TSTP Solution File: LAT035-1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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 : Sun Jul 17 05:59:02 EDT 2022

% Result   : Unsatisfiable 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   40 (  19 unt;   0 nHn;  35 RR)
%            Number of literals    :   70 (  69 equ;  34 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    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   23 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(k_on_join,axiom,
    k(join(U,V)) = meet(k(U),k(V)) ).

cnf(k_on_bottom,axiom,
    k(n0) = n1 ).

cnf(f_on_meet,axiom,
    f(meet(U,V)) = join(f(U),f(V)) ).

cnf(f_on_top,axiom,
    f(n1) = n0 ).

cnf(comp_join_hemimorphism,negated_conjecture,
    ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb)))
    | f(k(n0)) != n0 ) ).

cnf(refute_0_0,plain,
    f(k(n0)) = f(k(n0)),
    introduced(tautology,[refl,[$fot(f(k(n0)))]]) ).

cnf(refute_0_1,plain,
    ( f(k(n0)) != f(k(n0))
    | k(n0) != n1
    | f(k(n0)) = f(n1) ),
    introduced(tautology,[equality,[$cnf( $equal(f(k(n0)),f(k(n0))) ),[1,0],$fot(n1)]]) ).

cnf(refute_0_2,plain,
    ( k(n0) != n1
    | f(k(n0)) = f(n1) ),
    inference(resolve,[$cnf( $equal(f(k(n0)),f(k(n0))) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    f(k(n0)) = f(n1),
    inference(resolve,[$cnf( $equal(k(n0),n1) )],[k_on_bottom,refute_0_2]) ).

cnf(refute_0_4,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_5,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_6,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_8,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( f(k(n0)) != f(n1)
    | f(n1) != n0
    | f(k(n0)) = n0 ),
    inference(subst,[],[refute_0_8:[bind(X,$fot(f(k(n0)))),bind(Y,$fot(f(n1))),bind(Z,$fot(n0))]]) ).

cnf(refute_0_10,plain,
    ( f(n1) != n0
    | f(k(n0)) = n0 ),
    inference(resolve,[$cnf( $equal(f(k(n0)),f(n1)) )],[refute_0_3,refute_0_9]) ).

cnf(refute_0_11,plain,
    f(k(n0)) = n0,
    inference(resolve,[$cnf( $equal(f(n1),n0) )],[f_on_top,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( f(k(n0)) != n0
    | n0 != n0
    | f(k(n0)) = n0 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(f(k(n0)),n0) ),[0],$fot(n0)]]) ).

cnf(refute_0_13,plain,
    ( n0 != n0
    | f(k(n0)) = n0 ),
    inference(resolve,[$cnf( $equal(f(k(n0)),n0) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb)))
    | n0 != n0 ),
    inference(resolve,[$cnf( $equal(f(k(n0)),n0) )],[refute_0_13,comp_join_hemimorphism]) ).

cnf(refute_0_15,plain,
    ( k(join(U,V)) != meet(k(U),k(V))
    | meet(k(U),k(V)) = k(join(U,V)) ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(k(join(U,V)))),bind(Y,$fot(meet(k(U),k(V))))]]) ).

cnf(refute_0_16,plain,
    meet(k(U),k(V)) = k(join(U,V)),
    inference(resolve,[$cnf( $equal(k(join(U,V)),meet(k(U),k(V))) )],[k_on_join,refute_0_15]) ).

cnf(refute_0_17,plain,
    meet(k(aa),k(bb)) = k(join(aa,bb)),
    inference(subst,[],[refute_0_16:[bind(U,$fot(aa)),bind(V,$fot(bb))]]) ).

cnf(refute_0_18,plain,
    f(meet(k(aa),k(bb))) = f(meet(k(aa),k(bb))),
    introduced(tautology,[refl,[$fot(f(meet(k(aa),k(bb))))]]) ).

cnf(refute_0_19,plain,
    ( f(meet(k(aa),k(bb))) != f(meet(k(aa),k(bb)))
    | meet(k(aa),k(bb)) != k(join(aa,bb))
    | f(meet(k(aa),k(bb))) = f(k(join(aa,bb))) ),
    introduced(tautology,[equality,[$cnf( $equal(f(meet(k(aa),k(bb))),f(meet(k(aa),k(bb)))) ),[1,0],$fot(k(join(aa,bb)))]]) ).

cnf(refute_0_20,plain,
    ( meet(k(aa),k(bb)) != k(join(aa,bb))
    | f(meet(k(aa),k(bb))) = f(k(join(aa,bb))) ),
    inference(resolve,[$cnf( $equal(f(meet(k(aa),k(bb))),f(meet(k(aa),k(bb)))) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    f(meet(k(aa),k(bb))) = f(k(join(aa,bb))),
    inference(resolve,[$cnf( $equal(meet(k(aa),k(bb)),k(join(aa,bb))) )],[refute_0_17,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( f(meet(U,V)) != join(f(U),f(V))
    | join(f(U),f(V)) = f(meet(U,V)) ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(f(meet(U,V)))),bind(Y,$fot(join(f(U),f(V))))]]) ).

cnf(refute_0_23,plain,
    join(f(U),f(V)) = f(meet(U,V)),
    inference(resolve,[$cnf( $equal(f(meet(U,V)),join(f(U),f(V))) )],[f_on_meet,refute_0_22]) ).

cnf(refute_0_24,plain,
    join(f(k(aa)),f(k(bb))) = f(meet(k(aa),k(bb))),
    inference(subst,[],[refute_0_23:[bind(U,$fot(k(aa))),bind(V,$fot(k(bb)))]]) ).

cnf(refute_0_25,plain,
    ( f(meet(k(aa),k(bb))) != f(k(join(aa,bb)))
    | join(f(k(aa)),f(k(bb))) != f(meet(k(aa),k(bb)))
    | join(f(k(aa)),f(k(bb))) = f(k(join(aa,bb))) ),
    inference(subst,[],[refute_0_8:[bind(X,$fot(join(f(k(aa)),f(k(bb))))),bind(Y,$fot(f(meet(k(aa),k(bb))))),bind(Z,$fot(f(k(join(aa,bb)))))]]) ).

cnf(refute_0_26,plain,
    ( f(meet(k(aa),k(bb))) != f(k(join(aa,bb)))
    | join(f(k(aa)),f(k(bb))) = f(k(join(aa,bb))) ),
    inference(resolve,[$cnf( $equal(join(f(k(aa)),f(k(bb))),f(meet(k(aa),k(bb)))) )],[refute_0_24,refute_0_25]) ).

cnf(refute_0_27,plain,
    join(f(k(aa)),f(k(bb))) = f(k(join(aa,bb))),
    inference(resolve,[$cnf( $equal(f(meet(k(aa),k(bb))),f(k(join(aa,bb)))) )],[refute_0_21,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( f(k(join(aa,bb))) != f(k(join(aa,bb)))
    | join(f(k(aa)),f(k(bb))) != f(k(join(aa,bb)))
    | f(k(join(aa,bb))) = join(f(k(aa)),f(k(bb))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(f(k(join(aa,bb))),join(f(k(aa)),f(k(bb)))) ),[1],$fot(f(k(join(aa,bb))))]]) ).

cnf(refute_0_29,plain,
    ( f(k(join(aa,bb))) != f(k(join(aa,bb)))
    | f(k(join(aa,bb))) = join(f(k(aa)),f(k(bb))) ),
    inference(resolve,[$cnf( $equal(join(f(k(aa)),f(k(bb))),f(k(join(aa,bb)))) )],[refute_0_27,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( f(k(join(aa,bb))) != f(k(join(aa,bb)))
    | n0 != n0 ),
    inference(resolve,[$cnf( $equal(f(k(join(aa,bb))),join(f(k(aa)),f(k(bb)))) )],[refute_0_29,refute_0_14]) ).

cnf(refute_0_31,plain,
    f(k(join(aa,bb))) = f(k(join(aa,bb))),
    introduced(tautology,[refl,[$fot(f(k(join(aa,bb))))]]) ).

cnf(refute_0_32,plain,
    n0 != n0,
    inference(resolve,[$cnf( $equal(f(k(join(aa,bb))),f(k(join(aa,bb)))) )],[refute_0_31,refute_0_30]) ).

cnf(refute_0_33,plain,
    n0 = n0,
    introduced(tautology,[refl,[$fot(n0)]]) ).

cnf(refute_0_34,plain,
    $false,
    inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_33,refute_0_32]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n021.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 29 19:56:42 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36  
% 0.13/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37  
%------------------------------------------------------------------------------