TSTP Solution File: ANA014-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : ANA014-2 : 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 : n027.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 19:10:26 EDT 2022

% Result   : Unsatisfiable 0.18s 0.44s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  111 (  57 unt;  16 typ;   0 def)
%            Number of atoms       :  396 ( 159 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  672 (  66   ~;  83   |;   0   &; 523   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   6 con; 0-3 aty)
%            Number of variables   :  152 (   0   ^ 152   !;   0   ?; 152   :)

% 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_HOL_Oinverse,type,
    c_HOL_Oinverse: $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_Omonoid__mult,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

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

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

thf(tp_class_Ring__and__Field_Ofield,type,
    class_Ring__and__Field_Ofield: $i > $o ).

thf(tp_class_Ring__and__Field_Oordered__field,type,
    class_Ring__and__Field_Oordered__field: $i > $o ).

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

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

thf(tp_v_c,type,
    v_c: $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__field @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).

thf(2,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oordered__idom @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).

thf(3,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Ofield @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).

thf(4,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).

thf(5,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).

thf(6,axiom,
    ! [T_a: $i,V_a: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T_a )
      | ( V_a = c_0 )
      | ( ( c_times @ ( c_HOL_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).

thf(7,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(8,axiom,
    ! [T_a: $i,V_x: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ( c_lessequals @ V_x @ V_x @ T_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(9,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_Osemigroup__mult__class_Omult__assoc_0) ).

thf(10,axiom,
    ! [T_a: $i,V_y: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
      | ( ( c_times @ c_1 @ V_y @ T_a )
        = V_y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_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__field @ 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_x @ V_U ) ) @ t_a ) @ ( c_times @ V_U @ ( c_times @ ( c_HOL_Oabs @ v_c @ t_a ) @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ V_U ) ) @ t_a ) @ t_a ) @ t_a ) @ t_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(15,negated_conjecture,
    v_c != c_0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(16,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[12]) ).

thf(17,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(18,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__idom @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(19,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ofield @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(20,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(21,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(22,plain,
    ( ( ! [T_a: $i,V_a: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T_a )
          | ( V_a = c_0 )
          | ( ( c_times @ ( c_HOL_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
            = c_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(23,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)],[7]) ).

thf(24,plain,
    ( ( ! [T_a: $i,V_x: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ( c_lessequals @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(25,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)],[9]) ).

thf(26,plain,
    ( ( ! [T_a: $i,V_y: $i] :
          ( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
          | ( ( c_times @ c_1 @ V_y @ T_a )
            = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(27,plain,
    ( ( class_Ring__and__Field_Oordered__field @ t_a )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(28,plain,
    ( ( ! [V_U: $i] :
          ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ V_U ) ) @ t_a ) @ ( c_times @ V_U @ ( c_times @ ( c_HOL_Oabs @ v_c @ t_a ) @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ V_U ) ) @ t_a ) @ t_a ) @ t_a ) @ t_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(29,plain,
    ( ( ( v_c != c_0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(30,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[16]) ).

thf(31,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T_a )
          | ! [V_a: $i] :
              ( ( V_a = c_0 )
              | ( ( c_times @ ( c_HOL_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
                = c_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[22]) ).

thf(32,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)],[23]) ).

thf(33,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[24]) ).

thf(34,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)],[25]) ).

thf(35,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
          | ! [V_y: $i] :
              ( ( c_times @ c_1 @ V_y @ T_a )
              = V_y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[26]) ).

thf(36,plain,
    ( ( ( v_c != c_0 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[29]) ).

thf(37,plain,
    ( ( ( v_c != c_0 ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(38,plain,
    ( ( ! [V_U: $i] :
          ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ V_U ) ) @ t_a ) @ ( c_times @ V_U @ ( c_times @ ( c_HOL_Oabs @ v_c @ t_a ) @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ V_U ) ) @ t_a ) @ t_a ) @ t_a ) @ t_a ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(39,plain,
    ( ( class_Ring__and__Field_Oordered__field @ t_a )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(40,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
          | ! [V_y: $i] :
              ( ( c_times @ c_1 @ V_y @ T_a )
              = V_y ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(41,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)],[34]) ).

thf(42,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(43,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)],[32]) ).

thf(44,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T_a )
          | ! [V_a: $i] :
              ( ( V_a = c_0 )
              | ( ( c_times @ ( c_HOL_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
                = c_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(45,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(46,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(47,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ofield @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(48,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__idom @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(49,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(50,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(51,plain,
    ( ( v_c = c_0 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(52,plain,
    ! [SV1: $i] :
      ( ( ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ SV1 ) ) @ t_a ) @ ( c_times @ SV1 @ ( c_times @ ( c_HOL_Oabs @ v_c @ t_a ) @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ SV1 ) ) @ t_a ) @ t_a ) @ t_a ) @ t_a ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(53,plain,
    ! [SV2: $i] :
      ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV2 )
        | ! [SY19: $i] :
            ( ( c_times @ c_1 @ SY19 @ SV2 )
            = SY19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(54,plain,
    ! [SV3: $i] :
      ( ( ! [SY20: $i] :
            ( ~ ( class_OrderedGroup_Osemigroup__mult @ SV3 )
            | ! [SY21: $i,SY22: $i] :
                ( ( c_times @ ( c_times @ SY20 @ SY21 @ SV3 ) @ SY22 @ SV3 )
                = ( c_times @ SY20 @ ( c_times @ SY21 @ SY22 @ SV3 ) @ SV3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(55,plain,
    ! [SV4: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV4 )
        | ! [SY23: $i] : ( c_lessequals @ SY23 @ SY23 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(56,plain,
    ! [SV5: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV5 )
        | ! [SY24: $i,SY25: $i] :
            ( ( c_HOL_Oabs @ ( c_times @ SY24 @ SY25 @ SV5 ) @ SV5 )
            = ( c_times @ ( c_HOL_Oabs @ SY24 @ SV5 ) @ ( c_HOL_Oabs @ SY25 @ SV5 ) @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(57,plain,
    ! [SV6: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV6 )
        | ! [SY26: $i] :
            ( ( SY26 = c_0 )
            | ( ( c_times @ ( c_HOL_Oinverse @ SY26 @ SV6 ) @ SY26 @ SV6 )
              = c_1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(58,plain,
    ! [SV7: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV7 )
        | ( class_OrderedGroup_Omonoid__mult @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(59,plain,
    ! [SV8: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV8 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(60,plain,
    ! [SV9: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV9 )
        | ( class_Ring__and__Field_Ofield @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(61,plain,
    ! [SV10: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV10 )
        | ( class_Ring__and__Field_Oordered__idom @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(62,plain,
    ! [SV11: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV11 )
        | ( class_Orderings_Oorder @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(63,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(64,plain,
    ! [SV1: $i] :
      ( ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ SV1 ) ) @ t_a ) @ ( c_times @ SV1 @ ( c_times @ ( c_HOL_Oabs @ v_c @ t_a ) @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ SV1 ) ) @ t_a ) @ t_a ) @ t_a ) @ t_a )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(65,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV2 ) )
        = $true )
      | ( ( ! [SY19: $i] :
              ( ( c_times @ c_1 @ SY19 @ SV2 )
              = SY19 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[53]) ).

thf(66,plain,
    ! [SV12: $i,SV3: $i] :
      ( ( ~ ( class_OrderedGroup_Osemigroup__mult @ SV3 )
        | ! [SY27: $i,SY28: $i] :
            ( ( c_times @ ( c_times @ SV12 @ SY27 @ SV3 ) @ SY28 @ SV3 )
            = ( c_times @ SV12 @ ( c_times @ SY27 @ SY28 @ SV3 ) @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(67,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV4 ) )
        = $true )
      | ( ( ! [SY23: $i] : ( c_lessequals @ SY23 @ SY23 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[55]) ).

thf(68,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV5 ) )
        = $true )
      | ( ( ! [SY24: $i,SY25: $i] :
              ( ( c_HOL_Oabs @ ( c_times @ SY24 @ SY25 @ SV5 ) @ SV5 )
              = ( c_times @ ( c_HOL_Oabs @ SY24 @ SV5 ) @ ( c_HOL_Oabs @ SY25 @ SV5 ) @ SV5 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(69,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV6 ) )
        = $true )
      | ( ( ! [SY26: $i] :
              ( ( SY26 = c_0 )
              | ( ( c_times @ ( c_HOL_Oinverse @ SY26 @ SV6 ) @ SY26 @ SV6 )
                = c_1 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[57]) ).

thf(70,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV7 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV7 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(71,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV8 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV8 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[59]) ).

thf(72,plain,
    ! [SV9: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV9 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ofield @ SV9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[60]) ).

thf(73,plain,
    ! [SV10: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV10 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__idom @ SV10 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[61]) ).

thf(74,plain,
    ! [SV11: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV11 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV11 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[62]) ).

thf(75,plain,
    ! [SV2: $i] :
      ( ( ( class_OrderedGroup_Omonoid__mult @ SV2 )
        = $false )
      | ( ( ! [SY19: $i] :
              ( ( c_times @ c_1 @ SY19 @ SV2 )
              = SY19 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(76,plain,
    ! [SV12: $i,SV3: $i] :
      ( ( ( ~ ( class_OrderedGroup_Osemigroup__mult @ SV3 ) )
        = $true )
      | ( ( ! [SY27: $i,SY28: $i] :
              ( ( c_times @ ( c_times @ SV12 @ SY27 @ SV3 ) @ SY28 @ SV3 )
              = ( c_times @ SV12 @ ( c_times @ SY27 @ SY28 @ SV3 ) @ SV3 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(77,plain,
    ! [SV4: $i] :
      ( ( ( class_Orderings_Oorder @ SV4 )
        = $false )
      | ( ( ! [SY23: $i] : ( c_lessequals @ SY23 @ SY23 @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(78,plain,
    ! [SV5: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV5 )
        = $false )
      | ( ( ! [SY24: $i,SY25: $i] :
              ( ( c_HOL_Oabs @ ( c_times @ SY24 @ SY25 @ SV5 ) @ SV5 )
              = ( c_times @ ( c_HOL_Oabs @ SY24 @ SV5 ) @ ( c_HOL_Oabs @ SY25 @ SV5 ) @ SV5 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(79,plain,
    ! [SV6: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV6 )
        = $false )
      | ( ( ! [SY26: $i] :
              ( ( SY26 = c_0 )
              | ( ( c_times @ ( c_HOL_Oinverse @ SY26 @ SV6 ) @ SY26 @ SV6 )
                = c_1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(80,plain,
    ! [SV7: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV7 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV7 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(81,plain,
    ! [SV8: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV8 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV8 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(82,plain,
    ! [SV9: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV9 )
        = $false )
      | ( ( class_Ring__and__Field_Ofield @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(83,plain,
    ! [SV10: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV10 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__idom @ SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(84,plain,
    ! [SV11: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV11 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV11 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(85,plain,
    ! [SV2: $i,SV13: $i] :
      ( ( ( ( c_times @ c_1 @ SV13 @ SV2 )
          = SV13 )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV2 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(86,plain,
    ! [SV12: $i,SV3: $i] :
      ( ( ( class_OrderedGroup_Osemigroup__mult @ SV3 )
        = $false )
      | ( ( ! [SY27: $i,SY28: $i] :
              ( ( c_times @ ( c_times @ SV12 @ SY27 @ SV3 ) @ SY28 @ SV3 )
              = ( c_times @ SV12 @ ( c_times @ SY27 @ SY28 @ SV3 ) @ SV3 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(87,plain,
    ! [SV4: $i,SV14: $i] :
      ( ( ( c_lessequals @ SV14 @ SV14 @ SV4 )
        = $true )
      | ( ( class_Orderings_Oorder @ SV4 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(88,plain,
    ! [SV5: $i,SV15: $i] :
      ( ( ( ! [SY29: $i] :
              ( ( c_HOL_Oabs @ ( c_times @ SV15 @ SY29 @ SV5 ) @ SV5 )
              = ( c_times @ ( c_HOL_Oabs @ SV15 @ SV5 ) @ ( c_HOL_Oabs @ SY29 @ SV5 ) @ SV5 ) ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__idom @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(89,plain,
    ! [SV6: $i,SV16: $i] :
      ( ( ( ( SV16 = c_0 )
          | ( ( c_times @ ( c_HOL_Oinverse @ SV16 @ SV6 ) @ SV16 @ SV6 )
            = c_1 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ofield @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(90,plain,
    ! [SV3: $i,SV17: $i,SV12: $i] :
      ( ( ( ! [SY30: $i] :
              ( ( c_times @ ( c_times @ SV12 @ SV17 @ SV3 ) @ SY30 @ SV3 )
              = ( c_times @ SV12 @ ( c_times @ SV17 @ SY30 @ SV3 ) @ SV3 ) ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(91,plain,
    ! [SV5: $i,SV18: $i,SV15: $i] :
      ( ( ( ( c_HOL_Oabs @ ( c_times @ SV15 @ SV18 @ SV5 ) @ SV5 )
          = ( c_times @ ( c_HOL_Oabs @ SV15 @ SV5 ) @ ( c_HOL_Oabs @ SV18 @ SV5 ) @ SV5 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__idom @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(92,plain,
    ! [SV6: $i,SV16: $i] :
      ( ( ( SV16 = c_0 )
        = $true )
      | ( ( ( c_times @ ( c_HOL_Oinverse @ SV16 @ SV6 ) @ SV16 @ SV6 )
          = c_1 )
        = $true )
      | ( ( class_Ring__and__Field_Ofield @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(93,plain,
    ! [SV19: $i,SV3: $i,SV17: $i,SV12: $i] :
      ( ( ( ( c_times @ ( c_times @ SV12 @ SV17 @ SV3 ) @ SV19 @ SV3 )
          = ( c_times @ SV12 @ ( c_times @ SV17 @ SV19 @ SV3 ) @ SV3 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(94,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[39,93,92,91,87,85,84,83,82,81,80,64,63,51]) ).

thf(95,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[94]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA014-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n027.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 06:13:15 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 13
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms:13,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:15,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.18/0.44  
% 0.18/0.44  ********************************
% 0.18/0.44  *   All subproblems solved!    *
% 0.18/0.44  ********************************
% 0.18/0.44  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:94,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.44  
% 0.18/0.44  %**** Beginning of derivation protocol ****
% 0.18/0.44  % SZS output start CNFRefutation
% See solution above
% 0.18/0.44  
% 0.18/0.44  %**** End of derivation protocol ****
% 0.18/0.44  %**** no. of clauses in derivation: 95 ****
% 0.18/0.44  %**** clause counter: 94 ****
% 0.18/0.44  
% 0.18/0.44  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:94,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------