%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN074-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n005.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 : Thu Jul 21 08:59:19 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   41 (   8 unt;  12 nHn;  30 RR)
%            Number of literals    :   93 (  59 equ;  47 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   36 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause_1,axiom,
    ( ~ big_f(X,Y)
    | X = a ) ).

cnf(clause_2,axiom,
    ( ~ big_f(X,Y)
    | Y = b ) ).

cnf(clause_3,axiom,
    ( X != a
    | Y != b
    | big_f(X,Y) ) ).

cnf(clause_8,negated_conjecture,
    ( Y != g(X)
    | big_f(f(X),Y)
    | f(X) = X ) ).

cnf(clause_10,negated_conjecture,
    ( f(X) != X
    | big_f(f(X),h(X,Z))
    | h(X,Z) = Z ) ).

cnf(clause_11,negated_conjecture,
    ( f(X) != X
    | h(X,Z) != Z
    | ~ big_f(f(X),h(X,Z)) ) ).

cnf(refute_0_0,plain,
    ( f(X) != X
    | ~ big_f(X,h(X,Z))
    | big_f(f(X),h(X,Z)) ),
    introduced(tautology,[equality,[$cnf( ~ big_f(f(X),h(X,Z)) ),[0],$fot(X)]]) ).

cnf(refute_0_1,plain,
    ( h(X,Z) != Z
    | ~ big_f(X,Z)
    | big_f(X,h(X,Z)) ),
    introduced(tautology,[equality,[$cnf( ~ big_f(X,h(X,Z)) ),[1],$fot(Z)]]) ).

cnf(refute_0_2,plain,
    ( f(X) != X
    | h(X,Z) != Z
    | ~ big_f(X,Z)
    | big_f(f(X),h(X,Z)) ),
    inference(resolve,[$cnf( big_f(X,h(X,Z)) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    ( f(X) != X
    | h(X,Z) != Z
    | ~ big_f(X,Z) ),
    inference(resolve,[$cnf( big_f(f(X),h(X,Z)) )],[refute_0_2,clause_11]) ).

cnf(refute_0_4,plain,
    ( f(a) != a
    | h(a,b) != b
    | ~ big_f(a,b) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(a)),bind(Z,$fot(b))]]) ).

cnf(refute_0_5,plain,
    ( ~ big_f(a,h(a,X_27))
    | h(a,X_27) = b ),
    inference(subst,[],[clause_2:[bind(X,$fot(a)),bind(Y,$fot(h(a,X_27)))]]) ).

cnf(refute_0_6,plain,
    ( f(X) != X
    | ~ big_f(f(X),h(X,Z))
    | big_f(X,h(X,Z)) ),
    introduced(tautology,[equality,[$cnf( big_f(f(X),h(X,Z)) ),[0],$fot(X)]]) ).

cnf(refute_0_7,plain,
    ( f(X) != X
    | h(X,Z) = Z
    | big_f(X,h(X,Z)) ),
    inference(resolve,[$cnf( big_f(f(X),h(X,Z)) )],[clause_10,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( f(a) != a
    | h(a,X_26) = X_26
    | big_f(a,h(a,X_26)) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(a)),bind(Z,$fot(X_26))]]) ).

cnf(refute_0_9,plain,
    ( ~ big_f(f(X_4),g(X_4))
    | f(X_4) = a ),
    inference(subst,[],[clause_1:[bind(X,$fot(f(X_4))),bind(Y,$fot(g(X_4)))]]) ).

cnf(refute_0_10,plain,
    ( g(X) != g(X)
    | f(X) = X
    | big_f(f(X),g(X)) ),
    inference(subst,[],[clause_8:[bind(Y,$fot(g(X)))]]) ).

cnf(refute_0_11,plain,
    g(X) = g(X),
    introduced(tautology,[refl,[$fot(g(X))]]) ).

cnf(refute_0_12,plain,
    ( f(X) = X
    | big_f(f(X),g(X)) ),
    inference(resolve,[$cnf( $equal(g(X),g(X)) )],[refute_0_11,refute_0_10]) ).

cnf(refute_0_13,plain,
    ( f(X_4) = X_4
    | big_f(f(X_4),g(X_4)) ),
    inference(subst,[],[refute_0_12:[bind(X,$fot(X_4))]]) ).

cnf(refute_0_14,plain,
    ( f(X_4) = X_4
    | f(X_4) = a ),
    inference(resolve,[$cnf( big_f(f(X_4),g(X_4)) )],[refute_0_13,refute_0_9]) ).

cnf(refute_0_15,plain,
    f(a) = a,
    inference(subst,[],[refute_0_14:[bind(X_4,$fot(a))]]) ).

cnf(refute_0_16,plain,
    ( a != a
    | f(a) != a
    | f(a) = a ),
    introduced(tautology,[equality,[$cnf( $equal(f(a),a) ),[0,0],$fot(a)]]) ).

cnf(refute_0_17,plain,
    ( a != a
    | f(a) = a ),
    inference(resolve,[$cnf( $equal(f(a),a) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( a != a
    | h(a,X_26) = X_26
    | big_f(a,h(a,X_26)) ),
    inference(resolve,[$cnf( $equal(f(a),a) )],[refute_0_17,refute_0_8]) ).

cnf(refute_0_19,plain,
    a = a,
    introduced(tautology,[refl,[$fot(a)]]) ).

cnf(refute_0_20,plain,
    ( h(a,X_26) = X_26
    | big_f(a,h(a,X_26)) ),
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_19,refute_0_18]) ).

cnf(refute_0_21,plain,
    ( h(a,X_27) = X_27
    | big_f(a,h(a,X_27)) ),
    inference(subst,[],[refute_0_20:[bind(X_26,$fot(X_27))]]) ).

cnf(refute_0_22,plain,
    ( h(a,X_27) = X_27
    | h(a,X_27) = b ),
    inference(resolve,[$cnf( big_f(a,h(a,X_27)) )],[refute_0_21,refute_0_5]) ).

cnf(refute_0_23,plain,
    h(a,b) = b,
    inference(subst,[],[refute_0_22:[bind(X_27,$fot(b))]]) ).

cnf(refute_0_24,plain,
    ( b != b
    | h(a,b) != b
    | h(a,b) = b ),
    introduced(tautology,[equality,[$cnf( $equal(h(a,b),b) ),[0,1],$fot(b)]]) ).

cnf(refute_0_25,plain,
    ( b != b
    | h(a,b) = b ),
    inference(resolve,[$cnf( $equal(h(a,b),b) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( b != b
    | f(a) != a
    | ~ big_f(a,b) ),
    inference(resolve,[$cnf( $equal(h(a,b),b) )],[refute_0_25,refute_0_4]) ).

cnf(refute_0_27,plain,
    b = b,
    introduced(tautology,[refl,[$fot(b)]]) ).

cnf(refute_0_28,plain,
    ( f(a) != a
    | ~ big_f(a,b) ),
    inference(resolve,[$cnf( $equal(b,b) )],[refute_0_27,refute_0_26]) ).

cnf(refute_0_29,plain,
    ( a != a
    | ~ big_f(a,b) ),
    inference(resolve,[$cnf( $equal(f(a),a) )],[refute_0_17,refute_0_28]) ).

cnf(refute_0_30,plain,
    ~ big_f(a,b),
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_19,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( a != a
    | b != b
    | big_f(a,b) ),
    inference(subst,[],[clause_3:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_32,plain,
    ( b != b
    | big_f(a,b) ),
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_19,refute_0_31]) ).

cnf(refute_0_33,plain,
    big_f(a,b),
    inference(resolve,[$cnf( $equal(b,b) )],[refute_0_27,refute_0_32]) ).

cnf(refute_0_34,plain,
    $false,
    inference(resolve,[$cnf( big_f(a,b) )],[refute_0_33,refute_0_30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYN074-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n005.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 Jul 12 05:52:36 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------