TSTP Solution File: PUZ142^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : PUZ142^1 : TPTP v8.2.0. Released v6.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.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 02:27:03 EDT 2024

% Result   : Theorem 3.42s 2.05s
% Output   : Refutation 3.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   75
% Syntax   : Number of formulae    :  104 (  68 unt;  32 typ;  16 def)
%            Number of atoms       :  120 (  55 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  274 (   9   ~;   0   |;   0   &; 257   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   32 (  29 usr;  27 con; 0-2 aty)
%            Number of variables   :   25 (   0   ^  22   !;   3   ?;  25   :)

% Comments : 
%------------------------------------------------------------------------------
thf(position_type,type,
    position: $tType ).

thf(direction_type,type,
    direction: $tType ).

thf(left_type,type,
    left: direction ).

thf(right_type,type,
    right: direction ).

thf(top_type,type,
    top: direction ).

thf(bottom_type,type,
    bottom: direction ).

thf(next_type,type,
    next: position > direction > position ).

thf(wall_type,type,
    wall: position > $o ).

thf(movelist_type,type,
    movelist: $tType ).

thf(nomove_type,type,
    nomove: movelist ).

thf(movedir_type,type,
    movedir: movelist > direction > movelist ).

thf(playerpos_type,type,
    playerpos: movelist > position ).

thf(c00_type,type,
    c00: position ).

thf(c10_type,type,
    c10: position ).

thf(c10_def,definition,
    ( c10
    = ( next @ c00 @ right ) ) ).

thf(c20_type,type,
    c20: position ).

thf(c20_def,definition,
    ( c20
    = ( next @ c10 @ right ) ) ).

thf(c30_type,type,
    c30: position ).

thf(c30_def,definition,
    ( c30
    = ( next @ c20 @ right ) ) ).

thf(c40_type,type,
    c40: position ).

thf(c40_def,definition,
    ( c40
    = ( next @ c30 @ right ) ) ).

thf(c01_type,type,
    c01: position ).

thf(c01_def,definition,
    ( c01
    = ( next @ c00 @ top ) ) ).

thf(c11_type,type,
    c11: position ).

thf(c11_def,definition,
    ( c11
    = ( next @ c10 @ top ) ) ).

thf(c21_type,type,
    c21: position ).

thf(c21_def,definition,
    ( c21
    = ( next @ c20 @ top ) ) ).

thf(c31_type,type,
    c31: position ).

thf(c31_def,definition,
    ( c31
    = ( next @ c30 @ top ) ) ).

thf(c41_type,type,
    c41: position ).

thf(c02_type,type,
    c02: position ).

thf(c02_def,definition,
    ( c02
    = ( next @ c01 @ top ) ) ).

thf(c12_type,type,
    c12: position ).

thf(c12_def,definition,
    ( c12
    = ( next @ c11 @ top ) ) ).

thf(c22_type,type,
    c22: position ).

thf(c22_def,definition,
    ( c22
    = ( next @ c21 @ top ) ) ).

thf(c32_type,type,
    c32: position ).

thf(c32_def,definition,
    ( c32
    = ( next @ c31 @ top ) ) ).

thf(c42_type,type,
    c42: position ).

thf(c03_type,type,
    c03: position ).

thf(c03_def,definition,
    ( c03
    = ( next @ c02 @ top ) ) ).

thf(c13_type,type,
    c13: position ).

thf(c13_def,definition,
    ( c13
    = ( next @ c12 @ top ) ) ).

thf(c23_type,type,
    c23: position ).

thf(c23_def,definition,
    ( c23
    = ( next @ c22 @ top ) ) ).

thf(c33_type,type,
    c33: position ).

thf(c33_def,definition,
    ( c33
    = ( next @ c32 @ top ) ) ).

thf(c43_type,type,
    c43: position ).

thf(16,axiom,
    ( ( wall @ c10 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10_axiom) ).

thf(56,plain,
    wall @ ( next @ c00 @ right ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(19,axiom,
    ( ( wall @ c20 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c20_axiom) ).

thf(60,plain,
    wall @ ( next @ ( next @ c00 @ right ) @ right ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(23,axiom,
    ( ( wall @ c30 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c30_axiom) ).

thf(65,plain,
    wall @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(15,axiom,
    ! [A: direction,B: direction,C: position] :
      ( ( next @ ( next @ C @ A ) @ B )
      = ( next @ ( next @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',next_comm) ).

thf(53,plain,
    ! [A: direction,B: direction,C: position] :
      ( ( next @ ( next @ C @ A ) @ B )
      = ( next @ ( next @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(28,axiom,
    ( ( wall @ c13 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c13_axiom) ).

thf(77,plain,
    wall @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ top ) @ top ) @ top ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(11,axiom,
    ( ( wall @ c02 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02_axiom) ).

thf(44,plain,
    wall @ ( next @ ( next @ c00 @ top ) @ top ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(24,axiom,
    ( ( wall @ c40 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c40_axiom) ).

thf(66,plain,
    wall @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ) @ right ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(6,axiom,
    ( ( wall @ c01 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01_axiom) ).

thf(35,plain,
    wall @ ( next @ c00 @ top ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(25,axiom,
    ! [A: position,B: movelist,C: direction] :
      ( ( ( playerpos @ B )
        = A )
     => ( ( wall @ ( next @ A @ C ) )
       => ( ( playerpos @ ( movedir @ B @ C ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',player_move_illegal) ).

thf(67,plain,
    ! [A: position,B: movelist,C: direction] :
      ( ( ( playerpos @ B )
        = A )
     => ( ( wall @ ( next @ A @ C ) )
       => ( ( playerpos @ ( movedir @ B @ C ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(9,axiom,
    ! [A: position] :
      ( ( next @ ( next @ A @ top ) @ bottom )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',top_bottom) ).

thf(40,plain,
    ! [A: position] :
      ( ( next @ ( next @ A @ top ) @ bottom )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(18,axiom,
    ( ( playerpos @ nomove )
    = c11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_axiom) ).

thf(58,plain,
    ( ( playerpos @ nomove )
    = ( next @ ( next @ c00 @ right ) @ top ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(7,axiom,
    ( ( wall @ c22 )
    = $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c22_axiom) ).

thf(36,plain,
    ~ ( wall @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ top ) @ top ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(21,axiom,
    ( ( wall @ c21 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c21_axiom) ).

thf(62,plain,
    wall @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ top ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(13,axiom,
    ( ( wall @ c12 )
    = $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c12_axiom) ).

thf(46,plain,
    ~ ( wall @ ( next @ ( next @ ( next @ c00 @ right ) @ top ) @ top ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(17,axiom,
    ( ( wall @ c00 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c00_axiom) ).

thf(57,plain,
    wall @ c00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(1,conjecture,
    ? [A: movelist] :
      ( ( playerpos @ A )
      = c31 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exercise) ).

thf(2,negated_conjecture,
    ~ ? [A: movelist] :
        ( ( playerpos @ A )
        = c31 ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(29,plain,
    ~ ? [A: movelist] :
        ( ( playerpos @ A )
        = ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ) @ top ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(20,axiom,
    ( ( wall @ c33 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c33_axiom) ).

thf(61,plain,
    wall @ ( next @ ( next @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ) @ top ) @ top ) @ top ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(27,axiom,
    ! [A: position] :
      ( ( next @ ( next @ A @ left ) @ right )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_right) ).

thf(74,plain,
    ! [A: position] :
      ( ( next @ ( next @ A @ left ) @ right )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(8,axiom,
    ( ( wall @ c32 )
    = $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c32_axiom) ).

thf(38,plain,
    ~ ( wall @ ( next @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ) @ top ) @ top ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(4,axiom,
    ( ( wall @ c42 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c42_axiom) ).

thf(33,plain,
    wall @ c42,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,axiom,
    ( ( wall @ c03 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03_axiom) ).

thf(45,plain,
    wall @ ( next @ ( next @ ( next @ c00 @ top ) @ top ) @ top ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,axiom,
    ( ( wall @ c43 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c43_axiom) ).

thf(32,plain,
    wall @ c43,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ( ( wall @ c41 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c41_axiom) ).

thf(34,plain,
    wall @ c41,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(14,axiom,
    ! [A: position,B: movelist,C: direction] :
      ( ( ( playerpos @ B )
        = A )
     => ( ~ ( wall @ ( next @ A @ C ) )
       => ( ( playerpos @ ( movedir @ B @ C ) )
          = ( next @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',player_move_legal) ).

thf(48,plain,
    ! [A: position,B: movelist,C: direction] :
      ( ( ( playerpos @ B )
        = A )
     => ( ~ ( wall @ ( next @ A @ C ) )
       => ( ( playerpos @ ( movedir @ B @ C ) )
          = ( next @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(22,axiom,
    ( ( wall @ c31 )
    = $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c31_axiom) ).

thf(63,plain,
    ~ ( wall @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ) @ top ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(26,axiom,
    ( ( wall @ c11 )
    = $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11_axiom) ).

thf(72,plain,
    ~ ( wall @ ( next @ ( next @ c00 @ right ) @ top ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(10,axiom,
    ( ( wall @ c23 )
    = $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c23_axiom) ).

thf(43,plain,
    wall @ ( next @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ top ) @ top ) @ top ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(88,plain,
    $false,
    inference(cvc4,[status(thm)],[56,60,65,53,77,44,66,35,67,40,58,36,62,46,57,29,61,74,38,33,45,32,34,48,63,72,43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : PUZ142^1 : TPTP v8.2.0. Released v6.2.0.
% 0.10/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n013.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  : 300
% 0.13/0.34  % DateTime : Sat May 18 10:57:23 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.82/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.12/0.95  % [INFO] 	 Parsing done (128ms). 
% 1.12/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.69/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ... 
% 1.89/1.37  % [INFO] 	 Axiom selection finished. Selected 26 axioms (removed 0 axioms). 
% 2.07/1.40  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.07/1.40  % [INFO] 	 Type checking passed. 
% 2.07/1.41  % [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 ... 
% 3.42/2.04  % External prover 'cvc4' found a proof!
% 3.42/2.04  % [INFO] 	 Killing All external provers ... 
% 3.42/2.04  % Time passed: 1574ms (effective reasoning time: 1083ms)
% 3.42/2.04  % 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)>
% 3.42/2.05  % Axioms used in derivation (26): c23_axiom, top_bottom, c11_axiom, c10_axiom, c31_axiom, c21_axiom, c43_axiom, c40_axiom, player_move_legal, c22_axiom, c41_axiom, c30_axiom, c03_axiom, player_move_illegal, c42_axiom, c32_axiom, c20_axiom, c13_axiom, c12_axiom, c00_axiom, c01_axiom, left_right, next_comm, c33_axiom, start_axiom, c02_axiom
% 3.42/2.05  % No. of inferences in proof: 56
% 3.42/2.05  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1574 ms resp. 1083 ms w/o parsing
% 3.81/2.11  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.81/2.11  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------