TSTP Solution File: GRP013-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n010.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 : Sat Jul 16 10:15:24 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  103 (  68 unt;   8 typ;   0 def)
%            Number of atoms       :  461 ( 131 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  880 ( 103   ~; 128   |;   0   &; 649   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   7 con; 0-3 aty)
%            Number of variables   :  294 (   0   ^ 294   !;   0   ?; 294   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $i ).

thf(tp_b,type,
    b: $i ).

thf(tp_c,type,
    c: $i ).

thf(tp_d,type,
    d: $i ).

thf(tp_identity,type,
    identity: $i ).

thf(tp_inverse,type,
    inverse: $i > $i ).

thf(tp_multiply,type,
    multiply: $i > $i > $i ).

thf(tp_product,type,
    product: $i > $i > $i > $o ).

thf(1,axiom,
    ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
      ( ~ ( product @ X @ Y @ U )
      | ~ ( product @ Y @ Z @ V )
      | ~ ( product @ X @ V @ W )
      | ( product @ U @ Z @ W ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).

thf(2,axiom,
    ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
      ( ~ ( product @ X @ Y @ U )
      | ~ ( product @ Y @ Z @ V )
      | ~ ( product @ U @ Z @ W )
      | ( product @ X @ V @ W ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).

thf(3,axiom,
    ! [X: $i,Y: $i,Z: $i,W: $i] :
      ( ~ ( product @ X @ Y @ Z )
      | ~ ( product @ X @ Y @ W )
      | ( Z = W ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).

thf(4,axiom,
    ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).

thf(5,axiom,
    ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).

thf(6,axiom,
    ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).

thf(7,axiom,
    ! [X: $i] : ( product @ X @ identity @ X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).

thf(8,axiom,
    ! [X: $i] : ( product @ identity @ X @ X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( product @ ( inverse @ A ) @ ( inverse @ B ) @ C )
      | ( product @ A @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverses_have_property) ).

thf(10,axiom,
    product @ ( inverse @ a ) @ ( inverse @ b ) @ d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_a_times_inverse_b_is_d) ).

thf(11,axiom,
    product @ a @ b @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).

thf(12,axiom,
    ! [A: $i] : ( product @ A @ A @ identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',squareness) ).

thf(13,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(14,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[13]) ).

thf(15,negated_conjecture,
    ~ ( product @ c @ d @ identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_times_d_is_identity) ).

thf(16,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ~ ( product @ Y @ Z @ V )
          | ~ ( product @ X @ V @ W )
          | ( product @ U @ Z @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(18,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ~ ( product @ Y @ Z @ V )
          | ~ ( product @ U @ Z @ W )
          | ( product @ X @ V @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(19,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
          ( ~ ( product @ X @ Y @ Z )
          | ~ ( product @ X @ Y @ W )
          | ( Z = W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(20,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(21,plain,
    ( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(22,plain,
    ( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(23,plain,
    ( ( ! [X: $i] : ( product @ X @ identity @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(24,plain,
    ( ( ! [X: $i] : ( product @ identity @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(25,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( product @ ( inverse @ A ) @ ( inverse @ B ) @ C )
          | ( product @ A @ C @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(26,plain,
    ( ( product @ ( inverse @ a ) @ ( inverse @ b ) @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(27,plain,
    ( ( product @ a @ b @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(28,plain,
    ( ( ! [A: $i] : ( product @ A @ A @ identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(29,plain,
    ( ( ~ ( product @ c @ d @ identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

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

thf(31,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( product @ X @ V @ W )
                  | ( product @ U @ Z @ W ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[17]) ).

thf(32,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( product @ U @ Z @ W )
                  | ( product @ X @ V @ W ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(33,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( product @ X @ Y @ Z )
          | ! [W: $i] :
              ( ~ ( product @ X @ Y @ W )
              | ( Z = W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(34,plain,
    ( ( ~ ( product @ c @ d @ identity ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(35,plain,
    ( ( ! [A: $i] : ( product @ A @ A @ identity ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(36,plain,
    ( ( product @ a @ b @ c )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(37,plain,
    ( ( product @ ( inverse @ a ) @ ( inverse @ b ) @ d )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(38,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( product @ ( inverse @ A ) @ ( inverse @ B ) @ C )
          | ( product @ A @ C @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(39,plain,
    ( ( ! [X: $i] : ( product @ identity @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(40,plain,
    ( ( ! [X: $i] : ( product @ X @ identity @ X ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(41,plain,
    ( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ identity ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(42,plain,
    ( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ identity ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(43,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(44,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( product @ X @ Y @ Z )
          | ! [W: $i] :
              ( ~ ( product @ X @ Y @ W )
              | ( Z = W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(45,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( product @ U @ Z @ W )
                  | ( product @ X @ V @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(46,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( product @ X @ V @ W )
                  | ( product @ U @ Z @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(47,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(48,plain,
    ( ( product @ c @ d @ identity )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(49,plain,
    ! [SV1: $i] :
      ( ( product @ SV1 @ SV1 @ identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(50,plain,
    ! [SV2: $i] :
      ( ( ! [SY26: $i,SY27: $i] :
            ( ~ ( product @ ( inverse @ SV2 ) @ ( inverse @ SY26 ) @ SY27 )
            | ( product @ SV2 @ SY27 @ SY26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(51,plain,
    ! [SV3: $i] :
      ( ( product @ identity @ SV3 @ SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(52,plain,
    ! [SV4: $i] :
      ( ( product @ SV4 @ identity @ SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(53,plain,
    ! [SV5: $i] :
      ( ( product @ ( inverse @ SV5 ) @ SV5 @ identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(54,plain,
    ! [SV6: $i] :
      ( ( product @ SV6 @ ( inverse @ SV6 ) @ identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(55,plain,
    ! [SV7: $i] :
      ( ( ! [SY28: $i] : ( product @ SV7 @ SY28 @ ( multiply @ SV7 @ SY28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(56,plain,
    ! [SV8: $i] :
      ( ( ! [SY29: $i,SY30: $i] :
            ( ~ ( product @ SV8 @ SY29 @ SY30 )
            | ! [SY31: $i] :
                ( ~ ( product @ SV8 @ SY29 @ SY31 )
                | ( SY30 = SY31 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(57,plain,
    ! [SV9: $i] :
      ( ( ! [SY32: $i,SY33: $i,SY34: $i] :
            ( ~ ( product @ SV9 @ SY32 @ SY33 )
            | ! [SY35: $i] :
                ( ~ ( product @ SY32 @ SY34 @ SY35 )
                | ! [SY36: $i] :
                    ( ~ ( product @ SY33 @ SY34 @ SY36 )
                    | ( product @ SV9 @ SY35 @ SY36 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(58,plain,
    ! [SV10: $i] :
      ( ( ! [SY37: $i,SY38: $i,SY39: $i] :
            ( ~ ( product @ SV10 @ SY37 @ SY38 )
            | ! [SY40: $i] :
                ( ~ ( product @ SY37 @ SY39 @ SY40 )
                | ! [SY41: $i] :
                    ( ~ ( product @ SV10 @ SY40 @ SY41 )
                    | ( product @ SY38 @ SY39 @ SY41 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(59,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(60,plain,
    ! [SV11: $i,SV2: $i] :
      ( ( ! [SY42: $i] :
            ( ~ ( product @ ( inverse @ SV2 ) @ ( inverse @ SV11 ) @ SY42 )
            | ( product @ SV2 @ SY42 @ SV11 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(61,plain,
    ! [SV12: $i,SV7: $i] :
      ( ( product @ SV7 @ SV12 @ ( multiply @ SV7 @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(62,plain,
    ! [SV13: $i,SV8: $i] :
      ( ( ! [SY43: $i] :
            ( ~ ( product @ SV8 @ SV13 @ SY43 )
            | ! [SY44: $i] :
                ( ~ ( product @ SV8 @ SV13 @ SY44 )
                | ( SY43 = SY44 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(63,plain,
    ! [SV14: $i,SV9: $i] :
      ( ( ! [SY45: $i,SY46: $i] :
            ( ~ ( product @ SV9 @ SV14 @ SY45 )
            | ! [SY47: $i] :
                ( ~ ( product @ SV14 @ SY46 @ SY47 )
                | ! [SY36: $i] :
                    ( ~ ( product @ SY45 @ SY46 @ SY36 )
                    | ( product @ SV9 @ SY47 @ SY36 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(64,plain,
    ! [SV15: $i,SV10: $i] :
      ( ( ! [SY49: $i,SY50: $i] :
            ( ~ ( product @ SV10 @ SV15 @ SY49 )
            | ! [SY51: $i] :
                ( ~ ( product @ SV15 @ SY50 @ SY51 )
                | ! [SY41: $i] :
                    ( ~ ( product @ SV10 @ SY51 @ SY41 )
                    | ( product @ SY49 @ SY50 @ SY41 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(65,plain,
    ! [SV16: $i,SV11: $i,SV2: $i] :
      ( ( ~ ( product @ ( inverse @ SV2 ) @ ( inverse @ SV11 ) @ SV16 )
        | ( product @ SV2 @ SV16 @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(66,plain,
    ! [SV17: $i,SV13: $i,SV8: $i] :
      ( ( ~ ( product @ SV8 @ SV13 @ SV17 )
        | ! [SY53: $i] :
            ( ~ ( product @ SV8 @ SV13 @ SY53 )
            | ( SV17 = SY53 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(67,plain,
    ! [SV18: $i,SV14: $i,SV9: $i] :
      ( ( ! [SY54: $i] :
            ( ~ ( product @ SV9 @ SV14 @ SV18 )
            | ! [SY55: $i] :
                ( ~ ( product @ SV14 @ SY54 @ SY55 )
                | ! [SY56: $i] :
                    ( ~ ( product @ SV18 @ SY54 @ SY56 )
                    | ( product @ SV9 @ SY55 @ SY56 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(68,plain,
    ! [SV19: $i,SV15: $i,SV10: $i] :
      ( ( ! [SY57: $i] :
            ( ~ ( product @ SV10 @ SV15 @ SV19 )
            | ! [SY58: $i] :
                ( ~ ( product @ SV15 @ SY57 @ SY58 )
                | ! [SY59: $i] :
                    ( ~ ( product @ SV10 @ SY58 @ SY59 )
                    | ( product @ SV19 @ SY57 @ SY59 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(69,plain,
    ! [SV16: $i,SV11: $i,SV2: $i] :
      ( ( ( ~ ( product @ ( inverse @ SV2 ) @ ( inverse @ SV11 ) @ SV16 ) )
        = $true )
      | ( ( product @ SV2 @ SV16 @ SV11 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(70,plain,
    ! [SV17: $i,SV13: $i,SV8: $i] :
      ( ( ( ~ ( product @ SV8 @ SV13 @ SV17 ) )
        = $true )
      | ( ( ! [SY53: $i] :
              ( ~ ( product @ SV8 @ SV13 @ SY53 )
              | ( SV17 = SY53 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(71,plain,
    ! [SV20: $i,SV18: $i,SV14: $i,SV9: $i] :
      ( ( ~ ( product @ SV9 @ SV14 @ SV18 )
        | ! [SY60: $i] :
            ( ~ ( product @ SV14 @ SV20 @ SY60 )
            | ! [SY61: $i] :
                ( ~ ( product @ SV18 @ SV20 @ SY61 )
                | ( product @ SV9 @ SY60 @ SY61 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(72,plain,
    ! [SV21: $i,SV19: $i,SV15: $i,SV10: $i] :
      ( ( ~ ( product @ SV10 @ SV15 @ SV19 )
        | ! [SY62: $i] :
            ( ~ ( product @ SV15 @ SV21 @ SY62 )
            | ! [SY63: $i] :
                ( ~ ( product @ SV10 @ SY62 @ SY63 )
                | ( product @ SV19 @ SV21 @ SY63 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(73,plain,
    ! [SV16: $i,SV11: $i,SV2: $i] :
      ( ( ( product @ ( inverse @ SV2 ) @ ( inverse @ SV11 ) @ SV16 )
        = $false )
      | ( ( product @ SV2 @ SV16 @ SV11 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(74,plain,
    ! [SV17: $i,SV13: $i,SV8: $i] :
      ( ( ( product @ SV8 @ SV13 @ SV17 )
        = $false )
      | ( ( ! [SY53: $i] :
              ( ~ ( product @ SV8 @ SV13 @ SY53 )
              | ( SV17 = SY53 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(75,plain,
    ! [SV20: $i,SV18: $i,SV14: $i,SV9: $i] :
      ( ( ( ~ ( product @ SV9 @ SV14 @ SV18 ) )
        = $true )
      | ( ( ! [SY60: $i] :
              ( ~ ( product @ SV14 @ SV20 @ SY60 )
              | ! [SY61: $i] :
                  ( ~ ( product @ SV18 @ SV20 @ SY61 )
                  | ( product @ SV9 @ SY60 @ SY61 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(76,plain,
    ! [SV21: $i,SV19: $i,SV15: $i,SV10: $i] :
      ( ( ( ~ ( product @ SV10 @ SV15 @ SV19 ) )
        = $true )
      | ( ( ! [SY62: $i] :
              ( ~ ( product @ SV15 @ SV21 @ SY62 )
              | ! [SY63: $i] :
                  ( ~ ( product @ SV10 @ SY62 @ SY63 )
                  | ( product @ SV19 @ SV21 @ SY63 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(77,plain,
    ! [SV17: $i,SV22: $i,SV13: $i,SV8: $i] :
      ( ( ( ~ ( product @ SV8 @ SV13 @ SV22 )
          | ( SV17 = SV22 ) )
        = $true )
      | ( ( product @ SV8 @ SV13 @ SV17 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(78,plain,
    ! [SV20: $i,SV18: $i,SV14: $i,SV9: $i] :
      ( ( ( product @ SV9 @ SV14 @ SV18 )
        = $false )
      | ( ( ! [SY60: $i] :
              ( ~ ( product @ SV14 @ SV20 @ SY60 )
              | ! [SY61: $i] :
                  ( ~ ( product @ SV18 @ SV20 @ SY61 )
                  | ( product @ SV9 @ SY60 @ SY61 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[75]) ).

thf(79,plain,
    ! [SV21: $i,SV19: $i,SV15: $i,SV10: $i] :
      ( ( ( product @ SV10 @ SV15 @ SV19 )
        = $false )
      | ( ( ! [SY62: $i] :
              ( ~ ( product @ SV15 @ SV21 @ SY62 )
              | ! [SY63: $i] :
                  ( ~ ( product @ SV10 @ SY62 @ SY63 )
                  | ( product @ SV19 @ SV21 @ SY63 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(80,plain,
    ! [SV17: $i,SV22: $i,SV13: $i,SV8: $i] :
      ( ( ( ~ ( product @ SV8 @ SV13 @ SV22 ) )
        = $true )
      | ( ( SV17 = SV22 )
        = $true )
      | ( ( product @ SV8 @ SV13 @ SV17 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[77]) ).

thf(81,plain,
    ! [SV9: $i,SV18: $i,SV23: $i,SV20: $i,SV14: $i] :
      ( ( ( ~ ( product @ SV14 @ SV20 @ SV23 )
          | ! [SY64: $i] :
              ( ~ ( product @ SV18 @ SV20 @ SY64 )
              | ( product @ SV9 @ SV23 @ SY64 ) ) )
        = $true )
      | ( ( product @ SV9 @ SV14 @ SV18 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(82,plain,
    ! [SV19: $i,SV10: $i,SV24: $i,SV21: $i,SV15: $i] :
      ( ( ( ~ ( product @ SV15 @ SV21 @ SV24 )
          | ! [SY65: $i] :
              ( ~ ( product @ SV10 @ SV24 @ SY65 )
              | ( product @ SV19 @ SV21 @ SY65 ) ) )
        = $true )
      | ( ( product @ SV10 @ SV15 @ SV19 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(83,plain,
    ! [SV17: $i,SV22: $i,SV13: $i,SV8: $i] :
      ( ( ( product @ SV8 @ SV13 @ SV22 )
        = $false )
      | ( ( SV17 = SV22 )
        = $true )
      | ( ( product @ SV8 @ SV13 @ SV17 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[80]) ).

thf(84,plain,
    ! [SV9: $i,SV18: $i,SV23: $i,SV20: $i,SV14: $i] :
      ( ( ( ~ ( product @ SV14 @ SV20 @ SV23 ) )
        = $true )
      | ( ( ! [SY64: $i] :
              ( ~ ( product @ SV18 @ SV20 @ SY64 )
              | ( product @ SV9 @ SV23 @ SY64 ) ) )
        = $true )
      | ( ( product @ SV9 @ SV14 @ SV18 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[81]) ).

thf(85,plain,
    ! [SV19: $i,SV10: $i,SV24: $i,SV21: $i,SV15: $i] :
      ( ( ( ~ ( product @ SV15 @ SV21 @ SV24 ) )
        = $true )
      | ( ( ! [SY65: $i] :
              ( ~ ( product @ SV10 @ SV24 @ SY65 )
              | ( product @ SV19 @ SV21 @ SY65 ) ) )
        = $true )
      | ( ( product @ SV10 @ SV15 @ SV19 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[82]) ).

thf(86,plain,
    ! [SV9: $i,SV18: $i,SV23: $i,SV20: $i,SV14: $i] :
      ( ( ( product @ SV14 @ SV20 @ SV23 )
        = $false )
      | ( ( ! [SY64: $i] :
              ( ~ ( product @ SV18 @ SV20 @ SY64 )
              | ( product @ SV9 @ SV23 @ SY64 ) ) )
        = $true )
      | ( ( product @ SV9 @ SV14 @ SV18 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(87,plain,
    ! [SV19: $i,SV10: $i,SV24: $i,SV21: $i,SV15: $i] :
      ( ( ( product @ SV15 @ SV21 @ SV24 )
        = $false )
      | ( ( ! [SY65: $i] :
              ( ~ ( product @ SV10 @ SV24 @ SY65 )
              | ( product @ SV19 @ SV21 @ SY65 ) ) )
        = $true )
      | ( ( product @ SV10 @ SV15 @ SV19 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(88,plain,
    ! [SV14: $i,SV23: $i,SV9: $i,SV25: $i,SV20: $i,SV18: $i] :
      ( ( ( ~ ( product @ SV18 @ SV20 @ SV25 )
          | ( product @ SV9 @ SV23 @ SV25 ) )
        = $true )
      | ( ( product @ SV14 @ SV20 @ SV23 )
        = $false )
      | ( ( product @ SV9 @ SV14 @ SV18 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(89,plain,
    ! [SV15: $i,SV21: $i,SV19: $i,SV26: $i,SV24: $i,SV10: $i] :
      ( ( ( ~ ( product @ SV10 @ SV24 @ SV26 )
          | ( product @ SV19 @ SV21 @ SV26 ) )
        = $true )
      | ( ( product @ SV15 @ SV21 @ SV24 )
        = $false )
      | ( ( product @ SV10 @ SV15 @ SV19 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(90,plain,
    ! [SV14: $i,SV23: $i,SV9: $i,SV25: $i,SV20: $i,SV18: $i] :
      ( ( ( ~ ( product @ SV18 @ SV20 @ SV25 ) )
        = $true )
      | ( ( product @ SV9 @ SV23 @ SV25 )
        = $true )
      | ( ( product @ SV14 @ SV20 @ SV23 )
        = $false )
      | ( ( product @ SV9 @ SV14 @ SV18 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(91,plain,
    ! [SV15: $i,SV21: $i,SV19: $i,SV26: $i,SV24: $i,SV10: $i] :
      ( ( ( ~ ( product @ SV10 @ SV24 @ SV26 ) )
        = $true )
      | ( ( product @ SV19 @ SV21 @ SV26 )
        = $true )
      | ( ( product @ SV15 @ SV21 @ SV24 )
        = $false )
      | ( ( product @ SV10 @ SV15 @ SV19 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(92,plain,
    ! [SV14: $i,SV23: $i,SV9: $i,SV25: $i,SV20: $i,SV18: $i] :
      ( ( ( product @ SV18 @ SV20 @ SV25 )
        = $false )
      | ( ( product @ SV9 @ SV23 @ SV25 )
        = $true )
      | ( ( product @ SV14 @ SV20 @ SV23 )
        = $false )
      | ( ( product @ SV9 @ SV14 @ SV18 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(93,plain,
    ! [SV15: $i,SV21: $i,SV19: $i,SV26: $i,SV24: $i,SV10: $i] :
      ( ( ( product @ SV10 @ SV24 @ SV26 )
        = $false )
      | ( ( product @ SV19 @ SV21 @ SV26 )
        = $true )
      | ( ( product @ SV15 @ SV21 @ SV24 )
        = $false )
      | ( ( product @ SV10 @ SV15 @ SV19 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[91]) ).

thf(94,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[36,93,92,83,73,61,59,54,53,52,51,49,48,37]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n010.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
% 0.19/0.34  % CPULimit : 300
% 0.19/0.34  % WCLimit  : 600
% 0.19/0.34  % DateTime : Mon Jun 13 11:11:09 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.19/0.35  
% 0.19/0.35   No.of.Axioms: 13
% 0.19/0.35  
% 0.19/0.35   Length.of.Defs: 0
% 0.19/0.35  
% 0.19/0.35   Contains.Choice.Funs: false
% 0.19/0.36  (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).....
% 0.20/0.43  
% 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/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).
% 0.20/0.43  
% 0.20/0.43  
% 0.20/0.43  %**** Beginning of derivation protocol ****
% 0.20/0.43  % SZS output start CNFRefutation
% See solution above
% 0.20/0.44  
% 0.20/0.44  %**** End of derivation protocol ****
% 0.20/0.44  %**** no. of clauses in derivation: 95 ****
% 0.20/0.44  %**** clause counter: 94 ****
% 0.20/0.44  
% 0.20/0.44  % 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)
%------------------------------------------------------------------------------