TSTP Solution File: ANA019-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : ANA019-2 : 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 : n014.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 19:10:30 EDT 2022

% Result   : Unsatisfiable 0.18s 0.42s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  121 (  58 unt;  19 typ;   0 def)
%            Number of atoms       :  474 ( 148 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  820 (  92   ~; 118   |;   0   &; 610   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  19 usr;   7 con; 0-3 aty)
%            Number of variables   :  141 (   0   ^ 141   !;   0   ?; 141   :)

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

thf(tp_c_1,type,
    c_1: $i ).

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

thf(tp_c_Suc,type,
    c_Suc: $i > $i ).

thf(tp_c_less,type,
    c_less: $i > $i > $i > $o ).

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

thf(tp_c_minus,type,
    c_minus: $i > $i > $i > $i ).

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

thf(tp_class_LOrder_Ojoin__semilorder,type,
    class_LOrder_Ojoin__semilorder: $i > $o ).

thf(tp_class_OrderedGroup_Olordered__ab__group__abs,type,
    class_OrderedGroup_Olordered__ab__group__abs: $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__cancel__semiring,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

thf(tp_t_a,type,
    t_a: $i ).

thf(tp_tc_nat,type,
    tc_nat: $i ).

thf(tp_v_f,type,
    v_f: $i > $i ).

thf(tp_v_h,type,
    v_h: $i > $i ).

thf(tp_v_x,type,
    v_x: $i ).

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

thf(1,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

thf(2,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

thf(3,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

thf(4,axiom,
    ! [T: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

thf(5,axiom,
    ! [T_a: $i,V_b: $i,V_a: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
      | ~ ( c_lessequals @ c_0 @ V_b @ T_a )
      | ~ ( c_lessequals @ c_0 @ V_a @ T_a )
      | ( c_lessequals @ c_0 @ ( c_times @ V_a @ V_b @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).

thf(6,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ~ ( c_less @ V_x @ V_y @ T_a )
      | ( c_lessequals @ V_x @ V_y @ T_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).

thf(7,axiom,
    ! [T_a: $i,V_a: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
      | ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ V_a @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).

thf(8,axiom,
    ! [T_a: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
      | ( ( c_HOL_Oabs @ c_0 @ T_a )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).

thf(9,axiom,
    ! [V_n: $i] :
      ( ( c_less @ c_0 @ V_n @ tc_nat )
      | ( V_n = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).

thf(10,axiom,
    ! [V_x: $i] :
      ( ~ ( c_less @ c_0 @ V_x @ tc_nat )
      | ( V_x
        = ( c_Suc @ ( c_minus @ V_x @ c_1 @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).

thf(11,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(12,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[11]) ).

thf(13,negated_conjecture,
    class_Ring__and__Field_Oordered__idom @ t_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

thf(14,negated_conjecture,
    ! [V_U: $i] :
      ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ V_U ) ) @ t_a ) @ ( c_times @ V_U @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ V_U ) ) @ t_a ) @ t_a ) @ t_a )
      | ~ ( c_less @ c_0 @ V_U @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(15,negated_conjecture,
    ! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ V_U ) ) @ t_a ) @ ( c_times @ v_x @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ V_U ) ) @ t_a ) @ t_a ) @ t_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(16,negated_conjecture,
    c_less @ c_0 @ v_x @ t_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(17,negated_conjecture,
    ( ( v_f @ c_0 )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(18,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[12]) ).

thf(19,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(20,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(21,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(22,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Ojoin__semilorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(23,plain,
    ( ( ! [T_a: $i,V_b: $i,V_a: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
          | ~ ( c_lessequals @ c_0 @ V_b @ T_a )
          | ~ ( c_lessequals @ c_0 @ V_a @ T_a )
          | ( c_lessequals @ c_0 @ ( c_times @ V_a @ V_b @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(24,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ~ ( c_less @ V_x @ V_y @ T_a )
          | ( c_lessequals @ V_x @ V_y @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(25,plain,
    ( ( ! [T_a: $i,V_a: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
          | ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ V_a @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(26,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
          | ( ( c_HOL_Oabs @ c_0 @ T_a )
            = c_0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(27,plain,
    ( ( ! [V_n: $i] :
          ( ( c_less @ c_0 @ V_n @ tc_nat )
          | ( V_n = c_0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(28,plain,
    ( ( ! [V_x: $i] :
          ( ~ ( c_less @ c_0 @ V_x @ tc_nat )
          | ( V_x
            = ( c_Suc @ ( c_minus @ V_x @ c_1 @ tc_nat ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(29,plain,
    ( ( class_Ring__and__Field_Oordered__idom @ t_a )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(30,plain,
    ( ( ! [V_U: $i] :
          ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ V_U ) ) @ t_a ) @ ( c_times @ V_U @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ V_U ) ) @ t_a ) @ t_a ) @ t_a )
          | ~ ( c_less @ c_0 @ V_U @ t_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(31,plain,
    ( ( ! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ V_U ) ) @ t_a ) @ ( c_times @ v_x @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ V_U ) ) @ t_a ) @ t_a ) @ t_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(32,plain,
    ( ( c_less @ c_0 @ v_x @ t_a )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(33,plain,
    ( ( ( v_f @ c_0 )
      = c_0 )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(34,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[18]) ).

thf(35,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
          | ! [V_b: $i] :
              ( ~ ( c_lessequals @ c_0 @ V_b @ T_a )
              | ! [V_a: $i] :
                  ( ~ ( c_lessequals @ c_0 @ V_a @ T_a )
                  | ( c_lessequals @ c_0 @ ( c_times @ V_a @ V_b @ T_a ) @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[23]) ).

thf(36,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_less @ V_x @ V_y @ T_a )
              | ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[24]) ).

thf(37,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
          | ! [V_a: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ V_a @ T_a ) @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[25]) ).

thf(38,plain,
    ( ( ! [V_n: $i] :
          ( ( V_n = c_0 )
          | ( c_less @ c_0 @ V_n @ tc_nat ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[27]) ).

thf(39,plain,
    ( ( ( v_f @ c_0 )
      = c_0 )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(40,plain,
    ( ( c_less @ c_0 @ v_x @ t_a )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(41,plain,
    ( ( ! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ V_U ) ) @ t_a ) @ ( c_times @ v_x @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ V_U ) ) @ t_a ) @ t_a ) @ t_a ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(42,plain,
    ( ( ! [V_U: $i] :
          ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ V_U ) ) @ t_a ) @ ( c_times @ V_U @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ V_U ) ) @ t_a ) @ t_a ) @ t_a )
          | ~ ( c_less @ c_0 @ V_U @ t_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(43,plain,
    ( ( class_Ring__and__Field_Oordered__idom @ t_a )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(44,plain,
    ( ( ! [V_x: $i] :
          ( ~ ( c_less @ c_0 @ V_x @ tc_nat )
          | ( V_x
            = ( c_Suc @ ( c_minus @ V_x @ c_1 @ tc_nat ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(45,plain,
    ( ( ! [V_n: $i] :
          ( ( V_n = c_0 )
          | ( c_less @ c_0 @ V_n @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(46,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
          | ( ( c_HOL_Oabs @ c_0 @ T_a )
            = c_0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(47,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
          | ! [V_a: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ V_a @ T_a ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(48,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_less @ V_x @ V_y @ T_a )
              | ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(49,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
          | ! [V_b: $i] :
              ( ~ ( c_lessequals @ c_0 @ V_b @ T_a )
              | ! [V_a: $i] :
                  ( ~ ( c_lessequals @ c_0 @ V_a @ T_a )
                  | ( c_lessequals @ c_0 @ ( c_times @ V_a @ V_b @ T_a ) @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(50,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Ojoin__semilorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(51,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(52,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(53,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(54,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(55,plain,
    ! [SV1: $i] :
      ( ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( c_Suc @ SV1 ) ) @ t_a ) @ ( c_times @ v_x @ ( c_HOL_Oabs @ ( v_h @ ( c_Suc @ SV1 ) ) @ t_a ) @ t_a ) @ t_a )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(56,plain,
    ! [SV2: $i] :
      ( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ SV2 ) ) @ t_a ) @ ( c_times @ SV2 @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ SV2 ) ) @ t_a ) @ t_a ) @ t_a )
        | ~ ( c_less @ c_0 @ SV2 @ t_a ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(57,plain,
    ! [SV3: $i] :
      ( ( ~ ( c_less @ c_0 @ SV3 @ tc_nat )
        | ( SV3
          = ( c_Suc @ ( c_minus @ SV3 @ c_1 @ tc_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(58,plain,
    ! [SV4: $i] :
      ( ( ( SV4 = c_0 )
        | ( c_less @ c_0 @ SV4 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(59,plain,
    ! [SV5: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV5 )
        | ( ( c_HOL_Oabs @ c_0 @ SV5 )
          = c_0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(60,plain,
    ! [SV6: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 )
        | ! [SY17: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY17 @ SV6 ) @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(61,plain,
    ! [SV7: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV7 )
        | ! [SY18: $i,SY19: $i] :
            ( ~ ( c_less @ SY18 @ SY19 @ SV7 )
            | ( c_lessequals @ SY18 @ SY19 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(62,plain,
    ! [SV8: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
        | ! [SY20: $i] :
            ( ~ ( c_lessequals @ c_0 @ SY20 @ SV8 )
            | ! [SY21: $i] :
                ( ~ ( c_lessequals @ c_0 @ SY21 @ SV8 )
                | ( c_lessequals @ c_0 @ ( c_times @ SY21 @ SY20 @ SV8 ) @ SV8 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(63,plain,
    ! [SV9: $i] :
      ( ( ~ ( class_LOrder_Ojoin__semilorder @ SV9 )
        | ( class_Orderings_Oorder @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(64,plain,
    ! [SV10: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV10 )
        | ( class_LOrder_Ojoin__semilorder @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(65,plain,
    ! [SV11: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV11 )
        | ( class_Ring__and__Field_Opordered__cancel__semiring @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(66,plain,
    ! [SV12: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV12 )
        | ( class_OrderedGroup_Olordered__ab__group__abs @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(67,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(68,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ SV2 ) ) @ t_a ) @ ( c_times @ SV2 @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ SV2 ) ) @ t_a ) @ t_a ) @ t_a ) )
        = $true )
      | ( ( ~ ( c_less @ c_0 @ SV2 @ t_a ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(69,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( c_less @ c_0 @ SV3 @ tc_nat ) )
        = $true )
      | ( ( SV3
          = ( c_Suc @ ( c_minus @ SV3 @ c_1 @ tc_nat ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[57]) ).

thf(70,plain,
    ! [SV4: $i] :
      ( ( ( SV4 = c_0 )
        = $true )
      | ( ( c_less @ c_0 @ SV4 @ tc_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(71,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV5 ) )
        = $true )
      | ( ( ( c_HOL_Oabs @ c_0 @ SV5 )
          = c_0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[59]) ).

thf(72,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 ) )
        = $true )
      | ( ( ! [SY17: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY17 @ SV6 ) @ SV6 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[60]) ).

thf(73,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV7 ) )
        = $true )
      | ( ( ! [SY18: $i,SY19: $i] :
              ( ~ ( c_less @ SY18 @ SY19 @ SV7 )
              | ( c_lessequals @ SY18 @ SY19 @ SV7 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[61]) ).

thf(74,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 ) )
        = $true )
      | ( ( ! [SY20: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY20 @ SV8 )
              | ! [SY21: $i] :
                  ( ~ ( c_lessequals @ c_0 @ SY21 @ SV8 )
                  | ( c_lessequals @ c_0 @ ( c_times @ SY21 @ SY20 @ SV8 ) @ SV8 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[62]) ).

thf(75,plain,
    ! [SV9: $i] :
      ( ( ( ~ ( class_LOrder_Ojoin__semilorder @ SV9 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(76,plain,
    ! [SV10: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV10 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV10 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(77,plain,
    ! [SV11: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV11 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV11 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(78,plain,
    ! [SV12: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV12 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV12 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(79,plain,
    ! [SV2: $i] :
      ( ( ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ SV2 ) ) @ t_a ) @ ( c_times @ SV2 @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ SV2 ) ) @ t_a ) @ t_a ) @ t_a )
        = $false )
      | ( ( ~ ( c_less @ c_0 @ SV2 @ t_a ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(80,plain,
    ! [SV3: $i] :
      ( ( ( c_less @ c_0 @ SV3 @ tc_nat )
        = $false )
      | ( ( SV3
          = ( c_Suc @ ( c_minus @ SV3 @ c_1 @ tc_nat ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(81,plain,
    ! [SV5: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV5 )
        = $false )
      | ( ( ( c_HOL_Oabs @ c_0 @ SV5 )
          = c_0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(82,plain,
    ! [SV6: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 )
        = $false )
      | ( ( ! [SY17: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY17 @ SV6 ) @ SV6 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(83,plain,
    ! [SV7: $i] :
      ( ( ( class_Orderings_Oorder @ SV7 )
        = $false )
      | ( ( ! [SY18: $i,SY19: $i] :
              ( ~ ( c_less @ SY18 @ SY19 @ SV7 )
              | ( c_lessequals @ SY18 @ SY19 @ SV7 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(84,plain,
    ! [SV8: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
        = $false )
      | ( ( ! [SY20: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY20 @ SV8 )
              | ! [SY21: $i] :
                  ( ~ ( c_lessequals @ c_0 @ SY21 @ SV8 )
                  | ( c_lessequals @ c_0 @ ( c_times @ SY21 @ SY20 @ SV8 ) @ SV8 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(85,plain,
    ! [SV9: $i] :
      ( ( ( class_LOrder_Ojoin__semilorder @ SV9 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[75]) ).

thf(86,plain,
    ! [SV10: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV10 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(87,plain,
    ! [SV11: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV11 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV11 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[77]) ).

thf(88,plain,
    ! [SV12: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV12 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV12 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[78]) ).

thf(89,plain,
    ! [SV2: $i] :
      ( ( ( c_less @ c_0 @ SV2 @ t_a )
        = $false )
      | ( ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_xa @ SV2 ) ) @ t_a ) @ ( c_times @ SV2 @ ( c_HOL_Oabs @ ( v_h @ ( v_xa @ SV2 ) ) @ t_a ) @ t_a ) @ t_a )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(90,plain,
    ! [SV6: $i,SV13: $i] :
      ( ( ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SV13 @ SV6 ) @ SV6 )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(91,plain,
    ! [SV7: $i,SV14: $i] :
      ( ( ( ! [SY22: $i] :
              ( ~ ( c_less @ SV14 @ SY22 @ SV7 )
              | ( c_lessequals @ SV14 @ SY22 @ SV7 ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(92,plain,
    ! [SV8: $i,SV15: $i] :
      ( ( ( ~ ( c_lessequals @ c_0 @ SV15 @ SV8 )
          | ! [SY23: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY23 @ SV8 )
              | ( c_lessequals @ c_0 @ ( c_times @ SY23 @ SV15 @ SV8 ) @ SV8 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(93,plain,
    ! [SV7: $i,SV16: $i,SV14: $i] :
      ( ( ( ~ ( c_less @ SV14 @ SV16 @ SV7 )
          | ( c_lessequals @ SV14 @ SV16 @ SV7 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(94,plain,
    ! [SV8: $i,SV15: $i] :
      ( ( ( ~ ( c_lessequals @ c_0 @ SV15 @ SV8 ) )
        = $true )
      | ( ( ! [SY23: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY23 @ SV8 )
              | ( c_lessequals @ c_0 @ ( c_times @ SY23 @ SV15 @ SV8 ) @ SV8 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[92]) ).

thf(95,plain,
    ! [SV7: $i,SV16: $i,SV14: $i] :
      ( ( ( ~ ( c_less @ SV14 @ SV16 @ SV7 ) )
        = $true )
      | ( ( c_lessequals @ SV14 @ SV16 @ SV7 )
        = $true )
      | ( ( class_Orderings_Oorder @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[93]) ).

thf(96,plain,
    ! [SV8: $i,SV15: $i] :
      ( ( ( c_lessequals @ c_0 @ SV15 @ SV8 )
        = $false )
      | ( ( ! [SY23: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY23 @ SV8 )
              | ( c_lessequals @ c_0 @ ( c_times @ SY23 @ SV15 @ SV8 ) @ SV8 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(97,plain,
    ! [SV7: $i,SV16: $i,SV14: $i] :
      ( ( ( c_less @ SV14 @ SV16 @ SV7 )
        = $false )
      | ( ( c_lessequals @ SV14 @ SV16 @ SV7 )
        = $true )
      | ( ( class_Orderings_Oorder @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(98,plain,
    ! [SV15: $i,SV8: $i,SV17: $i] :
      ( ( ( ~ ( c_lessequals @ c_0 @ SV17 @ SV8 )
          | ( c_lessequals @ c_0 @ ( c_times @ SV17 @ SV15 @ SV8 ) @ SV8 ) )
        = $true )
      | ( ( c_lessequals @ c_0 @ SV15 @ SV8 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(99,plain,
    ! [SV15: $i,SV8: $i,SV17: $i] :
      ( ( ( ~ ( c_lessequals @ c_0 @ SV17 @ SV8 ) )
        = $true )
      | ( ( c_lessequals @ c_0 @ ( c_times @ SV17 @ SV15 @ SV8 ) @ SV8 )
        = $true )
      | ( ( c_lessequals @ c_0 @ SV15 @ SV8 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[98]) ).

thf(100,plain,
    ! [SV15: $i,SV8: $i,SV17: $i] :
      ( ( ( c_lessequals @ c_0 @ SV17 @ SV8 )
        = $false )
      | ( ( c_lessequals @ c_0 @ ( c_times @ SV17 @ SV15 @ SV8 ) @ SV8 )
        = $true )
      | ( ( c_lessequals @ c_0 @ SV15 @ SV8 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV8 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(101,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[39,100,97,90,89,88,87,86,85,81,80,70,67,55,43,40]) ).

thf(102,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[101]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jul  8 02:58:06 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 15
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms:15,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:17,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.18/0.42  
% 0.18/0.42  ********************************
% 0.18/0.42  *   All subproblems solved!    *
% 0.18/0.42  ********************************
% 0.18/0.42  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:101,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.42  
% 0.18/0.42  %**** Beginning of derivation protocol ****
% 0.18/0.42  % SZS output start CNFRefutation
% See solution above
% 0.18/0.42  
% 0.18/0.42  %**** End of derivation protocol ****
% 0.18/0.42  %**** no. of clauses in derivation: 102 ****
% 0.18/0.42  %**** clause counter: 101 ****
% 0.18/0.42  
% 0.18/0.42  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:101,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------