%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LAT271-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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 : Sun Jul 17 06:01:55 EDT 2022

% Result   : Unsatisfiable 0.13s 0.34s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   5 unt;   0 nHn;   9 RR)
%            Number of literals    :   15 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-4 aty)
%            Number of variables   :    8 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_conjecture_2,negated_conjecture,
    c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) ).

cnf(cls_conjecture_6,negated_conjecture,
    c_in(v_x,v_S,t_a) ).

cnf(cls_conjecture_7,negated_conjecture,
    ~ c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ).

cnf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
    ( ~ c_in(V_x,V_S,T_a)
    | ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
    | c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ).

cnf(refute_0_0,plain,
    ( ~ c_in(X_5,v_S,t_a)
    | ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
    | c_in(c_Pair(v_a,X_5,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
    inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_a,$fot(v_a)),bind(V_b,$fot(v_b)),bind(V_r,$fot(v_r)),bind(V_x,$fot(X_5))]]) ).

cnf(refute_0_1,plain,
    ( ~ c_in(X_5,v_S,t_a)
    | c_in(c_Pair(v_a,X_5,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
    inference(resolve,[$cnf( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )],[cls_conjecture_2,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ c_in(v_x,v_S,t_a)
    | c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
    inference(subst,[],[refute_0_1:[bind(X_5,$fot(v_x))]]) ).

cnf(refute_0_3,plain,
    c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
    inference(resolve,[$cnf( c_in(v_x,v_S,t_a) )],[cls_conjecture_6,refute_0_2]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_3,cls_conjecture_7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LAT271-2 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Wed Jun 29 18:10:30 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34  
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.34  
%------------------------------------------------------------------------------