TSTP Solution File: ANA038-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : ANA038-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n003.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 : Thu Jul 14 19:10:44 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   91 (  44 unt;  15 typ;   0 def)
%            Number of atoms       :  395 ( 104 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  757 (  86   ~; 111   |;   0   &; 560   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   7 con; 0-3 aty)
%            Number of variables   :  157 (   0   ^ 157   !;   0   ?; 157   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_0,type,
    c_0: $i ).

thf(tp_c_HOL_Oabs,type,
    c_HOL_Oabs: $i > $i > $i ).

thf(tp_c_Orderings_Omax,type,
    c_Orderings_Omax: $i > $i > $i > $i ).

thf(tp_c_lessequals,type,
    c_lessequals: $i > $i > $i > $o ).

thf(tp_c_times,type,
    c_times: $i > $i > $i > $i ).

thf(tp_class_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $i > $o ).

thf(tp_class_Orderings_Oorder,type,
    class_Orderings_Oorder: $i > $o ).

thf(tp_class_Ring__and__Field_Oordered__idom,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

thf(tp_class_Ring__and__Field_Opordered__semiring,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

thf(tp_t_b,type,
    t_b: $i ).

thf(tp_v_b,type,
    v_b: $i > $i ).

thf(tp_v_c,type,
    v_c: $i ).

thf(tp_v_ca,type,
    v_ca: $i ).

thf(tp_v_g,type,
    v_g: $i > $i ).

thf(tp_v_xa,type,
    v_xa: $i ).

thf(1,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).

thf(2,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

thf(3,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Orderings_Olinorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

thf(4,axiom,
    ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
      | ~ ( c_lessequals @ V_a @ V_b @ T_a )
      | ~ ( c_lessequals @ c_0 @ V_c @ T_a )
      | ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).

thf(5,axiom,
    ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ~ ( c_lessequals @ V_y @ V_z @ T_a )
      | ~ ( c_lessequals @ V_x @ V_y @ T_a )
      | ( c_lessequals @ V_x @ V_z @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).

thf(6,axiom,
    ! [T_b: $i,V_y: $i,V_x: $i] :
      ( ~ ( class_Orderings_Olinorder @ T_b )
      | ( c_lessequals @ V_y @ ( c_Orderings_Omax @ V_x @ V_y @ T_b ) @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Ole__maxI2_0) ).

thf(7,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(8,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[7]) ).

thf(9,negated_conjecture,
    class_Ring__and__Field_Oordered__idom @ t_b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).

thf(10,negated_conjecture,
    ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ v_xa ) @ t_b ) @ ( c_times @ ( c_Orderings_Omax @ v_c @ v_ca @ t_b ) @ ( v_g @ v_xa ) @ t_b ) @ t_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).

thf(11,negated_conjecture,
    c_lessequals @ ( c_HOL_Oabs @ ( v_b @ v_xa ) @ t_b ) @ ( c_times @ v_ca @ ( v_g @ v_xa ) @ t_b ) @ t_b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(12,negated_conjecture,
    c_lessequals @ c_0 @ ( v_g @ v_xa ) @ t_b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(13,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[8]) ).

thf(14,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(15,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(16,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(17,plain,
    ( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
          | ~ ( c_lessequals @ V_a @ V_b @ T_a )
          | ~ ( c_lessequals @ c_0 @ V_c @ T_a )
          | ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(18,plain,
    ( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ~ ( c_lessequals @ V_y @ V_z @ T_a )
          | ~ ( c_lessequals @ V_x @ V_y @ T_a )
          | ( c_lessequals @ V_x @ V_z @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(19,plain,
    ( ( ! [T_b: $i,V_y: $i,V_x: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_b )
          | ( c_lessequals @ V_y @ ( c_Orderings_Omax @ V_x @ V_y @ T_b ) @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(20,plain,
    ( ( class_Ring__and__Field_Oordered__idom @ t_b )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(21,plain,
    ( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ v_xa ) @ t_b ) @ ( c_times @ ( c_Orderings_Omax @ v_c @ v_ca @ t_b ) @ ( v_g @ v_xa ) @ t_b ) @ t_b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(22,plain,
    ( ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ v_xa ) @ t_b ) @ ( c_times @ v_ca @ ( v_g @ v_xa ) @ t_b ) @ t_b )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(23,plain,
    ( ( c_lessequals @ c_0 @ ( v_g @ v_xa ) @ t_b )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(24,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[13]) ).

thf(25,plain,
    ( ( ! [T_a: $i,V_a: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
          | ! [V_b: $i] :
              ( ~ ( c_lessequals @ V_a @ V_b @ T_a )
              | ! [V_c: $i] :
                  ( ~ ( c_lessequals @ c_0 @ V_c @ T_a )
                  | ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[17]) ).

thf(26,plain,
    ( ( ! [T_a: $i,V_y: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_z: $i] :
              ( ~ ( c_lessequals @ V_y @ V_z @ T_a )
              | ! [V_x: $i] :
                  ( ~ ( c_lessequals @ V_x @ V_y @ T_a )
                  | ( c_lessequals @ V_x @ V_z @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(27,plain,
    ( ( ! [T_b: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_b )
          | ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Orderings_Omax @ V_x @ V_y @ T_b ) @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(28,plain,
    ( ( c_lessequals @ c_0 @ ( v_g @ v_xa ) @ t_b )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(29,plain,
    ( ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ v_xa ) @ t_b ) @ ( c_times @ v_ca @ ( v_g @ v_xa ) @ t_b ) @ t_b )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(30,plain,
    ( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ v_xa ) @ t_b ) @ ( c_times @ ( c_Orderings_Omax @ v_c @ v_ca @ t_b ) @ ( v_g @ v_xa ) @ t_b ) @ t_b ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(31,plain,
    ( ( class_Ring__and__Field_Oordered__idom @ t_b )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(32,plain,
    ( ( ! [T_b: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_b )
          | ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Orderings_Omax @ V_x @ V_y @ T_b ) @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(33,plain,
    ( ( ! [T_a: $i,V_y: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_z: $i] :
              ( ~ ( c_lessequals @ V_y @ V_z @ T_a )
              | ! [V_x: $i] :
                  ( ~ ( c_lessequals @ V_x @ V_y @ T_a )
                  | ( c_lessequals @ V_x @ V_z @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(34,plain,
    ( ( ! [T_a: $i,V_a: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
          | ! [V_b: $i] :
              ( ~ ( c_lessequals @ V_a @ V_b @ T_a )
              | ! [V_c: $i] :
                  ( ~ ( c_lessequals @ c_0 @ V_c @ T_a )
                  | ( c_lessequals @ ( c_times @ V_a @ V_c @ T_a ) @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(35,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(36,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(37,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(38,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(39,plain,
    ( ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ v_xa ) @ t_b ) @ ( c_times @ ( c_Orderings_Omax @ v_c @ v_ca @ t_b ) @ ( v_g @ v_xa ) @ t_b ) @ t_b )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(40,plain,
    ! [SV1: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV1 )
        | ! [SY14: $i,SY15: $i] : ( c_lessequals @ SY14 @ ( c_Orderings_Omax @ SY15 @ SY14 @ SV1 ) @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(41,plain,
    ! [SV2: $i] :
      ( ( ! [SY16: $i] :
            ( ~ ( class_Orderings_Oorder @ SV2 )
            | ! [SY17: $i] :
                ( ~ ( c_lessequals @ SY16 @ SY17 @ SV2 )
                | ! [SY18: $i] :
                    ( ~ ( c_lessequals @ SY18 @ SY16 @ SV2 )
                    | ( c_lessequals @ SY18 @ SY17 @ SV2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(42,plain,
    ! [SV3: $i] :
      ( ( ! [SY19: $i] :
            ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV3 )
            | ! [SY20: $i] :
                ( ~ ( c_lessequals @ SY19 @ SY20 @ SV3 )
                | ! [SY21: $i] :
                    ( ~ ( c_lessequals @ c_0 @ SY21 @ SV3 )
                    | ( c_lessequals @ ( c_times @ SY19 @ SY21 @ SV3 ) @ ( c_times @ SY20 @ SY21 @ SV3 ) @ SV3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(43,plain,
    ! [SV4: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV4 )
        | ( class_Orderings_Olinorder @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(44,plain,
    ! [SV5: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV5 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(45,plain,
    ! [SV6: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV6 )
        | ( class_Orderings_Oorder @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(46,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(47,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV1 ) )
        = $true )
      | ( ( ! [SY14: $i,SY15: $i] : ( c_lessequals @ SY14 @ ( c_Orderings_Omax @ SY15 @ SY14 @ SV1 ) @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(48,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV2 )
        | ! [SY22: $i] :
            ( ~ ( c_lessequals @ SV7 @ SY22 @ SV2 )
            | ! [SY23: $i] :
                ( ~ ( c_lessequals @ SY23 @ SV7 @ SV2 )
                | ( c_lessequals @ SY23 @ SY22 @ SV2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(49,plain,
    ! [SV8: $i,SV3: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV3 )
        | ! [SY24: $i] :
            ( ~ ( c_lessequals @ SV8 @ SY24 @ SV3 )
            | ! [SY25: $i] :
                ( ~ ( c_lessequals @ c_0 @ SY25 @ SV3 )
                | ( c_lessequals @ ( c_times @ SV8 @ SY25 @ SV3 ) @ ( c_times @ SY24 @ SY25 @ SV3 ) @ SV3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(50,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV4 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[43]) ).

thf(51,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV5 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[44]) ).

thf(52,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV6 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(53,plain,
    ! [SV1: $i] :
      ( ( ( class_Orderings_Olinorder @ SV1 )
        = $false )
      | ( ( ! [SY14: $i,SY15: $i] : ( c_lessequals @ SY14 @ ( c_Orderings_Omax @ SY15 @ SY14 @ SV1 ) @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(54,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV2 ) )
        = $true )
      | ( ( ! [SY22: $i] :
              ( ~ ( c_lessequals @ SV7 @ SY22 @ SV2 )
              | ! [SY23: $i] :
                  ( ~ ( c_lessequals @ SY23 @ SV7 @ SV2 )
                  | ( c_lessequals @ SY23 @ SY22 @ SV2 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[48]) ).

thf(55,plain,
    ! [SV8: $i,SV3: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV3 ) )
        = $true )
      | ( ( ! [SY24: $i] :
              ( ~ ( c_lessequals @ SV8 @ SY24 @ SV3 )
              | ! [SY25: $i] :
                  ( ~ ( c_lessequals @ c_0 @ SY25 @ SV3 )
                  | ( c_lessequals @ ( c_times @ SV8 @ SY25 @ SV3 ) @ ( c_times @ SY24 @ SY25 @ SV3 ) @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(56,plain,
    ! [SV4: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV4 )
        = $false )
      | ( ( class_Orderings_Olinorder @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(57,plain,
    ! [SV5: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV5 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(58,plain,
    ! [SV6: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV6 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(59,plain,
    ! [SV1: $i,SV9: $i] :
      ( ( ( ! [SY26: $i] : ( c_lessequals @ SV9 @ ( c_Orderings_Omax @ SY26 @ SV9 @ SV1 ) @ SV1 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(60,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ( class_Orderings_Oorder @ SV2 )
        = $false )
      | ( ( ! [SY22: $i] :
              ( ~ ( c_lessequals @ SV7 @ SY22 @ SV2 )
              | ! [SY23: $i] :
                  ( ~ ( c_lessequals @ SY23 @ SV7 @ SV2 )
                  | ( c_lessequals @ SY23 @ SY22 @ SV2 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(61,plain,
    ! [SV8: $i,SV3: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
        = $false )
      | ( ( ! [SY24: $i] :
              ( ~ ( c_lessequals @ SV8 @ SY24 @ SV3 )
              | ! [SY25: $i] :
                  ( ~ ( c_lessequals @ c_0 @ SY25 @ SV3 )
                  | ( c_lessequals @ ( c_times @ SV8 @ SY25 @ SV3 ) @ ( c_times @ SY24 @ SY25 @ SV3 ) @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(62,plain,
    ! [SV1: $i,SV10: $i,SV9: $i] :
      ( ( ( c_lessequals @ SV9 @ ( c_Orderings_Omax @ SV10 @ SV9 @ SV1 ) @ SV1 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(63,plain,
    ! [SV2: $i,SV11: $i,SV7: $i] :
      ( ( ( ~ ( c_lessequals @ SV7 @ SV11 @ SV2 )
          | ! [SY27: $i] :
              ( ~ ( c_lessequals @ SY27 @ SV7 @ SV2 )
              | ( c_lessequals @ SY27 @ SV11 @ SV2 ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV2 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(64,plain,
    ! [SV3: $i,SV12: $i,SV8: $i] :
      ( ( ( ~ ( c_lessequals @ SV8 @ SV12 @ SV3 )
          | ! [SY28: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY28 @ SV3 )
              | ( c_lessequals @ ( c_times @ SV8 @ SY28 @ SV3 ) @ ( c_times @ SV12 @ SY28 @ SV3 ) @ SV3 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(65,plain,
    ! [SV2: $i,SV11: $i,SV7: $i] :
      ( ( ( ~ ( c_lessequals @ SV7 @ SV11 @ SV2 ) )
        = $true )
      | ( ( ! [SY27: $i] :
              ( ~ ( c_lessequals @ SY27 @ SV7 @ SV2 )
              | ( c_lessequals @ SY27 @ SV11 @ SV2 ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(66,plain,
    ! [SV3: $i,SV12: $i,SV8: $i] :
      ( ( ( ~ ( c_lessequals @ SV8 @ SV12 @ SV3 ) )
        = $true )
      | ( ( ! [SY28: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY28 @ SV3 )
              | ( c_lessequals @ ( c_times @ SV8 @ SY28 @ SV3 ) @ ( c_times @ SV12 @ SY28 @ SV3 ) @ SV3 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(67,plain,
    ! [SV2: $i,SV11: $i,SV7: $i] :
      ( ( ( c_lessequals @ SV7 @ SV11 @ SV2 )
        = $false )
      | ( ( ! [SY27: $i] :
              ( ~ ( c_lessequals @ SY27 @ SV7 @ SV2 )
              | ( c_lessequals @ SY27 @ SV11 @ SV2 ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(68,plain,
    ! [SV3: $i,SV12: $i,SV8: $i] :
      ( ( ( c_lessequals @ SV8 @ SV12 @ SV3 )
        = $false )
      | ( ( ! [SY28: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY28 @ SV3 )
              | ( c_lessequals @ ( c_times @ SV8 @ SY28 @ SV3 ) @ ( c_times @ SV12 @ SY28 @ SV3 ) @ SV3 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[66]) ).

thf(69,plain,
    ! [SV11: $i,SV2: $i,SV7: $i,SV13: $i] :
      ( ( ( ~ ( c_lessequals @ SV13 @ SV7 @ SV2 )
          | ( c_lessequals @ SV13 @ SV11 @ SV2 ) )
        = $true )
      | ( ( c_lessequals @ SV7 @ SV11 @ SV2 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV2 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(70,plain,
    ! [SV12: $i,SV8: $i,SV3: $i,SV14: $i] :
      ( ( ( ~ ( c_lessequals @ c_0 @ SV14 @ SV3 )
          | ( c_lessequals @ ( c_times @ SV8 @ SV14 @ SV3 ) @ ( c_times @ SV12 @ SV14 @ SV3 ) @ SV3 ) )
        = $true )
      | ( ( c_lessequals @ SV8 @ SV12 @ SV3 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(71,plain,
    ! [SV11: $i,SV2: $i,SV7: $i,SV13: $i] :
      ( ( ( ~ ( c_lessequals @ SV13 @ SV7 @ SV2 ) )
        = $true )
      | ( ( c_lessequals @ SV13 @ SV11 @ SV2 )
        = $true )
      | ( ( c_lessequals @ SV7 @ SV11 @ SV2 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[69]) ).

thf(72,plain,
    ! [SV12: $i,SV8: $i,SV3: $i,SV14: $i] :
      ( ( ( ~ ( c_lessequals @ c_0 @ SV14 @ SV3 ) )
        = $true )
      | ( ( c_lessequals @ ( c_times @ SV8 @ SV14 @ SV3 ) @ ( c_times @ SV12 @ SV14 @ SV3 ) @ SV3 )
        = $true )
      | ( ( c_lessequals @ SV8 @ SV12 @ SV3 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[70]) ).

thf(73,plain,
    ! [SV11: $i,SV2: $i,SV7: $i,SV13: $i] :
      ( ( ( c_lessequals @ SV13 @ SV7 @ SV2 )
        = $false )
      | ( ( c_lessequals @ SV13 @ SV11 @ SV2 )
        = $true )
      | ( ( c_lessequals @ SV7 @ SV11 @ SV2 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(74,plain,
    ! [SV12: $i,SV8: $i,SV3: $i,SV14: $i] :
      ( ( ( c_lessequals @ c_0 @ SV14 @ SV3 )
        = $false )
      | ( ( c_lessequals @ ( c_times @ SV8 @ SV14 @ SV3 ) @ ( c_times @ SV12 @ SV14 @ SV3 ) @ SV3 )
        = $true )
      | ( ( c_lessequals @ SV8 @ SV12 @ SV3 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(75,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[28,74,73,62,58,57,56,46,39,31,29]) ).

thf(76,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[75]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : ANA038-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n003.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 : Fri Jul  8 05:29:12 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.36  
% 0.20/0.36   No.of.Axioms: 10
% 0.20/0.36  
% 0.20/0.36   Length.of.Defs: 0
% 0.20/0.36  
% 0.20/0.36   Contains.Choice.Funs: false
% 0.20/0.36  (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:12,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.20/0.43  
% 0.20/0.43  ********************************
% 0.20/0.43  *   All subproblems solved!    *
% 0.20/0.43  ********************************
% 0.20/0.43  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:75,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.43  
% 0.20/0.43  %**** Beginning of derivation protocol ****
% 0.20/0.43  % SZS output start CNFRefutation
% See solution above
% 0.20/0.43  
% 0.20/0.43  %**** End of derivation protocol ****
% 0.20/0.43  %**** no. of clauses in derivation: 76 ****
% 0.20/0.43  %**** clause counter: 75 ****
% 0.20/0.43  
% 0.20/0.43  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:75,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------