TSTP Solution File: RNG045+1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : RNG045+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 02:37:33 EDT 2024

% Result   : Theorem 4.27s 2.51s
% Output   : Refutation 4.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   33 (   9 unt;   9 typ;   0 def)
%            Number of atoms       :   77 (  33 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  320 (   2   ~;   0   |;  40   &; 265   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   25 (   0   ^  25   !;   0   ?;  25   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sdtasdt0_type,type,
    sdtasdt0: $i > $i > $i ).

thf(sdtpldt0_type,type,
    sdtpldt0: $i > $i > $i ).

thf(xx_type,type,
    xx: $i ).

thf(xy_type,type,
    xy: $i ).

thf(xu_type,type,
    xu: $i ).

thf(xv_type,type,
    xv: $i ).

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

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

thf(smndt0_type,type,
    smndt0: $i > $i ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C ) )
     => ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr) ).

thf(52,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C ) )
     => ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).

thf(57,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).

thf(28,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1,conjecture,
    ( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
    = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xx @ xu ) @ ( sdtasdt0 @ xx @ xv ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xy @ xu ) @ ( sdtasdt0 @ xy @ xv ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
   != ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xx @ xu ) @ ( sdtasdt0 @ xx @ xv ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xy @ xu ) @ ( sdtasdt0 @ xy @ xv ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(13,plain,
    ( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
   != ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xx @ xu ) @ ( sdtasdt0 @ xx @ xv ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xy @ xu ) @ ( sdtasdt0 @ xy @ xv ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(12,axiom,
    ( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
    = ( sdtpldt0 @ ( sdtasdt0 @ xx @ ( sdtpldt0 @ xu @ xv ) ) @ ( sdtasdt0 @ xy @ ( sdtpldt0 @ xu @ xv ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__733) ).

thf(59,plain,
    ( ( sdtasdt0 @ ( sdtpldt0 @ xx @ xy ) @ ( sdtpldt0 @ xu @ xv ) )
    = ( sdtpldt0 @ ( sdtasdt0 @ xx @ ( sdtpldt0 @ xu @ xv ) ) @ ( sdtasdt0 @ xy @ ( sdtpldt0 @ xu @ xv ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSort) ).

thf(18,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( aScalar0 @ ( smndt0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).

thf(16,plain,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( aScalar0 @ ( smndt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( ( ( sdtpldt0 @ A @ sz0z00 )
          = A )
        & ( ( sdtpldt0 @ sz0z00 @ A )
          = A )
        & ( ( sdtasdt0 @ A @ sz0z00 )
          = sz0z00 )
        & ( ( sdtasdt0 @ sz0z00 @ A )
          = sz0z00 )
        & ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
          = sz0z00 )
        & ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
          = sz0z00 )
        & ( ( smndt0 @ ( smndt0 @ A ) )
          = A )
        & ( ( smndt0 @ sz0z00 )
          = sz0z00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).

thf(30,plain,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( ( ( sdtpldt0 @ A @ sz0z00 )
          = A )
        & ( ( sdtpldt0 @ sz0z00 @ A )
          = A )
        & ( ( sdtasdt0 @ A @ sz0z00 )
          = sz0z00 )
        & ( ( sdtasdt0 @ sz0z00 @ A )
          = sz0z00 )
        & ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
          = sz0z00 )
        & ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
          = sz0z00 )
        & ( ( smndt0 @ ( smndt0 @ A ) )
          = A )
        & ( ( smndt0 @ sz0z00 )
          = sz0z00 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C ) )
     => ( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
          = ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
        & ( ( sdtpldt0 @ A @ B )
          = ( sdtpldt0 @ B @ A ) )
        & ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
          = ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
        & ( ( sdtasdt0 @ A @ B )
          = ( sdtasdt0 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).

thf(19,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C ) )
     => ( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
          = ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
        & ( ( sdtpldt0 @ A @ B )
          = ( sdtpldt0 @ B @ A ) )
        & ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
          = ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
        & ( ( sdtasdt0 @ A @ B )
          = ( sdtasdt0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(9,axiom,
    ( ( aScalar0 @ xx )
    & ( aScalar0 @ xy )
    & ( aScalar0 @ xu )
    & ( aScalar0 @ xv ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__674) ).

thf(47,plain,
    ( ( aScalar0 @ xx )
    & ( aScalar0 @ xy )
    & ( aScalar0 @ xu )
    & ( aScalar0 @ xv ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(3,axiom,
    aScalar0 @ sz0z00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).

thf(15,plain,
    aScalar0 @ sz0z00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(61,plain,
    $false,
    inference(cvc4,[status(thm)],[52,57,28,13,59,18,16,30,19,47,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : RNG045+1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n027.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Sat May 18 12:04:08 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 1.00/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/1.17  % [INFO] 	 Parsing done (178ms). 
% 1.49/1.18  % [INFO] 	 Running in sequential loop mode. 
% 2.03/1.57  % [INFO] 	 eprover registered as external prover. 
% 2.03/1.57  % [INFO] 	 cvc4 registered as external prover. 
% 2.03/1.58  % [INFO] 	 Scanning for conjecture ... 
% 2.24/1.68  % [INFO] 	 Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ... 
% 2.35/1.74  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 7 axioms). 
% 2.61/1.79  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.67/1.80  % [INFO] 	 Type checking passed. 
% 2.67/1.80  % [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 ... 
% 4.27/2.50  % External prover 'cvc4' found a proof!
% 4.27/2.50  % [INFO] 	 Killing All external provers ... 
% 4.27/2.51  % Time passed: 2030ms (effective reasoning time: 1320ms)
% 4.27/2.51  % 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)>
% 4.27/2.51  % Axioms used in derivation (10): mArith, mMulSc, mScSort, m__674, mDistr, mNegSc, mSZeroSc, m__733, mSumSc, mScZero
% 4.27/2.51  % No. of inferences in proof: 24
% 4.27/2.51  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2030 ms resp. 1320 ms w/o parsing
% 4.27/2.57  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.27/2.57  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------