n,b),Y),f(Y))) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    apply(Y,f(Y)) != apply(apply(apply(n,b),Y),f(Y)),
    inference(resolve,[$cnf( $equal(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y)))) )],[refute_0_12,prove_fixed_point]) ).

cnf(refute_0_14,plain,
    apply(apply(apply(X_86,X_87),X_86),f(apply(apply(X_86,X_87),X_86))) != apply(apply(apply(n,b),apply(apply(X_86,X_87),X_86)),f(apply(apply(X_86,X_87),X_86))),
    inference(subst,[],[refute_0_13:[bind(Y,$fot(apply(apply(X_86,X_87),X_86)))]]) ).

cnf(refute_0_15,plain,
    apply(apply(apply(b,X),apply(Z,X_11)),Z) = apply(X,apply(apply(Z,X_11),Z)),
    inference(subst,[],[b_definition:[bind(Y,$fot(apply(Z,X_11)))]]) ).

cnf(refute_0_16,plain,
    apply(apply(apply(n,apply(b,X_4)),Y),Z) = apply(apply(apply(apply(b,X_4),Z),Y),Z),
    inference(subst,[],[n_definition:[bind(X,$fot(apply(b,X_4)))]]) ).

cnf(refute_0_17,plain,
    apply(apply(apply(b,X_4),Z),Y) = apply(X_4,apply(Z,Y)),
    inference(subst,[],[b_definition:[bind(X,$fot(X_4)),bind(Y,$fot(Z)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_18,plain,
    ( apply(apply(apply(b,X_4),Z),Y) != apply(X_4,apply(Z,Y))
    | apply(apply(apply(n,apply(b,X_4)),Y),Z) != apply(apply(apply(apply(b,X_4),Z),Y),Z)
    | apply(apply(apply(n,apply(b,X_4)),Y),Z) = apply(apply(X_4,apply(Z,Y)),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(n,apply(b,X_4)),Y),Z),apply(apply(apply(apply(b,X_4),Z),Y),Z)) ),[1,0],$fot(apply(X_4,apply(Z,Y)))]]) ).

cnf(refute_0_19,plain,
    ( apply(apply(apply(n,apply(b,X_4)),Y),Z) != apply(apply(apply(apply(b,X_4),Z),Y),Z)
    | apply(apply(apply(n,apply(b,X_4)),Y),Z) = apply(apply(X_4,apply(Z,Y)),Z) ),
    inference(resolve,[$cnf( $equal(apply(apply(apply(b,X_4),Z),Y),apply(X_4,apply(Z,Y))) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    apply(apply(apply(n,apply(b,X_4)),Y),Z) = apply(apply(X_4,apply(Z,Y)),Z),
    inference(resolve,[$cnf( $equal(apply(apply(apply(n,apply(b,X_4)),Y),Z),apply(apply(apply(apply(b,X_4),Z),Y),Z)) )],[refute_0_16,refute_0_19]) ).

cnf(refute_0_21,plain,
    apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z) = apply(apply(apply(b,X),apply(Z,X_11)),Z),
    inference(subst,[],[refute_0_20:[bind(Y,$fot(X_11)),bind(X_4,$fot(apply(b,X)))]]) ).

cnf(refute_0_22,plain,
    ( apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z) != apply(apply(apply(b,X),apply(Z,X_11)),Z)
    | apply(apply(apply(b,X),apply(Z,X_11)),Z) = apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z) ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z))),bind(Y0,$fot(apply(apply(apply(b,X),apply(Z,X_11)),Z)))]]) ).

cnf(refute_0_23,plain,
    apply(apply(apply(b,X),apply(Z,X_11)),Z) = apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z),
    inference(resolve,[$cnf( $equal(apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z),apply(apply(apply(b,X),apply(Z,X_11)),Z)) )],[refute_0_21,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( apply(apply(apply(b,X),apply(Z,X_11)),Z) != apply(X,apply(apply(Z,X_11),Z))
    | apply(apply(apply(b,X),apply(Z,X_11)),Z) != apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z)
    | apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z) = apply(X,apply(apply(Z,X_11),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,X),apply(Z,X_11)),Z),apply(X,apply(apply(Z,X_11),Z))) ),[0],$fot(apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z))]]) ).

cnf(refute_0_25,plain,
    ( apply(apply(apply(b,X),apply(Z,X_11)),Z) != apply(X,apply(apply(Z,X_11),Z))
    | apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z) = apply(X,apply(apply(Z,X_11),Z)) ),
    inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),apply(Z,X_11)),Z),apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z)) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    apply(apply(apply(n,apply(b,apply(b,X))),X_11),Z) = apply(X,apply(apply(Z,X_11),Z)),
    inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),apply(Z,X_11)),Z),apply(X,apply(apply(Z,X_11),Z))) )],[refute_0_15,refute_0_25]) ).

cnf(refute_0_27,plain,
    apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86) = apply(apply(n,b),apply(apply(X_86,X_87),X_86)),
    inference(subst,[],[refute_0_26:[bind(X,$fot(apply(n,b))),bind(Z,$fot(X_86)),bind(X_11,$fot(X_87))]]) ).

cnf(refute_0_28,plain,
    ( apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86) != apply(apply(n,b),apply(apply(X_86,X_87),X_86))
    | apply(apply(n,b),apply(apply(X_86,X_87),X_86)) = apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86) ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86))),bind(Y0,$fot(apply(apply(n,b),apply(apply(X_86,X_87),X_86))))]]) ).

cnf(refute_0_29,plain,
    apply(apply(n,b),apply(apply(X_86,X_87),X_86)) = apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86),
    inference(resolve,[$cnf( $equal(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86),apply(apply(n,b),apply(apply(X_86,X_87),X_86))) )],[refute_0_27,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( apply(apply(apply(X_86,X_87),X_86),f(apply(apply(X_86,X_87),X_86))) != apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86),f(apply(apply(X_86,X_87),X_86)))
    | apply(apply(n,b),apply(apply(X_86,X_87),X_86)) != apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86)
    | apply(apply(apply(X_86,X_87),X_86),f(apply(apply(X_86,X_87),X_86))) = apply(apply(apply(n,b),apply(apply(X_86,X_87),X_86)),f(apply(apply(X_86,X_87),X_86))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(X_86,X_87),X_86),f(apply(apply(X_86,X_87),X_86))),apply(apply(apply(n,b),apply(apply(X_86,X_87),X_86)),f(apply(apply(X_86,X_87),X_86)))) ),[1,0],$fot(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86))]]) ).

cnf(refute_0_31,plain,
    ( apply(apply(apply(X_86,X_87),X_86),f(apply(apply(X_86,X_87),X_86))) != apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86),f(apply(apply(X_86,X_87),X_86)))
    | apply(apply(apply(X_86,X_87),X_86),f(apply(apply(X_86,X_87),X_86))) = apply(apply(apply(n,b),apply(apply(X_86,X_87),X_86)),f(apply(apply(X_86,X_87),X_86))) ),
    inference(resolve,[$cnf( $equal(apply(apply(n,b),apply(apply(X_86,X_87),X_86)),apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86)) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    apply(apply(apply(X_86,X_87),X_86),f(apply(apply(X_86,X_87),X_86))) != apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),X_86),f(apply(apply(X_86,X_87),X_86))),
    inference(resolve,[$cnf( $equal(apply(apply(apply(X_86,X_87),X_86),f(apply(apply(X_86,X_87),X_86))),apply(apply(apply(n,b),apply(apply(X_86,X_87),X_86)),f(apply(apply(X_86,X_87),X_86)))) )],[refute_0_31,refute_0_14]) ).

cnf(refute_0_33,plain,
    apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))))) != apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))))),
    inference(subst,[],[refute_0_32:[bind(X_86,$fot(apply(n,apply(b,apply(b,apply(n,b))))))]]) ).

cnf(refute_0_34,plain,
    apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))))) = apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))))),
    introduced(tautology,[refl,[$fot(apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))))))]]) ).

cnf(refute_0_35,plain,
    $false,
    inference(resolve,[$cnf( $equal(apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))))),apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X_87),apply(n,apply(b,apply(b,apply(n,b)))))))) )],[refute_0_34,refute_0_33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : COL044-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12  % 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 10:18:58 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 12.64/12.85  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.64/12.85  
% 12.64/12.85  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.64/12.85  
%------------------------------------------------------------------------------