TSTP Solution File: RNG050+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : RNG050+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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  : 300s
% DateTime : Tue May 21 02:38:12 EDT 2024

% Result   : Theorem 49.32s 8.59s
% Output   : Refutation 49.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   37 (  10 unt;   8 typ;   0 def)
%            Number of atoms       :   72 (  31 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  188 (  33   ~;  23   |;   4   &; 116   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   14 (   0   ^  14   !;   0   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(aVector0_type,type,
    aVector0: $i > $o ).

thf(aDimensionOf0_type,type,
    aDimensionOf0: $i > $i ).

thf(sz00_type,type,
    sz00: $i ).

thf(xs_type,type,
    xs: $i ).

thf(sdtlseqdt0_type,type,
    sdtlseqdt0: $i > $i > $o ).

thf(sz0z00_type,type,
    sz0z00: $i ).

thf(sdtasasdt0_type,type,
    sdtasasdt0: $i > $i > $i ).

thf(aScalar0_type,type,
    aScalar0: $i > $o ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( ( aDimensionOf0 @ A )
            = ( aDimensionOf0 @ B ) )
          & ( ( aDimensionOf0 @ B )
            = sz00 ) )
       => ( ( sdtasasdt0 @ A @ B )
          = sz0z00 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).

thf(87,plain,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( ( aDimensionOf0 @ A )
            = ( aDimensionOf0 @ B ) )
          & ( ( aDimensionOf0 @ B )
            = sz00 ) )
       => ( ( sdtasasdt0 @ A @ B )
          = sz0z00 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(88,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aVector0 @ A )
      | ~ ( aVector0 @ B )
      | ( ( aDimensionOf0 @ A )
       != ( aDimensionOf0 @ B ) )
      | ( ( aDimensionOf0 @ B )
       != sz00 )
      | ( ( sdtasasdt0 @ A @ B )
        = sz0z00 ) ),
    inference(cnf,[status(esa)],[87]) ).

thf(89,plain,
    ! [B: $i,A: $i] :
      ( ( ( aDimensionOf0 @ A )
       != ( aDimensionOf0 @ B ) )
      | ( ( aDimensionOf0 @ B )
       != sz00 )
      | ( ( sdtasasdt0 @ A @ B )
        = sz0z00 )
      | ~ ( aVector0 @ A )
      | ~ ( aVector0 @ B ) ),
    inference(lifteq,[status(thm)],[88]) ).

thf(23,axiom,
    aScalar0 @ sz0z00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).

thf(101,plain,
    aScalar0 @ sz0z00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( sdtlseqdt0 @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).

thf(168,plain,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( sdtlseqdt0 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(169,plain,
    ! [A: $i] :
      ( ~ ( aScalar0 @ A )
      | ( sdtlseqdt0 @ A @ A ) ),
    inference(cnf,[status(esa)],[168]) ).

thf(475,plain,
    ! [A: $i] :
      ( ( sdtlseqdt0 @ A @ A )
      | ( ( aScalar0 @ sz0z00 )
       != ( aScalar0 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[101,169]) ).

thf(476,plain,
    sdtlseqdt0 @ sz0z00 @ sz0z00,
    inference(pattern_uni,[status(thm)],[475:[bind(A,$thf( sz0z00 ))]]) ).

thf(1,conjecture,
    ( ( ( ( aDimensionOf0 @ xs )
       != sz00 )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
   => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ( ( ( ( aDimensionOf0 @ xs )
         != sz00 )
       => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(41,plain,
    ~ ( ( ( ( aDimensionOf0 @ xs )
         != sz00 )
       => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(42,plain,
    ~ ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ),
    inference(cnf,[status(esa)],[41]) ).

thf(563,plain,
    ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) )
   != ( sdtlseqdt0 @ sz0z00 @ sz0z00 ) ),
    inference(paramod_ordered,[status(thm)],[476,42]) ).

thf(564,plain,
    ( ( sz0z00 != sz0z00 )
    | ( ( sdtasasdt0 @ xs @ xs )
     != sz0z00 ) ),
    inference(simp,[status(thm)],[563]) ).

thf(565,plain,
    ( ( sdtasasdt0 @ xs @ xs )
   != sz0z00 ),
    inference(simp,[status(thm)],[564]) ).

thf(3942,plain,
    ! [B: $i,A: $i] :
      ( ( ( aDimensionOf0 @ A )
       != ( aDimensionOf0 @ B ) )
      | ( ( aDimensionOf0 @ B )
       != sz00 )
      | ~ ( aVector0 @ A )
      | ~ ( aVector0 @ B )
      | ( ( sdtasasdt0 @ A @ B )
       != ( sdtasasdt0 @ xs @ xs ) ) ),
    inference(paramod_ordered,[status(thm)],[89,565]) ).

thf(3943,plain,
    ( ( ( aDimensionOf0 @ xs )
     != ( aDimensionOf0 @ xs ) )
    | ( ( aDimensionOf0 @ xs )
     != sz00 )
    | ~ ( aVector0 @ xs )
    | ~ ( aVector0 @ xs ) ),
    inference(pattern_uni,[status(thm)],[3942:[bind(A,$thf( xs )),bind(B,$thf( xs ))]]) ).

thf(3956,plain,
    ( ( ( aDimensionOf0 @ xs )
     != sz00 )
    | ~ ( aVector0 @ xs ) ),
    inference(simp,[status(thm)],[3943]) ).

thf(33,axiom,
    aVector0 @ xs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542) ).

thf(156,plain,
    aVector0 @ xs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(43,plain,
    ( ( ( aDimensionOf0 @ xs )
      = sz00 )
    | ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
    inference(cnf,[status(esa)],[41]) ).

thf(44,plain,
    ( ( ( aDimensionOf0 @ xs )
      = sz00 )
    | ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
    inference(lifteq,[status(thm)],[43]) ).

thf(173,plain,
    ( ( ( aDimensionOf0 @ xs )
      = sz00 )
    | $false ),
    inference(rewrite,[status(thm)],[44,42]) ).

thf(174,plain,
    ( ( aDimensionOf0 @ xs )
    = sz00 ),
    inference(simp,[status(thm)],[173]) ).

thf(4092,plain,
    ( ( sz00 != sz00 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[3956,156,174]) ).

thf(4093,plain,
    $false,
    inference(simp,[status(thm)],[4092]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : RNG050+1 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n024.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sat May 18 12:22:24 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.98/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.13  % [INFO] 	 Parsing done (195ms). 
% 1.30/1.15  % [INFO] 	 Running in sequential loop mode. 
% 2.05/1.51  % [INFO] 	 nitpick registered as external prover. 
% 2.05/1.51  % [INFO] 	 Scanning for conjecture ... 
% 2.13/1.60  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.28/1.63  % [INFO] 	 Found a conjecture (or negated_conjecture) and 38 axioms. Running axiom selection ... 
% 2.47/1.70  % [INFO] 	 Axiom selection finished. Selected 38 axioms (removed 0 axioms). 
% 2.47/1.76  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.76/1.78  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.76/1.79  % [INFO] 	 Type checking passed. 
% 2.76/1.80  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 49.32/8.58  % [INFO] 	 Killing All external provers ... 
% 49.32/8.59  % Time passed: 8116ms (effective reasoning time: 7433ms)
% 49.32/8.59  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 49.32/8.59  % Axioms used in derivation (4): mDefSPZ, mSZeroSc, mLERef, m__1542
% 49.32/8.59  % No. of inferences in proof: 29
% 49.32/8.59  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8116 ms resp. 7433 ms w/o parsing
% 49.32/8.64  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.32/8.64  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------