TSTP Solution File: TOP050-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : TOP050-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n022.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 21 21:31:50 EDT 2022

% Result   : Unsatisfiable 1.61s 1.79s
% Output   : CNFRefutation 1.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   70
% Syntax   : Number of formulae    :  155 ( 121 unt;  34 typ;   0 def)
%            Number of atoms       :  289 ( 197 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  590 (   6   ~;   0   |;   0   &; 584   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   33 (  33   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   37 (  34 usr;  34 con; 0-31 aty)
%            Number of variables   :   32 (   0   ^  32   !;   0   ?;  32   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a1,type,
    a1: $i ).

thf(tp_a10,type,
    a10: $i ).

thf(tp_a11,type,
    a11: $i ).

thf(tp_a12,type,
    a12: $i ).

thf(tp_a13,type,
    a13: $i ).

thf(tp_a14,type,
    a14: $i ).

thf(tp_a15,type,
    a15: $i ).

thf(tp_a16,type,
    a16: $i ).

thf(tp_a17,type,
    a17: $i ).

thf(tp_a18,type,
    a18: $i ).

thf(tp_a19,type,
    a19: $i ).

thf(tp_a2,type,
    a2: $i ).

thf(tp_a20,type,
    a20: $i ).

thf(tp_a21,type,
    a21: $i ).

thf(tp_a22,type,
    a22: $i ).

thf(tp_a23,type,
    a23: $i ).

thf(tp_a24,type,
    a24: $i ).

thf(tp_a25,type,
    a25: $i ).

thf(tp_a26,type,
    a26: $i ).

thf(tp_a27,type,
    a27: $i ).

thf(tp_a28,type,
    a28: $i ).

thf(tp_a29,type,
    a29: $i ).

thf(tp_a3,type,
    a3: $i ).

thf(tp_a30,type,
    a30: $i ).

thf(tp_a31,type,
    a31: $i ).

thf(tp_a32,type,
    a32: $i ).

thf(tp_a4,type,
    a4: $i ).

thf(tp_a5,type,
    a5: $i ).

thf(tp_a6,type,
    a6: $i ).

thf(tp_a7,type,
    a7: $i ).

thf(tp_a8,type,
    a8: $i ).

thf(tp_a9,type,
    a9: $i ).

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

thf(tp_tuple,type,
    tuple: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(1,axiom,
    ( ( product @ a32 @ a21 )
    = a1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_32) ).

thf(2,axiom,
    ( ( product @ a31 @ a3 )
    = a32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_31) ).

thf(3,axiom,
    ( ( product @ a30 @ a23 )
    = a31 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_30) ).

thf(4,axiom,
    ( ( product @ a29 @ a1 )
    = a30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_29) ).

thf(5,axiom,
    ( ( product @ a28 @ a3 )
    = a29 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_28) ).

thf(6,axiom,
    ( ( product @ a27 @ a21 )
    = a28 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_27) ).

thf(7,axiom,
    ( ( product @ a26 @ a1 )
    = a27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_26) ).

thf(8,axiom,
    ( ( product @ a25 @ a23 )
    = a26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_25) ).

thf(9,axiom,
    ( ( product @ a24 @ a3 )
    = a25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_24) ).

thf(10,axiom,
    ( ( product @ a23 @ a21 )
    = a24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_23) ).

thf(11,axiom,
    ( ( product @ a22 @ a31 )
    = a23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_22) ).

thf(12,axiom,
    ( ( product @ a21 @ a25 )
    = a22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_21) ).

thf(13,axiom,
    ( ( product @ a20 @ a29 )
    = a21 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_20) ).

thf(14,axiom,
    ( ( product @ a19 @ a11 )
    = a20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_19) ).

thf(15,axiom,
    ( ( product @ a18 @ a15 )
    = a19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_18) ).

thf(16,axiom,
    ( ( product @ a17 @ a9 )
    = a18 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_17) ).

thf(17,axiom,
    ( ( product @ a16 @ a19 )
    = a17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_16) ).

thf(18,axiom,
    ( ( product @ a15 @ a5 )
    = a16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_15) ).

thf(19,axiom,
    ( ( product @ a14 @ a17 )
    = a15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_14) ).

thf(20,axiom,
    ( ( product @ a13 @ a7 )
    = a14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_13) ).

thf(21,axiom,
    ( ( product @ a12 @ a19 )
    = a13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_12) ).

thf(22,axiom,
    ( ( product @ a11 @ a5 )
    = a12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_11) ).

thf(23,axiom,
    ( ( product @ a10 @ a7 )
    = a11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).

thf(24,axiom,
    ( ( product @ a9 @ a17 )
    = a10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_09) ).

thf(25,axiom,
    ( ( product @ a8 @ a5 )
    = a9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_08) ).

thf(26,axiom,
    ( ( product @ a7 @ a19 )
    = a8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_07) ).

thf(27,axiom,
    ( ( product @ a5 @ a15 )
    = a6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_06) ).

thf(28,axiom,
    ( ( product @ a4 @ a11 )
    = a5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_05) ).

thf(29,axiom,
    ( ( product @ a3 @ a29 )
    = a4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_04) ).

thf(30,axiom,
    ( ( product @ a2 @ a25 )
    = a3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_03) ).

thf(31,axiom,
    ( ( product @ a1 @ a31 )
    = a2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).

thf(32,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( product @ ( product @ X @ Y ) @ Z )
      = ( product @ ( product @ X @ Z ) @ ( product @ Y @ Z ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_02) ).

thf(33,axiom,
    ! [X: $i,Y: $i] :
      ( ( product @ ( product @ X @ Y ) @ Y )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).

thf(34,axiom,
    ! [X: $i] :
      ( ( product @ X @ X )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).

thf(35,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(36,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[35]) ).

thf(37,negated_conjecture,
    ( tuple @ a1 @ a30 @ a31 @ a2 @ a24 @ a25 @ a3 @ a28 @ a29 @ a4 @ a10 @ a11 @ a5 @ a14 @ a15 @ a6 @ a7 @ a18 @ a19 @ a8 @ a9 @ a16 @ a17 @ a12 @ a13 @ a20 @ a21 @ a22 @ a23 @ a26 @ a27 )
 != ( tuple @ a2 @ a31 @ a32 @ a3 @ a25 @ a26 @ a4 @ a29 @ a30 @ a5 @ a11 @ a12 @ a6 @ a15 @ a16 @ a7 @ a8 @ a19 @ a20 @ a9 @ a10 @ a17 @ a18 @ a13 @ a14 @ a21 @ a22 @ a23 @ a24 @ a27 @ a28 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).

thf(38,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[36]) ).

thf(39,plain,
    ( ( ( product @ a32 @ a21 )
      = a1 )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(40,plain,
    ( ( ( product @ a31 @ a3 )
      = a32 )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(41,plain,
    ( ( ( product @ a30 @ a23 )
      = a31 )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(42,plain,
    ( ( ( product @ a29 @ a1 )
      = a30 )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(43,plain,
    ( ( ( product @ a28 @ a3 )
      = a29 )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(44,plain,
    ( ( ( product @ a27 @ a21 )
      = a28 )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(45,plain,
    ( ( ( product @ a26 @ a1 )
      = a27 )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(46,plain,
    ( ( ( product @ a25 @ a23 )
      = a26 )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(47,plain,
    ( ( ( product @ a24 @ a3 )
      = a25 )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(48,plain,
    ( ( ( product @ a23 @ a21 )
      = a24 )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(49,plain,
    ( ( ( product @ a22 @ a31 )
      = a23 )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(50,plain,
    ( ( ( product @ a21 @ a25 )
      = a22 )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(51,plain,
    ( ( ( product @ a20 @ a29 )
      = a21 )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(52,plain,
    ( ( ( product @ a19 @ a11 )
      = a20 )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(53,plain,
    ( ( ( product @ a18 @ a15 )
      = a19 )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(54,plain,
    ( ( ( product @ a17 @ a9 )
      = a18 )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(55,plain,
    ( ( ( product @ a16 @ a19 )
      = a17 )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(56,plain,
    ( ( ( product @ a15 @ a5 )
      = a16 )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(57,plain,
    ( ( ( product @ a14 @ a17 )
      = a15 )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(58,plain,
    ( ( ( product @ a13 @ a7 )
      = a14 )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(59,plain,
    ( ( ( product @ a12 @ a19 )
      = a13 )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(60,plain,
    ( ( ( product @ a11 @ a5 )
      = a12 )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(61,plain,
    ( ( ( product @ a10 @ a7 )
      = a11 )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(62,plain,
    ( ( ( product @ a9 @ a17 )
      = a10 )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(63,plain,
    ( ( ( product @ a8 @ a5 )
      = a9 )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(64,plain,
    ( ( ( product @ a7 @ a19 )
      = a8 )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(65,plain,
    ( ( ( product @ a5 @ a15 )
      = a6 )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(66,plain,
    ( ( ( product @ a4 @ a11 )
      = a5 )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(67,plain,
    ( ( ( product @ a3 @ a29 )
      = a4 )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(68,plain,
    ( ( ( product @ a2 @ a25 )
      = a3 )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(69,plain,
    ( ( ( product @ a1 @ a31 )
      = a2 )
    = $true ),
    inference(unfold_def,[status(thm)],[31]) ).

thf(70,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( product @ ( product @ X @ Y ) @ Z )
          = ( product @ ( product @ X @ Z ) @ ( product @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(71,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( product @ ( product @ X @ Y ) @ Y )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(72,plain,
    ( ( ! [X: $i] :
          ( ( product @ X @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(73,plain,
    ( ( ( ( tuple @ a1 @ a30 @ a31 @ a2 @ a24 @ a25 @ a3 @ a28 @ a29 @ a4 @ a10 @ a11 @ a5 @ a14 @ a15 @ a6 @ a7 @ a18 @ a19 @ a8 @ a9 @ a16 @ a17 @ a12 @ a13 @ a20 @ a21 @ a22 @ a23 @ a26 @ a27 )
       != ( tuple @ a2 @ a31 @ a32 @ a3 @ a25 @ a26 @ a4 @ a29 @ a30 @ a5 @ a11 @ a12 @ a6 @ a15 @ a16 @ a7 @ a8 @ a19 @ a20 @ a9 @ a10 @ a17 @ a18 @ a13 @ a14 @ a21 @ a22 @ a23 @ a24 @ a27 @ a28 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(74,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[38]) ).

thf(75,plain,
    ( ( ( ( tuple @ a1 @ a30 @ a31 @ a2 @ a24 @ a25 @ a3 @ a28 @ a29 @ a4 @ a10 @ a11 @ a5 @ a14 @ a15 @ a6 @ a7 @ a18 @ a19 @ a8 @ a9 @ a16 @ a17 @ a12 @ a13 @ a20 @ a21 @ a22 @ a23 @ a26 @ a27 )
       != ( tuple @ a2 @ a31 @ a32 @ a3 @ a25 @ a26 @ a4 @ a29 @ a30 @ a5 @ a11 @ a12 @ a6 @ a15 @ a16 @ a7 @ a8 @ a19 @ a20 @ a9 @ a10 @ a17 @ a18 @ a13 @ a14 @ a21 @ a22 @ a23 @ a24 @ a27 @ a28 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[73]) ).

thf(76,plain,
    ( ( ( ( tuple @ a1 @ a30 @ a31 @ a2 @ a24 @ a25 @ a3 @ a28 @ a29 @ a4 @ a10 @ a11 @ a5 @ a14 @ a15 @ a6 @ a7 @ a18 @ a19 @ a8 @ a9 @ a16 @ a17 @ a12 @ a13 @ a20 @ a21 @ a22 @ a23 @ a26 @ a27 )
       != ( tuple @ a2 @ a31 @ a32 @ a3 @ a25 @ a26 @ a4 @ a29 @ a30 @ a5 @ a11 @ a12 @ a6 @ a15 @ a16 @ a7 @ a8 @ a19 @ a20 @ a9 @ a10 @ a17 @ a18 @ a13 @ a14 @ a21 @ a22 @ a23 @ a24 @ a27 @ a28 ) ) )
    = $true ),
    inference(copy,[status(thm)],[75]) ).

thf(77,plain,
    ( ( ! [X: $i] :
          ( ( product @ X @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[72]) ).

thf(78,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( product @ ( product @ X @ Y ) @ Y )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[71]) ).

thf(79,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( product @ ( product @ X @ Y ) @ Z )
          = ( product @ ( product @ X @ Z ) @ ( product @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[70]) ).

thf(80,plain,
    ( ( ( product @ a1 @ a31 )
      = a2 )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(81,plain,
    ( ( ( product @ a2 @ a25 )
      = a3 )
    = $true ),
    inference(copy,[status(thm)],[68]) ).

thf(82,plain,
    ( ( ( product @ a3 @ a29 )
      = a4 )
    = $true ),
    inference(copy,[status(thm)],[67]) ).

thf(83,plain,
    ( ( ( product @ a4 @ a11 )
      = a5 )
    = $true ),
    inference(copy,[status(thm)],[66]) ).

thf(84,plain,
    ( ( ( product @ a5 @ a15 )
      = a6 )
    = $true ),
    inference(copy,[status(thm)],[65]) ).

thf(85,plain,
    ( ( ( product @ a7 @ a19 )
      = a8 )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(86,plain,
    ( ( ( product @ a8 @ a5 )
      = a9 )
    = $true ),
    inference(copy,[status(thm)],[63]) ).

thf(87,plain,
    ( ( ( product @ a9 @ a17 )
      = a10 )
    = $true ),
    inference(copy,[status(thm)],[62]) ).

thf(88,plain,
    ( ( ( product @ a10 @ a7 )
      = a11 )
    = $true ),
    inference(copy,[status(thm)],[61]) ).

thf(89,plain,
    ( ( ( product @ a11 @ a5 )
      = a12 )
    = $true ),
    inference(copy,[status(thm)],[60]) ).

thf(90,plain,
    ( ( ( product @ a12 @ a19 )
      = a13 )
    = $true ),
    inference(copy,[status(thm)],[59]) ).

thf(91,plain,
    ( ( ( product @ a13 @ a7 )
      = a14 )
    = $true ),
    inference(copy,[status(thm)],[58]) ).

thf(92,plain,
    ( ( ( product @ a14 @ a17 )
      = a15 )
    = $true ),
    inference(copy,[status(thm)],[57]) ).

thf(93,plain,
    ( ( ( product @ a15 @ a5 )
      = a16 )
    = $true ),
    inference(copy,[status(thm)],[56]) ).

thf(94,plain,
    ( ( ( product @ a16 @ a19 )
      = a17 )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(95,plain,
    ( ( ( product @ a17 @ a9 )
      = a18 )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(96,plain,
    ( ( ( product @ a18 @ a15 )
      = a19 )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(97,plain,
    ( ( ( product @ a19 @ a11 )
      = a20 )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(98,plain,
    ( ( ( product @ a20 @ a29 )
      = a21 )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(99,plain,
    ( ( ( product @ a21 @ a25 )
      = a22 )
    = $true ),
    inference(copy,[status(thm)],[50]) ).

thf(100,plain,
    ( ( ( product @ a22 @ a31 )
      = a23 )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(101,plain,
    ( ( ( product @ a23 @ a21 )
      = a24 )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(102,plain,
    ( ( ( product @ a24 @ a3 )
      = a25 )
    = $true ),
    inference(copy,[status(thm)],[47]) ).

thf(103,plain,
    ( ( ( product @ a25 @ a23 )
      = a26 )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(104,plain,
    ( ( ( product @ a26 @ a1 )
      = a27 )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(105,plain,
    ( ( ( product @ a27 @ a21 )
      = a28 )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(106,plain,
    ( ( ( product @ a28 @ a3 )
      = a29 )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(107,plain,
    ( ( ( product @ a29 @ a1 )
      = a30 )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(108,plain,
    ( ( ( product @ a30 @ a23 )
      = a31 )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(109,plain,
    ( ( ( product @ a31 @ a3 )
      = a32 )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(110,plain,
    ( ( ( product @ a32 @ a21 )
      = a1 )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(111,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[74]) ).

thf(112,plain,
    ( ( ( tuple @ a1 @ a30 @ a31 @ a2 @ a24 @ a25 @ a3 @ a28 @ a29 @ a4 @ a10 @ a11 @ a5 @ a14 @ a15 @ a6 @ a7 @ a18 @ a19 @ a8 @ a9 @ a16 @ a17 @ a12 @ a13 @ a20 @ a21 @ a22 @ a23 @ a26 @ a27 )
      = ( tuple @ a2 @ a31 @ a32 @ a3 @ a25 @ a26 @ a4 @ a29 @ a30 @ a5 @ a11 @ a12 @ a6 @ a15 @ a16 @ a7 @ a8 @ a19 @ a20 @ a9 @ a10 @ a17 @ a18 @ a13 @ a14 @ a21 @ a22 @ a23 @ a24 @ a27 @ a28 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(113,plain,
    ! [SV1: $i] :
      ( ( ( product @ SV1 @ SV1 )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(114,plain,
    ! [SV2: $i] :
      ( ( ! [SY6: $i] :
            ( ( product @ ( product @ SV2 @ SY6 ) @ SY6 )
            = SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(115,plain,
    ! [SV3: $i] :
      ( ( ! [SY7: $i,SY8: $i] :
            ( ( product @ ( product @ SV3 @ SY7 ) @ SY8 )
            = ( product @ ( product @ SV3 @ SY8 ) @ ( product @ SY7 @ SY8 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(116,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(117,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( product @ ( product @ SV2 @ SV4 ) @ SV4 )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[114]) ).

thf(118,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ! [SY9: $i] :
            ( ( product @ ( product @ SV3 @ SV5 ) @ SY9 )
            = ( product @ ( product @ SV3 @ SY9 ) @ ( product @ SV5 @ SY9 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(119,plain,
    ! [SV6: $i,SV5: $i,SV3: $i] :
      ( ( ( product @ ( product @ SV3 @ SV5 ) @ SV6 )
        = ( product @ ( product @ SV3 @ SV6 ) @ ( product @ SV5 @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(120,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[80,119,117,116,113,112,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81]) ).

thf(121,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[120]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : TOP050-1 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n022.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 : Sun May 29 03:44:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 35
% 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:35,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:37,loop_count:0,foatp_calls:0,translation:fof_full)...
% 1.61/1.79  
% 1.61/1.79  ********************************
% 1.61/1.79  *   All subproblems solved!    *
% 1.61/1.79  ********************************
% 1.61/1.79  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:35,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:120,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.61/1.79  
% 1.61/1.79  %**** Beginning of derivation protocol ****
% 1.61/1.79  % SZS output start CNFRefutation
% See solution above
% 1.61/1.79  
% 1.61/1.79  %**** End of derivation protocol ****
% 1.61/1.79  %**** no. of clauses in derivation: 121 ****
% 1.61/1.79  %**** clause counter: 120 ****
% 1.61/1.79  
% 1.61/1.79  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:35,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:120,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------