TSTP Solution File: GRP189-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP189-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n003.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 10:16:52 EDT 2022

% Result   : Unsatisfiable 0.13s 0.41s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  110 ( 103 unt;   7 typ;   0 def)
%            Number of atoms       :  267 ( 177 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  572 (   6   ~;   0   |;   0   &; 566   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  196 (   0   ^ 196   !;   0   ?; 196   :)

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

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

thf(tp_greatest_lower_bound,type,
    greatest_lower_bound: $i > $i > $i ).

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

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

thf(tp_least_upper_bound,type,
    least_upper_bound: $i > $i > $i ).

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

thf(1,axiom,
    ! [Y: $i,Z: $i,X: $i] :
      ( ( multiply @ ( greatest_lower_bound @ Y @ Z ) @ X )
      = ( greatest_lower_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).

thf(2,axiom,
    ! [Y: $i,Z: $i,X: $i] :
      ( ( multiply @ ( least_upper_bound @ Y @ Z ) @ X )
      = ( least_upper_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).

thf(3,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( multiply @ X @ ( greatest_lower_bound @ Y @ Z ) )
      = ( greatest_lower_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).

thf(4,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( multiply @ X @ ( least_upper_bound @ Y @ Z ) )
      = ( least_upper_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).

thf(5,axiom,
    ! [X: $i,Y: $i] :
      ( ( greatest_lower_bound @ X @ ( least_upper_bound @ X @ Y ) )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).

thf(6,axiom,
    ! [X: $i,Y: $i] :
      ( ( least_upper_bound @ X @ ( greatest_lower_bound @ X @ Y ) )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).

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

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

thf(9,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( least_upper_bound @ X @ ( least_upper_bound @ Y @ Z ) )
      = ( least_upper_bound @ ( least_upper_bound @ X @ Y ) @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).

thf(10,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( greatest_lower_bound @ X @ ( greatest_lower_bound @ Y @ Z ) )
      = ( greatest_lower_bound @ ( greatest_lower_bound @ X @ Y ) @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).

thf(11,axiom,
    ! [X: $i,Y: $i] :
      ( ( least_upper_bound @ X @ Y )
      = ( least_upper_bound @ Y @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).

thf(12,axiom,
    ! [X: $i,Y: $i] :
      ( ( greatest_lower_bound @ X @ Y )
      = ( greatest_lower_bound @ Y @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).

thf(13,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( multiply @ ( multiply @ X @ Y ) @ Z )
      = ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).

thf(14,axiom,
    ! [X: $i] :
      ( ( multiply @ ( inverse @ X ) @ X )
      = identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).

thf(15,axiom,
    ! [X: $i] :
      ( ( multiply @ identity @ X )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).

thf(16,axiom,
    ! [X: $i,Y: $i] :
      ( ( inverse @ ( multiply @ X @ Y ) )
      = ( multiply @ ( inverse @ Y ) @ ( inverse @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p38b_3) ).

thf(17,axiom,
    ! [X: $i] :
      ( ( inverse @ ( inverse @ X ) )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p38b_2) ).

thf(18,axiom,
    ( ( inverse @ identity )
    = identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p38b_1) ).

thf(19,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(20,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[19]) ).

thf(21,negated_conjecture,
    ( greatest_lower_bound @ b @ ( least_upper_bound @ a @ b ) )
 != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p38b) ).

thf(22,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[20]) ).

thf(23,plain,
    ( ( ! [Y: $i,Z: $i,X: $i] :
          ( ( multiply @ ( greatest_lower_bound @ Y @ Z ) @ X )
          = ( greatest_lower_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(24,plain,
    ( ( ! [Y: $i,Z: $i,X: $i] :
          ( ( multiply @ ( least_upper_bound @ Y @ Z ) @ X )
          = ( least_upper_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(25,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( multiply @ X @ ( greatest_lower_bound @ Y @ Z ) )
          = ( greatest_lower_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(26,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( multiply @ X @ ( least_upper_bound @ Y @ Z ) )
          = ( least_upper_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(27,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( greatest_lower_bound @ X @ ( least_upper_bound @ X @ Y ) )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(28,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( least_upper_bound @ X @ ( greatest_lower_bound @ X @ Y ) )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(29,plain,
    ( ( ! [X: $i] :
          ( ( greatest_lower_bound @ X @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(30,plain,
    ( ( ! [X: $i] :
          ( ( least_upper_bound @ X @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(31,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( least_upper_bound @ X @ ( least_upper_bound @ Y @ Z ) )
          = ( least_upper_bound @ ( least_upper_bound @ X @ Y ) @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(32,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( greatest_lower_bound @ X @ ( greatest_lower_bound @ Y @ Z ) )
          = ( greatest_lower_bound @ ( greatest_lower_bound @ X @ Y ) @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(33,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( least_upper_bound @ X @ Y )
          = ( least_upper_bound @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(34,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( greatest_lower_bound @ X @ Y )
          = ( greatest_lower_bound @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(35,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( multiply @ ( multiply @ X @ Y ) @ Z )
          = ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(36,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ ( inverse @ X ) @ X )
          = identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(37,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ identity @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(38,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( inverse @ ( multiply @ X @ Y ) )
          = ( multiply @ ( inverse @ Y ) @ ( inverse @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(39,plain,
    ( ( ! [X: $i] :
          ( ( inverse @ ( inverse @ X ) )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(40,plain,
    ( ( ( inverse @ identity )
      = identity )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(41,plain,
    ( ( ( ( greatest_lower_bound @ b @ ( least_upper_bound @ a @ b ) )
       != b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(42,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[22]) ).

thf(43,plain,
    ( ( ( ( greatest_lower_bound @ b @ ( least_upper_bound @ a @ b ) )
       != b ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[41]) ).

thf(44,plain,
    ( ( ( ( greatest_lower_bound @ b @ ( least_upper_bound @ a @ b ) )
       != b ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(45,plain,
    ( ( ( inverse @ identity )
      = identity )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(46,plain,
    ( ( ! [X: $i] :
          ( ( inverse @ ( inverse @ X ) )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(47,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( inverse @ ( multiply @ X @ Y ) )
          = ( multiply @ ( inverse @ Y ) @ ( inverse @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(48,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ identity @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(49,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ ( inverse @ X ) @ X )
          = identity ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(50,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( multiply @ ( multiply @ X @ Y ) @ Z )
          = ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(51,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( greatest_lower_bound @ X @ Y )
          = ( greatest_lower_bound @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(52,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( least_upper_bound @ X @ Y )
          = ( least_upper_bound @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(53,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( greatest_lower_bound @ X @ ( greatest_lower_bound @ Y @ Z ) )
          = ( greatest_lower_bound @ ( greatest_lower_bound @ X @ Y ) @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(54,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( least_upper_bound @ X @ ( least_upper_bound @ Y @ Z ) )
          = ( least_upper_bound @ ( least_upper_bound @ X @ Y ) @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(55,plain,
    ( ( ! [X: $i] :
          ( ( least_upper_bound @ X @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(56,plain,
    ( ( ! [X: $i] :
          ( ( greatest_lower_bound @ X @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(57,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( least_upper_bound @ X @ ( greatest_lower_bound @ X @ Y ) )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(58,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( greatest_lower_bound @ X @ ( least_upper_bound @ X @ Y ) )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(59,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( multiply @ X @ ( least_upper_bound @ Y @ Z ) )
          = ( least_upper_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(60,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( multiply @ X @ ( greatest_lower_bound @ Y @ Z ) )
          = ( greatest_lower_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(61,plain,
    ( ( ! [Y: $i,Z: $i,X: $i] :
          ( ( multiply @ ( least_upper_bound @ Y @ Z ) @ X )
          = ( least_upper_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(62,plain,
    ( ( ! [Y: $i,Z: $i,X: $i] :
          ( ( multiply @ ( greatest_lower_bound @ Y @ Z ) @ X )
          = ( greatest_lower_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(63,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(64,plain,
    ( ( ( greatest_lower_bound @ b @ ( least_upper_bound @ a @ b ) )
      = b )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(65,plain,
    ! [SV1: $i] :
      ( ( ( inverse @ ( inverse @ SV1 ) )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(66,plain,
    ! [SV2: $i] :
      ( ( ! [SY36: $i] :
            ( ( inverse @ ( multiply @ SV2 @ SY36 ) )
            = ( multiply @ ( inverse @ SY36 ) @ ( inverse @ SV2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(67,plain,
    ! [SV3: $i] :
      ( ( ( multiply @ identity @ SV3 )
        = SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(68,plain,
    ! [SV4: $i] :
      ( ( ( multiply @ ( inverse @ SV4 ) @ SV4 )
        = identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(69,plain,
    ! [SV5: $i] :
      ( ( ! [SY37: $i,SY38: $i] :
            ( ( multiply @ ( multiply @ SV5 @ SY37 ) @ SY38 )
            = ( multiply @ SV5 @ ( multiply @ SY37 @ SY38 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(70,plain,
    ! [SV6: $i] :
      ( ( ! [SY39: $i] :
            ( ( greatest_lower_bound @ SV6 @ SY39 )
            = ( greatest_lower_bound @ SY39 @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(71,plain,
    ! [SV7: $i] :
      ( ( ! [SY40: $i] :
            ( ( least_upper_bound @ SV7 @ SY40 )
            = ( least_upper_bound @ SY40 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(72,plain,
    ! [SV8: $i] :
      ( ( ! [SY41: $i,SY42: $i] :
            ( ( greatest_lower_bound @ SV8 @ ( greatest_lower_bound @ SY41 @ SY42 ) )
            = ( greatest_lower_bound @ ( greatest_lower_bound @ SV8 @ SY41 ) @ SY42 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(73,plain,
    ! [SV9: $i] :
      ( ( ! [SY43: $i,SY44: $i] :
            ( ( least_upper_bound @ SV9 @ ( least_upper_bound @ SY43 @ SY44 ) )
            = ( least_upper_bound @ ( least_upper_bound @ SV9 @ SY43 ) @ SY44 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(74,plain,
    ! [SV10: $i] :
      ( ( ( least_upper_bound @ SV10 @ SV10 )
        = SV10 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(75,plain,
    ! [SV11: $i] :
      ( ( ( greatest_lower_bound @ SV11 @ SV11 )
        = SV11 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(76,plain,
    ! [SV12: $i] :
      ( ( ! [SY45: $i] :
            ( ( least_upper_bound @ SV12 @ ( greatest_lower_bound @ SV12 @ SY45 ) )
            = SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(77,plain,
    ! [SV13: $i] :
      ( ( ! [SY46: $i] :
            ( ( greatest_lower_bound @ SV13 @ ( least_upper_bound @ SV13 @ SY46 ) )
            = SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(78,plain,
    ! [SV14: $i] :
      ( ( ! [SY47: $i,SY48: $i] :
            ( ( multiply @ SV14 @ ( least_upper_bound @ SY47 @ SY48 ) )
            = ( least_upper_bound @ ( multiply @ SV14 @ SY47 ) @ ( multiply @ SV14 @ SY48 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(79,plain,
    ! [SV15: $i] :
      ( ( ! [SY49: $i,SY50: $i] :
            ( ( multiply @ SV15 @ ( greatest_lower_bound @ SY49 @ SY50 ) )
            = ( greatest_lower_bound @ ( multiply @ SV15 @ SY49 ) @ ( multiply @ SV15 @ SY50 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(80,plain,
    ! [SV16: $i] :
      ( ( ! [SY51: $i,SY52: $i] :
            ( ( multiply @ ( least_upper_bound @ SV16 @ SY51 ) @ SY52 )
            = ( least_upper_bound @ ( multiply @ SV16 @ SY52 ) @ ( multiply @ SY51 @ SY52 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(81,plain,
    ! [SV17: $i] :
      ( ( ! [SY53: $i,SY54: $i] :
            ( ( multiply @ ( greatest_lower_bound @ SV17 @ SY53 ) @ SY54 )
            = ( greatest_lower_bound @ ( multiply @ SV17 @ SY54 ) @ ( multiply @ SY53 @ SY54 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(82,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(83,plain,
    ! [SV18: $i,SV2: $i] :
      ( ( ( inverse @ ( multiply @ SV2 @ SV18 ) )
        = ( multiply @ ( inverse @ SV18 ) @ ( inverse @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(84,plain,
    ! [SV19: $i,SV5: $i] :
      ( ( ! [SY55: $i] :
            ( ( multiply @ ( multiply @ SV5 @ SV19 ) @ SY55 )
            = ( multiply @ SV5 @ ( multiply @ SV19 @ SY55 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(85,plain,
    ! [SV20: $i,SV6: $i] :
      ( ( ( greatest_lower_bound @ SV6 @ SV20 )
        = ( greatest_lower_bound @ SV20 @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(86,plain,
    ! [SV21: $i,SV7: $i] :
      ( ( ( least_upper_bound @ SV7 @ SV21 )
        = ( least_upper_bound @ SV21 @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(87,plain,
    ! [SV22: $i,SV8: $i] :
      ( ( ! [SY56: $i] :
            ( ( greatest_lower_bound @ SV8 @ ( greatest_lower_bound @ SV22 @ SY56 ) )
            = ( greatest_lower_bound @ ( greatest_lower_bound @ SV8 @ SV22 ) @ SY56 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(88,plain,
    ! [SV23: $i,SV9: $i] :
      ( ( ! [SY57: $i] :
            ( ( least_upper_bound @ SV9 @ ( least_upper_bound @ SV23 @ SY57 ) )
            = ( least_upper_bound @ ( least_upper_bound @ SV9 @ SV23 ) @ SY57 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(89,plain,
    ! [SV24: $i,SV12: $i] :
      ( ( ( least_upper_bound @ SV12 @ ( greatest_lower_bound @ SV12 @ SV24 ) )
        = SV12 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(90,plain,
    ! [SV25: $i,SV13: $i] :
      ( ( ( greatest_lower_bound @ SV13 @ ( least_upper_bound @ SV13 @ SV25 ) )
        = SV13 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(91,plain,
    ! [SV26: $i,SV14: $i] :
      ( ( ! [SY58: $i] :
            ( ( multiply @ SV14 @ ( least_upper_bound @ SV26 @ SY58 ) )
            = ( least_upper_bound @ ( multiply @ SV14 @ SV26 ) @ ( multiply @ SV14 @ SY58 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(92,plain,
    ! [SV27: $i,SV15: $i] :
      ( ( ! [SY59: $i] :
            ( ( multiply @ SV15 @ ( greatest_lower_bound @ SV27 @ SY59 ) )
            = ( greatest_lower_bound @ ( multiply @ SV15 @ SV27 ) @ ( multiply @ SV15 @ SY59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(93,plain,
    ! [SV28: $i,SV16: $i] :
      ( ( ! [SY60: $i] :
            ( ( multiply @ ( least_upper_bound @ SV16 @ SV28 ) @ SY60 )
            = ( least_upper_bound @ ( multiply @ SV16 @ SY60 ) @ ( multiply @ SV28 @ SY60 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(94,plain,
    ! [SV29: $i,SV17: $i] :
      ( ( ! [SY61: $i] :
            ( ( multiply @ ( greatest_lower_bound @ SV17 @ SV29 ) @ SY61 )
            = ( greatest_lower_bound @ ( multiply @ SV17 @ SY61 ) @ ( multiply @ SV29 @ SY61 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(95,plain,
    ! [SV30: $i,SV19: $i,SV5: $i] :
      ( ( ( multiply @ ( multiply @ SV5 @ SV19 ) @ SV30 )
        = ( multiply @ SV5 @ ( multiply @ SV19 @ SV30 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(96,plain,
    ! [SV31: $i,SV22: $i,SV8: $i] :
      ( ( ( greatest_lower_bound @ SV8 @ ( greatest_lower_bound @ SV22 @ SV31 ) )
        = ( greatest_lower_bound @ ( greatest_lower_bound @ SV8 @ SV22 ) @ SV31 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(97,plain,
    ! [SV32: $i,SV23: $i,SV9: $i] :
      ( ( ( least_upper_bound @ SV9 @ ( least_upper_bound @ SV23 @ SV32 ) )
        = ( least_upper_bound @ ( least_upper_bound @ SV9 @ SV23 ) @ SV32 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(98,plain,
    ! [SV33: $i,SV26: $i,SV14: $i] :
      ( ( ( multiply @ SV14 @ ( least_upper_bound @ SV26 @ SV33 ) )
        = ( least_upper_bound @ ( multiply @ SV14 @ SV26 ) @ ( multiply @ SV14 @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(99,plain,
    ! [SV34: $i,SV27: $i,SV15: $i] :
      ( ( ( multiply @ SV15 @ ( greatest_lower_bound @ SV27 @ SV34 ) )
        = ( greatest_lower_bound @ ( multiply @ SV15 @ SV27 ) @ ( multiply @ SV15 @ SV34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(100,plain,
    ! [SV35: $i,SV28: $i,SV16: $i] :
      ( ( ( multiply @ ( least_upper_bound @ SV16 @ SV28 ) @ SV35 )
        = ( least_upper_bound @ ( multiply @ SV16 @ SV35 ) @ ( multiply @ SV28 @ SV35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(101,plain,
    ! [SV36: $i,SV29: $i,SV17: $i] :
      ( ( ( multiply @ ( greatest_lower_bound @ SV17 @ SV29 ) @ SV36 )
        = ( greatest_lower_bound @ ( multiply @ SV17 @ SV36 ) @ ( multiply @ SV29 @ SV36 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(102,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[45,101,100,99,98,97,96,95,90,89,86,85,83,82,75,74,68,67,65,64]) ).

thf(103,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[102]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP189-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 14 06:12:25 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 19
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.36  (rf:0,axioms:19,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:21,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.13/0.41  
% 0.13/0.41  ********************************
% 0.13/0.41  *   All subproblems solved!    *
% 0.13/0.41  ********************************
% 0.13/0.41  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,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:102,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.42  
% 0.13/0.42  %**** Beginning of derivation protocol ****
% 0.13/0.42  % SZS output start CNFRefutation
% See solution above
% 0.13/0.42  
% 0.13/0.42  %**** End of derivation protocol ****
% 0.13/0.42  %**** no. of clauses in derivation: 103 ****
% 0.13/0.42  %**** clause counter: 102 ****
% 0.13/0.42  
% 0.13/0.42  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,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:102,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------