%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ANA021-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %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  : 300s
% DateTime : Wed Aug 30 17:13:55 EDT 2023

% Result   : Unsatisfiable 0.21s 0.59s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   27 (   8 unt;  14 typ;   0 def)
%            Number of atoms       :   18 (   6 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   13 (   8   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (   8   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :    7 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    c_0: $i ).

tff(decl_23,type,
    tc_nat: $i ).

tff(decl_24,type,
    c_less: ( $i * $i * $i ) > $o ).

tff(decl_25,type,
    c_1: $i ).

tff(decl_26,type,
    c_minus: ( $i * $i * $i ) > $i ).

tff(decl_27,type,
    c_Suc: $i > $i ).

tff(decl_28,type,
    v_f: $i > $i ).

tff(decl_29,type,
    t_a: $i ).

tff(decl_30,type,
    c_HOL_Oabs: ( $i * $i ) > $i ).

tff(decl_31,type,
    v_c: $i ).

tff(decl_32,type,
    v_h: $i > $i ).

tff(decl_33,type,
    c_times: ( $i * $i * $i ) > $i ).

tff(decl_34,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(decl_35,type,
    v_x: $i ).

cnf(cls_conjecture_2,negated_conjecture,
    c_lessequals(c_HOL_Oabs(v_f(c_Suc(X1)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(X1)),t_a),t_a),t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_NatBin_OSuc__pred_H_0,axiom,
    ( X1 = c_Suc(c_minus(X1,c_1,tc_nat))
    | ~ c_less(c_0,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).

cnf(cls_conjecture_4,negated_conjecture,
    ~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(cls_Nat_Onot__gr0_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | X1 = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).

cnf(cls_conjecture_3,negated_conjecture,
    v_x != c_0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(c_0_5,negated_conjecture,
    c_lessequals(c_HOL_Oabs(v_f(c_Suc(X1)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(X1)),t_a),t_a),t_a),
    cls_conjecture_2 ).

cnf(c_0_6,axiom,
    ( X1 = c_Suc(c_minus(X1,c_1,tc_nat))
    | ~ c_less(c_0,X1,tc_nat) ),
    cls_NatBin_OSuc__pred_H_0 ).

cnf(c_0_7,negated_conjecture,
    ~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
    cls_conjecture_4 ).

cnf(c_0_8,negated_conjecture,
    ( c_lessequals(c_HOL_Oabs(v_f(X1),t_a),c_times(v_c,c_HOL_Oabs(v_h(X1),t_a),t_a),t_a)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    ~ c_less(c_0,v_x,tc_nat),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_10,axiom,
    ( c_less(c_0,X1,tc_nat)
    | X1 = c_0 ),
    cls_Nat_Onot__gr0_0 ).

cnf(c_0_11,negated_conjecture,
    v_x != c_0,
    cls_conjecture_3 ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : ANA021-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.34  % Computer : n013.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit   : 300
% 0.17/0.34  % WCLimit    : 300
% 0.17/0.34  % DateTime   : Fri Aug 25 18:20:32 EDT 2023
% 0.17/0.34  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.59  % Version  : CSE_E---1.5
% 0.21/0.59  % Problem  : theBenchmark.p
% 0.21/0.59  % Proof found
% 0.21/0.59  % SZS status Theorem for theBenchmark.p
% 0.21/0.59  % SZS output start Proof
% See solution above
% 0.21/0.59  % Total time : 0.004000 s
% 0.21/0.59  % SZS output end Proof
% 0.21/0.59  % Total time : 0.006000 s
%------------------------------------------------------------------------------