TSTP Solution File: GRP002-10 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP002-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sat Jul 16 10:15:18 EDT 2022

% Result   : Unsatisfiable 17.82s 18.06s
% Output   : CNFRefutation 17.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   33
% Syntax   : Number of formulae    :  110 (  96 unt;  14 typ;   0 def)
%            Number of atoms       :  248 ( 164 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  839 (   6   ~;   0   |;   0   &; 833   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;  11 con; 0-4 aty)
%            Number of variables   :  218 (   0   ^ 218   !;   0   ?; 218   :)

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

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

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

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

thf(tp_h,type,
    h: $i ).

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

thf(tp_ifeq,type,
    ifeq: $i > $i > $i > $i > $i ).

thf(tp_ifeq2,type,
    ifeq2: $i > $i > $i > $i > $i ).

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

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

thf(tp_k,type,
    k: $i ).

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

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

thf(tp_true,type,
    true: $i ).

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

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

thf(3,axiom,
    ! [X: $i,Y: $i,W: $i,Z: $i] :
      ( ( ifeq2 @ ( product @ X @ Y @ W ) @ true @ ( ifeq2 @ ( product @ X @ Y @ Z ) @ true @ Z @ W ) @ W )
      = W ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).

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

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

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

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

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

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ifeq @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ifeq2 @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).

thf(11,axiom,
    ! [X: $i,Y: $i] :
      ( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ Y @ X @ identity ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity_2) ).

thf(12,axiom,
    ! [X: $i,Y: $i] :
      ( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ X @ Y @ identity ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity_1) ).

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

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

thf(15,negated_conjecture,
    ( product @ k @ ( inverse @ b ) @ identity )
 != true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).

thf(16,negated_conjecture,
    ( ( product @ j @ ( inverse @ h ) @ k )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).

thf(17,negated_conjecture,
    ( ( product @ h @ b @ j )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_b_is_j) ).

thf(18,negated_conjecture,
    ( ( product @ d @ ( inverse @ b ) @ h )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).

thf(19,negated_conjecture,
    ( ( product @ c @ ( inverse @ a ) @ d )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).

thf(20,negated_conjecture,
    ( ( product @ a @ b @ c )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).

thf(21,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[14]) ).

thf(22,plain,
    ( ( ! [Y: $i,Z: $i,V: $i,X: $i,W: $i,U: $i] :
          ( ( ifeq @ ( product @ Y @ Z @ V ) @ true @ ( ifeq @ ( product @ X @ V @ W ) @ true @ ( ifeq @ ( product @ X @ Y @ U ) @ true @ ( product @ U @ Z @ W ) @ true ) @ true ) @ true )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(23,plain,
    ( ( ! [U: $i,Z: $i,W: $i,Y: $i,V: $i,X: $i] :
          ( ( ifeq @ ( product @ U @ Z @ W ) @ true @ ( ifeq @ ( product @ Y @ Z @ V ) @ true @ ( ifeq @ ( product @ X @ Y @ U ) @ true @ ( product @ X @ V @ W ) @ true ) @ true ) @ true )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(24,plain,
    ( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
          ( ( ifeq2 @ ( product @ X @ Y @ W ) @ true @ ( ifeq2 @ ( product @ X @ Y @ Z ) @ true @ Z @ W ) @ W )
          = W ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(25,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( product @ X @ Y @ ( multiply @ X @ Y ) )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(26,plain,
    ( ( ! [X: $i] :
          ( ( product @ X @ ( inverse @ X ) @ identity )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(27,plain,
    ( ( ! [X: $i] :
          ( ( product @ ( inverse @ X ) @ X @ identity )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(28,plain,
    ( ( ! [X: $i] :
          ( ( product @ X @ identity @ X )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(29,plain,
    ( ( ! [X: $i] :
          ( ( product @ identity @ X @ X )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(30,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ifeq @ A @ A @ B @ C )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(31,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ifeq2 @ A @ A @ B @ C )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(32,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ Y @ X @ identity ) @ true )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(33,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ X @ Y @ identity ) @ true )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(34,plain,
    ( ( ( ( product @ k @ ( inverse @ b ) @ identity )
       != true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(35,plain,
    ( ( ( product @ j @ ( inverse @ h ) @ k )
      = true )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(36,plain,
    ( ( ( product @ h @ b @ j )
      = true )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(37,plain,
    ( ( ( product @ d @ ( inverse @ b ) @ h )
      = true )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(38,plain,
    ( ( ( product @ c @ ( inverse @ a ) @ d )
      = true )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(39,plain,
    ( ( ( product @ a @ b @ c )
      = true )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(40,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[21]) ).

thf(41,plain,
    ( ( ( ( product @ k @ ( inverse @ b ) @ identity )
       != true ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[34]) ).

thf(42,plain,
    ( ( ( product @ a @ b @ c )
      = true )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(43,plain,
    ( ( ( product @ c @ ( inverse @ a ) @ d )
      = true )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(44,plain,
    ( ( ( product @ d @ ( inverse @ b ) @ h )
      = true )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(45,plain,
    ( ( ( product @ h @ b @ j )
      = true )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(46,plain,
    ( ( ( product @ j @ ( inverse @ h ) @ k )
      = true )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(47,plain,
    ( ( ( ( product @ k @ ( inverse @ b ) @ identity )
       != true ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(48,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ X @ Y @ identity ) @ true )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(49,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ifeq @ ( product @ X @ X @ Y ) @ true @ ( product @ Y @ X @ identity ) @ true )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(50,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ifeq2 @ A @ A @ B @ C )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(51,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ifeq @ A @ A @ B @ C )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(52,plain,
    ( ( ! [X: $i] :
          ( ( product @ identity @ X @ X )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(53,plain,
    ( ( ! [X: $i] :
          ( ( product @ X @ identity @ X )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(54,plain,
    ( ( ! [X: $i] :
          ( ( product @ ( inverse @ X ) @ X @ identity )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(55,plain,
    ( ( ! [X: $i] :
          ( ( product @ X @ ( inverse @ X ) @ identity )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(56,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( product @ X @ Y @ ( multiply @ X @ Y ) )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(57,plain,
    ( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
          ( ( ifeq2 @ ( product @ X @ Y @ W ) @ true @ ( ifeq2 @ ( product @ X @ Y @ Z ) @ true @ Z @ W ) @ W )
          = W ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(58,plain,
    ( ( ! [U: $i,Z: $i,W: $i,Y: $i,V: $i,X: $i] :
          ( ( ifeq @ ( product @ U @ Z @ W ) @ true @ ( ifeq @ ( product @ Y @ Z @ V ) @ true @ ( ifeq @ ( product @ X @ Y @ U ) @ true @ ( product @ X @ V @ W ) @ true ) @ true ) @ true )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(59,plain,
    ( ( ! [Y: $i,Z: $i,V: $i,X: $i,W: $i,U: $i] :
          ( ( ifeq @ ( product @ Y @ Z @ V ) @ true @ ( ifeq @ ( product @ X @ V @ W ) @ true @ ( ifeq @ ( product @ X @ Y @ U ) @ true @ ( product @ U @ Z @ W ) @ true ) @ true ) @ true )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(60,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(61,plain,
    ( ( ( product @ k @ ( inverse @ b ) @ identity )
      = true )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(62,plain,
    ! [SV1: $i] :
      ( ( ! [SY32: $i] :
            ( ( ifeq @ ( product @ SV1 @ SV1 @ SY32 ) @ true @ ( product @ SV1 @ SY32 @ identity ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(63,plain,
    ! [SV2: $i] :
      ( ( ! [SY33: $i] :
            ( ( ifeq @ ( product @ SV2 @ SV2 @ SY33 ) @ true @ ( product @ SY33 @ SV2 @ identity ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(64,plain,
    ! [SV3: $i] :
      ( ( ! [SY34: $i,SY35: $i] :
            ( ( ifeq2 @ SV3 @ SV3 @ SY34 @ SY35 )
            = SY34 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(65,plain,
    ! [SV4: $i] :
      ( ( ! [SY36: $i,SY37: $i] :
            ( ( ifeq @ SV4 @ SV4 @ SY36 @ SY37 )
            = SY36 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(66,plain,
    ! [SV5: $i] :
      ( ( ( product @ identity @ SV5 @ SV5 )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(67,plain,
    ! [SV6: $i] :
      ( ( ( product @ SV6 @ identity @ SV6 )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(68,plain,
    ! [SV7: $i] :
      ( ( ( product @ ( inverse @ SV7 ) @ SV7 @ identity )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(69,plain,
    ! [SV8: $i] :
      ( ( ( product @ SV8 @ ( inverse @ SV8 ) @ identity )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(70,plain,
    ! [SV9: $i] :
      ( ( ! [SY38: $i] :
            ( ( product @ SV9 @ SY38 @ ( multiply @ SV9 @ SY38 ) )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(71,plain,
    ! [SV10: $i] :
      ( ( ! [SY39: $i,SY40: $i,SY41: $i] :
            ( ( ifeq2 @ ( product @ SV10 @ SY39 @ SY40 ) @ true @ ( ifeq2 @ ( product @ SV10 @ SY39 @ SY41 ) @ true @ SY41 @ SY40 ) @ SY40 )
            = SY40 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(72,plain,
    ! [SV11: $i] :
      ( ( ! [SY42: $i,SY43: $i,SY44: $i,SY45: $i,SY46: $i] :
            ( ( ifeq @ ( product @ SV11 @ SY42 @ SY43 ) @ true @ ( ifeq @ ( product @ SY44 @ SY42 @ SY45 ) @ true @ ( ifeq @ ( product @ SY46 @ SY44 @ SV11 ) @ true @ ( product @ SY46 @ SY45 @ SY43 ) @ true ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(73,plain,
    ! [SV12: $i] :
      ( ( ! [SY47: $i,SY48: $i,SY49: $i,SY50: $i,SY51: $i] :
            ( ( ifeq @ ( product @ SV12 @ SY47 @ SY48 ) @ true @ ( ifeq @ ( product @ SY49 @ SY48 @ SY50 ) @ true @ ( ifeq @ ( product @ SY49 @ SV12 @ SY51 ) @ true @ ( product @ SY51 @ SY47 @ SY50 ) @ true ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(74,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(75,plain,
    ! [SV13: $i,SV1: $i] :
      ( ( ( ifeq @ ( product @ SV1 @ SV1 @ SV13 ) @ true @ ( product @ SV1 @ SV13 @ identity ) @ true )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(76,plain,
    ! [SV14: $i,SV2: $i] :
      ( ( ( ifeq @ ( product @ SV2 @ SV2 @ SV14 ) @ true @ ( product @ SV14 @ SV2 @ identity ) @ true )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(77,plain,
    ! [SV15: $i,SV3: $i] :
      ( ( ! [SY52: $i] :
            ( ( ifeq2 @ SV3 @ SV3 @ SV15 @ SY52 )
            = SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(78,plain,
    ! [SV16: $i,SV4: $i] :
      ( ( ! [SY53: $i] :
            ( ( ifeq @ SV4 @ SV4 @ SV16 @ SY53 )
            = SV16 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(79,plain,
    ! [SV17: $i,SV9: $i] :
      ( ( ( product @ SV9 @ SV17 @ ( multiply @ SV9 @ SV17 ) )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(80,plain,
    ! [SV18: $i,SV10: $i] :
      ( ( ! [SY54: $i,SY55: $i] :
            ( ( ifeq2 @ ( product @ SV10 @ SV18 @ SY54 ) @ true @ ( ifeq2 @ ( product @ SV10 @ SV18 @ SY55 ) @ true @ SY55 @ SY54 ) @ SY54 )
            = SY54 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(81,plain,
    ! [SV19: $i,SV11: $i] :
      ( ( ! [SY56: $i,SY57: $i,SY58: $i,SY59: $i] :
            ( ( ifeq @ ( product @ SV11 @ SV19 @ SY56 ) @ true @ ( ifeq @ ( product @ SY57 @ SV19 @ SY58 ) @ true @ ( ifeq @ ( product @ SY59 @ SY57 @ SV11 ) @ true @ ( product @ SY59 @ SY58 @ SY56 ) @ true ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(82,plain,
    ! [SV20: $i,SV12: $i] :
      ( ( ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
            ( ( ifeq @ ( product @ SV12 @ SV20 @ SY60 ) @ true @ ( ifeq @ ( product @ SY61 @ SY60 @ SY62 ) @ true @ ( ifeq @ ( product @ SY61 @ SV12 @ SY63 ) @ true @ ( product @ SY63 @ SV20 @ SY62 ) @ true ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(83,plain,
    ! [SV21: $i,SV15: $i,SV3: $i] :
      ( ( ( ifeq2 @ SV3 @ SV3 @ SV15 @ SV21 )
        = SV15 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(84,plain,
    ! [SV22: $i,SV16: $i,SV4: $i] :
      ( ( ( ifeq @ SV4 @ SV4 @ SV16 @ SV22 )
        = SV16 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(85,plain,
    ! [SV23: $i,SV18: $i,SV10: $i] :
      ( ( ! [SY64: $i] :
            ( ( ifeq2 @ ( product @ SV10 @ SV18 @ SV23 ) @ true @ ( ifeq2 @ ( product @ SV10 @ SV18 @ SY64 ) @ true @ SY64 @ SV23 ) @ SV23 )
            = SV23 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(86,plain,
    ! [SV24: $i,SV19: $i,SV11: $i] :
      ( ( ! [SY65: $i,SY66: $i,SY67: $i] :
            ( ( ifeq @ ( product @ SV11 @ SV19 @ SV24 ) @ true @ ( ifeq @ ( product @ SY65 @ SV19 @ SY66 ) @ true @ ( ifeq @ ( product @ SY67 @ SY65 @ SV11 ) @ true @ ( product @ SY67 @ SY66 @ SV24 ) @ true ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(87,plain,
    ! [SV25: $i,SV20: $i,SV12: $i] :
      ( ( ! [SY68: $i,SY69: $i,SY70: $i] :
            ( ( ifeq @ ( product @ SV12 @ SV20 @ SV25 ) @ true @ ( ifeq @ ( product @ SY68 @ SV25 @ SY69 ) @ true @ ( ifeq @ ( product @ SY68 @ SV12 @ SY70 ) @ true @ ( product @ SY70 @ SV20 @ SY69 ) @ true ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(88,plain,
    ! [SV26: $i,SV23: $i,SV18: $i,SV10: $i] :
      ( ( ( ifeq2 @ ( product @ SV10 @ SV18 @ SV23 ) @ true @ ( ifeq2 @ ( product @ SV10 @ SV18 @ SV26 ) @ true @ SV26 @ SV23 ) @ SV23 )
        = SV23 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(89,plain,
    ! [SV27: $i,SV24: $i,SV19: $i,SV11: $i] :
      ( ( ! [SY71: $i,SY72: $i] :
            ( ( ifeq @ ( product @ SV11 @ SV19 @ SV24 ) @ true @ ( ifeq @ ( product @ SV27 @ SV19 @ SY71 ) @ true @ ( ifeq @ ( product @ SY72 @ SV27 @ SV11 ) @ true @ ( product @ SY72 @ SY71 @ SV24 ) @ true ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(90,plain,
    ! [SV28: $i,SV25: $i,SV20: $i,SV12: $i] :
      ( ( ! [SY73: $i,SY74: $i] :
            ( ( ifeq @ ( product @ SV12 @ SV20 @ SV25 ) @ true @ ( ifeq @ ( product @ SV28 @ SV25 @ SY73 ) @ true @ ( ifeq @ ( product @ SV28 @ SV12 @ SY74 ) @ true @ ( product @ SY74 @ SV20 @ SY73 ) @ true ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(91,plain,
    ! [SV29: $i,SV27: $i,SV24: $i,SV19: $i,SV11: $i] :
      ( ( ! [SY75: $i] :
            ( ( ifeq @ ( product @ SV11 @ SV19 @ SV24 ) @ true @ ( ifeq @ ( product @ SV27 @ SV19 @ SV29 ) @ true @ ( ifeq @ ( product @ SY75 @ SV27 @ SV11 ) @ true @ ( product @ SY75 @ SV29 @ SV24 ) @ true ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(92,plain,
    ! [SV30: $i,SV28: $i,SV25: $i,SV20: $i,SV12: $i] :
      ( ( ! [SY76: $i] :
            ( ( ifeq @ ( product @ SV12 @ SV20 @ SV25 ) @ true @ ( ifeq @ ( product @ SV28 @ SV25 @ SV30 ) @ true @ ( ifeq @ ( product @ SV28 @ SV12 @ SY76 ) @ true @ ( product @ SY76 @ SV20 @ SV30 ) @ true ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(93,plain,
    ! [SV31: $i,SV29: $i,SV27: $i,SV24: $i,SV19: $i,SV11: $i] :
      ( ( ( ifeq @ ( product @ SV11 @ SV19 @ SV24 ) @ true @ ( ifeq @ ( product @ SV27 @ SV19 @ SV29 ) @ true @ ( ifeq @ ( product @ SV31 @ SV27 @ SV11 ) @ true @ ( product @ SV31 @ SV29 @ SV24 ) @ true ) @ true ) @ true )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(94,plain,
    ! [SV32: $i,SV30: $i,SV28: $i,SV25: $i,SV20: $i,SV12: $i] :
      ( ( ( ifeq @ ( product @ SV12 @ SV20 @ SV25 ) @ true @ ( ifeq @ ( product @ SV28 @ SV25 @ SV30 ) @ true @ ( ifeq @ ( product @ SV28 @ SV12 @ SV32 ) @ true @ ( product @ SV32 @ SV20 @ SV30 ) @ true ) @ true ) @ true )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(95,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[42,94,93,88,84,83,79,76,75,74,69,68,67,66,61,46,45,44,43]) ).

thf(96,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[95]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP002-10 : TPTP v8.1.0. Released v7.3.0.
% 0.13/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n007.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 : Mon Jun 13 17:19:24 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 18
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 0
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.38  (rf:0,axioms:18,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:20,loop_count:0,foatp_calls:0,translation:fof_full).....
% 17.82/18.06  
% 17.82/18.06  ********************************
% 17.82/18.06  *   All subproblems solved!    *
% 17.82/18.06  ********************************
% 17.82/18.06  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,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:95,loop_count:0,foatp_calls:1,translation:fof_full)
% 17.82/18.06  
% 17.82/18.06  %**** Beginning of derivation protocol ****
% 17.82/18.06  % SZS output start CNFRefutation
% See solution above
% 17.82/18.06  
% 17.82/18.06  %**** End of derivation protocol ****
% 17.82/18.06  %**** no. of clauses in derivation: 96 ****
% 17.82/18.06  %**** clause counter: 95 ****
% 17.82/18.06  
% 17.82/18.06  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,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:95,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------