TSTP Solution File: RNG086+2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : RNG086+2 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 02:38:18 EDT 2024

% Result   : Theorem 6.24s 2.82s
% Output   : Refutation 6.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   28 (   5 unt;  11 typ;   0 def)
%            Number of atoms       :   57 (  15 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  175 (  16   ~;   8   |;  32   &; 119   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   26 (   0   ^   6   !;  20   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sdtpldt1_type,type,
    sdtpldt1: $i > $i > $i ).

thf(aElementOf0_type,type,
    aElementOf0: $i > $i > $o ).

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

thf(aElement0_type,type,
    aElement0: $i > $o ).

thf(xI_type,type,
    xI: $i ).

thf(xJ_type,type,
    xJ: $i ).

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

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

thf(xz_type,type,
    xz: $i ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(17,axiom,
    ( ? [A: $i,B: $i] :
        ( ( aElementOf0 @ A @ xI )
        & ( aElementOf0 @ B @ xJ )
        & ( ( sdtpldt0 @ A @ B )
          = xx ) )
    & ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
    & ? [A: $i,B: $i] :
        ( ( aElementOf0 @ A @ xI )
        & ( aElementOf0 @ B @ xJ )
        & ( ( sdtpldt0 @ A @ B )
          = xy ) )
    & ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
    & ( aElement0 @ xz ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__901) ).

thf(73,plain,
    ( ? [A: $i,B: $i] :
        ( ( aElementOf0 @ A @ xI )
        & ( aElementOf0 @ B @ xJ )
        & ( ( sdtpldt0 @ A @ B )
          = xx ) )
    & ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
    & ? [A: $i,B: $i] :
        ( ( aElementOf0 @ A @ xI )
        & ( aElementOf0 @ B @ xJ )
        & ( ( sdtpldt0 @ A @ B )
          = xy ) )
    & ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
    & ( aElement0 @ xz ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(74,plain,
    ( ? [A: $i] :
        ( ( aElementOf0 @ A @ xI )
        & ? [B: $i] :
            ( ( aElementOf0 @ B @ xJ )
            & ( ( sdtpldt0 @ A @ B )
              = xx ) ) )
    & ( aElementOf0 @ xx @ ( sdtpldt1 @ xI @ xJ ) )
    & ? [A: $i] :
        ( ( aElementOf0 @ A @ xI )
        & ? [B: $i] :
            ( ( aElementOf0 @ B @ xJ )
            & ( ( sdtpldt0 @ A @ B )
              = xy ) ) )
    & ( aElementOf0 @ xy @ ( sdtpldt1 @ xI @ xJ ) )
    & ( aElement0 @ xz ) ),
    inference(miniscope,[status(thm)],[73]) ).

thf(81,plain,
    ( ( sdtpldt0 @ sk1 @ sk2 )
    = xx ),
    inference(cnf,[status(esa)],[74]) ).

thf(84,plain,
    ( ( sdtpldt0 @ sk1 @ sk2 )
    = xx ),
    inference(lifteq,[status(thm)],[81]) ).

thf(1,conjecture,
    ? [A: $i,B: $i] :
      ( ( aElementOf0 @ A @ xI )
      & ( aElementOf0 @ B @ xJ )
      & ( xx
        = ( sdtpldt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ? [A: $i,B: $i] :
        ( ( aElementOf0 @ A @ xI )
        & ( aElementOf0 @ B @ xJ )
        & ( xx
          = ( sdtpldt0 @ A @ B ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(29,plain,
    ~ ? [A: $i,B: $i] :
        ( ( aElementOf0 @ A @ xI )
        & ( aElementOf0 @ B @ xJ )
        & ( xx
          = ( sdtpldt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(30,plain,
    ~ ? [A: $i] :
        ( ( aElementOf0 @ A @ xI )
        & ? [B: $i] :
            ( ( aElementOf0 @ B @ xJ )
            & ( xx
              = ( sdtpldt0 @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[29]) ).

thf(31,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ xI )
      | ~ ( aElementOf0 @ B @ xJ )
      | ( xx
       != ( sdtpldt0 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(32,plain,
    ! [B: $i,A: $i] :
      ( ( ( sdtpldt0 @ A @ B )
       != xx )
      | ~ ( aElementOf0 @ A @ xI )
      | ~ ( aElementOf0 @ B @ xJ ) ),
    inference(lifteq,[status(thm)],[31]) ).

thf(321,plain,
    ! [B: $i,A: $i] :
      ( ~ ( aElementOf0 @ A @ xI )
      | ~ ( aElementOf0 @ B @ xJ )
      | ( ( sdtpldt0 @ sk1 @ sk2 )
       != ( sdtpldt0 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[84,32]) ).

thf(322,plain,
    ( ~ ( aElementOf0 @ sk1 @ xI )
    | ~ ( aElementOf0 @ sk2 @ xJ ) ),
    inference(pattern_uni,[status(thm)],[321:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(83,plain,
    aElementOf0 @ sk1 @ xI,
    inference(cnf,[status(esa)],[74]) ).

thf(76,plain,
    aElementOf0 @ sk2 @ xJ,
    inference(cnf,[status(esa)],[74]) ).

thf(451,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[322,83,76]) ).

thf(452,plain,
    $false,
    inference(simp,[status(thm)],[451]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : RNG086+2 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n008.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 12:05:39 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.90/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.36/1.08  % [INFO] 	 Parsing done (168ms). 
% 1.36/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.91/1.42  % [INFO] 	 nitpick registered as external prover. 
% 1.91/1.42  % [INFO] 	 Scanning for conjecture ... 
% 1.99/1.51  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.99/1.52  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 1.99/1.53  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.15/1.55  % [INFO] 	 Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ... 
% 2.26/1.61  % [INFO] 	 Axiom selection finished. Selected 26 axioms (removed 0 axioms). 
% 2.26/1.64  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.26/1.64  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.26/1.65  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.26/1.65  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.26/1.66  % [INFO] 	 Type checking passed. 
% 2.50/1.66  % [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 ... 
% 6.24/2.81  % [INFO] 	 Killing All external provers ... 
% 6.24/2.81  % Time passed: 2350ms (effective reasoning time: 1712ms)
% 6.24/2.81  % 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)>
% 6.24/2.82  % Axioms used in derivation (1): m__901
% 6.24/2.82  % No. of inferences in proof: 17
% 6.24/2.82  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2350 ms resp. 1712 ms w/o parsing
% 6.24/2.84  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.24/2.84  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------