TSTP Solution File: RNG008-3 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : RNG008-3 : 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 : n024.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 : Mon Jul 18 20:33:56 EDT 2022

% Result   : Unsatisfiable 0.19s 0.50s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  102 (  95 unt;   7 typ;   0 def)
%            Number of atoms       :  243 ( 161 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  428 (   6   ~;   0   |;   0   &; 422   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :  144 (   0   ^ 144   !;   0   ?; 144   :)

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

thf(tp_add,type,
    add: $i > $i > $i ).

thf(tp_additive_identity,type,
    additive_identity: $i ).

thf(tp_additive_inverse,type,
    additive_inverse: $i > $i ).

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

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

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

thf(1,axiom,
    ! [X: $i] :
      ( ( add @ X @ ( additive_inverse @ X ) )
      = additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).

thf(2,axiom,
    ! [X: $i] :
      ( ( add @ X @ additive_identity )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).

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

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

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

thf(6,axiom,
    ! [X: $i,Y: $i] :
      ( ( multiply @ ( additive_inverse @ X ) @ Y )
      = ( additive_inverse @ ( multiply @ X @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse2) ).

thf(7,axiom,
    ! [X: $i,Y: $i] :
      ( ( multiply @ X @ ( additive_inverse @ Y ) )
      = ( additive_inverse @ ( multiply @ X @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse1) ).

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

thf(9,axiom,
    ! [X: $i] :
      ( ( multiply @ additive_identity @ X )
      = additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_id2) ).

thf(10,axiom,
    ! [X: $i] :
      ( ( multiply @ X @ additive_identity )
      = additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_id1) ).

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

thf(12,axiom,
    ( ( additive_inverse @ additive_identity )
    = additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_identity) ).

thf(13,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( multiply @ ( add @ X @ Y ) @ Z )
      = ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).

thf(14,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( multiply @ X @ ( add @ Y @ Z ) )
      = ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).

thf(15,axiom,
    ! [X: $i] :
      ( ( add @ ( additive_inverse @ X ) @ X )
      = additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_inverse) ).

thf(16,axiom,
    ! [X: $i] :
      ( ( add @ additive_identity @ X )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).

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

thf(18,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(19,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[18]) ).

thf(20,negated_conjecture,
    ( multiply @ b @ a )
 != c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).

thf(21,negated_conjecture,
    ( ( multiply @ a @ b )
    = c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).

thf(22,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ! [X: $i] :
          ( ( add @ X @ ( additive_inverse @ X ) )
          = additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(24,plain,
    ( ( ! [X: $i] :
          ( ( add @ X @ additive_identity )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

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

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

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

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

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

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

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

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

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

thf(34,plain,
    ( ( ( additive_inverse @ additive_identity )
      = additive_identity )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

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

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

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

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

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

thf(40,plain,
    ( ( ( ( multiply @ b @ a )
       != c ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

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

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

thf(43,plain,
    ( ( ( ( multiply @ b @ a )
       != c ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[40]) ).

thf(44,plain,
    ( ( ( multiply @ a @ b )
      = c )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(45,plain,
    ( ( ( ( multiply @ b @ a )
       != c ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

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

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

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

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

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

thf(51,plain,
    ( ( ( additive_inverse @ additive_identity )
      = additive_identity )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

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

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

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

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

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

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

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

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

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

thf(61,plain,
    ( ( ! [X: $i] :
          ( ( add @ X @ additive_identity )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(62,plain,
    ( ( ! [X: $i] :
          ( ( add @ X @ ( additive_inverse @ X ) )
          = additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

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

thf(64,plain,
    ( ( ( multiply @ b @ a )
      = c )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

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

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

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

thf(68,plain,
    ! [SV4: $i] :
      ( ( ! [SY28: $i,SY29: $i] :
            ( ( multiply @ SV4 @ ( add @ SY28 @ SY29 ) )
            = ( add @ ( multiply @ SV4 @ SY28 ) @ ( multiply @ SV4 @ SY29 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(69,plain,
    ! [SV5: $i] :
      ( ( ! [SY30: $i,SY31: $i] :
            ( ( multiply @ ( add @ SV5 @ SY30 ) @ SY31 )
            = ( add @ ( multiply @ SV5 @ SY31 ) @ ( multiply @ SY30 @ SY31 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(70,plain,
    ! [SV6: $i] :
      ( ( ( additive_inverse @ ( additive_inverse @ SV6 ) )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(71,plain,
    ! [SV7: $i] :
      ( ( ( multiply @ SV7 @ additive_identity )
        = additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(72,plain,
    ! [SV8: $i] :
      ( ( ( multiply @ additive_identity @ SV8 )
        = additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(73,plain,
    ! [SV9: $i] :
      ( ( ! [SY32: $i] :
            ( ( additive_inverse @ ( add @ SV9 @ SY32 ) )
            = ( add @ ( additive_inverse @ SV9 ) @ ( additive_inverse @ SY32 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(74,plain,
    ! [SV10: $i] :
      ( ( ! [SY33: $i] :
            ( ( multiply @ SV10 @ ( additive_inverse @ SY33 ) )
            = ( additive_inverse @ ( multiply @ SV10 @ SY33 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(75,plain,
    ! [SV11: $i] :
      ( ( ! [SY34: $i] :
            ( ( multiply @ ( additive_inverse @ SV11 ) @ SY34 )
            = ( additive_inverse @ ( multiply @ SV11 @ SY34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(76,plain,
    ! [SV12: $i] :
      ( ( ! [SY35: $i,SY36: $i] :
            ( ( add @ ( add @ SV12 @ SY35 ) @ SY36 )
            = ( add @ SV12 @ ( add @ SY35 @ SY36 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(77,plain,
    ! [SV13: $i] :
      ( ( ! [SY37: $i] :
            ( ( add @ SV13 @ SY37 )
            = ( add @ SY37 @ SV13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(78,plain,
    ! [SV14: $i] :
      ( ( ! [SY38: $i,SY39: $i] :
            ( ( multiply @ ( multiply @ SV14 @ SY38 ) @ SY39 )
            = ( multiply @ SV14 @ ( multiply @ SY38 @ SY39 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(79,plain,
    ! [SV15: $i] :
      ( ( ( add @ SV15 @ additive_identity )
        = SV15 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(80,plain,
    ! [SV16: $i] :
      ( ( ( add @ SV16 @ ( additive_inverse @ SV16 ) )
        = additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(81,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(82,plain,
    ! [SV17: $i,SV4: $i] :
      ( ( ! [SY40: $i] :
            ( ( multiply @ SV4 @ ( add @ SV17 @ SY40 ) )
            = ( add @ ( multiply @ SV4 @ SV17 ) @ ( multiply @ SV4 @ SY40 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(83,plain,
    ! [SV18: $i,SV5: $i] :
      ( ( ! [SY41: $i] :
            ( ( multiply @ ( add @ SV5 @ SV18 ) @ SY41 )
            = ( add @ ( multiply @ SV5 @ SY41 ) @ ( multiply @ SV18 @ SY41 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(84,plain,
    ! [SV19: $i,SV9: $i] :
      ( ( ( additive_inverse @ ( add @ SV9 @ SV19 ) )
        = ( add @ ( additive_inverse @ SV9 ) @ ( additive_inverse @ SV19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(85,plain,
    ! [SV20: $i,SV10: $i] :
      ( ( ( multiply @ SV10 @ ( additive_inverse @ SV20 ) )
        = ( additive_inverse @ ( multiply @ SV10 @ SV20 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(86,plain,
    ! [SV21: $i,SV11: $i] :
      ( ( ( multiply @ ( additive_inverse @ SV11 ) @ SV21 )
        = ( additive_inverse @ ( multiply @ SV11 @ SV21 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(87,plain,
    ! [SV22: $i,SV12: $i] :
      ( ( ! [SY42: $i] :
            ( ( add @ ( add @ SV12 @ SV22 ) @ SY42 )
            = ( add @ SV12 @ ( add @ SV22 @ SY42 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(88,plain,
    ! [SV23: $i,SV13: $i] :
      ( ( ( add @ SV13 @ SV23 )
        = ( add @ SV23 @ SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(89,plain,
    ! [SV24: $i,SV14: $i] :
      ( ( ! [SY43: $i] :
            ( ( multiply @ ( multiply @ SV14 @ SV24 ) @ SY43 )
            = ( multiply @ SV14 @ ( multiply @ SV24 @ SY43 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(90,plain,
    ! [SV25: $i,SV17: $i,SV4: $i] :
      ( ( ( multiply @ SV4 @ ( add @ SV17 @ SV25 ) )
        = ( add @ ( multiply @ SV4 @ SV17 ) @ ( multiply @ SV4 @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(91,plain,
    ! [SV26: $i,SV18: $i,SV5: $i] :
      ( ( ( multiply @ ( add @ SV5 @ SV18 ) @ SV26 )
        = ( add @ ( multiply @ SV5 @ SV26 ) @ ( multiply @ SV18 @ SV26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(92,plain,
    ! [SV27: $i,SV22: $i,SV12: $i] :
      ( ( ( add @ ( add @ SV12 @ SV22 ) @ SV27 )
        = ( add @ SV12 @ ( add @ SV22 @ SV27 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(93,plain,
    ! [SV28: $i,SV24: $i,SV14: $i] :
      ( ( ( multiply @ ( multiply @ SV14 @ SV24 ) @ SV28 )
        = ( multiply @ SV14 @ ( multiply @ SV24 @ SV28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(94,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[44,93,92,91,90,88,86,85,84,81,80,79,72,71,70,67,66,65,64,51]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon May 30 18:46:06 EDT 2022
% 0.13/0.33  % 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
% 0.13/0.35  (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).....
% 0.19/0.50  
% 0.19/0.50  ********************************
% 0.19/0.50  *   All subproblems solved!    *
% 0.19/0.50  ********************************
% 0.19/0.50  % 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:94,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.50  
% 0.19/0.50  %**** Beginning of derivation protocol ****
% 0.19/0.50  % SZS output start CNFRefutation
% See solution above
% 0.19/0.50  
% 0.19/0.50  %**** End of derivation protocol ****
% 0.19/0.50  %**** no. of clauses in derivation: 95 ****
% 0.19/0.50  %**** clause counter: 94 ****
% 0.19/0.50  
% 0.19/0.50  % 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:94,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------