TSTP Solution File: GRP767-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP767-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n018.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 10:19:55 EDT 2022

% Result   : Unsatisfiable 25.98s 26.15s
% Output   : CNFRefutation 25.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   33
% Syntax   : Number of formulae    :  124 ( 113 unt;  11 typ;   0 def)
%            Number of atoms       :  293 ( 195 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  826 (   6   ~;   0   |;   0   &; 820   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :  212 (   0   ^ 212   !;   0   ?; 212   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_difference,type,
    difference: $i > $i > $i ).

thf(tp_eta,type,
    eta: $i > $i ).

thf(tp_i,type,
    i: $i > $i ).

thf(tp_j,type,
    j: $i > $i ).

thf(tp_l,type,
    l: $i > $i > $i > $i ).

thf(tp_one,type,
    one: $i ).

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

thf(tp_quotient,type,
    quotient: $i > $i > $i ).

thf(tp_t,type,
    t: $i > $i > $i ).

thf(tp_x0,type,
    x0: $i ).

thf(tp_x1,type,
    x1: $i ).

thf(1,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( t @ ( eta @ A ) @ ( product @ B @ C ) )
      = ( product @ ( t @ ( eta @ A ) @ B ) @ ( t @ ( eta @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos20) ).

thf(2,axiom,
    ! [A: $i,B: $i] :
      ( ( t @ A @ B )
      = ( quotient @ ( product @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos19) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( l @ A @ A @ ( product @ B @ C ) )
      = ( product @ ( l @ A @ A @ B ) @ ( l @ A @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos18) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( l @ A @ B @ C )
      = ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos17) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( product @ ( eta @ A ) @ ( product @ B @ C ) )
      = ( product @ ( product @ ( eta @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( product @ A @ ( product @ B @ ( eta @ A ) ) )
      = ( product @ ( product @ A @ B ) @ ( eta @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos15) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( product @ A @ ( product @ ( eta @ A ) @ B ) )
      = ( product @ ( j @ ( j @ A ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( product @ ( i @ ( i @ A ) ) @ B )
      = ( product @ ( eta @ A ) @ ( product @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( eta @ A )
      = ( product @ ( i @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( product @ ( i @ A ) @ A )
      = ( product @ A @ ( j @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( j @ A )
      = ( quotient @ one @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( i @ A )
      = ( difference @ A @ one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) )
      = ( quotient @ ( quotient @ ( product @ C @ ( product @ A @ B ) ) @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( difference @ A @ ( product @ ( product @ A @ B ) @ C ) )
      = ( quotient @ ( product @ B @ ( product @ C @ A ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( product @ ( quotient @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( quotient @ ( product @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).

thf(17,axiom,
    ! [A: $i,B: $i] :
      ( ( difference @ A @ ( product @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( product @ A @ ( difference @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( product @ one @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( product @ A @ one )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).

thf(21,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(22,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[21]) ).

thf(23,negated_conjecture,
    ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
 != ( j @ x1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

thf(24,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[22]) ).

thf(25,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( t @ ( eta @ A ) @ ( product @ B @ C ) )
          = ( product @ ( t @ ( eta @ A ) @ B ) @ ( t @ ( eta @ A ) @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(26,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( t @ A @ B )
          = ( quotient @ ( product @ A @ B ) @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(27,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( l @ A @ A @ ( product @ B @ C ) )
          = ( product @ ( l @ A @ A @ B ) @ ( l @ A @ A @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(28,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( l @ A @ B @ C )
          = ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(29,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( product @ ( eta @ A ) @ ( product @ B @ C ) )
          = ( product @ ( product @ ( eta @ A ) @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(30,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( product @ A @ ( product @ B @ ( eta @ A ) ) )
          = ( product @ ( product @ A @ B ) @ ( eta @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(31,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( product @ A @ ( product @ ( eta @ A ) @ B ) )
          = ( product @ ( j @ ( j @ A ) ) @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(32,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( product @ ( i @ ( i @ A ) ) @ B )
          = ( product @ ( eta @ A ) @ ( product @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(33,plain,
    ( ( ! [A: $i] :
          ( ( eta @ A )
          = ( product @ ( i @ A ) @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(34,plain,
    ( ( ! [A: $i] :
          ( ( product @ ( i @ A ) @ A )
          = ( product @ A @ ( j @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(35,plain,
    ( ( ! [A: $i] :
          ( ( j @ A )
          = ( quotient @ one @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(36,plain,
    ( ( ! [A: $i] :
          ( ( i @ A )
          = ( difference @ A @ one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(37,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) )
          = ( quotient @ ( quotient @ ( product @ C @ ( product @ A @ B ) ) @ B ) @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(38,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( difference @ A @ ( product @ ( product @ A @ B ) @ C ) )
          = ( quotient @ ( product @ B @ ( product @ C @ A ) ) @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(39,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( product @ ( quotient @ A @ B ) @ B )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(40,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( quotient @ ( product @ A @ B ) @ B )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(41,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( difference @ A @ ( product @ A @ B ) )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(42,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( product @ A @ ( difference @ A @ B ) )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(43,plain,
    ( ( ! [A: $i] :
          ( ( product @ one @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(44,plain,
    ( ( ! [A: $i] :
          ( ( product @ A @ one )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(45,plain,
    ( ( ( ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
       != ( j @ x1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(46,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[24]) ).

thf(47,plain,
    ( ( ( ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
       != ( j @ x1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[45]) ).

thf(48,plain,
    ( ( ( ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
       != ( j @ x1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[47]) ).

thf(49,plain,
    ( ( ! [A: $i] :
          ( ( product @ A @ one )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(50,plain,
    ( ( ! [A: $i] :
          ( ( product @ one @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(51,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( product @ A @ ( difference @ A @ B ) )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(52,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( difference @ A @ ( product @ A @ B ) )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(53,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( quotient @ ( product @ A @ B ) @ B )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(54,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( product @ ( quotient @ A @ B ) @ B )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(55,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( difference @ A @ ( product @ ( product @ A @ B ) @ C ) )
          = ( quotient @ ( product @ B @ ( product @ C @ A ) ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(56,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) )
          = ( quotient @ ( quotient @ ( product @ C @ ( product @ A @ B ) ) @ B ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(57,plain,
    ( ( ! [A: $i] :
          ( ( i @ A )
          = ( difference @ A @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(58,plain,
    ( ( ! [A: $i] :
          ( ( j @ A )
          = ( quotient @ one @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(59,plain,
    ( ( ! [A: $i] :
          ( ( product @ ( i @ A ) @ A )
          = ( product @ A @ ( j @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(60,plain,
    ( ( ! [A: $i] :
          ( ( eta @ A )
          = ( product @ ( i @ A ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(61,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( product @ ( i @ ( i @ A ) ) @ B )
          = ( product @ ( eta @ A ) @ ( product @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(62,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( product @ A @ ( product @ ( eta @ A ) @ B ) )
          = ( product @ ( j @ ( j @ A ) ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(63,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( product @ A @ ( product @ B @ ( eta @ A ) ) )
          = ( product @ ( product @ A @ B ) @ ( eta @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(64,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( product @ ( eta @ A ) @ ( product @ B @ C ) )
          = ( product @ ( product @ ( eta @ A ) @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(65,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( l @ A @ B @ C )
          = ( difference @ ( product @ A @ B ) @ ( product @ A @ ( product @ B @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(66,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( l @ A @ A @ ( product @ B @ C ) )
          = ( product @ ( l @ A @ A @ B ) @ ( l @ A @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(67,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( t @ A @ B )
          = ( quotient @ ( product @ A @ B ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(68,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( t @ ( eta @ A ) @ ( product @ B @ C ) )
          = ( product @ ( t @ ( eta @ A ) @ B ) @ ( t @ ( eta @ A ) @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(69,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(70,plain,
    ( ( ( product @ ( j @ ( j @ x0 ) ) @ ( j @ ( product @ x1 @ x0 ) ) )
      = ( j @ x1 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(71,plain,
    ! [SV1: $i] :
      ( ( ( product @ SV1 @ one )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(72,plain,
    ! [SV2: $i] :
      ( ( ( product @ one @ SV2 )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(73,plain,
    ! [SV3: $i] :
      ( ( ! [SY40: $i] :
            ( ( product @ SV3 @ ( difference @ SV3 @ SY40 ) )
            = SY40 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(74,plain,
    ! [SV4: $i] :
      ( ( ! [SY41: $i] :
            ( ( difference @ SV4 @ ( product @ SV4 @ SY41 ) )
            = SY41 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(75,plain,
    ! [SV5: $i] :
      ( ( ! [SY42: $i] :
            ( ( quotient @ ( product @ SV5 @ SY42 ) @ SY42 )
            = SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(76,plain,
    ! [SV6: $i] :
      ( ( ! [SY43: $i] :
            ( ( product @ ( quotient @ SV6 @ SY43 ) @ SY43 )
            = SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(77,plain,
    ! [SV7: $i] :
      ( ( ! [SY44: $i,SY45: $i] :
            ( ( difference @ SV7 @ ( product @ ( product @ SV7 @ SY44 ) @ SY45 ) )
            = ( quotient @ ( product @ SY44 @ ( product @ SY45 @ SV7 ) ) @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(78,plain,
    ! [SV8: $i] :
      ( ( ! [SY46: $i,SY47: $i] :
            ( ( difference @ ( product @ SV8 @ SY46 ) @ ( product @ SV8 @ ( product @ SY46 @ SY47 ) ) )
            = ( quotient @ ( quotient @ ( product @ SY47 @ ( product @ SV8 @ SY46 ) ) @ SY46 ) @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(79,plain,
    ! [SV9: $i] :
      ( ( ( i @ SV9 )
        = ( difference @ SV9 @ one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(80,plain,
    ! [SV10: $i] :
      ( ( ( j @ SV10 )
        = ( quotient @ one @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(81,plain,
    ! [SV11: $i] :
      ( ( ( product @ ( i @ SV11 ) @ SV11 )
        = ( product @ SV11 @ ( j @ SV11 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(82,plain,
    ! [SV12: $i] :
      ( ( ( eta @ SV12 )
        = ( product @ ( i @ SV12 ) @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(83,plain,
    ! [SV13: $i] :
      ( ( ! [SY48: $i] :
            ( ( product @ ( i @ ( i @ SV13 ) ) @ SY48 )
            = ( product @ ( eta @ SV13 ) @ ( product @ SV13 @ SY48 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(84,plain,
    ! [SV14: $i] :
      ( ( ! [SY49: $i] :
            ( ( product @ SV14 @ ( product @ ( eta @ SV14 ) @ SY49 ) )
            = ( product @ ( j @ ( j @ SV14 ) ) @ SY49 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(85,plain,
    ! [SV15: $i] :
      ( ( ! [SY50: $i] :
            ( ( product @ SV15 @ ( product @ SY50 @ ( eta @ SV15 ) ) )
            = ( product @ ( product @ SV15 @ SY50 ) @ ( eta @ SV15 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(86,plain,
    ! [SV16: $i] :
      ( ( ! [SY51: $i,SY52: $i] :
            ( ( product @ ( eta @ SV16 ) @ ( product @ SY51 @ SY52 ) )
            = ( product @ ( product @ ( eta @ SV16 ) @ SY51 ) @ SY52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(87,plain,
    ! [SV17: $i] :
      ( ( ! [SY53: $i,SY54: $i] :
            ( ( l @ SV17 @ SY53 @ SY54 )
            = ( difference @ ( product @ SV17 @ SY53 ) @ ( product @ SV17 @ ( product @ SY53 @ SY54 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(88,plain,
    ! [SV18: $i] :
      ( ( ! [SY55: $i,SY56: $i] :
            ( ( l @ SV18 @ SV18 @ ( product @ SY55 @ SY56 ) )
            = ( product @ ( l @ SV18 @ SV18 @ SY55 ) @ ( l @ SV18 @ SV18 @ SY56 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(89,plain,
    ! [SV19: $i] :
      ( ( ! [SY57: $i] :
            ( ( t @ SV19 @ SY57 )
            = ( quotient @ ( product @ SV19 @ SY57 ) @ SV19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(90,plain,
    ! [SV20: $i] :
      ( ( ! [SY58: $i,SY59: $i] :
            ( ( t @ ( eta @ SV20 ) @ ( product @ SY58 @ SY59 ) )
            = ( product @ ( t @ ( eta @ SV20 ) @ SY58 ) @ ( t @ ( eta @ SV20 ) @ SY59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(91,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(92,plain,
    ! [SV21: $i,SV3: $i] :
      ( ( ( product @ SV3 @ ( difference @ SV3 @ SV21 ) )
        = SV21 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(93,plain,
    ! [SV22: $i,SV4: $i] :
      ( ( ( difference @ SV4 @ ( product @ SV4 @ SV22 ) )
        = SV22 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(94,plain,
    ! [SV23: $i,SV5: $i] :
      ( ( ( quotient @ ( product @ SV5 @ SV23 ) @ SV23 )
        = SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(95,plain,
    ! [SV24: $i,SV6: $i] :
      ( ( ( product @ ( quotient @ SV6 @ SV24 ) @ SV24 )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(96,plain,
    ! [SV25: $i,SV7: $i] :
      ( ( ! [SY60: $i] :
            ( ( difference @ SV7 @ ( product @ ( product @ SV7 @ SV25 ) @ SY60 ) )
            = ( quotient @ ( product @ SV25 @ ( product @ SY60 @ SV7 ) ) @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(97,plain,
    ! [SV26: $i,SV8: $i] :
      ( ( ! [SY61: $i] :
            ( ( difference @ ( product @ SV8 @ SV26 ) @ ( product @ SV8 @ ( product @ SV26 @ SY61 ) ) )
            = ( quotient @ ( quotient @ ( product @ SY61 @ ( product @ SV8 @ SV26 ) ) @ SV26 ) @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(98,plain,
    ! [SV27: $i,SV13: $i] :
      ( ( ( product @ ( i @ ( i @ SV13 ) ) @ SV27 )
        = ( product @ ( eta @ SV13 ) @ ( product @ SV13 @ SV27 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(99,plain,
    ! [SV28: $i,SV14: $i] :
      ( ( ( product @ SV14 @ ( product @ ( eta @ SV14 ) @ SV28 ) )
        = ( product @ ( j @ ( j @ SV14 ) ) @ SV28 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(100,plain,
    ! [SV29: $i,SV15: $i] :
      ( ( ( product @ SV15 @ ( product @ SV29 @ ( eta @ SV15 ) ) )
        = ( product @ ( product @ SV15 @ SV29 ) @ ( eta @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(101,plain,
    ! [SV30: $i,SV16: $i] :
      ( ( ! [SY62: $i] :
            ( ( product @ ( eta @ SV16 ) @ ( product @ SV30 @ SY62 ) )
            = ( product @ ( product @ ( eta @ SV16 ) @ SV30 ) @ SY62 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(102,plain,
    ! [SV31: $i,SV17: $i] :
      ( ( ! [SY63: $i] :
            ( ( l @ SV17 @ SV31 @ SY63 )
            = ( difference @ ( product @ SV17 @ SV31 ) @ ( product @ SV17 @ ( product @ SV31 @ SY63 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(103,plain,
    ! [SV32: $i,SV18: $i] :
      ( ( ! [SY64: $i] :
            ( ( l @ SV18 @ SV18 @ ( product @ SV32 @ SY64 ) )
            = ( product @ ( l @ SV18 @ SV18 @ SV32 ) @ ( l @ SV18 @ SV18 @ SY64 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(104,plain,
    ! [SV33: $i,SV19: $i] :
      ( ( ( t @ SV19 @ SV33 )
        = ( quotient @ ( product @ SV19 @ SV33 ) @ SV19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(105,plain,
    ! [SV34: $i,SV20: $i] :
      ( ( ! [SY65: $i] :
            ( ( t @ ( eta @ SV20 ) @ ( product @ SV34 @ SY65 ) )
            = ( product @ ( t @ ( eta @ SV20 ) @ SV34 ) @ ( t @ ( eta @ SV20 ) @ SY65 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(106,plain,
    ! [SV35: $i,SV25: $i,SV7: $i] :
      ( ( ( difference @ SV7 @ ( product @ ( product @ SV7 @ SV25 ) @ SV35 ) )
        = ( quotient @ ( product @ SV25 @ ( product @ SV35 @ SV7 ) ) @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(107,plain,
    ! [SV36: $i,SV26: $i,SV8: $i] :
      ( ( ( difference @ ( product @ SV8 @ SV26 ) @ ( product @ SV8 @ ( product @ SV26 @ SV36 ) ) )
        = ( quotient @ ( quotient @ ( product @ SV36 @ ( product @ SV8 @ SV26 ) ) @ SV26 ) @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(108,plain,
    ! [SV37: $i,SV30: $i,SV16: $i] :
      ( ( ( product @ ( eta @ SV16 ) @ ( product @ SV30 @ SV37 ) )
        = ( product @ ( product @ ( eta @ SV16 ) @ SV30 ) @ SV37 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[101]) ).

thf(109,plain,
    ! [SV38: $i,SV31: $i,SV17: $i] :
      ( ( ( l @ SV17 @ SV31 @ SV38 )
        = ( difference @ ( product @ SV17 @ SV31 ) @ ( product @ SV17 @ ( product @ SV31 @ SV38 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[102]) ).

thf(110,plain,
    ! [SV39: $i,SV32: $i,SV18: $i] :
      ( ( ( l @ SV18 @ SV18 @ ( product @ SV32 @ SV39 ) )
        = ( product @ ( l @ SV18 @ SV18 @ SV32 ) @ ( l @ SV18 @ SV18 @ SV39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[103]) ).

thf(111,plain,
    ! [SV40: $i,SV34: $i,SV20: $i] :
      ( ( ( t @ ( eta @ SV20 ) @ ( product @ SV34 @ SV40 ) )
        = ( product @ ( t @ ( eta @ SV20 ) @ SV34 ) @ ( t @ ( eta @ SV20 ) @ SV40 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[105]) ).

thf(112,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[70,111,110,109,108,107,106,104,100,99,98,95,94,93,92,91,82,81,80,79,72,71]) ).

thf(113,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[112]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRP767-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jun 13 20:40:58 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.21/0.37  
% 0.21/0.37   No.of.Axioms: 21
% 0.21/0.37  
% 0.21/0.37   Length.of.Defs: 0
% 0.21/0.37  
% 0.21/0.37   Contains.Choice.Funs: false
% 0.21/0.38  .
% 0.21/0.38  (rf:0,axioms:21,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:23,loop_count:0,foatp_calls:0,translation:fof_full)......
% 25.98/26.15  
% 25.98/26.15  ********************************
% 25.98/26.15  *   All subproblems solved!    *
% 25.98/26.15  ********************************
% 25.98/26.15  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:112,loop_count:0,foatp_calls:1,translation:fof_full)
% 25.98/26.15  
% 25.98/26.15  %**** Beginning of derivation protocol ****
% 25.98/26.15  % SZS output start CNFRefutation
% See solution above
% 25.98/26.15  
% 25.98/26.15  %**** End of derivation protocol ****
% 25.98/26.15  %**** no. of clauses in derivation: 113 ****
% 25.98/26.15  %**** clause counter: 112 ****
% 25.98/26.15  
% 25.98/26.15  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:112,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------