%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV860-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 20:40:25 EDT 2022

% Result   : Unsatisfiable 0.92s 1.10s
% Output   : CNFRefutation 0.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (   8 unt;   0 nHn;  14 RR)
%            Number of literals    :   22 (  11 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    3 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_evaln__elim__cases_I1_J_0,axiom,
    ( V_t = V_s
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ) ).

cnf(cls_conjecture_0,negated_conjecture,
    hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) ).

cnf(cls_conjecture_2,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb)) ).

cnf(refute_0_0,plain,
    ( ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb)
    | v_xb = v_xa ),
    inference(subst,[],[cls_evaln__elim__cases_I1_J_0:[bind(V_n,$fot(v_n)),bind(V_s,$fot(v_xa)),bind(V_t,$fot(v_xb))]]) ).

cnf(refute_0_1,plain,
    v_xb = v_xa,
    inference(resolve,[$cnf( c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb) )],[cls_conjecture_1,refute_0_0]) ).

cnf(refute_0_2,plain,
    hAPP(hAPP(v_P,v_x),v_xb) = hAPP(hAPP(v_P,v_x),v_xb),
    introduced(tautology,[refl,[$fot(hAPP(hAPP(v_P,v_x),v_xb))]]) ).

cnf(refute_0_3,plain,
    ( hAPP(hAPP(v_P,v_x),v_xb) != hAPP(hAPP(v_P,v_x),v_xb)
    | v_xb != v_xa
    | hAPP(hAPP(v_P,v_x),v_xb) = hAPP(hAPP(v_P,v_x),v_xa) ),
    introduced(tautology,[equality,[$cnf( $equal(hAPP(hAPP(v_P,v_x),v_xb),hAPP(hAPP(v_P,v_x),v_xb)) ),[1,1],$fot(v_xa)]]) ).

cnf(refute_0_4,plain,
    ( v_xb != v_xa
    | hAPP(hAPP(v_P,v_x),v_xb) = hAPP(hAPP(v_P,v_x),v_xa) ),
    inference(resolve,[$cnf( $equal(hAPP(hAPP(v_P,v_x),v_xb),hAPP(hAPP(v_P,v_x),v_xb)) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    hAPP(hAPP(v_P,v_x),v_xb) = hAPP(hAPP(v_P,v_x),v_xa),
    inference(resolve,[$cnf( $equal(v_xb,v_xa) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( hAPP(hAPP(v_P,v_x),v_xb) != hAPP(hAPP(v_P,v_x),v_xa)
    | ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
    | hBOOL(hAPP(hAPP(v_P,v_x),v_xb)) ),
    introduced(tautology,[equality,[$cnf( ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb)) ),[0],$fot(hAPP(hAPP(v_P,v_x),v_xa))]]) ).

cnf(refute_0_7,plain,
    ( ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
    | hBOOL(hAPP(hAPP(v_P,v_x),v_xb)) ),
    inference(resolve,[$cnf( $equal(hAPP(hAPP(v_P,v_x),v_xb),hAPP(hAPP(v_P,v_x),v_xa)) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
    inference(resolve,[$cnf( hBOOL(hAPP(hAPP(v_P,v_x),v_xb)) )],[refute_0_7,cls_conjecture_2]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) )],[cls_conjecture_0,refute_0_8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV860-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n011.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 : Thu Jun 16 00:49:21 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.92/1.10  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.92/1.10  
% 0.92/1.10  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.92/1.10  
%------------------------------------------------------------------------------