TSTP Solution File: PUZ008-1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : PUZ008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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  7 08:03:28 EDT 2024

% Result   : Unsatisfiable 3.53s 2.06s
% Output   : Refutation 3.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   42 (  13 unt;   9 typ;   0 def)
%            Number of atoms       :   53 (   0 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  714 (  22   ~;  20   |;   0   &; 672   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :  114 (   0   ^ 114   !;   0   ?; 114   :)

% Comments : 
%------------------------------------------------------------------------------
thf(achievable_type,type,
    achievable: $i > $i > $i > $o ).

thf(west_type,type,
    west: $i > $i > $i ).

thf(m_type,type,
    m: $i > $i ).

thf(n0_type,type,
    n0: $i ).

thf(c_type,type,
    c: $i > $i ).

thf(east_type,type,
    east: $i > $i > $i ).

thf(s_type,type,
    s: $i > $i ).

thf(boatonwest_type,type,
    boatonwest: $i ).

thf(boatoneast_type,type,
    boatoneast: $i ).

thf(15,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( achievable @ ( west @ A @ B ) @ C @ ( east @ ( m @ ( s @ D ) ) @ ( c @ ( s @ ( s @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extra_cannibal_meal_on_east_bank) ).

thf(41,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( achievable @ ( west @ A @ B ) @ C @ ( east @ ( m @ ( s @ D ) ) @ ( c @ ( s @ ( s @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ B ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',missionary_west_to_east) ).

thf(22,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ B ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ ( s @ B ) ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ ( s @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_cannibals_west_to_east) ).

thf(42,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ ( s @ B ) ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ ( s @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ ( s @ D ) ) ) )
      | ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',missionary_and_cannibal_east_to_west) ).

thf(24,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ ( s @ D ) ) ) )
      | ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( achievable @ ( west @ A @ B ) @ C @ ( east @ ( m @ ( s @ D ) ) @ ( c @ ( s @ ( s @ ( s @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_extra_cannibals_meal_on_east_bank) ).

thf(21,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( achievable @ ( west @ A @ B ) @ C @ ( east @ ( m @ ( s @ D ) ) @ ( c @ ( s @ ( s @ ( s @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,axiom,
    achievable @ ( west @ ( m @ ( s @ ( s @ ( s @ n0 ) ) ) ) @ ( c @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) @ boatonwest @ ( east @ ( m @ n0 ) @ ( c @ n0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',start_on_west_bank) ).

thf(33,plain,
    achievable @ ( west @ ( m @ ( s @ ( s @ ( s @ n0 ) ) ) ) @ ( c @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) @ boatonwest @ ( east @ ( m @ n0 ) @ ( c @ n0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ ( s @ C ) ) ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ ( s @ ( s @ A ) ) ) @ ( c @ B ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_missionaries_east_to_west) ).

thf(28,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ ( s @ C ) ) ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ ( s @ ( s @ A ) ) ) @ ( c @ B ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ B ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',missionary_east_to_west) ).

thf(38,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ B ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ~ ( achievable @ ( west @ ( m @ n0 ) @ ( c @ n0 ) ) @ A @ ( east @ ( m @ ( s @ ( s @ ( s @ n0 ) ) ) ) @ ( c @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_can_get_to_east_bank) ).

thf(17,plain,
    ! [A: $i] :
      ~ ( achievable @ ( west @ ( m @ n0 ) @ ( c @ n0 ) ) @ A @ ( east @ ( m @ ( s @ ( s @ ( s @ n0 ) ) ) ) @ ( c @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ ( s @ A ) ) ) ) @ B @ ( east @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extra_cannibal_meal_on_west_bank) ).

thf(32,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ ( s @ A ) ) ) ) @ B @ ( east @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ ( s @ ( s @ A ) ) ) @ ( c @ B ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ ( s @ C ) ) ) @ ( c @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_missionaries_west_to_east) ).

thf(34,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ ( s @ ( s @ A ) ) ) @ ( c @ B ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ ( s @ C ) ) ) @ ( c @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ ( s @ ( s @ A ) ) ) ) ) @ B @ ( east @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_extra_cannibals_meal_on_west_bank) ).

thf(40,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ ( s @ ( s @ A ) ) ) ) ) @ B @ ( east @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(6,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ D ) ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cannibal_east_to_west) ).

thf(26,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ D ) ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ ( s @ D ) ) ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ ( s @ B ) ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_cannibals_east_to_west) ).

thf(36,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ ( s @ D ) ) ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ ( s @ B ) ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cannibal_west_to_east) ).

thf(30,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(2,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ ( s @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',missionary_and_cannibal_west_to_east) ).

thf(19,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ ( s @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(44,plain,
    $false,
    inference(e,[status(thm)],[41,22,42,24,21,33,28,38,17,32,34,40,26,36,30,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : PUZ008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.16/0.17  % Command  : run_Leo-III %s %d
% 0.18/0.39  % Computer : n026.cluster.edu
% 0.18/0.39  % Model    : x86_64 x86_64
% 0.18/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39  % Memory   : 8042.1875MB
% 0.18/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39  % CPULimit : 300
% 0.18/0.39  % WCLimit  : 300
% 0.18/0.39  % DateTime : Mon May  6 13:45:09 EDT 2024
% 0.18/0.39  % CPUTime  : 
% 1.06/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.13  % [INFO] 	 Parsing done (187ms). 
% 1.28/1.15  % [INFO] 	 Running in sequential loop mode. 
% 1.79/1.43  % [INFO] 	 eprover registered as external prover. 
% 1.79/1.43  % [INFO] 	 cvc4 registered as external prover. 
% 1.79/1.43  % [INFO] 	 Scanning for conjecture ... 
% 2.11/1.51  % [INFO] 	 Found a conjecture and 15 axioms. Running axiom selection ... 
% 2.23/1.56  % [INFO] 	 Axiom selection finished. Selected 15 axioms (removed 0 axioms). 
% 2.23/1.60  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.23/1.60  % [INFO] 	 Type checking passed. 
% 2.23/1.61  % [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 ... 
% 3.25/2.06  % External prover 'e' found a proof!
% 3.25/2.06  % [INFO] 	 Killing All external provers ... 
% 3.25/2.06  % Time passed: 1495ms (effective reasoning time: 909ms)
% 3.25/2.06  % 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)>
% 3.25/2.06  % Axioms used in derivation (15): cannibal_west_to_east, two_extra_cannibals_meal_on_west_bank, two_cannibals_west_to_east, cannibal_east_to_west, extra_cannibal_meal_on_east_bank, missionary_and_cannibal_east_to_west, missionary_east_to_west, missionary_west_to_east, two_missionaries_east_to_west, two_missionaries_west_to_east, two_extra_cannibals_meal_on_east_bank, extra_cannibal_meal_on_west_bank, two_cannibals_east_to_west, start_on_west_bank, missionary_and_cannibal_west_to_east
% 3.25/2.06  % No. of inferences in proof: 33
% 3.53/2.06  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1495 ms resp. 909 ms w/o parsing
% 3.74/2.18  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.74/2.18  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------