%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n013.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 20:29:46 EDT 2022

% Result   : Unsatisfiable 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   29 (   9 unt;   6 nHn;  27 RR)
%            Number of literals    :   60 (   0 equ;  31 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   17 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause_1,axiom,
    ( ~ q1(X,Y,Z)
    | ~ less_or_equalish(X,Y)
    | q2(X,Y,Z) ) ).

cnf(clause_2,axiom,
    ( ~ q1(X,Y,Z)
    | less_or_equalish(X,Y)
    | q3(X,Y,Z) ) ).

cnf(clause_3,axiom,
    ( ~ q2(X,Y,Z)
    | q4(X,Y,Y) ) ).

cnf(clause_4,axiom,
    ( ~ q3(X,Y,Z)
    | q4(X,Y,X) ) ).

cnf(less_or_equal_reflexivity,axiom,
    less_or_equalish(X,X) ).

cnf(all_less_or_equal,axiom,
    ( less_or_equalish(X,Y)
    | less_or_equalish(Y,X) ) ).

cnf(clause_5,negated_conjecture,
    q1(a,b,c) ).

cnf(clause_6,negated_conjecture,
    ( ~ q4(a,b,W)
    | ~ less_or_equalish(a,W)
    | ~ less_or_equalish(b,W)
    | ~ less_or_equalish(W,a) ) ).

cnf(clause_7,negated_conjecture,
    ( ~ q4(a,b,W)
    | ~ less_or_equalish(a,W)
    | ~ less_or_equalish(b,W)
    | ~ less_or_equalish(W,b) ) ).

cnf(refute_0_0,plain,
    ( ~ less_or_equalish(a,b)
    | ~ less_or_equalish(b,b)
    | ~ q4(a,b,b) ),
    inference(subst,[],[clause_7:[bind(W,$fot(b))]]) ).

cnf(refute_0_1,plain,
    ( ~ q2(a,b,c)
    | q4(a,b,b) ),
    inference(subst,[],[clause_3:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).

cnf(refute_0_2,plain,
    ( ~ less_or_equalish(a,b)
    | ~ q1(a,b,c)
    | q2(a,b,c) ),
    inference(subst,[],[clause_1:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).

cnf(refute_0_3,plain,
    ( ~ less_or_equalish(a,b)
    | q2(a,b,c) ),
    inference(resolve,[$cnf( q1(a,b,c) )],[clause_5,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( less_or_equalish(a,b)
    | less_or_equalish(b,a) ),
    inference(subst,[],[all_less_or_equal:[bind(X,$fot(b)),bind(Y,$fot(a))]]) ).

cnf(refute_0_5,plain,
    ( ~ less_or_equalish(a,a)
    | ~ less_or_equalish(b,a)
    | ~ q4(a,b,a) ),
    inference(subst,[],[clause_6:[bind(W,$fot(a))]]) ).

cnf(refute_0_6,plain,
    ( ~ q3(a,b,c)
    | q4(a,b,a) ),
    inference(subst,[],[clause_4:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).

cnf(refute_0_7,plain,
    ( ~ q1(a,b,c)
    | less_or_equalish(a,b)
    | q3(a,b,c) ),
    inference(subst,[],[clause_2:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).

cnf(refute_0_8,plain,
    ( less_or_equalish(a,b)
    | q3(a,b,c) ),
    inference(resolve,[$cnf( q1(a,b,c) )],[clause_5,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( less_or_equalish(a,b)
    | q4(a,b,a) ),
    inference(resolve,[$cnf( q3(a,b,c) )],[refute_0_8,refute_0_6]) ).

cnf(refute_0_10,plain,
    ( ~ less_or_equalish(a,a)
    | ~ less_or_equalish(b,a)
    | less_or_equalish(a,b) ),
    inference(resolve,[$cnf( q4(a,b,a) )],[refute_0_9,refute_0_5]) ).

cnf(refute_0_11,plain,
    less_or_equalish(a,a),
    inference(subst,[],[less_or_equal_reflexivity:[bind(X,$fot(a))]]) ).

cnf(refute_0_12,plain,
    ( ~ less_or_equalish(b,a)
    | less_or_equalish(a,b) ),
    inference(resolve,[$cnf( less_or_equalish(a,a) )],[refute_0_11,refute_0_10]) ).

cnf(refute_0_13,plain,
    less_or_equalish(a,b),
    inference(resolve,[$cnf( less_or_equalish(b,a) )],[refute_0_4,refute_0_12]) ).

cnf(refute_0_14,plain,
    q2(a,b,c),
    inference(resolve,[$cnf( less_or_equalish(a,b) )],[refute_0_13,refute_0_3]) ).

cnf(refute_0_15,plain,
    q4(a,b,b),
    inference(resolve,[$cnf( q2(a,b,c) )],[refute_0_14,refute_0_1]) ).

cnf(refute_0_16,plain,
    ( ~ less_or_equalish(a,b)
    | ~ less_or_equalish(b,b) ),
    inference(resolve,[$cnf( q4(a,b,b) )],[refute_0_15,refute_0_0]) ).

cnf(refute_0_17,plain,
    ~ less_or_equalish(b,b),
    inference(resolve,[$cnf( less_or_equalish(a,b) )],[refute_0_13,refute_0_16]) ).

cnf(refute_0_18,plain,
    less_or_equalish(b,b),
    inference(subst,[],[less_or_equal_reflexivity:[bind(X,$fot(b))]]) ).

cnf(refute_0_19,plain,
    $false,
    inference(resolve,[$cnf( less_or_equalish(b,b) )],[refute_0_18,refute_0_17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SWV001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue Jun 14 23:15:29 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36  
% 0.13/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37  
%------------------------------------------------------------------------------