%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN075-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 08:59:20 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   44 (  11 unt;  10 nHn;  30 RR)
%            Number of literals    :   96 (  60 equ;  50 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   :   56 (   5 sgn)

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

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

cnf(clause_4,negated_conjecture,
    ( ~ big_f(Y,f(X))
    | Y != g(X)
    | f(X) = X ) ).

cnf(clause_6,negated_conjecture,
    ( Y != g(X)
    | big_f(Y,f(X))
    | f(X) = X ) ).

cnf(clause_9,negated_conjecture,
    ( f(X) != X
    | big_f(h(X,Z),f(X))
    | h(X,Z) = Z ) ).

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

cnf(refute_0_0,plain,
    ( a != a
    | b != b
    | big_f(a,b) ),
    inference(subst,[],[clause_3:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_1,plain,
    a = a,
    introduced(tautology,[refl,[$fot(a)]]) ).

cnf(refute_0_2,plain,
    ( b != b
    | big_f(a,b) ),
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    b = b,
    introduced(tautology,[refl,[$fot(b)]]) ).

cnf(refute_0_4,plain,
    big_f(a,b),
    inference(resolve,[$cnf( $equal(b,b) )],[refute_0_3,refute_0_2]) ).

cnf(refute_0_5,plain,
    ( h(X,Z) != Z
    | ~ big_f(Z,f(X))
    | big_f(h(X,Z),f(X)) ),
    introduced(tautology,[equality,[$cnf( ~ big_f(h(X,Z),f(X)) ),[0],$fot(Z)]]) ).

cnf(refute_0_6,plain,
    ( f(X) != X
    | ~ big_f(Z,X)
    | big_f(Z,f(X)) ),
    introduced(tautology,[equality,[$cnf( ~ big_f(Z,f(X)) ),[1],$fot(X)]]) ).

cnf(refute_0_7,plain,
    ( f(X) != X
    | h(X,Z) != Z
    | ~ big_f(Z,X)
    | big_f(h(X,Z),f(X)) ),
    inference(resolve,[$cnf( big_f(Z,f(X)) )],[refute_0_6,refute_0_5]) ).

cnf(refute_0_8,plain,
    ( f(X) != X
    | h(X,Z) != Z
    | ~ big_f(Z,X) ),
    inference(resolve,[$cnf( big_f(h(X,Z),f(X)) )],[refute_0_7,clause_10]) ).

cnf(refute_0_9,plain,
    ( g(X) != g(X)
    | f(X) = X
    | big_f(g(X),f(X)) ),
    inference(subst,[],[clause_6:[bind(Y,$fot(g(X)))]]) ).

cnf(refute_0_10,plain,
    g(X) = g(X),
    introduced(tautology,[refl,[$fot(g(X))]]) ).

cnf(refute_0_11,plain,
    ( f(X) = X
    | big_f(g(X),f(X)) ),
    inference(resolve,[$cnf( $equal(g(X),g(X)) )],[refute_0_10,refute_0_9]) ).

cnf(refute_0_12,plain,
    ( f(X_9) = X_9
    | big_f(g(X_9),f(X_9)) ),
    inference(subst,[],[refute_0_11:[bind(X,$fot(X_9))]]) ).

cnf(refute_0_13,plain,
    ( g(X) != g(X)
    | ~ big_f(g(X),f(X))
    | f(X) = X ),
    inference(subst,[],[clause_4:[bind(Y,$fot(g(X)))]]) ).

cnf(refute_0_14,plain,
    ( ~ big_f(g(X),f(X))
    | f(X) = X ),
    inference(resolve,[$cnf( $equal(g(X),g(X)) )],[refute_0_10,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( ~ big_f(g(X_9),f(X_9))
    | f(X_9) = X_9 ),
    inference(subst,[],[refute_0_14:[bind(X,$fot(X_9))]]) ).

cnf(refute_0_16,plain,
    f(X_9) = X_9,
    inference(resolve,[$cnf( big_f(g(X_9),f(X_9)) )],[refute_0_12,refute_0_15]) ).

cnf(refute_0_17,plain,
    f(X) = X,
    inference(subst,[],[refute_0_16:[bind(X_9,$fot(X))]]) ).

cnf(refute_0_18,plain,
    ( X != X
    | f(X) != X
    | f(X) = X ),
    introduced(tautology,[equality,[$cnf( $equal(f(X),X) ),[0,0],$fot(X)]]) ).

cnf(refute_0_19,plain,
    ( X != X
    | f(X) = X ),
    inference(resolve,[$cnf( $equal(f(X),X) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( X != X
    | h(X,Z) != Z
    | ~ big_f(Z,X) ),
    inference(resolve,[$cnf( $equal(f(X),X) )],[refute_0_19,refute_0_8]) ).

cnf(refute_0_21,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_22,plain,
    ( h(X,Z) != Z
    | ~ big_f(Z,X) ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_21,refute_0_20]) ).

cnf(refute_0_23,plain,
    ( h(X,a) != a
    | ~ big_f(a,X) ),
    inference(subst,[],[refute_0_22:[bind(Z,$fot(a))]]) ).

cnf(refute_0_24,plain,
    ( ~ big_f(h(X_13,X_14),X_13)
    | h(X_13,X_14) = a ),
    inference(subst,[],[clause_1:[bind(X,$fot(h(X_13,X_14))),bind(Y,$fot(X_13))]]) ).

cnf(refute_0_25,plain,
    ( f(X) != X
    | ~ big_f(h(X,Z),f(X))
    | big_f(h(X,Z),X) ),
    introduced(tautology,[equality,[$cnf( big_f(h(X,Z),f(X)) ),[1],$fot(X)]]) ).

cnf(refute_0_26,plain,
    ( f(X) != X
    | h(X,Z) = Z
    | big_f(h(X,Z),X) ),
    inference(resolve,[$cnf( big_f(h(X,Z),f(X)) )],[clause_9,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( X != X
    | h(X,Z) = Z
    | big_f(h(X,Z),X) ),
    inference(resolve,[$cnf( $equal(f(X),X) )],[refute_0_19,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( h(X,Z) = Z
    | big_f(h(X,Z),X) ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_21,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( h(X_13,X_14) = X_14
    | big_f(h(X_13,X_14),X_13) ),
    inference(subst,[],[refute_0_28:[bind(X,$fot(X_13)),bind(Z,$fot(X_14))]]) ).

cnf(refute_0_30,plain,
    ( h(X_13,X_14) = X_14
    | h(X_13,X_14) = a ),
    inference(resolve,[$cnf( big_f(h(X_13,X_14),X_13) )],[refute_0_29,refute_0_24]) ).

cnf(refute_0_31,plain,
    h(X,a) = a,
    inference(subst,[],[refute_0_30:[bind(X_13,$fot(X)),bind(X_14,$fot(a))]]) ).

cnf(refute_0_32,plain,
    ( a != a
    | h(X,a) != a
    | h(X,a) = a ),
    introduced(tautology,[equality,[$cnf( $equal(h(X,a),a) ),[0,1],$fot(a)]]) ).

cnf(refute_0_33,plain,
    ( a != a
    | h(X,a) = a ),
    inference(resolve,[$cnf( $equal(h(X,a),a) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( a != a
    | ~ big_f(a,X) ),
    inference(resolve,[$cnf( $equal(h(X,a),a) )],[refute_0_33,refute_0_23]) ).

cnf(refute_0_35,plain,
    ~ big_f(a,X),
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_1,refute_0_34]) ).

cnf(refute_0_36,plain,
    ~ big_f(a,b),
    inference(subst,[],[refute_0_35:[bind(X,$fot(b))]]) ).

cnf(refute_0_37,plain,
    $false,
    inference(resolve,[$cnf( big_f(a,b) )],[refute_0_4,refute_0_36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYN075-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n007.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 : Tue Jul 12 03:47:48 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------