TSTP Solution File: ANA017-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : ANA017-2 : 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 : n008.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 19:10:28 EDT 2022

% Result   : Unsatisfiable 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   93 (  47 unt;  14 typ;   0 def)
%            Number of atoms       :  364 ( 118 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  848 (  70   ~;  87   |;   0   &; 691   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :  166 (   0   ^ 166   !;   0   ?; 166   :)

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

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

thf(tp_class_OrderedGroup_Osemigroup__mult,type,
    class_OrderedGroup_Osemigroup__mult: $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_f,type,
    v_f: $i > $i ).

thf(tp_v_x,type,
    v_x: $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__semiring @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

thf(3,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).

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_c @ V_a @ T_a ) @ ( c_times @ V_c @ V_b @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).

thf(5,axiom,
    ! [T_a: $i,V_a: $i,V_b: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
      | ( ( c_HOL_Oabs @ ( c_times @ V_a @ V_b @ T_a ) @ T_a )
        = ( c_times @ ( c_HOL_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs @ V_b @ T_a ) @ T_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).

thf(6,axiom,
    ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__mult @ T_a )
      | ( ( c_times @ ( c_times @ V_a @ V_b @ T_a ) @ V_c @ T_a )
        = ( c_times @ V_a @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_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,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(9,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[8]) ).

thf(10,negated_conjecture,
    class_Ring__and__Field_Oordered__idom @ t_b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

thf(11,negated_conjecture,
    ! [V_U: $i] :
      ~ ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ v_c @ ( v_b @ ( v_x @ V_U ) ) @ t_b ) @ t_b ) @ ( c_times @ V_U @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ V_U ) ) @ t_b ) @ t_b ) @ t_b ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(12,negated_conjecture,
    ! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ V_U ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_f @ V_U ) @ t_b ) @ t_b ) @ t_b ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(13,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[9]) ).

thf(14,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(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_OrderedGroup_Osemigroup__mult @ 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_c @ V_a @ T_a ) @ ( c_times @ V_c @ V_b @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(18,plain,
    ( ( ! [T_a: $i,V_a: $i,V_b: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
          | ( ( c_HOL_Oabs @ ( c_times @ V_a @ V_b @ T_a ) @ T_a )
            = ( c_times @ ( c_HOL_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(19,plain,
    ( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
          ( ~ ( class_OrderedGroup_Osemigroup__mult @ T_a )
          | ( ( c_times @ ( c_times @ V_a @ V_b @ T_a ) @ V_c @ T_a )
            = ( c_times @ V_a @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(20,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(21,plain,
    ( ( class_Ring__and__Field_Oordered__idom @ t_b )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(22,plain,
    ( ( ! [V_U: $i] :
          ~ ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ v_c @ ( v_b @ ( v_x @ V_U ) ) @ t_b ) @ t_b ) @ ( c_times @ V_U @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ V_U ) ) @ t_b ) @ t_b ) @ t_b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(23,plain,
    ( ( ! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ V_U ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_f @ V_U ) @ t_b ) @ t_b ) @ 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_c @ V_a @ T_a ) @ ( c_times @ V_c @ V_b @ T_a ) @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[17]) ).

thf(26,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
          | ! [V_a: $i,V_b: $i] :
              ( ( c_HOL_Oabs @ ( c_times @ V_a @ V_b @ T_a ) @ T_a )
              = ( c_times @ ( c_HOL_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(27,plain,
    ( ( ! [T_a: $i,V_a: $i] :
          ( ~ ( class_OrderedGroup_Osemigroup__mult @ T_a )
          | ! [V_b: $i,V_c: $i] :
              ( ( c_times @ ( c_times @ V_a @ V_b @ T_a ) @ V_c @ T_a )
              = ( c_times @ V_a @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(28,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)],[20]) ).

thf(29,plain,
    ( ( ! [V_U: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ V_U ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_f @ V_U ) @ t_b ) @ t_b ) @ t_b ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(30,plain,
    ( ( ! [V_U: $i] :
          ~ ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ v_c @ ( v_b @ ( v_x @ V_U ) ) @ t_b ) @ t_b ) @ ( c_times @ V_U @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ V_U ) ) @ t_b ) @ t_b ) @ t_b ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(31,plain,
    ( ( class_Ring__and__Field_Oordered__idom @ t_b )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(32,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)],[28]) ).

thf(33,plain,
    ( ( ! [T_a: $i,V_a: $i] :
          ( ~ ( class_OrderedGroup_Osemigroup__mult @ T_a )
          | ! [V_b: $i,V_c: $i] :
              ( ( c_times @ ( c_times @ V_a @ V_b @ T_a ) @ V_c @ T_a )
              = ( c_times @ V_a @ ( c_times @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(34,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
          | ! [V_a: $i,V_b: $i] :
              ( ( c_HOL_Oabs @ ( c_times @ V_a @ V_b @ T_a ) @ T_a )
              = ( c_times @ ( c_HOL_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(35,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_c @ V_a @ T_a ) @ ( c_times @ V_c @ V_b @ T_a ) @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(36,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(37,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(38,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(39,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(40,plain,
    ! [SV1: $i] :
      ( ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ SV1 ) @ t_b ) @ ( c_times @ v_ca @ ( c_HOL_Oabs @ ( v_f @ SV1 ) @ t_b ) @ t_b ) @ t_b )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(41,plain,
    ! [SV2: $i] :
      ( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ v_c @ ( v_b @ ( v_x @ SV2 ) ) @ t_b ) @ t_b ) @ ( c_times @ SV2 @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ SV2 ) ) @ t_b ) @ t_b ) @ t_b ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(42,plain,
    ! [SV3: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV3 )
        | ! [SY18: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY18 @ SV3 ) @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(43,plain,
    ! [SV4: $i] :
      ( ( ! [SY19: $i] :
            ( ~ ( class_OrderedGroup_Osemigroup__mult @ SV4 )
            | ! [SY20: $i,SY21: $i] :
                ( ( c_times @ ( c_times @ SY19 @ SY20 @ SV4 ) @ SY21 @ SV4 )
                = ( c_times @ SY19 @ ( c_times @ SY20 @ SY21 @ SV4 ) @ SV4 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(44,plain,
    ! [SV5: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV5 )
        | ! [SY22: $i,SY23: $i] :
            ( ( c_HOL_Oabs @ ( c_times @ SY22 @ SY23 @ SV5 ) @ SV5 )
            = ( c_times @ ( c_HOL_Oabs @ SY22 @ SV5 ) @ ( c_HOL_Oabs @ SY23 @ SV5 ) @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(45,plain,
    ! [SV6: $i] :
      ( ( ! [SY24: $i] :
            ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV6 )
            | ! [SY25: $i] :
                ( ~ ( c_lessequals @ SY24 @ SY25 @ SV6 )
                | ! [SY26: $i] :
                    ( ~ ( c_lessequals @ c_0 @ SY26 @ SV6 )
                    | ( c_lessequals @ ( c_times @ SY26 @ SY24 @ SV6 ) @ ( c_times @ SY26 @ SY25 @ SV6 ) @ SV6 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(46,plain,
    ! [SV7: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV7 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(47,plain,
    ! [SV8: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV8 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(48,plain,
    ! [SV9: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV9 )
        | ( class_OrderedGroup_Olordered__ab__group__abs @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(49,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(50,plain,
    ! [SV2: $i] :
      ( ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ v_c @ ( v_b @ ( v_x @ SV2 ) ) @ t_b ) @ t_b ) @ ( c_times @ SV2 @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ SV2 ) ) @ t_b ) @ t_b ) @ t_b )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(51,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV3 ) )
        = $true )
      | ( ( ! [SY18: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY18 @ SV3 ) @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[42]) ).

thf(52,plain,
    ! [SV10: $i,SV4: $i] :
      ( ( ~ ( class_OrderedGroup_Osemigroup__mult @ SV4 )
        | ! [SY27: $i,SY28: $i] :
            ( ( c_times @ ( c_times @ SV10 @ SY27 @ SV4 ) @ SY28 @ SV4 )
            = ( c_times @ SV10 @ ( c_times @ SY27 @ SY28 @ SV4 ) @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(53,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV5 ) )
        = $true )
      | ( ( ! [SY22: $i,SY23: $i] :
              ( ( c_HOL_Oabs @ ( c_times @ SY22 @ SY23 @ SV5 ) @ SV5 )
              = ( c_times @ ( c_HOL_Oabs @ SY22 @ SV5 ) @ ( c_HOL_Oabs @ SY23 @ SV5 ) @ SV5 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[44]) ).

thf(54,plain,
    ! [SV11: $i,SV6: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV6 )
        | ! [SY29: $i] :
            ( ~ ( c_lessequals @ SV11 @ SY29 @ SV6 )
            | ! [SY30: $i] :
                ( ~ ( c_lessequals @ c_0 @ SY30 @ SV6 )
                | ( c_lessequals @ ( c_times @ SY30 @ SV11 @ SV6 ) @ ( c_times @ SY30 @ SY29 @ SV6 ) @ SV6 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(55,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV7 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV7 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[46]) ).

thf(56,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV8 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV8 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(57,plain,
    ! [SV9: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV9 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[48]) ).

thf(58,plain,
    ! [SV3: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV3 )
        = $false )
      | ( ( ! [SY18: $i] : ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SY18 @ SV3 ) @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(59,plain,
    ! [SV10: $i,SV4: $i] :
      ( ( ( ~ ( class_OrderedGroup_Osemigroup__mult @ SV4 ) )
        = $true )
      | ( ( ! [SY27: $i,SY28: $i] :
              ( ( c_times @ ( c_times @ SV10 @ SY27 @ SV4 ) @ SY28 @ SV4 )
              = ( c_times @ SV10 @ ( c_times @ SY27 @ SY28 @ SV4 ) @ SV4 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(60,plain,
    ! [SV5: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV5 )
        = $false )
      | ( ( ! [SY22: $i,SY23: $i] :
              ( ( c_HOL_Oabs @ ( c_times @ SY22 @ SY23 @ SV5 ) @ SV5 )
              = ( c_times @ ( c_HOL_Oabs @ SY22 @ SV5 ) @ ( c_HOL_Oabs @ SY23 @ SV5 ) @ SV5 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(61,plain,
    ! [SV11: $i,SV6: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV6 ) )
        = $true )
      | ( ( ! [SY29: $i] :
              ( ~ ( c_lessequals @ SV11 @ SY29 @ SV6 )
              | ! [SY30: $i] :
                  ( ~ ( c_lessequals @ c_0 @ SY30 @ SV6 )
                  | ( c_lessequals @ ( c_times @ SY30 @ SV11 @ SV6 ) @ ( c_times @ SY30 @ SY29 @ SV6 ) @ SV6 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[54]) ).

thf(62,plain,
    ! [SV7: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV7 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV7 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(63,plain,
    ! [SV8: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV8 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV8 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(64,plain,
    ! [SV9: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV9 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(65,plain,
    ! [SV3: $i,SV12: $i] :
      ( ( ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ SV12 @ SV3 ) @ SV3 )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(66,plain,
    ! [SV10: $i,SV4: $i] :
      ( ( ( class_OrderedGroup_Osemigroup__mult @ SV4 )
        = $false )
      | ( ( ! [SY27: $i,SY28: $i] :
              ( ( c_times @ ( c_times @ SV10 @ SY27 @ SV4 ) @ SY28 @ SV4 )
              = ( c_times @ SV10 @ ( c_times @ SY27 @ SY28 @ SV4 ) @ SV4 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(67,plain,
    ! [SV5: $i,SV13: $i] :
      ( ( ( ! [SY31: $i] :
              ( ( c_HOL_Oabs @ ( c_times @ SV13 @ SY31 @ SV5 ) @ SV5 )
              = ( c_times @ ( c_HOL_Oabs @ SV13 @ SV5 ) @ ( c_HOL_Oabs @ SY31 @ SV5 ) @ SV5 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__idom @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(68,plain,
    ! [SV11: $i,SV6: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV6 )
        = $false )
      | ( ( ! [SY29: $i] :
              ( ~ ( c_lessequals @ SV11 @ SY29 @ SV6 )
              | ! [SY30: $i] :
                  ( ~ ( c_lessequals @ c_0 @ SY30 @ SV6 )
                  | ( c_lessequals @ ( c_times @ SY30 @ SV11 @ SV6 ) @ ( c_times @ SY30 @ SY29 @ SV6 ) @ SV6 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(69,plain,
    ! [SV4: $i,SV14: $i,SV10: $i] :
      ( ( ( ! [SY32: $i] :
              ( ( c_times @ ( c_times @ SV10 @ SV14 @ SV4 ) @ SY32 @ SV4 )
              = ( c_times @ SV10 @ ( c_times @ SV14 @ SY32 @ SV4 ) @ SV4 ) ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV4 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(70,plain,
    ! [SV5: $i,SV15: $i,SV13: $i] :
      ( ( ( ( c_HOL_Oabs @ ( c_times @ SV13 @ SV15 @ SV5 ) @ SV5 )
          = ( c_times @ ( c_HOL_Oabs @ SV13 @ SV5 ) @ ( c_HOL_Oabs @ SV15 @ SV5 ) @ SV5 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__idom @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(71,plain,
    ! [SV6: $i,SV16: $i,SV11: $i] :
      ( ( ( ~ ( c_lessequals @ SV11 @ SV16 @ SV6 )
          | ! [SY33: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY33 @ SV6 )
              | ( c_lessequals @ ( c_times @ SY33 @ SV11 @ SV6 ) @ ( c_times @ SY33 @ SV16 @ SV6 ) @ SV6 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(72,plain,
    ! [SV17: $i,SV4: $i,SV14: $i,SV10: $i] :
      ( ( ( ( c_times @ ( c_times @ SV10 @ SV14 @ SV4 ) @ SV17 @ SV4 )
          = ( c_times @ SV10 @ ( c_times @ SV14 @ SV17 @ SV4 ) @ SV4 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV4 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(73,plain,
    ! [SV6: $i,SV16: $i,SV11: $i] :
      ( ( ( ~ ( c_lessequals @ SV11 @ SV16 @ SV6 ) )
        = $true )
      | ( ( ! [SY33: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY33 @ SV6 )
              | ( c_lessequals @ ( c_times @ SY33 @ SV11 @ SV6 ) @ ( c_times @ SY33 @ SV16 @ SV6 ) @ SV6 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(74,plain,
    ! [SV6: $i,SV16: $i,SV11: $i] :
      ( ( ( c_lessequals @ SV11 @ SV16 @ SV6 )
        = $false )
      | ( ( ! [SY33: $i] :
              ( ~ ( c_lessequals @ c_0 @ SY33 @ SV6 )
              | ( c_lessequals @ ( c_times @ SY33 @ SV11 @ SV6 ) @ ( c_times @ SY33 @ SV16 @ SV6 ) @ SV6 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(75,plain,
    ! [SV16: $i,SV11: $i,SV6: $i,SV18: $i] :
      ( ( ( ~ ( c_lessequals @ c_0 @ SV18 @ SV6 )
          | ( c_lessequals @ ( c_times @ SV18 @ SV11 @ SV6 ) @ ( c_times @ SV18 @ SV16 @ SV6 ) @ SV6 ) )
        = $true )
      | ( ( c_lessequals @ SV11 @ SV16 @ SV6 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(76,plain,
    ! [SV16: $i,SV11: $i,SV6: $i,SV18: $i] :
      ( ( ( ~ ( c_lessequals @ c_0 @ SV18 @ SV6 ) )
        = $true )
      | ( ( c_lessequals @ ( c_times @ SV18 @ SV11 @ SV6 ) @ ( c_times @ SV18 @ SV16 @ SV6 ) @ SV6 )
        = $true )
      | ( ( c_lessequals @ SV11 @ SV16 @ SV6 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[75]) ).

thf(77,plain,
    ! [SV16: $i,SV11: $i,SV6: $i,SV18: $i] :
      ( ( ( c_lessequals @ c_0 @ SV18 @ SV6 )
        = $false )
      | ( ( c_lessequals @ ( c_times @ SV18 @ SV11 @ SV6 ) @ ( c_times @ SV18 @ SV16 @ SV6 ) @ SV6 )
        = $true )
      | ( ( c_lessequals @ SV11 @ SV16 @ SV6 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(78,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[31,77,72,70,65,64,63,62,50,49,40]) ).

thf(79,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[78]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA017-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n008.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 : Fri Jul  8 04:00:23 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 10
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 0
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.36  (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)....
% 0.20/0.60  
% 0.20/0.60  ********************************
% 0.20/0.60  *   All subproblems solved!    *
% 0.20/0.60  ********************************
% 0.20/0.60  % SZS status Unsatisfiable for /export/starexec/sandbox/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:78,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.60  
% 0.20/0.60  %**** Beginning of derivation protocol ****
% 0.20/0.60  % SZS output start CNFRefutation
% See solution above
% 0.20/0.60  
% 0.20/0.60  %**** End of derivation protocol ****
% 0.20/0.60  %**** no. of clauses in derivation: 79 ****
% 0.20/0.60  %**** clause counter: 78 ****
% 0.20/0.60  
% 0.20/0.60  % SZS status Unsatisfiable for /export/starexec/sandbox/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:78,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------