%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV002-1 : 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 : Wed Jul 20 20:29:47 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   32 (  15 unt;   3 nHn;  30 RR)
%            Number of literals    :   58 (  21 equ;  26 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :   14 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(transitivity_of_less_than,axiom,
    ( less_than(X,Z)
    | ~ less_than(X,Y)
    | ~ less_than(Y,Z) ) ).

cnf(all_related,axiom,
    ( less_than(X,Y)
    | less_than(Y,X)
    | X = Y ) ).

cnf(x_not_less_than_x,axiom,
    ~ less_than(X,X) ).

cnf(clause_5,negated_conjecture,
    less_than(a(j),a(k)) ).

cnf(clause_6,negated_conjecture,
    ( less_than(X,i)
    | ~ less_than(X,j)
    | ~ less_than(a(X),a(k)) ) ).

cnf(clause_9,negated_conjecture,
    ~ less_than(q,i) ).

cnf(clause_10,negated_conjecture,
    ~ less_than(j,q) ).

cnf(clause_11,negated_conjecture,
    less_than(a(q),a(j)) ).

cnf(refute_0_0,plain,
    ( less_than(j,q)
    | less_than(q,j)
    | j = q ),
    inference(subst,[],[all_related:[bind(X,$fot(j)),bind(Y,$fot(q))]]) ).

cnf(refute_0_1,plain,
    ( ~ less_than(a(q),a(k))
    | ~ less_than(q,j)
    | less_than(q,i) ),
    inference(subst,[],[clause_6:[bind(X,$fot(q))]]) ).

cnf(refute_0_2,plain,
    ( ~ less_than(a(j),X_20)
    | ~ less_than(a(q),a(j))
    | less_than(a(q),X_20) ),
    inference(subst,[],[transitivity_of_less_than:[bind(X,$fot(a(q))),bind(Y,$fot(a(j))),bind(Z,$fot(X_20))]]) ).

cnf(refute_0_3,plain,
    ( ~ less_than(a(j),X_20)
    | less_than(a(q),X_20) ),
    inference(resolve,[$cnf( less_than(a(q),a(j)) )],[clause_11,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ less_than(a(j),a(k))
    | less_than(a(q),a(k)) ),
    inference(subst,[],[refute_0_3:[bind(X_20,$fot(a(k)))]]) ).

cnf(refute_0_5,plain,
    less_than(a(q),a(k)),
    inference(resolve,[$cnf( less_than(a(j),a(k)) )],[clause_5,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ less_than(q,j)
    | less_than(q,i) ),
    inference(resolve,[$cnf( less_than(a(q),a(k)) )],[refute_0_5,refute_0_1]) ).

cnf(refute_0_7,plain,
    ~ less_than(q,j),
    inference(resolve,[$cnf( less_than(q,i) )],[refute_0_6,clause_9]) ).

cnf(refute_0_8,plain,
    ( less_than(j,q)
    | j = q ),
    inference(resolve,[$cnf( less_than(q,j) )],[refute_0_0,refute_0_7]) ).

cnf(refute_0_9,plain,
    j = q,
    inference(resolve,[$cnf( less_than(j,q) )],[refute_0_8,clause_10]) ).

cnf(refute_0_10,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_11,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_12,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( j != q
    | q = j ),
    inference(subst,[],[refute_0_12:[bind(X0,$fot(j)),bind(Y0,$fot(q))]]) ).

cnf(refute_0_14,plain,
    q = j,
    inference(resolve,[$cnf( $equal(j,q) )],[refute_0_9,refute_0_13]) ).

cnf(refute_0_15,plain,
    a(q) = a(q),
    introduced(tautology,[refl,[$fot(a(q))]]) ).

cnf(refute_0_16,plain,
    ( a(q) != a(q)
    | q != j
    | a(q) = a(j) ),
    introduced(tautology,[equality,[$cnf( $equal(a(q),a(q)) ),[1,0],$fot(j)]]) ).

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

cnf(refute_0_18,plain,
    a(q) = a(j),
    inference(resolve,[$cnf( $equal(q,j) )],[refute_0_14,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( ~ less_than(a(q),a(j))
    | a(q) != a(j)
    | less_than(a(j),a(j)) ),
    introduced(tautology,[equality,[$cnf( less_than(a(q),a(j)) ),[0],$fot(a(j))]]) ).

cnf(refute_0_20,plain,
    ( ~ less_than(a(q),a(j))
    | less_than(a(j),a(j)) ),
    inference(resolve,[$cnf( $equal(a(q),a(j)) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    less_than(a(j),a(j)),
    inference(resolve,[$cnf( less_than(a(q),a(j)) )],[clause_11,refute_0_20]) ).

cnf(refute_0_22,plain,
    ~ less_than(a(j),a(j)),
    inference(subst,[],[x_not_less_than_x:[bind(X,$fot(a(j)))]]) ).

cnf(refute_0_23,plain,
    $false,
    inference(resolve,[$cnf( less_than(a(j),a(j)) )],[refute_0_21,refute_0_22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n007.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 Jun 14 14:10:24 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.41  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41  
% 0.19/0.41  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.41  
%------------------------------------------------------------------------------